Results 31 to 40 of about 41,706 (192)
On Some Lie Bialgebra Structures on Polynomial Algebras and their Quantization [PDF]
, 2007 We study classical twists of Lie bialgebra structures on the polynomial current algebra $\mathfrak{g}[u]$, where $\mathfrak{g}$ is a simple complex finite-dimensional Lie algebra.
A. A. Stolin +32 more
core +2 more sources
Journal of Taibah University for Science, 2020 This article deals with the development of the number of periodic solutions for ordinary differential equations. We investigated focal values for first-order non-autonomous differential equation for periodic solutions from a fine focus $\mathfrak {z}=0 $.
Saima Akram +4 more
doaj +1 more source
Perspectives in Education, 2023 This article focuses on first-year university students’ understanding of concepts related to third-degree polynomial and trigonometric functions that they encountered during their study of Grade 12 mathematics.
Aneshkumar Maharaj
doaj +1 more source
On generalized trigonometric functions and series of rational functions
, 2017 Here we introduce a way to construct generalized trigonometric functions associated with any complex polynomials, and the well known trigonometric functions can be seen to associate with polynomial $x^2-1$.
Yu, Han
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A Levinson-Galerkin algorithm for regularized trigonometric approximation
, 1999 Trigonometric polynomials are widely used for the approximation of a smooth function $f$ from a set of nonuniformly spaced samples $\{f(x_j)\}_{j=0}^{N-1}$.
Strohmer, Thomas
core +3 more sources
Bethe Equations "on the Wrong Side of Equator" [PDF]
, 1998 We analyse the famous Baxter's $T-Q$ equations for $XXX$ ($XXZ$) spin chain and show that apart from its usual polynomial (trigonometric) solution, which provides the solution of Bethe-Ansatz equations, there exists also the second solution which should ...
Baxter R J +10 more
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Neighborliness of the symmetric moment curve [PDF]
, 2011 We consider the convex hull B_k of the symmetric moment curve U(t)=(cos t, sin t, cos 3t, sin 3t, ..., cos (2k-1)t, sin (2k-1)t) in R^{2k}, where t ranges over the unit circle S= R/2pi Z. The curve U(t) is locally neighborly: as long as t_1, ..., t_k lie
Alexander Barvinok +3 more
core +3 more sources
Approximation of classes B^ω_p,θ of periodic functions of several variables by polynomials with spectrum from cubic areas (in Ukrainian) [PDF]
Математичні Студії, 2011 We have obtained exact order estimates for error of approximation of classes B^ω_p,θ of periodic functions of several variables by trigonometric polynomials with spectrum from cubic areas.
S. A. Stasyuk
doaj
Covariance of the number of real zeros of a random trigonometric polynomial
International Journal of Mathematics and Mathematical Sciences, 2006 For random coefficients aj and bj we consider a random trigonometric polynomial defined as Tn(θ)=∑j=0n{ajcosjθ+bjsinjθ}. The expected number of real zeros of Tn(θ) in the interval (0,2π) can be easily obtained. In this note we show that this number is
K. Farahmand, M. Sambandham
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Communications on Pure and Applied Mathematics, EarlyView.ABSTRACT The leading‐order asymptotic behavior of the solution of the Cauchy initial‐value problem for the Benjamin–Ono equation in L2(R)$L^2(\mathbb {R})$ is obtained explicitly for generic rational initial data u0$u_0$. An explicit asymptotic wave profile uZD(t,x;ε)$u^\mathrm{ZD}(t,x;\epsilon)$ is given, in terms of the branches of the multivalued ...
Elliot Blackstone +3 more
wiley +1 more source