On Filippov’s implicit functions lemma

A Semi Derivation Lemma on Bv Functions

This paper presents a proof of a derivation lemma on the space of BV functions. The origin of this question can be found in the context of the image matching in the framework of large deformation diffeomorphisms. To compute the geodesic equations on the space of diffeomorphisms, one needs this result, which also gives the structure of the initial momentum, i.e. the central tool in the Hamiltoni...

Approximating Subadditive Hadamard Functions on Implicit Matrices

An important challenge in the streaming model is to maintain small-space approximations of entrywise functions performed on a matrix that is generated by the outer product of two vectors given as a stream. In other works, streams typically define matrices in a standard way via a sequence of updates, as in the work of Woodruff [22] and others. We describe the matrix formed by the outer product, ...

On Implicit Functions in Nonsmooth Analysis

We study systems of equations, F (x) = 0, given by piecewise differentiable functions F : R ! R, k " n. The focus is on the representability of the solution set locally as an (n # k)-dimensional Lipschitz manifold. For that, nonsmooth versions of inverse function theorems are applied. It turns out that their applicability depends on the choice of a particular basis. To overcome this obstacle we...

Test functions, distributions, and Sobolev’s lemma

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...