Showing papers on "Elementary function published in 1988"

General and unified solution for perfect fluid homogeneous and isotropie cosmological models

Abstract: The general and unified solution for spatially homogeneous and isotropic cosmologies containing a perfect fluid [equation of statep=(γ−1)ρ] is determined in terms of hypergeometric functions. A set of four infinitely denumerable sequences of solutions consistent with the energy conditions are shown to exist in terms of elementary functions. A generation mechanism yields the construction of all the solutions in each sequence. Using the conformal form of the metric and putting the field equations in the form of that describing the classical motion of a particle subject to a linear force, the general solution is then determined in parametric form. Closed models are analogous to harmonic oscillators, and their lifetimes are determined as an explicit function ofγ, both for conformal and cosmological times.

Exact field calculations for asymmetrical finite-pole-tip ring heads

Abstract: An exact solution is given for the fields of an infinitely permeable asymmetrical finite-pole-tip ring head. The solution is obtained by conformal mapping and is expressed in terms of elliptic integrals and elementary functions. Using the method of undetermined coefficients, it is shown how to decompose the Schwarz-Christoffel integral into elementary functions and elliptic integrals. For each given pole geometry, the constants appearing in the Schwarz-Christoffel formula are calculated once. Then the fields at various points in the poles domain are calculated using Newton's method and the formulas for the decomposition of the Schwarz-Christoffel integral. >

Computer Image Generation Using Elementary Functions Matched to Human Vision

Abstract: Visual representation in biological visual systems appears to be accomplished by a scheme of image decomposition into a finite set of localized operators which resemble the form of Gabor Elementary Functions (GEF). These functions achieve the lowest bound on the joint entropy, defined as the product of effective spatial extent and frequency bandwidth.

Key agreements based on function composition

Abstract: Two protocols are presented that accomplish the same goal as the original Diffie-Hellman protocol, namely, to establish a common secret key using only public messages They are based on n-fold composition of some suitable elementary function The first protocol is shown to fail always when the elementary function is chosen to be linear This does not preclude its use for a suitable nonlinear elementary function The second protocol is shown to be equivalent to the Diffie-Hellman protocol when the elementary function is chosen to be linear Some examples are given to illustrate the use of both protocols It is still an open problem whether the presented approach allows for an improvement in terms of speed and/or security over the original DH-protocol

Function computing element

Abstract: PURPOSE:To calculate an elementary function such as trigonometric function at a high speed and with high accuracy by using a memory of small capacity to give an arithmetic operation to each of divided minor sections by means of an optimized polynomial of a low degree. CONSTITUTION:A quantizer 2 selects the higher rank bits of the input data and reads out a coefficient memory 4 via an address obtained by combining said higher rank bits with the lower rank bits of an address register 3. A selection circuit 5 selects these bits. A multiplier 6 multiplies the value selected by the circuit 5 by the value of an input register 1. This added value is added with the output of the memory 4 by an adder 6. The output of this addition is selected by the circuit 5 and multiplied by the value of the register 1. This arithmetic operation is repeated twice and finally the output of the adder 7 is extracted as the function value. Thus, the polynomial arithmetic is carried out in a divided minor section by means of an optimized coefficient. As a result, an elementary function is calculated at a high speed and with high accuracy.

A Dilogarithmic Extension of Liouville's Theorem on Integration in Finite Terms

Abstract: : The result obtained generalizes Liouville's Theorem by allowing, in addition to the elementary functions, dilogarithms to appear in the integral of an elementary function. The basic conclusion is that an associated function to the dilogarithm, if dilogarithms appear in the integral, appears linearly, with logarithms appearing in a non-linear way.

Convergence of simultaneous padé approximants for a class of functions

Abstract: This paper investigates rational approximations of a Markov function that have the highest order of contact with it at infinity, and whose denominators are invariant under multiplication of their argument by a root of unity of some fixed degree (such approximations are used in many number-theoretical problems). The approximations converge under mild restrictions on the measure. Moreover, the denominators of the approximants and the corresponding functions of the second kind have logarithmic asymptotics expressible in terms of a certain extremal measure which, in the simplest case, is the Tchebycheff measure. An explicit form is found for the extremal measure in the general case; in fact, the inverse of the distribution function is expressed in terms of elementary functions, the power moments are calculated, and the Markov function of the extremal measure is connected with algebraic equations and generalized hypergeometric functions.Bibliography: 10 titles.

Existence of solutions and iterations for nonlinear equations

Abstract: Publisher Summary This chapter discusses the iterations for nonlinear equations and the use of interval analysis to prove the existence of solutions of an equation. It is well-known that if for a real continuous function f: ℝ → ℝ, there exist reals a and b where a < b such that f(a) f(b) ≤ 0, then there exists an x* ∈ [a, b] such that f (x*)= 0. Furthermore, x* can be computed by the well-known bisection process. If, however, the condition f (a) f (b) ≤ 0 does not hold, then there is no statement possible whether there is a zero in [a, b] or not. Under practical aspects, the requirement that the interval arithmetic evaluation exists is not restrictive. Most mappings that appear in numerical computation are composed of the four algebraic operations and of the elementary functions for which interval arithmetic evaluations can be defined in a natural manner.

How to compute the n-fold convolution power of elementary functions without numerical integration

Abstract: A formula is developed which allows to calculate then-fold convolution power of elementary functions recursively.

Random walks for on-lattice DLA simulations

Abstract: Two efficient ways to accelerate on-lattice DLA simulations without introducing any bias are presented. The first requires one-dimensional tables but little arithmetic; the second needs no tables but necessitates the evaluation of a few elementary functions.