Abstract In his celebrated article, Aronson established Gaussian bounds for the fundamental solution to Cauchy problem governed by a second order divergence form operator with uniformly elliptic coefficients. We extend Aronson’s proof of upper heat kernel estimates nonlocal operators whose jumping satisfies pointwise bound and energy is coercive. A detailed given in Euclidean space extensions d...

The Gauss–Bonnet formula finds applications in various fundamental fields. Global or local analysis on the basis of this is possible only integral form since depends choice a simple region an orientable smooth surface S. objective present paper to construct differential relation metric properties concerned at point Pointwise S through relation, which expected provide new geometrical insights in...

In this paper, we show that a pointwise symmetric pre-isotonic preclosure function is uniquely determined the pairs of sets it separates. We then show that when the preclosure function of the domain is pre-isotonic and the pre-closure function of the codomain is pre-isotonic and pointwise-pre-symmetric, functions which separate only those pairs of sets which are already separated are precontinu...

We shall show that, for any given point p on a Riemannian manifold (M, g0), there is a pointwise conformal metric g = -Dg0 in which the g-geodesic sphere centered at p with radius r has constant mean curvature 1 /r for all sufficiently small r . Furthermore, the exponential map of g at p is a measure preserving map in a small ball around p . INTRODUCTION This note is devoted to studying the mea...

We show that the metric operator for a pseudo-supersymmetric Hamiltonian that has at least one negative real eigenvalue is necessarily indefinite. We introduce pseudoHermitian fermion (phermion) and abnormal phermion algebras and provide a pair of basic realizations of the algebra of N = 2 pseudo-supersymmetric quantum mechanics in which pseudo-supersymmetry is identified with either a boson-ph...

Relativistic massive bosons with spin one are considered in several quantization schemes. In all of them the system is shown described by a non-Hermitian Hamiltonian H 6= H and helicity operator Λ. Constructively we show that in all of the contemplated schemes both these operators H and Λ prove simultaneously PT −symmetric, i.e., pseudo-Hermitian with respect to a certain not too complicated in...

We extend the concept of fuzzy integral based on ⊕-decomposable measure from nonnegative fuzzy measurable function to extended real-valued fuzzy measurable function. Further investigations of fuzzy integrals based on pseudo-additive decomposable measure are carried out. Meanwhile, the space (S(μ),σ(·,·)) of all fuzzy measurable function will be proved to be a pseudo-metric space. Finally, as an...

In this paper we study the property of generic global rigidity for frameworks of graphs embedded in d-dimensional complex space and in a d-dimensional pseudo-Euclidean space (R with a metric of indefinite signature). We show that a graph is generically globally rigid in Euclidean space iff it is generically globally rigid in a complex or pseudo-Euclidean space. We also establish that global rig...

In this paper we establish new forward and backward versions of Ekeland’s variational principle for the class of strictly-decreasing forward(resp. backward-) lower-semicontinuou functionals in pseudo-quasimetric spaces. We do not require that the space under consideration either is complete or enjoys the limit uniqueness property due to the fact that the collections of forward and backward limi...

We model pseudo–Finsler geometries, with pseudo–Euclidean signatures of metrics, for two classes of four dimensional nonholonomic manifolds: a) tangent bundles with two dimensional base manifolds and b) pseudo–Riemannian/ Einstein manifolds. Such spacetimes are enabled with nonholonomic distributions and associated nonlinear connection structures and theirs metrics are solutions of the field eq...