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.

Long term stability studies of particle storage rings using polynomial Maps

Long-term stability studies of particle storage rings can not be carried out using conventional numerical integration algorithms. We require symplectic integration algorithms which are both fast and accurate. In this paper, we study a symplectic integration method wherein the sym-plectic map representing the Hamiltonian system is refactorized using polynomial symplectic maps. This method is used to perform long term integration on a particle storage ring.

Constant weight codes based on ideals of commutative rings

We present a construction of constant weight codes based on the prime ideals of a Noetherian commutative ring. The coding scheme is based on the uniqueness of the primary decomposition of ideals in Noetherian rings. The source alphabet consists of a set of radical ideals constructed from a chosen subset of the prime spectrum of the ring. The distance function between two radical ideals is taken to be the Hamming metric based on the symmetric distance between sets. As an application we construct codes for random networks employing SAF routing.

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.

On the linkage of mesospheric planetary waves with those of the lower atmosphere and ionosphere: A case study from Indian low latitudes

In this paper we study the planetary-scale wave features using concurrent observations of mesospheric wind and temperature, ionospheric h'F, and tropospheric wind from Tirunelveli, Gadanki, and Kolhapur, all located in the Indian low latitudes, made during February 2009. Our investigations reveal that 3 to 5 day periodicity, characterized as ultrafast Kelvin (UFK) waves, was persistent throughout the atmosphere during this period. These waves show clear signatures of upward wave propagation from troposphere to the upper mesosphere, linking the ionosphere through a clear correlation between mesospheric winds and h'F variations. We also note that the amplitude of this wave decreased as we moved away from the equator. These results are the first of their kind from Indian sector, portraying the vertical as well as latitudinal characteristics of the 3 to 5 day UFK waves simultaneously from the troposphere to the ionosphere.

Design of corona control rings for EHV/UHV line hardwares and substations

The components of EHV/UHV lines and substations can produce significant corona. To limit the consequent Radio Interference and Audible Noise on these systems, suitable corona control rings are employed. The shapes of these rings could vary from circular to rectangular with smooth bends. Many manufacturers seem to adopt trial and error method for arriving at the final design. As such neither the present testing standard nor the final design adopted consider the practical scenario like corona produced by deposition of dirt, bird droppings, etc. The present work aims to make a first step in addressing this practically important problem. This requires an accurate evaluation of the electric field and a reliable method for the evaluation of corona inception. Based on a thorough survey of pertinent literature, the critical avalanche criteria as applicable to large electrodes, has been adopted. Taking the rain drop on the surface as the biggest protrusion, conducting protrusions modeled as semi-ellipsoid is considered as representative for deposition of dust or the boundary of bird droppings etc. Through examples of 4 00 kV and 765 kV class toroidal corona rings, the proposed method is demonstrated. This work is believed to be useful to corona ring manufacturers for EHV/UHV systems.

Successful data recovery from oscillation photographs containing strong polycrystalline diffraction rings from an unknown small-molecule contaminant: preliminary structure solution of Salmonella typhimurium pyridoxal kinase (PdxK)

Pyridoxal kinase (PdxK; EC 2.7.1.35) belongs to the phosphotransferase family of enzymes and catalyzes the conversion of the three active forms of vitamin B-6, pyridoxine, pyridoxal and pyridoxamine, to their phosphorylated forms and thereby plays a key role in pyridoxal 5 `-phosphate salvage. In the present study, pyridoxal kinase from Salmonella typhimurium was cloned and overexpressed in Escherichia coli, purified using Ni-NTA affinity chromatography and crystallized. X-ray diffraction data were collected to 2.6 angstrom resolution at 100 K. The crystal belonged to the primitive orthorhombic space group P2(1)2(1)2(1), with unitcell parameters a = 65.11, b = 72.89, c = 107.52 angstrom. The data quality obtained by routine processing was poor owing to the presence of strong diffraction rings caused by a polycrystalline material of an unknown small molecule in all oscillation images. Excluding the reflections close to powder/polycrystalline rings provided data of sufficient quality for structure determination. A preliminary structure solution has been obtained by molecular replacement with the Phaser program in the CCP4 suite using E. coli pyridoxal kinase (PDB entry 2ddm) as the phasing model. Further refinement and analysis of the structure are likely to provide valuable insights into catalysis by pyridoxal kinases.

Reduced Grobner bases and Macaulay-Buchberger Basis Theorem over Noetherian rings

In this paper, we extend the characterization of Zx]/(f), where f is an element of Zx] to be a free Z-module to multivariate polynomial rings over any commutative Noetherian ring, A. The characterization allows us to extend the Grobner basis method of computing a k-vector space basis of residue class polynomial rings over a field k (Macaulay-Buchberger Basis Theorem) to rings, i.e. Ax(1), ... , x(n)]/a, where a subset of Ax(1), ... , x(n)] is an ideal. We give some insights into the characterization for two special cases, when A = Z and A = ktheta(1), ... , theta(m)]. As an application of this characterization, we show that the concept of Border bases can be extended to rings when the corresponding residue class ring is a finitely generated, free A-module. (C) 2014 Elsevier B.V. All rights reserved.

Analysis of cracked and un-cracked semicircular rings under symmetric loading

Edge cracked specimens have been widely utilized for fracture testing. Edge cracked semicircular disk (ECSD) specimen has now been well characterized with regard to its form factor and weight function. This paper presents a modified semicircular ring version of this specimen to enhance the form factor in general while retaining other desirable features. The efficacy of the modified design is proved by combining theory of elasticity solutions with finite element results to arrive at the optimum design geometry. New insights emerging from this work are used to theoretically re-examine the arch-tension and the four-point bend specimens. (C) 2014 Elsevier Ltd. All rights reserved.

Structural variations in aromatic 2 pi-electron three-membered rings of the main group elements

Structural variations of different Z pi-aromatic three-membered ring systems of main group elements, especially group 14 and 13 elements as compared to the classical description of cyclopropenyl cation has been reviewed in this article. The structures of heavier analogues as well as group 13 analogues of cyclopropenyl cation showed an emergence of dramatic structural patterns which do not conform, to the general norms of carbon chemistry. Isolobal analogies between the main group fragments have been efficiently used to explain the peculiarities observed in these three-membered ring systems.

A faster algorithm for testing polynomial representability of functions over finite integer rings

Given a function from Z(n) to itself one can determine its polynomial representability by using Kempner function. In this paper we present an alternative characterization of polynomial functions over Z(n) by constructing a generating set for the Z(n)-module of polynomial functions. This characterization results in an algorithm that is faster on average in deciding polynomial representability. We also extend the characterization to functions in several variables. (C) 2015 Elsevier B.V. All rights reserved.

Measurement of Large Dipolar Couplings of a Liquid Crystal with Terminal Phenyl Rings and Estimation of the Order Parameters

NMR spectroscopy is a powerful means of studying liquid-crystalline systems at atomic resolutions. Of the many parameters that can provide information on the dynamics and order of the systems, H-1-C-13 dipolar couplings are an important means of obtaining such information. Depending on the details of the molecular structure and the magnitude of the order parameters, the dipolar couplings can vary over a wide range of values. Thus the method employed to estimate the dipolar couplings should be capable of estimating both large and small dipolar couplings at the same time. For this purpose, we consider here a two-dimensional NMR experiment that works similar to the insensitive nuclei enhanced by polarization transfer (INEPT) experiment in solution. With the incorporation of a modification proposed earlier for experiments with low radio frequency power, the scheme is observed to enable a wide range of dipolar couplings to be estimated at the same time. We utilized this approach to obtain dipolar couplings in a liquid crystal with phenyl rings attached to either end of the molecule, and estimated its local order parameters.

Similarity of Matrices Over Local Rings of Length Two

Let R be a (commutative) local principal ideal ring of length two, for example, the ring R = Z/p(2)Z with p prime. In this paper, we develop a theory of normal forms for similarity classes in the matrix rings M-n (R) by interpreting them in terms of extensions of R t]-modules. Using this theory, we describe the similarity classes in M-n (R) for n <= 4, along with their centralizers. Among these, we characterize those classes which are similar to their transposes. Non-self-transpose classes are shown to exist for all n > 3. When R has finite residue field of order q, we enumerate the similarity classes and the cardinalities of their centralizers as polynomials in q. Surprisingly, the polynomials representing the number of similarity classes in M-n (R) turn out to have non-negative integer coefficients.

X-Ray Studies On The Bilayer Structure Of Trypsin-Treated Rat-Brain Myelin

Trypsin-treated rat brain myelin was subjected to biochemical and X-ray studies. Untreated myelin gave rise to a pattern of three rings with a fundamental repeat period of 155 Angstrom consisting of two bilayers per repeat period, whereas myelin treated with trypsin showed a fundamental repeat period of 75 Angstrom with one bilayer per repeat period. The integrated raw intensity of the h=4 reflection with respect to the h=2 reflection is 0.38 for untreated myelin. The corresponding value reduced to 0.23, 0.18, 0.17 for myelin treated with 5, 10, 40 units of trypsin per mg of myelin, respectively, for 30 min at 30 degrees C. The decrease in relative raw intensity of the higher-order reflection relative to the lower-order reflection is suggestive of a disordering of the phosphate groups upon trypsin treatment or an increased mosaicity of the membrane or a combination of both these effects, However, trypsin treatment does not lead to a complete breakdown of the membrane, The integrated intensity of the h=1 reflection, though weak, is above the measurable threshold for untreated myelin, whereas the corresponding intensity is below the measurable threshold for trypsin-treated myelin, indicating a possible asymmetric to symmetric transition of the myelin bilayer structure about its centre after trypsin treatment.

Statistical analysis of the position of the monsoon trough

Using surface charts at 0330GMT, the movement df the monsoon trough during the months June to September 1990 al two fixed longitudes, namely 79 degrees E and 85 degrees E, is studied. The probability distribution of trough position shows that the median, mean and mode occur at progressively more northern latitudes, especially at 85 degrees E, with a pronounced mode that is close to the northern-most limit reached by the trough. A spectral analysis of the fluctuating latitudinal position of the trough is carried out using FFT and the Maximum Entropy Method (MEM). Both methods show significant peaks around 7.5 and 2.6 days, and a less significant one around 40-50 days. The two peaks at the shorter period are more prominent at the eastern longitude. MEM shows an additional peak around 15 days. A study of the weather systems that occurred during the season shows them to have a duration around 3 days and an interval between systems of around 9 days, suggesting a possible correlation with the dominant short periods observed in the spectrum of trough position.