On level sets of Darboux 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...

Level Sets and Distance Functions

This paper is concerned with the simulation of the Partial Diierential Equation (PDE) driven evolution of a closed surface by means of an implicit representation. In most applications, the natural choice for the implicit representation is the signed distance function to the closed surface. Osher and Sethian propose to evolve the distance function with a Hamilton-Jacobi equation. Unfortunately t...

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

Level Sets of Functions and Symmetry Sets of Surface Sections

We prove that the level sets of a real C function of two variables near a non-degenerate critical point are of class C [s/2] and apply this to the study of planar sections of surfaces close to the singular section by the tangent plane at an elliptic or hyperbolic point, and in particular at an umbilic point. We go on to use the results to study symmetry sets of the planar sections. We also anal...

Level sets and minimum volume sets of probability density functions

Summarizing the whole support of a random variable into minimum volume sets of its probability density function is studied in the paper. We prove that the level sets of a probability density function correspond to minimum volume sets and also determine the conditions for which the inverse proposition is verified. The distribution function of the level cuts of a density function is also introduc...