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On Strongest Algebraic Program Invariants.
Publication Type: Academic Journal
Source(s): Journal of the ACM. Oct2023, Vol. 70 Issue 5, p1-22. 22p.
Abstract: A polynomial program is one in which all assignments are given by polynomial expressions and in which all branching is nondeterministic (as opposed to conditional). Given such a program, an algebraic invariant is one that is defined by polynomial equat...
Some Identities of Fully Degenerate Dowling Polynomials and Numbers.
Publication Type: Academic Journal
Source(s): Discrete Dynamics in Nature & Society. 11/14/2023, p1-9. 9p.
Abstract: Recently, Kim-Kim introduced the degenerate Whitney numbers of the first and second kind involving the degenerate Dowling polynomials and numbers. In this paper, we introduce the fully degenerate Dowling polynomials and the fully degenerate Bell polyno...
Properties of Multivariable Hermite Polynomials in Correlation with Frobenius–Genocchi Polynomials.
Publication Type: Academic Journal
Source(s): Mathematics (2227-7390). Nov2023, Vol. 11 Issue 21, p4523. 17p.
Abstract: The evolution of a physical system occurs through a set of variables, and the problems can be treated based on an approach employing multivariable Hermite polynomials. These polynomials possess beneficial properties exhibited in functional and differen...
Local Sensitivity of Failure Probability through Polynomial Regression and Importance Sampling.
Publication Type: Academic Journal
Source(s): Mathematics (2227-7390). Oct2023, Vol. 11 Issue 20, p4357. 19p.
Abstract: Evaluating the failure probability of a system is essential in order to assess its reliability. This probability may significantly depend on deterministic parameters such as distribution parameters or design parameters. The sensitivity of the failure p...
An Application of Rouché's Theorem to Delimit the Zeros of a Certain Class of Robustly Stable Polynomials.
Publication Type: Academic Journal
Source(s): Mathematics (2227-7390). Oct2023, Vol. 11 Issue 20, p4244. 12p.
Abstract: An important problem related to the study of the robust stability of a linear system that presents variation in terms of an uncertain parameter consists of understanding the variation in the roots of a system's characteristic polynomial in terms of the...
A Study on Generalized Degenerate Form of 2D Appell Polynomials via Fractional Operators.
Publication Type: Academic Journal
Source(s): Fractal & Fractional. Oct2023, Vol. 7 Issue 10, p723. 14p.
Abstract: This paper investigates the significance of generating expressions, operational principles, and defining characteristics in the study and development of special polynomials. The focus is on a novel generalized family of degenerate 2D Appell polynomials...
Derivations and representations of commutative algebras verifying a polynomial identity of degree five.
Publication Type: Academic Journal
Source(s): European Journal of Pure & Applied Mathematics. Oct2023, Vol. 16 Issue 4, p2145-2155. 11p.
Abstract: In this paper we study a class of commutative non associative algebras satisfying a polynomial identity of degree five. We show that under the assumption of the existence of a non-zero idempotent, any commutative algebra verifying such an identity admi...
Design of Polynomial Observer-Based Control of Fractional-Order Power Systems.
Publication Type: Academic Journal
Source(s): Mathematics (2227-7390). Nov2023, Vol. 11 Issue 21, p4450. 11p.
Abstract: This research addresses the problem of globally stabilizing a distinct category of fractional-order power systems (F-OP) by employing an observer-based methodology. To address the inherent nonlinearity in these systems, we leverage a Takagi–Sugeno (TS)...
The mixed virtual element discretization for highly-anisotropic problems: the role of the boundary degrees of freedom.
Publication Type: Academic Journal
Source(s): Mathematics in Engineering. 2023, Vol. 5 Issue 6, p1-32. 32p.
Abstract: In this paper, we discuss the accuracy and the robustness of the mixed Virtual Element Methods when dealing with highly anisotropic diffusion problems. In particular, we analyze the performance of different approaches which are characterized by differe...
A Polynomial Synthesis Approach to Design and Control an LCL-Filter-Based PWM Rectifier with Extended Functions Validated by SIL Simulations.
Publication Type: Academic Journal
Source(s): Energies (19961073). Nov2023, Vol. 16 Issue 21, p7382. 15p.
Abstract: Controlling a PWM rectifier can be challenging due to the bilinear nature of its averaged model. This paper introduces the use of the Butterworth approach to design and control an LCL-filter-based PWM rectifier with power quality functions. By leveragi...