Walsh series and adjustment of functions on small sets

On Walsh-fourier Series^)

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 ...

Integral of Fine Computable functions and Walsh Fourier series

We define the effective integrability of Fine-computable functions and effectivize some fundamental limit theorems in the theory of Lebesgue integral such as Bounded Convergence Theorem and Dominated Convergence Theorem. It is also proved that the Walsh-Fourier coefficients of an effectively integrable Finecomputable function form an E-computable sequence of reals and converge effectively to ze...

On Pre-θ-Open Sets and Two Classes of Functions

study of hash functions based on chaotic maps

توابع درهم نقش بسیار مهم در سیستم های رمزنگاری و پروتکل های امنیتی دارند. در سیستم های رمزنگاری برای دستیابی به احراز درستی و اصالت داده دو روش مورد استفاده قرار می گیرند که عبارتند از توابع رمزنگاری کلیددار و توابع درهم ساز. توابع درهم ساز، توابعی هستند که هر متن با طول دلخواه را به دنباله ای با طول ثابت تبدیل می کنند. از جمله پرکاربردترین و معروف ترین توابع درهم می توان توابع درهم ساز md4, md...

On the computability of Walsh functions

The Haar and the Walsh functions are proved to be computable with respect to the Fine-metric dF which is induced from the in-nite product = {0; 1}{1;2; :::} with the weighted product metric dC of the discrete metric on {0; 1}. Although they are discontinuous functions on [0; 1] with respect to the Euclidean metric, they are continuous functions on ( ; dC) and on ([0; 1]; dF). On ( ; dC), comput...