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## Fabian, Marián J.

Compute Distance To:
 Author ID: fabian.marian-j Published as: Fabian, Marián; Fabian, Marian; Fabian, Marian J.; Fabian, Marián J.; Fabian, Marían; Fabián, Marián; Fabian, M. more...less
 Documents Indexed: 64 Publications since 1977, including 3 Books Reviewing Activity: 48 Reviews Co-Authors: 28 Co-Authors with 46 Joint Publications 830 Co-Co-Authors
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### Co-Authors

 18 single-authored 12 Zizler, Vaclav E. 8 Montesinos Santalucia, Vicente 5 Cibulka, Radek 5 Mordukhovich, Boris S. 3 Cheng, Lixin 3 Cúth, Marek 3 Godefroy, Gilles 3 Hájek, Petr 3 Ioffe, Alexander Davidovich 2 Bartl, David 2 Borwein, Jonathan Michael 2 Habala, Petr 2 Henrion, René 2 Kruger, Alexander Y. 2 Lajara, Sebastián 2 Loewen, Philip D. 2 Outrata, Jiří V. 2 Revalski, Julian Petrov 1 Aussel, Didier 1 Chen, Shaoxiong 1 Finet, Catherine 1 González, Alma L. 1 Kalenda, Ondřej F. K. 1 Kolář, Jan 1 Pelant, Jan 1 Roubal, Tomáš 1 Troyanski, Stanimir L. 1 Wang, Shawn Xianfu
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### Serials

 5 Journal of Mathematical Analysis and Applications 5 Proceedings of the American Mathematical Society 4 Journal of Convex Analysis 4 Set-Valued and Variational Analysis 3 Studia Mathematica 3 Commentationes Mathematicae Universitatis Carolinae 3 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 3 Bulletin of the Polish Academy of Sciences, Mathematics 2 Israel Journal of Mathematics 2 Časopis Pro Pěstování Matematiky 2 Czechoslovak Mathematical Journal 2 Set-Valued Analysis 2 CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC 1 Acta Universitatis Carolinae. Mathematica et Physica 1 Bulletin of the Australian Mathematical Society 1 Archiv der Mathematik 1 Canadian Journal of Mathematics 1 Functiones et Approximatio. Commentarii Mathematici 1 Journal of Functional Analysis 1 Proceedings of the London Mathematical Society. Third Series 1 Tokyo Journal of Mathematics 1 Mathematical Programming. Series A. Series B 1 Serdica Mathematical Journal 1 Annales Academiae Scientiarum Fennicae. Mathematica 1 Vietnam Journal of Mathematics 1 Journal of Nonlinear and Convex Analysis 1 RACSAM. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas 1 Canadian Mathematical Society Series of Monographs and Advanced Texts 1 Journal of Fixed Point Theory and Applications 1 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 1 Nonlinear Analysis. Theory, Methods & Applications
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### Fields

 54 Functional analysis (46-XX) 19 Calculus of variations and optimal control; optimization (49-XX) 15 Global analysis, analysis on manifolds (58-XX) 11 Operator theory (47-XX) 8 General topology (54-XX) 2 Real functions (26-XX) 2 Convex and discrete geometry (52-XX) 2 Operations research, mathematical programming (90-XX) 1 History and biography (01-XX) 1 Mathematical logic and foundations (03-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Approximations and expansions (41-XX)

### Citations contained in zbMATH Open

53 Publications have been cited 911 times in 738 Documents Cited by Year
Banach space theory. The basis for linear and nonlinear analysis. Zbl 1229.46001
Fabian, Marián; Habala, Petr; Hájek, Petr; Montesinos, Vicente; Zizler, Václav
2011
Functional analysis and infinite-dimensional geometry. Zbl 0981.46001
Fabian, Marián; Habala, Petr; Hájek, Petr; Montesinos Santalucía, Vicente; Pelant, Jan; Zizler, Václav
2001
Gâteaux differentiability of convex functions and topology. Weak Asplund spaces. Zbl 0883.46011
Fabian, Marián J.
1997
Error bounds: necessary and sufficient conditions. Zbl 1192.49018
Fabian, Marian J.; Henrion, René; Kruger, Alexander Y.; Outrata, Jiří V.
2010
Subdifferentiability and trustworthiness in the light of a new variational principle of Borwein and Preiss. Zbl 0714.49022
Fabian, Marian
1989
The dual of every Asplund space admits a projectional resolution of the identity. Zbl 0692.46012
Fabian, Marián; Godefroy, Gilles
1988
Sequential normal compactness versus topological normal compactness in variational analysis. Zbl 1038.46016
Fabian, Marián; Mordukhovich, Boris S.
2003
The structure of uniformly Gâteaux smooth Banach spaces. Zbl 1027.46012
Fabian, Marián; Godefroy, Gilles; Zizler, Václav
2001
About error bounds in metric spaces. Zbl 1306.49026
Fabian, Marian J.; Henrion, René; Kruger, Alexander Y.; Outrata, Jiří V.
2012
Nonsmooth characterizations of Asplund spaces and smooth variational principles. Zbl 0927.49012
Fabian, Marián; Mordukhovich, Boris S.
1998
Lipschitz smooth points of convex functions and isomorphic characterizations of Hilbert spaces. Zbl 0549.46025
Fabian, Marián
1985
A note on regularity of sets and of distance functions in Banach space. Zbl 0801.49015
Borwein, Jonathan M.; Fabian, Marian
1994
On primal regularity estimates for single-valued mappings. Zbl 1327.49030
Cibulka, Radek; Fabian, Marián; Ioffe, Alexander D.
2015
On classes of subdifferentiability spaces of Ioffe. Zbl 0639.46010
Fabian, Marián
1988
Uniform Eberlein compacta and uniformly Gâteaux smooth norms. Zbl 0974.46025
Fabian, Marián; Hájek, Petr; Zizler, Václav
1997
Smoothness in Banach spaces. Selected problems. Zbl 1112.46007
Fabian, Marian; Montesinos, Vicente; Zizler, Václav
2006
Separable reductions and rich families in the theory of Fréchet subdifferentials. Zbl 1350.49012
Fabian, Marián; Ioffe, Alexander
2016
Rich families and projectional skeletons in Asplund WCG spaces. Zbl 1368.46019
Cúth, Marek; Fabian, Marián
2017
Separable reduction and supporting properties of Fréchet-like normals in Banach spaces. Zbl 0936.49011
Fabian, Marián; Mordukhovich, Boris S.
1999
A note on Robinson-Ursescu and Lyusternik-Graves theorem. Zbl 1275.49025
2013
A Banach space admits a locally uniformly rotund norm if its dual is a Vašák space. Zbl 0764.46012
Fabián, Marián; Troyanski, Stanimir
1990
Separable reduction in the theory of Fréchet subdifferentials. Zbl 1284.49016
Fabian, Marián; Ioffe, Alexander
2013
Asplund spaces characterized by rich families and separable reduction of Fréchet subdifferentiability. Zbl 1352.46019
Cúth, Marek; Fabian, Marián
2016
Projections in duals to Asplund spaces made without Simons’ lemma. Zbl 1339.46011
Cúth, Marek; Fabian, Marián
2015
On a dual locally uniformly rotund norm on a dual Vašák space. Zbl 0815.46018
Fabian, Marián
1991
Separable reduction and extremal principles in variational analysis. Zbl 1061.49015
Fabian, Marián; Mordukhovich, Boris S.
2002
Weakly compact sets and smooth norms in Banach spaces. Zbl 1007.46011
Fabian, Marián; Montesinos, Vicente; Zizler, Václav
2002
Pointwise semicontinuous smooth norms. Zbl 1007.46008
Fabian, Marián; Montesinos, Vicente; Zizler, Václav
2002
Smooth renormings of the Lebesgue-Bochner function space $$L^1(\mu ,X)$$. Zbl 1262.46007
Fabian, Marián; Lajara, Sebastián
2012
A one perturbation variational principle and applications. Zbl 1047.49022
Borwein, Jonathan; Cheng, Lixin; Fabian, Marían; Revalski, Julian P.
2004
Filling analytic sets by the derivatives of $$C^1$$-smooth bumps. Zbl 1107.46032
Fabian, Marián; Kalenda, Ondrej F. K.; Kolár, Jan
2005
Overclasses of the class of Radon-Nikodým compact spaces. Zbl 1149.46017
Fabian, Marián
2006
Theory of Frechet cones. Zbl 0487.46027
Fabian, Marian
1982
A variational principle in reflexive spaces with Kadec-Klee norm. Zbl 1181.46012
Fabian, Marián; Revalski, Julian
2009
Concerning interior mapping theorem. Zbl 0393.46008
Fabian, Marian
1979
On Stegall’s smooth variational principle. Zbl 1117.46014
Fabian, Marián; Finet, Catherine
2007
Single-directional properties of quasi-monotone operators. Zbl 1300.47055
Aussel, Didier; Fabian, Marián
2013
A note on Asplund generated Banach spaces. Zbl 0946.46016
Fabian, Marián; Godefroy, Gilles; Zizler, Václav
1999
The product of a Gâteaux differentiability space and a separable space is a Gâteaux differentiability space. Zbl 1003.46026
Cheng, Lixin; Fabian, Marián
2001
On uniformly Gâteaux smooth $$C^{(n)}$$-smooth norms on separable Banach spaces. Zbl 1011.46010
Fabian, Marián; Zizler, Václav
1999
Projectional resolution of the identity sometimes implies weakly compact generating. Zbl 0771.47012
Fabian, Marián
1990
Differentiability via one sided directional derivatives. Zbl 0431.26004
Fabian, Marian
1981
Gul’ko, descriptive, and Gruenhage compact spaces. Zbl 1228.46015
Fabian, M.; Montesinos, V.; Zizler, V.
2010
Subdifferential calculus in Asplund generated spaces. Zbl 1109.46043
Fabian, Marián; Loewen, Philip D.; Mordukhovich, Boris S.
2006
On Nash-Moser-Ekeland inverse mapping theorem. Zbl 1429.58020
2019
An inverse mapping theorem in Fréchet-Montel spaces. Zbl 1446.49014
Cibulka, Radek; Fabian, Marián; Roubal, Tomáš
2020
WCG spaces and their subspaces grasped by projectional skeletons. Zbl 1447.46018
Fabian, Marián; Montesinos, Vicente
2018
On singlevaluedness and (strong) upper semicontinuity of maximal monotone mappings. Zbl 0347.47027
Fabian, Marian
1977
Once more of continuity of maximal monotone mappings. Zbl 0347.47028
Fabian, Marian
1977
Can Pourciau’s open mapping theorem be derived from Clarke’s inverse mapping theorem easily? Zbl 1460.46003
Bartl, David; Fabian, Marián
2021
Continuous selections for inverse mappings in Banach spaces. Zbl 07329660
2021
On coincidence of Pettis and McShane integrability. Zbl 1349.46045
Fabian, Marián
2015
Rotund renormings in spaces of Bochner integrable functions. Zbl 1348.46010
Fabian, Marián; Lajara, Sebastián
2016
Can Pourciau’s open mapping theorem be derived from Clarke’s inverse mapping theorem easily? Zbl 1460.46003
Bartl, David; Fabian, Marián
2021
Continuous selections for inverse mappings in Banach spaces. Zbl 07329660
2021
An inverse mapping theorem in Fréchet-Montel spaces. Zbl 1446.49014
Cibulka, Radek; Fabian, Marián; Roubal, Tomáš
2020
On Nash-Moser-Ekeland inverse mapping theorem. Zbl 1429.58020
2019
WCG spaces and their subspaces grasped by projectional skeletons. Zbl 1447.46018
Fabian, Marián; Montesinos, Vicente
2018
Rich families and projectional skeletons in Asplund WCG spaces. Zbl 1368.46019
Cúth, Marek; Fabian, Marián
2017
Separable reductions and rich families in the theory of Fréchet subdifferentials. Zbl 1350.49012
Fabian, Marián; Ioffe, Alexander
2016
Asplund spaces characterized by rich families and separable reduction of Fréchet subdifferentiability. Zbl 1352.46019
Cúth, Marek; Fabian, Marián
2016
Rotund renormings in spaces of Bochner integrable functions. Zbl 1348.46010
Fabian, Marián; Lajara, Sebastián
2016
On primal regularity estimates for single-valued mappings. Zbl 1327.49030
Cibulka, Radek; Fabian, Marián; Ioffe, Alexander D.
2015
Projections in duals to Asplund spaces made without Simons’ lemma. Zbl 1339.46011
Cúth, Marek; Fabian, Marián
2015
On coincidence of Pettis and McShane integrability. Zbl 1349.46045
Fabian, Marián
2015
A note on Robinson-Ursescu and Lyusternik-Graves theorem. Zbl 1275.49025
2013
Separable reduction in the theory of Fréchet subdifferentials. Zbl 1284.49016
Fabian, Marián; Ioffe, Alexander
2013
Single-directional properties of quasi-monotone operators. Zbl 1300.47055
Aussel, Didier; Fabian, Marián
2013
About error bounds in metric spaces. Zbl 1306.49026
Fabian, Marian J.; Henrion, René; Kruger, Alexander Y.; Outrata, Jiří V.
2012
Smooth renormings of the Lebesgue-Bochner function space $$L^1(\mu ,X)$$. Zbl 1262.46007
Fabian, Marián; Lajara, Sebastián
2012
Banach space theory. The basis for linear and nonlinear analysis. Zbl 1229.46001
Fabian, Marián; Habala, Petr; Hájek, Petr; Montesinos, Vicente; Zizler, Václav
2011
Error bounds: necessary and sufficient conditions. Zbl 1192.49018
Fabian, Marian J.; Henrion, René; Kruger, Alexander Y.; Outrata, Jiří V.
2010
Gul’ko, descriptive, and Gruenhage compact spaces. Zbl 1228.46015
Fabian, M.; Montesinos, V.; Zizler, V.
2010
A variational principle in reflexive spaces with Kadec-Klee norm. Zbl 1181.46012
Fabian, Marián; Revalski, Julian
2009
On Stegall’s smooth variational principle. Zbl 1117.46014
Fabian, Marián; Finet, Catherine
2007
Smoothness in Banach spaces. Selected problems. Zbl 1112.46007
Fabian, Marian; Montesinos, Vicente; Zizler, Václav
2006
Overclasses of the class of Radon-Nikodým compact spaces. Zbl 1149.46017
Fabian, Marián
2006
Subdifferential calculus in Asplund generated spaces. Zbl 1109.46043
Fabian, Marián; Loewen, Philip D.; Mordukhovich, Boris S.
2006
Filling analytic sets by the derivatives of $$C^1$$-smooth bumps. Zbl 1107.46032
Fabian, Marián; Kalenda, Ondrej F. K.; Kolár, Jan
2005
A one perturbation variational principle and applications. Zbl 1047.49022
Borwein, Jonathan; Cheng, Lixin; Fabian, Marían; Revalski, Julian P.
2004
Sequential normal compactness versus topological normal compactness in variational analysis. Zbl 1038.46016
Fabian, Marián; Mordukhovich, Boris S.
2003
Separable reduction and extremal principles in variational analysis. Zbl 1061.49015
Fabian, Marián; Mordukhovich, Boris S.
2002
Weakly compact sets and smooth norms in Banach spaces. Zbl 1007.46011
Fabian, Marián; Montesinos, Vicente; Zizler, Václav
2002
Pointwise semicontinuous smooth norms. Zbl 1007.46008
Fabian, Marián; Montesinos, Vicente; Zizler, Václav
2002
Functional analysis and infinite-dimensional geometry. Zbl 0981.46001
Fabian, Marián; Habala, Petr; Hájek, Petr; Montesinos Santalucía, Vicente; Pelant, Jan; Zizler, Václav
2001
The structure of uniformly Gâteaux smooth Banach spaces. Zbl 1027.46012
Fabian, Marián; Godefroy, Gilles; Zizler, Václav
2001
The product of a Gâteaux differentiability space and a separable space is a Gâteaux differentiability space. Zbl 1003.46026
Cheng, Lixin; Fabian, Marián
2001
Separable reduction and supporting properties of Fréchet-like normals in Banach spaces. Zbl 0936.49011
Fabian, Marián; Mordukhovich, Boris S.
1999
A note on Asplund generated Banach spaces. Zbl 0946.46016
Fabian, Marián; Godefroy, Gilles; Zizler, Václav
1999
On uniformly Gâteaux smooth $$C^{(n)}$$-smooth norms on separable Banach spaces. Zbl 1011.46010
Fabian, Marián; Zizler, Václav
1999
Nonsmooth characterizations of Asplund spaces and smooth variational principles. Zbl 0927.49012
Fabian, Marián; Mordukhovich, Boris S.
1998
Gâteaux differentiability of convex functions and topology. Weak Asplund spaces. Zbl 0883.46011
Fabian, Marián J.
1997
Uniform Eberlein compacta and uniformly Gâteaux smooth norms. Zbl 0974.46025
Fabian, Marián; Hájek, Petr; Zizler, Václav
1997
A note on regularity of sets and of distance functions in Banach space. Zbl 0801.49015
Borwein, Jonathan M.; Fabian, Marian
1994
On a dual locally uniformly rotund norm on a dual Vašák space. Zbl 0815.46018
Fabian, Marián
1991
A Banach space admits a locally uniformly rotund norm if its dual is a Vašák space. Zbl 0764.46012
Fabián, Marián; Troyanski, Stanimir
1990
Projectional resolution of the identity sometimes implies weakly compact generating. Zbl 0771.47012
Fabian, Marián
1990
Subdifferentiability and trustworthiness in the light of a new variational principle of Borwein and Preiss. Zbl 0714.49022
Fabian, Marian
1989
The dual of every Asplund space admits a projectional resolution of the identity. Zbl 0692.46012
Fabian, Marián; Godefroy, Gilles
1988
On classes of subdifferentiability spaces of Ioffe. Zbl 0639.46010
Fabian, Marián
1988
Lipschitz smooth points of convex functions and isomorphic characterizations of Hilbert spaces. Zbl 0549.46025
Fabian, Marián
1985
Theory of Frechet cones. Zbl 0487.46027
Fabian, Marian
1982
Differentiability via one sided directional derivatives. Zbl 0431.26004
Fabian, Marian
1981
Concerning interior mapping theorem. Zbl 0393.46008
Fabian, Marian
1979
On singlevaluedness and (strong) upper semicontinuity of maximal monotone mappings. Zbl 0347.47027
Fabian, Marian
1977
Once more of continuity of maximal monotone mappings. Zbl 0347.47028
Fabian, Marian
1977
all top 5

### Cited by 680 Authors

 28 Mordukhovich, Boris S. 26 Hájek, Petr 26 Montesinos Santalucia, Vicente 23 Rodríguez Ruiz, José 20 Fabian, Marián J. 20 Kalenda, Ondřej F. K. 18 Zizler, Vaclav E. 17 Kruger, Alexander Y. 15 Fabian, Martin 14 Guirao, Antonio José 13 Huynh Van Ngai 13 Orihuela, José 11 Borwein, Jonathan Michael 11 Cibulka, Radek 10 Aviles Lopez, Antonio 10 Cheng, Lixin 10 Lajara, Sebastián 10 Penot, Jean-Paul 10 Raja, Matias 10 Spurný, Jiří 10 Théra, Michel A. 10 Troyanski, Stanimir L. 10 Wang, Bingwu 9 Cúth, Marek 9 Ioffe, Alexander Davidovich 9 Pfitzner, Hermann 9 Thibault, Lionel 8 López-Cerdá, Marco Antonio 8 Uderzo, Amos 7 Cascales, Bernardo 7 Chuong, Thai Doan 7 Godefroy, Gilles 7 Johanis, Michal 7 Kadets, Vladimir M. 7 Koszmider, Piotr B. 7 Moors, Warren B. 6 Aron, Richard Martin 6 Banakh, Taras Onufrievich 6 Brzdęk, Janusz 6 García-Lirola, Luis Carlos 6 Kąkol, Jerzy 6 Peralta, Antonio M. 6 Popa, Dorian 6 Talponen, Jarno 5 Azagra, Daniel 5 Correa, Claudia 5 Deville, Robert 5 Fry, Robb Charles 5 Holá, Ľubica 5 Pernecká, Eva 5 Rosendal, Christian 5 Shao, Yongheng 5 Smith, Richard James 5 Somaglia, Jacopo 5 Vanderwerff, Jon D. 5 Wang, Shawn Xianfu 5 Zheng, Xiyin 4 Bounkhel, Messaoud 4 Calabuig, José Manuel 4 Correa, Rafael 4 Dantas, Sheldon 4 De Bernardi, Carlo Alberto 4 Durea, Marius 4 Fonf, Vladimir P. 4 Gfrerer, Helmut 4 Hantoute, Abderrahim 4 Jiménez-Sevilla, Mar 4 Jordá, Enrique 4 Jourani, Abderrahim 4 Kania, Tomasz 4 Kurka, Ondřej 4 Lassonde, Marc 4 Laustsen, Niels Jakob 4 Martín Suarez, Miguel 4 Martínez-Cervantes, Gonzalo 4 Mehlitz, Patrick 4 Mercourakis, Sophocles 4 Nam, Nguyen Mau 4 Ng, Kung-Fu 4 Nghia, Tran Thai An 4 Pérez-Aros, Pedro 4 Pérez Hernández, Antonio 4 Procházka, Antonín 4 Rondoš, Jakub 4 Rueda Zoca, Abraham 4 Ruiz Galán, Manuel 4 Rychtár, Jan 4 Sánchez-Pérez, Enrique Alfonso 4 Thao, Nguyen Hieu 4 Tkachuk, Vladimir Vladimirovich 4 Xu, Bing 4 Yang, Xiaoqi 4 Zagrodny, Dariusz 3 Abrahamsen, Trond Arnold 3 Acosta Vigil, María Dolores 3 Angosto, Carlos 3 Argyros, Spiros A. 3 Aussel, Didier 3 Azé, Dominique 3 Baias, Alina-Ramona ...and 580 more Authors
all top 5

### Cited in 149 Serials

 100 Journal of Mathematical Analysis and Applications 51 Proceedings of the American Mathematical Society 38 Journal of Functional Analysis 38 Set-Valued and Variational Analysis 30 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 21 Journal of Optimization Theory and Applications 21 Topology and its Applications 16 Israel Journal of Mathematics 15 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 15 Transactions of the American Mathematical Society 15 Positivity 14 Studia Mathematica 14 Optimization 14 Mathematical Programming. Series A. Series B 12 Bulletin of the Australian Mathematical Society 12 Journal of Convex Analysis 11 SIAM Journal on Optimization 9 Banach Journal of Mathematical Analysis 8 Rocky Mountain Journal of Mathematics 8 Journal of Global Optimization 8 Acta Mathematica Sinica. English Series 8 Journal of the Australian Mathematical Society 8 Mediterranean Journal of Mathematics 8 Optimization Letters 7 Advances in Mathematics 7 Nonlinear Analysis. Theory, Methods & Applications 6 Czechoslovak Mathematical Journal 6 Mathematische Annalen 6 Vietnam Journal of Mathematics 5 Monatshefte für Mathematik 5 Linear Algebra and its Applications 5 Journal of Fixed Point Theory and Applications 4 Archiv der Mathematik 4 Mathematics of Operations Research 4 Mathematische Zeitschrift 4 Results in Mathematics 4 Revista Matemática Iberoamericana 4 The Journal of Geometric Analysis 4 Revista Matemática Complutense 4 Fixed Point Theory and Applications 3 Bulletin of the London Mathematical Society 3 Duke Mathematical Journal 3 Illinois Journal of Mathematics 3 Inventiones Mathematicae 3 Journal of Approximation Theory 3 Journal of Soviet Mathematics 3 Mathematische Nachrichten 3 Numerical Functional Analysis and Optimization 3 SIAM Journal on Control and Optimization 3 Annals of Operations Research 3 Set-Valued Analysis 2 Applicable Analysis 2 Annali di Matematica Pura ed Applicata. Serie Quarta 2 Commentationes Mathematicae Universitatis Carolinae 2 Functiones et Approximatio. Commentarii Mathematici 2 Functional Analysis and its Applications 2 Fundamenta Mathematicae 2 Integral Equations and Operator Theory 2 Publications of the Research Institute for Mathematical Sciences, Kyoto University 2 Acta Mathematica Hungarica 2 Annals of Pure and Applied Logic 2 Constructive Approximation 2 Applied Mathematics Letters 2 Journal of Scientific Computing 2 Aequationes Mathematicae 2 Journal de Mathématiques Pures et Appliquées. Neuvième Série 2 Indagationes Mathematicae. New Series 2 Computational Optimization and Applications 2 Bulletin des Sciences Mathématiques 2 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 2 Abstract and Applied Analysis 2 Journal of Inequalities and Applications 2 Acta Mathematica Scientia. Series B. (English Edition) 2 Bulletin of the Brazilian Mathematical Society. New Series 2 Central European Journal of Mathematics 2 Journal of Function Spaces and Applications 2 Science China. Mathematics 2 Journal of Function Spaces 2 Proceedings of the American Mathematical Society. Series B 2 Advances in Operator Theory 1 Computers & Mathematics with Applications 1 Communications in Mathematical Physics 1 Discrete Mathematics 1 Houston Journal of Mathematics 1 International Journal of Control 1 Indian Journal of Pure & Applied Mathematics 1 Journal of Mathematical Physics 1 Mathematical Notes 1 Russian Mathematical Surveys 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 The Mathematical Intelligencer 1 Beiträge zur Algebra und Geometrie 1 Annales de l’Institut Fourier 1 The Annals of Statistics 1 Dissertationes Mathematicae 1 Glasgow Mathematical Journal 1 Journal of Computational and Applied Mathematics 1 Journal of Differential Equations 1 Journal of the London Mathematical Society. Second Series 1 Kybernetika ...and 49 more Serials
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### Cited in 46 Fields

 461 Functional analysis (46-XX) 195 Calculus of variations and optimal control; optimization (49-XX) 132 Operator theory (47-XX) 132 Operations research, mathematical programming (90-XX) 117 General topology (54-XX) 51 Global analysis, analysis on manifolds (58-XX) 37 Real functions (26-XX) 28 Mathematical logic and foundations (03-XX) 27 Approximations and expansions (41-XX) 25 Measure and integration (28-XX) 21 Convex and discrete geometry (52-XX) 19 Numerical analysis (65-XX) 17 Partial differential equations (35-XX) 15 Difference and functional equations (39-XX) 15 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 14 Topological groups, Lie groups (22-XX) 9 Order, lattices, ordered algebraic structures (06-XX) 9 Dynamical systems and ergodic theory (37-XX) 7 Harmonic analysis on Euclidean spaces (42-XX) 6 Linear and multilinear algebra; matrix theory (15-XX) 6 Functions of a complex variable (30-XX) 5 Group theory and generalizations (20-XX) 5 Ordinary differential equations (34-XX) 5 Abstract harmonic analysis (43-XX) 5 Differential geometry (53-XX) 4 Nonassociative rings and algebras (17-XX) 4 Probability theory and stochastic processes (60-XX) 3 Combinatorics (05-XX) 3 Integral equations (45-XX) 3 Manifolds and cell complexes (57-XX) 3 Statistics (62-XX) 3 Systems theory; control (93-XX) 2 History and biography (01-XX) 2 Several complex variables and analytic spaces (32-XX) 1 General and overarching topics; collections (00-XX) 1 Number theory (11-XX) 1 Commutative algebra (13-XX) 1 Algebraic geometry (14-XX) 1 Category theory; homological algebra (18-XX) 1 $$K$$-theory (19-XX) 1 Potential theory (31-XX) 1 Sequences, series, summability (40-XX) 1 Geometry (51-XX) 1 Algebraic topology (55-XX) 1 Optics, electromagnetic theory (78-XX) 1 Classical thermodynamics, heat transfer (80-XX)

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# Does converting an FIR filter from causal to non-causal remove phase delay?

Let's say I have a causal 3-tap FIR filter:

$$y[n] = ax[n] + bx[n-1] + cx[n-2]$$

Assuming I have access to all the data prior to filtering and generate a similar non-causal filter:

$$y[n] = ax[n+1] + bx[n] + cx[n-1]$$

Would this new filter have the same frequency response but with different phase delay?

In general if you have a causal odd length $$N$$ FIR filter $$h[n]$$, defined for indices $$n\in[0,N-1]$$, moving the center bin to index $$n=0$$ means shifting the impulse response to the left by $$(N-1)/2$$ samples:

$$\tilde{h}[n]=h\left[n+\frac{N-1}{2}\right]\tag{1}$$

In the frequency domain this is equivalent to

$$\tilde{H}(e^{j\omega})=H(e^{j\omega})e^{j\omega (N-1)/2}\tag{2}$$

from which it follows that

$$\big|\tilde{H}(e^{j\omega})\big|=\big|H(e^{j\omega})\big|\tag{3}$$

and

$$\tilde{\phi}(\omega)=\phi(\omega)+\omega (N-1)/2\tag{4}$$

where $$\phi(\omega)$$ and $$\tilde{\phi}(\omega)$$ are the phases of $$H(e^{j\omega})$$ and $$\tilde{H}(e^{j\omega})$$, respectively.

If the coefficients $$h[n]$$ are symmetric with respect to the center tap, then $$\tilde{H}(e^{j\omega})$$ will be purely real-valued, if they are anti-symmetric, $$\tilde{H}(e^{j\omega})$$ will be purely imaginary, in all other cases, $$\tilde{H}(e^{j\omega})$$ will be a complex-valued function.

• I would add that if the original length $N-1$, causal filter $h[n]$ is linear phase, that means that $$h[N-1-n] = h[n]$$ and $$\phi(\omega) = -\omega \frac{N-1}{2}$$ which causes $\tilde{\phi}(\omega) = 0$ for all $\omega$. that means that $\tilde{H}(e^{j \omega})$ is purely real. – robert bristow-johnson Dec 4 '20 at 8:21
• @robertbristow-johnson: Yes, or purely imaginary, for type III linear phase. – Matt L. Dec 4 '20 at 11:04
• So does "shifting the impulse response to the left by (N−1)/2 samples" result in a zero phase filter? or just reduced phase? – Izzo Dec 4 '20 at 14:35
• @Izzo: You get a zero-phase filter only if the impulse response is symmetric. That is what I meant by saying that $\tilde{H}(e^{j\omega})$ becomes purely real-valued, which is the same a zero-phase. – Matt L. Dec 4 '20 at 15:06
• So because FIR is linear phase, it will have symmetric impulse response. Hence zero phase after shifting. – Izzo Dec 4 '20 at 15:19

Correct. The magnitude response would be the same and the phase response would be summed with $$\omega$$ (omega).

• What does "phase response would be summed with omega" mean? – Izzo Dec 4 '20 at 0:02
• The frequency response is a function of angular frequency, omega. By shifting the coefficients by one, that is equivalent to changing the phase of the frequency response by adding omega to phase. Put another way the group delay is one sample less for all frequencies. – Dan Szabo Dec 4 '20 at 0:48

Linear phase delay is the same as constant time delay. If you can offset the time of the output referenced to the input, forward or backward, you can change the slope of the phase versus frequency curve to any slope you like.


text:
## Saturday, December 29, 2007

### The burden of spending

Over the 12 months to October 2007, home prices in the 20 largest metropolitan areas declined by 6.1 percent. And they have fallen every month since January. With less equity to borrow from, homeowners could cut their spending. As a second whammy, a large volume of adjustable rate mortgages are scheduled to reset to higher interest rates between 2008 and 2012. The burden of higher monthly payments could force households to reduce their expenditures too.

Economic growth and consumer debt are inextricably connected in the U.S. And it’s been that way for so long that it’s easy to forget why and what that implies.

Spending has outpaced personal income since the mid 1980s. Households saved ten percent of disposable income in 1985, five percent in the mid 1990s, and then nothing in 2005. (See chart 1, maroon series, scale on the left axis.)

Chart 1 (click to enlarge)

Low interest rates motivated the consumption ramp-up. Loose monetary policy played its part, but it would be incorrect to blame it all on the Fed. The massive accumulation of wealth by developing countries lowered the opportunity cost of spending, as Alan Greenspan has explained.

Interest rates motivated it, but the borrowing spree was made possible by innovations in the financial sector that increased the supply of debt. The introduction of the FICO score in the early 1990s improved the assessment of a borrower’s creditworthiness – or at least lenders believe so. By pegging interest rates to an index, instead of offering fixed rates, lenders transferred some financial risk to borrowers. Securitization of debt balances shifted some more of that risk off the lenders’ balance sheets.

The problem with a growth path based on borrowing and spending is that it has a natural end. An individual’s debt limit is determined by her creditworthiness, income capacity and collateral. That limit may be high relative to current income, and it may even be unknown to the borrower — after all, it’s up to the lender to draw the line. But once debt balances reach that limit, spending can grow only as fast as income (minus debt payments). Consumption is pinned to the vagaries of income. At the aggregate level, that means that economic growth is more vulnerable to unemployment and to the swings of the stock and real estate markets.

For instance, back in 2001 unemployment was rising, investment fell sharply, and share prices crashed. But overall the economy held up better than expected. Why? One explanation lies in real estate wealth. That year house prices rose by nine percent and consumers borrowed against home equity.

As a gauge of the current level of indebtedness, households now spend almost 15 percent of their disposable income on interest payments, including mortgages. (See chart 1, blue series, scale on the right axis.) If you include repayment of principal, the fraction of debt payments is much larger. Debt repayments are linked to interest rates, and hence subject to unforeseeable increases. Hence the worry about mortgage resets.

The main variables that determine spending and access to debt are outside the policymaker’s control. The cost of borrowing depends on the world level and distribution of savings. Lenders will continue to improve their assessment and management of risk, thus reducing the cost of credit. And central banks are capable of controlling inflation, but not of preventing asset bubbles or stimulating long-run growth.

But don’t despair: tax policy can mend our spending ways. First of all, do no harm. Tax laws can distort the cost of borrowing. The Tax Reform Act of 1986 partially addressed this issue by getting rid of the deduction for interest paid on consumer debt (credit card and uncollateralized loans). The deduction for mortgage interest should go next. I concede that there’s a (weak) case for subsidizing home ownership. But these days a house is much more than a place to live: it’s a piggy bank to draw from. There is no reason why the government should subsidize that.

Second, replace the personal income tax with a tax on consumption. A basic tenet of economics is that if you tax something you get less of it. An income tax punishes work. Instead, the government could levy a tax on the difference between income and contributions to savings. The new tax could be progressive, rather than flat, and could include personal deductions, just like the current personal income tax.

The main obstacle to those tax policies is political. The mortgage interest deduction is popular, and a consumption tax is still regarded as an oddity. No presidential candidate who actually cares about being elected would make such proposals. Perhaps in 2012, if the then incumbent president can afford it. Changing the nature of American economic growth is a cause worthy of spending political capital on.

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Anonymous said...

Don't you mean EXCLUDING mortgage interest? Otherwise, how could debt service be equal to zero as a percentage of disposable income at 2 points on your chart.

Ian said...

Warren Buffet agrees with you, calling for a progressive consumption tax. And, Mr. Huckabee's FairTax fills the bill.

Economist Dale Jorgensen, Harvard University, was commissioned to find out what portion of current prices were represented by costs for complying with the federal income tax code (i.e., embedded tax costs). He concluded that 22% (average) of every retail dollar, spent by consumers, constituted a price-embedded tax. Thus, in addition to individual income tax and FICA withholding, individuals are unwittingly paying these unseen, embedded business tax costs with every purchase of a new product, or service.

Under FairTax, prices would fall, due to removal of embedded business tax-related costs. Concurrently, wages may rise due to a mix of factors, including reversion of withheld pay (or some portion thereof) to employees, advancement opportunities due to business expansion resulting from retained earnings, and/or increased demand for labor accompanying increased competition (from that expansion). Where profits (or wages) appear lucrative, competition will move into the market space, driving out excesses (immediately present after FairTax is enacted), arriving at new "market-adjusted" prices.

For FairTax to constitute 23% of new transaction cost (i.e., "market-adjusted" price plus FairTax), a mark-up of 29.9% (tax exclusive rate) on the new "market-adjusted" price is necessary. (Before balking, consider what we're paying now if income tax rates are converted to tax-exclusive sales tax rates on net income instead of percentage of gross income. The following figures can be compared to the 29.9% FairTax mark-up: Fifteen pct bracket = 17.6%, twenty-five pct bracket = 33.3%, twenty-eight pct bracket = 38.9% (! really), and thirty-five pct bracket = 53.8% (! that's how bad it is).

In order to make FairTax a progressive consumption tax (such as that recently called for by Warren Buffett), all citizen-families are simply sent a monthly consumption [tax] allowance, called a "prebate." This prebate is intended to reimburse taxes on necessities for every citizen family without need for record-keeping or reporting. Moreover, the direct payment bypasses the creation of a tax code specifying exempted products and services around which a lobbyist industry could grow. The amount is variable, based on family size, and is equal to the FairTax rate on poverty-level spending, as defined by the Dept. of Commerce. At present, a family of one would receive ~$200/month, a family of four, ~$500/month. Thus, the "effective" FairTax rate paid by citizens, will *never* equal the full 23%. Of course, U.S. visitors (legal, and illegal) will pay the full FairTax when they purchase anything new, at retail (used are not taxed again). Under FairTax, working families will have their whole paychecks (minus any state or local income tax withholding) plus their monthly family prebate.

Additionally, citizens will no longer have to spend the average 50 hours per year preparing their federal tax returns. Having more monthly income may result in using credit less, and saving more. Larger savings will make it easier to purchase a home, at a lower interest rate and monthly payment. (Thus, mortgage deductions are no longer applicable when income is not the basis for taxation).

But is FairTax actually "fairer"? To provide substantive answers, Prof.'s Kotlikoff and Rapson (10/06) have concluded,

"...the FairTax imposes much lower average taxes on working-age households than does the current system. The FairTax broadens the tax base from what is now primarily a system of labor income taxation to a system that taxes, albeit indirectly, both labor income and existing wealth. By including existing wealth in the effective tax base, much of which is owned by rich and middle-class elderly households, the FairTax is able to tax labor income at a lower effective rate and, thereby, lower the average lifetime tax rates facing working-age Americans.

"Consider, as an example, a single household age 30 earning $50,000. The household’s average tax rate under the current system is 21.1 percent. It’s 13.5 percent under the FairTax. Since the FairTax would preserve the purchasing power of Social Security benefits and also provide a tax rebate, older low-income workers who will live primarily or exclusively on Social Security would be better off. As an example, the average remaining lifetime tax rate for an age 60 married couple with$20,000 of earnings falls from its current value of 7.2 percent to -11.0 percent under the FairTax. As another example, compare the current 24.0 percent remaining lifetime average tax rate of a married age 45 couple with $100,000 in earnings to the 14.7 percent rate that arises under the FairTax." Further, per Jokischa and Kotlikoff (2005) ... "...once one moves to generations postdating the baby boomers there are positive welfare gains for all income groups in each cohort. Under a 23 percent FairTax policy, the poorest members of the generation born in 1990 enjoy a 13.5 percent welfare gain. Their middle-class and rich contemporaries experience 5 and 2 percent welfare gains, respectively. The welfare gains are largest for future generations. Take the cohort born in 2030. The poorest members of this cohort enjoy a huge 26 percent improvement in their well-being. For middle class members of this birth group, there's a 12 percent welfare gain. And for the richest members of the group, the gain is 5 percent." The current income-based tax system is also more expensive to run, because of the manner in which the tax code is gamed by politicians and lobbyists. Politicians realize great power, and attract constituencies for support, by granting tax favors (i.e., credits, deductions, exemptions) through lobbyists. Fully, fifty-three percent of Washington lobbyists are there because of the tax code! The tax code is continually changing, making it more complex - more difficult to understand. And, the salaries and costs of tax lawyers and lobbyists end up in higher prices of the products and services we buy. Additionally, the time and money required to keep records, file returns, report for audits, retain accounting and legal help, pay IRS penalties and interest, is time and money lost for other productive, or recreational, activities. Depriving us of the use of withheld wages increases our expenses through zero-interest withholding, inflation, return preparation time, and interest paid on credit cards and loans that otherwise may not have been necessary. Summed up, the cost of tax compliance, nationally, has been estimated to range anywhere from$265 billion to twice that amount, depending on the extent to which tax-avoidance consultation is sought and utilized. These expenses constitute a substantial hidden tax which is incomprehensible to the average working American. And the FairTax gets rid of all of it for most Americans, and most of it for business owners.

We, as FairTax advocates, believe that government should serve We, the People, with a fair tax system that will not enable politicians to pit poor against rich (creating barriers to achieve wealth, adding tax penalty to the sacrifices made for personal success). Nor do we want politicians to continue using business as a tool to hide taxes from consumers, often villifying business, which discourages entrepreneuship, personal achievement, economic growth. Liberty and happiness depends on restoring the fruits of labor to those who produce them. We believe that the tax function should align with economic growth, not against it, that government should be paid for in the same manner as working Americans - when, and because, something is sold!

As things stand at present, the system primarily benefits politicans who cater to special interests through lobbyists who game the tax code. The politician seeks to capture them as constituent voting blocks, dependent on continued syphoning of taxpayer dollars to their members' benefit. This is increasingly repugnant to the average working American who often finds it difficult to meet the needs of his, or her, own family in an environment where federal and state business income taxes substantially contribute to trade inequities resulting in the loss of American jobs! Thus, the Sovereign are continually degraded by features of Congress's income tax policy. The most rapidly-growing needs-based "special interest" group has become the Citizens! You see? Congress has nearly all the power; and We, the People, have become We, the Serfs, robbed and enslaved. Getting the federal government's hands out of our family paychecks is the single most important reason to replace the income tax with a consumption tax, the FairTax.

Many of us have joined FairTax.org in order to build a national movement to free ourselves, our family pocketbooks, and our businesses from confiscation of income, and punishment of productivity. And this we say to our federal representatives,

"Either scrap the code and enact the FairTax, or we intend on replacing you with someone who will."

(May reproduce in whole or part. - Ian)

Francisco said...

In response to anonymous on 12/30/07: the scale for debt service is on the right axis, not the left.

Sorry it took me a while to respond: I've been away from the internet for a few days.

Thanks for stopping by.

Francisco said...

In response to Ian (1/2/2008)
Thanks a lot for leaving such a long and thoughtful comment.

My post didn't endorse FairTax, just an expenditure tax: "a tax on the difference between income and contributions to savings."

I believe one can simplify the tax code, stimulate saving, and have a progressive tax system, without resorting to FairTax.

To be honest, I don't know how the tax I propose would fare against FairTax, but your comments are illuminating. I'll continue to study FairTax and maybe write a post about it in the future.

Thanks! Please come back to EconWeekly.

Francisco

Forastero said...

It is a very interesting blog for the non studied people in economics. I´ll read as frequently as I can in case of any of these issues afects to Spain.
From Spain, a frustrated econocmist wrote!


text:
## Archive for the ‘history’ Category

### Cédric Villani and other academics at Assemblée Nationale

June 25, 2017

[Posted on june 25, 2017.]

Some observations on the newly elected members of Assemblée Nationale:

***

In other news:

• Jean-Pierre Kahane passed away at 90
• Peter Scholze, who has recently been elected to the Leopoldina, has a recent preprint titled Étale cohomology of diamonds which is not yet on the arXiv.
• a 10-year-old in Cameroon who enjoys math is nearing the end of the high school curriculum there, hopefully he’ll then get the University-level education he deserves (and surely he’s not the only one)
• I’ve updated my list of Diamond OA journals in mathematics to include Acta Mathematica and Arkiv för Matematik
• a strange editor’s note in the current issue of Annals of Mathematics, whereby they withdraw a 2001 paper without saying why, and it appears that the paper was never cited in the 16 ensuing years (at least according to google scholar), which is very odd.[update: see this story on Retraction Watch (h/t anon)]

Paris, France by Bob Hall on flickr

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### Some february 2017 newslets

February 18, 2017

[Posted on february 18, 2017.]

Firstly, some recent items:

Also to be noted, two upcoming auctions:

• on march 14 (estimated at €20,000/30,000) in Paris, arare copy of the 1637 first edition of Descartes’ Discours de la Méthode (containing the famous appendix La Géométrie)
• on february 22 (estimated at €200/300) in Lyon, a 326 pages manuscript c.1810 on dynamics and other topics (author unknown) [edit: won by the floor at €280]

Finally, it appears this blog was started 10 years ago, in what was definitely another era: before Polymaths, MO, arxiv overlay journals…and all the new official youtube channels in math and beyond.

### Who was Joseph Ser ?

August 25, 2016

In an interesting paper, Iaroslav Blagouchine has presented, among other things, the equivalence of the explicit analytic continuation of $\zeta$ due to Hasse  (in this 1930 paper) $\zeta(s)=\frac{1}{1-s}\sum_{n=0}^{\infty}\frac{1}{n+1}\sum_{k=0}^n(-1)^k \begin{pmatrix}n\\ k\end{pmatrix} (k+1)^{1-s}$  with one derived 4 years earlier by a Joseph Ser (in this paper) $\zeta(s)=\frac{1}{1-s}\sum_{n=0}^{\infty}\frac{1}{n+2}\sum_{k=0}^n(-1)^k \begin{pmatrix}n\\ k\end{pmatrix} (k+1)^{-s}$.

It may be that these could help improve the situation regarding the location of the non-trivial zeros of $\zeta$, although of course the classical Mertens approach with logs and the trigonometric identity cannot be mimicked here due to the ever growing number of terms added for each new $n$.

But who was Joseph Ser then ? There’s a short wikipedia bio saying that nothing much is known about him. There seems to be a genealogical entry for him here, with little more details beyond dates.  I couldn’t find his name among Normaliens nor Polytechniciens. He also doesn’t appear in the list of pre-1901 professeurs agrégés, and neither in the list of PhDs compiled by Hélène Gispert in her book.

As for published material, Numdam has 3 papers from him, where only the earliest one has a tiny indication: Nantes.  One can also find that a book of Ser, Les Calculs Formels des Séries de Factorielles, got a quite unfavorable review  in Bull AMS, while the same book got a more positive review in L’Enseignement Mathématique. And finally, he seems to have authored several articles in Mathesis, at least until 1953 when he was well into his seventies.

Feel free to comment if you know more about his work and career.

Caniculaire. (Metz, late august 2016, Public Domain.)

### Quick observations concerning the Séminaire Bourbaki

June 21, 2015

Since the next Séminaire Bourbaki is due to take place next saturday, it is a good opportunity to make some quick observations.

Started in 1948, its goal as an expository seminar was clear from the start: the very first exposé was by H. Cartan on the work of Koszul rather than on his own results, and many recent advances were presented at the seminar (e.g. the same year Pisot reviewed the elementary proof of the PNT by Selberg and by Erdős).

The first issues regroup several years, and in 1968 things settled on the current format : 4 sessions during the academic year, held in november, january, march, and june. The year 2014-2015 is its 67th year, and will end with the 1103th exposé. One can notice the following :

### Most of Grothendieck’s manuscripts to be digitized

June 18, 2015

According to an article by Stéphane Foucart in Le Monde, it has been announced at the Grothendieck conference in Montpellier that :

• about 15,000 pages of manuscripts held by the university were now in the process of being digitized (that’s the archive that was given to Jean Malgoire in the 1990’s, which in turn he donated to the university)
• about 50,000 pages found in Grothendieck’s Lasserre home will be digited by the Bibliothèque Nationale de France (of Gallica fame), once legal hurdles are cleared, and which contain a mix of mathematical and non-mathematical texts

Let’s see : assuming 50% of mathematical content, that’s (15,000+50,000)/2=32,500 pages.  Chopping that into bunches of 200 pages, that’s about 162 books. In comparison, Euler’s Collected Works are said to fill 60 to 80 books…

### The Tombstone of Madame du Châtelet (1706-1749)

April 5, 2015

In 2006, to mark the tricentenary of the birth of first ever frenchwoman scientist, Émilie Du Châtelet, an exhibition was organized in Paris by Elizabeth Badinter (booklet here).

Then, a few years ago, several newly found mathematics and physics manuscripts written by la Marquise du Châtelet were sold at an important Christie’s sale.

What about the final resting place of such a fine woman? Well, it is a very sober black tombstone in Saint-Jacques church, in Lunéville. Elisabeth Badinter, and Annie Jourdain, tried to have something done so that it is not walked over by the faithfull, but there were no protective barriers when I visited a few days ago.

By the way, the Château de Lunéville, which sadly was ravaged by a fire in 2003, has been nicely restaured over a decade, and is well worth a visit. I went there early enough to catch a nice april cold fog.

### Auctions of mathematical texts

February 12, 2015

On saturday in Royan there will be on offer (for about €300/350) a handwritten set of lecture notes of Cauchy’s 1824 course on Calcul différentiel et intégral, taken by Lamoricière.  It may well beat that estimate by some margin.

Indeed, last december, the own annotated copy of Hugens’ Horologium Oscillatorium Sive de Motu Pendulorum ad Horologia Aptato Demonstrationes Geometricae (1673), went for \$965,000 after an estimate of 150,000/200,000.

A month earlier, a 1931 offprint of Gödel’s Über Formal Unentscheidbare Sätze der Principia Mathematica und verwandlter Systeme I, achieved £104,500 after an estimate of £12,000/£16,000.

So, there seems to be a market for the rare and historically important items, that’s not too surprising but the level is pretty high (I guess all it takes is just a couple of mathematically enclined high-ranking google executives, or the likes…). And it’s not only auctions, fixed price items exist too, like these 3 manuscript pages by Gauss available for €65,000.

Update: the aforementioned sale has been broadcast online earlier today, and those handwritten notes indeed attracted interest, with a little fight between the floor and online bids ending at €1,300.

### Pangaea Ultima

December 31, 2014

Four years ago I mentionned Ron Blakey’s video of evolving continents on the great SpaceRip channel.   Last september they posted an updated beautiful version with much more detailed maps, converging to Pangaea Ultima:

### Preserving documents of Hermite and Picard IV: other items

December 16, 2014

[You are currently viewing a post that is part of a series : the story ; Hermite’s 1892 jubilee ; Picard’s youth ; Other items.]

Together with the jubilee papers, there were three other documents (pictures) :

1) a letter in german from Hermann Schwarz, from the 2nd of june 1893, concerning the great gold medal for science awarded to Hermite by the Kaiser Wilhelm II. There’s an hilarious letter of Hermite to Stieltjes from the 17th of may 1893, where he complains that a small 5-franc sized gold medal that didn’t bear his name had been delivered to him without previous notice nor explanations, and that he had been treated like a dog by the emperor (!!), and had written to Schwarz about it.  This explains that, then. (The portfolio that I couldn’t buy, mentionned in the first post, apparently contained the french translation of that Schwarz letter).  The medal itself is unaccounted for…

2) a letter from Matthias Lerch from the 29th of december 1892, which discussed some results, and also contains a nasty anti-semitic statement. (I don’t think that Hermite shared that kind of opinion, it’d be truly disappointing if he did!)

3) the draft of a letter by Hermite from the 15th of june 1893 thanking the king of Greece for…yet another gold medal.

Appart from that, a late twist was that in mid-november a fifth (!) seller came-up in the ebay auctions, this time with some genealogical documents and pictures of Picard (you can see them here), in particular one dating from 1889 upon his election to the Académie des Sciences (aged 33, now that is a moustache…)

and another one from 1939, a couple years before his death. One sees a very large library behind him, probably full of interesting items!

From this seller I finally learned that in the summer of 2014 an old house had been advertised for clearing, and the belongings sold to different people locally.

At this point it is unclear if most of what was sold then has been preserved: it is odd that the documents do not contain any of Picard’s reprints from before 1883, yet he had lots of papers before that.  It is also suspicious that only one Hermite manuscript would be there.  I’m fearing that some of the most interesting items have discreetly made it to specialized resellers and wealthy private collectors.

Obviously, I’m not expecting all of Picard’s library to have been available anyway: he had five children, three of which died around WW1 while the two remaining daughters married physicists Louis Dunoyer de Segonzac and Jean Villey-Desmeserets (who had four children, one of whom had preserved those documents). So Picard’s library has thus probably been split between his pupils and the sons-in-law physicists in the 1940s, and then between the children and grand-children of all of them.  It was already known that the Villey branch had some items, since in 1970 Pierre Dugac had documented part of the correspondance between Hermite and Stieltjes (which, it is mentionned, had later been given to the Archives de l’Académie des Sciences), but what else there were is as yet unsettled.

This little detective story ends here, for now at least, but it’s been exciting. I cannot begin to imagine the thrill that it must be to make an important archeological find, like the wonderful Kasta Tomb, or indeed any other major discovery

### Preserving documents of Hermite and Picard III: Picard’s youth

December 16, 2014

[You are currently viewing a post that is part of a series : the story ; Hermite’s 1892 jubilee ; Picard’s youth ; Other items.]

In a nutshell, Émile Picard has been one of the main french mathematicians of the 1880-1920 era. He’s been precocious (earning his doctorate in 1877 aged 20), prolific (from the full list of his notes to Comptes-Rendu de l’Académie des Sciences, one sees he had 8-10 per year at the beginning, not to mention his longer papers in other journals), and very versatile (he touched on most subjects of those times, including relations with physics).  He thus obtained lots of honors, including Pleanary Speaker (1908) and President (1920) of an ICM, and Grand-Croix de la Légion d’Honneur (the highest, very select, grade). In 1917 he became permanent secretary of the Académie des Sciences, and controlled most of what was being published in France, sometimes to ill-effects.

But in this post we’ll focus on his early career, since that’s what the documents obtained shed some light on (see the story). They can be broken into three parts : (a) a stack of letters that Picard’s mother had kept, (b) Picard’s own copy of his 1886-87 Cours d’Analyse, (c) reprints of many papers, and books written by him.

About that last item (c) I shall say no more, since they are just what appeared in print at the time with no handwritten additions (so the content available in libraries or online –see numdam for many papers, and archive.org for some papers and his books— is identical).

Next we turn to (b) :

According to the Académie des Sciences, in 1885, after junior positions in Paris and Toulouse, Picard became the tenured professor of the Chaire de Calcul Différentiel et Intégral at Faculté des Sciences de Paris (until 1897 when he took up another position). In 1887, his course was edited (here is the GDZ digitized copy) by l’Association Amicale des élèves et anciens élèves.  This served as a precursor to Picard’s highly regarded Traité d’Analyse (vol. 1, vol. 2, vol. 3) a few years later.

The copy obtained was Picard’s, and contains lots of handwritten additions. I’ve put pictures of all of them on this online album on flickr (and if you want to see in larger size you must remove the final part of the URL and add instead /sizes/h/  e.g. like on this picture). To help locate them in the book I’ve usually taken first a picture of the page number next to (or behind) which they have been made.

These additions must then date from between 1887 and 1890 (when the new Traité appeared).  I’m no history specialist, but I did try to see if among them one could find the first occurence of one of Picard’s ideas. Net result: probably not, or not entirely at least. Historians will tell in due course, hopefully.

For example, as mentioned in his footnote on page 531 of vol.3 of his Traité, Picard first extended the ideas of Galois theory to linear ODEs in 1883 (in this CRAS note) and later came back to it in 1887 (the year of our copy, then).  We do find some pages (starting here) where he discusses what became later known as the Picard-Vessiot group of an ODE. He uses different inks, so it looks like he wrote that in stages as ideas came to him, but was that just material for his students, or stuff for his own understanding ? Tom Archibald wrote on that topic a paper that probably settles the issue (but it’s behind a paywall and I haven’t read it yet).

There are also two pages (one, two) that mention birational transformations and cycles in relation to a theorem of Max Noether, when it is known that Picard’s involment in then nascent algebraic geometry ranges from 1884 to 1905, according to Houzel’s chapter in Gispert’s book (see also Lefschetz’s 1968 autobiographical sketch in Bull. AMS, as well as the introduction to Kleiman’s paper The Picard Scheme).

The parts on more traditional topics like uniform continuity probably don’t contain anything new, since according to Hairer and Wanner’s excellent Analysis by its History these concepts date back from much earlier.  But perhaps the parts on existence of solutions of ODEs do (the chapter starts here) : after all, Picard’s method of successive approximations dates precisely from about 1888 (the method itself dating back to Liouville but not applied to existence results, see Archibald’s very interesting paper, in particular page 86 onwards).

That’s it for the mathematical part of the documents. We now turn to the more biographical part (a), which helps correct some inaccuracies in online biographies, and adds new material.

When I obtained the stack of letters that Picard’s mother had kept, they were all mixed (probably by the seller). After reading them, it appears they can be organised into the following twelve substacks :

(a) Letters adressed to Élisa Picard (née Plocq) on the occasion of her mariage in 1852 (nothing about Émile there then).

(c) Letters to Élisa on the occasion of her husband’s death in 1872, after a long illness.

(d) Letters from Alexandre Plocq and his wife. He was a cousin of Élisa and had been entrusted as the one to provide guidance to Émile and his younger brother Édouard.  Indeed it seems to have been a good choice : in those letters this Alexandre appears as a very righteous man, with high regard for studies and hard work. He himself enjoyed a high social status as Ingénieur en Chef des Ponts et Chaussées at the harbor of Dunkerque, which he obtained as a former top student of l’X (École Polytechnique). In particular, he appears to have been instrumental in both children obtaining a full bursary to study.

(e) Letters of congratulations adressed to Élisa on the occasion of academic successes of her sons.

(f) Letters to Élisa from a cousin living in New-York (an uncle of Émile then).

(g) Letters adressed to Émile during his youth, including one (probably) from Classicist Charles Graux when Émile obtained his doctorate, as well as some earlier ones from the american uncle, and from Alexandre Plocq suggesting to wait for the results of l’X before choosing École Normale Supérieure (so preaching a little bit for his chapel here, but he then wrote to Élisa that she should accept Émile’s choice)

(h) Letters to Élisa from Émile. There are several ones from 1887, including some not very sympathetic remarks about his father-in-law Hermite (who, apparently, was a bit of a grumpy old man by then), and the occasional odd XIXth century idea (“le passage du col du géant n’est vraiment pas à recommander pour la coqueluche“). There’s also an earlier touching one from october 29th, 1880 where Émile (aged 24) finds Hermite’s daughter “de mieux en mieux et elle me plait infiniement” but wonders how to know whether M & Mme Hermite have any plans for himself, and asks his mother what she makes of this.

(i) Letters to Élisa by the Hermite family. It includes a letter from Monsieur Hermite dated november 13th, 1880, in which he accepts to give the hand of his daughter to Émile (so the latter must have proposed in early november, perhaps after a letter from his mother). The tone of the letter is both solemn and humorous, Hermite adding “Venez donc, chère Madame, prendre la grande part qui est due dans notre bonheur, venez traiter et résoudre des problèmes dont la solution demande notre réunion” (Quick translation: “Come thus, dear Madam, to take the great part that is due in our joy, come adress and solve problems whose solution requires our union“.)

(k) Letters to Émile from his younger brother Édouard. This brother was also very talented, he entered l’X and became a top student there (and became Ingénieur des Ponts et Chaussées, just like his mentor Alexandre Plocq). Although they also met in Paris, Édouard tells Émile how he is doing academically (note: in France marks are out of 20, e.g. 17 is quite good, especially for oral exams such as colles).

(l) Letters to Élisa from the brother Édouard, including many from Algeria where he later worked (I must say I haven’t read most of those).

Next post : Other items.


text:
# 0.2 The deconvolution method

 Page 1 / 1
The inverse filter approach to echo cancellation.

## Deconvolution

The output of a linear time-invariant (LTI) system is the convolution of the input signal with the impulse response of the system. If the classroom is modeled as an LTI system, then the output echoed signal, $y\left(t\right)$ , is the convolution of the input signal, $x\left(t\right)$ , with the room's impulse response, $h\left(t\right)$ .

The process of deconvolution involves designing an inverse filter ĥ(t) that is convolved with the echoed output signal to retrieve the original signal $x\left(t\right)$ . This can be done in either the time domain or frequency domain:

• Time domain: Use the deconv() method in Matlab on the echoed signal and the impulse response of the classroom in order to extract the de-echoed signal.
• Frequency domain: Take the Fast Fourier Transform (FFT) of both the impulse response of the room and the echoed signal. Point-wise divide the echoed signal by the transfer function, then take the inverse FFT of the result to extract the de-echoed signal.

However in practice, the system adds noise to input signal, meaning that if the signal-to-noise ratio is too low, the inverse filter will yield a noisy signal that poorly approximates the input.

## Finding the impulse response

A system is characterized at all frequencies by taking its impulse response . This is done by exciting a system with a Dirac delta function . The Dirac Delta Function is defined as:

$\delta \left(x\right)=\left\{\begin{array}{cc}+\infty ,& x=0\\ 0,& x\ne 0\end{array}\right\}$
$\underset{-\infty }{\overset{\infty }{\int }}\delta \left(x\right)dx=1$
The Dirac Delta Function is a distribution that is infinitely tall and infinitely narrow at 0, and the area under the Dirac Delta Function is defined to be 1.

However, it is practically impossible to excite a room with the ideal Dirac Delta function. Consequently, we used three methods to approximate the room's impulse response:

• Balloon Pop: filling a latex balloon with air and bursting it.
• Pseudo Dirac: using the dirac() function in Matlab to generate a vector of zeros with a single one in the center, then playing it using the sound() function.
• Sine-sweep Method:
1. Generate a logarithmically increasing sine signal over a desired frequency range (20 Hz to 20 KHz for this application)
2. Create an inverse chirp filter that time reverses the chirp and shifts it to become a causal signal (so that it exists in positive time). Then, divide the magnitude of the spectrum of the inverse filter by the square of the magnitude of the spectrum of the chirp signal.
The time shift inverts the phase of the chirp leading to linear phase after the convolution and the second set of operations neutralizes the squaring of the magnitude of the spectrum caused by the convolution.
• Convolve the chirp response of the room with the inverse chirp filter to get the impulse response of the room.

This logarithmically increasing sine signal can be characterized in the time domain by the following equation:

$x\left(t\right)=\mathrm{sin}\left[{\frac{T{\omega }_{1}}{\mathrm{ln}\left(\frac{{\omega }_{2}}{{\omega }_{1}}\right)}}^{\left({e}^{\frac{t}{T}\mathrm{ln}\left(\frac{{\omega }_{2}}{{\omega }_{1}}\right)}-1\right)}\right]$

where ${\omega }_{1}$ is the initial radian frequency and ${\omega }_{2}$ is the ﬁnal radian frequency of the sweep of duration $T$ .

## Sine sweep

To measure the response, we used:

• A small guitar amplifier with a relatively flat response facing the desks
• A directional cardioid microphone 2 meters from the amplifier at a thirty degree angle
• A microphone preamplifier
• An Apple Macbook Pro Laptop using Audacity for recording

## Problems

Several factors make this model unrealistic:

• Realistically, speakers move around and face different directions when they move. Our impulse responses are highly specific to the position of the signal's source. The information we get is based on the amplifier being stationary and facing a single direction.
• The impulse response is also time-varying. If even one person leaves, the average absorption coefficient of all the objects in the room changes and, per the Sabine equation, the reverberation time of the room also changes. People and objects are continually shifting, constantly affecting how the sound reflects around the room.

Time-varying adaptive filters are more sensible for problems such as suppressing reverberations in the OEDK classroom.

I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Abigail
for teaching engĺish at school how nano technology help us
Anassong
How can I make nanorobot?
Lily
how did you get the value of 2000N.What calculations are needed to arrive at it
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• Volume 40, Issue 3

June 2017,   pages  427-614

• Electrochemical impedance studies of capacity fading of electrodeposited ZnO conversion anodes in Li-ion battery

Electrodeposited ZnO coatings suffer severe capacity fading when used as conversion anodes in sealed Li cells. Capacity fading is attributed to (i) the large charge transfer resistance, $R_{\rm ct}$ (300–700 $\Omega$) and (ii) the low Li$^+$ ion diffusion coefficient, D$^+_{\rm Li}$ (10$^{−15}$ to 10$^{−13}$ cm$^2$ s$^{−1}$). The measured value of R$_{\rm ct}$ is nearly 10 times higher and D$^+_{\rm Li}$ 10–100 times lower than the corresponding values for Cu$_2$O, which delivers a stable reversible capacity.

• SU-8 photoresist-derived electrospun carbon nanofibres as high-capacity anode material for lithium ion battery

A binder-free carbon nanofibres web over stainless-steel wafer current collector was fabricated by controlled pyrolysis of electrospun SU-8 photoresist nanofibres. Electrochemical performance of the as-prepared carbon nanofibresweb was investigated by performing charge–discharge experiments at different current densities. At low current density (37.2 mA g$^{−1}, 0.1$C$), SU-8-derived carbon nanofabric showed a large initial discharge capacity (1417 mAh g$^{−1}$) with sufficiently higher initial coulombic efficiency ($\sim$55%). More importantly, this carbon nanofibres web also exhibited excellent rate performance with considerably higher specific capacities at higher current densities (358 mAh g$^{−1}$at 1C). This superior electrochemical performance, in particular at high current rates, can be attributed to small lithium ion diffusion length andresilience in entangled carbon nanofibres to accommodate volume changes during charging and discharging. • Effect of composition on the polarization and ohmic resistances of LSM/YSZ composite cathodes in solid oxide fuel cell La0.8Sr0.2MnO$_3$−$\delta$(LSM)/8 mol% yttria-stabilized ZrO$_2$(YSZ) (LSM/YSZ) composite cathodes with varying composition are studied for both polarization and ohmic resistance by electrochemical impedance spectroscopy. It was found that total resistance and polarization resistance are lowest for the composite with 60 wt% of LSM (LSM60/YSZ40). However, the ohmic resistance was highest for the same composition and amounted to 60% of the total resistance value. Compositional dependence of resistances has been explained based on the variations of the triple phase boundaries and width of the O$_2$−ion migration path with the composition of the electrode. Based on the observed area specific ohmic resistance values for the composite cathodes, it is proposed to verify the advantages of LSM/YSZ over LSM cathode in anode-supported solidoxide fuel cell with thin electrolyte. • Properties of biocomposites based on titanium scaffolds with a different porosity Open-porous titanium scaffolds have been widely investigated for orthopaedic and dental applications because of their ability to form composites via bone in growth into pores and promote implant fixation with mother bone. In this work, porous titanium scaffolds coated with a diamond-like carbon were produced, and their ability to form biocomposites was evaluated through in vivo experiments. Three types of the open-porous scaffolds made of spongy titanium granules (porosity 0.3, 0.4 and 0.5, Young’s modulus 4.4, 3.5 and 0.6 GPa) were implanted into a bone defect of sheep. Time dependences ofthe Young’s modulus of titanium scaffold–bone tissue biocomposites were determined through the measurement of Young’s modulus of the extracted scaffolds after 4, 8, 24 and 52 weeks of surgery. The Young’s modulus of biocomposite is dependent not only on the time of composite formation but also on the porosity of scaffold. • Synthesis and characterization of ZnO nanostructures with varying morphology Uniform fine particles of zinc oxide were prepared in three different morphologies and sizes by the controlled precipitation process from aqueous solutions of zinc nitrate in the presence of ethylene glycol. Ammonium hydroxidesolution was used as the precipitant. Composition of the reactant solution, pH and temperature significantly affected the particle uniformity with respect to shape and size. Uniformity in the particles morphological feature was achieved under a narrow set of experimental conditions. pH of the reactant solutions and isoelectric point of zinc oxide were considered the master variables, controlling the particle size. One of the batch of the as-prepared zinc oxide particles was calcined at 750$^{\circ}$C, which increased its crystallinity, changed its various lattice parameters, Zn–O bond length and preferred orientationof the crystal$hkl$planes. Calcination had little effect on the original morphology of the zinc oxide particles. • Structural and optical properties of ZnO thin films prepared by laser ablation using target of ZnO powder mixture with glue ZnO thin films were deposited on ITO/glass substrates by pulsed laser deposition (PLD) using two different kinds of targets. One of the targets was made of pure ZnO powder and the other one consisted of a mixture of ZnO powder with cyanoacrylate glue. The structural and morphological properties of the films obtained using both targets were compared, in order to determine which one produces samples with properties more suitable for their use as buffer and antireflective layer in CdTe-based solar cells, also different heterostructures were deposited to study the optical properties of the obtained thin films and their utility in the applications mentioned before. The films deposited with the mixture powder target were polycrystalline with preferential orientations in the planes (100) and (101) with a high transmittance in the range of 70–90% in the 540–850 nm wavelength region and showed a high resistivity of$\sim$1.30$\times$102$\Omega$cm$^{−1}$, such properties are considered to be appropriate for thin films that are wanted to be used as a buffer and antireflective layer in CdTe solar cells. • SiO$_2$/TiO$_2$multi-layered thin films with self-cleaning and enhanced optical properties Self-cleaning, high transmittance glazing was obtained by cold spray deposition for glazings. The thin films contain TiO$_2$, SiO$_2$and Au nanoparticles in different structures which allow for tailoring the optical, hydrophilic and photocatalytic properties. The crystallinity, morphology and surface energy were correlated with the optical transmittanceand reflectance; the transmittance increased from 89.45 (for the glass substrate) to 91.76% when Au nanoparticles were used in the tandem layered structures. The samples containing alternating multi-layered SiO$_2$and TiO$_2$thin films without gold nanoparticles show hydrophilic surface; for these layers, the photocatalytic efficiency reaches 40% under simulated solar radiation. A conditioning effect based on adsorption was observed to increase the photocatalytic efficiency. These highly transparent coatings are well suited for glazings and fenestration, showing the self-cleaning effect based on combinedsuperhydrophilicity and photocatalysis. • Dependence of the textural properties and surface species of ZnO photocatalytic materials on the type of precipitating agent used in the hydrothermal synthesis Three different precipitating agents (NaOH, NH$_4$(H)CO$_3$and CO(NH$_2$)$_2$) have been applied for the hydrothermalsynthesis of ZnO powder materials, aiming at obtaining various types of porosity and surface species on ZnO. The synthesis procedures were carried out in the presence and in the absence of tri-block copolymer Pluronic (P123,EO20PO70EO20). These materials were characterized by powder X-ray diffraction (PXRD), X-ray photoelectron spectroscopy (XPS), scanning electron microscopy (SEM)–energy-dispersive X-ray spectroscopy (EDX), BET method and TG–differential thermal analysis (DTA) method, and their photocatalytic activities were tested in the removal azo dye Reactive Black 5 (RB5). The urea precipitant yields spongy-like surface forms and the greatest share of mesopores. It has the highest specific surface area, highest degree of crystallinity of wurtzite ZnO phase and largest content of surface OHgroups in comparison with the other two precipitants. The zinc hydroxycarbonate intermediate phase is missing in the case of NaOH as precipitating agent; therefore, it manifests poorer textural characteristics. The morphology of P123-modified sample is different and consists of needle-shaped particles. The urea-precipitated samples display superior performance inthe photocatalytic oxidation reaction, compared with the other precipitated samples. The other two precipitating agents are inferior in regard to their photocatalytic activity due to greater share of micropores (not well-illuminated inner surface) and different surface morphologies. • A study on structural stability of bismuth titanate with lanthanum doping for improved ferroelectric properties Bismuth titanate (Bi$_4$Ti$_3$O$_{12}$) with different lanthanum (La) concentrations (0.25, 0.50, 0.75 and 1.0 mol%) was successfully prepared via soft combustion route. It was found that the change of diffraction peaks shown by X-ray diffraction is attributed to the doping effect in Bi$_4$Ti$_3$O$_{12}$. This was also supported by the presence of additional peak that correspondsto La in the range of 800–860 eV, proved by X-ray photoelectron spectroscopy. In addition, the enlarged region of Bi 4f, Bi 4d, Ti 2p, La 3d and O 1s of doping sample was clearly seen after deconvolution. Based on binding energy position, it can be unambiguously stated that the Ti ions in the tetravalent state are surrounded by the perovskite layer of Bi$_4$Ti$_3$O$_{12}$, whichmay also imply the formation of oxygen vacancies in the vicinity of the Bi$_2$O$_2$layer. In comparison with Bi$_4$Ti$_3$O$_{12}$, thegreen emission intensity was abruptly decreased with La doping. This indicates that La doping suppresses the formation of oxygen vacancies by stabilizing the adjacent oxide ions. Thus, the improved polarization shown by ferroelectric hysteresis loop is associated with the reduction in oxygen and bismuth vacancies due to La doping. • Flexible composite via rapid titania coating by microwave-assisted hydrothermal synthesis The aim of this work was to prepare a flexible nanocomposite from ultra-fine titanium oxide (TiO$_2$) growth on carbon fibre via microwave-assisted hydrothermal synthesis (MHS) and to evaluate its photocatalytic properties. The TiO$_2$nanoparticles were directly grown on the carbon fibre (CF). Thus, a study comparing the conventional titania coating vs. the MHS were performed. The significant layer interaction as a function of the coating method on the visible and dark dye photodegradation performance was observed. Techniques such as X-ray diffraction, electron microscopy (field-emission scanning electron microscope (FESEM)), Raman spectroscopy, among others were used aiming to characterize the different route samples. This study reports a reproducible and single method to manufacture of nanocomposites through the growth ofTiO$_2$nanoparticle on CF by MHS that allow controlling the thickness layer. Similar procedure of synthesized nanocomposite could be applied in different chemical compositions to advanced applications, based on the electrochemical nanostructure. • Ultrasonic-assisted fabrication of superhydrophobic ZnO nanowall films Zinc oxide-based superhydrophobic surfaces were fabricated on aluminium oxide-seeded glass substrates via sonochemical approach by varying the parameter, the sonication time duration. The fabricated structures have nanowall-like morphology with an average long axis length and thickness of$\sim$300 and$\sim$40 nm, respectively. The surface roughness createdby surface-modified ZnO nanowalls and the air pockets trapped within the dense nanowalls, transformed the hydrophobic glass substrates into superhydrophobic surfaces with water contact angle of 156$^{\circ}$during 20 min of sonication. An independent analysis was carried out to study the growth of ZnO nanowalls over glass substrates in the absence of the aluminium oxide seed layer and sonication process. The results suggested that the synergistic effect of the aluminium oxide seed layer and sonochemical process can enable the formation of ZnO nanowall structures favourable for superhydrophobic property. A possible growth mechanism of ZnO nanowalls formation during sonication process has been discussed in detail. • Partially decomposed PVP as a surface modification of ZnO, CdO, ZnS and CdS nanostructures for enhanced stability and catalytic activity towards sulphamethoxazole degradation In order to prepare stable and efficient photocatalysts, a microwave-furnace-assisted method using ethylene glycol (EG) as a solvent has been employed to obtain metal oxides and metal sulphides nanocatalysts with partial decompositionof the polyvinylpyrrolidone (PVP) cap (P-ZnO, P-CdO, P-ZnS and P-CdS); this associates the protective functionality of PVP with enhanced catalytic activity due to effective carriers transfer. The as-produced catalysts characterization revealed an extended growth of metal oxides compared with metal sulphides, which is attributed to the competition of EG as the source of oxygen with PVP to capsulate metal oxides during the synthesis. Infrared spectra confirmed the PVP–metal complexation and partial decomposition of the polymer. Metal sulphides exhibited a better catalytic activity compared with metal oxides for sulphamethoxazole degradation in UVC light owing to their size and morphology impact; further, P-CdS induced 71% antibiotic degradation after 10 h of illumination with visible light compared with only 48% for P-ZnS, 29% for P-ZdO and 20% for P-CdO due to improved light absorption. Interestingly, around 86% degradation was induced by mixing P-CdS with P-ZnS in 80:20% ratio, indicating an enhanced visible light activity due to improved electron–hole pair separation and high redox potential of P-ZnS. • Characterization and optical properties of Pr$_2$O$_3$-doped molybdenum lead-borate glasses Pr$^{3+}$doped molybdenum lead-borate glasses with the chemical composition 75PbO−[25–($x+y$)B$_2$O$_3$]–$y$MoO$_3$–$x$Pr$_2$O$_3$(where$x = 0.5$and 1.0 mol% and y = 0 and 5 mol%) were prepared by conventional melt-quenching technique. Thermal, optical and structural analyses are carried out using DSC, UV and FTIR spectra. The physical parameters,like glass transition ($T_g$), stability factor ($\Delta T$), optical energy band gap ($E_{gopt}$), of these glasses have been determined as a function of dopant concentration. The$T_g$and optical energy gaps of these glasses were found to be in the range of 290–350$^{\circ}$C and 2.45–2.7 eV, respectively. Stability of the glass doped with Pr$^{3+}$is found to be moderate ($\sim$40). The results are discussed using the structural model of Mo–lead-borate glass • Polymer-assisted co-precipitation route for the synthesis of Al$_2$O$_3$–13% TiO$_2$nanocomposite The present investigation reveals the effect of processing parameters on the properties of alumina–titania (Al$_2$O$_3$–TiO$_2$) nanocomposites. A polymer-assisted (Pluronic P123 triblock co-polymer) co-precipitation route has been employed to synthesize Al$_2$O$_3$–TiO$_2$nanoparticles. As a surfactant, pluronic P123 polymer exhibits hydrophobic as well as the hydrophilic nature simultaneously which detains the agglomeration and hence the nano size particle have been obtained. Effect of surfactant concentration on morphology and particle size of product has also been investigated. Thermal behaviour of the prepared powder samples have been studied using differential scanning calorimeter/thermal gravimetric analysis and dilatometer. Formation of aluminium-titanate (Al$_2$TiO$_5$) phase has been confirmed using X-ray diffraction analysis. It has been observed by field emission scanning electron microscopy analysis that the particle size reduced effectively (below 100 nm) when polymer-assisted co-precipitation route is used instead of the simple co-precipitation technique. A highly dense microstructure of sintered samples has been obtained, driven by reduced particle size. • Temperature-dependent gas transport and its correlation with kinetic diameter in polymer nanocomposite membrane Activation energies for permeation of polymer nanocomposite membrane have not been reported so far. A tradeoff relation between permeability and selectivity shows that as permeability increases, the selectivity decreases. Attempts have been made to see this trade-off relation at relatively higher temperature. It is found that selectivity decreases drasticallywith increasing temperature.Apolymer–matrix compositewas prepared by adding silica nanoparticles using casting method. Pure gas permeability was measured using a constant volume–variable pressure method at different temperature ranges from 35 to 70$^{\circ}$C. The Van’t Hoff relation was used to estimate the activation energy for permeation. It is found to decrease as compared with virgin polycarbonate and it increases with kinetic diameter. For the first time, the permeability and selectivity for nanocomposite membrane are reported as a function of temperature. Activation energies for different gases have beencalculated for nanocomposite membrane and comparedwith that of virgin polymer membrane. Decrease in activation energies for permeation ($E_p$) with increasing kinetic diameter has been observed for both the membranes. Selectivity reduces with temperature for both the membranes.Mechanical and thermal properties of nanocomposite membrane have been investigatedusing a dynamic mechanical analyser and differential scanning calorimetry, respectively. Scanning electron microscopy has been used to study surface morphology. The results show modification in physical properties due to incorporation of silica nanoparticles. • Ultrasonic and structural features of some borosilicate glasses modified with heavy metals A quaternary glass system Na$_{1.4}$B$_{2.8}$Si$_x$Pb$_{0.3−x}$O$_{5.2+x}$, with$0 \lt x \lt 0.3$, was prepared and studied by Fourier transform infrared spectroscopy, density and ultrasonic techniques to debate the issue of the role of SiO2 in the structureof lead alkali borate glasses. The results indicate that SiO2 generates an abundance of bridging oxygen atoms, [BO$_4$] and [SiO$_4$] structural units and changes the bonds B–O–B and Pb–O–B to Si–O–Si and B–O–Si. The latter bonds have higher bond strength and higher average force constant than the former bonds. Therefore, the glass structure becomes contractedand compacted, which decreases its molar volume and increases its rigidity. This concept was asserted from the increase in the ultrasonic velocity, Debye temperature and elastic moduli with the increase of SiO2 content. The present compositional dependence of the elastic moduli was interpreted in terms of the electron–phonon anharmonic interactions and the polarizationof Si$^{4+}$cation. A good correlation was observed between the experimentally determined elastic moduli and those computed according to the Makishima–Mackenzie model. • Evaluation of the elastic properties of monovalent oxides using TeO$_2$-based glasses Quaternary tellurite glasses with composition 75TeO$_2$–5WO$_3$–15Nb$_2$O$_5$–5M$_x$O$_y$in mol%, where M$_x$O$_y$=(Na$_2$O, Ag$_2$O, ZnO, MgO, CuO, NiO, TiO$_2$, MnO$_2$), were prepared by the normal melt-quenching method. The ultrasonic velocities (longitudinal and shear) were measured in these glasses using the pulse-echo technique at room temperature. Their elastic moduli, microhardness and Debye temperature were calculated and discussed in terms of the modifier’s ionicity and quantitatively in terms of number of bonds per unit volume and the cross-link density. In this study, the values of ultrasonic velocities, elastic moduli, Debye temperature and microhardness were found to be strongly dependent on three factors, namely: (i) modifier’s ionicity; (ii) trigonal pyramid (TeO$_3$)/trigonal bipyramid (TeO$_4$) ratio; and (iii) glass transition temperature$T_g$. We used the Makishima and Mackenzie’s model to calculate the theoretical elastic moduli and to indicatethat the experimental values were in good agreement with the theoretical values. • Cation substitution induced blue-shift of optical band gap in nanocrystalline Zn$_{(1−x)}$Ca$_x$O thin films deposited by sol–gel dip coating technique Transparent nanocrystalline Zn${(1−x)}$Ca$_{x}O ($0 ≤ x ≤ 0.20$) thin films were deposited on glass substrates by sol–gel dip coating method. The X-ray diffraction (XRD) pattern revealed the polycrystalline nature of the films withhexagonal wurtzite structure and confirmed the non-existence of the secondary phase corresponding to CaO indicating the monophasic nature of the deposited films. The crystallinity of the films deteriorated with higher dopant concentration due to the segregation or separation of dopant ions in grain boundaries. The lattice parameters and the unit cell volume increased to a higher Ca-dopant concentration. This was due to the successful incorporation of Ca2+ ions with larger ionic radius inthe host zinc oxide (ZnO) lattice. The optical transmittance spectra of the samples showed transmittances above 60% in thevisible spectral range and the absorption edge in the near ultra-violet region got blue-shifted with cation substitution. Theestimated optical energy gaps confirmed the band gap widening with increase in Ca-dopant concentration. The calculatedvalues increased from 3.30 eV for undoped ZnO to 3.73 eV for Zn0.8Ca0.2O thin films giving 13.03% enhancement in theenergy gap value due to the electronic perturbation caused by cation substitution as well as deterioration in crystallinity.

• Study of $\beta$-phase development in spin-coated PVDF thick films

A study was conducted to ascertain the effect of variation in spin speed and baking temperature on $\beta$-phase content in the spin-coated poly(vinylidene fluoride) (PVDF) thick films ($\sim$4−25 $\mu$m). Development of $\beta$-phase is dependent on film stretching and crystallization temperature. Therefore, to study the development of $\beta$-phase in films, stretching is achieved by spinning and crystallization temperature is adjusted by means of baking. PVDF films are characterized using Fourier transform infrared spectroscopy, X-ray diffraction, differential scanning calorimetry, and scanning electronmicroscopy. It is observed that crystallization temperature lower than 60$^{\circ}$C and increase in spin speed increases the $\beta$-phasecontent in PVDF films. Crystallization temperature above 60$^{\circ}$C reduces $\beta$-phase content and increases α-phase content. It was also observed that viscosity of the PVDF solution affects the β-phase development in films at a particular spin speed.

• Effects of electrolyte concentration and current density on the properties of electro-deposited NiFeW alloy coatings

NiWP alloy coatings were prepared by electrodeposition, and the effects of ferrous chloride (FeCl$_2$), sodium tungstate (Na$_2$WO$_4$) and current density ($D_K$) on the properties of the coatings were studied. The results show that upon increasing the concentration of FeCl$_2$, initially the Fe content of the coating increased and then tended to be stable; the deposition rate and microhardness of coating decreased when the cathodic current efficiency ($\eta$) initially increased and then decreased; and for a FeCl$_2$ concentration of 3.6 gl$^{−1}, the cathodic current efficiency reached its maximum of 74.23%. Upon increasing the concentration of Na$_2$WO$_4$, the W content and microhardness of the coatings increased; the deposition rate andthe cathode current efficiency initially increased and then decreased. The cathodic current efficiency reached the maximum value of 70.33% with a Na$_2$WO$_4$concentration of 50 gl$^{−1}$, whereas the deposition rate is maximum at 8.67$\mu$mh$^{−1}$with a Na$_2$WO$_4$concentration of 40 gl$^{−1}$. Upon increasing the$D_K$, the deposition rate, microhardness, Fe and W content of the coatings increased, the cathodic current efficiency increases first increased and then decreased. When$D_K$was 4 A dm$^{−2}$,the current efficiency reached the maximum of 73.64%. • Dependency of annealing behaviour on grain size in Al–TiC composite produced by accumulative roll bonding This work investigates the effect of grain size on annealing behaviour in both coarse-grained and ultrafinegrained Al–TiC composite processed by accumulative roll bonding (ARB). Microstructural analysis indicates that annealingbehaviour of the specimens are essentially determined by the level of strain accumulation or number of ARB cycles, i.e., recrystallization phenomenon are accelerated by increasing the level of strain accumulation or number of ARB cycles. Microstructure analysis illustrates that annealing treatment at 200 or 250$^{\circ}$C for the 1-cycle ARB-processed Al–TiC compositehaving coarse grains does not lead to the recrystallization phenomenon, indicating that only recovery appears. In contrast, partial recrystallization occurred after annealing at 250$^{\circ}$C in the 7-cycle ARB-processed Al–TiC composite having ultrafine grains. Furthermore, annealing treatment significantly enhanced elongation for both ultrafine as well as coarse-grained Al–TiC composites in spite of the fact that yield and ultimate strength decreased during annealing treatment. The results proved that yield strength and tensile strengths for both 1-cycle and 7-cycle ARB-processed Al–TiC composites gradually decreased by annealing treatments between 200 and 300$^{\circ}$C. In contrast, ultimate elongation drastically improved by about 100% after annealing at the aforementioned conditions. • Synthesis of fluorescent diblock copolymer nanoparticle supported catalyst for the reduction of Cr(VI), p-nitrophenol and rhodamine 6G dye: a comparative study A fluorescent diblock copolymer nanocomposite (DBCNC) was synthesized by ring opening polymerization (ROP) method using rhodamine 6G (R6G) dye as an initiator through bulk polymerization technique. ROP of caprolactonewas carried out at 160$^{\circ}$C for 2 h under nitrogen atmosphere in the presence of stannous octoate (Sn(Oct)$_2$) as a catalyst followed by the ROP of tetrahydrofuran in the presence of phthalicanhydride as a co-monomer. Thus, synthesized fluorescent DBCNC was characterized by various analytical tools such as FTIR spectroscopy, UV–visible spectroscopy fluorescenceemission spectroscopy, DSC, TGA and FESEM. The catalytic reduction of p-nitrophenol (NiP), Cr(VI) and R6G was carried out in the presence of DBCNC as a catalyst with the help of UV–visible spectrophotometer. The apparent rate constant ($k_{app}$) and induction time ($T_i$) were determined from the UV–visible spectral data. The nanosized V$_2$O$_5$was prepared by a simplechemical reduction of bulk-sized V$_2$O$_5$by using sodium borohydride (NaBH$_4$) as a reducing agent. During the DBC formation, 0.01 g of nanosized V$_2$O$_5$was added. This type of polymer supports the catalyst which is very much useful in the catalysis industry because of its easy separation and recyclable property. • Carrier concentration effect and other structure-related parameters on lattice thermal conductivity of Si nanowires Lattice thermal conductivity (LTC) of Si bulk and nanowires (NWs) with diameter 22, 37, 50, 56, 98 and 115 nm was investigated in the temperature range 3–300 K using a modified Callaway model that contains both longitudinal and transverse modes. Using proper equations, mean bond length, lattice parameter, unit cell volume, mass density, melting temperature, longitudinal and transverse Debye temperature and group velocity for all transverse and longitudinal modes were calculated for each NW diameter mentioned. Surface roughness, Gruneisen parameter and impurity were used as adjustable parameters to fit theoretical results with experimental curves. In addition, values of electron concentration and dislocation density were determined. There are some phonon scattering mechanisms assumed, which are Umklapp and normal processes, imperfections, phonon confinement, NW boundaries, electrons scattering and dislocation. Dislocationdensity less than 10$^{14}$m$^{−2}$for NWs and 10$^{12}$m$^{−2}$for bulk has no effect on LTC. Also, electron concentration less than 10$^{22}$m$^{−3}$for NWs and 10$^{16}$m$^{−3}$for the bulk has no effect. On increasing dislocation density and electron concentration, LTC comparably decreases. • Preparation, characterization and mechanical properties of k-Carrageenan/SiO$_2$nanocomposite films for antimicrobial food packaging Kappa-Carrageenan (KCG) films have been formulated as a packaging material. This study has been conducted to investigate the effect of incorporating SiO$_2$nanoparticles inside the KCG matrix, with the aim of enhancing the mechanical and antimicrobial properties of KCG for reinforcement purposes. Films were prepared by solution casting technique with 1.0, 3.0 and 5.0 wt% of SiO$_2$nano-filler content taking neat KCG as the reference for the study. Structural characterizations of the prepared nanocomposite films were carried out by Fourier transform infrared, scanning electron microscope (SEM) andtransmission electron microscope (TEM) techniques. SEM and TEM showed homogeneous dispersion of SiO$_2$nanoparticles in the KCG matrix. The tensile strength increased significantly by introducing the SiO$_2$nanoparticles into the KCG matrix, in which KCG/SiO$_2$films have greater tensile strength (53.9 MPa) when compared to the KCG polymer (46.8 MPa). The moisture uptake (MU) of nanocomposites decreased when SiO2 was introduced into the polymer matrix. The barrier property of the prepared KCG-based nanocomposite films decreased oxygen transmission rate with loading of different wt%of SiO$_2$. SiO$_2$nanoparticle-loaded films produced higher zones of inhibition against Staphylococcus aureus and Escherichia coli strains compared to polymer film. This study was intended to find the applications for KCG films containing SiO$_2\$ nanoparticles to enhance the shelf-life of foods in the form of biodegradable wrapper.

• # Bulletin of Materials Science

Current Issue
Volume 40 | Issue 6
October 2017