Related papers: Non-commutative Combinatorial Inverse Systems
We show that the strength of non-commutativity could play a role in determining the boundary condition of a physical problem. As a toy model we consider the inverse square problem in non-commutative space. The scale invariance of the system…
In the current work, the author present a symbolic algorithm for finding the determinant of any general nonsingular cyclic heptadiagonal matrices and inverse of anti-cyclic heptadiagonal matrices. The algorithms are mainly based on the work…
Given a non-contracting trajectory of a nonlinear system, we consider the question of designing an input perturbation that makes the perturbed trajectory contracting. This paper stresses the analogy of this question with the classical…
Quantum nonrelativistic systems with $2\times2$ matrix potentials are investigated. Physically, they simulate charged or neutral fermions with non-trivial dipole momenta, interacting with an external electric field. Assuming rotationally…
By using the quasi-determinant the construction of Gel'fand et al. leads to the inverse of a matrix with noncommuting entries. In this work we offer a new method that is more suitable for physical purposes and motivated by deformation…
This paper introduce the notion of output contraction that expands the contraction notion to the time-varying nonlinear systems with output. It pertains to the systems' property that any pair of outputs from the system converge to each…
In the literature of stochastic orders, one rarely finds results that can be considered as criteria for the non-comparability of random variables. In this paper, we provide results that enable researchers to use simple tools to conclude…
We argue that there should exist a "noncommutative Fourier transform" which should identify functions of noncommutative variables (say, of matrices of indeterminate size) and ordinary functions or measures on the space of paths. Some…
Use of certain non-commuting variables is considered in first-order differential equations. Superspace variables are discussed within the setting of first-order ordinary differential equations and n-ary algebras. Results on quadratic…
We provide a permutation-invariant version of the Koml\'os' theorem for non-negative random variables. The proof is quite elementary in the sense that it did not use the Axiom of Choice, and was based on a recent result in [3].
In this survey we discuss the notion of combinatorial interpretation in the context of Algebraic Combinatorics and related areas. We approach the subject from the Computational Complexity perspective. We review many examples, state a…
By suitable examples we illustrate an algorithm for composition of inverse problems.
Short nonstandard proofs are given for some results about infinite systems of equations in infinitely many variables.
General non-commutative supersymmetric quantum mechanics models in two and three dimensions are constructed and some two and three dimensional examples are explicitly studied. The structure of the theory studied suggest other possible…
A finite spin system invariant under a symmetry group G is a very illustrative example of the finite group action on a set of mappings f:X->Y. In the case of spin systems X is a set of spin carriers and Y contains 2s+1 z-components -s<=m<=s…
When a mathematical or computational model is used to analyse some system, it is usual that some parameters resp.\ functions or fields in the model are not known, and hence uncertain. These parametric quantities are then identified by…
We extend integrable systems on quad-graphs, such as the Hirota equation and the cross-ratio equation, to the non-commutative context, when the fields take values in an arbitrary associative algebra. We demonstrate that the…
We summarize our recent findings, where we proposed a framework for learning a Kolmogorov model, for a collection of binary random variables. More specifically, we derive conditions that link outcomes of specific random variables, and…
A new class of Semantic Numeration Systems, namely, positive rational Semantic Numeration Systems is introduced. For cardinal semantic operators, differences in the formation of carry (common carry) and remainders are defined. The…
With multiple outcomes in empirical research, a common strategy is to define a composite outcome as a weighted average of the original outcomes. However, the choices of weights are often subjective and can be controversial. We propose an…