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1. v, œK̗_, YƐ}, 1980N11.
2. cv, K.W. Hipel, N.M. Fraser, v, RtNg̐, 㐔w, 1988N10.
3. ؏rG, v, FORTRAN77 œKvO~O, gX, 1991N4.
4. ؏rG, v, œK̎@, o, 1993N7. [: ŗD@, ]q (), }oŌi, k, 1997]
5. v, v, qX, 1996N9.
6. Rh, v, vɂvZ, qX, 2001N1.
7. v, œK̊b, qX, 2001N 4. [: ŗDb, ыM (), ȊwoŎ, k, 2011].
8. RMY, v, v@, Ri, 2008N5.
9. v, VŁEv, qX, 2011N2.

#### E@iSMj

1. v, nq, V́uv@v, crv, cgY (), 㐔w, 1995N3.
2. v, U\ƃASY VI, T uύtv (lodb)v, d (), ߑȊw, 1999N7.
3. v, Hŵ, P, V߁uœK͖̃L[[hv, swHwwȐHwR[X (), 㐔w, 2000N2iŁF2005N1j.
4. v, fO\L߂ā\, V́uύt̐fv, cY, r֎q, y (), ߑȊw, 2015N3.

#### E@ҏ

1. M. Fukushima and L. Qi, eds., Reformulation -- Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods, Kluwer Academic Publishers, Boston, 1998.
2. M. Fukushima and T. Tsuchiya, eds., Festschrift in honor of Professor Masao Iri's 65th birthday, Optimization Methods and Software, Vol. 10, No.2, December 1998.
3. T. Ibaraki, M. Fukushima, A. Tamura and Y. Yamamoto, eds., Special Issue on New Trends in Mathematical Programming, Journal of the Operations Research Society of Japan, Vol. 43, No. 1, March 2000.
4. M. Fukushima and L. Qi, eds., Special Issue on Nonsmooth and Smoothing Methods, Computational Optimization and Applications, Vol. 17, Nos. 2/3, December 2000.
5. M. Fukushima and Y.X. Yuan, eds., Special Issue on the Second Japanese-Sino Optimization Meeting, September 25--27, 2002, Kyoto Japan, Optimization Methods and Software, Vol. 18, Nos. 2/3, April/August 2003.
6. M. Fukushima and L. Qi, eds., Special Issue on the 6th International Conference on Optimization: Techniques and Applications, Computational Optimization and Applications, Vol. 35, No. 1, September 2006.
7. M. Fukushima and S.Y. Wang, eds., Special Issue on Optimization and Control Applications, Optimization and Engineering, Vol. 8, No. 3, September 2007.
8. M. Fukushima, M. Gaudioso, F. Giannessi and D. Pallaschke, Special Issue dedicated to Professor Vladimir F. Demyanov on the occasion of his 70 th birthday, Optimization Methods and Software, Vol. 25, No. 1, February 2010.
9. X. Chen and M. Fukushima, eds., Special Issue dedicated Professor Liqun Qi on the occasion of his 65th birthday, Computational Optimization and Applications, Vol. 50, No. 2, October 2011.
10. cl, p, L, cK, im, v (), HwT, qX, 2011.

#### E@TEnhubNiSMj

1. dqʐMnhubN, dqʐMw, I[, 1988N3 (SM).
2. gȊwT, gX, 1990N5 (SM).
3. ASYT, o, 1994N9 (SM).
4. Vŏ񏈗nhubN, 񏈗w, I[, 1995N11 (SM).
5. \tgRs[eBOpW, qX, 1996N5 (SM).
6. OR T 2000, {Iy[VYET[w, ȋZAoŎ, 2000N5 (SM).
7. œK݌vnhubN, qX, 2003N2 (SM).
8. gwT4, gX, 2007N3 (SM).
9. ȊwT2, ۑP, 2009N12iSMj.
10. qEwnhubNEpҁCqXC2011N8 (SM).

#### E@_ (ǕtGE}Ȃ)

1. H. Mine, K. Ohno and M. Fukushima, Multilevel decomposition of nonlinear programming problems by dynamic programming, Journal of Mathematical Analysis and Applications 53 (1976), pp. 7-27.
2. H. Mine, K. Ohno and M. Fukushima, Decomposition of nonlinear chance-constrained programming problems by dynamic programming, Journal of Mathematical Analysis and Applications 56 (1976), pp. 211-222.
3. H. Mine, K. Ohno and M. Fukushima, A "conjugate" interior penalty method for certain convex programs, SIAM Journal on Control and Optimization 15 (1977), pp. 747-755.
4. H. Mine and M. Fukushima, Penalty function theory for general convex programming problems, Journal of Optimization Theory and Applications 24 (1978), pp. 287-301.
5. H. Mine and M. Fukushima, Application of Fenchel's duality theorem to penalty methods in convex programming, Memoirs of the Faculty of Engineering, Kyoto University 40 (1978), pp. 30-39.
6. H. Mine, M. Fukushima and Y. Fujii, A dual approach to the generalized multifacility location problems with arbitrary norms, Proceedings of the International Conference on Cybernetics and Society , Tokyo , November 1978, pp. 678-683.
7. H. Mine, M. Fukushima and Y.J. Ryang, Parametric nonlinear programming for general cases and its application to some problems, Memoirs of the Faculty of Engineering, Kyoto University 40 (1978), pp. 198-211
8. H. Mine, M. Fukushima and N. Navarrete, Jr., A new method of ranking: The relative position ranking, Memoirs of the Faculty of Engineering, Kyoto University 41 (1979), pp. 109-115.
9. H. Mine and M. Fukushima, Decomposition of multiple criteria mathematical programming problems by dynamic programming, International Journal of Systems Science 10 (1979), pp. 557-566.
10. N. Navarrete, Jr., M. Fukushima and H. Mine, A new ranking method based on relative position estimate and its extensions, IEEE Transactions on Systems, Man and Cybernetics SMC-9 (1979), pp. 681-689.
11. H. Mine, M. Fukushima and Y.J. Ryang, On solving a certain multi-parametric nonlinear programming problems, Memoirs of the Faculty of Engineering, Kyoto University (1980), pp. 404-412.
12. N. Navarrete, Jr., M. Fukushima and H. Mine, A qualitative multicriteria ranking method for project selection, Proceedings of the International Conference on Industrial System Engineering and Management in Developing Countries , Bangkok , November 1980, pp. 481-493.
13. H. Mine, M. Fukushima and N. Navarrete, Jr., A fuzzy preference model in decision making, Memoirs of the Faculty of Engineering, Kyoto University 43 (1981), pp. 145-158.
14. H. Mine and M. Fukushima, A minimization method for the sum of a convex function and a continuously differentiable function, Journal of Optimization Theory and Applications 33 (1981), pp. 9-23.
15. H. Mine, M. Fukushima and Y.J. Ryang, Methods of parametric non-linear programming, International Journal of Systems Science 12 (1981), pp. 95-110.
16. M. Fukushima and H. Mine, A generalized proximal point algorithm for certain nonconvex minimization problems, International Journal of Systems Science 12 (1981), pp. 989-1000.
17. M. Fukushima, A finitely convergent algorithm for convex inequalities, IEEE Transactions on Automatic Control AC-27 (1982), pp. 1126-1127.
18. M. Fukushima, Y. Morinaga and H. Mine, A heuristic decomposition approach to optimal control in a water supply model, European Journal of Operational Research 11 (1982), pp. 338-348.
19. M. Fukushima, An outer approximation algorithm for solving general convex programs, Operations Research 31 (1983), pp. 101-113.
20. H. Mine, M. Fukushima, K. Ishikawa and I. Sawa, An algorithm for the assignment problem with stochastic side constraints, Memoirs of the Faculty of Engineering, Kyoto University 45 (1983), pp. 26-35.
21. M. Fukushima, A fixed point approach to certain convex programs with applications in stochastic programming, Mathematics of Operations Research 8 (1983), pp. 517-524.
22. M. Fukushima, On the convergence of a class of outer approximation algorithms for convex programs, Journal of Computational and Applied Mathematics 10 (1984), pp. 147-156.
23. N. Sagara and M. Fukushima, A continuation method for solving separable nonlinear least squares problems, Journal of Computational and Applied Mathematics 10 (1984), pp. 157-161.
24. M. Fukushima, A modified Frank-Wolfe algorithm for solving the traffic assignment problem, Transportation Research 18B (1984), pp. 169-177.
25. M. Fukushima, On the dual approach to the traffic assignment problem, Transportation Research 18B (1984), pp. 235-245.
26. M. Fukushima, A nonsmooth optimization approach to nonlinear multicommodity network flow problems, Journal of the Operations Research Society of Japan 27 (1984), pp. 151-176.
27. M. Fukushima, A descent algorithm for nonsmooth convex optimization, Mathematical Programming 30 (1984), pp. 163-175.
28. H. Mine, M. Fukushima and Y. Tanaka, On the use of $\epsilon$-most-active constraints in an exact penalty function method for nonlinear optimization, IEEE Transactions on Automatic Control AC-29 (1984), pp. 1040-1042.
29. M. Fukushima, On the generalized variational inequalities, Proceedings of the International Seminar on Operations Research and Systems , Kyoto, November 1985, pp. 35-50.
30. M. Fukushima, E. Yamakawa and H. Mine, On dual differentiable exact penalty functions for equality constrained optimization, Journal of the Operations Research Society of Japan 28 (1985), pp. 302-316.
31. M. Fukushima, A relaxed projection method for variational inequalities, Mathematical Programming 35 (1986), pp. 58-70.
32. M. Fukushima and Y. Yamamoto, A second-order algorithm for continuous-time nonlinear optimal control problems, IEEE Transactions on Automatic Control AC-31 (1986), pp. 673-676.
33. M. Fukushima, A successive quadratic programming algorithm with global and superlinear convergence properties, Mathematical Programming 35 (1986), pp. 253-264.
34. N. Sagara and M. Fukushima, A new predictor-corrector method for solving unconstrained minimization problems, Journal of Computational and Applied Mathematics 16 (1986), pp. 343-354.
35. S. Hashizume, M. Fukushima, N. Katoh and T. Ibaraki, Approximation algorithms for combinatorial fractional programming problems, Mathematical Programming 37 (1987), pp. 255-267.
36. Y. Tanaka, M. Fukushima and T. Hasegawa, An implementable $L_\infty$ penalty function method for semi-infinite optimization, International Journal of Systems Science 18 (1987), pp. 1563-1568.
37. M. Fukushima and T. Itoh, A dual approach to asymmetric traffic equilibrium problems, Mathematica Japonica 32 (1987), pp. 701-721.
38. N. Sagara and M. Fukushima, An efficient predictor-corrector method for solving nonlinear equations, Journal of Computational and Applied Mathematics 19 (1987), pp. 343-349.
39. v, V䒼q, ؏rG, ŏpɑ΂_@, VXeƐ, 31 (1987), pp. 837-843.
40. T. Itoh, M. Fukushima and T. Ibaraki, An iterative method for variational inequalities with application to traffic equilibrium problems, Journal of the Operations Research Society of Japan 31 (1988), pp. 82-103.
41. Y. Tanaka, M. Fukushima and T. Ibaraki, A comparative study of several semi-infinite nonlinear programming algorithms, European Journal of Operational Research 36 (1988), pp. 92-100.
42. Y. Tanaka, M. Fukushima and T. Ibaraki, A globally convergent SQP method for semi-infinite nonlinear optimization, Journal of Computational and Applied Mathematics 23 (1988), pp. 141-153.
43. M. Fukushima, Solving inequality constrained optimization problems by differential homotopy continuation methods, Journal of Mathematical Analysis and Applications 133 (1988), pp. 109-121.
44. v, ji, ؏rG, ŏ؍XVASYɂ, dqʐMw_, J71-A (1988), pp. 1979-1982.
45. R. Katsura, M. Fukushima and T. Ibaraki, Interior methods for nonlinear minimum cost network flow problems, Journal of the Operations Research Society of Japan 32 (1989), pp. 174-199.
46. E. Yamakawa, M. Fukushima and T. Ibaraki, An efficient trust region algorithm for minimizing nondifferentiable composite functions, SIAM Journal on Scientific and Statistical Computing 10 (1989), pp. 562-580.
47. Y. Tanaka, M. Fukushima and T. Ibaraki, On generalized pseudoconvex functions, Journal of Mathematical Analysis and Applications 144 (1989), pp. 342-355.
48. H. Nagamochi, M. Fukushima and T. Ibaraki, Relaxation methods for the strictly convex multicommodity flow problem with capacity constraints on individual commodities, Networks 20 (1990), pp. 409-426.
49. M. Fukushima, A conjugate gradient algorithm for sparse linear inequalities, Journal of Computational and Applied Mathematics 30 (1990), pp. 329-339.
50. M. Fukushima, A successive quadratic programming method for a class of constrained nonsmooth optimization problems, Mathematical Programming 49 (1991), pp. 231-251.
51. N. Sagara and M. Fukushima, A hybrid method for nonlinear least squares problem with simple bounds, Journal of Computational and Applied Mathematics 36 (1991), pp. 149-157.
52. ጴBN, v, ؏rG, K͔vɑ΂钀 v敪@, VXew_, 4 (1991), pp. 473-480.
53. S. Ibaraki, M. Fukushima and T. Ibaraki, Dual-based Newton methods for nonlinear minimum cost network flow problems, Journal of the Operations Research Society of Japan 34 (1991), pp. 263-286.
54. M. Fukushima, Equivalent differentiable optimization problems and descent methods for asymmetric variational inequality problems, Mathematical Programming 53 (1992), pp. 99-110.
55. M. Fukushima, K. Takazawa, S. Ohsaki and T. Ibaraki, Successive linearization methods for large-scale nonlinear programming problems, Japan Journal of Industrial and Applied Mathematics 9 (1992), pp. 117-132.
56. ҖV, v, ؏rG, Iʗz̃lbg[NEf, VXew_, 5 (1992), pp. 257-264.
57. M. Fukushima, Application of the alternating direction method of multipliers to separable convex programming problems, Computational Optimization and Applications 1 (1992), pp. 93-111.
58. S. Ibaraki , M. Fukushima and T. Ibaraki, Primal-dual proximal point algorithm for linearly constrained convex programming problems, Computational Optimization and Applications 1 (1992), pp. 207-226.
59. K. Taji, M. Fukushima and T. Ibaraki, A globally convergent Newton method for solving strongly monotone variational inequalities, Mathematical Programming 58 (1993), pp. 369-383.
60. T. Wakahara, M. Fukushima and T. Ibaraki, A practical approach to decomposable nonlinear programming problems, Journal of the Operations Research Society of Japan 36 (1993), pp. 1-12.
61. Y. Shimazu, M. Fukushima and T. Ibaraki, A successive over-relaxation method for quadratic programming problems with interval constraints, Journal of the Operations Research Society of Japan 36 (1993), pp. 73-89.
62. J. Eckstein and M. Fukushima, Some reformulations and applications of the alternating direction method of multipliers, Large Scale Optimization: State of the Art, W.W. Hager, D.W. Hearn and P.M. Pardalos (eds.), Kluwer Academic Publishers B.V., 1994, pp. 115-134.
63. M. Tsujino, M. Fukushima and T. Ibaraki, A model of time-varying flow on a congested multidestination network, Asia-Pacific Journal of Operational Research 11 (1994), pp. 141-153.
64. S. Ibaraki and M. Fukushima, Primal-dual proximal point algorithm for multicommodity network flow problems, Journal of the Operations Research Society of Japan 37 (1994), pp. 297-309.
65. K. Taji and M. Fukushima, Optimization based globally convergent method for the nonlinear complementarity problems, Journal of the Operations Research Society of Japan 37 (1994), pp. 310-331.
66. K. Iwaoka, M. Fukushima and T. Ibaraki, A primal-dual proximal point algorithm for variational inequality problems, Variational Inequalities and Network Equilibrium Problems , F. Giannessi and A. Maugeri (eds.), Plenum Press, 1995, pp. 143-153.
67. F[i, v, ˉe@ƂĂ̌덷td@, VXew_ 8 (1995), pp. 204-211.
68. N. Sagara and M. Fukushima, A hybrid method for solving the nonlinear least squares problem with linear inequality constraints, Journal of the Operations Research Society of Japan 38 (1995), pp. 55-69.
69. N. Yamashita and M. Fukushima, On stationary points of the implicit Lagrangian for nonlinear complementarity problems, Journal of Optimization Theory and Applications 84 (1995), pp. 653-663.
70. K. Taji and M. Fukushima, A globally convergent Newton method for solving variational inequality problems with inequality constraints, Recent Advances in Nonsmooth Optimization , D.-Z. Du, L. Qi and R. Womersley (eds.), World Scientific Publishers, pp. 405-417, 1995.
71. T. Sugimoto, M. Fukushima and T. Ibaraki, A parallel relaxation method for quadratic programming problems with interval constraints, Journal of Computational and Applied Mathematics 60 (1995), pp. 219-236.
72. N. Machida , M. Fukushima and T. Ibaraki, A multisplitting method for symmetric linear complementarity problems, Journal of Computational and Applied Mathematics 62 (1995), pp. 217-227.
73. M. Fukushima, M. Haddou, V.H. Nguyen, J.-J. Strodiot, T. Sugimoto and E. Yamakawa , A parallel descent algorithm for convex programming, Computational Optimization and Applications 5 (1996), pp. 5-37.
74. M. Fukushima, The primal Douglas-Rachford splitting algorithm for a class of monotone mappings with application to the traffic equilibrium problem, Mathematical Programming 72 (1996), pp. 1-15.
75. S. Ibaraki and M. Fukushima, Partial proximal method of multipliers for convex programming problems, Journal of the Operations Research Society of Japan 39 (1996), pp. 213-229.
76. P. Tseng, N. Yamashita and M. Fukushima, Equivalence of complementarity problems to differentiable minimization: A unified approach, SIAM Journal on Optimization 6 (1996), pp. 446-460.
77. M. Fukushima, Merit functions for variational inequality and complementarity problems, Nonlinear Optimization and Applications , G. Di Pillo and F. Giannessi (eds.), Plenum Press, 1996, pp. 155-170.
78. E. Yamakawa and M. Fukushima, A block-parallel conjugate gradient method for separable quadratic programming problems, Journal of the Operations Research Society of Japan 39 (1996), pp. 407-427.
79. K. Taji and M. Fukushima, A new merit function and a successive quadratic programming algorithm for variational inequality problems, SIAM Journal on Optimization 6 (1996), pp. 704-713.
80. C. Kanzow and M. Fukushima, Equivalence of the generalized complementarity problem to differentiable unconstrained minimization, Journal of Optimization Theory and Applications 90 (1996), pp. 581-603.
81. M. Fukushima and L. Qi, A globally and superlinearly convergent algorithm for nonsmooth convex minimization, SIAM Journal on Optimization 6 (1996), pp. 1106-1120.
82. Rh, N, v, QRXgi헬ɑ΂^oΓ_@, Journal of the Operations Research Society of Japan 39 (1996), pp. 566-591.
83. K. Tatsumi and M. Fukushima, A successive projection method for binary pattern recognition with multilayer feedforward neural networks, International Journal of Systems Science 27 (1996), pp. 917-923.
84. N. Yamashita and M. Fukushima, Modified Newton methods for solving a semismooth reformulation of monotone complementarity problems, Mathematical Programming (Series B) 76 (1997), pp. 469-491.
85. N. Yamashita and M. Fukushima, Equivalent unconstrained minimization and global error bounds for variational inequality problems, SIAM Journal on Control and Optimization 35 (1997), pp. 273-284.
86. M. Fukushima and J.-S. Pang, Minimizing and stationary sequences of merit functions for complementarity problems and variational inequalities, Complementarity and Variational Problems: State of the Art, M.C. Ferris and J.-S. Pang (eds.), SIAM , Philadelphia , 1997, pp. 91-104.
87. D. Sun, M. Fukushima and L. Qi, A computable generalized Hessian of the D-gap function and Newton-type methods for variational inequality problems, Complementarity and Variational Problems: State of the Art, M.C. Ferris and J.-S. Pang (eds.), SIAM , Philadelphia , 1997, pp. 452-472.
88. N. Yamashita, K. Taji and M. Fukushima, Unconstrained optimization reformulations of variational inequality problems, Journal of Optimization Theory and Applications 92 (1997), pp. 439-456.
89. Rh, qp, v, \2vɑ΂񓯊^ubNASY, VXew_ 10 (1997), pp. 248-258.
90. C. Kanzow, N. Yamashita and M. Fukushima, New NCP-functions and their properties, Journal of Optimization Theory and Applications 94 (1997), pp. 115-135.
91. F[i, v, Kw^j[lbg[Nɑ΂钀ˉe@̉, VXew_ 11 (1998), pp. 77-85.
92. H. Jiang, M. Fukushima, L. Qi and D. Sun, A trust region method for solving generalized complementarity problems, SIAM Journal on Optimization 8 (1998), pp. 140-157.
93. M. Fukushima, Z.-Q. Luo and J.-S. Pang, A globally convergent sequential quadratic programming algorithm for mathematical programs with linear complementarity constraints, Computational Optimization and Applications 10 (1998), pp. 5-34.
94. M. Okada, K. Taji and M. Fukushima, Probabilistic analysis of 2-opt for travelling salesman problems, International Journal of Systems Science 29 (1998), pp. 297-310.
95. 䂭݂, F[i, v, 񎟃RXg 0-1 vɑ΂ߎ@, dqʐMw_ J81-A (1998), pp. 649-657.
96. M. Fukushima, Parallel variable transformation in unconstrained optimization, SIAM Journal on Optimization 8 (1998), pp. 658-672.
97. M. Fukushima and J.-S. Pang, Some feasibility issues in mathematical programs with equilibrium constraints, SIAM Journal on Optimization 8 (1998), pp. 673-681.
98. C. Kanzow and M. Fukushima, Theoretical and numerical investigation of the D-gap function for box constrained variational inequalities, Mathematical Programming 83 (1998), pp. 55-87.
99. N. Yamashita and M. Fukushima, A new merit function and a descent method for semidefinite complementarity problems, Reformulation: Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods, M. Fukushima and L. Qi (eds.), Kluwer Academic Publishers B.V., 1998, pp. 405-420.
100. C. Kanzow and M. Fukushima, Solving box constrained variational inequalities by using the natural residual with D-gap function globalization, Operations Research Letters 23 (1998), pp. 45-51.
101. D. Li and M. Fukushima, A derivative-free line search and DFP method for symmetric equations with global and superlinear convergence, Numerical Functional Analysis and Optimization 20 (1999), pp. 59-77.
102. Rh, v, 2Aɑ΂ݕ搔@̃xNgvZ@ɂs, VXew_ 12 (1999), pp. 313-315.
103. J.-S. Pang and M. Fukushima, Complementarity constraint qualifications and simplified B-stationarity conditions for mathematical programs with equilibrium constraints, Computational Optimization and Applications 13 (1999), pp. 111-136.
104. E. Yamakawa and M. Fukushima, Testing parallel variable transformation, Computational Optimization and Applications 13 (1999), pp. 253-274.
105. J.M. Peng, C. Kanzow and M. Fukushima, A hybrid Josephy-Newton method for solving box constrained variational inequality problems via the D-gap function, Optimization Methods and Software 10 (1999), pp. 687-710.
106. X. Chen and M. Fukushima, Proximal quasi-Newton methods for nondifferentiable convex optimization, Mathematical Programming 85 (1999), pp. 313-334.
107. M. Shibata, N. Yamashita and M. Fukushima, The extended semidefinite linear complementarity problem: A reformulation approach, Nonlinear Analysis and Convex Analysis, W. Takahashi and T. Tanaka (eds.), World Scientific, Singapore , 1999, pp. 326-332.
108. M. Fukushima and J.-S. Pang, Convergence of a smoothing continuation method for mathematical programs with complementarity constraints, Ill-Posed Variational Problems and Regularization Techniques, Lecture Notes in Economics and Mathematical Systems,Vol. 477, M. Thera and R. Tichatschke (eds.), Springer-Verlag, Berlin/Heidelberg, 1999, pp. 99-110.
109. J.M. Peng and M. Fukushima, A hybrid Newton method for solving the variational inequality problem via the D-gap function, Mathematical Programming 86 (1999), pp. 367-386.
110. D. Li and M. Fukushima, A globally and superlinearly convergent Gauss-Newton based BFGS method for symmetric nonlinear equations, SIAM Journal on Numerical Analysis 35 (1999), pp. 152-172.
111. A.I. Rauf and M. Fukushima, A globally convergent BFGS method for nonsmooth convex optimization, Journal of Optimization Theory and Applications. 104 (2000), pp. 539-558.
112. K. Yamada, N. Yamashita and M. Fukushima, A new derivative-free descent method for the nonlinear complementarity problem, Nonlinear Optimization and Related Topics, G. Di Pillo and F. Giannessi, eds., Kluwer Academic Publishers, 2000, pp. 463-487.
113. D. Li and M. Fukushima, A derivative-free line search and global convergence of Broyden-like method for nonlinear equations, Optimization Methods and Software 13 (2000), pp. 181-201.
114. M. Kyono and M. Fukushima, Nonlinear proximal decomposition method for convex programming, Journal of Optimization Theory and Applications 106 (2000), pp. 357-372.
115. D. Li and M. Fukushima, Smoothing Newton and quasi-Newton methods for mixed complementarity problems, Computational Optimization and Applications 17 (2000), pp. 203-230.
116. N. Yamashita, J. Imai and M. Fukushima, The proximal point algorithm for the P_0 complementarity problem, Complementarity: Applications, Algorithms and Extensions, M.C. Ferris, O.L. Mangasarian and J.-S. Pang (eds.), Kluwer Academic Publishers, 2001, pp. 361-379.
117. N. Yamashita and M. Fukushima, The proximal point algorithm with genuine superlinear convergence for the monotone complementarity problem, SIAM Journal on Optimization 11 (2001), pp. 364-379.
118. D. Li and M. Fukushima, A modified BFGS method and its global convergence in nonconvex minimization, Journal of Computational and Applied Mathematics 129 (2001), pp. 15-35.
119. D. Li and M. Fukushima, On the global convergence of BFGS method for nonconvex unconstrained optimization problems, SIAM Journal on Optimization 11 (2001), pp. 1054-1064.
120. D. Li, N. Yamashita and M. Fukushima, Nonsmooth equation based BFGS method for solving KKT systems in mathematical programming, Journal of Optimization Theory and Applications 109 (2001), pp. 123-167.
121. J.P. Zeng, D. Li and M. Fukushima, Weighted max-norm estimate of additive Schwarz iteration scheme for solving linear complementarity problems, Journal of Computational and Applied Mathematics 131 (2001), pp. 1-14.
122. N. Yamashita, C. Kanzow, T. Morimoto and M. Fukushima, An infeasible interior proximal method convex programming problems with linear constraints, Journal of Nonlinear and Convex Analysis 2 (2001), pp. 139-156.
123. N. Yamashita and M. Fukushima, On the rate of convergence of the Levenberg-Marquardt method, Computing [Suppl] 15 (2001), pp. 239-249.
124. M. Fukushima, Z.-Q. Luo and P. Tseng, Smoothing functions for second-order-cone complementarity problems, SIAM Journal on Optimization 12 (2001), pp. 436-460.
125. M. Sasaki and M. Fukushima, Stackelberg hub location problem, Journal of the Operations Research Society of Japan 44 (2001), pp. 390-402.
126. D. Li and M. Fukushima, Globally convergent Broyden-like methods for semismooth equations and applications to VIP, NCP and MCP, Annals of Operations Research 102 (2001), pp. 71-97.
127. M. Fukushima and P. Tseng, An implementable active-set algorithm for computing a B-stationary point of the mathematical program with linear complementarity constraints, SIAM Journal on Optimization 12 (2002), pp. 724-739, [Erratum: ibid. 17 (2007), pp. 1253-1257.].
128. ]{, v, vZXYƂɂ鎞nœK̂߂̒Qv敪@, VXew_ 15 (2002), pp. 34-40.
129. K. Tatsumi, T. Tanino and M. Fukushima, Global convergence property of error back-propagation method for recurrent neural networks, Operations Research/ Management Science at Work, E. Kozan and A. Ohuchi (eds.), Kluwer Academic Publishers, 2002, pp. 227-242.
130. H. Dan, N. Yamashita and M. Fukushima, Convergence properties of the inexact Levenberg-Marquardt method under local error bound conditions, Optimization Methods and Software 17 (2002), pp. 605-626.
131. A.-R. Hedar and M. Fukushima, Hybrid simulated annealing and direct search method for nonlinear global optimization, Optimization Methods and Software 17 (2002), pp. 891-912.
132. H. Dan, N. Yamashita and M. Fukushima, A superlinearly convergent algorithm for the monotone complementarity problem without uniqueness and nondegeneracy conditions, Mathematics of Operations Research 27 (2002), pp. 743-753.
133. A.-R. Hedar and M. Fukushima, Simplex coding genetic algorithm for the global optimization of nonlinear functions, Multi-Objective Programming and Goal Programming, T. Tanino, T. Tanaka and M. Inuiguchi, eds., Springer-Verlag, Berlin-Heidelberg, 2003, pp. 135-140.
134. R.S. Bipasha, K. Yamada, N. Yamashita and M. Fukushima, A linearly convergent descent method for strongly monotone variational inequality problems, Journal of Nonlinear and Convex Analysis 4 (2003), pp. 15-23.
135. G.H. Lin and M. Fukushima, Some exact penalty results for nonlinear programs and their applications to mathematical programs with equilibrium constraints, Journal of Optimization Theory and Applications 118 (2003), pp. 67-80.
136. G.H. Lin and M. Fukushima, New relaxation method for mathematical programs with complementarity constraints, Journal of Optimization Theory and Applications 118 (2003), pp. 81-116.
137. M. Fukushima, Z.-Q. Luo and P. Tseng, A sequential quadratically constrained quadratic programming method for differentiable convex minimization, SIAM Journal on Optimization 13 (2003), pp. 1098-1119.
138. H. Moriyama, N. Yamashita and M. Fukushima, The incremental Gauss-Newton algorithm with adaptive  stepsize rule, Computational Optimization and Applications 26 (2003), pp. 107-141.
139. M. Sasaki and M. Fukushima, On the hub-and-spoke model with arc capacity constraints, Journal of the Operations Research Society of Japan 46 (2003), pp. 409-428.
140. A.-R. Hedar and M. Fukushima, Minimizing multimodal functions by simplex coding genetic algorithm, Optimization Methods and Software 18 (2003), pp. 265-282.
141. X. Chen and M. Fukushima, A smoothing method for a mathematical program with P-matrix linear complementarity constraints, Computational Optimization and Applications 27 (2004), pp. 223-246.
142. N. Yamashita, H. Dan and M. Fukushima, On the identification of degenerate indices in the nonlinear complementarity problem with the proximal point algorithm, Mathematical Programming 99 (2004), pp. 377-397.
143. D.H. Li, M. Fukushima, L. Qi and N. Yamashita, Regularized Newton methods for convex minimization problems with singular solutions, Computational Optimization and Applications 28 (2004), pp. 131-147.
144. FMYC쐣lCxiFCv, ^pł̕vg̍œKێv, VXew_ 17 (2004), pp. 390-400D
145. C. Kanzow, N. Yamashita and M. Fukushima, Levenberg-Marquardt methods for constrained nonlinear equations with strong local convergence properties, Journal of Computational and Applied Mathematics 172 (2004), pp. 375-397.
146. A.-R. Hedar and M. Fukushima, Heuristic pattern search and its hybridization with simulated annealing for nonlinear global optimization, Optimization Methods and Software 19 (2004), pp. 291-308.
147. G.H. Lin and M. Fukushima, A modified relaxation scheme for mathematical programs with complementarity constraints, Annals of Operations Research 133 (2005), pp. 63-84.
148. J.-S. Pang and M. Fukushima, Quasi-variational inequalities, generalized Nash equilibria, and multi-leader-follower games, Computational Management Science 2 (2005), pp. 21-56 [Erratum: ibid. 6 (2009), pp. 373-375.].
149. S. Hayashi, T. Yamaguchi, N. Yamashita and M. Fukushima, A matrix splitting method for symmetric affine second-order cone complementarity problems, Journal of Computational and Applied Mathematics 175 (2005), pp. 335-353.
150. G.H. Lin and M. Fukushima, A class of stochastic mathematical programs with complementarity constraints: Reformulations and algorithms, Journal of Industrial and Management Optimization 1 (2005), pp. 99-122.
151. N. Sagara and M. Fukushima, A trust region method for nonsmooth convex optimization, Journal of Industrial and Management Optimization 1 (2005), pp. 171-180.
152. C. Ling, X. Chen, M. Fukushima and L. Qi, A smoothing implicit programming approach for solving a class of stochastic generalized semi-infinite programming problems, Pacific Journal of Optimization 1 (2005), pp. 127-145.
153. G.H. Lin and M. Fukushima, Regularization method for stochastic mathematical programs with complementarity constraints, European Series of Applied and Industrial Mathematics (ESAIM):  Control, Optimization and the Calculus of Variations (COCV). 11 (2005), pp. 252-265.
154. S. Hayashi, N. Yamashita and M. Fukushima, A combined smoothing and regularization method for monotone second-order cone complementarity problems, SIAM Journal on Optimization 15 (2005), pp. 593-615.
155. C. Kanzow, C. Nagel, H. Kato and M. Fukushima, Successive linearization methods for nonlinear semidefinite programs, Computational Optimization and Applications 31 (2005), pp. 251-273.
156. FMYCaMCꍪNƁCv, {݉^pɂƃZLeB̍œK, VXew_ 18 (2005), pp. 146-155D
157. S. Hayashi, N. Yamashita and M. Fukushima, Robust Nash equilibria and second-order cone complementarity problems, Journal of Nonlinear and Convex Analysis 6 (2005), pp. 283-296.
158. N. Yamashita and M. Fukushima, On the level-boundedness of the natural residual function for variational inequality problems, Pacific Journal of Optimization 1 (2005), pp. 625-630.
159. X. Chen and M. Fukushima, Expected residual minimization method for stochastic linear complementarity problems, Mathematics of Operations Research 30 (2005), pp. 1022-1038.
160. P.Y. Nie, L.H. Chen and M. Fukushima, Dynamic programming approach to discrete time dynamic feedback Stackelberg games with independent and dependent followers, European Journal of Operational Research 169 (2006), pp. 310-328.
161. P. Zhong and M. Fukushima, A new multi-class support vector algorithm, Optimization Methods and Software 21 (2006), pp. 359-372.
162. BYCbǗCvCLbVU[up[Q[WSۏ،D\̍œK݌v, {Iy[VYT[wa_ 49 (2006), pp. 62-88D
163. G.H. Lin and M. Fukushima, Hybrid approach with active set identification for mathematical programs with complementarity constraints, Journal of Optimization Theory and Applications 128 (2006), pp. 1-28.
164. G.H. Lin and M. Fukushima, New reformulations for stochastic nonlinear complementarity problems, Optimization Methods and Software 21 (2006), pp. 551-564.
165. M. Fukushima, How to deal with uncertainty Some recent attempts, International Journal of Information Technology & Decision Making 5 (2006), pp. 623-637.
166. A.-R. Hedar and M. Fukushima, Derivative-free filter simulated annealing method for constrained continuous global optimization, Journal of Global Optimization 35 (2006), 521-549.
167. A.-R. Hedar and M. Fukushima, Tabu Search directed by direct search methods for nonlinear global optimization, European Journal of Operational Research 170 (2006), pp. 329-349.
168. X.W. Liu and M. Fukushima, Parallelizable preprocessing method for multistage stochastic programming problems, Journal of Optimization Theory and Applications 131 (2006), 327-346.
169. P. Zhong and M. Fukushima, Regularized nonsmooth Newton method for multi-class support vector machines, Optimization Methods and Software  22 (2007), pp. 225-236.
170. P. Zhong and M. Fukushima, Second order cone programming formulations for robust multi-class classification, Neural Computation 19 (2007), pp. 258-282.
171. H. Kato and M. Fukushima, An SQP-type algorithm for nonlinear second-order cone programs, Optimization Letters 1 (2007), pp. 129-144.
172. ]{, v, dvgɂ^[rהz̑IœK, VXew_ 20 (2007), pp. 76-83.
173. M. Fukushima, A class of gap functions for quasi-variational inequality problems, Journal of Industrial and Management Optimization 3 (2007), pp. 165-171.
174. M.-A.Majig, A.-R. Hedar and M. Fukushima, Hybrid evolutionary algorithm for solving general variational inequality problems, Journal of Global Optimization 38 (2007), pp. 637-651.
175. H. Fang, X. Chen and M. Fukushima, Stochastic $R_0$ matrix linear complementarity problems, SIAM Journal on Optimization 18 (2007), pp. 482-506.
176. Z. Wang and M. Fukushima, A finite algorithm for almost linear complementarity problems, Numerical Functional Analysis and Optimization 28 (2007), pp. 1387-1403.
177. D.S. Huang, Y. Kai, F.J. Fabozzi and M. Fukushima, An optimal design of collateralized mortgage obligation with PAC-companion structure using dynamic cash reserve, European Journal of Operational Research 177 (2007), pp. 1134-1152.
178. D.S. Huang, F.J. Fabozzi and M. Fukushima, Robust portfolio selection with uncertain exit time using worst-case VaR strategy, Operations Research Letters 35 (2007), pp. 627-635.
179. G.H. Lin, X. Chen and M. Fukushima, New restricted NCP functions and their applications to stochastic NCP and stochastic MPEC, Optimization 56 (2007), pp. 641-653.
180. R.P. Agdeppa, N. Yamashita and M. Fukushima, The traffic equilibrium problem with nonadditive costs and its monotone mixed complementarity problem formulation, Transportation Research B 41 (2007), pp. 862-874.
181. D.S. Huang, S.S. Zhu, F.J. Fabozzi and M. Fukushima, Portfolio selection with uncertain exit time: A robust CVaR approach, Journal of Economic Dynamics and Control 32 (2008), pp. 594-623.
182. M. Nishihara and M. Fukushima, Evaluation of firm's loss due to incomplete information in real investment decision, European Journal of Operational Research 188 (2008), pp. 569-585.
183. R.P. Agdeppa, N. Yamashita and M. Fukushima, An implicit programming approach for the road pricing problem with nonadditive route costs, Journal of Industrial and Management Optimization 4 (2008), pp. 183-197.
184. A.-R. Hedar, J. Wang and M. Fukushima, Tabu search for attribute reduction in rough set theory, Soft Computing 12 (2008), pp. 909-918.
185. Y. Fang, L.H. Chen and M. Fukushima, A mixed R&D projects and securities portfolio selection model, European Journal of Operational Research 185 (2008), pp. 700-715.
186. cmCvCv@ɂR[WFl[VVXe̍œK݌vCVXew_ 21 (2008), pp. 201-210.
187. cmCvCZԂł̕וϓlƒpRdrVXẻ^pœKCdCw_ B 128 (2008), pp. 1497-1504D
188. G.H. Lin, H. Xu and M. Fukushima, Monte Carlo and quasi-Monte Carlo sampling methods for a class of stochastic mathematical programs with equilibrium constraints, Mathematical Methods of Operations Research 67 (2008), pp. 423-441.
189. G.H. Lin, X. Chen and M. Fukushima, Solving stochastic mathematical programs with equilibrium constraints via approximation and smoothing implicit programming with penalization, Mathematical Programming 116 (2009), pp. 343-368.
190. X. Chen, C. Zhang and M. Fukushima, Robust solution of monotone stochastic linear complementarity problems, Mathematical Programming. 117 (2009), pp. 51-80.
191. C. Kanzow, I. Ferenczi and M. Fukushima, On the local convergence of semismooth Newton methods for linear and nonlinear second-order cone programs without strict complementarity, SIAM Journal on Optimization 20 (2009), pp. 297-320.
192. R. Nishimura, S. Hayashi and M. Fukushima, Robust Nash equilibria in N-person non-cooperative games: Uniqueness and reformulation, Pacific Journal of Optimization 5 (2009), pp. 237-259.
193. cmCvCmv@ɂR[WFl[VVXẻ^pœKCdCw_ B 129 (2009), pp. 765-775.
194. M.-A. Majig, B. Barsbold, R. Enkhbat and M. Fukushima, A global optimization approach for solving non-monotone variational inequality problems, Optimization 58 (2009), pp. 871-881.
195. D.S. Huang, B.M. Yu, F.J. Fabozzi and M. Fukushima, CAViaR-based forecast for oil price risk, Energy Economics 31 (2009), pp. 511-518.
196. S.S. Zhu and M. Fukushima, Worst-case conditional Value-at-Risk with application to robust portfolio management, Operations Research 57 (2009), pp. 1155-1168.
197. D. Huang, S.S. Zhu, F.J. Fabozzi and M. Fukushima, Portfolio selection under distributional uncertainty: A relative robust CVaR approach, European Journal of Operational Research 203 (2010), pp.185-194.
198. R.P. Agdeppa, N. Yamashita and M. Fukushima, Convex expected residual models for stochastic affine variational inequality problems and its application to the traffic equilibrium problem, Pacific Journal of Optimization 6 (2010), pp. 3-19.
199. M.-A. Majig, A.-R. Hedar and M. Fukushima, A hybrid evolutionary algorithm for global optimization,, Optimization and Optimal Control: Theory and Applications, A. Chinchuluun, P.M. Pardalos, R. Enkhbat and I. Tseveendorj (eds), Springer, 2010, pp. 169-184.
200. K. Kubota and M. Fukushima, Gap function approach to the generalized Nash equilibrium problem, Journal of Optimization Theory and Applications 144 (2010), pp. 511-531.
201. M.-A.Majig and M. Fukushima, Restricted-step Josephy-Newton method for general variational inequalities with polyhedral constraints, Pacific Journal of Optimization 6 (2010), pp. 375-390.
202. D.S. Huang, B.M. Yu, Z.D. Lu, F.J. Fabozzi, S. Forcardi and M. Fukushima, Index-exciting CAViaR: A new empirical time-varying risk model, Studies in Nonlinear Dynamics & Econometrics 14 (2), Article 1 (2010).
203. G.H. Lin and M. Fukushima, Stochastic equilibrium problems and stochastic mathematical programs with equilibrium constraints: A survey, Pacific Journal of Optimization 6 (2010), pp. 455-482.
204. T. Yan and M. Fukushima, Smoothing method for mathematical programs with symmetric cone complementarity constraints, Optimization 60 (2011), pp. 113-128.
205. K. Nabetani, P. Tseng and M. Fukushima, Parametrized variational inequality approaches to generalized Nash equilibrium problems with shared constraints, Computational Optimization and Applications 48 (2011), pp. 423-452.
206. A.R. Hedar, E. Mabrouk and M. Fukushima, Tabu programming: A new problem solver through adaptive memory programming over tree data structures, International Journal of Information Technology & Decision Making 10 (2011), pp. 373-406.
207. M. Fukushima, Restricted generalized Nash equilibria and controlled penalty algorithm, Computational Management Science 8 (2011), pp. 201-218.
208. B.T. Ong and M. Fukushima, Genetic algorithm with automatic termination and search space rotation, Memetic Computing 3 (2011), pp. 111-127.
209. E. Mabrouk, J.C.H. Castro and M. Fukushima, Prime number generation using memetic programming, Artificial Life and Robotics 16 (2011), pp. 53-56.
210. K. Hamatani and M. Fukushima, Pricing American options with uncertain volatility through stochastic linear complementarity models, Computational Optimization and Applications 50 (2011), pp. 263-286.
211. YrCcmCvCR[Xtmv@ɂX}[gnEX̉^pœKCdCw_B 131 (2011), pp. 885—895.
212. M. Hu and M. Fukushima, Variational inequality formulation of a class of multi-leader-follower games, Journal of Optimization Theory and Applications 151 (2011), pp. 455-473.
213. B.T. Ong and M. Fukushima, Global optimization via differential evolution with automatic termination, Numerical Algebra, Control and Optimization 2 (2012), pp. 57-67.
214. M. Fukushima, SOR- and Jacobi-type iterative methods for solving $\ell_1$-$\ell_2$ problems by way of Fenchel duality, Optimization Letters 6 (2012), pp. 679-686.
215. A. von Heusinger, C. Kanzow and M. Fukushima, Newtonfs method for computing a normalized equilibrium in the generalized Nash game through fixed point formulation, Mathematical Programming. 132 (2012), pp. 99-123.
216. R. Nishimura, S. Hayashi and M. Fukushima, Semidefinite complementarity reformulation for robust Nash equilibrium problems with Euclidean uncertainty sets, Journal of Global Optimization 53 (2012), pp. 187-215.
217. C.P. Bras, M. Fukushima, J.J. Judice and S.S. Rosa, Variational inequality formulation of the asymmetric eigenvalue complementarity problem and its solution by means of gap functions, Pacific Journal of Optimization 8 (2012), pp. 197-215.
218. M. Hu and M. Fukushima, Smoothing approach to Nash equilibrium formulations for a class of equilibrium problems with shared complementarity constraints, Computational Optimization and Applications 52 (2012), pp. 415-437.
219. K. Ruan and M. Fukushima, Robust portfolio selection with a combined WCVaR and factor model, Journal of Industrial and Management Optimization 8 (2012), pp. 343-362.
220. T. Okuno, S. Hayashi and M. Fukushima, A regularized explicit exchange method for semi-infinite programs with an infinite number of conic constraints, SIAM Journal on Optimization 22 (2012), pp. 1009-1028.
221. E.H. Fukuda, P.J.S. Silva and M. Fukushima, Differentiable exact penalty functions for nonlinear second-order cone programs, SIAM Journal on Optimization 22 (2012), pp. 1607-1633.
222. Y.B. Zhao and M. Fukushima, Rank-one solutions for homogeneous linear matrix equations over the positive semidefinite cone, Applied Mathematics and Computation 219 (2013), pp. 5569-5583.
223. {[CcmCv, ␫2vɑ΂镽@ƃX}[gnEX^]vւ̓Kp, VXew_ 26 (2013), pp. 34-44D
224. J. Ang, M. Fukushima, F. Meng, T. Noda and J. Sun, Establishing Nash equilibrium of the manufacturer-supplier game in supply chain management, Journal of Global Optimization 56 (2013), pp. 1297-1312.
225. H. Yamamura, T. Okuno, S. Hayashi and M. Fukushima, A smoothing SQP method for mathematical programs with linear second-order cone complementarity constraints, Pacific Journal of Optimization 9 (2013), pp. 345-372.
226. R. Nishimura, S. Hayashi and M. Fukushima, SDP reformulation for robust optimization problems based on nonconvex QP duality, Computational Optimization and Applications 55 (2013), pp. 21-47.
227. M. Hu and M. Fukushima, Existence, uniqueness, and computation of robust Nash equilibria in a class of multi-leader-follower games, SIAM Journal on Optimization 23 (2013), pp. 894-916.
228. A. Dreves, A. von Heusinger, C. Kanzow and M. Fukushima, A globalized Newton method for the computation of normalized Nash equilibria, Journal of Global Optimization 56 (2013), pp. 327-340.
229. S. Yamanaka and M. Fukushima, A branch-and-bound method for absolute value programs, Optimization 63 (2014), pp. 305-319.
230. L.M. Fernandes, J.J. Judice, H.D. Sherali and M. Fukushima, On the computation of all eigenvalues for the eigenvalue complementarity problem, Journal of Global Optimization 59 (2014), pp. 307-326.
231. M. Kono and M. Fukushima, A regularized outer approximation method for monotone semi-infinite variational inequality problems, Pacific Journal of Optimization 10 (2014), pp. 735-748.
232. L.M. Fernandes, J.J. Judice, M. Fukushima and A.N. Iusem, On the symmetric quadratic eigenvalue complementarity problem, Optimization Methods and Software 29 (2014), pp. 751-770.
233. T. Okuno and M. Fukushima, Local reduction based SQP-type method for semi-infinite programs with an infinite number of second-order cone constraints, Journal of Global Optimization 60 (2014), pp. 25-48.
234. B.T. Ong and M. Fukushima, Automatically terminated particle swarm optimization with principal component analysis, International Journal of Information Technology and Decision Making 14 (2015), pp. 171-194.
235. M. Hu and M. Fukushima, Multi-leader-follower games: Models, methods and applications, Journal of the Operations Research Society of Japan 58 (2015), pp. 1-23.
236. C.P. Bras, M. Fukushima, A.N. Iusem and J.J. Judice, On the quadratic eigenvalue complementarity problem over a general convex cone, Applied Mathematics and Computation 271 (2015), pp. 594-608.
237. L.M. Fernandes, M. Fukushima, J.J. Judice and H.D. Sherali, The second-order cone eigenvalue complementarity problem, Optimization Methods and Software 31 (2016), pp. 24-52.
238. E.H. Fukuda and M. Fukushima, The use of squared slack variables in nonlinear second-order cone programming, Journal of Optimization Theory and Applications 170 (2016), pp. 394-418.
239. I. Takami, M. Fukushima, F. Yamada, T. Yamamoto, F. Yamada and T. Mori, Optimal maintenance management of flood control infrastructure, Proceedings of the 11th International Conference on Reliability, Maintainability and Safety (ICRMS 2016), Hangzhou, China, October 2016, CD-ROM, 8 pages.
240. E.H. Fukuda and M. Fukushima, A note on the squared slack variables technique for nonlinear optimization, Journal of the Operations Research Society of Japan 60 (2017), pp. 262-270.
241. B.F. Lourenco, E.H. Fukuda and M. Fukushima, Optimality conditions for nonlinear semidefinite programming via squared slack variables, to appear in Mathematical Programming.
242. B.F. Lourenco, E.H. Fukuda and M. Fukushima, Optimality conditions for problems over symmetric cones and a simple augmented Lagrangian method, to appear in Mathematics of Operations Research.

#### E@_

1. v, s\ȍœKɑ΂鐔v@(1)(2), Iy[VYET[, 23 (1978), pp. 317-324, 384-393.
2. v, v@̓WJ-I: v@̑oΗ_, VXeƐ, 24 (1980), pp. 537-546.
3. v, v@̓WJ-III: j[g@, VXeƐ, 24 (1980), pp. 668-679.
4. M. Fukushima, A summary of numerical algorithms in nonsmooth optimization, Proceedings of the 3rd Mathematical Programming Symposium, Japan, Tokyo, October 1982, pp. 63-78.
5. M. Fukushima, Solution methods for variational inequalities, Proceedings of the 6th Mathematical Programming Symposium, Japan, Tokyo, November 1985, pp. 75-95.
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16. cGG, v, 2v2XbNϐ@, Iy[VYET[, 59 (2014), pp. 707-715.

< Last update: August 29, 2017>


text:
Use this URL to cite or link to this record in EThOS: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.699318
Title: The geometry and representation theory of superconformal quantum mechanics
Author: Singleton, Andrew John
ISNI:       0000 0004 5989 0095
Awarding Body: University of Cambridge
Current Institution: University of Cambridge
Date of Award: 2016
Availability of Full Text:
 Access from EThOS: Full text unavailable from EThOS. Please try the link below. Access from Institution:
Abstract:
We study aspects of the quantum mechanics of nonlinear $\sigma$-models with superconformal invariance. The connection between the differential geometry of the target manifold and symmetries of the quantum mechanics is explored, resulting in a classification of spaces admitting $\mathcal{N}=(n,n)$ superconformal invariance with $n=1,2,4$. We construct the corresponding superalgberas $\mathfrak{su}(1,1|1),~\mathfrak{u}(1,1|2)$ and $\mathfrak{osp}(4^*|4)$ explicitly. The low-energy dynamics of Yang-Mills instantons is an example of the latter and arises naturally in the discrete light-cone quantisation (DLCQ) of certain superconformal field theories. In particular, we study in some detail the quantum mechanics arising in the DLCQ of the six-dimensional (2,0) theory and four-dimensional $\mathcal{N}=4$ SUSY Yang-Mills. In the (2,0) case we carry out a detailed study of the representation theory of the light-cone superalgebra $\mathfrak{osp}(4^*|4)$. We give a complete classification of the unitary irreducible representations and their branching at the unitarity bound, and use this information to construct the superconformal index for $\mathfrak{osp}(4^*|4)$. States contribute to the index if and only if they are in the cohomology of a particular supercharge, which we identify as the $L^2$ Dolbeault cohomology of instanton moduli space with values in a real line bundle. In the SUSY Yang-Mills case the target space is the Coulomb branch of an elliptic quiver gauge theory, and as such is a scale-invariant special Kähler manifold. We describe a new type of $\sigma$-model with $\mathcal{N}=(4,4)$ superconformal symmetry and $U(1)\times SO(6)$ R-symmetry which exists on any such manifold. These models exhibit $\mathfrak{su}(1,1|4)$ invariance and we give an explicit construction of the superalgebra in terms of known functions. Consideration of the spectral problem for the dilatation operator in these models leads to a deformation which we interpret, via an extension of the moduli space approximation, as an anti-self-dual spacetime magnetic field coupling to the topological instanton current.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.699318  DOI:
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text:
# BibLaTeX Biber in TeXnicCenter does not produce bibliography

I recently changed to backend=biber after some problems with encoding in bibtex8 ( Biblatex encoding ). Everything seemed to work fine until I added some references and updated the bibliography file. The new references remained undefined. I removed all "additional" files (like .aux etc.) from the project folder and ran LaTeX three times. All the references were now undefined and even no .blg file is produced. So I had a look in the internet and found someone with a similar problem in a German LaTeX community. He used to work with Texmaker, and apparently the problem was that biber was trying to get the information from .aux file instead of .bcf file. That user changed this manually in Texmaker and everything started working. However, another user suggested that within TeXnicCenter (which I am using) this doesn't need to be done as this is already indicated by %tm. Now I am completely lost as to how to fix the problem.

Here is an MWE:

\documentclass{scrartcl}

\usepackage[british]{babel}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}

\usepackage[style=authoryear-comp, maxnames=1, doi=false, url=false, bibencoding=utf8, backend=biber]{biblatex}

\bibliography{litthesis}

\begin{document}

This is my text \parencite{Hong2006}

\newpage

\printbibliography
\end{document}

And here is the bibliography:

@article{Hong2006,
author = {Hong, Seungpyo and Leroueil, Pascale R and Janus, Elizabeth K and Peters, Jennifer L and Kober, Mary-Margaret and Islam, Mohammad T and Orr, Bradford G and Baker, James R and Holl, Mark M Banaszak},
title = {Interaction of polycationic polymers with supported lipid bilayers and cells: nanoscale hole formation and enhanced membrane permeability.},
journal = {Bioconjug Chem},
volume = {17},
number = {3},
pages = {728-734},
year = {2006}
}

Here is what's written in the .log-file:

Package biblatex Info: Trying to load bibliographic data...

No file mwe.bbl.

Does anyone have an idea what's going wrong?

-
You have to run Biber. –  egreg May 1 '12 at 14:21
@egreg Well, how do I do this in TeXnicCenter? –  AnjaM May 1 '12 at 14:25
It is completely impossible that biber is trying to get information from the .aux file. It ignores the .aux file. When you tell biblatex you are using biber with "backend=biber" (or no option at all, in upcoming biblatex 2.0), it writes a special .bcf XML file which biber uses to get its information. –  PLK May 1 '12 at 20:29
@PLK Well, I just repeated what a member of another community wrote that helped him. Anyway, the problem still remains that biber fails to produce bibliography, and this problem seems not only to occur for me. Do you have any idea why this happens? backend=bibtex8 works fine in this respect, so it shouldn't be a problem of the .bib file. –  AnjaM May 2 '12 at 8:25

As we found out on golatex.de the problem is quite similar to the one in this question and this question.

biber was complaining:

data source C:\Users\<user>\AppData\Local\Temp\par-416e6a61\cache-46f2da95c5284272f49f4e60b997c7e3f24afb19\recode_data.xml not found in .
Compilation failed in require at Biber/Utils.pm line 21.
BEGIN failed--compilation aborted at Biber/Utils.pm line 21.
Compilation failed in require at Biber/Utils.pm line 8.
BEGIN failed--compilation aborted at Biber/Utils.pm line 8.
Compilation failed in require at (eval 24) line 2.
...propagated at C:/strawberry/perl/lib/base.pm line 94.
BEGIN failed--compilation aborted at Biber.pm line 5.
Compilation failed in require at script/biber-MSWIN line 17.
BEGIN failed--compilation aborted at script/biber-MSWIN line 17.

The solution suggested by @egreg and @pmav99, resp., to the other questions -- namely deleting the par-<some string> directory in the temporary folder -- solved the issue here as well.

-
Works on Mac to. Thanks a lot. –  Ivo Looser Nov 3 '14 at 19:44


text:
# How DynaQ behaves in stochastic world in comparison with other reinforcement learning algorithms?

I came across of implementations of a bunch of algorithms on stochastic windy gridworld. This is the graph comparing their performance:

So clearly, it seems that DynaQ performs better than all other algorithms. Also, as $$n$$ goes on increasing, the performance of DynaQ also goes on increasing. But somehow I feel this contradicts with what Sutton and Barto says in the book (section 8.3):

Models may be incorrect because the environment is stochastic and only a limited number of samples have been observed, … When the model is incorrect, the planning process is likely to compute a suboptimal policy. So, I was wondering why DynaQ does not perform poorly than Q learning for "stochastic" windy gridworld.

Q1. Is it that the authors did not want to compare DynaQ with Q learning, but say in general, with the above quoted statement? (this might be the case as the corresponding paragraph does not mention Q learning at all)

Q2. Can no amount of stochasticity (in any environment, not just windy gridworld) make DynaQ perform poorer than Q-learning? (for windy grid world, we may consider making all column stochastic instead of just windy columns or wind may take us to five different states instead of three)

Q3. The quoted sentence says "only a limited number of samples have been observed". What does it refer to by "samples"? Inner loop or outer loop (f)? My logic is that it must be an outer loop as for getting correct T and R values for a given state, we must pass through it several times. That is, we should have completed a large number of episodes. But, then the term "sample" is used in the context of model learning (Loop (f)). So is my logic incorrect?

Q4. Also, for the stochastic world, which has the incorrect model at some point in time of DynaQ execution, does larger $$n$$ leads to a more incorrect model or a less incorrect model?

Q3 and Q4 arose because I am not able to visualize how (correct/incorrect) policies will result in a stochastic world, say for halfway through the second episode, as given in the book for the deterministic world:

PS: The main question is as it appears in the title. I have formed four subquestions so that answerer can opt to focus answer on them individually to answer question in the title from all possible aspects.

• In any case, I noticed that you also asked this question on Stats SE. Try to avoid cross-duplication.
– nbro
Feb 17 at 14:32


text: Next, divide the number one by the number of years of returns you're considering. Enter the geometric average annual rate of return. $$\text{Effective Annual Return}\ (\text{r}) \\= \left[\text{1} + \frac{\text{Nominal Rate of Return}}{\text{n}} \right] ^ \text{n} - \text{1}$$eval(ez_write_tag([[468,60],'xplaind_com-box-3','ezslot_12',104,'0','0'])); Where n is the number of compounding periods per year. Annual Return is calculated using the formula given below Annual Return = (Ending Value / Initial Value) (1 / No. The formula for an average rate of return is derived by dividing the average annual net earnings after taxes or return on the investment by the original investment or the average investment during the life of the project and then expressed in terms of percentage. The formula requires two inputs: (a) nominal_rate which is nominal annual rate on the investment and (b) npery which is the number of compounding periods per year. If we earned 5% in a quarter there is no guarantee that we will be able to replicate these returns over the next three quarters in the year. Where r is the effective annual return that captures the effect of compounding, another formula to arrive at the future value is $1 × (1 + r). This works because there are 12 months in a year. However this may not always be possible. 5% of the money which equals$15,000 is put invested in a bank time deposit paying 6% compounded monthly. Compound Annual Growth Rate (CAGR) CAGR stands for Compound Annual Growth Rate. I’ll admit that the equation has no place in everyday life – it should be restricted to Excel spreadsheets and only allowed to see the light of day once a year (preferably after year-end). Mark is a university student whose parents set up a trust to finance his university education. nper - Number of periods. =IF (E7=”Yes”,F5*0.0825,0) In this example, the formula in F7 is saying IF (E7 = “Yes”, then calculate the Total Amount in F5 * 8.25%, otherwise no Sales Tax is due so return 0) If Excel formulas are unfamiliar to you, you could benefit greatly from our completely free Basic Skills E-book, which teaches the basics of Excel formulas. Suppose it's 2015, and you own shares (it doesn't matter how many) of the stock. We hope you like the work that has been done, and if you have any suggestions, your feedback is highly valuable. There are two options for calculating the annualized return depending on the available information. In one of our previous articles, we unveiled the power of compound interest and how to calculate it in Excel. Returns the yield on a security that pays periodic interest. It's a nice way to see how the portfolio has done, but it doesn't tell you anything about the portfolio's volatility or how it's done on a "risk-adjusted basis," so it isn't very useful by itself when you're comparing investments. hope this will help u #xls, IT Dept releases a calendar to make the tax journey of taxpayers easier, ICMAI issues Tax Bulletin for January 2021, ICAI Handbook on GST- Downloadable latest editions, GST - Due Date Compliance Calendar for January 2021 and Recent Updates on The Portal, Few good habits / Resolution for New Year 2021, Updates on Direct & Indirect Taxes | ICAI & ICSI Updates | Corporate laws | Insolvency | SEBI | RBI | Economy & Finance - 29.12.2020. Excel formulas can also be developed using cell references.Continuing with our example, you would not enter the numbers 3 and 2, but instead would name cells where these numbers have been entered (see Using Cell References below for more on cell naming).When you write a formula this way, the formula cell always shows the sum of the numbers in … Option 1: When you are given the annual returns for each year of the investment period, then: Where: R 1 – The annual return for year 1, R 2 is the annual return for year 2, and so on; n – The number of years you wish to annualize After the second compounding period, the investment value will rise to $10,816 [=$10,400 × (1 + 4%)]. #xlsx Submitted By: Sanjay Bhiku Polekar. IRR is the abbreviation of the Internal Rate of Return. You may want to create a function that returns a static value each time it is called – a bit like a constant. The syntax of the IRR function in excel is “=IRR (values, [guess])”. This article describes the formula syntax and usage of the YIELD function in Microsoft Excel. The total shareholder return formula methodology many companies use in their annual report, 10-K filing, or proxy statement is fundamentally different. So the formula in E2 is saying IF (Actual is Greater than Budgeted, then Subtract the Budgeted amount from the Actual amount, otherwise return nothing). Calculate the effective annual return. The Excel IF Statement function tests a given condition and returns one value for a TRUE result, and another for a FALSE result. The CAGR Formula It help to Prepare a Draft return before going to Update data on GST Portal. To annualize data from a single month, the formula will be: =[Value for 1 month] * 12. Get equivalent interest rate for growth. This section must contain one positive and one negative value. Access notes and question bank for CFA® Level 1 authored by me at AlphaBetaPrep.comeval(ez_write_tag([[250,250],'xplaind_com-large-leaderboard-2','ezslot_4',136,'0','0'])); XPLAIND.com is a free educational website; of students, by students, and for students. A subtle variation of this problem can occur if there is one or more spaces before the equal sign. We need a single annual rate that when applied to the initial value of the investment will give $10,816. This can be written in equation form as: $$\text{\1} \times (\text{1} + \text{r}) = \text{\1} \times \left[ \text{1} + \frac{\text{Nominal Rate of Return}}{\text{n}} \right] ^ \text{n}$$eval(ez_write_tag([[468,60],'xplaind_com-medrectangle-4','ezslot_1',133,'0','0'])); $$\text{1} + \text{r} = \left[\text{1} + \frac{\text{Nominal Rate of Return}}{\text{n}} \right] ^ \text{n}$$. Effective annual return is the rate that when applied to the initial investment will give a future value equal to the value arrived at after the compounding process. When return on investment is compounded more than once in a year, return earned in each compounding period in added to the investment value which results in a return higher than nominal rate of return in subsequent compounding periods. ( In memory of My Father ). This is where the concept of effective annual return becomes relevant. Next, raise this result to the power of 1 divided by the number of years. For example, if sales total more than$5,000, then return a "Yes" for Bonus, else, return a "No". Function GetValue As Integer GetValue = 50. In actuality, the growth rate should vary from year to year. Download Annual Return (Excel ) - Corporate Law. The compound annual growth rate (CAGR) shows the rate of return of an investment over a certain period of time, expressed in annual percentage terms. We can also create nested IF statements On this page, we provide the necessary formulas that explain how to calculate the annualized rate of return. Let’s say you put $10,000 in a fixed-income investment that pays 8% per annum compounded semiannually. The formula requires two inputs: (a) nominal_rate which is nominal annual rate on the investment and (b) npery which is the number of compounding periods per year. All formulas in Excel must begin with an equal sign (=). Note: in other words, to calculate the CAGR of an investment in Excel, divide the value of the investment at the end by the value of the investment at the start. If you leave this out, Excel will simply treat the formula as text: Broken formula example - no equal sign (=) Space before equal sign. If, on the other hand, you have monthly returns for separate months, then you will annualize the returns using the following formula: APY = (1+r 1)* (1+r 2) * (1+r 3) * (1+r 4) * (1+r 5) * (1+r 6) * (1+r 7) * (1+r 8) * (1+r 9) * (1+r 10) * (1+r 11) * (1+r 12) – 1 You can see that if we apply 8% to$10,000, we get $10,800 after the first year. To calculate the Compound Annual Growth Rate in Excel, there is a basic formula =((End Value/Start Value)^(1/Periods) -1. Download Other files in Corporate Law category, India's largest network for finance professionals, This is Schedule V under Co. Act 1956 which is required to be filed within 60 days of AGM , excel format helps to reduce the size of form attachment . Purpose . $$\text{Effective Annual Return}\ (\text{monthly compounding}) \\= \left[\text{1} + \frac{\text{6%}}{\text{12}}\right]^{\text{12}} - \text{1} \\= \text{6.168%}$$eval(ez_write_tag([[250,250],'xplaind_com-banner-1','ezslot_3',135,'0','0'])); EAR can also be calculated using Microsoft Excel EFFECT function. = PV * (1 + i/n)nt Let’s take an example … 3. Note: This formula assumes all dividends paid during the holding period were reinvested. If you were to run the function, the function would always return the value of 50. Select a blank cell, for example Cell E3, enter the below formula into it, and press the Enter key. Return value . GSTR9 annual return consists of details like outward taxable supplies, input tax credit availed, advance received etc. I want to calculate the cumulative return of a series of monthly fund returns over a monthly, quarterly and annual basis. GSTR-9 being annual return format in Excel with Formula in each Table & With Instruction sheet in summery Format to help in Preparing a Draft of Annual Return. by Obaidullah Jan, ACA, CFA and last modified on Jun 3, 2019Studying for CFA® Program? Finally, subtract 1 from this result. You can use RRI to calculate Compound Annual Growth Rate (CAGR) in Excel. The XIRR function can figure it out easily. In other words, it is a summary of the entire year you have declared monthly in the form of GSTR 1, GSTR 2 and GSTR 3B. CAGR is the year-over-year average growth rate over a period of time. The tutorial explains what the Compound Annual Growth Rate is, and how to make a clear and easy-to-understand CAGR formula in Excel. Annual Return = (Simple Return +1) ^ (1 / Years Held)-1 Let's use Campbell Soup as an example. Calculated interest rate. hope this will help u #xls The CAGR formula below does the trick. Other files by the user. An Excel formula to annualize data . Note that IRR () doesn’t assume that the interval is years. 2. Annualized portfolio return gives an investor a sense of how a portfolio has performed on an average annual basis over a period of time. Don't Confuse Different Shareholder Return Formulas . This rate is 8.16% [=($10,816 − $10,000) ÷$10,000] which is exactly the effective annual return. IRR method is helpful when you need to find the CAGR (Compound Annual Growth Rate) value for different value payments which has been made during the specific time period. Let's connect. Due to this phenomenon, the future value of investment is higher than the future value arrived at by simply applying the nominal rate of return to the initial investment value. The 8% nominal annual return doesn’t capture the effect of compounding. YIELD(settlement, maturity, rate, pr, redemption, frequency, [basis]) Important: Dates should be entered by using the DATE function, or as results of other formulas or functions. End Function. Calculate the effective annual return. For those investors who still have their G-card, this can be a terrifying equation to tackle. Excel calculates the average annual rate of return as 9.52%. The formula you need to enter to work out effective annual return = EFFECT(6%, 12). The value of your investment after the first six month will be $10,400 [=$10,000 × (1 + 4%)]. on 09 April 2019. The Excel RRI function returns an equivalent interest rate for the growth of an investment. Using these three factors, you can find out the future value of your investment with a certain compounded interest rate. Calculate rate of return for a share of stock in Excel For example, you purchased the stock on 2015/5/10 at $15.60, sold it on 2017/10/13 at$25.30, and get dividends every year as below screenshot shown. An investor purchased a share at a price of $5 and he had purchased 1,000 shared in year 2017 after one year he decides to sell them at a price of$ pv - Present value of investment. Use YIELD to calculate bond yield. Improve Formulas with Cell References . Annualized returns however have one limitation – they assume that we will be able to reinvest the money at the same rate. Subtracting 1 from both sides:eval(ez_write_tag([[580,400],'xplaind_com-box-4','ezslot_2',134,'0','0'])); $$\text{r} = \left[\text{1} + \frac{\text{Nominal Rate of Return}}{\text{n}} \right] ^ \text{n} - \text{1}$$. Effective annual return (EAR) is the annual rate that captures the magnifying effect of multiple compounding periods per year of an investment. Remember that when you enter formulas in Excel, you double-click on the cell and put it in formula mode by pressing the equals key (=). Description. Syntax =RRI (nper, pv, fv) Arguments . This is Schedule V under Co. Act 1956 which is required to be filed within 60 days of AGM , excel format helps to reduce the size of form attachment . Annual returns = (1+0.06)^(365/100) – 1 = 23.69%. One thing we can do, is to annualize returns. Below is … You are welcome to learn a range of topics from accounting, economics, finance and more. Effective Annual Return monthly compounding 1 6% 12 12 1 6.168% EAR can also be calculated using Microsoft Excel EFFECT function. of Years) – 1 Annual Return = ($210 /$100) 1 / 5 – 1 Annual Return = 16.0% When Excel is in formula mode, type in the formula. Values mean the total range of number which is representing the cash flows. Syntax. FV of $1 investment after n compounding periodseval(ez_write_tag([[336,280],'xplaind_com-medrectangle-3','ezslot_0',105,'0','0'])); $$= \text{\1} \times \left[ \frac{\text{1} + \text{nominal rate of return}}{\text{n}} \right] ^\text{n}$$. Today, we'll take a step further and explore different ways to compute Compound Annual Growth Rate (CAGR). Average Rate of Return Formula Mathematically, it is represented as, Thank you. See screenshot: =(C12/C3)^(1/(10-1))-1 Annualized return formula. 1. 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# Thread: Proving step to full proof

1. ## Proving step to full proof

I was doing a proof to prove that there exists arbitrarily long strings of composite numbers.
In more technical language, for every $\displaystyle m\in {N}$, there exists a n such that
$\displaystyle n, n+1, n+2, n+3,..., n+m$ is composite

to do so, I let $\displaystyle n=m!$,(for m>3) then we get the sequence:
$\displaystyle m!, m!+1, m!+2, m!+3,..., m!+m$

Every element of this sequence is obviously divisible by some integer, except $\displaystyle m!+1.$

Now I must prove that m!+1 is always an composite. I have no idea how to do this. I tried induction and contradiction.

2. Originally Posted by I-Think
I was doing a proof to prove that there exists arbitrarily long strings of composite numbers.
In more technical language, for every $\displaystyle m\element{N}$, there exists a n such that
$\displaystyle n, n+1, n+2, n+3,..., n+m$ is prime

to do so, I let $\displaystyle n=m!$,(for m>3) then we get the sequence:
$\displaystyle m!, m!+1, m!+2, m!+3,..., m!+m$

Every element of this sequence is obviously divisible by some integer, except $\displaystyle m!+1.$

Now I must prove that m!+1 is always an integer. I have no idea how to do this. I tried induction and contradiction.
There are so many typos in this I think you should correct them before expecting a reply.

Also this is number theory.

To show that for any $\displaystyle n\in \mathbb{N}$ there is a set of $\displaystyle n$ consecutive composites choose $\displaystyle $$m so that \displaystyle m=n+1. Then \displaystyle m!+2, m!+3,.. m!+m are all composite, and there are \displaystyle m-1=n of these. CB 3. Originally Posted by I-Think Now I must prove that m!+1 is always an composite. I have no idea how to do this. I tried induction and contradiction. Help please You can't since if \displaystyle$$ m=2$ then $\displaystyle m!+1=5$ is prime

CB

4. I apologize for the typos. I also apologize for posting this in the wrong forum but I did not expect the problem to involve Number Theory, as it is a topic I had not yet covered.

And as for proving that $\displaystyle m!+1$is always composite, I had stated it was over the range $\displaystyle m>3$

5. Let n = (m+2)! + 2

P.S: m! + 1 is composite when m = p-1 for some prime p > 3.

6. Originally Posted by i-think
i apologize for the typos. I also apologize for posting this in the wrong forum but i did not expect the problem to involve number theory, as it is a topic i had not yet covered.

And as for proving that $\displaystyle m!+1$is always composite, i had stated it was over the range $\displaystyle m>3$
ok 11!+1

cb

7. Infact following should work

n = (m+1)! + 2


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# What Is 2/25 as a Decimal + Solution With Free Steps

The fraction 2/25 as a decimal is equal to 0.08.

Fraction is a mathematical concept that allows us to figure out the number of equal parts into which we can divide an object or quantity. In its representation, its two components are separated from one another by a line. The component on top of the dash or line is regarded as the Numerator, and the component at the bottom is recognized as the Denominator. While the Division process is depicted by the line between these two.

In most cases, it is desirable to change fractions into their decimal representations because the decimals are simpler to work with and comprehend than fractions. There are several ways to carry out this conversion. Long Division is one of them.

This article provides a detailed explanation of converting a fraction of 2/25 into its decimal value.

## Solution

A fraction must initially be changed into a division to resolve. We accomplish this by classifying its elements of fraction, depending on their function. As a consequence, we get the fraction’s numerator as a number, which we have to divide. And denominator is the number that will divide it.

The given example, therefore, yields a dividend of 2 and a divisor of 25.

Dividend = 2

Divisor = 25

The result obtained by the division of two numbers is known as Quotient. The term Remainder is used when there is a value that is still present after the division.

Quotient = Dividend $\div$ Divisor = 2 $\div$ 25

Figure 1

## 2/25 Long Division Method

We are trying to solve the fraction 2/25.

2 $\div$ 25

To begin resolving a division issue, the type of fraction must be determined. If the fraction we were given was proper, it would have a smaller dividend than the divisor and require a decimal point in the quotient. Whereas when the fraction is incorrect, it does not require a Decimal Point because its equivalent value is higher than 1.

As it can be seen that the presented fraction of 2/25 has a denominator or divisor that is more than the dividend. Because of this, we will add a decimal point to the quotient, which is accomplished when the dividend is multiplied by 10. Multiplying the dividend 2 by 10 results in the value of 20, which is then divided by 25.

20 $\div$ 25 = 0

25 x 0 = 0

20 – 0 = 20 is the left-over value. The remainder is once more multiplied by 10, but this time decimal point is not required to be inserted in the quotient again. We now have 200 to divide by 25.

200 $\div$ 25 = 0

25 x 8 = 200

Nothing remains behind, at this point.

200-200 = 0

Zero remainder indicates that further division is not required, and the fraction is thus transformed to its appropriate decimal value, which is 0.08.

Images/mathematical drawings are created with GeoGebra.


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# Wave theory limit of geometric optics? [duplicate]

Why is geometric optics the low wavelength limit of the wave theory of light? I can't seem to grasp why either a low or high wavelength limit would be necessary.

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Visualise it and it would be clear . –  Dimensio1n0 Aug 11 '13 at 2:29

## marked as duplicate by Emilio Pisanty, Dan, Qmechanic♦Aug 11 '13 at 3:38

Actually I would answer this almost exactly as @EmilioPisanty answered the a very like question -

this is the way that Born and Wolf "Principles of Optics" do it.

However, I would add as a footnote the following intuitive points:

There is one, unique class of Maxwell Equation solution that fulfills the Eikonal equation exactly and these are the plane waves: their wavevectors are the "rays" in ray optics. These are exactly light travelling in straight lines. However, they are also altogether "delocalized" - spread out evenly over all space, so strictly you can't talk about a ray at a particular place. What one finds in practice though is that if waves are approximately plane so that their phase fronts are flat over several wavelengths or more, they do not tend to spread out much as they propagate. Lasers are the same: the wider your beam, the less it diverges, indeed the divergence angle $\times$ beamwidth product is constant. So you can represent the field coming from a region wherein the phase fronts are flat as a plane wave along the ray with it tail in that region. Another good example is the phased array and dish antennas. They set up a field that is locally plane over many wavelengths, thus achieving a very tight beam. The ray is the spatial analogy of the ideal bandlimited AND time-limited signal often talked about in systems analysis. Theoretically, if something is time-limited, it has infinite bandwidth, but one can do practical analysis by assuming the "ideal" (strictly impossible) case. This is what we do when we draw rays.

Indeed intuitive comments like this lead to the "Ansatz" that Emilio talks of in his other answer: you assume the field is a plane wave multiplied by an "envelope" function that varies slowly in space. The Eikonal equation then results from putting the assumed solution into MAxwell's equations and making approximations.

Does all this sound familiar - it should do: it's exactly how the Heisenberg uncertainty principle works: the momentum operator is just a scalar multiplication in a space that is the Fourier transformed space wherein the position operator amounts to a scalar multiplication. So, the momentum corresponds to wavevectors (the directions of rays) and positions to a place where we can nail the rays' tails down. As long as we don't demand too much precision in either direction or position, rays are a useful model of all waves in this way.

Footnote: I should also say thank you to Emilio Pisanty for bringing to my attention the analogy between the Hamilton Jacobi and Eikonal equation in the answer cited above. I have never really appreciated that until today. Now the standard quantisation procedure Poisson bracket $\mapsto$ Lie bracket suddenly really makes sense to me.

Edit: The following is a code that you can import into Wolfram Mathematica to do diffraction calculations. You can play with the beam width and so forth and simulate how well the beam will propagate without spreading for different beamwidths and wavelengths. Lines beginning in "#" are comments: Mathematica will read the following if you ask it to open a "text file".

#Index Rotation for Rotated Fourier Transform

[Kappa][k_,n_]:=If[k >= n/2,k-n,k]

#Whether the phase of the diffraction operator is imaginary (i.e. whether wave is evanescent) when the domain width is n samples and the wavelength is Lambda (in samples)

PhaseImaginary[k_,n_,[Lambda]_]:=1-([Kappa][k,n]/n [Lambda])^2<0

#Diffraction Phase Calculation: assume wavelength Lambda (in samples) and propagate through axial distance z

DiffractionPhase[k_,n_,[Lambda],z]:=If[z>= 0,2 [Pi] z/[Lambda] (-1+Sqrt[1-([Kappa][k,n]/n [Lambda])^2]),If[PhaseImaginary[k,n,[Lambda]], -2 [Pi] z/[Lambda],2 [Pi] z/[Lambda] (-1+Sqrt[1-([Kappa][k,n]/n [Lambda])^2])]]

#Diffraction Calculation: Take List x (assumed field samples), assume wavelength Lambda (in samples) and propagate through axial distance z (also in samples)

Diffract[x_,[Lambda],z]:= InverseFourier[Table[Exp[I DiffractionPhase[k,n,[Lambda],z]],{k,0,n-1}] Fourier[x]]

#Domain Width in samples

n:=2048;

#Beam Width in samples

w:= 200;

#Beam Offset in samples

[Delta]:=n/4;

#Beam Tilt Relative z axis (Radians)

[Alpha]:=0.7;

#Beam Wavelength (in samples)

[Lambda]:=20;

#Gaussian Beam

x:= Table[Exp[-((2 (k - [Delta])^2)/w^2)] Exp[2 [Pi] I/[Lambda] (k-[Delta]) Sin[[Alpha]]],{k,0,n-1}]

#Square Input Beam

x:= Table[If[Abs[k-[Delta]]

ListPlot[Abs[Diffract[x,[Lambda],1000]]^2,PlotRange->All]

ListPlot3D[Table[Abs[Diffract[x,[Lambda],10z]]^2,{z,0,100}],PlotRange->All]

-


text:
# Graham's Law

Written by Jerry Ratzlaff. Posted in Properties

Graham's Law also known as Graham's Law of Effusion is the rate at which gases disperse is inversely proportional to the square root of their mass. Or you could say the process in which one gas scatters itself within another.

## formula

$$\frac {R_1} {R_2} = \sqrt { \frac { M_2 } { M_1 } }$$

Where:

$$R_1$$ = the rate of effusion of the first gas (volume or number of moles per unit time)

$$R_2$$ = the rate of effusion for the second gas

$$M_1$$ = molar mass of gas one

$$M_2$$ = molar mass of gas two


text:
# TikZ: add options to existing style

within \tikzset{...} I defined

row 1/.style={
nodes={
fill=black,
text=white,
%font=\bfseries
}
}

such that for every table/matrix the first row is black with white text. When I now manually add

row 1/.style={nodes={text height=1em, text depth=3em}}

to a specific matrix the other options I used within the tikzset (fill=black, text=white) are gone, so I would have to write them again in that row 1/.style:

row 1/.style={nodes={text height=1em, text depth=3em, fill=black, text=white}}

Is it possible to just ADD the 2 options above to the already defined ones?

## 1 Answer

As mentioned in section 82.4.4 Defining Styles of the TikZ manual (for version 3.0.1a, dated 29 Aug 2015), you can use stylename/.append style={<options>} to append to the end of an existing style. (There is also .prefix style which prepends to the style.)

So for your specific case, use

row 1/.append style={nodes={text height=1em, text depth=3em}}

(That this works also relies on the fact that nodes is a shorthand for every node/.append style={}.)

Complete example:

\documentclass{standalone}
\usepackage{tikz}
\usetikzlibrary{matrix}
\tikzset{row 1/.style={
nodes={
fill=black,
text=white,
%font=\bfseries
}
}}

\begin{document}

\begin{tikzpicture}
\matrix [matrix of nodes] { a & b \\ c& d \\ e & f \\};
\end{tikzpicture}

\tikzset{row 1/.append style={nodes={text height=1em, text depth=3em}}}

\begin{tikzpicture}
\matrix [matrix of nodes] { a & b \\ c& d \\ e & f \\};
\end{tikzpicture}
\end{document}