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Possibility of gravitational repulsion in General Relativity is discussed and astronomical data in favor of cosmological acceleration are described. The problem of vacuum energy is emphasized and possible ways of its solution are indicated.…
The Implicit and Inverse Function Theorems are special cases of a general Implicit/Inverse Function Theorem which can be easily derived from either theorem. The theorems can thus be easily deduced from each other via the generalized…
This Resource Letter provides some guidance on issues that arise in teaching general relativity at both the undergraduate and graduate levels. Particular emphasis is placed on strategies for presenting the mathematical material needed for…
It made that the new symmetric property, the binary law, existed newly in our time and space at the thing except the symmetric property of the principle of general relativity which is already known in this paper clear. The introduction of…
A generalized reciprocal theorem is formulated for the motion and hydrodynamic force moments of an active particle in an arbitrary background flow of a (weakly nonlinear) complex fluid. This formalism includes as special cases a number of…
We develop a random model for relation algebras. We prove some preliminary results and pose questions that lay out a new direction of research.
On a Riemann surface there are relations among the periods of holomorphic differential forms, called Riemann's relations. If one looks carefully in Riemann's proof, one notices that he uses iterated integrals. What I have done in this paper…
In the present paper, we introduce a multibasic extension of the Ehrhart theory. We give a multibasic extension of Ehrhart polynomials and Ehrhart series. We also show that an analogue of Ehrhart reciprocity holds for multibasic Ehrhart…
The article consist of two main parts: an analog of the Leray Theory for Singular Varieties and its application to the Theory of Parshin's Residues. The first part is independent from the second. It uses the theory of Whitney…
A general rate theory for resonance energy transfer is formulated to incorporate any degrees of freedom (e.g., rotation, vibration, exciton, and polariton) as well as coherently-coupled composite states. The compact rate expression allows…
This paper provides two characterizations of regularity for near-vector spaces: first, by expressing them as a direct sum of vector spaces over division rings formed by distributive elements; second, by expressing their dimension in term of…
In this letter we reflect on the propagation of gravitational waves in alternative theories of gravity, which are typically formulated using extra gravitational degrees of freedom in comparison to General Relativity. We propose to…
We prove a general form of Green Formula and Cauchy Integral Theorem for arbitrary closed rectifiable curves in the plane.
A general information-theoretic framework for deriving physical laws is presented and a principle of informational physics is enunciated within its context. Existing approaches intended to derive physical laws from information-theoretic…
In this work, the experiment is discussed on the verification of the principle of universality of gravitational interactions and some related problems of gravity theory and physics of elementary particles. The meaning of this proposal lies…
In this paper, we generalize an elementary real-analysis result to a class of topological vector spaces. We also give an example of a topological vector space to which the result cannot be generalized.
We study a generalization of conditional probability for arbitrary ordered vector spaces. A related problem is that of assigning a numerical value to one vector relative to another. We characterize the groups for which these generalized…
Vector fields with components which are generalized zero-forms are constructed. Inner products with generalized forms, Lie derivatives and Lie brackets are computed. The results are shown to generalize previously reported results for…
We show that the definition of an algebraic basis for a vector space allows the construction of an isomorphism with the one here called Algebraic Vector Space. Although the concept does not bring anything new, we mention some of the…
The main aim of this paper is to generalize the concept of vector space by the hyperstructure. We generalize some definitions such as hypersubspaces, linear combination, Hamel basis, linearly dependence and linearly independence. A few…