# All Questions

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### Bounded power series on the closed unit disk

Consider the function $f(z) = \sum\frac 1{n^5+in^2-zn^5}$. Is it bounded on the closed unit disk ? (Ofcourse it is convergent on the closed unit disk.)
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### Simple question about notation: formulas starting with a quantification

Let $C\subset\mathbb{R}$ and suppose that $f:C\to2^C$ is a point to set map. Suppose that $f(x)$ is a set containing only negative real numbers for every $x\in C$. Are there any problems with the ...
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### On linear integer programs with infinitely many solutions

Suppose that a linear system of inequalities $Ax \le b$ with integral coefficients has an infinite number of integral solutions $x$. Can one conclude that there is a ray containing infinitely many ...
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### Who was the first to mention the nine problem? [on hold]

When Cantor published his seminal diagonal argument, he used binary code and did not distinguish the real numbers 0.1000… and 0.0111… Later, Koenig found a way to save the diagonal argument in binary ...
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Let $q_i$ for $i=1,\ldots,m$ be the columns of the matrix $Q\in\mathbb{R}^{n\times m}$, $n>m$, which are pairwise orthonormal ( i.e. $q_i^\top q_j = \begin{cases} 1 & \text{if}\quad i=j \\ 0 ... 0answers 63 views ### An inequality improvement on AMM 11145 I have asked the same question in math.stackexchange, I am reposting it here, looking for answers: How to show that for$a_1,a_2,\cdots,a_n >0$real numbers and for$n \ge 3$: ... 0answers 52 views ### Wreath product of an abelian group with a nilpotent group By work of Coulbois, the wreath product of two finitely generated free abelian group is$LERF$; i.e, every finitely generated group of this wreath product is closed in the profinite topology. Is there ... 2answers 333 views ### Can all the sporadic groups be expressed as permutation groups based on a single big cycle? Working on M11, I came up with that it can be generated using the following permutations: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10] [[2, 0, 1, 7], [3, 4, 5, 6]] [[4, 0, 6, 7], [2, 3, 1, 5]] [[0, 7], [4, 6], ... 0answers 21 views ### traces of fractional Sobolev spaces W^{s,p} with 0<s<1/p I've stumbled upon a problem involving the trace of a function in a fractional Sobolev space of the form$W^{s,2}(H)$, where$H$is a half-plane in$\mathbb{R}^2$. Would it be possible to define a ... 0answers 45 views ### Show that$G$a group? [on hold] Suppose that$G$is a semigroup , and for every$a$in$G$there is unique$a^*$in$G$that$aa^*a=a$Prove that$G$is a group. 1answer 75 views ### When can you canonically extend an ultrafilter after forcing? Suppose that$V$is a model of$\sf ZFC$, and fix some regular$\kappa$, say$\omega_1$for practical purposes. Let$\cal U$be an ultrafilter on$\omega_1$in$V$which is non-principal and even ... 0answers 47 views ### Inequality for the maximum of Gaussian variables Let$X=(X_1,\dots,X_n)$and$Y=(Y_1,\dots,Y_n)$be centered Gaussian vectors with variance matrix$\Gamma_X$and$\Gamma_Y$. We assume that the matrix$\Gamma_Y-\Gamma_X$is positive definite. Is it ... 0answers 27 views ### Compact factors of Lie groups; possibly varying definitions Let$G$be a real connected semisimple Lie group. Are the following equivalent?: (1)$G$has no proper cocompact Normal subgroups. (2)$G$has no proper cocompact connected Normal subgroups. In ... 1answer 67 views ### about the horizontal lift in a principal bundle I'm currently studying Fibre Bundle by Nakahara's book, and I'm a bit confused about the following: Imagine we have a Principal Bundle$P(M,G)$with open chart {$U_i$} and a local section ... 0answers 87 views ### Was “arithmetical translation” (coding in the Goedel sense) ever a part of Hilbert's Program? Was "arithmetical translation" (that is, coding in the Goedel sense) ever a part of Hilbert's Program? I ask this question for several reasons: i) it gives the numerals |, ||, |||,.... an ersatz ... 0answers 24 views ### conformal deformation with fixed boundaries For a flat plane with certain boundary, e.g., a rectangular patch, is it possible to conformally displace or deform such patch to a curved bump with exact same boundary? In this thesis, Dr. Keenan ... 0answers 54 views ### Advanced use of commutation matrices [on hold] I am aware of matrix operators vec and kronecker product, commutation matrices and various related identities like stated in ... 0answers 197 views ### Hypothesis test beyond simple hypotheses (mathematical statistics) In mathematical statistics, the following problem (simple hypothesis test) is considered: given a data sample, test the hypothesis$H_0$stating that all sampled values are values of a random variable ... 0answers 47 views ### exponential tail bound for conditional probability I am aware of exponential tail probabilities for unconditional probability (for ex: Normal). Are there any similar results available for conditional probability (w.r.t to a sigma field) in literature ... 0answers 35 views ### Solution of the system of differential equations Consider that we are working in the polynomial ring$\mathbb{C}[x]$. Suppose we have the following system of linear differential equations: $$\left\{\begin{matrix} L_1(y)=f_1\\ L_2(y)=f_2 ... 1answer 85 views ### Equalizing Geometric means of Graph Cycles Consider a strongly connected directed graph G. I have been stuck on the following question: can you assign real numbers in [0,1] to each edge of G so that the geometric mean of all cycles are ... 0answers 99 views ### Definition of a normed ring A normed ring "should" be a monoid object in the monoidal category of normed abelian groups. There are (at least) two choices of morphisms of normed groups, namely bounded or short homomorphisms, ... 1answer 33 views ### Maximal chromatic number with a fixed number of edges Given a graph G with m edges, what is the maximum chromatic number \chi(G) that the graph can have? My guess is that \chi(G) \leq r(m) where r(m) := \max\{k\in \mathbb{N}: \frac{k(k-1)}{2} ... 1answer 70 views ### Tight binomial left tail bound Let X \sim \text{Bin}(n,p). Wikipedia claims$$\mathbf P[X \leq (p-\epsilon)n ] \leq e^{ - 2 \epsilon^2 n}.$$This follows from Hoeffding's inequality ... 1answer 142 views ### The difference between Hilbert Scheme and Chow Scheme I am confused by Hilbert Scheme and Chow Scheme. Whenever you have a point in hilbert scheme, take its fiber in the universal family and take its fumdamental class, we get a point in Chow Scheme; and ... 1answer 121 views ### Jensen formula in \mathbb{C}^n? Let f:\mathbb{C}\to\mathbb{C} be an entire function with zero set X\subset \mathbb{C}. Jensen's formula reads$$ \log(|f(0)|)+\int_0^R\frac{|X\cap B_t(0)|}{t}dt = ... 1answer 93 views ### Strongly real elements of odd order in sporadic finite simple groups Recall that an element of a finite group is said to be real if it is conjugate to its inverse, and strongly real if the conjugating element can be chosen to be an involution. Question: Is it true ... 0answers 64 views ### Algebraic independence criterion Is there any criterion for checking algebraic independence of a set of polynomials in$n$variables in terms of the leading monomials with respect to some monomial order ? The Jacobian criterion is ... 1answer 55 views ### F-points of product of closed subgroups vs. product of F-points, F a local field, reference? Let$F$be a finite extension of$\mathbb Q_p$, where p is an odd prime. Let$G$be a connected reductive group defined over$F$. Let$M, H$be closed$F$-subgroups of$G$(in particular, I'm ... 2answers 207 views ### Factorization of a matrix as a product of a symmetric and a skew-symmetric matrix When can an$n\times n$matrix$M$be written as a product$M=AB$, where$A^T=A$and$B^T=-B$? For example, a necessary condition is that the trace of$M$vanishes. In this case, it is easy ... 1answer 258 views ### P.G.Goerss, J.F.Jardine, “Simplicial Homotopy Theory” prerequisites I know that such questions may be better suited for math.stackexchange, but I believe that that the topic of simplicial homotopy theory is advanced enough for mathoverflow. Besides, I know that there ... 0answers 84 views ### Is the positive existential theory undecidable? Could you tell if the positive existential theory of$\mathbb{C}[e^{\mu x} \mid \mu \in \mathbb{C}]$is undecidable in the language$\{+, \cdot , \frac{d}{dx} , 0, 1, e^x\}$? How can we prove the ... 0answers 137 views ### all subsets borel Assume Martin's axiom plus$\neg CH$. It is well known, via almost disjoint forcing, that every set of reals of size less than continuum is an example of a metric space whose subsets are all ... 2answers 547 views ### A new result on the Diophantine equation$x^3 + y^3 +z^3 = 3$[on hold] The above Diophantine equation is unknown to have any further integer solutions other than$(x, y, z) = (1, 1, 1)$and$(4, 4, -5)$. I am a prospective undergraduate mathematics student in Zimbabwe ... 1answer 296 views ### Okounkov-Vershik approach to representation theory of$S_n$This is a rather soft question. I was wondering if someone could explain on a fundamental and intuitive level, what the Okounkov-Vershik approach to representation theory of$S_n$is all about. It's ... 1answer 53 views ### Complexity of Deciding Feasibility of a system of linear inequalities over restricted variables I am working out an interesting problem and would like some help with this particular sub problem: Suppose we have a matrix$ M =\left\lbrace a_{ij}\right\rbrace $of size$n\times m$where$ ...
Let $K$ and $L$ be simplicial complexes as given, and let $\phi:|K|\to|L|$ be the continuous map, where $A=\phi(a)$, $B=\phi(b)$, and so on. Check whether the map $\phi$ has a simplicial ...