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A general formalism is developed for constructing modified Hamiltonian dynamical systems which preserve a canonical equilibrium distribution by adding a time evolution equation for a single additional thermostat variable. When such systems…
Due to the absence of symmetries under time and spatial translations in a general curved spacetime, the energy and momentum of matter is not conserved as it is in flat space. This means, for example, that the flux of matter energy through a…
We investigate regularity properties of generalized conjugate functions induced by a general coupling function and the associated generalized proximal mapping. Our main results provide verifiable conditions ensuring local single-valuedness,…
This work introduces ``generalized meshes", a type of meshes suited for the discretization of partial differential equations in non-regular geometries. Generalized meshes extend regular simplicial meshes by allowing for overlapping elements…
The conditions for N=1 supersymmetry in type II supergravity have been previously reformulated in terms of generalized complex geometry. We improve that reformulation so as to completely eliminate the remaining explicit dependence on the…
Geometric inequalities of classical differential geometry are used to extend to higher dimensional spacetimes the Penrose-Gibbons isoperimetric inequalities and the hoop conjecture of general reltivity.
Co lombeau's construction of generalized functions (in its special variant) is extended to a theory of generalized sections of vector bundles. As particular cases, generalized tensor analysis and exterior algebra are studied. A point value…
The aim of this paper is to present some fixed point theorems for generalized contractions by altering distance functions in a complete cone metric spaces endowed with a partial order. We also generalize fixed point theorems of J. Harjani,…
An effective mathematical framework based on Presymplectic Geometry for dealing with the "phase space picture" of timeless dynamics in General Relativity is presented. In General Relativity, the presence of the scalar Hamiltonian constraint…
We consider a scenario of large-scale modification of gravity that does not invoke extra degrees of freedom but includes coupling between baryonic matter and dark matter in the Einstein frame. The total matter energy density follows the…
A unified scheme for treating generalized superselection sectors is proposed on the basis of the notion of selection criteria to characterize states of relevance to each specific domain in quantum physics, ranging from the relativistic…
Deriving analytical expressions of dielectric permittivities is required for numerical and physical modeling of optical systems and the soar of non-hermitian photonics motivates their prolongation in the complex plane. Analytical models are…
In this article, we investigate some fixed point results satisfying a new generalized $\Delta$-implicit contractive condition in ordered complete multiplicative $\mathbf{G}_\mathcal{M}-$metric space. Also, some new definitions and fixed…
In this paper, we introduce the concept of partial extended b-metric spaces (PEBMS) as a unification and generalization of extended b-metric spaces and partial b-metric spaces. This new structure incorporates a point-dependent control…
Generalized Functions play a central role in the understanding of differential equations containing singularities and nonlinearities. Introducing infinitesimals and infinities to deal with these obstructions leads to controversies…
We outline a new model in which generalised uncertainty relations are obtained without modified commutation relations. While existing models introduce modified phase space volumes for the canonical degrees of freedom, we introduce new…
We consider the renormalization of general gauge theories on curved space-time background, with the main assumption being the existence of a gauge-invariant and diffeomorphism invariant regularization. Using the Batalin-Vilkovisky (BV)…
In many applications, one deals with nonsmooth functions, e.g., in nonsmooth dynamical systems, nonsmooth mechanics, or nonsmooth optimization. In order to establish theoretical results, it is often beneficial to regularize the nonsmooth…
We propose an alternative condition for the solvability of the Dirichlet problem for the minimal surface equation that applies to non-mean convex domains. We introduce a structural condition, obtained from a second-order ordinary…
(Abridged Abstract) This paper deals with a number of technical achievements that are instrumental for a dis-solution of the so-called {\it Hole Argument} in general relativity. The work is carried through in metric gravity for the class of…