Related papers: On some generalizations of real numbers representa…

This is an introduction to the Atlas of Lie Groups and Representations software, for computing representation and structure theory of real reductive groups. The user is led through the basic commands of the software, via numerous examples.…

The purpose of this short paper is to identify the mathematical essence of the superiorization methodology. This methodology has been developed in recent years while attempting to solve specific application-oriented problems. Consequently,…

In this paper we explore the representation property over sets. This property generalizes constructibility, however is weak enough to enable us to prove that the class of theories $T$ whose models are representable is exactly the class of…

We give an overview on recent results concerning additive unit representations. Furthermore the solutions of some open questions are included. The central problem is whether and how certain rings are (additively) generated by their units.…

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…

In this paper, we consider representations of integers as sums of generalized heptagonal numbers with a prescribed number of repeats of each heptagonal number appearing in the sum. In particular, we investigate the classification of such…

The aim of this paper is to analyze the reconstructability of quantum mechanics from classical conditional probabilities representing measurement outcomes conditioned on measurement choices. We will investigate how the quantum mechanical…

Since the early twentieth century, it has been understood that mathematical definitions and proofs can be represented in formal systems systems with precise grammars and rules of use. Building on such foundations, computational proof…

We state and prove a general summation identity. The identity is then applied to derive various summation formulas involving the generalized harmonic numbers and related quantities. Interesting results, mostly new, are obtained for both…

Researchers are often perplexed when their machine learning algorithms are required to deal with complex number. Various strategies are commonly employed to project complex number into real number, although it is frequently sacrificing the…

Regularization and Bayesian methods for system identification have been repopularized in the recent years, and proved to be competitive w.r.t. classical parametric approaches. In this paper we shall make an attempt to illustrate how the use…

Binary relations are an important abstraction arising in many data representation problems. The data structures proposed so far to represent them support just a few basic operations required to fit one particular application. We identify…

Enumerative Geometry is concerned with the number of solutions to a structured system of polynomial equations, when the structure comes from geometry. Enumerative real algebraic geometry studies real solutions to such systems, particularly…

Axiomatizing mathematical structures is a goal of Mathematical Logic. Axiomatizability of the theories of some structures have turned out to be quite difficult and challenging, and some remain open. However axiomatization of some…

This is an overview of higher structural constructions in physics. The main motivations of our current attempt are as follows: (i) to provide a brief introduction to derived algebraic geometry, (ii) to understand how derived objects…

A quantum system at equilibrium is represented by a corresponding classical system, chosen to reproduce thermodynamic and structural properties. The motivation is to allow application of classical strong coupling theories and molecular…

For a large class of finite W algebras, the defining relations of a Yangian are proved to be satisfied. Therefore such finite W algebras appear as realisations of Yangians. This result is useful to determine properties of such W algebra…

We give a brief introduction to (upper) cluster algebras and their quantization using examples. Then we present several important families of bases for these algebras using topological models. We also discuss tropical properties of these…

In this work, we introduce a new generalized integral transform involving many potentially known or new transforms as special cases. Basic properties of the new integral transform, that investigated in this work, include the existence…

We propose that observables in quantum theory are properly understood as representatives of symmetry-invariant quantities relating one system to another, the latter to be called a reference system. We provide a rigorous mathematical…