We introduce and study the Koszul complex for a Hecke R-matrix. Its cohomologies, called the Berezinian, are used to de ne quantum superdeterminant for a Hecke R-matrix. Their behaviour with respect to Hecke sum of R-matrices is studied. Given a Hecke R-matrix in n-dimensional vector space, we construct a Hecke R-matrix in 2n-dimensional vector space commuting with a di erential. The notion of ...

We consider the di?erential equation f<sup>''</sup> +A(z)f<sup>'</sup> +B(z)f = 0, where A(z) and B(z) are entire complex functions. improve various restrictions on coe?cients prove that all non-trivial solutions of in?nite order.

dae and pdae are systems of ordinary and partial di erential-algebraic equations with constraints. They occur frequently in applications such as constrained multibody mechanics, space-craft control and incompressible uid dynamics. A dae has di erential index r if a minimum of r+1 di erentiations of it are required before no new constraints are obtained. While dae of low di erential index (0 or ...

This paper considers the security of iterated block ciphers against the di erential cryptanalysis introduced by Biham and Shamir Di erential cryptanalysis is a chosen plaintext attack on secret key block ciphers that are based on iterating a cryptographically weak function r times e g the round Data Encryption Standard DES It is shown that the success of such attacks on an r round cipher depend...

"In this paper we investigate the existence of solutions initial value problems (IVP for short), partial hyperbolic functional and neutral differential inclusions fractional order involving Caputo derivative with finite delay by using nonlinear alternative Frigon type multivalued admissible contraction in Frechet spaces."

This paper considers the security of iterated block ciphers against the di erential cryptanalysis introduced by Biham and Shamir. Di erential cryptanalysis is a chosen-plaintext attack on secret-key block ciphers that are based on iterating a cryptographically weak function r times (e.g., the 16-round Data Encryption Standard (DES) ). It is shown that the success of such attacks on an r-round c...

Cryptosystem designers frequently assume that secrets will be manipulated in closed, reliable computing environments. Unfortunately, actual computers and microchips leak information about the operations they process. This paper examines speci c methods for analyzing power consumption measurements to nd secret keys from tamper resistant devices. We also discuss approaches for building cryptosyst...

We propose a new technique called Di erential Cluster Analysis for side-channel key recovery attacks. This technique uses cluster analysis to detect internal collisions and it combines features from previously known collision attacks and Di erential Power Analysis. It captures more general leakage features and can be applied to algorithmic collisions as well as implementation speci c collisions...

We present hidden veri cation as a means to make the power of computational logic available to users of computer algebra systems while shielding them from its complexity. We have implemented in PVS a library of facts about elementary and transcendental functions, and automatic procedures to attempt proofs of continuity, convergence and di erentiability for functions in this class. These are cal...

A 2nd-order, L-stable Rosenbrock method from the eld of sti ordinary di erential equations is studied for application to atmospheric dispersion problems describing photochemistry, advective and turbulent di usive transport. Partial di erential equation problems of this type occur in the eld of air pollution modelling. The focal point of the paper is to examine the Rosenbrock method for reliable...