in this paper, using the tools involving measures of noncompactness and darbo fixed point theorem forcondensing operator, we study the existence of solutions for a large class of generalized nonlinear quadraticfunctional integral equations. also, we show that solutions of these integral equations are locally attractive.furthermore, we present an example to show the efficiency and usefulness of ...

the existence of infinitely many solutions is established for a class of nonlinear functionals involving the p-biharmonic operator with nonhomoge- neous neumann boundary conditions. using a recent critical-point theorem for nonsmooth functionals and under appropriate behavior of the nonlinear term and nonhomogeneous neumann boundary conditions, we obtain the result.

We identify Melrose’s suspended algebra of pseudodifferential operators with a subalgebra of the algebra of parametric pseudodifferential operators with parameter space R. For a general algebra of parametric pseudodifferential operators, where the parameter space may now be a cone Γ ⊂ Rp, we construct a unique “symbol valued trace”, which extends the L2–trace on operators of small order. This c...

As a tool to carry out the quantization of gauge theory on a noncommutative space, we present a Dirac operator that behaves as a line element of the canonical noncommutative space. Utilizing this operator, we construct the Dixmier trace, which is the regularized trace for infinite-dimensional matrices. We propose the possibility of solving the cosmological constant problem by applying our gauge...

Goulden, I.P., A linear operator for symmetric functions and tableaux in a strip with given trace, Discrete Mathematics 99 (1992) 69-77. The sum of Schur symmetric functions in a countable set of variables, over partitions with given trace and upper bound on the number of parts, is evaluated. This generalizes results of Gordon (1971). The method is to extend an analogous sum in a finite set of ...

We consider a bosonic system of N particles with a repulsive interaction. The states of the system are given by elements of the Hilbert space Ls(R 3N ), the subspace of L(R ) consisting of permutation symmetric wave functions. We are interested in describing the time evolution of special initial wave functions ψN ∈ Ls(R ) that exhibit complete Bose-Einstein condensation. For a given wave functi...

We investigate the behaviour of the remainder term R(E) in the Weyl formula #fnjE n Eg = Vol(M) (4) d=2 ?(d=2 + 1) E d=2 + R(E) for the eigenvalues E n of a Schrr odinger operator on a d-dimensional compact Rieman-nian manifold all of whose geodesics are closed. We show that R(E) is of the form E (d?1)=2 (p E), where (x) is an almost periodic function of Besicovitch class B 2 which has a limit ...

Let G be a step two nilpotent Lie group. In this paper, we give necessary and sufficient conditions on the operator valued symbols σ such that associated pseudo-differential operators Tσ are in class of Hilbert-Schmidt operators. As key to prove this, define (μ,ν)-Weyl transform derive trace formula for with L2(R2n). We show L2(G) same as symbol L2(R2n+r+k×R2n+r+k). Further, present characteriz...

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