Median Sets and Median Number of a Graph

A profile is a finite sequence of vertices of a graph. The set of all vertices of the graph which minimises the sum of the distances to the vertices of the profile is the median of the profile. Any subset of the vertex set such that it is the median of some profile is called a median set. The number of median sets of a graph is defined to be the median number of the graph. In this paper, we identify the median sets of various classes of graphs such as Kp − e, Kp,q forP > 2, and wheel graph and so forth. The median numbers of these graphs and hypercubes are found out, and an upper bound for the median number of even cycles is established.We also express the median number of a product graph in terms of the median number of their factors.

Median graphs, the remoteness function, periphery transversals, and geodetic number two

A periphery transversal of a median graph G is introduced as a set of vertices that meets all the peripheral subgraphs of G. Using this concept, median graphs with geodetic number 2 are characterized in two ways. They are precisely the median graphs that contain a periphery transversal of order 2 as well as the median graphs for which there exists a profile such that the remoteness function is constant on G. Moreover, an algorithm is presented that decides in O(mlog n) time whether a given graph G with n vertices and m edges is a median graph with geodetic number 2. Several additional structural properties of the remoteness function on hypercubes and median graphs are obtained and some problems listed

Impact of ICT on Library and Information Science: Major Shifts and Practices in CUSAT Central Library

Information is knowledge, facts or data. For the purpose of enabling the users to assimilate information, it should be repacked. Knowledge becomes information when it is externalized i.e. put in to the process of communication. The effectiveness of communication technology depends how well it provides its clients with information rapidly, economically and authentically. A large number of ICT enabled services including OPAC; e-resources etc. are available in the university library. Studies have been done to find the impact of ICT on different sections of CUSAT library by observing the activities of different sections; discussions with colleagues and visitors; and analyzing the entries in the library records. The results of the studies are presented here in the form of a paper.

Molecular genetic profiling of functional genes of pearl oyster, Pinctada fucata

There are a number of genes involved in the regulation of functional process in marine bivalves. In the case of pearl oyster, some of these genes have major role in the immune/defence function and biomineralization process involved in the pearl formation in them. As secondary filter feeders, pearl oysters are exposed to various kinds of stressors like bacteria, viruses, pesticides, industrial wastes, toxic metals and petroleum derivatives, making susceptible to diseases. Environmental changes and ambient stress also affect non-specific immunity, making the organisms vulnerable to infections. These stressors can trigger various cellular responses in the animals in their efforts to counteract the ill effects of the stress on them. These include the expression of defence related genes which encode factors such as antioxidant genes, pattern recognition receptor proteins etc. One of the strategies to combat these problems is to get insight into the disease resistance genes, and use them for disease control and health management. Similarly, although it is known that formation of pearl in molluscs is mediated by specialized proteins which are in turn regulated by specific genes encoding them, there is a paucity of sufficient information on these genes.In view of the above facts, studies on the defence related and pearl forming genes of the pearl oyster assumes importance from the point of view of both sustainable fishery management and aquaculture. At present, there is total lack of sufficient knowledge on the functional genes and their expressions in the Indian pearl oyster Pinctada fucata. Hence this work was taken up to identify and characterize the defence related and pearl forming genes, and study their expression through molecular means, in the Indian pearl oyster Pinctada fucata which are economically important for aquaculture at the southeast coast of India. The present study has successfully carried out the molecular identification, characterization and expression analysis of defence related antioxidant enzyme genes and pattern recognition proteins genes which play vital role in the defence against biotic and abiotic stressors. Antioxidant enzyme genes viz., Cu/Zn superoxide dismutase (Cu/Zn SOD), glutathione peroxidise (GPX) and glutathione-S-transferase (GST) were studied. Concerted approaches using the various molecular tools like polymerase chain reaction (PCR), random amplification of cDNA ends (RACE), molecular cloning and sequencing have resulted in the identification and characterization of full length sequences (924 bp) of the Cu/Zn SOD, most important antioxidant enzyme gene. BLAST search in NCBI confirmed the identity of the gene as Cu/Zn SOD. The presence of the characteristic amino acid sequences such as copper/zinc binding residues, family signature sequences and signal peptides were found out. Multiple sequence alignment comparison and phylogenetic analysis of the nucleotide and amino acid sequences using bioinformatics tools like BioEdit,MEGA etc revealed that the sequences were found to contain regions of diversity as well as homogeneity. Close evolutionary relationship between P. fucata and other aquatic invertebrates was revealed from the phylogenetic tree constructed using SOD amino acid sequence of P. fucata and other invertebrates as well as vertebrates

Asymptotics of number fields and the Cohen-Lenstra heuristics

We study the asymptotics conjecture of Malle for dihedral groups Dl of order 2l, where l is an odd prime. We prove the expected lower bound for those groups. For the upper bounds we show that there is a connection to class groups of quadratic number fields. The asymptotic behavior of those class groups is predicted by the Cohen-Lenstra heuristics. Under the assumption of this heuristic we are able to prove the expected upper bounds.

On the equivariant Tamagawa number conjecture for abelian extensions of a quadratic imaginary field

Let k be a quadratic imaginary field, p a prime which splits in k/Q and does not divide the class number hk of k. Let L denote a finite abelian extention of k and let K be a subextention of L/k. In this article we prove the p-part of the Equivariant Tamagawa Number Conjecture for the pair (h0(Spec(L)),Z[Gal(L/K)]).

The Parity of the Number of Irreducible Factors for Some Pentanomials

It is well known that Stickelberger-Swan theorem is very important for determining reducibility of polynomials over a binary field. Using this theorem it was determined the parity of the number of irreducible factors for some kinds of polynomials over a binary field, for instance, trinomials, tetranomials, self-reciprocal polynomials and so on. We discuss this problem for type II pentanomials namely x^m +x^{n+2} +x^{n+1} +x^n +1 \in\ IF_2 [x]. Such pentanomials can be used for efficient implementing multiplication in finite fields of characteristic two. Based on the computation of discriminant of these pentanomials with integer coefficients, it will be characterized the parity of the number of irreducible factors over IF_2 and be established the necessary conditions for the existence of this kind of irreducible pentanomials.

Parity of the Number of Irreducible Factors for Composite Polynomials

Various results on parity of the number of irreducible factors of given polynomials over finite fields have been obtained in the recent literature. Those are mainly based on Swan’s theorem in which discriminants of polynomials over a finite field or the integral ring Z play an important role. In this paper we consider discriminants of the composition of some polynomials over finite fields. The relation between the discriminants of composed polynomial and the original ones will be established. We apply this to obtain some results concerning the parity of the number of irreducible factors for several special polynomials over finite fields.

Influence of occupation number of single particle levels on K - K charge transfer in collisions of 90 keV - Ne{^9+} on Ne

The influence of the occupation of the single particle levels on the impact parameter dependent K - K charge transfer occuring in collisions of 90 keV Ne{^9+} on Ne was studied using coupled channel calculations. The energy eigenvalues and matrixelements for the single particle levels were taken from ab initio self consistent MO-LCAO-DIRAC-FOCK-SLATER calculations with occupation numbers corresponding to the single particle amplitudes given by the coupled channel calculations.

Algorithms for Tamagawa Number Conjectures

In dieser Arbeit werden Algorithmen zur Untersuchung der äquivarianten Tamagawazahlvermutung von Burns und Flach entwickelt. Zunächst werden Algorithmen angegeben mit denen die lokale Fundamentalklasse, die globale Fundamentalklasse und Tates kanonische Klasse berechnet werden können. Dies ermöglicht unter anderem Berechnungen in Brauergruppen von Zahlkörpererweiterungen. Anschließend werden diese Algorithmen auf die Tamagawazahlvermutung angewendet. Die Epsilonkonstantenvermutung kann dadurch für alle Galoiserweiterungen L|K bewiesen werden, bei denen L in einer Galoiserweiterung E|Q vom Grad kleiner gleich 15 eingebettet werden kann. Für die Tamagawazahlvermutung an der Stelle 1 wird ein Algorithmus angegeben, der die Vermutung für ein gegebenes Fallbeispiel L|Q numerischen verifizieren kann. Im Spezialfall, dass alle Charaktere rational oder abelsch sind, kann dieser Algorithmus die Vermutung für L|Q sogar beweisen.

Analysis of the relationship between the number of citations and the quality evaluated by experts in psychology journals

Resumen tomado de la publicaci??n

Number Theory

Lecture notes for a number theory course

How do I get the Chapter number in Table or Figure captions to restart in Appendices using the University thesis template in Word 2010?

If you have added the Chapter number to your Table or Figure captions they will show as 1.1, 1.2 and so on. This is linked to the numbering used in the Heading 1 style. However, once you get to the Appendices the last Chapter number will continue throughout the Appendices as the Appendix heading isn't Heading 1. So what you need to do is get Word to understand that the style from which it should be picking up the first part of the Caption has changed and that it will need to restart the numbering again in each subsequent Appendix. This isn't too complex but you must follow the instructions to the letter or else it won't work.