# All Questions

0answers
29 views

### About the proof of the Morse lemma

In the Chang's book "Infinite dimensional Morse theory and multiple solution problems" the Morse lemma is a special case of the spliting lemma but i dont understand in the proof why ...
2answers
11 views

### Linear Programm with matrix

Is there a name for problems like this min norm(Cx) Ax = b where C is a matrix and norm is the maximum norm. This is kind of like a linear Programm. Could this be rewritten as linear programm? Or Any ...
0answers
17 views

0answers
22 views

### How to define the distributional Hessian for a convex function on a $C^0$ Riemannian manifold?

M is a $C^1$ manifold with a $C^0$ Riemannian metric, f is a convex function on M. How to define a functional on M which can represent $Hessf$? For example: for $\Delta f$ we can define the ...
0answers
17 views

0answers
100 views

Hi I have the following problems concerning quadratic and ternary forms. Any help would be greatly appreciated. $3\displaystyle\sum_{x, y\in\mathbb{Z}}q^{x^2+xy+7y^2}=3\displaystyle\sum_{x, ... 0answers 48 views ### Are semigroups with finite-to-one right multiplication “moving”? A semigroup$S$is moving if$S$is infinite, and for all finite$F\subseteq S$and infinite$A\subseteq S$, there are$a_{1},\dots,a_{k}\in A$such that, for all but finitely many$s\in S$, $$... 0answers 23 views ### How can I decode efficiently a triple-error-correcting binary BCH code? In a given BCH(N,K) T=3 code over GF(2^m), there are ways to find the error locations in a given N-bit codeword directly from the syndromes without going through the normal Berlekamp-Massey and Chien ... 0answers 168 views ### What can be said about the Fourier transforms of characteristic functions? What can be said about the Fourier transform of the characteristic function 1_A, where A\subset \mathbb{R}^n is of finite Lebesgue measure? In particular, What properties are common to ... 2answers 113 views ### Random walk in a convex body or convex polytope Let \Delta be a convex body (i.e. a compact convex subset) or a convex polytope in \mathbb{R}^n. Let x be a point inside \Delta and consider a (uniform) random walk starting at x inside ... 2answers 155 views ### Lie's Theorem in characteristic p Let K be an algebraically closed field with characteristic 0 and V be a Lie sub-algebra of M_n(K), the n\times n matrices over K. If V is solvable, then, according to Lie's theorem, V ... 1answer 171 views ### Action of a profinite group Let G be a finitely generated profinite group, p a prime number. Put$$ V = \prod_{i \in I} \mathbb{Z}_p$$a (profinite) group equipped with the product topology (for convenience,$I$may be ... 0answers 26 views ### Injectivity of a linear logistic transform The motivation for this question has to do with neural networks, but it is essentially a purely mathematical question. Suppose you have a perceptron with one hidden layer, a bias, and a logistic ... 0answers 43 views ### Measure generated by Semigroup$\exp[-t|p|]$I am studying Ingrid Daubechies' paper 'An Uncertainty Principle for Fermions with Generalized Kinetic Energy'. On page 514, the measure$\mu_{x,y;t}$is introduced as generated by the semigroup ... 0answers 63 views ### Fixed point of a function on the circle Consider a circle$C$with radius of$r$, we place$m$balls(treated as point) randomly on it, and each ball$i$has the mass$m_i$. We define a function$\varphi:C\rightarrow C$which maps$x\in C$... 1answer 245 views ### Prime races à la Mertens I have just read the nice survey by Granville and Martin about prime races. I wonder what happens if one changes the rules for the prime races as follows. Fix$q$a modulus (an integer$>1$). For ... 0answers 18 views ### Does there exist a base$\{e_j\}_{j\geq 1}$of$H(\Omega)$such that$\{e_j\}_{j\geq 1}$is linearly independent in$L^2(\omega)^d$? Does there exist a base$\{e_j\}_{j\geq 1}$of$H(\Omega)$such that$\{e_j\}_{j\geq 1}$is linearly independent in$L^2(\omega)^d$? Where$\omega\subset\subset \Omega$with$\Omega$is a$C^2$... 0answers 27 views ### Can the generalized divisor summatory function$D_z$be expressed explicitly in terms of Zeta Zeros? Mertens function has, by residues, an explicit formula of$M(n)=\displaystyle\sum_{\rho}\frac{x^\rho}{\rho\zeta'(\rho)}-2+\sum_{n=1}^\infty\frac{(-1)^{2 n}(2\pi)^{2n}}{(2n)! n \zeta(2n+1)x^{2n}}$... 0answers 112 views ### Is liminf|(n*sinn)|=0 as n tends to infinity? [duplicate] One of my friends asked me that is$\varliminf |nsinn|=0$? I think maybe it has some relations with Number theory, But I don't know how to solve it. If you know the answer, please tell me since it ... 1answer 53 views ### Dropping rank of IA automorphisms Is there a natural way to map a given IA automorphism$\alpha\in Aut(F(X_n))$to$Aut(F(X_{n-1}))$? Think about braids. A pure braid on$n$strands can be naturally mapped to a braid on$n-1$strands ... 1answer 144 views ### Derived category of a hypersurface Let$X$be a smooth projective variety over$\mathbb{C}$, and$H \subset X$be a smooth hypersurface. Many properties of an ambient variety$X$could somehow inherit to the hypersurface$H$, I was ... 1answer 118 views ### Examples of Maass forms with eigenvalue 1/4 For what I have heard, Maass forms of (Laplacian) eigenvalue$1/4\$ on modular surfaces are somewhat special. But I don't know where to look for explicit examples. (In fact, one form came here on MO ...

15 30 50 per page