Quantum field theories based on interactions which contain the Moyal star product suffer, in the general case when time does not commute with space, from several diseases: quantum equation of motions contain unusual terms, conserved currents can not be defined and the residual spacetime symmetry is not maintained. All these problems have the same origin: time ordering does not commute with taki...

Abstract The main result is an equality type mean value theorem for tangentially convex functions in terms of tangential subdifferentials, which generalizes the classical one differentiable functions, as well Wegge functions. new then applied, analogously to what done case, characterize, context, Lipschitz increasingness with respect ordering induced by a closed cone, convexity, and quasiconvex...

We provide a porosity based approach to the differentiability and continuity of real valued functions on separable Banach spaces, when the function is monotone with respect to an ordering induced by a convex cone K with non-empty interior. We also show that the set of nowhere K-monotone functions has a σ-porous complement in the space of the continuous functions.

Bogdan and Kolumbán [3] gave sufficient conditions for closedness of the solution map defined on the set of parameters. They considered the parametric equilibrium problems governed by topological pseudomonotone maps depending on a parameter. In this paper we generalize this result for parametric vector equilibrium problems with trifunctions. Let X and Y be Hausdorff topological spaces and P , t...

Let E be a real Banach space of operators ordered by a cone K. We give a sufficient condition for that each chain which is bounded above has a supremum. This condition is satisfied in several classical cases, as for the Loewner ordering on the space of all symmetric operators on a Hilbert space, for example. MSC classification (2010): 46B40, 47L07

It is well known that the classical contraction mapping principle of Banach is a fundamental result in fixed point theory. Several authors have obtained various extensions and generalizations of Banach’s theorems by considering contractive mappings on different metric spaces. Huang and Zhang [1] have replaced real numbers by ordering Banach space and have defined a cone metric space. They have ...

i P is closed, nonempty, and P / {0}, ii a, b ∈ R, a, b ≥ 0, and x, y ∈ P imply that ax by ∈ P, iii x ∈ P and −x ∈ P imply that x 0. The space E can be partially ordered by the cone P ⊂ E; by defining, x ≤ y if and only if y − x ∈ P . Also, we write x y if y − x ∈ int P , where int P denotes the interior of P . A cone P is called normal if there exists a constant K > 0 such that 0 ≤ x ≤ y impli...

Pseudo-exhaustive testing involves applying all possible input patterns to the individual output cones of a combinational circuit. Based on our new algebraic results, we have derived both generic (cone-independent) and circuit-specific (cone-dependent) bounds on minimal length of test required so that each cone in a circuit is exhaustively tested. For any circuit with five or fewer outputs, and...

The Coulomb interaction among massless Dirac fermions in graphene is unscreened around the isotropic Dirac points, causing a logarithmic velocity renormalization and a cone reshaping. In less symmetric Dirac materials possessing anisotropic cones with tilted axes, the Coulomb interaction can provide still more exotic phenomena, which have not been experimentally unveiled yet. Here, using site-s...

An application area of vertex enumeration problem (VEP) is the usage within objective space based linear/convex vector optimization algorithms whose aim to generate (an approximation of) Pareto frontier. In such algorithms, VEP, which defined in space, solved each iteration and it has a special structure. Namely, recession cone polyhedron be generated ordering cone. We consider give detailed de...