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The ith singular value of a transfer matrix need not be a differentiable function of frequency where its multiplicity is greater than one. We show that near a local maximum, however, the largest singu...
A local mountain pass type result for a system of nonlinear Schrodinger equations.
A RESULT ON RICCI CURVATURE AND THE SECOND BETTI NUMBER     A RESULT  RICCI CURVATURE  THE SECOND BETTI NUMBER       font style='font-size:12px;'> 2018/4/19
We prove that the second Betti number of a compact Riemannian manifoldvanishes under certain Ricci curved restriction.
Abstract: This paper is concerned with stability conditions for the positive feedback interconnection of negative imaginary systems. A generalization of the negative imaginary lemma is derived, which ...
Frobenius' result on simple groups of order (p^3-p)/2     Frobenius' result  Group Theory       font style='font-size:12px;'> 2011/9/15
Abstract: The complete list of pairs of non-isomorphic finite simple groups having the same order is well-known. In particular for p>3, PSL_2(Z/p) is the "only" simple group of order (p^3-p)/2. It's l...
Abstract: We use the Dong-Sogge-Zelditch formula to obtain a lower bound for the volume of the nodal sets of eigenfunctions. Our result improves the recent results of Sogge-Zelditch and in dimensions ...
A finite set X  n with a weight function w : X 0    is called Euclidean t-design in n  (supported by p concentric spheres) if the following condition ho...
A result in the Ho and Lee's model     result  Ho  Lee's model       font style='font-size:12px;'> 2010/9/20
A result in the Ho and Lee's model.
A symmetry result on Reinhardt domains     Reinhardt domains  math       font style='font-size:12px;'> 2010/11/23
We show the following symmetry property of a bounded Reinhardt domain $\Omega$ in $\mathbb{C}^{n+1}$: let $M=\partial\Omega$ be the smooth boundary of $\Omega$ and let $h$ be the Second Fundamental F...
A symmetry result on submanifolds of space forms and Applications     submanifolds  space forms  Applications       font style='font-size:12px;'> 2010/11/11
In this paper we prove a symmetry result on submanifolds of codimension one in a n + 1-dimensional space form, related to the geodesic distance function and to the normal curvature of some fixed vect...
A finite time blowup result for quadratic ODE's     blowup  quadratic ODE's       font style='font-size:12px;'> 2010/11/9
This short paper is dedicated to Mauricio Peixoto who abstracted the practical theory of ODE's and to David Rand who applied the subsequent powerful abstract theory to practical problems.
Political and social activists are rightfully concerned about future generations: whenever a country borrows money, or an environmental situation worsens, this means, in effect, that we impose an addi...
We deal with a nonconvex and nonlocal variational problem coming from thin-film micro-magnetics. It consists in a free-energy functional depending on two small parameters " and  and defined over vec...
A result of Lemmermeyer on class numbers      Lemmermeyer  class numbers        font style='font-size:12px;'> 2010/12/9
I present Franz Lemmermeyer’s proof that if p is a prime ≡ 9 (16) then the class number of Qp 1 4  is ≡ 2 (4).
We devise a fairly general sufficient condition ensuring that the endomorphism monoid of a countably infinite ultrahomogeneous structure (i.e. a Fra¨ıss´e limit) embeds all countable semigr...

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