The Herzog-Vasconcelos conjecture for affine semigroup rings

Let S be a simplicial affine semigroup such that its semigroup ring A = k[S] is Buchsbaum. We prove for such A the Herzog-Vasconcelos conjecture: If the A-module Der(k)A of k-linear derivations of A has finite projective dimension then it is free and hence A is a polynomial ring by the well known graded case of the Zariski-Lipman conjecture.

A Note on Linear Codes over Semigroup Rings

In this paper, we introduced new construction techniques of BCH, alternant, Goppa, Srivastava codes through the semigroup ring B[X; 1 3Z0] instead of the polynomial ring B[X; Z0], where B is a finite commutative ring with identity, and for these constructions we improve the several results of [1]. After this, we present a decoding principle for BCH, alternant and Goppa codes which is based on modified Berlekamp-Massey algorithm. This algorithm corrects all errors up to the Hamming weight t ≤ r/2, i.e., whose minimum Hamming distance is r + 1.

Galois orders in skew monoid rings

We introduce a new class of noncommutative rings - Galois orders, realized as certain subrings of invariants in skew semigroup rings, and develop their structure theory. The class of Calms orders generalizes classical orders in noncommutative rings and contains many important examples, such as the Generalized Weyl algebras, the universal enveloping algebra of the general linear Lie algebra, associated Yangians and finite W-algebras (C) 2010 Elsevier Inc All rights reserved

Constructions of codes through the semigroup ring B[X; 1/2(2)Z(0)] and encoding

For any finite commutative ring B with an identity there is a strict inclusion B[X; Z(0)] subset of B[X; Z(0)] subset of B[X; 1/2(2)Z(0)] of commutative semigroup rings. This work is a continuation of Shah et al. (2011) [8], in which we extend the study of Andrade and Palazzo (2005) [7] for cyclic codes through the semigroup ring B[X; 1/2; Z(0)] In this study we developed a construction technique of cyclic codes through a semigroup ring B[X; 1/2(2)Z(0)] instead of a polynomial ring. However in the second phase we independently considered BCH, alternant, Goppa, Srivastava codes through a semigroup ring B[X; 1/2(2)Z(0)]. Hence we improved several results of Shah et al. (2011) [8] and Andrade and Palazzo (2005) [7] in a broader sense. Published by Elsevier Ltd

Encoding through generalized polynomial codes

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Goppa codes through polynomials of B[X;(1/2^2)Z_0] and its decoding principle

In this paper, we present a decoding principle for Goppa codes constructed by generalized polynomials, which is based on modified Berlekamp-Massey algorithm. This algorithm corrects all errors up to the Hamming weight $t\leq 2r$, i.e., whose minimum Hamming distance is $2^{2}r+1$.

Hyperbolicity of semigroup algebras

Let A be a finite-dimensional Q-algebra and Gamma subset of A a Z-order. We classify those A with the property that Z(2) negated right arrow U(Gamma) and refer to this as the hyperbolic property. We apply this in case A = K S is a semigroup algebra, with K = Q or K = Q(root-d). A complete classification is given when KS is semi-simple and also when S is a non-semi-simple semigroup. (c) 2008 Elsevier Inc. All rights reserved.

HYPERBOLICITY OF SEMIGROUP ALGEBRAS II

In 1996, Jespers and Wang classified finite semigroups whose integral semigroup ring has finitely many units. In a recent paper, Iwaki-Juriaans-Souza Filho continued this line of research by partially classifying the finite semigroups whose rational semigroup algebra contains a Z-order with hyperbolic unit group. In this paper, we complete this classification and give an easy proof that deals with all finite semigroups.

Fabrication of SiGe rings and holes on Si(001) by flash annealing

We show that SiGe islands are transformed into nanoholes and rings by annealing treatments only and without Si capping. Rings are produced by a rapid flash heating at temperatures higher than the melting point of Ge, whereas nanoholes are produced by several minute annealing. The rings are markedly rich in Si with respect to the pristine islands, suggesting that the evolution path from islands to rings is driven by the selective dissolution of Ge occurring at high temperature.

Design of multi-frequency microstrip antennas using multiple rings

An electromagnetically coupled feed arrangement is proposed for simultaneously exciting multiple concentric ring antennas for multi-frequency operation. This has a multi-layer dielectric configuration in which a transmission line is embedded below the layer containing radiating rings. Energy coupled to these rings from the line beneath is optimised by suitably adjusting the location and dimensions of stubs on the line. It has been shown that the resonant frequencies of these rings do not change as several of these single-frequency antennas are combined to form a multi-resonant antenna. Furthermore, all radiators are forced to operate at their primary mode and some harmonics of the lower resonant frequency rings appearing within the frequency range are suppressed when combined. The experimental prototype antenna has three resonant frequencies at which it has good radiation characteristics.

Fast Public Key Cryptosystem Based On Matrix Rings

A public key cryptosystem is proposed, which is based on the assumption that finding the square root of an element in a large finite ring is computationally infeasible in the absence of a knowledge of the ring structure. The encryption and decryption operations are very fast, and the data expansion is 1:2.

Sol → gel transition with rings in a finite polycondensing system in solution

We report a theoretical formulation for the mean cluster size distribution in a finite polycondensing system. Expressions for the mean number of n-mers with j bonds ( nj) are developed. Numerical calculations show that while the non-cyclic molecules make the dominant contribution to the small clusters, the large clusters are dominated by cyclic structures. The number of particles in ringless chains, n n,n-1, decays monotonically with n at all extents of reaction, but n n becomes bimodal near the gel point. We also find that the solvent plays an important role in the cluster size distribution.

Welfare outcomes for 3- and 6-month-old beef calves in a tropical environment castrated surgically or by applying rubber rings

Castration of cattle using rubber rings is becoming increasingly popular due to the perceived ease of the procedure and greater operator safety when compared with surgical castration. Few comparative studies have investigated the effects of different castration methods and calf age on welfare outcomes, particularly in a tropical environment. Thirty Belmont Red (a tropically adapted breed), 3-month-old (liveweight 71–119 kg) and 30, 6-month-old (liveweight 141–189 kg) calves were assigned to a two age × three castration (surgical, ring and sham) treatment factorial study (Surg3, Surg6, Ring3, Ring6, Sham3 and Sham6, n = 10 for each treatment group). Welfare outcomes were assessed post-castration using: behaviour for 2 weeks; blood parameters (cortisol and haptoglobin concentrations) to 4 weeks; wound healing to 5 weeks; and liveweights to 6 weeks. More Surg calves struggled during castration compared with Sham and Ring (P < 0.05, 90 ± 7% vs. 20 ± 9% and 24 ± 10%) and performed more struggles (1.9 ± 0.2, 1.1 ± 0.3 and 1.1 ± 0.3 for Surg, Sham and Ring, respectively), suggesting that surgical castration caused most pain during performance of the procedure. A significant (P < 0.05) time × castration method × age interaction for plasma cortisol revealed that concentrations decreased most rapidly in Sham; the Ring6 calves failed to show reduced cortisol concentrations at 2 h post-castration, unlike other treatment groups. By 7 h post-castration, all treatment groups had similar concentrations. A significant (P < 0.01) interaction between time and castration method showed that haptoglobin concentrations increased slightly to 0.89 and 0.84 mg/mL for Surg and Ring, respectively over the first 3 days post-castration. Concentrations for Surg then decreased to levels similar to Sham by day 21 and, although concentrations for Ring decreased on day 7 to 0.76 mg/mL, they increased significantly on day 14 to 0.97 mg/mL before reducing to concentrations similar to the other groups (0.66 mg/mL) by day 21. Significantly (P < 0.05) more of the wounds of the 3-month compared with the 6-month calves scored as ‘healed’ at day 7 (74% vs. 39%), while more (P = 0.062) of the Surg than Ring scored as ‘healed’ at day 21 (60% vs. 29%). At day 14 there were significantly (P < 0.05) fewer healed wounds in Ring6 compared with other treatment groups (13% vs. 40–60%). Liveweight gain was significantly (P < 0.05) greater in 3-month (0.53 kg/day) than in 6-month calves (0.44 kg/day) and in Sham calves (P < 0.001, 0.54 kg/day), than in Ring (0.44 kg/day) and Surg (0.48 kg/day) calves. Overall, welfare outcomes were slightly better for Surg than Ring calves due to reduced inflammation and faster wound healing, with little difference between age groups.