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.

Properties and algorithms of the hyper-star graph and its related graphs

The hyper-star interconnection network was proposed in 2002 to overcome the drawbacks of the hypercube and its variations concerning the network cost, which is defined by the product of the degree and the diameter. Some properties of the graph such as connectivity, symmetry properties, embedding properties have been studied by other researchers, routing and broadcasting algorithms have also been designed. This thesis studies the hyper-star graph from both the topological and algorithmic point of view. For the topological properties, we try to establish relationships between hyper-star graphs with other known graphs. We also give a formal equation for the surface area of the graph. Another topological property we are interested in is the Hamiltonicity problem of this graph. For the algorithms, we design an all-port broadcasting algorithm and a single-port neighbourhood broadcasting algorithm for the regular form of the hyper-star graphs. These algorithms are both optimal time-wise. Furthermore, we prove that the folded hyper-star, a variation of the hyper-star, to be maixmally fault-tolerant.

The mechanism of the regulation of energy distribution between photosystems 1 and 2 in the cyanobacterium Synechococcus sp. strain PCC 7002 /

Cyanobacteria are able to regulate the distribution of absorbed light energy between photo systems 1 and 2 in response to light conditions. The mechanism of this regulation (the state transition) was investigated in the marine cyanobacterium Synechococcus sp. strain PCC 7002. Three cell types were used: the wild type, psaL mutant (deletion of a photo system 1 subunit thought to be involved in photo system 1 trimerization) and the apcD mutant (a deletion of a phycobilisome subunit thought to be responsible for energy transfer to photo system 1). Evidence from 77K fluorescence emission spectroscopy, room temperature fluorescence and absorption cross-section measurements were used to determine a model of energy distribution from the phycobilisome and chlorophyll antennas in state 1 and state 2. The data confirm that in state 1 the phycobilisome is primarily attached to PS2. In state 2, a portion of the phycobilisome absorbed light energy is redistributed to photo system 1. This energy is directly transferred to photo system 1 by one of the phycobilisome terminal emitters, the product of the apcD gene, rather than via the photo system 2 chlorophyll antenna by spillover (energy transfer between the photo system 2 and photo system 1 chlorophyll antenna). The data also show that energy absorbed by the photo system 2 chlorophyll antenna is redistributed to photo system 1 in state 2. This could occur in one of two ways; by spillover or in a way analogous to higher plants where a segment of the chlorophyll antenna is dissociated from photo system 2 and becomes part of the photo system 1 antenna. The presence of energy transfer between neighbouring photo system 2 antennae was determined at both the phycobilisome and chlorophyll level, in states 1 and 2. Increases in antenna absorption cross-section with increasing reaction center closure showed that there is energy transfer (connectivity) between photosystem 2 antennas. No significant difference was shown in the amount of connectivity under these four conditions.

Gadamer's transformation of hermeneutics : from Dilthey to Heidegger

Abstract: The purpose of this paper is to show how Gadamer's hermeneutics synthesizes the insights of both Heidegger and Dilthey in order to introduce a new hermeneutics. Gadamer's hermeneutics is based not only on the priority of ontology, as Heidegger insists, and neither is it only a product of life which can be objectively understood through study and rigorous method, as Dilthey suggests. For Gadamer, hermeneutics is the bringing together of ontology in terms of history. By this synthesis Gadamer not only places himself within the context of a Lebensphilosophie, but also shows that it is within language that Being can be disclosed according to a lived context. Throughout this paper the philosophies ofDilthey and Heidegger are explicated within a historical context as to bring out how, and why, Gadamer sees the need to surpass these philosophies. Through Gadamer's philosophy of play and the game, language, the dialogical model, application, and the fusion of horizons we can see how Gadamer's critique and questioning of these two philosophy leads to his new hermeneutics. Special attention is paid to the role in which these two contrasting philosophies were used to complement each other in the product of Gadamer' s philosophical hermeneutics as it is presented in his major work Truth andMethod. For Gadamer, the task of understanding is never complete. Therefore, his hermeneutics remains a dynamic structure with which we can always question the past and our traditions. This paper seeks to show his philosophical movements within these questions

An HPLC method for simultaneous determination of residual benomyl and MBC on apple foliage without cleanup

A simple High Performance Liquid Chromatograph (HPLC) method has been developed to identify benamyl (methyl 1- (butylcarbamoyl)-2-benzimidazole carbamate) and MBC (methyl 2-benzimidazole carbamat~ residues on apple leaves without cleanup. Sample leaves are freeze dried in a Mason jar and residues are then extracted by tumbling them in chloroform containing 5,000 microgram per milliliter of n-propyl isocyanate (PIC) at 10 C. To the extract, n-butyl isocyanate (BIC) was added at 5,000 microgram per milliliter and 20 microliter of this mixture injected onto the HPLC system. Separation is accomplished by the use of a Brownlee LiChrosorb silica gel column with a guard column and' operated with a mixed mobile phase consisting of chloroform and hexane (4:1) saturated with water. MBC, a degradation product of benomyl is identified if present as methyl l-(npropyl carbamoyl)-2-benzimidazole carbamate (MBC-n-PIC). Both benomyl and MBC-n-PIC can be detected with aKUltraviolet (UV) detector (280nm) at a concentration as low as 0.2 microgram per milliliter in apple leaves. The fate of benomyl on apple foliage after spray application of benomyl (Ben late 50 per cent wettable powder) was investigated by the method thus described. Benomyl quickly dissipated during the first 3-7 days, but the dissipatio'n sltowed down thereafter. In contrast, the concentration of MBC in leaves gradually increased after repeated applications of Benlate.

Developmental variations in the peripheral erythrocytic system of the rainbow trout, Salmo gairdneri

The peripheral circulating erythrocytic system of the rainbow trout, l3 almo gairdner , was examined in vitro in relation differences in the morphology and multiple hemoglobin system organization of adult and juvenile red cells. Cells were separated by velocity sedimentation under unit gravity, a procedure requiring red cell exposure to an incubation medium for periods of at least three hours. Therefore , this must provide an environment in which red cells remain in a condition approximaing normalcy. Previous studies having demonstrated commonly employed media to be ineffective in this regard , a medium was developed through modification of Cortl and saline. One of the principal additions to this me dium , norepinephrine, altered cell regulation of intracellular calcium, magnesium and chloride concentrations. Catecholamine involvement was also suggeste d in the synthes is of hemoglobin . The procedure was found to separtate cells primarily by density and, to a lesser extent, by shape. Characterization of red cells revealed two subpopulations to exist . The first comprised the bulk of the cell population, and were of greater l ength, width, volume and major:minor axis ratio than the smaller population; these were adult cells. The later, juvenile cells were of smaller overall size and were more spherical in shape . Juvenile cells also possessed fewer electrophore tpically distinguishable isomorphs than did adults with only eight of eleven hemoglobin component s typically found With maturation,hemoglobin complement with the development of three more bands. The total complement of the adult cell contained 7 cathodal bands and four anodal hemoglobin isomorphs. Bands acquired with maturation comprised the smallest percentage of the cells hemoglobin. each averaging less than one-percent of the total. Whether these additional bands are derived through degradation and reaggregation of existing components or are the product of pe gQy2 synthesis is not yet known.

Some aspects of the chemistry of 1, 3, 4 - Thiadiazolium salts and related compounds

The work described in this thesis has been divided into seven sections. The first section involves the preparation of N'-acyl-N'-arylN- benzothiohydrazides by the acylation of N'-aryl-N-benzothiohydrazides and is followed by a brief discussion of their possible conformation in solution. The second section deals with the preparation of 1,3,4-thiadiazolium salts by the action of perchloric acid/acetic anhydride on N'-acylN'- aryl-N-benzothiohydrazides and also by the reaction of N'-arylN- benzothiohydrazides with nitriles in an acidic medium. The preparation of 2-methylthio-I,3,4-thiadiazolium methosulfate by methylating the corresponding thione is also described. The third section deals with the reaction of 2-phenyl- and 2-methyl-I,3,4-thiadiazolium salts with alcohols in the presence of base. The stability and spectra of these compounds are discussed. Treatment of the 2-methyl-I,3,4-thiadiazolium salt with base was found to give rise to a dimeric anhydrobase and evidence supporting its structure is given. The anhydrobase could be trapped by a variety of acylating and thioacylating agents before dimerization occurred. In the fourth section, the reaction of N'-acyl-N'-aryl-N-benzothiohydrazides with a variety of acid anhydrides is described. These compounds were found to be identical with those obtained by acylating the anhydrobase. The mass spectral fragmentation of these compounds is described and the anomolous product obtained upon thiobenzoylation of 3-methyl-l-phenyl-pyrazal-5-one is also discussed. The fifth section deals with thioacyl derivatives of the anhydrobase which were prepared by the action of phosphorus pentasulfide upon the oxygen analogues and also obtained as the major product of the reaction of thioacetic acid with compounds related to N'-aryl-N-benzothiohydrazides. The mass spectra and p.m.r. spectra of these compounds are discussed. In the sixth section, the reaction of the 2-methylthio-l,3,4- thiadiazolium salt with active methylene compounds to give acyl and diacyl derivatives of the anhydrobase is described. Some aspects of these compounds are discussed. The seventh section describes the synthesis of ncyanine~' type dyes incorporating the l,3,4-thiadiazole ring and their spectra are briefly discussed.

Effect of iron on reactivity of vanillin in wine models /

Phenolic compounds are important components of grapes and wines. They have been found to have important roles in grape and wine systems and properties that are beneficial for human health. Vanillin (3-methoxy-4-hydroxybenzaldehyde) is a phenolic compound coming from the oxidative degradation of lignin in oak-barrels during the aging of wine. Vanillin is an important flavour component of wine and its concentration in wine influences significantly the aroma and flavour of wine. The concentration of vanillin in wine is affected by various factors including the presence of metal ions. In this work, by using HPLC, HPLC-MS, and MS technologies, iron (III) cations were found to affect the oxidation of vanillin in a model system of wine, and the product of the oxidation was identified as divanillin. The mechanism of the redox reaction between vanillin and Fe^"^ is thought to follow that of other phenol oxidations. Increasing the concentration of Fe ^ in the model system accelerates divanillin production. The best pH condition for the divanillin production in the system is the range of 3.0 ~ 3.5. Increasing temperature from 20°C to 40°C accelerates the divanillin production. Divanillin was found to exist in three commercial red wines in this work. Keeping the storage temperature cool and decreasing the contact of grapes and wines with iron are two major measures suggested by this work in order to decrease the oxidation of vanillin during the making and aging of wine.

Towards a just community: an examination of the development of cultural citizenship rights in Canada from a communitarian perspective

The notion of citizenship, while a basic human right, has come under scrutiny. It was once assumed a liberal inspired regime of citizenship rights would reign as the primary ideological perspective in the Western world, however this has not been the case. Numerous competing paradigms have questioned the premise upon which liberal guarantees of citizenship rights are based. In particular, communitarianism has subjected liberal rights discourse to a closer examination. Communitarian theory holds that universalist principles negate any articulation of community and its internal diversity, such as cultural citizenship. It is this understanding of citizenship that has taken hold in Canada. The Canadian political experience illustrates a number of attributes associated with communitarian thought. It is a collectivist society that articulates a notion of the common good, acknowledges the internal diversity of its citizens and possesses a highly developed deliberative democratic process. To this end, Canada can be described as being more communitarian than liberal in nature in the process it has adopted to address citizenship rights. However, the type of commuIiitarianism displayed in Canada differs from the political models examined by such scholars as Michael Sandel, Iris Marion Young or Will Kymlicka. Cultural citizenship rights are fluid and malleable in Canada. While no clear guarantees of citizenship rights exist, there is a common commitment by Canadians to engage in a fair, open and inclusive deliberative process. This model is unique to Canada; it cannot be exported in that it is a product of Canadian political culture. As a result, the contemporary demands of cultural citizenship are dealt with effectively and democratically in Canada in that the proper mechanisms for public deliberation exist.

Square Root Finding In Graphs

Abstract: Root and root finding are concepts familiar to most branches of mathematics. In graph theory, H is a square root of G and G is the square of H if two vertices x,y have an edge in G if and only if x,y are of distance at most two in H. Graph square is a basic operation with a number of results about its properties in the literature. We study the characterization and recognition problems of graph powers. There are algorithmic and computational approaches to answer the decision problem of whether a given graph is a certain power of any graph. There are polynomial time algorithms to solve this problem for square of graphs with girth at least six while the NP-completeness is proven for square of graphs with girth at most four. The girth-parameterized problem of root fining has been open in the case of square of graphs with girth five. We settle the conjecture that recognition of square of graphs with girth 5 is NP-complete. This result is providing the complete dichotomy theorem for square root finding problem.

Using PageRank Algorithm in Analyzing Dictionary Graphs and PageRank in Dynamic Graphs

In this thesis we are going to analyze the dictionary graphs and some other kinds of graphs using the PagerRank algorithm. We calculated the correlation between the degree and PageRank of all nodes for a graph obtained from Merriam-Webster dictionary, a French dictionary and WordNet hypernym and synonym dictionaries. Our conclusion was that PageRank can be a good tool to compare the quality of dictionaries. We studied some artificial social and random graphs. We found that when we omitted some random nodes from each of the graphs, we have not noticed any significant changes in the ranking of the nodes according to their PageRank. We also discovered that some social graphs selected for our study were less resistant to the changes of PageRank.