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A vector-tensor theory of gravity that was introduced in an earlier publication is analyzed in detail and its consequences for early universe cosmology are examined. The multiple light cone structure of the theory generates different speeds…
We establish the reciprocity law along a vertical curve for residues of differential forms on arithmetic surfaces, and describe Grothendieck's trace map of the surface as a sum of residues. Points at infinity are then incorporated into the…
In multi-agent systems, cooperative behavior is largely determined by the network structure which dictates the interactions among neighboring agents. These interactions often exhibit multidimensional features, either as relationships of…
The existence of a fundamental scale is expected to be a key feature of quantum gravity. Many approaches take this property as a starting assumption. Here, instead, we take a less conventional viewpoint based on a critical inspection of…
We generalize first-species counterpoint theory to arbitrary rings and obtain some new counting and maximization results that enrich the theory of admitted successors, pointing to a structural approach, beyond computations. The…
In this article we discuss a generalized Wirtinger inequality.
In this work we introduce reciprocity functors, construct the associated K-group of a family of reciprocity functors, which itself is a reciprocity functor, and compute it in several different cases. It may be seen as a first attempt to get…
Isotopic pairs and their representations are considered in a general framework of the vector superalgebra. Numerous examples of finite-dimensional and infinite-dimensional isotopic pairs are discussed. Several types of their representations…
We derive certain constraints on the reflection matrix for reflection from a plane, nonmagnetic, optically anisotropic surface using a reciprocity theorem stated long ago by van de Hulst in the context of scattering of polarized light. The…
We provide a complete structure theorem for involutory matrices. This yields a new approach to principal angles between subspaces and provide a series of nice formulae for these angles.
The paper constructs a generalized metrical multi-time Lagrange space, which allows a natural development of relativistic geometrical optics theories, in a general setting.
These are some informal notes concerning topological vector spaces, with a brief overview of background material and basic notions, and emphasis on examples related to classical analysis.
A generalization of the quotient integral formula is presented and some of its properties are investigated. Also the relations between two function spaces related to the spacial homogeneous spaces are derived by using general quotient…
We present the first steps of interaction spaces theory, a universal mathematical theory of complex systems which is able to embed cellular automata, agent based models, master equation based models, stochastic or deterministic, continuous…
This paper formulates generalized versions of the general principle of relativity and of the principle of equivalence that can be applied to general abstract spaces. It is shown that when the principles are applied to the Hilbert space of a…
The division between two vectors belonging to the same vector space is obtained by elementary procedures of vector algebra and is defined by a matrix. This representation is obtained for two and three dimensional vector spaces. A new vector…
We prove that if a subset of the d-dimensional vector space over a finite field is large enough, then it contains many k-tuples of mutually orthogonal vectors.
This is a review with the ambitious goal of covering the recent progress in: 1) universal relations (in general relativity and alternative theories of gravity), and 2) neutron star models in alternative theories. We also aim to be…
The implications of the Lorentz reciprocity theorem for a scatterer connected to waveguides with arbitrary modes, including degenerate, evanescent, and complex modes, are discussed. In general it turns out that a matrix $CS$ is symmetric,…
A plethora of vector-space representations for words is currently available, which is growing. These consist of fixed-length vectors containing real values, which represent a word. The result is a representation upon which the power of many…