text:
• ### Type Ia supernova Hubble diagram with near-infrared and optical observations(1505.07707)

March 23, 2018 astro-ph.CO
We main goal of this paper is to test whether the NIR peak magnitudes of SNe Ia could be accurately estimated with only a single observation obtained close to maximum light, provided the time of B band maximum and the optical stretch parameter are known. We obtained multi-epoch UBVRI and single-epoch J and H photometric observations of 16 SNe Ia in the redshift range z=0.037-0.183, doubling the leverage of the current SN Ia NIR Hubble diagram and the number of SNe beyond redshift 0.04. This sample was analyzed together with 102 NIR and 458 optical light curves (LCs) of normal SNe Ia from the literature. The analysis of 45 well-sampled NIR LCs shows that a single template accurately describes them if its time axis is stretched with the optical stretch parameter. This allows us to estimate the NIR peak magnitudes even with one observation obtained within 10 days from B-band maximum. We find that the NIR Hubble residuals show weak correlation with DM_15 and E(B-V), and for the first time we report a possible dependence on the J_max-H_max color. The intrinsic NIR luminosity scatter of SNe Ia is estimated to be around 0.10 mag, which is smaller than what can be derived for a similarly heterogeneous sample at optical wavelengths. In conclusion, we find that SNe Ia are at least as good standard candles in the NIR as in the optical. We showed that it is feasible to extended the NIR SN Ia Hubble diagram to z=0.2 with very modest sampling of the NIR LCs, if complemented by well-sampled optical LCs. Our results suggest that the most efficient way to extend the NIR Hubble diagram to high redshift would be to obtain a single observation close to the NIR maximum. (abridged)
• ### PISCO: The Pmas/ppak Integral-field Supernova hosts COmpilation(1802.01589)

We present the Pmas/ppak Integral-field Supernova hosts COmpilation (PISCO) which comprises Integral Field Spectroscopy (IFS) of 232 supernova (SN) host galaxies, that hosted 272 SNe, observed over several semesters with the 3.5m telescope at the Calar Alto Observatory (CAHA). PISCO is the largest collection of SN host galaxies observed with wide-field IFS, totaling 466,347 individual spectra covering a typical spatial resolution of $\sim$380 pc. While focused studies regarding specific SN Ia- related topics will be published elsewhere, this paper aims to present the properties of the SN environments with stellar population (SP) synthesis and the gas-phase ISM, providing additional results separating stripped-envelope SNe into their subtypes. With 11,270 HII regions detected in all galaxies, we present for the first time an HII region statistical analysis, that puts HII regions that have hosted SNe in context with all other SF clumps within their galaxies. SNe Ic are associated to more metal-rich, higher EW(H{\alpha}) and higher SF rate environments within their host galaxies than the mean of all HII regions detected within each host, on contrary SNe IIb occur at the most different environments compared to other CC SNe types. We find two clear components of young and old SP at SNe IIn locations. We find that SNe II fast-decliners (IIL) tend to explode at locations where {\Sigma}SFR is more intense. Finally, we outline how a future dedicated IFS survey of galaxies in parallel to an untargeted SN search would overcome the biases in current environmental studies.
• ### Nearby supernova host galaxies from the CALIFA Survey: II. SN environmental metallicity(1603.07808)

The metallicity of a supernova (SN) progenitor, together with its mass, is one of the main parameters that rules their outcome. We present a metallicity study of 115 nearby SN host galaxies (0.005<z<0.03) which hosted 142 SNe using Integral Field Spectroscopy (IFS) from the CALIFA survey. Using O3N2 we found no statistically significant differences between the gas-phase metallicities at the locations of the three main SN types (Ia, Ib/c and II) all having ~8.50$\pm$0.02 dex. The total galaxy metallicities are also very similar and we argue that this is because our sample consists only of SNe discovered in massive galaxies (log(M/Msun)>10 dex) by targeted searches. We also found no evidence that the metallicity at the SN location differs from the average metallicity at the GCD of the SNe. By extending our SN sample with published metallicities at the SN location, we studied the metallicity distributions for all SN subtypes split into SN discovered in targeted and untargeted searches. We confirm a bias toward higher host masses and metallicities in the targeted searches. Combining data from targeted and untargeted searches we found a sequence from higher to lower local metallicity: SN Ia, Ic, and II show the highest metallicity, which is significantly higher than SN Ib, IIb, and Ic-BL. Our results support the picture of SN Ib resulting from binary progenitors and, at least part of, SN Ic being the result of single massive stars stripped of their outer layers by metallicity driven winds. We studied several proxies of the local metallicity frequently used in the literature and found that the total host metallicity allows for the estimation of the metallicity at the SN location with an accuracy better than 0.08 dex and very small bias. In addition, weak AGNs not seen in total spectra may only weakly bias (by 0.04 dex) the metallicity estimate from integrated spectra. (abridged)
• ### Shape of the oxygen abundance profiles in CALIFA face-on spiral galaxies(1601.01542)

Jan. 7, 2016 astro-ph.GA
We measured the gas abundance profiles in a sample of 122 face-on spiral galaxies observed by the CALIFA survey and included all spaxels whose line emission was consistent with star formation. This type of analysis allowed us to improve the statistics with respect to previous studies, and to properly estimate the oxygen distribution across the entire disc to a distance of up to 3-4 disc effective radii (r$_e$). We confirm the results obtained from classical HII region analysis. In addition to the general negative gradient, an outer flattening can be observed in the oxygen abundance radial profile. An inner drop is also found in some cases. There is a common abundance gradient between 0.5 and 2.0 r$_e$ of $\alpha_{O/H} = -\,0.075\,\rm{dex}/r_e$ with a scatter of $\sigma = 0.016\,\rm{dex}/r_e$ when normalising the distances to the disc effective radius. By performing a set of Kolmogorov-Smirnov tests, we determined that this slope is independent of other galaxy properties, such as morphology, absolute magnitude, and the presence or absence of bars. In particular, barred galaxies do not seem to display shallower gradients, as predicted by numerical simulations. Interestingly, we find that most of the galaxies in the sample with reliable oxygen abundance values beyond $\sim 2$ effective radii (57 galaxies) present a flattening of the abundance gradient in these outer regions. This flattening is not associated with any morphological feature, which suggests that it is a common property of disc galaxies. Finally, we detect a drop or truncation of the abundance in the inner regions of 27 galaxies in the sample; this is only visible for the most massive galaxies.
• ### Diversity in extinction laws of Type Ia supernovae measured between $0.2$ and $2\,\mu\mathrm{m}$(1504.02101)

July 8, 2015 astro-ph.HE
We present ultraviolet (UV) observations of six nearby Type~Ia supernovae (SNe~Ia) obtained with the Hubble Space Telescope, three of which were also observed in the near-IR (NIR) with Wide-Field Camera~3. UV observations with the Swift satellite, as well as ground-based optical and near-infrared data provide complementary information. The combined data-set covers the wavelength range $0.2$--$2~\mu$m. By also including archival data of SN 2014J, we analyse a sample spanning observed colour excesses up to $E(B-V)=1.4~$mag. We study the wavelength dependent extinction of each individual SN and find a diversity of reddening laws when characterised by the total-to-selective extinction $R_V$. In particular, we note that for the two SNe with $E(B-V)\gtrsim1~$mag, for which the colour excess is dominated by dust extinction, we find $R_V=1.4\pm0.1$ and $R_V=2.8\pm0.1$. Adding UV photometry reduces the uncertainty of fitted $R_V$ by $\sim50\,$% allowing us to also measure $R_V$ of individual low-extinction objects which point to a similar diversity, currently not accounted for in the analyses when SNe~Ia are used for studying the expansion history of the universe.
• ### CALIFA, the Calar Alto Legacy Integral Field Area survey. III. Second public data release(1409.8302)

Sept. 29, 2014 astro-ph.GA
This paper describes the Second Public Data Release (DR2) of the Calar Alto Legacy Integral Field Area (CALIFA) survey. The data for 200 objects are made public, including the 100 galaxies of the First Public Data Release (DR1). Data were obtained with the integral-field spectrograph PMAS/PPak mounted on the 3.5 m telescope at the Calar Alto observatory. Two different spectral setups are available for each galaxy, (i) a low-resolution V500 setup covering the wavelength range 3745-7500 \AA\ with a spectral resolution of 6.0 \AA\ (FWHM), and (ii) a medium-resolution V1200 setup covering the wavelength range 3650-4840 \AA\ with a spectral resolution of 2.3 \AA\ (FWHM). The sample covers a redshift range between 0.005 and 0.03, with a wide range of properties in the Color-Magnitude diagram, stellar mass, ionization conditions, and morphological types. All released cubes were reduced with the latest pipeline, including improved spectrophotometric calibration, spatial registration and spatial resolution. The spectrophotometric calibration is better than 6% and the median spatial resolution is 2.5". Altogether the second data release contains over 1.5 million spectra. It is available at http://califa.caha.es/DR2.
• ### Nearby supernova host galaxies from the CALIFA Survey: I. Sample, data analysis, and correlation to star-forming regions(1409.1623)

Sept. 18, 2014 astro-ph.GA, astro-ph.HE
[Abridged] We use optical IFS of nearby SN host galaxies provided by the CALIFA Survey with the goal of finding correlations in the environmental parameters at the location of different SN types. We recover the sequence in association of different SN types to the star-forming regions by using several indicators of the ongoing and recent SF related to both the ionized gas and the stellar populations. While the total ongoing SF is on average the same for the three SN types, SNe Ibc/IIb tend to happen closer to star-forming regions and occur in higher SF density locations compared to SNe II and SNe~Ia, the latter showing the weakest correlation. SNe~Ia host galaxies have on average masses that are $\sim$0.3-0.8~dex higher than CC SNe hosts due to a larger fraction of old stellar populations in the SNe~Ia hosts. Using the recent SN~Ia delay-time distribution and the SFHs of the galaxies, we show that the SN~Ia hosts in our sample should presently produce a factor 2 more SNe~Ia than the CC~SN hosts. Since both types are in hosts with similar SF rate and hence similar CC~SN rate, this can explain the mass difference between the SN~Ia and CC~SN hosts, and reinforce the finding that at least part of SNe~Ia should originate from very old progenitors. Comparing the mean SFH of the eight least massive galaxies to that of the massive SF SN~Ia hosts we find that the low-mass galaxies formed their stars over more extended time than the massive SN~Ia hosts. We estimate that the low-mass galaxies should produce by a factor of 10 less SNe~Ia, and a factor of 3 less CC~SNe than the high-mass group. Therefore the ratio between the number of CC~SNe and SNe~Ia is expected to increase with decreasing the galaxy mass. CC~SNe tend to explode at positions with younger stellar populations than the galaxy average, but the galaxy properties at SNe~Ia locations are one average the same as the global ones.
• ### The peculiar extinction law of SN2014J measured with The Hubble Space Telescope(1404.2595)

The wavelength-dependence of the extinction of Type Ia SN2014J in the nearby galaxy M82 has been measured using UV to near-IR photometry obtained with the Hubble Space Telescope, the Nordic Optical Telescope, and the Mount Abu Infrared Telescope. This is the first time that the reddening of a SN Ia is characterized over the full wavelength range of $0.2$-$2$ microns. A total-to-selective extinction, $R_V\geq3.1$, is ruled out with high significance. The best fit at maximum using a Galactic type extinction law yields $R_V = 1.4\pm0.1$. The observed reddening of SN2014J is also compatible with a power-law extinction, $A_{\lambda}/A_V = \left( {\lambda}/ {\lambda_V} \right)^{p}$ as expected from multiple scattering of light, with $p=-2.1\pm0.1$. After correction for differences in reddening, SN2014J appears to be very similar to SN2011fe over the 14 broad-band filter light curves used in our study.
• ### The O3N2 and N2 abundance indicators revisited: improved calibrations based on CALIFA and Te-based literature data(1307.5316)

July 19, 2013 astro-ph.CO
The use of IFS is since recently allowing to measure the emission line fluxes of an increasingly large number of star-forming galaxies both locally and at high redshift. The main goal of this study is to review the most widely used empirical oxygen calibrations, O3N2 and N2, by using new direct abundance measurements. We pay special attention to the expected uncertainty of these calibrations as a function of the index value or abundance derived and the presence of possible systematic offsets. This is possible thanks to the analysis of the most ambitious compilation of Te-based HII regions to date. This new dataset compiles the Te-based abundances of 603 HII regions extracted from the literature but also includes new measurements from the CALIFA survey. Besides providing new and improved empirical calibrations for the gas abundance, we also present here a comparison between our revisited calibrations with a total of 3423 additional CALIFA HII complexes with abundances derived using the ONS calibration by Pilyugin et al. (2010). The combined analysis of Te-based and ONS abundances allows us to derive their most accurate calibration to date for both the O3N2 and N2 single-ratio indicators, in terms of all statistical significance, quality and coverage of the space of parameters. In particular, we infer that these indicators show shallower abundance dependencies and statistically-significant offsets compared to those of Pettini and Pagel (2004), Nagao et al. (2006) and P\'erez-Montero and Contini (2009). The O3N2 and N2 indicators can be empirically applied to derive oxygen abundances calibrations from either direct abundance determinations with random errors of 0.18 and 0.16, respectively, or from indirect ones (but based on a large amount of data) reaching an average precision of 0.08 and 0.09 dex (random) and 0.02 and 0.08 dex (systematic; compared to the direct estimations),respectively.
• ### Comparison of progenitor mass estimates for the type IIP SN 2012A(1305.5789)

May 24, 2013 astro-ph.SR
• ### High luminosity, slow ejecta and persistent carbon lines: SN 2009dc challenges thermonuclear explosion scenarios(1011.5665)

Jan. 10, 2011 astro-ph.SR
SN 2009dc shares similarities with normal Type Ia supernovae, but is clearly overluminous, with a (pseudo-bolometric) peak luminosity of log(L) = 43.47 [erg/s]. Its light curves decline slowly over half a year after maximum light, and the early-time near-IR light curves show secondary maxima, although the minima between the first and second peaks are not very pronounced. Bluer bands exhibit an enhanced fading after ~200 d, which might be caused by dust formation or an unexpectedly early IR catastrophe. The spectra of SN 2009dc are dominated by intermediate-mass elements and unburned material at early times, and by iron-group elements at late phases. Strong C II lines are present until ~2 weeks past maximum, which is unprecedented in thermonuclear SNe. The ejecta velocities are significantly lower than in normal and even subluminous SNe Ia. No signatures of CSM interaction are found in the spectra. Assuming that the light curves are powered by radioactive decay, analytic modelling suggests that SN 2009dc produced ~1.8 solar masses of 56Ni assuming the smallest possible rise time of 22 d. Together with a derived total ejecta mass of ~2.8 solar masses, this confirms that SN 2009dc is a member of the class of possible super-Chandrasekhar-mass SNe Ia similar to SNe 2003fg, 2006gz and 2007if. A study of the hosts of SN 2009dc and other superluminous SNe Ia reveals a tendency of these SNe to explode in low-mass galaxies. A low metallicity of the progenitor may therefore be an important pre-requisite for producing superluminous SNe Ia. We discuss a number of explosion scenarios, ranging from super-Chandrasekhar-mass white-dwarf progenitors over dynamical white-dwarf mergers and Type I 1/2 SNe to a core-collapse origin of the explosion. None of the models seem capable of explaining all properties of SN 2009dc, so that the true nature of this SN and its peers remains nebulous.
• ### NTT and NOT spectroscopy of SDSS-II supernovae(1011.5869)

Nov. 26, 2010 astro-ph.CO
Context. The SDSS-II Supernova Survey, conducted between 2005 and 2007, was designed to detect a large number of Type Ia supernovae (SNe Ia) around z~0.2, the redshift "gap" between low-z and high-z SN searches. The survey has provided multi-band photometric lightcurves for variable targets, and SN candidates were scheduled for spectroscopic observations, primarily to provide SN classification and accurate redshifts. We present SN spectra obtained in 2006 and 2007 using the NTT and the NOT. Aims. We provide an atlas of SN spectra in the range z =0.03-0.32 that complements the well-sampled lightcurves from SDSS-II in the forthcoming three-year SDSS SN cosmology analysis. The sample can, for example, be used for spectral studies of SNe Ia, which are critical for understanding potential systematic effects when SNe are used to determine cosmological distances. Methods. The spectra were reduced in a uniform manner, and special care was taken in estimating the uncertainties for the different processing steps. Host-galaxy light was subtracted when possible and the SN type fitted using the SuperNova IDentification code (SNID). We also present comparisons between spectral and photometric dating using SALT lightcurve fits to the photometry from SDSS-II, as well as the global distribution of our sample in terms of the lightcurve parameters: stretch and colour. Results. We report new spectroscopic data from 141 SNe Ia, mainly between -9 and +15 days from lightcurve maximum, including a few cases of multi-epoch observations. This homogeneous, host-galaxy subtracted, SN Ia spectroscopic sample is among the largest such data sets and unique in its redshift interval. The sample includes two potential SN 1991T-like SNe (SN 2006on and SN 2007ni) and one potential SN 2002cx-like SN (SN 2007ie). In addition, the new compilation includes spectra from 23 confirmed Type II and 8 Type Ib/c SNe.
• ### Near-IR search for lensed supernovae behind galaxy clusters: I. Observations and transient detection efficiency(0908.4176)

Sept. 3, 2009 astro-ph.CO
Massive galaxy clusters at intermediate redshift can magnify the flux of distant background sources by several magnitudes and we exploit this effect to search for lensed distant supernovae that may otherwise be too faint to be detected. A supernova search was conducted at near infrared wavelengths using the ISAAC instrument at the VLT. The galaxy clusters Abell 1689, Abell 1835 and AC114 were observed at multiple epochs of 2 hours of exposure time, separated by a month. Image-subtraction techniques were used to search for transient objects with light curve properties consistent with supernovae, both in our new and archival ISAAC/VLT data. The limiting magnitude of the individual epochs was estimated by adding artificial stars to the subtracted images. Most of the epochs reach 90% detection efficiency at SZ(J) ~= 23.8-24.0 mag (Vega). Two transient objects, both in archival images of Abell 1689 and AC114, were detected. The transient in AC114 coincides - within the position uncertainty - with an X-ray source and is likely to be a variable AGN at the cluster redshift. The transient in Abell 1689 was found at SZ=23.24 mag, ~0.5 arcsec away from a galaxy with photometric redshift z=0.6 +/-0.15. The light curves and the colors of the transient are consistent with a reddened Type IIP supernova at redshift z=0.59 +/- 0.05. The lensing model of Abell 1689 predicts ~1.4 mag of magnification at the position of the transient, making it the most magnified supernova ever found and only the second supernova found behind a galaxy cluster. Our pilot survey has demonstrated the feasibility to find distant gravitationally magnified supernovae behind massive galaxy clusters. One likely supernova was found behind Abell 1689, in accordance with the expectations for this survey, as shown in an accompanying analysis paper.


text:
Content of present website is being moved to www.lukoe.com/finance . Registration of www.opentradingsystem.com will be discontinued on 2020-08-14.
 I. Basic math.
 II. Pricing and Hedging.
 III. Explicit techniques.
 IV. Data Analysis.
 V. Implementation tools.
 VI. Basic Math II.
 VII. Implementation tools II.
 1 Calculational Linear Algebra.
 A. Quadratic form minimum.
 B. Method of steepest descent.
 C. Method of conjugate directions.
 D. Method of conjugate gradients.
 E. Convergence analysis of conjugate gradient method.
 F. Preconditioning.
 G. Recursive calculation.
 H. Parallel subspace preconditioner.
 2 Wavelet Analysis.
 3 Finite element method.
 4 Construction of approximation spaces.
 5 Time discretization.
 6 Variational inequalities.
 VIII. Bibliography
 Notation. Index. Contents.

Recursive calculation.

roposition

(Recursive calculation) Suppose then for any and the sequence converges to the solution of the equation

 (Recursive equation)

Proof

We subtract the relationships and obtain Hence

There following are (at least) two ways one can arrive to the equation ( Recursive equation ) starting from the equation ( Linear equation ).

Proposition

(Reduction scheme 1) Suppose a non-singular matrix has the decomposition with an invertible matrix then the solution of the equation ( Linear equation ) also satisfies the equation

Proof

We calculate

Proposition

(Reduction scheme 2) Let are two non-singular matrixes then the solution of the equation ( Linear equation ) also satisfies the equation

Proof

We calculate

For both propositions ( Reduction scheme 1 ) and ( Reduction scheme 2 ) we want to almost invert the matrix of the original problem ( Linear equation ). The same is true for the preconditioner of the section ( Preconditioning ). It appears that preconditioner the section ( Preconditioning ) may be used as a matrix of the proposition ( Reduction scheme 2 ), provided that the condition holds. The reverse statement is also true. However, the preconditioned conjugate gradient technique converges faster as the following proposition shows.

Proposition

Assume that is symmetric, is symmetric positive definite and then is symmetric positive definite, (see the formula ( Condition number ) for definition of ) and (Compare with the proposition ( Convergence of conjugate gradient method )).

Proof

First, we prove that is positive definite. Assume the contrary: there exists an eigenvector of with non positive eigenvalue . Then The term is positive by assumption of the proposition. Then we cannot have . We arrive to a contradiction.

Next, we estimate . By we have Hence Finally, we estimate . The function is increasing for . Indeed, Hence,

 Notation. Index. Contents.
 Copyright 2007

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# Radiation in space and its effects on chemical reactions?

I know that one current area of research is ways to protect astronauts from ionizing radiation when they venture out of the atmosphere of Earth, but would that same ionizing radiation be a cause of concern when performing chemical reactions in space or in the atmosphere of planets with little atmosphere?

I'm aware that radiation like ultraviolet, which is present in sunlight here on Earth, is used in organic chemistry for the homolytic fission of halides, but I'm not sure how much higher energy radiation might affect other reactions.

• Nice question and there is also Microwave chemistry and if i am correct space has background microwave radiation – Eka May 3 '15 at 16:15
• Isn't the clue in the name of the phenomenon, ionising radiation? The electromagnetic energy is strong enough to remove electrons. This would normally cause chemical changes to occur, much like in a mass spectrometer. If visible light can cleave bromine and UV can cause changes in vitamin D derivatives and stilbene to cyclise, I would anticipate ionising radiation to affect molecules much like it would chemicals in the cells in your body. – Beerhunter Aug 8 '15 at 20:48

## 1 Answer

It depends....

First let's define the "problem space".

Chemical reactions are typically driven by a few eV (electron volts). "Ionizing radiation" can be keV or MeV which is vastly excessive. In fact that amount of energy is so massive that it would "rip up" the chemical bonding in any material. Only solid metals would be somewhat stable since the 3D lattice locks the atoms into place. $\ce{NaCl}$ for example could decompose to Na metal and $\ce{Cl_2}$ gas.

Any sort of chemical reaction in space has to have a container of some sort which would mitigate the penetration of the ionizing radiation somewhat. But it surely won't stop all of the ionizing radiation. There are nuclear experiments that are conducted a mile underground to try to remove cosmic particles.

The primary source of ionizing radiation in our solar system is the sun. So more distance from the sun is your friend.

"Performing chemical reactions in space" sort of implies that a human is doing the reactions. A biological entity is going to be more effected than any vat of chemicals. So in an environment which humans or plants could safely operate, then performing chemical reactions won't be a problem.


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# Imaginary time dependent operators: (anti)commutation relations

If I know trivial (anti)commutation relation for some operators (let's say Fermi operators), I can only use it if they are in the same moment of time. If I have their time dependence and they don't have to be observed in the same moment of time, then those (anti)commutation relations are not that trivial and so I can't use them that way.

But what about imaginary time dependence (via the exponential factor)? For example, let's consider Fermi operators in Heisenberg picture, or Dirac (interaction) picture. Do they have some trivial (anti)commutation relations that can be used or not?

• You can use them in a time-ordered operator $T_\tau$.
– Jack
Aug 7, 2021 at 23:57

$$\{c_{k_1}(t_1),c^\dagger_{k_2}(t_2)\}=\delta_{k_1k_2}\delta(t_1-t_2)\tag{1}$$
$$\{c_{k_1}(\tau_1),c^\dagger_{k_2}(\tau_2)\}=\delta_{k_1k_2}\delta(\tau_1-\tau_2)\tag{2}$$


text:
Stability of the densities of invariant measures for piecewise affine expanding non-renormalizable maps
Annales de l'I.H.P. Physique théorique, Volume 66 (1997) no. 1, pp. 137-144.
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Galeeva, R. Stability of the densities of invariant measures for piecewise affine expanding non-renormalizable maps. Annales de l'I.H.P. Physique théorique, Volume 66 (1997) no. 1, pp. 137-144. http://www.numdam.org/item/AIHPA_1997__66_1_137_0/

[1] V. Baladi, S. Isola and B. Schmitt, Transfer Operator for Piecewise Affine Approximations for Interval Maps, Ann. Inst. Henri Poincaré, 62, 1995, pp. 251-256. | Numdam | MR | Zbl

[2] V. Baladi and L.-S. Young, On the Spectra of Randomly Pertubed Expanding Maps, Commun. Math. Phys., 156, 1993, pp. 355-385 | MR | Zbl

(see also erratum Comm. Math. Phys., 166, 1994, pp. 219-220). | MR

[3] R. Galeeva, M. Martens and Ch. Tresser, Inducing, Slopes and Conjugacy Classes, Preprint Stony Brook, 1994, submitted to Israel Journal of Math. | MR

[4] G. Keller, Stochastic stability in some chaotic dynamical systems, Mh. Math., 94, 1982, pp. 313-333. | MR | Zbl

[5] A. Lasota and Y. Yorke, On the existence of invariant measures for piecewise monotone transformations, Trans. Amer. math. Soc., 183, 1973, pp. 481-488. | MR | Zbl

[6] R. Mañé, Ergodic Theory and Differentiable Dynamics, vol. 8, Springer-Verlag, 1987. | MR

[7] M. Martens and Ch. Tresser, Forcing of Periodic Orbits for Interval Maps and Renormalization of Piecewise Linear Affine Maps, Preprint Stony Brook, 1994.


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# zbMATH — the first resource for mathematics

Algebraic reduction of twistor spaces of Hopf surfaces. (English) Zbl 1002.32014
Twistor theory provides a rich supply of compact complex 3-manifolds. Even if $$S$$ is a conformally flat compact 4-manifold, its associated twistor space can have a rich function theory. Consider, for example, Hopf surfaces $$S(\alpha_1,\alpha_2)$$ obtained as the quotient of $${\mathbb C}^2\setminus\{0\}$$ by $$(z_1,z_2)\mapsto(\alpha_1 z_1,\alpha_2 z_2)$$ for $$\alpha_i\in{\mathbb C}$$ with $$|\alpha_1|=|\alpha_2|>1$$. For generic parameters $$\alpha_i$$, the corresponding twistor space $$Z=Z(\alpha_1,\alpha_2)$$ has no meromorphic functions but for special values, it can have algebraic dimension $$1$$ or $$2$$. In case $$Z$$ has algebraic dimension 1, there is a meromorphic mapping $$f:Z\to Y$$ onto a nonsingular curve $$Y$$. In this case, the author identifies the fibres as either Hopf surfaces or as having normalisation a nonsingular ruled surface of genus one.

##### MSC:
 32J17 Compact complex $$3$$-folds 32L25 Twistor theory, double fibrations (complex-analytic aspects) 14J30 $$3$$-folds
##### Keywords:
Hopf surface; twistor space; algebraic reduction


text:
Scout YYF II

Time Limit: 1000MS

Memory Limit: 65536K

Description

After the dangerous "mine road", YYF has finally enter the enemy's base, which is a round glass building. However, this is totally a trap! There are no enemy in the base but bombs instead. Some time after YYF enter the base, the enemy's detectors find him and ignite the bomb system to kill him. As a professional scout, YYF feels the bomb and choose a best direction to run. When a bomb explodes, it will destroy a circle area including the boundary which becomes larger and larger. YYF runs very fast in the same speed as the radius of bomb area grows. If he can run out of the base before the explosions destroy him, he will be safe after that. Now you are given the YYF's and bombs' initial places, please calculate that if our couragous scout can possibly save himself.

Input

The input contains many test cases ended with EOF. The first line of each test case is N (1 ≤ N ≤ 10) and R (1 ≤ R ≤ 1000), standing for the number of bombs and the radius of the base. The center of the base is always at (0,0). The second line of each test case is two real numbers standing for the initial place of YYF. In the next N lines, each contains two real numbers standing for the initial place of a bomb. It is guaranteed that all the initial places is in the base.

Output

For each test case, if YYF can escape safely, output "Yes" in a single line, otherwise "No" instead.

Sample Input

2 10
0 0
1 0
-1 0
4 10
0 0
1 0
-1 0
0 1
0 -1

Sample Output

Yes
No

Source

POJ Monthly Contest - 2009.08.23, Simon


text:
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# How to Use Conditional Formatting in Microsoft Excel

Formatting is a must, but conditional formatting is even more powerful. Conditional formatting changes how a cell appears, based upon what's inside the cell.

In the screenshot above, you can see the power of conditional formatting. I've setup a very basic rule that turns the background of a cell with a positive value green, while a negative value will turn red.The only thing that changes is the background color based on the value.

Other examples of conditional formatting could include:

• Putting all negative numbers in a list of data in red.
• Creating data bars to give a visual representation of the largest and smallest items in your data set.
• Using icons to indicate the highest and lowest values in a list of data.

When you write conditional formatting, the formatting adjusts to what's in the cell. In this tutorial, you'll find out how easy it is to use conditional formatting in Excel.

## How to Apply Conditional Formatting in Excel (Watch & Learn)

In this video, I'll walk you through some of the easiest ways to apply conditional formatting. You'll get an over-the-shoulder look at how I use conditional formatting in Excel to highlight important data.

## 1. Using Built-in Conditional Formatting

Spreadsheets can be overwhelming at times. The good news is that conditional formatting in Excel is easy to get started with thanks to Excel's built-in styles.

We're going to take a look at Excel's built-in styles for conditional formatting. For each of these styles, you can apply them by highlighting the list of data you want to format, and then finding the Conditional Formatting button on the Home tab of the ribbon.

Once you've opened the Excel conditional formatting menu, choose one of the options to begin applying conditional formatting.

### Highlight Cells

Choosing the highlight cells option allows you to conditionally format cells on a variety of factors. Click on Conditional Formatting and choose one of the options from the Highlight Cells Rules menu to get started with conditional formatting.

Think of these options as presets for conditional formatting. Here's how each work:

• Greater Than - Format cells greater than a value that you set.
• Less Than -  Format cells lower than a value you set.
• Between - Give conditional formatting to a range of values, and highlight cells between those values.
• Equal To - Format a cell when it is exactly equal to a value you set.
• Text that Contains - Format cells that contain strings of text.
• A Date Occurring - Conditional formatting based upon the date in a cell.
• Duplicate Values - Quick conditional formats for a list of data with duplicates.

Let's look at an example. I'll choose Greater Than for my example. Then, I'll set a value in the pop up window. In the screenshot below, I set my value to be $22,000, and used the "Green fill..." option. As you can see, Excel applied conditional formatting in the preview, and all values greater than$22,000 were highlighted in green.

This menu is a great way to customize your conditional formatting rules. You can easily build rules for how to format your cells by starting with the "Highlight Cells" option.

### Apply Top/Bottom Rules

Another great way to set Excel conditional formatting is with the Top/Bottom Rules option. You can easily choose to highlight the top and bottom 10 items in a list, or apply another option.

Click on the Conditional Formatting option, choose the Top/Bottom Rules panel, and then choose one of the formatting options shown.

In my case, I'll choose the Above Average option to highlight all of the sales amounts that are above the average in the set.

The pop up window is very similar to the prior example, and we'll select Green Fill... from the dropdown.

Notice in the screenshot above that Excel automatically highlights in green any of the cells in green.

## 2. Use Built-In Styles in Excel

The options we've looked at so far require giving Excel some rules. If you want the fastest way to add conditional formatting, try out some of the options below.

### Work With Data Bars

One of the quickest ways to add meaning to your spreadsheet is to choose the data bars option. Data bars will place bars inside of cells that represent the "size" of the data in your list.

To apply a data bar conditional format, highlight your data first. Then, find the Data Bars option and choose from one of the gradient or solid fill options.

The screenshot below shows the power of data bars to illustrate data. In the January 2017 column, the green gradient bars correspond in length to the amount. The lowest amounts have the shortest bars, while higher amounts have longer bars.

Data bars are a great illustration of the power of conditional formatting in Excel. Notice how much easier it is to find the largest amounts than the February column, just by scanning the lengths of the bars.

### Apply Color Scales

Color scales really draw attention to the highest and lowest values in a list of data. After you've highlighted your data, return to the Conditional Formatting option, and choose one of the options from the Color Scales menu.

The color scales in the thumbnails represent the colors that will be applied to your data. I'll choose the first icon in the list, and you can check out the results below:

In the example above, the best sales result has a dark green background, while the lowest value is in red. All of the other values are in shades of yellow and green, to represent the salesperson's performance.

The color scales option has a variety of Excel conditional formatting rules. Try out several of the other thumbnails to apply other colors to your data.

Icon sets are another great way to add some extra style to your spreadsheet. In my example, I'm going to highlight my data, and choose some arrows from the conditional formatting options.

The icon sets include arrows to show changes in data, as well as other icons like flags and bars to show data right inside of the cell.

In the data below, I have a percent change column to show how the salesperson performed versus the prior month. This is a great way to visually represent your data.

All of these conditional formats adapt when the data changes. If the sales figures changed, Excel would automatically change the icon accordingly.

Usually, I start with one of the built-in styles and modify it to my liking. It's much easier to use a built in conditional formatting option and tweak it, instead of writing your own from scratch.

## Recap and Keep Learning

This tutorial covered Excel conditional formatting. You learned how to add styles to your cells that change dynamically based upon what's inside of the cell.

Here's the thing: using formatting makes your spreadsheets easier to read. But using conditional formatting in Excel helps you add insight directly to your cells. It allows you to glance through your data and understand it rapidly.


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Two dices are rolled. If both dices
Question:

Two dices are rolled. If both dices have six faces numbered $1,2,3,5,7$ and 11 , then the probability that the sum of the numbers on the top faces is less than or equal to 8 is :

1. (1) $\frac{4}{9}$

2. (2) $\frac{17}{36}$

3. (3) $\frac{5}{12}$

4. (4) $\frac{1}{2}$

Correct Option: , 2

Solution:

$n(E)=5+4+4+3+1=17$

So, $P(E)=\frac{17}{36}$


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# Profit Maximization problem in linear programming where orderring new raw materials is allowed

My problem is this:

A factory manufactures two types of jewels.

Each one of them consists of gold and two
kinds of
gems- diamonds and pearls.

Every unit of jewel No. 1 consists of 3
diamonds, 5 pearls and 0.3 grams of gold. A
unit of Jewel NO. 1 is sold by the price of
200$, and its demand is 10. Every unit of jewel No. 2 consists of 1 diamond, 1 pearl and 0.1 grams of gold. A unit of Jewel NO. 2 is sold by the price of 70$, and its demand is 17.

It takes 15 minutes to set one gem ( Diamond
or pearl ) on a jewel( 1 or 2 ), and it
takes 20 minutes to polish a jewel.

The factory has a total of 80 diamonds, 120
pearls, 30 grams of gold, 400 Working
hours, and has an option of
purchasing extra gems in the price of 30$$per a diamond, and 20$$ per a pearl.

Model this problem in terms of linear
programming

Now, without extra gems, this would have been my solution( Where x1 and x2 are the amounts of jewel 1 and jewel 2 to be manufactured ):

Max{200x1+70x2}

s.t

3x1+x2<=80

5x1+x2<=120

[15*(3+5)+20]x1<=400*60
[15*(1+1)+20]x2<=400*60

0.3x1+0.1x2<=30

x1<=10
x<=17

My issue is I can't really figure out how to combine the extra gems part into the constraints. Can sombody give a piece of advice?

Even without the extra gems, your formulation needs some correction. Where you have a pair of constraints (one for $$x_1$$ and one for $$x_2$$), you should instead have a single constraint (involving both $$x_1$$ and $$x_2$$) for the shared resource. Also, the demands should impose upper bounds (rather than lower bounds) on $$x_i$$, because you cannot sell more than the demand.
For the extra gems, introduce two more decision variables, say $$d$$ and $$p$$, for the number of extra diamonds and pearls, respectively. Then include $$-30d-20p$$ in the objective function. And modify the corrected resource constraints. For example, the corrected diamond constraint $$3x_1+x_2 \le 80$$ becomes instead $$3x_1+x_2 \le 80+d$$.


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1. Mar 12, 2009

quasar987

(1) For a continuous map f:S^n-->S^n, the induced map in top homology is, up to identification of H_n(S^n) with Z, just multiplication by an integer, and this integer is defined as the degree of f. (in Hatcher: http://www.math.cornell.edu/~hatcher/AT/ATpage.html)

Now, in the event that f is a homeomorphism, it follows from the elementary properties of the degree that deg(f)=±1. After this remark, Hatcher adds that in applications, it is usually not hard to determine which it is between +1 and -1.

Can someone give an example illustrating how one decides between +1 and -1?

(2) How to see why the above definition of degree coincide with the one in terms of preimage of regular value in the case of a differentiable f?

Thanks.

2. Mar 21, 2009

wofsy

Give the sphere an orientation. A smooth homeomorphism that preserves orientation will have degree one. If it reverses orientation it will have degree minus one. This you can tell from the determinant of the Jacobian at any point where the Jacobian has maximal rank.

If the map is not differentiable but only continuous it may be difficult to tell.
In general you need to follow the fundamental cycle,C, as it is mapped into the sphere
to the cycle, f(C), and decide whether C-f(C) is a boundary.

If two differentiable maps are homotopic then they have the same degree. This is always true.

But for spheres the converse is also true. It two maps from a manifold into a sphere have the same degree then they are homotopic.

Good examples of maps of arbitrary positive degree on S^2 are complex polynomials on the Riemann sphere.

Last edited: Mar 21, 2009


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# zbMATH — the first resource for mathematics

## Gualdani, Maria Pia

Compute Distance To:
 Author ID: gualdani.maria-pia Published as: Gualdani, Maria Pia; Gualdani, Maria; Gualdani, M. P.; Gualdani, Maria P.; Gualdini, Maria Pia; Gualdani, M. Homepage: https://web.ma.utexas.edu/users/gualdani/ External Links: MGP · Google Scholar · ResearchGate · dblp
 Documents Indexed: 27 Publications since 2003
all top 5

#### Co-Authors

 2 single-authored 7 González, María del Mar 6 Zamponi, Nicola 4 Carrillo de la Plata, José Antonio 4 Martínez Gamba, Irene 3 Jüngel, Ansgar 2 Daus, Esther S. 2 Guillen, Nestor 2 Mouhot, Clément 2 Sparber, Christof 2 Toscani, Giuseppe 1 Arnold, Anton 1 Caffarelli, Luis Ángel 1 Chayes, Lincoln 1 Di Francesco, Marco 1 Kim, Inwon Christina 1 Mischler, Stéphane 1 Schonbek, Maria Elena 1 Shahgholian, Henrik 1 Sharp, Richard W. 1 Solà-Morales, Joan 1 Xu, Jingjing 1 Zhang, Ping 1 Zhang, Xinyu
all top 5

#### Serials

 3 SIAM Journal on Mathematical Analysis 2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2 Acta Applicandae Mathematicae 2 Communications in Partial Differential Equations 2 Communications in Mathematical Sciences 1 Applied Mathematics and Optimization 1 Journal of Differential Equations 1 Monatshefte für Mathematik 1 Applied Mathematics Letters 1 Publicacions Matemàtiques 1 European Journal of Applied Mathematics 1 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 1 Mémoires de la Société Mathématique de France. Nouvelle Série 1 Calculus of Variations and Partial Differential Equations 1 Bulletin des Sciences Mathématiques 1 Bollettino della Unione Matematica Italiana. Serie VIII. Sezione B. Articoli di Ricerca Matematica 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Kinetic and Related Models 1 Analysis & PDE
all top 5

#### Fields

 26 Partial differential equations (35-XX) 7 Fluid mechanics (76-XX) 7 Statistical mechanics, structure of matter (82-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Operator theory (47-XX) 2 Numerical analysis (65-XX) 2 Mechanics of deformable solids (74-XX) 1 Real functions (26-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Functional analysis (46-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Quantum theory (81-XX)

#### Citations contained in zbMATH Open

22 Publications have been cited 205 times in 165 Documents Cited by Year
Factorization of non-symmetric operators and exponential $$H$$-theorem. Zbl 06889665
Gualdani, M. P.; Mouhot, C.
2017
Analysis of the viscous quantum hydrodynamic equations for semiconductors. Zbl 1076.82049
Gualdini, Maria Pia; Jüngel, Ansgar
2004
Classical solutions for a nonlinear Fokker-Planck equation arising in computational neuroscience. Zbl 1282.35382
Carrillo, José A.; González, María D. M.; Gualdani, Maria P.; Schonbek, Maria E.
2013
Exponential decay in time of solutions of the viscous quantum hydrodynamic equations. Zbl 1042.82047
Gualdani, M. P.; Jüngel, A.; Toscani, G.
2003
Finite speed of propagation in porous media by mass transportation methods. Zbl 1049.35110
Carrillo, José Antonio; Gualdani, Maria Pia; Toscani, Giuseppe
2004
Global existence and uniqueness of solutions to a model of price formation. Zbl 1228.35007
Chayes, Lincoln; Del Mar González, María; Gualdani, Maria Pia; Kim, Inwon
2009
Estimates for radial solutions of the homogeneous Landau equation with Coulomb potential. Zbl 1378.35325
Gualdani, Maria; Guillen, Nestor
2016
A nonlinear fourth-order parabolic equation with nonhomogeneous boundary conditions. Zbl 1102.35045
Gualdani, Maria Pia
2006
On the blowing up of solutions to quantum hydrodynamic models on bounded domains. Zbl 1173.35106
Gamba, Irene M.; Gualdani, Maria Pia; Zhang, Ping
2009
Asymptotics for a free boundary model in price formation. Zbl 1215.35173
González, María del Mar; Gualdani, Maria Pia
2011
The Wigner-Fokker-Planck equation: stationary states and large time behavior. Zbl 1253.82065
Arnold, Anton; Gamba, Irene M.; Gualdani, Maria Pia; Mischler, Stéphane; Mouhot, Clement; Sparber, Christof
2012
Asymptotics for a symmetric equation in price formation. Zbl 1175.91067
González, María del Mar; Gualdani, Maria Pia
2009
An adaptable discontinuous Galerkin scheme for the Wigner-Fokker-Planck equation. Zbl 1185.65180
Gamba, Irene M.; Gualdani, Maria Pia; Sharp, Richard W.
2009
On $$A_p$$ weights and the Landau equation. Zbl 1404.35078
Gualdani, Maria; Guillen, Nestor
2019
Convergence of an entropic semi-discretization for nonlinear Fokker-Planck equations in $$\mathbb R^d$$. Zbl 1152.35317
Carrillo, J. A.; Gualdani, M. P.; Jüngel, A.
2008
Semidiscretization and long-time asymptotics of nonlinear diffusion equations. Zbl 1145.35028
Carrillo, José A.; di Francesco, Marco; Gualdani, Maria P.
2007
A note on the time decay of solutions for the linearized Wigner-Poisson system. Zbl 1180.35435
Gamba, Irene M.; Gualdani, Maria Pia; Sparber, Christof
2009
A discrete Bernoulli free boundary problem. Zbl 1333.35352
del Mar Gonzalez, M.; Gualdani, M.; Shahgholian, H.
2014
Longtime behavior and weak-strong uniqueness for a nonlocal porous media equation. Zbl 1427.35113
Daus, Esther S.; Gualdani, Maria; Zamponi, Nicola
2020
Some non-standard Sobolev spaces, interpolation and its application to PDE. Zbl 1257.35108
González, María del Mar; Gualdani, Maria Pia
2012
Instability and bifurcation in a trend depending price formation model. Zbl 1345.35141
González, María del Mar; Gualdani, Maria Pia; Solà-Morales, Joan
2016
Existence of weak solutions to a continuity equation with space time nonlocal Darcy law. Zbl 1459.35233
Caffarelli, Luis; Gualdani, Maria; Zamponi, Nicola
2020
Longtime behavior and weak-strong uniqueness for a nonlocal porous media equation. Zbl 1427.35113
Daus, Esther S.; Gualdani, Maria; Zamponi, Nicola
2020
Existence of weak solutions to a continuity equation with space time nonlocal Darcy law. Zbl 1459.35233
Caffarelli, Luis; Gualdani, Maria; Zamponi, Nicola
2020
On $$A_p$$ weights and the Landau equation. Zbl 1404.35078
Gualdani, Maria; Guillen, Nestor
2019
Factorization of non-symmetric operators and exponential $$H$$-theorem. Zbl 06889665
Gualdani, M. P.; Mouhot, C.
2017
Estimates for radial solutions of the homogeneous Landau equation with Coulomb potential. Zbl 1378.35325
Gualdani, Maria; Guillen, Nestor
2016
Instability and bifurcation in a trend depending price formation model. Zbl 1345.35141
González, María del Mar; Gualdani, Maria Pia; Solà-Morales, Joan
2016
A discrete Bernoulli free boundary problem. Zbl 1333.35352
del Mar Gonzalez, M.; Gualdani, M.; Shahgholian, H.
2014
Classical solutions for a nonlinear Fokker-Planck equation arising in computational neuroscience. Zbl 1282.35382
Carrillo, José A.; González, María D. M.; Gualdani, Maria P.; Schonbek, Maria E.
2013
The Wigner-Fokker-Planck equation: stationary states and large time behavior. Zbl 1253.82065
Arnold, Anton; Gamba, Irene M.; Gualdani, Maria Pia; Mischler, Stéphane; Mouhot, Clement; Sparber, Christof
2012
Some non-standard Sobolev spaces, interpolation and its application to PDE. Zbl 1257.35108
González, María del Mar; Gualdani, Maria Pia
2012
Asymptotics for a free boundary model in price formation. Zbl 1215.35173
González, María del Mar; Gualdani, Maria Pia
2011
Global existence and uniqueness of solutions to a model of price formation. Zbl 1228.35007
Chayes, Lincoln; Del Mar González, María; Gualdani, Maria Pia; Kim, Inwon
2009
On the blowing up of solutions to quantum hydrodynamic models on bounded domains. Zbl 1173.35106
Gamba, Irene M.; Gualdani, Maria Pia; Zhang, Ping
2009
Asymptotics for a symmetric equation in price formation. Zbl 1175.91067
González, María del Mar; Gualdani, Maria Pia
2009
An adaptable discontinuous Galerkin scheme for the Wigner-Fokker-Planck equation. Zbl 1185.65180
Gamba, Irene M.; Gualdani, Maria Pia; Sharp, Richard W.
2009
A note on the time decay of solutions for the linearized Wigner-Poisson system. Zbl 1180.35435
Gamba, Irene M.; Gualdani, Maria Pia; Sparber, Christof
2009
Convergence of an entropic semi-discretization for nonlinear Fokker-Planck equations in $$\mathbb R^d$$. Zbl 1152.35317
Carrillo, J. A.; Gualdani, M. P.; Jüngel, A.
2008
Semidiscretization and long-time asymptotics of nonlinear diffusion equations. Zbl 1145.35028
Carrillo, José A.; di Francesco, Marco; Gualdani, Maria P.
2007
A nonlinear fourth-order parabolic equation with nonhomogeneous boundary conditions. Zbl 1102.35045
Gualdani, Maria Pia
2006
Analysis of the viscous quantum hydrodynamic equations for semiconductors. Zbl 1076.82049
Gualdini, Maria Pia; Jüngel, Ansgar
2004
Finite speed of propagation in porous media by mass transportation methods. Zbl 1049.35110
Carrillo, José Antonio; Gualdani, Maria Pia; Toscani, Giuseppe
2004
Exponential decay in time of solutions of the viscous quantum hydrodynamic equations. Zbl 1042.82047
Gualdani, M. P.; Jüngel, A.; Toscani, G.
2003
all top 5

#### Cited by 228 Authors

 11 Gualdani, Maria Pia 9 Carrillo de la Plata, José Antonio 7 Mischler, Stéphane 6 Cáceres, María-José 6 López, José Luis 5 Carrapatoso, Kleber 5 Chen, Li 5 Dong, Jianwei 5 Dreher, Michael 5 González, María del Mar 4 Caffarelli, Luis Ángel 4 Guo, Boling 4 Jüngel, Ansgar 4 Markowich, Peter Alexander 4 Tanré, Etienne 4 Tristani, Isabelle 4 Wang, Guangwu 4 Wu, Kung-Chien 4 Yang, Jianwei 4 Zamponi, Nicola 3 Cañizo, José Alfredo 3 Chen, Xiuqing 3 Delarue, François 3 Duan, Renjun 3 Dumont, Grégory 3 Inglis, James D. 3 Lods, Bertrand 3 Perthame, Benoît 3 Schneider, Ricarda 3 Toscani, Giuseppe 3 Wagner, Wolfgang 3 Wolfram, Marie-Therese 3 Zhu, Junhui 2 Alonso, Ricardo J. 2 Bagland, Véronique 2 Briant, Marc 2 Burger, Martin 2 Ciraolo, Giulio 2 Di Francesco, Marco 2 Evans, Josephine 2 Martínez Gamba, Irene 2 Henry, Jacques 2 Hwang, Hyung Ju 2 Imbert, Cyril 2 Jang, Jin Woo 2 Ju, Qiangchang 2 Lafleche, Laurent 2 Lattanzio, Corrado 2 Ledger, Sean 2 Li, Fucai 2 Liang, Bo 2 Lin, Yu-Chu 2 Lou, Guangpu 2 Magnanini, Rolando 2 Matthes, Daniel 2 Montejo-Gámez, Jesús 2 Mouhot, Clément 2 Muscato, Orazio 2 Nieto, Juanjo 2 Osberger, Horst 2 Pietschmann, Jan-Frederik 2 Rubenthaler, Sylvain 2 Salort, Delphine 2 Schnur, Johannes 2 Shahgholian, Henrik 2 Silvestre, Luis E. 2 Snelson, Stanley 2 Søjmark, Andreas 2 Soler, Juan S. 2 Strain, Robert M. 2 Sun, Baoyan 2 Tang, Tong 2 Tarniceriu, Carmen Oana 2 Wang, Yong 2 Yang, Tong 2 Yang, Yong 2 Zhao, Huijiang 1 Abdallah, Mohamed Ahmed 1 Abedin, Farhan 1 Amster, Pablo 1 Antonelli, Paolo 1 Arnold, Anton 1 Bae, Hantaek 1 Balagué, Daniel 1 Bansil, Mohit 1 Bouin, Emeric 1 Calvez, Vincent 1 Cao, Chuqi 1 Cao, Yunbai 1 Carnevale, Giada Cianfarani 1 Chen, Jingrun 1 Cheng, Ming 1 Chevallier, Julien 1 Choi, Young-Pil 1 Cont, Rama 1 Cormier, Quentin 1 Daus, Esther S. 1 Deng, Chubo 1 Desvillettes, Laurent 1 Di Michele, Federica ...and 128 more Authors
all top 5

#### Cited in 75 Serials

 10 Kinetic and Related Models 9 Archive for Rational Mechanics and Analysis 8 SIAM Journal on Mathematical Analysis 7 Journal of Differential Equations 6 Journal of Mathematical Analysis and Applications 6 Journal of Statistical Physics 6 Communications in Partial Differential Equations 5 Acta Applicandae Mathematicae 4 Journal of Mathematical Physics 4 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 4 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 4 Multiscale Modeling & Simulation 3 Communications in Mathematical Physics 3 Mathematical Methods in the Applied Sciences 3 Monatshefte für Mathematik 3 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 3 Acta Mathematicae Applicatae Sinica. English Series 3 Journal de Mathématiques Pures et Appliquées. Neuvième Série 3 Discrete and Continuous Dynamical Systems 3 Comptes Rendus. Mathématique. Académie des Sciences, Paris 3 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 2 Applicable Analysis 2 Journal of Computational Physics 2 Proceedings of the American Mathematical Society 2 Quarterly of Applied Mathematics 2 Physica D 2 Applied Numerical Mathematics 2 The Annals of Applied Probability 2 Stochastic Processes and their Applications 2 NoDEA. Nonlinear Differential Equations and Applications 2 Bulletin des Sciences Mathématiques 2 Journal de l’École Polytechnique – Mathématiques 1 Inverse Problems 1 Journal d’Analyse Mathématique 1 Journal of Mathematical Biology 1 Nonlinearity 1 Theoretical and Mathematical Physics 1 Advances in Mathematics 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Applied Mathematics and Computation 1 Applied Mathematics and Optimization 1 Archiv der Mathematik 1 Bulletin of the London Mathematical Society 1 Indiana University Mathematics Journal 1 Journal of Functional Analysis 1 Manuscripta Mathematica 1 Chinese Annals of Mathematics. Series B 1 International Journal of Mathematics 1 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni 1 Journal of Dynamics and Differential Equations 1 Journal of Nonlinear Science 1 SIAM Journal on Scientific Computing 1 Calculus of Variations and Partial Differential Equations 1 St. Petersburg Mathematical Journal 1 Computational and Applied Mathematics 1 Electronic Journal of Probability 1 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 International Journal of Theoretical and Applied Finance 1 Acta Mathematica Sinica. English Series 1 Nonlinear Analysis. Real World Applications 1 Journal of Evolution Equations 1 Foundations of Computational Mathematics 1 Complex Variables and Elliptic Equations 1 Frontiers of Mathematics in China 1 Mathematical Modelling of Natural Phenomena 1 SIAM Journal on Financial Mathematics 1 The Journal of Mathematical Neuroscience 1 Journal of Theoretical Biology 1 Stochastic and Partial Differential Equations. Analysis and Computations 1 Nanoscale Systems: Mathematical Modeling, Theory and Applications 1 EMS Surveys in Mathematical Sciences 1 Annals of PDE 1 Séminaire Laurent Schwartz. EDP et Applications 1 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings and Surveys 1 Annales Henri Lebesgue
all top 5

#### Cited in 23 Fields

 139 Partial differential equations (35-XX) 61 Statistical mechanics, structure of matter (82-XX) 44 Fluid mechanics (76-XX) 18 Biology and other natural sciences (92-XX) 17 Operator theory (47-XX) 15 Probability theory and stochastic processes (60-XX) 13 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 12 Numerical analysis (65-XX) 10 Quantum theory (81-XX) 8 Ordinary differential equations (34-XX) 6 Integral equations (45-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 3 Mechanics of deformable solids (74-XX) 3 Optics, electromagnetic theory (78-XX) 3 Operations research, mathematical programming (90-XX) 2 General and overarching topics; collections (00-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Global analysis, analysis on manifolds (58-XX) 1 Combinatorics (05-XX) 1 Real functions (26-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Functional analysis (46-XX) 1 Relativity and gravitational theory (83-XX)


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Regular version of the site

## Any component of moduli of polarized hyperkähler manifolds is dense in its deformation space

Journal de Mathématiques Pures et Appliquées. 2014. Vol. 101. No. 2. P. 188-197.
Ananʼin S., Verbitsky M.
Let M be a compact hyperkähler manifold, and W the coarse moduli of complex deformations of M. Every positive integer class v in H^2(M) defines a divisor Dv in W consisting of all algebraic manifolds polarized by v. We prove that every connected component of this divisor is dense in W.


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# Correspondence between $O(n)$-instantons on $S^4$ and holomorphic bundles over $\mathbb{P}^3$

Theorem 2.9 on page 49 of Atiyah's Geometry of Yang-Mills Fields states that there is a natural correspondence between $U(n)$-instantons on $S^4$ and holomorphic vector bundles of rank $n$ over $\mathbb{P}^3$ with a positive real form (essentially a hermitian inner product compatible with the real structure on $\mathbb{P}^3$). A key result used to associate a holomorphic bundle to an instanton is Theorem 1.2 on page 46 which asserts that on an hermitian vector bundle $E$ equipped with a metric connection $\nabla$ over a complex manifold there is a unique holomorphic structure on E such that $\nabla$ is the Chern connection of $E$. This theorem is used on the lifted bundle with lifted metric and connection (the lift is given by pullback with the twistor fibration map).

Atiyah says that Theorem 2.9 "can easily be generalized to the orthogonal and symplectic case". I can't see how to go from instanton to holomorphic bundle in the orthogonal case if Theorem 1.2 doesn't apply (the lifted bundle will have a quadratic form, not a hermitian form).

Thoughts?

• This is explained in more detail here (remark 3 on p.332). In the $O(n)$ case you can take the complexification of the standard representation on $R^n$. This gives an hermitian vector bundle of rank $n$ on $S^4$, to which you can apply Theorem 2.9. – Gil Bor Feb 8 '18 at 19:50


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Any way to strengthen font weight/darkness/heaviness?

I use TeTeX with fairly basic packages:

\usepackage [koi8-r] {inputenc}
\usepackage [russian] {babel}
\usepackage {cmap}
\usepackage {amssymb}
\usepackage {verbatim}
\usepackage {titlesec}
\usepackage {courier}
\usepackage {pscyr}
\usepackage {amsmath}

The default font family is rmdefault. Font witdth and height and the bold font are perfect, but the strokes of the regular text and formulas fonts are too thin, so the printed document is uncomfortable to read. Is there a way to fix this?

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Out of interest, why do you use teTeX, rather than an up to date distribution? –  Ian Thompson Aug 29 '13 at 20:47
I use FreeBSD, there is still no binary packets of LiveTeX. LiveTeX can be compiled manually without problems, but i couldn't install decent cyrillic fonts like pscyr. On the other hand TeTeX runs out of the box and there is pscyr package. So far tetex does what i need. But i know that it is extremely outdated. –  Ordev Agens Aug 30 '13 at 18:42

Unfortunately, Computer Modern (and its derivatives) are thin, since Dr. Knuth measured actual physical matrices rather than printed samples, and modern printing techniques don't get the increase in weight caused by ink gain and impression which the hot metal Monotype Modern 8a was designed for.

There are some options in the METAFONT source for controlling the heaviness, but these aren't available when using CM-Super or Latin Modern, or a Type 1 version of Computer Modern. See Latin Modern vs cm-super? for a discussion of the differences between Latin Modern and CM-Super (which you're using).

For actual printing, you could set the MF options and generate new bitmaps to use (as a Type 3 bitmap font), but that's an awkward solution. Some computer display systems allow one to configure the settings for type display on an LCD and one can bias them to result in heavier fonts, but that's a rather extreme solution.

Computer Modern's Typewriter font is much heavier than Courier though, so I find it odd that you're explicitly choosing to use the latter.

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Thank you very much for your reply. Courier is included for using Listings package. It doesn't affect regular text. I tried to use package times and lmodern. But it didn't change anything. –  Ordev Agens Aug 30 '13 at 18:51
Latin Modern should have pretty much the same appearance as Computer Modern --- it was designed to be a drop-in replacement. Odd that times didn't have a marked change. If you're willing to change fonts, have you tried \usepackage{mathptmx}? Or see if there's some other option you like here on Will Robertson's nifty page: tug.org/mactex/fonts/LaTeX_Preamble-Font_Choices.html –  WillAdams Aug 30 '13 at 18:55
This helped, thank you so much. Math font is stronger now. Cheers. –  Ordev Agens Aug 30 '13 at 22:41
After googling some more I did the following: \renewcommand{\rmdefault}{ftm} and \boldmath. Text still could be better a bit stronger, but math is astonishing. –  Ordev Agens Aug 31 '13 at 8:02


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# Laplace Transform and Fourier Transform of a function

I have this transfer function: $$h(t)= -\frac{1}{16}te^{-2t}$$ and the Laplace Transform is: $$H(s) = \frac{-\frac{1}{16}}{(s+2)^{2}}$$ I know that to find the Fourier Transform, I would just replace s with jw $$H(j\omega) = \frac{-\frac{1}{16}}{(j\omega+2)^{2}}$$ But, the Fourier Transform table says: $$tf(t) \Leftrightarrow j\frac{d}{d\omega}\hat{f}(\omega)$$ And the Fourier transform of $$e^{-2t} \Leftrightarrow \frac{1}{j\omega + 2}$$

$$-\frac{1}{16}te^{-2t} \Leftrightarrow \frac{j\frac{1}{16}}{(j\omega + 2)^{2}}$$

So, the final answer is not the same as $H(j\omega)$!

Do you see any thing wrong here? Please guide me!

When you differentiate, there is another $j$ in the numerator giving $j^2$.
Also, your $h(t)$ should be $$h(t)= -\frac{1}{16}te^{-2t} ~{\mathbf u(t)}$$


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# Tag Info

15

I think that one of your problems is that (as you observed in your comments) Neumann conditions are not the conditions you are looking for, in the sense that they do not imply the conservation of your quantity. To find the correct condition, rewrite your PDE as $$\frac{\partial \phi}{\partial t} = \frac{\partial}{\partial x}\left( D\frac{\partial \phi}{\... 15 This is a well-framed question and a very useful thing to understand. Korrok is correct to refer you to von Neumann analysis and LeVeque's book. I can add a bit more to that. I'd like to write a detailed answer, but at the moment I only have time for a short one: With \alpha=\beta=1/2, you get a method that is absolutely stable for arbitrarily large ... 10 Generally speaking, you'll want to use an implicit method for parabolic equations (the diffusion part) -- explicit schemes for parabolic PDE need to have a very short timestep to be stable. Conversely, for the hyperbolic part (advection) you'll want an explicit method as it's cheaper and doesn't disrupt the symmetry of the linear system you have to solve by ... 8 Solving partial differential equations with explicit timestepping methods relies on meeting a certain CFL condition for stability. Since you are using a forward Euler timestepping scheme, you must ensure that your timestep is small enough compared to the grid spacing. In the case of the heat equation (Fick's 2nd law is a heat equation), your CFL number C ... 8 It's easy to derive that equation from Fick's law. You have this diffusion equation as:$$\frac{\partial C}{\partial t} = D \nabla^{2} C$$The mean square displacement weighted by the concentration profile is defined as:$$\langle r^{2}(t) \rangle = \int_{\Omega} |\vec{r}|^{2} C(\vec{r},t) d^{3} \vec{r}$$The time-evolution of this mean square ... 5 I think it might be ill-posed, since the time-dependent parts are linearly dependent. If you add your two time-dependent equations together, you get a time-independent equation: (\alpha(x)u_x)_x + (\beta(x) v_x)_x = 0. Do your initial conditions satisfy this equation? 5 This is possible (see [1]) but uncommon, as it requires Monte Carlo moves that alter the current conformations by a very small perturbation. In that setting of "small" Metropolis MC moves, it is usually easier (both in theory and in practice) to just use Molecular Dynamics instead. [1] Kikuchi, K., Yoshida, M., Maekawa, T., & Watanabe, H. (1991). ... 5 It is in some cases possible to map the dynamics obtained in MC simulations to other (more realistic) dynamics, especially for the case of dense colloidal suspensions. The following two papers talk about the problems and caveats of performing such a mapping: http://aip.scitation.org/doi/10.1063/1.3414827 (spherical particles) http://aip.scitation.org/doi/10.... 5 First off, the PDE can be rewritten instead as$$\frac{\partial C}{\partial t} = \frac{\partial}{\partial x}C\frac{\partial C}{\partial x}$$or, by applying the product rule in reverse again, as$$\frac{\partial C}{\partial t} = \frac{1}{2}\frac{\partial^2}{\partial x^2}C^2.$$This equation is often referred to as the porous medium equation or the slow ... 5 Yes, the problem with mixed boundary conditions is well posed. What's not clear to me is this: Why do you approximate the derivative via the two-sides approximation? Shouldn't it be enough to just the following?$$ \frac{f_6 - f_{6-\Delta x}}{\Delta x} = 0. $$In your animations, what is the size of \Delta x? Your curve looks very smooth, which can be ... 4 That's not a simple question in my opinion. It is like if you were doing an experiment in a box and you just want to simulate the center of it. But obviously, the solution in the center of the box depends on what happens in the rest of the box. That is probably why it is a difficult problem to state. I have no definite answer to this question, but I still ... 4 The answer is yes. Drift diffusion = advection-diffusion. You will find this rather frequently: different disciplines, trying to describe the phenomena in their field, assign names to the equations they derive that have meaning for this discipline. Other disciplines come up with the same equations, in different contexts, and name them differently. It's still ... 4 That's a modelling problem, not a CS one. This will depend on what is diffusing and on the reasons why 2D is relevant. You may want to give physical details and ask this on physics.SE. Alternatively if you just want to get your hand in with solving diffusion, then the numbers don't have to reflect a physical fact (especially if you have diffusion only, the ... 4 More generally, the equation you are solving is $$\frac{\partial u}{\partial t} = \nabla \cdot \left( D(x) \nabla u \right) \quad ,$$ where the first nabla operator represents the divergence operator, and the second represents the gradient operator. Your equation is the special case for a one-dimensional cartesian coordinate ... 3 The Crank-Nicolson discretization of this equation will read$$ \frac{T^n-T^{n-1}}{\Delta t} = \frac 12 \left[ \partial_x \left((T^n)^{5/2} \partial_x T^n\right) + \partial_x \left((T^{n-1})^{5/2} \partial_x T^{n-1}\right) \right] $$which is a nonlinear, time-independent, elliptic partial differential equation in T^n. The way to solve such ... 3 You should rearrange the terms so that all of the n+1 terms are together on one side of the equals sign and all of the n terms are on them other. Then you will have a system of non-linear equations like:$$ A(u^{n+1}_i) u^{n+1}_i=b $$Where A is a non-linear matrix. Then you can use something like Newton-Raphson to linearize the system and your ... 3 In statistics the widely used test for checking if the distribution is gaussian is the Jarque-Bera test. Koizumi [1] presents an equivalent test for the multivariate case. I don't know if there something ready to use in C++, Fortran, or Python. However, at first sight, the test looks easy to implement. [1] - Koizumi, Kazuyuki, Naoya Okamoto, and Takashi Seo.... 3 The best method I know of for this problem is by Griffiths. 3 You just add the diffusion along the other dimensions. This superposition from orthogonal directions makes some sense, as they are independent. So, going by wikipedia for Fick's second law of diffusion in 1D:$$ \frac{\partial \psi}{\partial t} = D \frac{\partial^2 \psi}{\partial x^2} $$We extend it to 2d as:$$ \frac{\partial \psi}{\partial t} = D \...

3

There is no reason to believe that two random fields with the same arithmetic mean would yield solutions that have anything to do with each other. In fact, for the case you consider, one might imagine that maybe the harmonic mean is actually a better indicator, but even that is unclear -- it could also be the geometric mean. Apart from this, you have to ...

2

You should never use explicit method for the diffusion equation. Implicit is unconditionally stable and just as easy to implement. Also if you use an implicit method (like backward Euler or Crank-Nicolson) it will not matter how small d is. In fact you could use a dirac delta function if you wanted. As far as speed goes, doing a implicit method with a ...

2

For the heat equation, the wave speed is infinite and this is reflected by the fact that you are solving a globally coupled differential equation if you are using an implicit time stepping scheme.

2

You need to unfold the positions after the simulation is done. I use the following subroutine: subroutine unfold_positions(L, X, Xu) ! Unwinds periodic positions. It is using the positions of particles from the ! first time step as a reference and then tracks them as they evolve possibly ! outside of this box. The X and Xu arrays are of the type X(:, j, i), ...

2

Your first test should be to compute the mean value and covariance matrix of your point sample. If these converge to the correct values as you increase the number of samples, you are, from a practical perspective on the safe side that your points indeed come from the correct distribution. Of course, in practice there are many distributions that have the ...

2

I would do it exactly how you describe, with the two following remarks. I would solve the two evolutions simultaneously. In the way you describe, you will need to store and retrieve all the time steps for the solution $u_A$. Instead, you could solve sequentially for $u_A$ and $u_B$ at each time step, since $u_B$ just requires two solutions for $u_A$. If you ...

2

At first glance, it looks like you are using the method of lines with forward Euler time steps. What WolfgangBangerth is getting at with his example is that even for a simple heat equation, the stability limit of forward Euler (namely, that $|\lambda\Delta{t}| < 1$) combined with the eigenvalues induced by a finite difference approximation of the ...

2

Interesting question. I too would like to know if this is mentioned anywhere explicitly. My guess is maybe this is a little too hard and not too useful to be used/taught. Perhaps someone can give a proper reference. My calculations (see code below) suggest, if I am not wrong, that for the equation  u_t = \mathcal{L}u, \qquad \mathcal{L}u = \nabla\cdot(D\...

2

One of the best ways to test a PDE solver is to use the method of manufactured solutions. Essentially, you modify the PDE (and discretization) by adding a source term that yields an exact solution known in advance. You can then compare your numerical solution against the exact solution for debugging purposes. You should test your numerical solution against a ...

2

You are applying Richardson extrapolation to increasingly-accurate independent sample paths of an OU process. How would this work even for independent identically normally distributed random variables $y_1,y_2,y_3,y_4\sim\mathrm{N}(\mu,\sigma^2)$? These have already "converged" to the true distribution $\mathrm{N}(\mu,\sigma^2)$, and you might expect the ...

2

If you want to obtain the diffusion coefficient for 2D from 3D you have to take a look how the 2D diffusion equation is derived from 3D equation. It will be integrated with respect to one of the spatial dimensions. Diffusion coefficient is a $3 \times 3$ tensor in 3D, in 2D it will be $2 \times 2$ tensor. So in my opinion you cannot simply take the value ...

Only top voted, non community-wiki answers of a minimum length are eligible


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# Is the superposition principle a postulate in electrostatics?

Consider two electrical point charges $q_1$ and $q_2$ described by the total charge distribution $\rho = \rho_1 + \rho_2 = q_1 \delta(\vec{r} - \vec{r_1}) + q_2 \delta(\vec{r} - \vec{r_2})$. The total electrical potential could then be calculated by $$\phi(\vec{r}) = \frac{1}{4 \pi \varepsilon_0} \int_V{\frac{\rho(\vec{r'})}{|\vec{r} - \vec{r'}|} d^3r'} = \frac{1}{4 \pi \varepsilon_0} \int_V{\frac{\rho_1(\vec{r'})}{|\vec{r} - \vec{r'}|} d^3r'} + \frac{1}{4 \pi \varepsilon_0} \int_V{\frac{\rho_2(\vec{r'})}{|\vec{r} - \vec{r'}|} d^3r'} = \phi_1 + \phi_2$$ as solution of the Poisson's equation, which can be derived from Maxwell's equations.

Since $\vec{E} = - \nabla \phi$ and the gradient operator is linear we have $$\vec{E} = - \nabla \phi = - \nabla (\phi_1 + \phi_2) = - \nabla \phi_1 - \nabla \phi_2 = \vec{E_1} + \vec{E_2}$$ what the superposition principle is claiming. The superposition principle is sometimes called a postulate in electrostatics. But couldn't it be "derived" in that way?

• One can't derive anything in physics, one can, at best, give different but equivalent formulations that are describing the observations equally well. – CuriousOne Aug 8 '16 at 4:58
• There are a lot of different choices of postulates you can start with. As you found, Maxwell's equations are enough to give you everything else. You can also start with a larger number of simpler postulates instead, possibly including the superposition principle. – knzhou Aug 8 '16 at 4:59
• But I'm not aware of any modern textbook that does this. Can you give an example of your claim? – knzhou Aug 8 '16 at 5:00
• Yes, it is an empirical postulate one starts with, that is eventually confirmed when writing down the full set of Maxwell's equations and realising they are linear come what may. – gented Aug 8 '16 at 7:43
• @knzhou: the line of arguments above wasn't taken from a textbook, it has been rather my own idea. So if you don't assume Maxwell's equations as postulate, do you have to include the superposition principle in that set of simpler postulates? – Ben Aug 9 '16 at 4:31

But couldn't it be "derived" in that way?

No, because your starting statement $\rho = \rho_1 + \rho_2$, assumes the superposition principle. Thus using your derivation to justify the superposition principle would be circular reasoning.

Principles, by their very definition, are not derived. Instead we empirically evaluate them with experiments. Theories are then built on these principles. There is no theoretical reason charge densities need add linearly (at least, not that I'm aware of), perhaps in a different universe they don't.

• Is $\rho = \rho_1 + \rho_2$ not like a definition for the "total charge density" as sum of the individual densities? Or the other way round is the superposition principle of electric fields equivalent to the fact, that the total charge density equals the sum of the single charge densities? – Ben Aug 9 '16 at 4:36
• The fact that the charges sum in the first place assumes the super-position principle. I'm not sure which is more fundamental and thus I'm not sure which way round it's best to think about it. On the one hand, it's conventional to think of charge producing electric fields, but on the other hand we only know charge exists because we measure its electric field. If you grant, via principle, that one is true then the other follows suit closely after, as you excellent derivation demonstrates :) – Judge Aug 9 '16 at 9:49
• How does summing two charges require the superposition principle? The latter is a property of fields propagation, the former is just summing two things to have the total. – gented Aug 9 '16 at 9:55
• Good question. Perhaps I've misunderstood the precise definition of the superposition principle. But given that charge/charge densities add linearly, and using Maxwell's equations you can get to fields with a linear transformation. Doesn't one lead to the other? If so, then it's a question of where exactly along the process does the super-position principle come in. Finally, in a more general sense the superposition principle just states that for linear systems, the resultant quantity is the sum of the individual quantities. Surely $\rho = \rho_1 + \rho_2$ is an example of this? – Judge Aug 9 '16 at 10:11

The Maxwell equations contain electrostatics as special case and are linear, so electrostatic's linearity in the electric field is already contained in the Maxwell equations. I see the linearity in the electric field as consequence of $\vec F = q \cdot \vec E$ (where $\vec F$ is a force, $q$ the charge and $\vec E$ the electric field) and the fact that forces (force vectors) are simply added up to give the total force.

Maxwell equations for electrostatics are $\nabla\cdot\vec D = \rho, \nabla\times \vec E = 0$. The second one tells you, that there is a potential field $\phi$ generating electric field as $\vec E = -\nabla \phi$.

Both equations are linear, it means if there is $\rho_1, \rho_2$ satisfying $\nabla\cdot \vec D_1 = \rho_1$ and $\nabla\cdot \vec D_2 = \rho_2$, then $\rho = \rho_1 + \rho_2$ must hold $\nabla\cdot (\vec D_1 + \vec D_2) = \rho$. Equation with circulation is trivial.

The important fact here is, that theory is constructed on Maxwell equations, not on their consequence $\vec E = - \nabla \phi$. The superposition is then another consequency of linearity of differential operators in equations (divergence and circulation). Realize at this point that superposition would hold even if you didn't construct potentials.


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Algebraic geometry seminar

from Thursday
June 01, 2017 to Sunday
December 31, 2017
 Show events for: All Events AGNES Algebraic geometry seminar Algebraic models in geometry seminar Am.Math.Soc. (AMS) Chapter Seminar Analysis Student Seminar Capsule Research Talks Colloquium Commencement Ceremony Comprehensive Exams Dynamical Systems Seminar Equivalence Method and Exterior Differential Systems Seminar First and Second Year Student Seminar Friday Summer Meeting Geometric Analysis Learning Seminar Geometry/Topology Seminar Grad / Postdoc Professional Development Seminar Graduate Student Seminar Graduate Topology Seminar Grant Proposal Panel Hodge Theory, Moduli and Representation Theory Holiday Party Joint Columbia-CUNY-Stony Brook General Relativity Seminar Math Club Math Day 2016 Math in Jeans Mathematical Writing Seminar Mathematics Education Colloquium Mathematics Summer Camp Mini Course / Dynamics Learning Seminar Mini-School in Geometry Minicourse in Real Enumerative Geometry New Graduate Students NY General Relativity Seminar RTG Colloquium RTG Seminar RTG Student Geometry Seminar Seminar in Topology and Symplectic Geometry Seminar on algebraic structures in physics Simons Colloquium Simons Lectures Series Singular metrics and direct images Special Algebra / Algebraic Geometry Seminar Special Analysis Seminar Special Colloquium Special Geometry/Topology Seminar Special Lectures Special Seminar in Algebraic Geometry Special Topology Seminar Student Algebraic Geometry Seminar Student Gauge Theory Seminar Student Seminar on Differential Geometry and Analysis Summer Workshop in Topology and Geometry Symplectic Geometry Reading Seminar Symplectic Geometry Seminar Thesis Defense Topology and Symplectic Geometry / Math of Gauge Fields seminar Women in Mathematics Instructions for subscribing to Stony Brook Math Department Calendars

 WednesdaySeptember 06, 20174:00 PM - 5:30 PM Math Tower P-131 Rob Silversmith, SCGP Gromov-Witten invariants of symmetric products of projective spaceThrough 3 general points and 6 general lines in $P^3$, there are exactly 190 twisted cubics; 190 is a (genus-zero) Gromov-Witten invariant of $P^3$. I will introduce Gromov-Witten invariants of a smooth complex projective variety X, and discuss how a torus action on X can help us compute its Gromov-Witten invariants. In the case when X is a toric variety, Kontsevich used this method to compute any Gromov-Witten invariant of X. Givental and Lian-Liu-Yau used Kontsevich’s computation to prove a mirror theorem, which states that genus-zero Gromov-Witten invariants of X have an interesting rigid structure, which had been previously predicted by physicists. I will discuss the difficulties that arise when X is not toric. In particular, I will talk about the nontoric orbifold $X=Sym^d(P^r)$, the symmetric product of projective space. By studying the equivariant geometry of $Sym^d(P^r)$, I extended the strategies of Givental/Lian-Liu-Yau to prove a mirror theorem for $Sym^d(P^r)$.

 WednesdaySeptember 13, 20174:00 PM - 5:30 PM Math Tower P-131 Francois Greer, Stony Brook University Elliptic Fibrations and Noether-Lefschetz TheoryThe mirror symmetry philosophy suggests that the Gromov-Witten series of an elliptic fibration should be a modular form. Using the theta correspondence from automorphic forms and the Hodge theory of surfaces, we give a proof of this statement for genus 0 and base degree 1, and compute the series explicitly in many examples. Time permitting, we will discuss some ideas on how to generalize to all genera and base degrees.

 WednesdaySeptember 20, 20174:00 PM - 5:30 PM Math Tower P-131 Philip Engel, Harvard Algebraic/symplectic K3 dictionarySingular integral-affine structures on the sphere arise in connection to K3 surface in two distinct ways: Algebraically, as the dual complex of the central fiber of a degenerating family, and symplectically, as the base of a Lagrangian torus fibration. The Teichmuller space of such structures thus provides a dictionary between algebraic and symplectic moduli. Joint work with Simion Filip proves various structure results on the Teichmuller space of integral-affine structures on S^2---it is itself a separated 44-dimensional integral-affine manifold, with a natural 24 dimensional foliation, whose leaf space maps to the positive cone in R^{2,18}. Heuristically, any extension of the universal family of polarized K3 surfaces to a toroidal compactification would necessarily correspond to a section of the foliation over a certain hyperplane in R^{2,18}. Thus, the existence of such a section constructed by hyperKahler rotation evinces a program to extend the universal family.

 WednesdayOctober 04, 20174:00 PM - 5:30 PM Math Tower P-131 Luca Schaffler, University of Massachusetts, Amherst The KSBA compactification of the moduli space of $D_{1,6}$-polarized Enriques surfacesIn this talk we describe the moduli compactification by stable pairs (also known as KSBA compactification) of a 4-dimensional family of Enriques surfaces, which arise as the bidouble covers of the blow up of the projective plane at three general points branched along a configuration of three pairs of lines. The chosen divisor is an appropriate multiple of the ramification locus. Using the theory of stable toric pairs we are able to study the degenerations parametrized by the boundary and its stratification. We relate this compactification to the Baily-Borel compactification of the same family of Enriques surfaces. Part of the boundary of this stable pairs compactification has a toroidal behavior, another part is isomorphic to the Baily-Borel compactification, and what remains is a mixture of these two. To conclude, we construct an explicit Looijenga semitoric compactification of this 4-dimensional family which we conjecture is isomorphic to the KSBA compactification studied.

 WednesdayOctober 11, 20174:00 PM - 5:30 PM Math Tower P-131 Xudong Zheng, J. Hopkins University The Hilbert scheme of points on singular surfacesThe Hilbert scheme of points on a quasi-projective variety parametrizes its zero-dimensional subschemes. When the variety is a singular surface, the geometry of the Hilbert scheme should reflect the singularity of the underlying surface. I will present a sufficient condition for the Hilbert scheme to be irreducible in terms of the singularity of the surface, namely, the surface has only Kleinian singularities, via a purely algebraic approach. I will also report work in progress on some geometric consequences following their irreducibility.

 MondayOctober 16, 20174:00 PM - 5:00 PM Math Tower P-131 Daniele Agostini, Visiting Stony Brook University Asymptotic syzygies and higher order embeddings.The syzygies of an algebraic variety are the algebraic relations between its equations, and they often encode surprising geometric informations about the variety. For example, recently Ein and Lazarsfeld proved that one can read the gonality of a curve off the syzygies of an embedding of very high degree. I will present a partial extension of this result in higher dimensions, especially in the case of surfaces.

 WednesdayOctober 18, 20174:00 PM - 5:00 PM Math Tower P-131 Harold Blum, U. Michigan, Ann Arbor Valuations, Singularities, and K-stabilityLet L be a line bundle on a projective variety X. We use valuations to measure the singularities of the linear system |mL| as m goes to infinity. Specifically, we consider the global log canonical threshold, also known as Tian’s alpha invariant, and the stability thresholds of L. The stability threshold generalizes an invariant recently introduced by Kento Fujita and Yuji Odaka. When X is a Fano variety, we show that the stability threshold detects the K-(semi)stability of X. This talk is based on joint work with Mattias Jonsson.

 WednesdayOctober 25, 20174:00 PM - 5:30 PM Math Tower P-131 Sebastian Casalaina-Martin, U. of Colorado,. Boulder TBATBA

 WednesdayNovember 01, 20174:00 PM - 5:30 PM Math Tower P-131 Inna Zakharevich, Cornell TBA

 WednesdayNovember 08, 20174:00 PM - 5:30 PM Math Tower P-131 Fedor Bogomolov, NYU TBATBA

 WednesdayNovember 15, 20174:00 PM - 5:30 PM Math Tower P-131 Nicolas Addington, U. Oregon TBATBA

 WednesdayNovember 22, 20174:00 PM - 5:30 PM Math Tower P-131 Happy TKSgiving!, Happy TKSgiving! Happy TKSgiving!Happy TKSgiving!

 WednesdayNovember 29, 20174:00 PM - 5:30 PM Math Tower P-131 Christian Schnell, Stony Brook University TBATBA

 WednesdayDecember 06, 20174:00 PM - 5:30 PM Math Tower P-131 Davesh Maulik, MIT TBATBA

 Show events for: All Events AGNES Algebraic geometry seminar Algebraic models in geometry seminar Am.Math.Soc. (AMS) Chapter Seminar Analysis Student Seminar Capsule Research Talks Colloquium Commencement Ceremony Comprehensive Exams Dynamical Systems Seminar Equivalence Method and Exterior Differential Systems Seminar First and Second Year Student Seminar Friday Summer Meeting Geometric Analysis Learning Seminar Geometry/Topology Seminar Grad / Postdoc Professional Development Seminar Graduate Student Seminar Graduate Topology Seminar Grant Proposal Panel Hodge Theory, Moduli and Representation Theory Holiday Party Joint Columbia-CUNY-Stony Brook General Relativity Seminar Math Club Math Day 2016 Math in Jeans Mathematical Writing Seminar Mathematics Education Colloquium Mathematics Summer Camp Mini Course / Dynamics Learning Seminar Mini-School in Geometry Minicourse in Real Enumerative Geometry New Graduate Students NY General Relativity Seminar RTG Colloquium RTG Seminar RTG Student Geometry Seminar Seminar in Topology and Symplectic Geometry Seminar on algebraic structures in physics Simons Colloquium Simons Lectures Series Singular metrics and direct images Special Algebra / Algebraic Geometry Seminar Special Analysis Seminar Special Colloquium Special Geometry/Topology Seminar Special Lectures Special Seminar in Algebraic Geometry Special Topology Seminar Student Algebraic Geometry Seminar Student Gauge Theory Seminar Student Seminar on Differential Geometry and Analysis Summer Workshop in Topology and Geometry Symplectic Geometry Reading Seminar Symplectic Geometry Seminar Thesis Defense Topology and Symplectic Geometry / Math of Gauge Fields seminar Women in Mathematics Instructions for subscribing to Stony Brook Math Department Calendars


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Browse > Computer Vision > Image Generation

# Image Generation Edit

144 papers with code · Computer Vision

Image generation (synthesis) is the task of generating new images from an existing dataset.

• Unconditional generation refers to generating samples unconditionally from the dataset, i.e. $p(y)$
• Conditional image generation (subtask) refers to generating samples conditionally from the dataset, based on a label, i.e. $p(y|x)$.

In this section, you can find state-of-the-art leaderboards for unconditional generation. For conditional generation, and other types of image generations, refer to the subtasks.

Trend Dataset Best Method Paper title Paper Code Compare

# Variational Discriminator Bottleneck: Improving Imitation Learning, Inverse RL, and GANs by Constraining Information Flow

Xue Bin Peng et al

By enforcing a constraint on the mutual information between the observations and the discriminator's internal representation, we can effectively modulate the discriminator's accuracy and maintain useful and informative gradients.

01 May 2019

# Improving MMD-GAN Training with Repulsive Loss Function

Wei Wang et al

To address this issue, we propose a repulsive loss function to actively learn the difference among the real data by simply rearranging the terms in MMD.

01 May 2019

# FFJORD: Free-Form Continuous Dynamics for Scalable Reversible Generative Models

Will Grathwohl et al

The result is a continuous-time invertible generative model with unbiased density estimation and one-pass sampling, while allowing unrestricted neural network architectures.

01 May 2019

# Probabilistic Semantic Embedding

Yue Jiao et al

We present an extension of a variational auto-encoder that creates semantically richcoupled probabilistic latent representations that capture the semantics of multiplemodalities of data.

01 May 2019

# COCO-GAN: Conditional Coordinate Generative Adversarial Network

Chieh Hubert Lin et al

The fact that the patch generation process is independent to each other inspires a wide range of new applications: firstly, "Patch-Inspired Image Generation" enables us to generate the entire image based on a single patch.

01 May 2019

# Structured Prediction using cGANs with Fusion Discriminator

Faisal Mahmood et al

We propose a novel method for incorporating conditional information into a generative adversarial network (GAN) for structured prediction tasks.

01 May 2019

# Generative Models from the perspective of Continual Learning

Timothée Lesort et al

We experiment with sequential tasks on three commonly used benchmarks for Continual Learning (MNIST, Fashion MNIST and CIFAR10).

01 May 2019

# Deli-Fisher GAN: Stable and Efficient Image Generation With Structured Latent Generative Space

Boli Fang et al

In this paper we propose the Deli-Fisher GAN, a GAN that generates photo-realistic images by enforcing structure on the latent generative space using similar approaches in \cite{deligan}.

01 May 2019

# Large Scale GAN Training for High Fidelity Natural Image Synthesis

Andrew Brock et al

Despite recent progress in generative image modeling, successfully generating high-resolution, diverse samples from complex datasets such as ImageNet remains an elusive goal.

01 May 2019

# Harmonizing Maximum Likelihood with GANs for Multimodal Conditional Generation

Soochan Lee et al

Recent advances in conditional image generation tasks, such as image-to-image translation and image inpainting, can largely be accounted to the success of conditional GAN models, which are often optimized by the joint use of the GAN loss with the reconstruction loss.

01 May 2019


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# PSP Bibliography

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Ambipolar Electric Field and Potential in the Solar Wind Estimated from Electron Velocity Distribution Functions

 Author Ber\vci\vc, Laura; c, Milan; Halekas, Jasper; Landi, Simone; Owen, Christopher; Verscharen, Daniel; Larson, Davin; Whittlesey, Phyllis; Badman, Samuel; Bale, Stuart.; Case, Anthony; Goetz, Keith; Harvey, Peter; Kasper, Justin; Korreck, Kelly; Livi, Roberto; MacDowall, Robert; Malaspina, David; Pulupa, Marc; Stevens, Michael; Keywords Parker Data Used; Solar wind; Space plasmas; Interplanetary particle acceleration; Collision processes; Space vehicle instruments; 1534; 1544; 826; 2065; 1548; Astrophysics - Solar and Stellar Astrophysics; Physics - Plasma Physics; Physics - Space Physics Abstract The solar wind escapes from the solar corona and is accelerated, over a short distance, to its terminal velocity. The energy balance associated with this acceleration remains poorly understood. To quantify the global electrostatic contribution to the solar wind dynamics, we empirically estimate the ambipolar electric field (E$_\ensuremath\parallel$) and potential (\ensuremath\Phi$_r,\ensuremath\infty$). We analyze electron velocity distribution functions (VDFs) measured in the near-Sun solar wind between 20.3 R$_S$ and 85.3 R$_S$ by the Parker Solar Probe. We test the predictions of two different solar wind models. Close to the Sun, the VDFs exhibit a suprathermal electron deficit in the sunward, magnetic-field- aligned part of phase space. We argue that the sunward deficit is a remnant of the electron cutoff predicted by collisionless exospheric models. This cutoff energy is directly linked to \ensuremath\Phi$_r,\ensuremath\infty$. Competing effects of E$_\ensuremath\parallel$ and Coulomb collisions in the solar wind are addressed by the Steady Electron Runaway Model (SERM). In this model, electron phase space is separated into collisionally overdamped and underdamped regions. We assume that this boundary velocity at small pitch angles coincides with the strahl break-point energy, which allows us to calculate E$_\ensuremath\parallel$. The obtained \ensuremath\Phi$_r,\ensuremath\infty$ and E$_\ensuremath\parallel$ agree well with theoretical expectations. They decrease with radial distance as power-law functions with indices \ensuremath\alpha$_\ensuremath\Phi$ = -0.66 and \ensuremath\alpha$_E$ = -1.69. We finally estimate the velocity gained by protons from electrostatic acceleration, which equals 77\% calculated from the exospheric models, and 44\% from the SERM model. Year of Publication 2021 Journal \apj Volume 921 Number of Pages 83 Section Date Published nov ISBN URL DOI 10.3847/1538-4357/ac1f1c