Results 211 to 220 of about 2,762,125 (247)

A Note on Fuzzy Cosine Function

International Journal of Fuzzy Systems, 2021
The arithmetic operations given between the Interval Type-2 Trapezoidal Fuzzy Numbers (IT2TrFN)s should satisfy the closeness property. Otherwise, the result encountered when the operations are used may be meaningless and not suitable for the purpose. The aim of this note is to show errors in the definitions using a non-closed division operation given ...
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Modified B function basis sets with generalized hyperbolic cosine functions [PDF]

Computational and Theoretical Chemistry, 2018
Efficient exponential type basis sets constructed from new hyperbolic cosine type B functions have been used in self consistent field calculations for the ground states of the atoms from Helium to Argon and their ions.
Murat Erturk, Emine Öztürk
exaly   +2 more sources

A Functional Equation for the Cosine on Semigroups with Endomorphisms

Vietnam Journal of Mathematics, 2022
Let \(S\) be a semigroup and \(\mathbb{F}\) a quadratically closed field of characteristic different from 2. Assume that \(\phi,\varphi\colon S\to S\) are two given endomorphisms and \(\mu\colon S\to \mathbb{F}\) is a given multiplicative mapping satisfying the condition \(\mu(x\varphi(x))=1\) for all \(x\in S\). Then the functional equation \[ f(x\phi(
Mohamed Ayoubi, Driss Zeglami
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Generalised cosine functions, basis and regularity properties [PDF]

Journal of Mathematical Analysis and Applications, 2016
We examine regularity and basis properties of the family of rescaled $p$-cosine functions. We find sharp estimates for their Fourier coefficients. We then determine two thresholds, $p_0 2$, such that this family is a Schauder basis of $L_s(0,1)$ for all $
Lyonell Boulton, Houry Melkonian
exaly   +2 more sources

A Functional Equation for the Cosine

Canadian Mathematical Bulletin, 1968
It is known [3], [5] that, the complex-valued solutions of(B)(apart from the trivial solution f(x)≡0) are of the form(C)(D)In case f is a measurable solution of (B), then f is continuous [2], [3] and the corresponding ϕ in (C) is also continuous and ϕ is of the form [1],(E)In this paper, the functional equation(P)where f is a complex-valued, measurable
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On a characteristic of cosine functions

Semigroup Forum, 2013
In this note, the notion of strongly continuous cosine function in a Banach space is investigated by using the Laplace transform, and some results are given. It is well known that this operator-valued function is the solution operator (i.e., propagator) for a well-posed incomplete second order abstract Cauchy problem in a Banach space.
Mei, Zhan-Dong, Peng, Ji-Gen, Zhang, Yang   +2 more
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Convoluted C-cosine functions and semigroups. Relations with ultradistribution and hyperfunction sines [PDF]

Journal of Mathematical Analysis and Applications, 2008
Convoluted C-cosine functions and semigroups in a Banach space setting extending the classes of fractionally integrated C-cosine functions and semigroups are systematically analyzed. Structural properties of such operator families are obtained. Relations
Stevan Pilipovic, M Kostic
exaly   +2 more sources

Digital Hardware for Sine-Cosine Function

IEEE Transactions on Computers, 1977
The design of a high-speed digital processor for the sine and cosine functions is discussed. The hardware provides a significant speed advantage over software calculations of these functions. The special processor provides floating point results of 35 bit accuracy within 40 μs after the argument is loaded.
David G. Steer, S. R. Penstone
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Evaluating the Cosine Function

The Mathematics Teacher, 1971
The cosine function is a mapping of real numbers into real numbers. The function is called cos, and the mapping is usually described with reference to a geometric figure that involves a number circle and a number line. (See fig. 1.)
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On the cosine-sine functional equation on groups

aequationes mathematicae, 2002
The authors find the solutions \(f,g\in C(G)\) of each of the functional equations \[ \frac{f(x+y)\pm f(x+\sigma y)}{2}=f(x)g(y)+g(x)f(y)+h(x)h(y), \;\forall x,y\in G \] where \(G\) is a topological Abelian group, \(\sigma :G\longrightarrow G\) is a continuous involutive automorphism of \(G\), and where \(C(G)\) denotes the algebra of continuous ...
Friis, P. de Place, Stetkær, H.
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