User yaoxiao - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-24T07:21:34Z http://mathoverflow.net/feeds/user/11966 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/123533/spectrum-theorem-for-p-adic-matrix-analysis Spectrum theorem for p-adic matrix analysis yaoxiao 2013-03-04T14:05:20Z 2013-03-18T14:01:05Z <p>Recently, I met a problem related to p-adic matrices in my research, the key of the problem can be summarized in the following way: 1: whether there exist spectrum theorem for p-adic matrix.\</p> <p>2: whether invertible p-adic matrix is dense in $$C_{p}^{n\times n}$$</p> <p>3:whether diagonalizable p-adic matrix is dense in $$C_{p}^{n \times n}$$ </p> <p>Any reference and comments will be appreciated.</p> http://mathoverflow.net/questions/84003/are-there-some-original-papers-or-books-related-to-applications-of-algebraic-topo Are there some original papers or books related to applications of algebraic topology and algebraic geometry in complex dynamic systems yaoxiao 2011-12-21T13:48:49Z 2013-03-10T06:06:50Z <p>Recently I have much interest in algebraic topology and algebraic geometry, I am a student of field of complex dynamic systems. According to my knowledge, my friends told me that there are many applications of algebraic geometry and algebraic topology in dimension of reduction in statistics and some other fields. I want to konw whether there exists some interesting applications of algebraic geometry and albebraic topology in dynamics system. Any comments and advice will be appreciated. Thanks.</p> http://mathoverflow.net/questions/123720/p-adic-lie-theory p-adic Lie theory yaoxiao 2013-03-06T08:30:57Z 2013-03-06T08:30:57Z <p>It is well known that exponential map in $C^{n\times n}$ will cover all non-sigular matrix $GL(n,C)$, which is a basic fact in Lie group and lie algebra theory, whether it is true for p-adic cases. </p> <p>Recent I may need facts in classical matrix analysis to be generalized in p-aidc matrix cases. something are really trivial, however some others may have essential difficulties at least to me. it is quite striking fact that entire p-adic map doesn't omit value in $C_{p}$, and the p-adic exponential map can not defined in whole $C_{p}$</p> <p>Any references and comments will be appreciated. </p> http://mathoverflow.net/questions/89274/the-dual-space-of-cx-x-is-noncompact-metric-space the dual space of C(X) (X is noncompact metric space) yaoxiao 2012-02-23T11:50:19Z 2012-11-01T13:21:56Z <p>It is well known that when X is compact space (or locally compact space), $C(X)={f:f X\rightarrow X \text{is continous,and bounded} }$ ,the dual space of $C(X) C(X)^{*}$is correspond to $M(X)$ space of Radon measure with bounded variation.</p> <p>However according to my knowledge. there are few books discuss case that when X is noncompact, for example complete vsperable metric space.</p> <p>even for the simplest example, when taking X is R, means real line, what does $(C(X))^{*}$ mean.</p> <p>Any advice and reference will be appreaciated.</p> http://mathoverflow.net/questions/109437/normal-family-for-several-complex-variable-from-cn-to-cn-u Normal Family for several complex variable (from $C^{n}$to$C^{n}\U$) yaoxiao 2012-10-12T06:44:38Z 2012-10-12T22:27:11Z <p>Recently I face up with a problem, which I realized that have close connection with the following problem. ${ f_{n} }_{n=1}^{\infty}$ is analytic map from $C^{n}$ to $C^{n}$\ $U$ where U is open neighborhood of 0, whether f is a normal family. </p> <p>I know when n=1, this is really Montel Normal family criterion, However I did know whether it is true for high dimension. also I heard that the for any two topological equivalent simple connected domain in$C^{n}$ $(n\geq 2)$, the probability of holomorphic equivalent for this two domain is 0. I want to know what is the precise statement for this theorem.</p> <p>Any advice and comments will be appreciated.</p> http://mathoverflow.net/questions/106676/if-fatou-set-has-a-multiply-connected-fatou-component-implies-every-component-of If Fatou set has a Multiply connected Fatou component implies every component of F(f) is bounded yaoxiao 2012-09-08T16:25:33Z 2012-09-09T14:24:28Z <p>Recently when I read a paper about Fatou component, I met the following theorem which cited in Professor Eremenko's paper "on the iteration of entire functions"</p> <p>If Fatou set has a Multiply connected Fatou component implies every component of F(f) is bounded.</p> <p>it is really known theorem proved by I.N Baker in his paper in "The domains of normality of an entire function". However I really did know how to find this paper. any comments and materials about this theorem will be very appreciated. thanks.</p> http://mathoverflow.net/questions/92249/a-problem-about-all-roots-in-the-left-half-plane a problem about All roots in the left half plane yaoxiao 2012-03-26T09:43:22Z 2012-03-26T10:21:28Z <p>Suppose a polynomial$u(x)=ax^{2}+bx+c$，with a b c positive,$g(x)=d*xe^{-\lambda_1 x}+fe^{-\lambda_2 x}$with d,f positve, let $H(x)=u(x)-g(x)$, when we reserach some bahavior of a dynamic system, we want to give some condtion such that all root of H(x) will locate in the half-left complex, however I did not how to deal with, any reference and advice will be appreatiated.</p> http://mathoverflow.net/questions/89204/triangle-equality-in-manifold triangle equality in manifold yaoxiao 2012-02-22T15:44:57Z 2012-02-22T17:53:44Z <p>For a generilized triangle on a manifold, (distance can be regarded as geodesic length)it is well known that for Eucilidean Geometry，the following is true:</p> <p>Consider a triangle $ABC$, $D$ is the midpoint of $BC$, then $AD\leq \frac{1}{2}(AB+AC)$</p> <p>what about some other cases in manifolds. according to my knowledge, it is also true in spheres with dimension n. However I did not konw general cases.</p> <p>Any advice will be appreaciated.</p> http://mathoverflow.net/questions/89205/weak-l-1-convergence-of-squares/89206#89206 Answer by yaoxiao for Weak L_1-convergence of squares yaoxiao 2012-02-22T16:06:21Z 2012-02-22T16:06:21Z <p>It is obvious true. $f_{k}\rightarrow f$ in$L^{1}$ strongly,(for $\forall p &lt;2$) $f_{k}^{2}\rightarrow f_{2}$ strongly, of course weakly, then $F=f^{2}$</p> http://mathoverflow.net/questions/77325/finite-groups-with-faithful-real-two-dimensional-representation finite groups with faithful real two dimensional representation yaoxiao 2011-10-06T03:50:25Z 2011-10-07T04:01:15Z <p>Recently I have met an interesting problem $\rho$: $G \rightarrow SL(2,R)$ be a faithful representions of a finite group by real 2\times 2 matrices of determinant 1, then we can get this group is cylic.</p> <p>what is more, how can we determine all finite groups wich have a faithful real two dimensional representation? I feel it have some connections with finite subgroup in $SL(2,R),SU_{2},U_{2}$</p> <p>more generally, determine all finite groups which have a faithful real n dimensional representation? </p> <p>I do not konw how I takle with these problems</p> http://mathoverflow.net/questions/60457/elementaryshortuseful/61196#61196 Answer by yaoxiao for Elementary+Short+Useful yaoxiao 2011-04-10T08:56:59Z 2011-04-10T08:56:59Z <p>Every matrix can be represented by the linear combinations of four orthogonal matrix</p> http://mathoverflow.net/questions/61112/is-there-any-conclusions-generalized-singular-value-decomposition-into-hilbert-sp Is there any conclusions generalized Singular Value Decomposition into Hilbert Space yaoxiao 2011-04-09T04:02:47Z 2011-04-10T03:35:44Z <p>Spectrum decomposition can be regarded as the generalizations of the following fact that: Every Hermitian matrix $A$ can be decomposed into $A=U^{*}\Lambda U$,where $U$ is a unitary matrix</p> <p>Singular vector decomposition can be expressed as Every Matrix $A_{mn}$ can be decomposed in to $A=U\Lambda V^{*}$, where $U$,and $V$ are unitary matrices. Does it can be extended in to decompostion of linear operators on Hilbert Space. ?</p> <p>I searched the internet and several traditional books about the topic "Singular Vector Decomposition into Hilbert space", However, to my disappointment, I find no similar conclusion. Thanks for your help.</p> http://mathoverflow.net/questions/51003/whether-the-system-of-matrix-equations-is-always-solvable Whether the system of matrix equations is always solvable yaoxiao 2011-01-03T10:38:20Z 2011-01-28T20:20:54Z <p>In recent days, I learned a linear algebra problem from one of my friends. It can be stated as follows.</p> <p>Given four matrices $A,B,C,D$, find three matrices $E,G,F$, not simultaneously zero, such that the following conditions (1), (2), (3) are satisfied: \begin{align*} (1) &amp;\quad AE=EA, \cr (2) &amp;\quad BG=GB, \cr (3) &amp;\quad AF-FB=ED-CG. \end{align*} The question is whether such $E,G,F$ always exist.</p> <p>Also it is obvious that we can obtain $E,G$ by (1) and (2) easily. However the hard die is to satisfy condition (3). I just know when $A$ and $B$ have different spectra, we can obtain $F$ in a unique way.</p> http://mathoverflow.net/questions/50936/how-to-prove-a-unit-norm-matrix-is-the-average-of-two-unitary-matrix How to prove a unit norm matrix is the average of two unitary matrix yaoxiao 2011-01-02T17:35:37Z 2011-01-02T19:48:54Z <p>thanks for your answers</p> http://mathoverflow.net/questions/123533/spectrum-theorem-for-p-adic-matrix-analysis Comment by yaoxiao yaoxiao 2013-03-04T15:03:15Z 2013-03-04T15:03:15Z @Will Sawin thanks for your comments. http://mathoverflow.net/questions/109614/whether-sina-covers-all-of-the-matrix-in-cn-times-n Comment by yaoxiao yaoxiao 2012-10-15T15:22:33Z 2012-10-15T15:22:33Z @Yemon Choi, sorry for my poor english, which I means is for every matrix $Y \in C^{n\times n}$, whether sin(X)=Y, has a solution. http://mathoverflow.net/questions/109437/normal-family-for-several-complex-variable-from-cn-to-cn-u/109497#109497 Comment by yaoxiao yaoxiao 2012-10-14T13:49:26Z 2012-10-14T13:49:26Z Thank you for your answer and statement. I know the proof of unit ball and polydisk are not holomorphically equivalent. http://mathoverflow.net/questions/106676/if-fatou-set-has-a-multiply-connected-fatou-component-implies-every-component-of/106733#106733 Comment by yaoxiao yaoxiao 2012-09-14T02:29:25Z 2012-09-14T02:29:25Z Thank you professor Eremenko. Your survey article is really great help, thanks. http://mathoverflow.net/questions/92249/a-problem-about-all-roots-in-the-left-half-plane Comment by yaoxiao yaoxiao 2012-03-26T13:33:45Z 2012-03-26T13:33:45Z @Willie Wong， I am sorry，It is just means times http://mathoverflow.net/questions/89204/triangle-equality-in-manifold Comment by yaoxiao yaoxiao 2012-02-22T23:34:33Z 2012-02-22T23:34:33Z @Joseph O'Rourke. Oh, thanks. Sorry for my poor statement, here I means the shortest geodesic http://mathoverflow.net/questions/89204/triangle-equality-in-manifold/89214#89214 Comment by yaoxiao yaoxiao 2012-02-22T23:32:42Z 2012-02-22T23:32:42Z @Anton Petrunin Sorry for my statement for this problem, I means the shortest geodesic,your counter example is just$AB=BC=AC=\frac{\pi}{3}$ http://mathoverflow.net/questions/84003/are-there-some-original-papers-or-books-related-to-applications-of-algebraic-topo/84026#84026 Comment by yaoxiao yaoxiao 2011-12-22T01:16:06Z 2011-12-22T01:16:06Z Thanks for your advice, last year a professor in Chern's institue have given a report about algebraic geometry's applications in dimension reuduction's about the accuracy test of Fisher's table test, which give me deep and powerful impression. http://mathoverflow.net/questions/77325/finite-groups-with-faithful-real-two-dimensional-representation/77329#77329 Comment by yaoxiao yaoxiao 2011-10-06T05:26:08Z 2011-10-06T05:26:08Z thanks for your answers， can you give me some materials about n=3，thanks http://mathoverflow.net/questions/61367/two-specific-sets-of-sums Comment by yaoxiao yaoxiao 2011-04-12T06:26:04Z 2011-04-12T06:26:04Z This is my first time to know about the MRB constant，does it play a very important part in number theory? http://mathoverflow.net/questions/61252/why-do-bernoulli-numbers-arise-everywhere Comment by yaoxiao yaoxiao 2011-04-11T02:56:33Z 2011-04-11T02:56:33Z According to history of mathematics, at the beginning of Bernoulli's original idea, he did not begin defined as the Taylor coefficients of the function x/(e^x-1) at 0. http://mathoverflow.net/questions/60457/elementaryshortuseful Comment by yaoxiao yaoxiao 2011-04-10T09:02:39Z 2011-04-10T09:02:39Z As far as I see， the theorem related to number “4” will be the best： First： four color theorem Second：Every positive integer can be represented by squares of four integers. Third: Every matrix can be represented by linear combinations of four matrix and so on http://mathoverflow.net/questions/60293/find-the-sum-of-a-series Comment by yaoxiao yaoxiao 2011-04-10T08:44:35Z 2011-04-10T08:44:35Z Without special functions, I am afraid we can not give a direct result on this problem http://mathoverflow.net/questions/61112/is-there-any-conclusions-generalized-singular-value-decomposition-into-hilbert-sp/61132#61132 Comment by yaoxiao yaoxiao 2011-04-09T12:33:21Z 2011-04-09T12:33:21Z Oh，thank you. may be this theorem &quot;Every bounded operator acting on a Hilbert space has a decomposition , where and is a partial isometry. This decomposition is called polar decomposition. If is invertible, then can be chosen to be unitary.&quot; given by mathworld is related to some deep operator theory. http://mathoverflow.net/questions/61112/is-there-any-conclusions-generalized-singular-value-decomposition-into-hilbert-sp/61121#61121 Comment by yaoxiao yaoxiao 2011-04-09T10:27:42Z 2011-04-09T10:27:42Z Thanks for Yemon Choi and Dennis Serre's comment.