Potential functions on Grassmannians of planes and cluster transformations

Grassmannians and Cluster Algebras

Non-defectivity of Grassmannians of Planes

Let Gr(k, n) be the Plücker embedding of the Grassmann variety of projective k-planes in Pn. For a projective variety X, let σs(X) denote the variety of its s − 1 secant planes. More precisely, σs(X) denotes the Zariski closure of the union of linear spans of s-tuples of points lying on X. We exhibit two functions s0(n) ≤ s1(n) such that σs(Gr(2, n)) has the expected dimension whenever n ≥ 9 an...

Continuity of super- and sub-additive transformations of continuous functions

We prove a continuity inheritance property for super- and sub-additive transformations of non-negative continuous multivariate functions defined on the domain of all non-negative points and vanishing at the origin. As a corollary of this result we obtain that super- and sub-additive transformations of continuous aggregation functions are again continuous aggregation 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...

Transformations of Grassmannians and automorphisms of classical groups

We consider transformations preserving certain linear structure in Grassmannians and give some generalization of the Fundamental Theorem of Projective Geometry and the Chow Theorem [Ch]. It will be exploited to study linear (k, n − k)-involutions, 1 < k < n − 1. The analogy of the J. Dieudonné and C. E. Rickart result will be obtained.