Weather derivatives are financial instruments that can be used by organizations or individuals to hedge risks associated with adverse weather conditions. conditions directly decrease profits affecting the volume of sales costs. This paper develops a methodology for temperature option pricing in equatorial regions. In this approach, is forecast combining deterministic and stochastic models. We f...

In this work, we will compare two approximation method based on hybrid Legendre andBlock-Pulse functions and a computational method for solving nonlinear Fredholm-Volterraintegral equations of the second kind which is based on replacement of the unknown functionby truncated series of well known Block-Pulse functions (BPfs) expansion

We discuss the effects of several sequence acceleration methods on the partial sums of Fourier series. For a large set of functions we show that these methods fail. 2000 Mathematics Subject Classification: 65B10, 65T10, 42A20

A general summability method of different orthogonal series is given with the help of an integrable function θ. As special cases the trigonometric Fourier, Walsh-, Walsh-Kaczmarz-, Vilenkinand Ciesielski-Fourier series and the Fourier transforms are considered. For each orthonormal system a different Hardy space is introduced and the atomic decomposition of these Hardy spaces are presented. A s...

A function or a real variable f is said to be periodic with period P if f(x+ P ) = f(x) holds for all x. Hence, if we know the values of f on an interval of length P , we know its values everywhere. If f is a function defined on an interval [a, b), we can extend f to a function defined for all x which is periodic of period b− a. We simply define f(x) to be f(x+ n(b− a)), where n is the integer ...

Every function f(x) which is of period 1 and Lebesgue integrable on [0, 1 ] may be expanded in a Walsh-Fourier series(3), f(x)~ ?.?=n ak\pk(x), where ak=fof(x)ypk(x)dx, k=0, 1, 2, • • • . Fine exhibited some of the basic similarities and differences between the trigonometric orthonormal system and the Walsh system. He identified the Walsh functions with the full set of characters of the dyadic ...

The purpose of this paper is to explore the basic question of the convergence of Fourier series. This paper will not delve into the deeper questions of convergence that measure theory illuminates, but requires only the basic principles set out by introductory real and complex analysis.

Just before 1800, the French mathematician/physicist/engineer Jean Baptiste Joseph Fourier made an astonishing discovery. As a result of his investigations into the partial differential equations modeling vibration and heat propagation in bodies, Fourier was led to claim that “every” function could be represented by an infinite series of elementary trigonometric functions — sines and cosines. A...