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In this paper a mathematically precise global (i.e. not the usual local) approach is presented to the variational principles of general relativistic classical field theories. Problems of the classic (usual) approaches are also discussed in…
Five-vectors theory of gravity is proposed, which admits an arbitrary choice of the energy density reference level. This theory is formulated as the constraint theory, where the Lagrange multipliers turn out to be restricted to some class…
The generalized divided differences are introduced. They are applied to investigate some properties characterizing generalized higher-order convexity. Among others some support-type property is proved.
A new proof for adjoint systems of linear equations is presented. The argument is built on the principles of Algorithmic Differentiation. Application to scalar multiplication sets the base line. Generalization yields adjoint inner vector,…
The goal of this survey is to introduce all the necessary concepts and theorems to provide a rigorous and self-contained proof of the Law of Quadratic Reciprocity and see how this is a useful tool to obtain results such as the problem of…
Distributed representations (such as those based on embeddings) and discrete representations (such as those based on logic) have complementary strengths. We explore one possible approach to combining these two kinds of representations. We…
The paper gives the main lines of a general theory for physical measurements.
It seems that the index theory for non-compact spaces has found its ultimate formulation in realm of coarse spaces and $K$-theory of related operator algebras. Relative and partitioned index theorems may be mentioned as two important and…
Continuing from part (I), we develop properties of real intersection theory that turns out to be an extension of the well-established theory in algebraic geometry.
We present an elementary proof concerning reciprocal transmittances and reflectances. The proof is direct, simple, and valid for the diverse objects that can be absorptive and induce diffraction and scattering, as long as the objects…
We announce a very general statement involving the rational quartic residue symbol $(m/p)_4$ and, more generally, Legendre symbols of the type ${a+b\sqrt{m}/p$. We show how our main theorem can be used to produce many older results such as…
We prove a simple inequality for a sum of squares of norms of two vectors in an inner product space. Next, using this inequality we derive the so--called "reverse uncertainty relation" and analyze its properties.
A more general notion of weight called admissible is introduced and then an investigation is carried out on the a.e. convergence of weighted strong laws of large numbers and their applications to weighted one-sided ergodic Hilbert…
In the present paper, a notion of M-basis and multi dimension of a multi vector space is introduced and some of its properties are studied.
We construct a general relativity formula for the law of gravity for material bodies. The formula contains three numeric parameters that are to be determined experimentally. If they are chosen from symmetry considerations, then the theory…
This paper presents an analysis of data from a gift-exchange-game experiment. The experiment was described in `The Impact of Social Comparisons on Reciprocity' by G\"achter et al. 2012. Since this paper uses state-of-art data science…
The paper is an introduction into General Ether Theory (GET). We start with few assumptions about an universal ``ether'' in a Newtonian space-time which fulfils \partial_t \rho + \partial_i (\rho v^i) = 0 \partial_t (\rho v^j) +…
The aim of this chapter is to present an introduction and also an overview of some of the most relevant results concerning positivity energy theorems in General Relativity. These theorems provide the answer to a long standing problem that…
In this paper, we prove a semistable reduction type theorem for multi-filtered vector spaces (or known as multi-weighted vector spaces).
We consider a functional analytic variant of the notion of Tate space, namely the category of those topological vector spaces which have a direct sum decomposition where one summand is nuclear Frechet space and the other is the dual of a…