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Stochastic differential equations (sdes) play an important role in physics but existing numerical methods for solving such equations are of low accuracy and poor stability. A general strategy for developing accurate and efficient schemes…
Solving a system of nonlinear inequalities is an important problem for which conventional numerical analysis has no satisfactory method. With a box-consistency algorithm one can compute a cover for the solution set to arbitrarily close…
This paper studies the identification of nonlinearly parameterized control systems in given experiments. Several identifiability criteria are established and an implementable algorithm is proposed for practicality with the convergence rate…
Encoding finite linear CSPs as Boolean formulas and solving them by using modern SAT solvers has proven to be highly effective, as exemplified by the award-winning sugar system. We here develop an alternative approach based on ASP. This…
We prove some existence results for a class of nonlinear fractional equations driven by a nonlocal operator.
This paper considers the problem of testing whether there exists a non-negative solution to a possibly under-determined system of linear equations with known coefficients. This hypothesis testing problem arises naturally in a number of…
The reliability and precision of numerically solving stochastic non-Markovian equations by standard numerical codes, more specifically, with the fourth-order Runge-Kutta routine for solving differential equations, is gauged by comparing the…
In this paper we carefully study the MSE performance of the linear analog codes. We have derived a lower bound of the MSE performance under Likelihood(ML) and Linear Minimal Mean Square Error(LMMSE) decoding criteria respectively. It is…
In this paper are examined general classes of linear and non-linear analytical systems of partial differential equations. Indeed the integrability conditions are found and if they are satisfied, the solutions are given as functional series…
Binary classification is a fundamental task in machine learning, with applications spanning various scientific domains. Whether scientists are conducting fundamental research or refining practical applications, they typically assess and…
This article introduces two new fractional operators with sine ($\sin$) and cosine ($\cos$) kernels, motivated by their fundamental role in modeling AC signals in electrical circuits. The operators are designed to improve the analysis of…
This work is devoted to find the numerical solutions of several one dimensional second-order ordinary differential equations. In a heuristic way, in such equations the quadratic logistic maps regarded as a local function are inserted within…
We present a decoder for nonbinary CWS quantum codes using the structure of union codes. The decoder runs in two steps: first we use a union of stabilizer codes to detect a sequence of errors, and second we build a new code, called union…
This paper is dedicated to present an exact solution for a nonlinear differential equation so-called Abel equation. This equation was known as one of the group of unsolvable differential equations. The present method is applicable for any…
The Numerical Assembly Technique is extended to investigate arbitrary planar frame structures with the focus on the computation of natural frequencies. This allows us to obtain highly accurate results without resorting to spatial…
Short nonstandard proofs are given for some results about infinite systems of equations in infinitely many variables.
In this article, we consider the decoding problem of affine Grassmann codes over nonbinary fields. We use matrices of different ranks to construct a large set consisting of parity checks of affine Grassmann codes, which are orthogonal with…
This paper presents a fast and effective computer algebraic method for analyzing and verifying non-linear integer arithmetic circuits using a novel algebraic spectral model. It introduces a concept of algebraic spectrum, a numerical form of…
In this article, the operator approach to modeling numeral systems is introduced. This approach can be useful for coding information and providing computer protection. Certain examples of such numeral systems are considered. In addition,…
We deliver a call to arms for probabilistic numerical methods: algorithms for numerical tasks, including linear algebra, integration, optimization and solving differential equations, that return uncertainties in their calculations. Such…