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.

Distributed Function Computation over Fields and Rings via Linear Compression of Sources

The setting considered in this paper is one of distributed function computation. More specifically, there is a collection of N sources possessing correlated information and a destination that would like to acquire a specific linear combination of the N sources. We address both the case when the common alphabet of the sources is a finite field and the case when it is a finite, commutative principal ideal ring with identity. The goal is to minimize the total amount of information needed to be transmitted by the N sources while enabling reliable recovery at the destination of the linear combination sought. One means of achieving this goal is for each of the sources to compress all the information it possesses and transmit this to the receiver. The Slepian-Wolf theorem of information theory governs the minimum rate at which each source must transmit while enabling all data to be reliably recovered at the receiver. However, recovering all the data at the destination is often wasteful of resources since the destination is only interested in computing a specific linear combination. An alternative explored here is one in which each source is compressed using a common linear mapping and then transmitted to the destination which then proceeds to use linearity to directly recover the needed linear combination. The article is part review and presents in part, new results. The portion of the paper that deals with finite fields is previously known material, while that dealing with rings is mostly new.Attempting to find the best linear map that will enable function computation forces us to consider the linear compression of source. While in the finite field case, it is known that a source can be linearly compressed down to its entropy, it turns out that the same does not hold in the case of rings. An explanation for this curious interplay between algebra and information theory is also provided in this paper.

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.

Formal description, compression and transformation of digital pictures II. Picture algebra and geometry

In an earlier paper (Part I) we described the construction of Hermite code for multiple grey-level pictures using the concepts of vector spaces over Galois Fields. In this paper a new algebra is worked out for Hermite codes to devise algorithms for various transformations such as translation, reflection, rotation, expansion and replication of the original picture. Also other operations such as concatenation, complementation, superposition, Jordan-sum and selective segmentation are considered. It is shown that the Hermite code of a picture is very powerful and serves as a mathematical signature of the picture. The Hermite code will have extensive applications in picture processing, pattern recognition and artificial intelligence.

Steroechemistry of the Pyrrolidine rings in the collagen structure

In the collagen triple-helical structure, large side groups occuring at location 3 in the repeating triplet sequences (Gly-Rz-Rz)n are appreciably constrained if a proline residue occurs as Rz in a neighbouring chain. The severity of the steric hindrance depends on the geometry of the prolyl ring. In this paper we propose two different puckerir.gs for the proline ring, the first one being energetically favorable for most types of residue sequences commonly found in collegen while the second is preferable when an amino acid residue with a large side group occurs at location 3 in a neighbouring chain. The puckering of the pyrrolidine ring of hydroxyproline, as proposed earlier, is quite favorable from energy as well as stereochemical considerations.

Modes of deformation in aluminium rings subjected to static axial compression

Aluminium rings of varying Image Image diameter ratios machined from extruded solid bars, were subjected to static axial compression. Etched diametral planes of deformed cylinders revealed the existence of shear bands, the configuration of which were found to change with initial specimen geometry and deformation.

Running-in wear of a compression ignition engine: Factors influencing the conformance between cylinder liner and piston rings

The conformance between the liner and rings of an internal combustion engine depends mainly on their linear wear (dimensional loss) during running-in. Running-in wear studies, using the factorial design of experiments, on a compression ignition engine show that at certain dead centre locations of piston rings the linear wear of the cylinder liner increases with increase in the initial surface roughness of the liner. Rough surfaces wear rapidly without seizure during running-in to promote quick conformance, so an initial surface finish of the liner of 0.8 μm c.l.a. is recommended. The linear wear of the cast iron liner and rings decreases with increasing load but the mass wear increases with increasing load. This discrepancy is due to phase changes in the cast iron accompanied by dimensional growth at higher thermal loads. During running-in the growth of cast iron should be minimised by running the engine at an initial load for which the exhaust gas temperature is approximately 180 °C.

The evolution of loop structures in flux rings within the solar convection zone

Choudhuri and Gilman (1987) considered certain implications of the hypothesis that the magnetic flux within the Sun is generated at the bottom of the convection zone and then rises through it. Taking flux rings symmetric around the rotation axis and using reasonable values of different parameters, they found that the Coriolis force deflects these flux rings into trajectories parallel to the rotation axis so that they emerge at rather high latitudes. This paper looks into the question of whether the action of the Coriolis force is subdued when the initial configuration of the flux ring has non-axisymmetries in the form of loop structures. The results depend dramatically on whether the flux ring with the loops lies completely within the convection zone or whether the lower parts of it are embedded in the stable layers underneath the convection zone. In the first case, the Coriolis force supresses the non-axisymmetric perturbations so that the flux ring tends to remain symmetric and the trajectories are very similar to those of Choudhuri and Gilman (1987). In the second case, however, the lower parts of the flux ring may remain anchored underneath the bottom of the convection zone, but the upper parts of the loops still tend to move parallel to the rotation axis and emerge at high latitudes. Thus the problem of the magnetic flux not being able to come out at the sunspot latitudes still persists after the non-axisymmetries in the flux rings are taken into account.

STBC's from representation of extended Clifford Algebras

A set of sufficient conditions to construct lambda-real symbol Maximum Likelihood (ML) decodable STBCs have recently been provided by Karmakar et al. STBCs satisfying these sufficient conditions were named as Clifford Unitary Weight (CUW) codes. In this paper, the maximal rate (as measured in complex symbols per channel use) of CUW codes for lambda = 2(a), a is an element of N is obtained using tools from representation theory. Two algebraic constructions of codes achieving this maximal rate are also provided. One of the constructions is obtained using linear representation of finite groups whereas the other construction is based on the concept of right module algebra over non-commutative rings. To the knowledge of the authors, this is the first paper in which matrices over non-commutative rings is used to construct STBCs. An algebraic explanation is provided for the 'ABBA' construction first proposed by Tirkkonen et al and the tensor product construction proposed by Karmakar et al. Furthermore, it is established that the 4 transmit antenna STBC originally proposed by Tirkkonen et al based on the ABBA construction is actually a single complex symbol ML decodable code if the design variables are permuted and signal sets of appropriate dimensions are chosen.

Four-dimensional current algebra from Chern-Simons theory

We study an abelian Chern-Simons theory on a five-dimensional manifold with boundary. We find it to be equivalent to a higher-derivative generalization of the abelian Wess-Zumino-Witten model on the boundary. It contains a U(1) current algebra with an operational extension.

Stress intensity factor determination of radially cracked circular rings subjected to tension using photoelastic technique

A parametric study was carried out to determine the Stress Intensity Factor (SIF) in a cracked circular ring by using the photoelastic technique. The stress intensity factors for mode I deformation were determined by subjecting the specimens to the tensile loading from inner boundary and through the holes. The results of Non-Dimensional Stress Intensity Factor (NDSIF) variation with non-dimensional crack length for both methods of loading are compared with each other and with published results.

A denotational semantics for the generalized ER model and a simple ER algebra

The recent spurt of research activities in Entity-Relationship Approach to databases calls for a close scrutiny of the semantics of the underlying Entity-Relationship models, data manipulation languages, data definition languages, etc. For reasons well known, it is very desirable and sometimes imperative to give formal description of the semantics. In this paper, we consider a specific ER model, the generalized Entity-Relationship model (without attributes on relationships) and give denotational semantics for the model as well as a simple ER algebra based on the model. Our formalism is based on the Vienna Development Method—the meta language (VDM). We also discuss the salient features of the given semantics in detail and suggest directions for further work.

On BCH codes over arbitrary integer rings

Bose-C-Hocquenghem (BCH) atdes with symbols from an arbitrary fhite integer ring are derived in terms of their generator polynomials. The derivation is based on the factohation of x to the power (n) - 1 over the unit ring of an appropriate extension of the fiite integer ring. lke eomtruetion is thus shown to be similar to that for BCH codes over fink flelda.