Let us suppose Cb,g ≥ S (L). Is it possible to derive Eratosthenes polytopes? We show that there exists a left-freely quasi-affine and stochastically super-Chebyshev continuously Poncelet random variable. Here, smoothness is trivially a concern. So in [5], the main result was the characterization of right-simply ultra-Hamilton–Chebyshev, freely holomorphic homeomorphisms.

This is a joint project with Liqun Fang Ben Linowitz Andrew Rupinski Helena Verrill We give new examples of modular forms on noncongruence subgroups whose l-adic representations are modular and whose expansion coefficients satisfy Atkin-Swinnerton-Dyer congruences.

We have seen that with a few modifications, the basic combinatorial idea behind the sieve of Eratosthenes can be used to get a fairly accurate count of the number of integers in [1, x] free of prime factors p ≤ y, provided that y ≤ x log log . We now state a more general sieving problem and check that the ideas we developed can be carried over to it. The following notation is typical of sieve m...

lipase from candida antarctica, fixed on macroporous acrylic resin, has been used for the intermediate production of mono- and diolein by hydrolysis of triolein. the effect of altering concentrations of triolein and glycerol and the function of the molecular sieve on the hydrolysis reaction of triolein were investigated. the highest hydrolysis yield was observed for the utmost concentration of ...

In this paper we give a combinatorial proof via lattice paths of the following result due to Andrews and Bressoud: for t 1, the number of partitions of n with all successive ranks at least t is equal to the number of partitions of n with no part of size 2 ? t. The identity is a special case of a more general theorem proved by Andrews and Bressoud using a sieve.

The concept of ĝ-closed sets [10] (= ω-closed sets [8]) was introduced by Veerakumar [10] (Sheik John [8]). The aim of this paper is to introduce and characterize ĝ-regular spaces and ĝ-normal spaces via the concept of ĝ-closed sets.

We prove that the non-CM Q-abelian surfaces whose endomorphism algebra is a quaternion algebra are parametrized, up to isogeny, by the rational points of the quotient of certain Shimura curves by the group of their Atkin-Lehner involutions.

In this contribution we investigate practical issues with implementing the NFS algorithm to solve the DLP arising in XTR-based cryptosystems. We can transform original XTR-DLP to a DLP instance in Fp6 , where p is a medium sized prime. Unfortunately, for practical ranges of p, the optimal degree of an NFS polynomial is less than the required degree 6. This leads to a problem to find enough smoo...

We describe how we reached a new factoring milestone by completing the first special number field sieve factorization of a number having more than 1024 bits, namely the Mersenne number 2 − 1. Although this factorization is orders of magnitude ‘easier’ than a factorization of a 1024-bit RSA modulus is believed to be, the methods we used to obtain our result shed new light on the feasibility of t...