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We provide suitable conditions under which the asymptotic limit of the Hilbert-Samuel coefficients of the Frobenius powers of an \mathfrak {m}-primary ideal exists in a Noetherian local ring (R,\mathfrak {m}) with prime characteristic p>0. This, in turn, gives an expression of the Hilbert-Kunz multiplicity of powers of the ideal. We also prove that for a face ring R of a simplicial complex and an ideal J generated by pure powers of the variables, the generalized Hilbert-Kunz function \ell (R/(J^{[q]})^k) is a polynomial for all q,k and also give an expression of the generalized Hilbert-Kunz multiplicity of powers of J in terms of Hilbert-Samuel multiplicity of J. We conclude by giving a counter-example to a conjecture proposed by I. Smirnov which connects the stability of an ideal with the asymptotic limit of the first Hilbert coefficient of the Frobenius power of the ideal. [ABSTRACT FROM AUTHOR]

We prove that the Hilbert-Kunz function of the ideal (I, It) of the Rees algebra R (I) , where I is an m -primary ideal of a 1-dimensional local ring (R , m) , is a quasi-polynomial in e, for large e. For s ∈ N , we calculate the Hilbert-Samuel function of the R-module I [ s ] and obtain an explicit description of the generalized Hilbert-Kunz function of the ideal (I , I t) R (I) when I is a parameter ideal in a Cohen-Macaulay local ring of dimension d ≥ 2 , proving that the generalized Hilbert-Kunz function is a piecewise polynomial in this case. [ABSTRACT FROM AUTHOR]

Let (R,) be an analytically unramified local ring of positive prime characteristic p. For an ideal I, let I* denote its tight closure. We introduce the tight Hilbert function HI*(n) = ℓ(R/In)) and the corresponding tight Hilbert polynomial PI*(n), where I is an m-primary ideal. It is proved that F-rationality can be detected by the vanishing of the first coefficient of PI*(n). We find the tight Hilbert polynomial of certain parameter ideals in hypersurface rings and Stanley-Reisner rings of simplicial complexes. [ABSTRACT FROM AUTHOR]

Increasing demand for high computing power led to the establishment of large-scale data centers. A data center is a collection of millions of servers. These large-scale data centers consume a huge amount of electrical energy. Managing these servers for provisioning and de-provisioning of resources in an automatic and efficient way is a great challenge. We attempt to minimise the power consumption by reducing the number of servers and maximizing the resource utilization of the servers that are in use through virtualization of resources. We work upon Virtual Machine Consolidation for consolidating them on fewer servers for maximizing resource utilization. In this article, we propose a resource request based heuristic for offloading the overloaded servers to optimise power consumption efficiency. [ABSTRACT FROM AUTHOR]

Cloud computing is a new paradigm for hosting and delivering services using the standard protocols of the Internet. It refers to a service-oriented architecture that offers ubiquitous and convenient computing, greater flexibility, on-demand services, reduced total cost of ownership, reduced information technology overhead for the end-user, and many other things. It allows access to a large amount of computing power in a fully virtualized mode by aggregating a configurable pool of resources that are rapidly provisioned and released dynamically. It also provides the capability to utilize scalable, distributed computing environments within the confines of the Internet with minimal management effort while keeping a single coherent system view. Cloud computing is constantly gaining popularity in the information technology industry, and so more and more issues and challenges are emerging that need to be handled for the success of this paradigm. This paper presents an introduction of cloud computing, and a comparative study of cloud computing and grids. Furthermore, we put forward pinpoint research issues in the cloud computing paradigm and a mathematical understanding of several issues among them. [ABSTRACT FROM AUTHOR]

Dyeing behaviour of four different natural dyes extracted from the leaves collected in a sustainable manner from respective dye containing plants has been studied on cotton fabric. A novel and ecofriendly mordanting technique has been devised for creating aluminium-tannate complex on cotton matrix. The new mordanting technique not only involves application of a modified sequence of mordanting chemicals but also employs addition of specific salts in water used in the dyeing process. The dyeing of the mordanted fabric has been carried out under acidic and alkaline conditions at different temperatures. The modified dyeing technique shows an overall improvement of 140-300% in colour strength along with the excellent fastness properties, such as washing, rubbing, perspiration and light. The overall results indicate that all the four natural dyes can be effectively and economically used for dyeing on cotton fabric. The entire chain of collection, extraction and dyeing methodology is environmentally and ecologically compatible. [ABSTRACT FROM AUTHOR]

We report a novel cytoplasmic male sterility (CMS) system in Brassica juncea (oilseed mustard) which could be used for production of hybrid seed in the crop. A male sterile plant identified in a microspore derived doubled haploid population of re-synthesized B. napus line ISN 706 was found to be a CMS as the trait was inherited from the female parent. This CMS, designated ‘126-1’, was subsequently transferred to ten different B. juncea varieties and lines through inter-specific crosses followed by recurrent backcrossing. The F1s of inter-specific crosses were invariably partially fertile, but irrespective of the variety/line used, the recipient lines became progressively male sterile over five to seven generations and could be maintained by crossing the male sterile lines with their normal counterparts. The male sterile lines were found to be stable for the trait under both long and short day conditions. CMS lines when crossed with lines other than the respective maintainer line were restored for fertility, implying that any variety could act as a restorer for ‘126-1’ cytoplasm in B. juncea. These unique features in maintenance and restoration of CMS lines coupled with near normal floral morphology of the CMS lines have allowed the use of ‘126-1’ cytoplasm for hybrid seed production. The uniqueness of ‘126-1’ has been further established by Southern hybridization with mitochondrial DNA probes and by a histological study of the development of male sterile anthers. [ABSTRACT FROM AUTHOR]

Abstract Analysis of the glucosinolate content and composition by high-pressure liquid chromatography indicated that varieties of Brassica juncea bred and grown in India have a high glucosinolate content characterized by the presence of 2-propenyl (allyl) and 3-butenyl as the major and 4-pentenyl as the minor fractions. In contrast, the B. juncea germplasm from other countries is characterized by the presence of 2-propenyl as the major glucosinolate fraction, trace amounts of 3-butenyl and a total lack of the 4-pentenyl types. In order to transfer the low glucosinolate trait to Indian B. juncea , the inheritance of total glucosinolates was investigated using doubled haploid (DH) populations derived from F1 (DH1 ) and BC1 (BC1 DH) of a cross between ‘Varuna’ (the most widely cultivated high glucosinolate variety of India) and ‘Heera’ (a non-allyl type low glucosinolate line). A total of 752 DH1 and 1263 BC1 DH gave rise to seven and 11 low glucosinolate (containing less than 18 µmol/g seed) individuals, respectively. On the basis of the frequency of the low glucosinolate individuals, the total glucosinolate was found to be under the control of seven genes. There was presence of both allyl and non-allyl types in DH1 and BC1 DH low-glucosinolate individuals and absence of 3-butenyl glucosinolate in some of the BC1 DH low glucosinolate individuals, indicating segregation for these fractions in the population. The size of the segregating DH population proved to be crucial for precise determination of the number of genes controlling the trait. Because of the large number of genes involved, incorporation of low glucosinolate trait in Indian B. juncea should be approached through doubled haploid (DH) breeding. [ABSTRACT FROM AUTHOR]

Alloplasmic lines of cultivated Brassica species with B. oxyrrhina cytoplasm are male-sterile and suffer from severe chlorosis. We developed male-sterile lines corrected for chlorosis by fusing protoplasts of CMS B. juncea (AABB) with ’oxy’ cytoplasm and normal B. oleracea (CC). A large number of male-sterile AABBCC somatic hybrids with desirable organelle combinations, i.e. chloroplasts of B. oleracea and mitochondria with recombinant genomes, were recovered. While no recombination was observed in the chloroplast genome, the mitochondrial genome showed extensive recombination that resulted in the appearance of totally novel banding patterns in some of the hybrids. Hybrids with a parental-type mitochondrial genome as well as recombinant patterns close to either of the parental types were also obtained. Using AABBCC somatic hybrids as bridging material, we transferred the desirable organelle combinations to B. juncea (AABB), B. napus (AACC), and B. carinata (BBCC). Many of these lines are now at advanced stages of backcrossing and show stable inheritance of the CMS character and do not suffer from chlorosis. [ABSTRACT FROM AUTHOR]

Eighteen genotypes of Brassica napus were crossed to a cytoplasmic male sterile (CMS) line of B. napus BO15 carrying B. tournefortu cytoplasm ('tour' cytoplasm). Fourteen genotypes were found to be stable maintainers of the 'tour' CMS. Of the remaining four genotypes, GSL-1 and 'Asahi-natane' were found to be heterozygous and 'Mangun' and 'Yudal' were homozygous for the restorer gene. Analysis of the F[SUB1] and F[SUB2] progenies of (CMS) BO15 × 'Mangun' and (CMS) BO15 × 'Yudal' showed that fertility restoration is controlled by a single dominant gene.The availability of a number of stable maintainer lines and the simple inheritance pattern of fertility restorer gene makes 'tour' CMS a useful system for hybrid seed production in rapeseed. [ABSTRACT FROM AUTHOR]

The objective of this study was to broaden the genetic base in oleiferous Brassica juncea by resynthesis, using 10 diverse parental lines of oleiferous B. rapa and two lines of B. nigra of both Indian and exotic origin. Out of 14 crosses attempted using B. rapa as the female parent, eight were successful. Embryo rescue was necessary to obtain interspecific plants. A total of 29 fertile interspecific plants were obtained after colchicine treatment. In the S2 generation, the expression of component characters in the majority of the resynthesized plants showed a negative trend. The resynthesized B. juncea lines are being maintained through repeated selfing and selection at each generation for desirable plant types. This process will continue till the progeny lines of the desirable plants achieve uniformity. [ABSTRACT FROM AUTHOR]

Brassica carinata (BBCC), a potential oilseed crop for dry land agriculture, is sensitive to high temperatures during germination and early stages of growth, which thereby restricts the possibility of using the residual soil moisture available after the rainy season for its cultivation. To overcome this problem, a three-genome hybrid, RCBB, was synthesized using Raphanus sativus (RR) and Brassica oleracea (CC) as donor sources for the desired heat tolerance. Protoplasts of RC hybrids obtained through sexual crosses between R. sativus (female) and B. oleracea (male) were fused with protoplasts of Brassica nigra (BB) to produce RCBB somatic hybrids. The hybrid colonies regenerated with an average frequency of 7.6%. Twelve out of 36 hybrids grown to maturity were characterized for their nuclear and organelle genomes. While all the hybrids showed the presence of B. nigra chloroplasts, 10 of the hybrids showed B. nigra -specific mitochondria and two had Raphanus -specific mitochondria. The somatic hybrids could be backcrossed to B. carinata . [ABSTRACT FROM AUTHOR]

A sensitive and rapid extractive spectrophotometer method has been developed for the assay of carvedilol in pharmaceutical formulations. The method is based on the formation of a chloroform soluble ion-pair complex between carvedilol and bromocresol green in an acidic medium. The complex shows absorption maximum at 415 nm and the system obeys Beer's law in the concentration range of 5-25 µg/ml. The results obtained by the proposed method were validated statistically and by recovery studies. [ABSTRACT FROM AUTHOR]

‘Polima’ cytoplasmic male sterility (CMS) was transferred from ‘Polima’ Brassica napus ‘ISN 706’ to five different cultivars of Brassica campestris (‘Pusa kalyani’, ‘Pant toria’, ‘Candle’, ‘Tobin’ and ‘ATC 94211’) by repeated backcrossing. It was observed that, while ‘Polima’ CMS manifested complete and stable male sterility in the nuclear backgrounds of ‘Pusa kalyani’, ‘Pant toria’, and ‘Tobin’, the cultivars ‘Candle’ and ‘ATC 94211’ possessed the restorer gene for this CMS in the heterozygous condition. An analysis of F1 and F2 generations of ‘Polima’ ‘Pusa kalyani’ × ‘Candle’ and ‘Polima’ ‘Pusa kalyani’ × ‘ATC 94211’ revealed that restoration is controlled by a single dominant gene. Identification of stable maintainers and restorers of ‘Polima’ CMS could facilitate the development of hybrid varieties in B. campestris. [ABSTRACT FROM AUTHOR]