Results 1  10
of
170
Rn+k
"... Today, we will begin the proof the the following theorem, first proved by Rene ́ Thom in what is possibly the best math PhD thesis of all time. See [1]. Theorem 0.1. The cobordism group of unoriented ndimensional manifolds is naturally isomorphic to the nth homotopy group of the Thom spectrum MO. T ..."
Abstract
 Add to MetaCart
Today, we will begin the proof the the following theorem, first proved by Rene ́ Thom in what is possibly the best math PhD thesis of all time. See [1]. Theorem 0.1. The cobordism group of unoriented ndimensional manifolds is naturally isomorphic to the nth homotopy group of the Thom spectrum MO
Lower bounds for the infimum of the spectrum of the Schrödinger operator in RN and the Sobolev inequalities
 JIPAM. J. Inequal. Pure Appl. Math
"... ABSTRACT. This article is concerned with the infimum e1 of the spectrum of the Schrödinger operator τ = − ∆ + q in RN, N ≥ 1. It is assumed that q − = max(0, −q) ∈ Lp (RN), where p ≥ 1 if N = 1, p> N/2 if N ≥ 2. The infimum e1 is estimated in terms of the Lpnorm of q − and the infimum λN,θ of ..."
Abstract

Cited by 10 (0 self)
 Add to MetaCart
ABSTRACT. This article is concerned with the infimum e1 of the spectrum of the Schrödinger operator τ = − ∆ + q in RN, N ≥ 1. It is assumed that q − = max(0, −q) ∈ Lp (RN), where p ≥ 1 if N = 1, p> N/2 if N ≥ 2. The infimum e1 is estimated in terms of the Lpnorm of q − and the infimum λ
Discreteness of the Spectrum for Some Differential Operators With Unbounded Coefficients in R^n
"... We give sufficient conditions for the discreteness of the spectrum of differential operators of the form Au = \Gamma\Deltau +hrF;rui in L 2 (R n ) where d(x) = e \GammaF (x) dx and for Schrödinger operators in L 2 (R n ). Our conditions are also necessary in the case of polynomial coeffic ..."
Abstract

Cited by 4 (1 self)
 Add to MetaCart
We give sufficient conditions for the discreteness of the spectrum of differential operators of the form Au = \Gamma\Deltau +hrF;rui in L 2 (R n ) where d(x) = e \GammaF (x) dx and for Schrödinger operators in L 2 (R n ). Our conditions are also necessary in the case of polynomial
The spectrum of a random geometric graph is concentrated
, 2004
"... Consider n points distributed uniformly in [0,1] d. Form a graph by connecting two points if their mutual distance is no greater than r(n). This gives a random geometric graph, G(Xn; r(n)), which is connected for appropriate r(n). We show that the spectral measure of the transition matrix of the s ..."
Abstract

Cited by 11 (0 self)
 Add to MetaCart
Consider n points distributed uniformly in [0,1] d. Form a graph by connecting two points if their mutual distance is no greater than r(n). This gives a random geometric graph, G(Xn; r(n)), which is connected for appropriate r(n). We show that the spectral measure of the transition matrix
REAL SPECTRUM AND THE ABSTRACT POSITIVSTELLENSATZ
"... Algebraic geometry emerged from the study of subsets of Cn defined by polynomial equations, namely algebraic sets. Parallel to this, real algebraic geometry emerged from studying subsets of Rn defined by polynomial equations and inequalities, namely semialgebraic sets. Like algebraic geometry, clas ..."
Abstract
 Add to MetaCart
Algebraic geometry emerged from the study of subsets of Cn defined by polynomial equations, namely algebraic sets. Parallel to this, real algebraic geometry emerged from studying subsets of Rn defined by polynomial equations and inequalities, namely semialgebraic sets. Like algebraic geometry
ON THE BOUNDARY OF THE ATTAINABLE SET OF THE DIRICHLET SPECTRUM
"... Abstract. Denoting by E ⊆ R2 the set of the pairs (λ1(Ω), λ2(Ω)) for all the open sets Ω ⊆ RN with unit measure, and by Θ ⊆ RN the union of two disjoint balls of half measure, we give an elementary proof of the fact that ∂E has horizontal tangent at its lowest point (λ1(Θ), λ2(Θ)). 1. ..."
Abstract
 Add to MetaCart
Abstract. Denoting by E ⊆ R2 the set of the pairs (λ1(Ω), λ2(Ω)) for all the open sets Ω ⊆ RN with unit measure, and by Θ ⊆ RN the union of two disjoint balls of half measure, we give an elementary proof of the fact that ∂E has horizontal tangent at its lowest point (λ1(Θ), λ2(Θ)). 1.
DISCRETE SPECTRUM OF QUANTUM TUBES
, 2006
"... A quantum tube is essentially a tubular neighborhood about an immersed complete manifold in some Euclidean space. To be more precise, let Σ ֒ → R n+k, k ≥ 1, n = dim(Σ), be an isometric immersion, where Σ is a complete, noncompact, orientable manifold. Then consider the resulting normal bundle T ⊥ Σ ..."
Abstract
 Add to MetaCart
T ⊥ Σ over Σ, and the submanifold F = {(x, ξ)x ∈ Σ, ξ < r} ⊂ T ⊥Σ for r small enough. The quan)), where tum tube is defined as the Riemannian manifold (F, f ∗ (ds2 E ds2 E is the Euclidean metric in Rn+k and the map f is defined by f(x, ξ) = x + ξ. If k = 1, then the quantum tube is also called
On absolute continuity of the spectrum of a periodic magnetic Schrödinger operator
, 2009
"... We consider the Schrödinger operator in R n, n ≥ 3, with the electric potential V and the magnetic potential A being periodic functions (with a common period lattice) and prove absolute continuity of the spectrum of the operator in question under some conditions which, in particular, are satisfied i ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
We consider the Schrödinger operator in R n, n ≥ 3, with the electric potential V and the magnetic potential A being periodic functions (with a common period lattice) and prove absolute continuity of the spectrum of the operator in question under some conditions which, in particular, are satisfied
THE DIMENSION SPECTRUM OF PROJECTED MEASURES ON RIEMANN MANIFOLDS
"... Abstract. In this work we first generalize the projection results concerning the dimension spectrum of projected measures on Rn to parametrized families of transversal mappings between smooth manifolds and measures on them. The projection theorems for the lower qdimension were first considered in [ ..."
Abstract
 Add to MetaCart
Abstract. In this work we first generalize the projection results concerning the dimension spectrum of projected measures on Rn to parametrized families of transversal mappings between smooth manifolds and measures on them. The projection theorems for the lower qdimension were first considered
Results 1  10
of
170