Acyclic 5-Choosability of Planar Graphs Without Adjacent Short Cycles

The conjecture claiming that every planar graph is acyclic 5-choosable[Borodin et al., 2002] has been verified for several restricted classes of planargraphs. Recently, O. V. Borodin and A. O. Ivanova, [Journal of Graph Theory,68(2), October 2011, 169-176], have shown that a planar graph is acyclically 5-choosable if it does not contain an i-cycle adjacent to a j-cycle, where 3<=j<=5 if i=3 and 4<=j<=6 if i=4. We improve the above mentioned result and prove that every planar graph without an i-cycle adjacent to a j-cycle with3<=j<=5 if i=3 and 4<=j<=5 if i=4 is acyclically 5-choosable.

Edge-choosability of Planar Graphs

According to the List Colouring Conjecture, if G is a multigraph then χ' (G)=χl' (G) . In this thesis, we discuss a relaxed version of this conjecture that every simple graph G is edge-(∆ + 1)-choosable as by Vizing’s Theorem ∆(G) ≤χ' (G)≤∆(G) + 1. We prove that if G is a planar graph without 7-cycles with ∆(G)≠5,6 , or without adjacent 4-cycles with ∆(G)≠5, or with no 3-cycles adjacent to 5-cycles, then G is edge-(∆ + 1)-choosable.

Backbone Colouring of Graphs

Consider an undirected graph G and a subgraph of G, H. A q-backbone k-colouring of (G,H) is a mapping f: V(G) {1, 2, ..., k} such that G is properly coloured and for each edge of H, the colours of its endpoints differ by at least q. The minimum number k for which there is a backbone k-colouring of (G,H) is the backbone chromatic number, BBCq(G,H). It has been proved that backbone k-colouring of (G,T) is at most 4 if G is a connected C4-free planar graph or non-bipartite C5-free planar graph or Cj-free, j∈{6,7,8} planar graph without adjacent triangles. In this thesis we improve the results mentioned above and prove that 2-backbone k-colouring of any connected planar graphs without adjacent triangles is at most 4 by using a discharging method. In the second part of this thesis we further improve these results by proving that for any graph G with χ(G) ≥ 4, BBC(G,T) = χ(G). In fact, we prove the stronger result that a backbone tree T in G exists, such that ∀ uv ∈ T, |f(u)-f(v)|=2 or |f(u)-f(v)| ≥ k-2, k = χ(G). For the case that G is a planar graph, according to Four Colour Theorem, χ(G) = 4; so, BBC(G,T) = 4.

Optimal and Robust Designs of Step-stress Accelerated Life Testing Experiments for Proportional Hazards Models

Accelerated life testing (ALT) is widely used to obtain reliability information about a product within a limited time frame. The Cox s proportional hazards (PH) model is often utilized for reliability prediction. My master thesis research focuses on designing accelerated life testing experiments for reliability estimation. We consider multiple step-stress ALT plans with censoring. The optimal stress levels and times of changing the stress levels are investigated. We discuss the optimal designs under three optimality criteria. They are D-, A- and Q-optimal designs. We note that the classical designs are optimal only if the model assumed is correct. Due to the nature of prediction made from ALT experimental data, attained under the stress levels higher than the normal condition, extrapolation is encountered. In such case, the assumed model cannot be tested. Therefore, for possible imprecision in the assumed PH model, the method of construction for robust designs is also explored.

Analyse bibliométrique des revues Canadian Journal of Communication et Communication 1974-2005

L’objectif de cette étude est de saisir une image des éléments explicitement reconnaissables de la recherche en communication visibles dans les revues savantes Canadian Journal of Communication et dans Communication de 1974 à 2005. Il s’agit d’une analyse bibliométrique des articles publiés par les chercheurs d’institutions canadiennes et de leurs références bibliographiques. La bibliométrie est « l’application de méthodes statistiques aux livres et aux autres moyens de communication » (Pritchard, 1969: 348-349). C’est la première fois qu’une analyse de ce type est tentée dans ce corpus particulier. Nous nous sommes appuyés sur des postulats théoriques provenant de la sociologie des sciences et des études en communication scientifique. L’idée maîtresse est la suivante : l’activité scientifique est un « continuum de création de nouvelles connaissances » (Vassallo, 1999), dont l’organisation est basée sur l’échange d’information (Price, 1963; Crane, 1972), qui se traduit en reconnaissance sociale, en autorité scientifique, et constitue un investissement pour l’acquisition de crédibilité (Merton, 1938; Hagstrom, 1965; Bourdieu, 1975; Latour et Woolgar, 1986). À partir de l’analyse des articles, nous identifions s’ils sont le résultat de recherches empiriques ou fondamentales, ou le produit d’une réflexion critique. Il s’agit aussi de détecter les approches méthodologiques et les techniques d’investigation utilisées, ainsi que les sujets qui y sont abordés par les chercheurs. Nous détectons également les principaux lieux de recherche (universités et types de départements). Nous analysons aussi les thématiques des articles. Enfin, nous analysons des références bibliographiques des articles afin de cerner les sources d’idées qui y sont décelables. Notre corpus principal comporte 1154 articles et 12 840 titres de documents en référence. L’analyse bibliométrique des articles révèle ainsi une recherche canadienne en communication d’emblée qualitative, intéressée pour les spécificités historiques, le contexte social et la compréhension des interrelations sous-jacentes aux phénomènes de communication, en particulier, au Canada et au Québec. Au cœur de ces études se distingue principalement l’application de l’analyse de contenu qualitative dans les médias en général. Cependant, à partir de 1980, l’exploration du cinéma, de l’audiovisuel, des nouvelles technologies de l’information et de la communication, ainsi que la multiplication des sujets de recherche, annoncent un déplacement dans l’ordre des intérêts. Communication et le CJC, se distinguent cependant par l’origine linguistique des chercheurs qui y publient ainsi que dans les thématiques. L’analyse des références bibliographiques, et de leurs auteurs, met en relief l’intérêt partagé des chercheurs d’institutions universitaires canadiennes pour les agences de réglementation et les politiques gouvernementales canadiennes s’appuyant souvent sur l’analyse de documents législatifs et de rapports de diverses commissions d’enquête du gouvernement canadien. L’analyse révèle aussi les principales inspirations théoriques et méthodologiques des chercheurs. Parmi les plus citées, on voit Innis, McLuhan, Habermas, Tuchman, Bourdieu, Foucault, Raboy, et Rogers. Mais ces références évoluent dans le temps. On voit aussi une distinction relativement claire entre les sources citées par la recherche francophone et la recherche anglophone.

Martin Heidegger and the problem of transcendence

Cette thèse a pour point de départ l’idée du jeune Heidegger selon laquelle le sens de l’être doit être recherché au moyen d’une phénoménologie ontologique, plus précisément par l’analytique existentiale du Dasein et la destruction de l’histoire de l’ontologie ; ou, comme nous l’interprétons, dans la transcendance du Dasein et la transcendance de l’être. L’étude du problème de la transcendance fait l’objet d’une approche phénoménologique, laquelle porte une attention particulière au vécu en tant que tel ainsi qu’aux conditions de possibilité de ce vécu, et repose sur une lecture attentive et critique des œuvres de Heidegger. C’est une telle approche phénoménologique qui nous permettra de mener à bien notre analyse du problème de la transcendance dans le corpus heideggérien. Nous serons par ailleurs en mesure d’aborder le débat opposant à ce sujet la tradition analytique (plus particulièrement l’approche pragmatiste) et la tradition continentale, notre étude s’inscrivant dans le cadre de cette dernière. Nous proposons ici une phénoménologie du problème de la transcendance qui fait également figure de phénoménologie du sens, de la possibilité et de la normativité. Prenant pour point de départ certaines contributions issues de la tradition continentale, nous soutenons que le sens de l’être peut être compris comme le problème de la transcendance. L’histoire de la philosophie doit être perturbée, déconstruite et repensée afin que le chemin de la philosophie, encore non pensé, puisse être mis au jour. L’accès à cet autre commencement doit être recherché dans la transcendance en tant que telle – de l’appel de la conscience fondé dans la nullité à l’encontre authentique avec la mort et l’ouverture de la temporalité ; de l’avènement historial de l’être jusqu’à, ultimement, le i! ! ! ! refus de l’être et le retrait du rien. L’événement (Ereignis) de l’être est donc compris comme processus de dépassement de soi à partir duquel la transcendance de l’être – ou, comme le formule Heidegger, la fin des questions – est possible.

Analysis of Some Queueing Models Related To N-Policy: Operations Research

This study is about the analysis of some queueing models related to N-policy.The optimal value the queue size has to attain in order to turn on a single server, assuming that the policy is to turn on a single server when the queue size reaches a certain number, N, and turn him off when the system is empty.The operating policy is the usual N-policy, but with random N and in model 2, a system similar to the one described here.This study analyses “ Tandem queue with two servers”.Here assume that the first server is a specialized one.In a queueing system,under N-policy ,the server will be on vacation until N units accumulate for the first time after becoming idle.A modified version of the N-policy for an M│M│1 queueing system is considered here.The novel feature of this model is that a busy service unit prevents the access of new customers to servers further down the line.It is deals with a queueing model consisting of two servers connected in series with a finite intermediate waiting room of capacity k.Here assume that server I is a specialized server.For this model ,the steady state probability vector and the stability condition are obtained using matrix – geometric method.

Some Generalizations of Fuzzy Metrizability

The main purpose of the study is to extent concept of the class of spaces called ‘generalized metric spaces’ to fuzzy context and investigates its properties. Any class of spaces defined by a property possessed by all metric spaces could technically be called as a class of ‘generalized metric spaces’. But the term is meant for classes, which are ‘close’ to metrizable spaces in some under certain kinds of mappings. The theory of generalized metric spaces is closely related to ‘metrization theory’. The class of spaces likes Morita’s M- spaces, Borges’s w-spaces, Arhangelskii’s p-spaces, Okuyama’s  spaces have major roles in the theory of generalized metric spaces. The thesis introduces fuzzy metrizable spaces, fuzzy submetrizable spaces and proves some characterizations of fuzzy submetrizable spaces, and also the fuzzy generalized metric spaces like fuzzy w-spaces, fuzzy Moore spaces, fuzzy M-spaces, fuzzy k-spaces, fuzzy -spaces study of their properties, prove some equivalent conditions for fuzzy p-spaces. The concept of a network is one of the most useful tools in the theory of generalized metric spaces. The -spaces is a class of generalized metric spaces having a network.

Analysis of Some Stochastic Inventory Models with Pooling Retrial of Customers

The thesis deals with analysis of some Stochastic Inventory Models with Pooling/Retrial of Customers.. In the first model we analyze an (s,S) production Inventory system with retrial of customers. Arrival of customers from outside the system form a Poisson process. The inter production times are exponentially distributed with parameter µ. When inventory level reaches zero further arriving demands are sent to the orbit which has capacity M(<∞). Customers, who find the orbit full and inventory level at zero are lost to the system. Demands arising from the orbital customers are exponentially distributed with parameter γ. In the model-II we extend these results to perishable inventory system assuming that the life-time of each item follows exponential with parameter θ. The study deals with an (s,S) production inventory with service times and retrial of unsatisfied customers. Primary demands occur according to a Markovian Arrival Process(MAP). Consider an (s,S)-retrial inventory with service time in which primary demands occur according to a Batch Markovian Arrival Process (BMAP). The inventory is controlled by the (s,S) policy and (s,S) inventory system with service time. Primary demands occur according to Poissson process with parameter λ. The study concentrates two models. In the first model we analyze an (s,S) Inventory system with postponed demands where arrivals of demands form a Poisson process. In the second model, we extend our results to perishable inventory system assuming that the life-time of each item follows exponential distribution with parameter θ. Also it is assumed that when inventory level is zero the arriving demands choose to enter the pool with probability β and with complementary probability (1- β) it is lost for ever. Finally it analyze an (s,S) production inventory system with switching time. A lot of work is reported under the assumption that the switching time is negligible but this is not the case for several real life situation.

Analysis of Some Single and Two Commodity Inventory Problems

This thesis is devoted to the study of some stochastic models in inventories. An inventory system is a facility at which items of materials are stocked. In order to promote smooth and efficient running of business, and to provide adequate service to the customers, an inventory materials is essential for any enterprise. When uncertainty is present, inventories are used as a protection against risk of stock out. It is advantageous to procure the item before it is needed at a lower marginal cost. Again, by bulk purchasing, the advantage of price discounts can be availed. All these contribute to the formation of inventory. Maintaining inventories is a major expenditure for any organization. For each inventory, the fundamental question is how much new stock should be ordered and when should the orders are replaced. In the present study, considered several models for single and two commodity stochastic inventory problems. The thesis discusses two models. In the first model, examined the case in which the time elapsed between two consecutive demand points are independent and identically distributed with common distribution function F(.) with mean  (assumed finite) and in which demand magnitude depends only on the time elapsed since the previous demand epoch. The time between disasters has an exponential distribution with parameter . In Model II, the inter arrival time of disasters have general distribution (F.) with mean  ( ) and the quantity destructed depends on the time elapsed between disasters. Demands form compound poison processes with inter arrival times of demands having mean 1/. It deals with linearly correlated bulk demand two Commodity inventory problem, where each arrival demands a random number of items of each commodity C1 and C2, the maximum quantity demanded being a (< S1) and b(of linearly correlated demand is also discussed

Clique Irreducibility of Some Iterative Classes of Graphs

In this paper, two notions, the clique irreducibility and clique vertex irreducibility are discussed. A graph G is clique irreducible if every clique in G of size at least two, has an edge which does not lie in any other clique of G and it is clique vertex irreducible if every clique in G has a vertex which does not lie in any other clique of G. It is proved that L(G) is clique irreducible if and only if every triangle in G has a vertex of degree two. The conditions for the iterations of line graph, the Gallai graphs, the anti-Gallai graphs and its iterations to be clique irreducible and clique vertex irreducible are also obtained.

On Distance Energy of Graphs

The D-eigenvalues of a graph G are the eigenvalues of its distance matrix D, and the D-energy ED(G) is the sum of the absolute values of its D-eigenvalues. Two graphs are said to be D-equienergetic if they have the same D-energy. In this note we obtain bounds for the distance spectral radius and D-energy of graphs of diameter 2. Pairs of equiregular D-equienergetic graphs of diameter 2, on p = 3t + 1 vertices are also constructed.

A Note on Energy of Some Graphs

Eigenvalue of a graph is the eigenvalue of its adjacency matrix. The energy of a graph is the sum of the absolute values of its eigenvalues. In this note we obtain analytic expressions for the energy of two classes of regular graphs.

Some classes of Turker equivalent graphs

Two graphs G and H are Turker equivalent if they have the same set of Turker angles. In this paper some Turker equivalent family of graphs are obtained.

A Study Of Frames In The Fuzzy And Intuitionist Fuzzy Contexts

The fuzzy set theory has a wider scope of applicability than classical set theory in solving various problems. Fuzzy set theory in the last three decades as a formal theory which got formalized by generalizing the original ideas and concepts in classical mathematical areas and as a very powerful modeling language, that can cope with a large fraction of uncertainties of real life situations. In Intuitionistic Fuzzy sets a new component degree of non membership in addition to the degree of membership in the case of fuzzy sets with the requirement that their sum be less than or equal to one. The main objective of this thesis is to study frames in Fuzzy and Intuitionistic Fuzzy contexts. The thesis proved some results such as ifµ is a fuzzy subset of a frame F, then µ is a fuzzy frame of F iff each non-empty level subset µt of µ is a subframe of F, the category Fuzzfrm of fuzzy frames has products and the category Fuzzfrm of fuzzy frames is complete. It define a fuzzy-quotient frame of F to be a fuzzy partition of F, that is, a subset of IF and having a frame structure with respect to new operations and study the notion of intuitionistic fuzzy frames and obtain some results and introduce the concept of Intuitionistic fuzzy Quotient frames. Finally it establish the categorical link between frames and intuitionistic fuzzy topologies.