Deformations of smooth functions on 2-torus

Deformations of Aane Torus Varieties

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 Unitary Deformations of Smooth Modular Representations

Let G be a locally Qp-analytic group and K a finite extension of Qp with residue field k. Adapting a strategy of B. Mazur (cf. [Maz89]) we use deformation theory to study the possible liftings of a given smooth G-representation ρ over k to unitary G-Banach space representations over K. The main result proves the existence of a universal deformation space in case ρ admits only scalar endomorphis...

Deformations of Smooth Toric Surfaces

For a complete, smooth toric variety Y , we describe the graded vector space T 1 Y . Furthermore, we show that smooth toric surfaces are unobstructed and that a smooth toric surface is rigid if and only if it is Fano. For a given toric surface we then construct homogeneous deformations by means of Minkowski decompositions of polyhedral subdivisions, compute their images under the Kodaira-Spence...

Non-standard smooth realization of translations on the torus

Let M be a smooth compact connected manifold, on which there exists an effective smooth circle action preserving a positive smooth volume. On M, we construct volume-preserving diffeomorphisms that are metrically isomorphic to ergodic translations on the torus, translations in which one given coordinate of the translation is an arbitrary Liouville number. To obtain this result, we explicitly con...