scholarly journals Positive Polynomials on Closed Boxes

2019 ◽  
Vol 20 (3) ◽  
pp. 509
Author(s):  
Marcio A. Diniz ◽  
R. B. Stern ◽  
Luis E. Salazar
Keyword(s):  
Analogous Result ◽  
Bernstein Polynomials ◽  
Positive Polynomials

We present two different proofs that positive polynomials on closed boxes of $\mathbb{R}^2$ can be written as bivariate Bernstein polynomials with strictly positive coefficients.Both strategies can be extended to prove the analogous result for polynomials that are positive on closed boxes of $\mathbb{R}^n$, $n>2$.

scholarly journals Numerical Analysis of Viscoelastic Rotating Beam with Variable Fractional Order Model Using Shifted Bernstein–Legendre Polynomial Collocation Algorithm

2021 ◽  
Vol 5 (1) ◽  
pp. 8
Author(s):  
Cundi Han ◽  
Yiming Chen ◽  
Da-Yan Liu ◽  
Driss Boutat
Keyword(s):  
Numerical Analysis ◽  
Fractional Order ◽  
Governing Equation ◽  
Numerical Solutions ◽  
Bernstein Polynomials ◽  
Matrix Product ◽  
Algebraic Equations ◽  
Rotating Beam ◽  
The Matrix ◽  
The Time Domain

This paper applies a numerical method of polynomial function approximation to the numerical analysis of variable fractional order viscoelastic rotating beam. First, the governing equation of the viscoelastic rotating beam is established based on the variable fractional model of the viscoelastic material. Second, shifted Bernstein polynomials and Legendre polynomials are used as basis functions to approximate the governing equation and the original equation is converted to matrix product form. Based on the configuration method, the matrix equation is further transformed into algebraic equations and numerical solutions of the governing equation are obtained directly in the time domain. Finally, the efficiency of the proposed algorithm is proved by analyzing the numerical solutions of the displacement of rotating beam under different loads.

scholarly journals Two matrix methods for solution of nonlinear and linear Lane-Emden type equations with mixed condition by operational matrix

2015 ◽  
Vol 4 (3) ◽  
pp. 420 ◽  
Author(s):  
Behrooz Basirat ◽  
Mohammad Amin Shahdadi
Keyword(s):  
Bernstein Polynomials ◽  
Operational Matrix ◽  
Numerical Procedure ◽  
Operational Matrices ◽  
Algebraic Equations ◽  
Mixed Condition ◽  
Matrix Methods ◽  
Numerical Examples ◽  
Linear Algebraic Equations ◽  
The Given

<p>The aim of this article is to present an efficient numerical procedure for solving Lane-Emden type equations. We present two practical matrix method for solving Lane-Emden type equations with mixed conditions by Bernstein polynomials operational matrices (BPOMs) on interval [<em>a; b</em>]. This methods transforms Lane-Emden type equations and the given conditions into matrix equation which corresponds to a system of linear algebraic equations. We also give some numerical examples to demonstrate the efficiency and validity of the operational matrices for solving Lane-Emden type equations (LEEs).</p>

scholarly journals The Non-Relativistic Many-Body Quantum-Mechanical Hamiltonian with Diamagnetic Current-Current Interaction

2021 ◽  
Author(s):  
Ladislaus Alexander Bányai
Keyword(s):  
Solid State ◽  
Analogous Result ◽  
Charged Particles ◽  
Coulomb Gauge ◽  
Quantum Mechanical ◽  
Photon Propagator ◽  
Coulomb Interactions ◽  
Many Body ◽  
Transverse Current ◽  
Current Interaction

AbstractWe extend the standard solid-state quantum mechanical Hamiltonian containing only Coulomb interactions between the charged particles by inclusion of the (transverse) current-current diamagnetic interaction starting from the non-relativistic QED restricted to the states without photons and neglecting the retardation in the photon propagator. This derivation is supplemented with a derivation of an analogous result along the non-rigorous old classical Darwin-Landau-Lifshitz argumentation within the physical Coulomb gauge.

Minimality and ergodicity of a generic analytic foliation of ℂ2

2008 ◽  
Vol 28 (5) ◽  
pp. 1533-1544
Author(s):  
T. GOLENISHCHEVA-KUTUZOVA ◽  
V. KLEPTSYN
Keyword(s):  
Analogous Result ◽  
Generic Polynomial ◽  
Analytic Foliation

AbstractIt is well known that a generic polynomial foliation of ℂ2 is minimal and ergodic. In this paper we prove an analogous result for analytic foliations.

Kantorovich-Bernstein polynomials

1990 ◽  
Vol 6 (4) ◽  
pp. 421-435 ◽  
Author(s):  
Zeev Ditzian ◽  
Xinlong Zhou
Keyword(s):  
Bernstein Polynomials

Ramsey's theorem for computably enumerable colorings

2001 ◽  
Vol 66 (2) ◽  
pp. 873-880 ◽  
Author(s):  
Tamara J. Hummel ◽  
Carl G. Jockusch
Keyword(s):  
Analogous Result ◽  
Computably Enumerable Set ◽  
Ramsey's Theorem ◽  
Ramsey’S Theorem ◽  
Computably Enumerable

AbstractIt is shown that for each computably enumerable set of n-element subsets of ω there is an infinite set A ⊆ ω such that either all n-element subsets of A are in or no n-element subsets of A are in . An analogous result is obtained with the requirement that A be replaced by the requirement that the jump of A be computable from 0(n). These results are best possible in various senses.

scholarly journals Hybrid Bernstein Block-Pulse Functions Method for Second Kind Integral Equations with Convergence Analysis

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Mohsen Alipour ◽  
Dumitru Baleanu ◽  
Fereshteh Babaei
Keyword(s):  
Integral Equation ◽  
Approximate Solution ◽  
Convergence Analysis ◽  
Bernstein Polynomials ◽  
Linear Equations ◽  
The Other ◽  
New Combination ◽  
System Of Linear Equations ◽  
Numerical Examples ◽  
Block Pulse Functions

We introduce a new combination of Bernstein polynomials (BPs) and Block-Pulse functions (BPFs) on the interval [0, 1]. These functions are suitable for finding an approximate solution of the second kind integral equation. We call this method Hybrid Bernstein Block-Pulse Functions Method (HBBPFM). This method is very simple such that an integral equation is reduced to a system of linear equations. On the other hand, convergence analysis for this method is discussed. The method is computationally very simple and attractive so that numerical examples illustrate the efficiency and accuracy of this method.

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