We show that for excellent, normal equicharacteristic rings with perfect residue fields the tight closure of an ideal is contained in its axes closure. First we prove this characteristic p. This achieved by using notion special established Huneke and Vraciu. By reduction to positive containment also holds 0. From deduce a ring finite type over C primary inside continuous

Compounds containing two alkyne groups in close vicinity at the rigid skeleton of camphorsulfonamide show unique reactivities when treated with electrophiles or catalytic amounts of platinum(II). The formed product structures depend not only on the reagents used but also on the substituents attached to the triple bonds. Cycloisomerisations with perfect atom economy lead to polycyclic heterocycl...

We identify a self-enforcing collusion protocol (a “bidding ring”) for non-repeated first-price auctions. Unlike previous work on the topic such as that by McAfee and McMillan [1992] and Marshall and Marx [2007], we allow for the existence of multiple cartels in the auction and do not assume that non-colluding agents have perfect knowledge about the number of colluding agents whose bids are sup...

LetW be a finite dimensional representation of a linearly reductive group G over a field k. Motivated by their work on classical rings of invariants, Levasseur and Stafford asked whether the ring of invariants under G of the symmetric algebra of W has a simple ring of differential operators. In this paper, we show that this is true in prime characteristic. Indeed, if R is a graded subring of a ...

We provide an irreducibility test in the ring $$\mathbb{K}[[x]][y]$$ whose complexity is quasi-linear with respect to discriminant valuation, assuming input polynomial $$F$$ square-free and $$\mathbb{K}$$ a perfect field of characteristic not dividing $$\deg(F)$$ . The algorithm uses theory approximate roots may be seen as generalisation Abhyankar's criterion case non-algebraically closed resid...

The emerging platform-based design paradigm poses enormous challenges to conceptualizing, implementing, verifying and programming today‟s complex System on Chip (SoC) design. Network-on-Chip (NoC) architecture provides a scalable, high performance and robust infrastructure for on-chip communication. Perfect Difference Network (PDN) based on the mathematical notion of Perfect Difference Set as a...

In recent workwith J.Mostovoy and T. Stanford, the author found that for every natural number n, a certain polynomial in the coefficients of the Conway polynomial is a primitive integer-valued degree n Vassiliev invariant, but that modulo 2, it becomes degree n-1. The conjecture then naturally suggests itself that these primitive invariants are congruent to integer-valued degree n-1 invariants....

Let R be ring and M a right R-module. This article introduces the concept of τ −⊕-supplemented modules as follows: Given a hereditary torsion theory in Mod-R with associated torsion functor τ we say that a module M is τ −⊕-supplemented when for every submodule N of M there exists a direct summand K of M such that M = N +K and N ∩K is τ−torsion, and M is called completely τ −⊕-supplemented if ev...

Multivariate Cryptography is one of the main candidates for creating post-quantum cryptosystems. Especially in the area of digital signatures, there exist many practical and secure multivariate schemes. However, there is a lack of more advanced schemes, such as schemes for oblivious transfer and signature schemes with special properties. While, in the last years, a number of multivariate ring s...

the concept of fuzzy soft γ-ring is introduced; and some properties of fuzzy soft γ-rings are given. then the definitions of fuzzy soft γ-ideals are proposed and some of their theories are considered.