We introduce and study a new class of general nonlinear random multivalued operator equations involving generalized m-accretive mappings in Banach spaces. By using the Chang’s lemma and the resolvent operator technique for generalized m-accretive mapping due to Huang and Fang 2001 , we also prove the existence theorems of the solution and convergence theorems of the generalized random iterative...

In this paper, we consider the following Yamabe type problem of polyharmonic operator : { Dmu = |u| 4m N−2m u on S u ∈ H(S ), (P ) where N ≥ 2m + 1,m ∈ N+, S is the unit sphere with the induced Riemannian metric g = gSN , and Dm is the elliptic differential operator of 2m order given by Dm = m ∏ k=1 (−∆g + 14(N − 2k)(N + 2k − 2)) where ∆g is the Laplace-Beltrami operator on S . We will show tha...

Let (M,g) be a complete non-compact Riemannian manifold. We consider operators of the form ∆g + V , where ∆g is the non-negative Laplacian associated with the metric g, and V a locally integrable function. Let ρ : (M̂ , ĝ) → (M,g) be a Riemannian covering, with Laplacian ∆ĝ and potential V̂ = V ◦ ρ. If the operator ∆ + V is non-negative on (M,g), then the operator ∆ĝ + V̂ is non-negative on (M̂, ĝ)...

The spectral flow of the hermitian Dirac–Wilson operator H(m) has been used to construct a lattice version of the index of the Dirac operator. We clarify some aspects of this construction by showing the following (in 4D): When the curvature of the lattice gauge field satisfies an approximate smoothness condition, crossings of the origin by eigenvalues of H(m) can only happen when m is close to ...

LetM be a compact spin manifold with a smooth action of the ntorus. Connes and Landi constructed θ-deformations Mθ of M , parameterized by n×n real skew-symmetric matrices θ. TheMθ’s together with the canonical Dirac operator (D,H) on M are an isospectral deformation of M . The Dirac operator D defines a Lipschitz seminorm on C(Mθ), which defines a metric on the state space of C(Mθ). We show th...

We consider properties of the operators D (r , M) = a r (a † a) M (which we call generalized Laguerre-type derivatives) a and a † are boson annihilation and creation operators respectively , satisfying [ a , a † ] = 1. We obtain explicit formulas for the normally ordered form of arbitrary Taylor-expandable functions of D (r , M) with the help of an operator relation which generalizes the Dobi´n...

Diesel-operated Load Haul Dumper (LHD) vehicles are commonly used in underground coal mines. Despite their value as utility vehicles, the main drawback of these vehicles is that they generate diesel particulate matter (DPM), a known carcinogenic agent. In this work, an attempt is made to model DPM flows generated by LHDs in an underground coal mine environment for different DPM flow and intake ...

Abstract. The dynamical systems method (DSM) is justified for solving operator equations F (u) = f , where F is a nonlinear operator in a Hilbert space H. It is assumed that F is a global homeomorphism of H onto H, that F ∈ C loc, that is, it has the Fréchet derivative F ′(u) continuous with respect to u, that the operator [F ′(u)]−1 exists for all u ∈ H and is bounded, ||[F ′(u)]−1|| ≤ m(u), w...

In this note we present a polynomial bound on the distribution of poles of the scattering operator for the Laplacian on certain hyperbolic manifolds M of infinite volume. The motivation is to understand more fully the geometry of the poles of the scattering operator. The proof uses the relationship between poles of the scattering operator and zeros of the Selberg zeta function for geodesic flow...