Let us assume we are given a stochastically symmetric, reducible, freely anti-characteristic homomorphism ν. Recently, there has been much interest in the derivation of essentially stable isomorphisms. We show that ρz,k is super-uncountable. It has long been known that √ 2Σ <  ∑ J ′′ ( 0, ω̂ ∪ √ 2 ) , r′ ≤ 0 sin−1(−Ξ) x(−1 √ 2,...,U∨‖η‖) , e = 2 [26]. In [22], the main result was the construct...

A short introduction to the use of the spectral theorem for self-adjoint operators in the theory of special functions is given. As the first example, the spectral theorem is applied to Jacobi operators, i.e. tridiagonal operators, on l(Z≥0), leading to a proof of Favard’s theorem stating that polynomials satisfying a three-term recurrence relation are orthogonal polynomials. We discuss the link...

The physicist R. Feynman advanced an idea of forming an abstract operator calculus for a finite number of noncommuting operators by attaching time indices to the operators. In joint work with G.W. Johnson, time-ordering measures are introduced to serve as weights for various functional calculi, such as the Weyl functional calculus (equal weights), the Kohn-Nirenberg or ordered functional calcul...

Based on classical plate theory, standard and spectral finite element methods are extended for vibration and dynamic stability of axially moving thin plates subjected to in-plane forces. The formulation of the standard method earned through Hamilton’s principle is independent of element type. But for solving numerical examples, an isoparametric quadrilateral element is developed using Lagrange ...

Based on classical plate theory, standard and spectral finite element methods are extended for vibration and dynamic stability of axially moving thin plates subjected to in-plane forces. The formulation of the standard method earned through Hamilton’s principle is independent of element type. But for solving numerical examples, an isoparametric quadrilateral element is developed using Lagrange ...

We present and exploit an analogy between lack of absolutely continuous spectrum for Schrödinger operators and natural boundaries for power series. Among our new results are generalizations of Hecke’s example and natural boundary examples for random power series where independence is not assumed.

Theorem 1 (Arora, Rao, Vazirani, 2004) There is an O( √ log n)-approximation algorithm for sparsest cut. The proof of the theorem uses a SDP relaxation in terms of vectors vi ∈ Rn for all i ∈ V . Define distances to be d(i, j) ≡ ‖vi − vj‖ and balls to be B(i, r) ≡ {j ∈ V | d(i, j) ≤ r}. We first showed that if there exists a vertex i ∈ V such that |B(i, 1/4)| ≥ n/4, then we can find a cut of sp...

We describe some aspects of spectral theory that involve algebraic considerations but need no analysis. Some of the important applications of the results are to the algebra of n× n matrices with entries that are polynomials or more general analytic functions. Short title: Algebraic Spectral Theory MSC subject classification: 47A56, 47C05, 15A22, 16Sxx, 16Bxx

We give a survey on some recent developments in the spectral theory of transfer operators, also called Ruelle-Perron-Frobenius (RPF) operators, associated to expanding and mixing dynamical systems. Different methods for spectral study are presented. Topics include maximal eigenvalue of RPF operators, smooth invariant measures, ergodic theory for chain of markovian projections, equilibrium state...