Results 31 to 40 of about 61,133 (171)

Nested formulas for cosine and inverse cosine functions based on Viète's formula for $π$ [PDF]

arXiv, 2020
In this article, we develop nested representations for cosine and inverse cosine functions, which is a generalization of Vi\`{e}te's formula for $\pi$. We explore a natural inverse relationship between these representations and develop numerical algorithms to compute them. Throughout this article, we perform numerical computation for various test cases,
arxiv  

Some applications of the sine and cosine integrals [PDF]

arXiv, 2012
We show how the sine and cosine integrals may be usefully employed in the evaluation of some more complex integrals.
arxiv  

Axial cosinoidal structured illumination using phase modulation [PDF]

arXiv, 2020
We propose a novel method for generating axial cosine structured light by using phase-only spatial light modulator. We implemented axial cosine structured light using holographic technique. The computer generates double concentric annular slits with different radius, a prism phase is applied on the slits to tilts the beam that incidents on the slits ...
arxiv  

Bounded Cosine Functions Close to Continuous Scalar Bounded Cosine Functions [PDF]

Integral Equations and Operator Theory, 2016
Let $(C(t))\_{t \in R}$ be a cosine function in a unital Banach algebra. We show that if $sup\_{t\in R}\Vert C(t)-cos(t)\Vert \textless{} 2$ for some continuous scalar bounded cosine function $(c(t))\_{t\in \R},$ then the closed subalgebra generated by $(C(t))\_{t\in R}$ is isomorphic to $\C^k$ for some positive integer $k.$ If, further, $sup\_{t\in \R}
openaire   +5 more sources

A Refinement of Vietoris Inequality for Cosine Polynomials [PDF]

arXiv, 2015
The classical Vietoris cosine inequality is refined by establishing a positive polynomial lower bound.
arxiv  

On the Spectrum of Cosine Functions

Journal of Mathematical Analysis and Applications, 1999
AbstractIn this paper we give characterizations of the resolvent set of the generatorAof a strongly continuous cosine functionC(t) in terms of certain solution properties of the differential equationu″(t)=Au(t)+f(t).
openaire   +2 more sources

Sine and cosine equations on commutative hypergroups [PDF]

arXiv, 2015
In this paper we describe the solutions of the functional equations expressing the addition theorems for sine and cosine on commutative hypergroups.
arxiv  

Extensions of the Cosine-Sine functional equation [PDF]

manuscript 2019, 2019
The aim of the present paper is to give extensions of the cosine-sine functional equation.
arxiv  

The Pseudo Cosine Sequences of a Distance-Regular Graph [PDF]

arXiv, 2003
Let $G$ denote a distance-regular graph with diameter $D\ge 3$, valency $k$, and intersection numbers $a_i$, $b_i$, $c_i$. By a {\it pseudo cosine sequence} of $G$ we mean a sequence of real numbers $s_0, s_1, ..., s_D$ such that $s_0=1$ and $c_i s_{i-1}+a_i s_i+b_i s_{i+1}=k s_1 s_i$ for $ 0 \le i \le D-1$.
arxiv  

Is Cosine-Similarity of Embeddings Really About Similarity? [PDF]

ACM Web Conference 2024 (WWW 2024 Companion)
Cosine-similarity is the cosine of the angle between two vectors, or equivalently the dot product between their normalizations. A popular application is to quantify semantic similarity between high-dimensional objects by applying cosine-similarity to a learned low-dimensional feature embedding.
arxiv   +1 more source