Excluding any graph as a minor allows a low tree-width 2-coloring

A theorem of Drinfel'd (Drinfel'd (1993)) classifies the Poisson homogeneous spaces of a Poisson Lie group (G,πG) via a special class of Lagrangian subalgebras of the Drinfel'd double of its Lie bialgebra. This result is extended in Liu et al. (1998) to a classification of the Poisson homogeneous spaces of a Poisson groupoid (G⇉P, πG) via a special class of Dirac structures in the Courant algebroid defined by the corresponding Lie bialgebroid. It is hence natural to ask what corresponds via these classifications, or extensions of them, to arbitrary Dirac structures in the Drinfel'd double or the Courant algebroid associated to a Poisson group(oid). We show in this thesis that there is a bigger class of Dirac structures that fits in this correspondence. They correspond naturally to Dirac homogeneous spaces of the Poisson group(oid). Dirac Lie groups and Dirac groupoids have been defined by Ortiz (2009) as a generalization of Poisson Lie groups, Poisson groupoids and presymplectic groupoids. We prove in an alternative manner the existence of a natural Lie bialgebra associated to a Dirac Lie group, and we find good candidates for the infinitesimal data of a Dirac groupoid; a square of morphisms of Lie algebroids associated to the multiplicative Dirac structure. These objects generalize simultaneously the Lie bialgebroid of Poisson groupoids and the IM-2-forms associated to presymplectic groupoids (Bursztyn et al. (2004)). We show also the existence of a Courant algebroid associated to these algebroids. This Courant algebroid structure is induced in a natural way by the ambient standard Courant algebroid TG ×G T*G and is isomorphic to the Courant algebroid AG ×P A*G in the Poisson case. We show that Dirac homogeneous spaces of Dirac Lie groups (respectively Dirac groupoids) correspond to certain classes of Dirac structures in the Drinfel'd double of the Lie bialgebra (respectively in the Courant algebroid). These results generalize the classification theorems in Drinfel'd (1993) and Liu et al. (1998). Along the way, we study involutive multiplicative foliations on Lie groupoids and show when and how there is a natural groupoid structure defined on the leaf spaces in the set of objects and the set of units of the Lie groupoid. This is a fact that is always true in the Lie group case, where a multiplicative foliation is automatically the left and right invariant image of an ideal in the Lie algebra, i.e., the leaves are the cosets of a normal subgroup of the Lie group.

In the range emptiness searching problem, we are given a set P of n points in Rd, and wish to preprocess them into a data structure that supports efficient range emptiness queries, in which we specify a range σ, which is a semi-algebraic set in Rd of some fixed kind, and wish to determine whether P ∩ σ = θ. Range emptiness searching arises in many applications, and has been treated by Matousek [15] in the special case where the ranges are halfspaces bounded by hyperplanes. In this paper we extend the analysis to the general semi-algebraic case, and show how to adapt Matousek's technique to this case, without the need to linearize the ranges into a higher-dimensional space. This yields more efficient solutions to several interesting problems, and we demonstrate the new technique in two applications:(i) An algorithm for ray shooting amid balls in R3, which uses O* (n) storage and preprocessing, and answers a query in O* (n2/3) time, improving the previous bound of O* (n3/47).(ii) An algorithm that preprocesses, in O*(n) time, a set P of n points in R3 into a data structure with O*(n) storage, so that, for any query line l or segment e, the point of P farthest from l or from e can be computed in O* (n1/2) time.Our technique is closely related to the notions of nearest- or farthest-neighbor generalized Voronoi diagrams, and of the union or intersection of geometric objects, where sharper bounds on the combinatorial complexity of these structures yield faster range emptiness searching algorithms. For example, in the case of ray shooting amid balls, the structure that arises in our algorithm is the Euclidean Voronoi diagram of lines in 3-space, and the performance of the algorithm depends on the complexity of such diagrams (for which tight bounds are still unknown).

This thesis focuses on the interplay of extremal combinatorics and finite geometry. Combinatorics is concerned with discrete (and usually finite) objects. Extremal combinatorics studies how large or how small a collection of finite objects can be under certain restrictions. Those objects can be sets, graphs, vectors, etc. These questions are often motivated by problems in information theory and computer science. Another branch of combinatorics is finite geometry over finite fields of order q. Although there is no field of order 1, certain substructures in finite geometry can be interpreted as versions of projective spaces for q = 1. A triangle in a projective plane is a good example of this phenomenon. Following an introductory chapter, Chapter 2 gives an overview of some classical problems and their q-analogues in extremal combinatorics. The most recent results for the q-analogues of Sperner's theorem, the Erdös-Ko-Rado theorem and several versions of Bollobás's theorem are described. For the q-analogue of the Hilton-Milner theorem we give some new results. We also give a new bound for the minimum size of the q-analogue of small maximal cliques. We conclude that sometimes results for a q-analogue can be obtained by using the same technique as in the original problem. In some cases the answer to the problem is even identical to that of the original problem. In other cases techniques used for the q-analogue could be used for improving bounds for the original problem. The third chapter describes the known results for the chromatic number of the Kneser graphs and gives new bounds for the chromatic number of the q-analogue. The vertices of a Kneser graph are subsets (of a fixed size) of a set, whereas two vertices are adjacent if they are disjoint in their subset representation. In 1955 M. Kneser conjectured the chromatic number of those graphs. In 1978 this was proven correct by L. Lóvasz. Two small cases in the projective space q-analogue were solved in 2001 by J. Eisfeld, L. Storme and P. Sziklai and in 2006 by A. Chowdhury, C. Godsil and G. Royle. We describe an asymptotic result for all cases (except for one parameter family, where we give a partial proof) using the bounds from the q-analogue of the Hilton-Milner theorem. Chapters 4, 5 and 6 describe other q-analogues of the Kneser graphs. In Chapter 4 we define a family of Kneser type graphs over pairs of incident points and hyperplanes of a projective space. We describe large maximal cocliques in these graphs and prove that for small dimensions these are the largest possible cocliques. We conjecture that this is the case for all dimensions. In Chapter 5 we extend the Kneser graphs to the case of finite polar spaces instead of finite projective spaces and in some cases give descriptions and chromatic numbers of these graphs. Chapter 6 describes the generalization of Kneser graphs over coset spaces of Chevalley groups (parameterized by q) with respect to parabolic subgroups. This encompasses all previous cases and extends to some interesting new cases. First we describe these graphs when q = 1 and give chromatic numbers for some families. Then we consider the graphs defined over coset spaces of Chevalley groups for general q with respect to parabolic subgroups and study what results of the q = 1 case can be translated to the general case. In this thesis we found different possibilities for the connection between the bounds for the q = 1 case and the case for general q. In some cases the bounds for the general case are identical to the bounds for q = 1. In other cases we obtain the bounds for q = 1 by taking the limit for q¿1 in the general bound. Other cases show a completely different bound in both cases.

Dλ-cycles in λ-claw-free graphs

In this paper, we extend Rothemund and Winfree's examination of the tile complexity of tile self-assembly [6]. They provided a lower bound of Ω(log N/log log N) on the tile complexity of assembling an N × N square for almost all N. Adleman et al. [1] gave a construction which achieves this bound. We consider whether the tile complexity for self-assembly can be reduced through several natural generalizations of the model. One of our results is a tile set of size O(√log N) which assembles an N × N square in a model which allows flexible glue strength between non-equal glues (This was independently discovered in [3]). This result is matched by a lower bound dictated by Kolmogorov complexity. For three other generalizations, we show that the Ω(log N/log log N) lower bound applies to N × N squares. At the same time, we demonstrate that there are some other shapes for which these generalizations allow reduced tile sets. Specifically, for thin rectangles with length N and width k, we provide a tighter lower bound of Ω(N(1/k)/k) for the standard model, yet we also give a construction which achieves O(log N/log log N) complexity in a model in which the temperature of the tile system is adjusted during assembly. We also investigate the problem of verifying whether a given tile system uniquely assembles into a given shape, and show that this problem is NP-hard.

Turán number of generalized triangles

The thesis titled antecedents and enablers of green supply chain practices focuses on one of the most contemporary issues in supply chain management. The literature review explores the existing literature and research work on green supply chain practices and develops a framework for the research. The research is qualitative in nature and data was collected from the three automobile component-manufacturing companies in India. Semi structured interviews were conducted over a period of 18 months. There were three objectives for this thesis: 1. Describing the current state of green supply chain practices? 2. What are the antecedents and enablers for green supply chain practices? 3. What are the underlying mechanisms, if any? The research work concludes by answering all the above three questions and also gives the future direction for research. The research work started by finding a gap for the empirical research in the context of green supply chain practices. The objective of the research was to focus on antecedents and enablers of green supply chain practices. Some contextual factors, inhibitors and consequences are also emerged during the pilot case study. The research work is rigor and to ensure the rigor of the research design, five-stage process was used to structure the methodology. As a final check author assessed his research against the four basic tests commonly used in empirical research; construct validity, internal validity, external validity and reliability. The research study has contributed both to the development and testing of theory relating to the antecedents and enablers of green supply chain practices. The review of literature provided a synthesis of the underpinning bodies of literature that has not previously been conducted in this way. This resulted in the identification of ten core green supply chain practices for the development of antecedents and enablers that created the foundation for author’s empirical investigation. It was found that previous studies have been largely theoretical. The empirical studies that do exist have focused on one particular dyadic relationship with in green supply chain practices. A double contribution has been made to testing the theory of green supply chain practices from a process and output perspective. As process perspective, a contribution has been made to methodology by developing a robust approach for conducting supply chain research beyond the dyad. From output perspective, the author has the empirical results from the three individual case studies and their cross-case comparison for dissemination to an academic audience. Specific contribution of this research to theory development include: 1. Development of macro model of green supply chain practices with the inputs from literature. 2. The synthesis of ten core green supply chain practices with antecedents and enablers from existing body of literature enriched through empirical testing 3. Empirical derivation of three contextual factors. Although the research work is new and contribute to the theory and practices, there are still some limitations of this research. Two minor limitations have been identified: 1. Generalizability of result to practice to practice: Due to the limited size of the case study approach, the results can only be generalized to theory and not to practice. 2. Variation in quality of information: The scope of data collection for all three case studies was same still the quality of information gathered was different. As good quality cross-case analysis was still possible but the relative strengths of the three cases varied. Overall the research work is original, rigor, and contributes to the existing theory and also paves the path for future research work in the area of green supply chain practices.

PURPOSE To evaluate the incidence of ultrathin ceramic veneer fracture over a period of 36 months and the possible relationship with local- and patient-related factors. MATERIALS AND METHODS Adult patients who received ceramic veneers for improvement in smile esthetics were selected from a private practice pool. Veneers were grouped as conventional ceramic veneers (prep) or ultrathin following either a minimal preparation (min-prep) or no tooth preparation (no-prep) protocol. After veneer bonding, all patients were followed up at intervals of 6 months up to 36 months. A panel of clinical outcomes was recorded. Patient satisfaction was assessed at 36 months. RESULTS The study sample was formed by 49 patients who received a total of 194 veneers. Twelve veneers were prep, 125 were min-prep, and 57 were no-prep. Total fracture occurrence was 9.8% in 13 participants. No fractures were observed in prep veneers, while 16 out of 125 min-prep and 3 out of 57 no-prep veneers had fractures. Most fractures (13 out of 19) occurred early, within the first 12 months after bonding. Out of 194 veneers, only 1 had a catastrophic failure (0.5%), 3 had large (≥ 1 mm) chippings (1.5%), and 15 had minor (< 1 mm) chippings (7.7%). A generalized estimating equation model revealed that the odds of veneer fracture were significantly higher in men (odds ratio [OR] = 11.29), in patients who exhibited tooth wear at baseline (OR = 5.54), and in central (OR = 13.56) and lateral (OR = 10.43) incisors compared to canines and premolars. All participants indicated that they would not change to a different restorative protocol in order to have a thicker restoration and possibly less risk of fracture. CONCLUSION Ultrathin ceramic veneers are a viable cosmetic dentistry treatment option that involves minimal or no tooth preparation. However, a tendency for increased early fractures was observed in the min-prep group.

This paper presents a study of English-Indonesian translation of the humorous utterances in Walt Disney’s Donald Duck comics. Twenty one Indonesian translated comics of the 2008 issues and their original English versions were used as the source of data. A total of 480 humorous English utterances were identified and verified by 4 native English speakers. These 480 English utterances and their translations were used as the data. Analyses of the collected data were then made to see the translation techniques used by the translator in translating the humorous utterances and to see the resulted pragmatic equivalence viewed from the equivalence of pragmatic force between the source text (ST) and target text (TT), involving implicture analysis of the utterances. The findings of the research reveal that 647 uses of translation techniques are made to translate the 480 utterances, as more than one techniques are used in some of the utterances. Seventeen out of 18 translation techniques proposed by Molina & Albir (2002) are chosen by the translator. It is also found out that the translator’s choice of translation techniques has resulted in 96.87% of the translated humorous utterances being equivalent in their pragmatic force, compared to the original English utterances. The use of such translation techniques as generalization, established equivalent, linguistic compression, amplification, literal translation, compensation, linguistic amplification, variation, particularization, borrowing, transposition, description, and calque has resulted in equivalent pragmatic force between ST and TT. Only minor portion (3.13%) of the translated text is not equivalent in its pragmatic force, and this is caused by the use of amplification, discursive creation, reduction, adaptation, and modulation techniques. The high rate of pragmatic equivalence shows the translator’s success in translating the text. Key words : implicature, pragmatic force, pragmatic equivalence, translation technique

Terms like commutativity degree, non-commuting graph and isoclinism are far well-known for much of the group theorists nowadays. There are so many papers about each of these concepts and also about their relationships in finite groups. Also, there are some recent researches about generalizing these notions in finite rings and their connexions.The concepts of commutativity degree and non-commuting graph are also extended to non-associative structures such as Moufang loops and some part of the known results in group theory in these contexts have been expanded to them.In this paper, we are going to generalize the notion of isoclinism in finite Moufang loops and then study the relationships between these three concepts. Among other results, we prove that two isoclinic finite Moufang loops have the same commutativity degree and if they have the same sizes of centers and commutants then they have isomorphic non-commuting graphs. Also, the converses of these results have been investigated.Furthermore, it has been proved that a finite simple group can be characterized by its non-commuting graph. We will prove the same is true for a finite simple Moufang loop by imposing one additional hypothesis, namely, the isoclinism of the regarding loops.

Recent innovation in the design of type theories—foundational systems of mathematics with a focus on constructivity—has produced the concept of interval variable, which can be used to capture relations between objects that carry computational content. We examine two such relationships in type theory: equality, in particularquotients, and arbitrary relations as applied in parametricity interpretations. Cubical type theory, a system using an interval-based formulation of equality, enables a permissive kind of content-carrying equality that includes in particularisomorphism. Cubical type theory provides a constructive interpretation of homotopy type theory and the Univalent Foundations, formalisms that introduced the idea of isomorphism as equality but which lack intrinsic computational meaning. The cubical approach to equality also rectifies long-standing deficiencies in the behavior ofquotients in type theory. We realize a system of generalized quotients for cubical type theory originally conceived in homotopy type theory, called higher inductive types, that merges the concepts of inductive type and quotient. Such a mutual generalization is particularly essential in the contentful equality setting, but also has significant applications to ordinary mathematics. Parametricity is, among other things, a proof technique for deriving propertiesof constructions performed in type theories, based on the idea that constructions preserve all relations between objects. Traditionally a meta-theoretical tool, recentwork has shown that parametricity properties can be integrated into a type theory itself using an interval-based system. We develop internal parametricity on top ofcubical type theory, examining the similarities and distinctions between the two applications of intervals, finding that a background of cubical equality improves thebehavior of internal parametricity, and applying internal parametricity as a tool to solve difficult problems in cubical type theory. We introduce a system of cohesionmodalities to express the interaction between parametric and non-parametric type theory, enabling the use of parametricity results in a non-parametric setting.

Kajal kaolin deposit is located ~20 km northwest of Hashtjin, Ardebil province. Field evidence and laboratory investigations show that the deposit is an alteration product of ignimbrites, tuffs, and trachy-andesites of Eocene age. According to mineralogical data, the major rock-forming minerals include kaolinite, montmorillonite, polygorskite, orthoclase, zeolite (stilbite), quartz, and chalcedony. Mass change calculations of elements, with assumption of Ti as immobile monitor element, indicate that leaching and fixation are two prominent regulators for concentration of major, minor, trace, and rare earth elements in the deposit. The distribution pattern of REEs, normalized to ignimbrite, in kaolin samples illustrates a weak fractionation of LREEs from HREEs coupled with strong negative Eu anomaly during the evolution of the deposit. Calculations of correlation coefficients among elements show that there is a high intrinsic correlation between HREEs in the studied samples. According to geochemical indices, it can be inferred that the hypogene alterations are superimposed by supergene ones in the course of evolution of the deposit. In accordance with the mode of distribution of elements in the deposit, it appears that the behavior of elements during kaolinization of ignimbrites was affected by the function of factors such as pH, redox potential, temperature variations, high fluid to rock ratio, preferential adsorption by clays and iron oxides, discrepancies in the stability rate of minerals, abundance of complex-forming ions (CO32-, F־, Cl־, PO43-, and SO42-), and isomorphic substitution. The obtained results indicate that epithermal acid-sulfate solutions along with acidic supergene solutions originated from oxidation of hypogene pyrites played an important role in development of the deposit. Further geochemical considerations show that clay minerals along with secondary phosphates like monazite, rabdophane, and xenotime are the potential hosts for REEs in the deposit.

An elliptic semiplane is a λ-fold of a symmetric 2-(v,k,λ) design, where parallelism is transitive. We prove existence and uniqueness of a 3-fold cover of a 2-(15,7,3) design, and give several constructions. Then we prove that the automorphism group is 3.Alt(7). The corresponding bipartite graph is a minimal graph with valency 7 and girth 6, which has automorphism group 3.Sym(7). A polynomial with real coefficients is called formally positive if all of the coefficients are positive. We conjecture that the determinant of a matrix appearing in the proof of the van der Waerden conjecture due to Egorychev is formally positive in all cases, and we prove a restricted version of this conjecture. This is closely related to a problem concerning a certain generalization of Latin rectangles. Let ω be a primitive nth root of unity over GF(2), and let m_i(x) be the minimal polynomial of ω^i. The code of length n = 2^r-1 generated by m_1(x)m_t(x) is denoted C^t_r. We give a recursive formula for the number of codewords of weight 4 in C^11_r for each r.

The aim of this paper is to classify all monogenic ternary semigroups, up to isomorphism. We divide them to two groups: finite and infinite. We show that every infinite monogenic ternary semigroup is isomorphic to the ternary semigroup O, the odd positive integers with ordinary addition. Then we prove that all finite monogenic ternary semigroups with the same index and the same period are isomorphic. We also investigate structure of finite monogenic ternary semigroups and we prove that any finite monogenic ternary semigroup is isomorphic to a quotient ternary semigroup.

New Heuristics and Adaptive Memory Procedures for Boolean Optimization Problems, Lars M. Hvattum, Arne Lokketangen, and Fred Glover Convergent Lagrangian Methods for Separable Nonlinear Integer Programming: Objective Level-Cut and Domain-Cut Methods, Duan Li, Xiaoling Sun, and Jun Wang The Generalized Assignment Problem, Robert M. Nauss Decomposition in Integer Linear Programming, Ted K. Ralphs and Matthew V. Galati Airline Scheduling Models and Solution Algorithms for the Temporary Closure of Airports, Shangyao Yan and Chung-Gee Lin Determining an Optimal Fleet Mix and Schedules: Part I - Single Source and Destination, Hanif D. Sherali and Salem M. Al-Yakoob Determining an Optimal Fleet Mix and Schedules: Part II - Multiple Sources and Destinations, and the Option of Leasing Transshipment Depots, Hanif D. Sherali and Salem M. Al-Yakoob An Integer Programming Model for the Optimization of Data Cycle Maps, David Panton, Maria John, and Andrew Mason Application of Column-Generation Techniques to Retail Assortment Planning, Govind P. Daruka and Udatta S. Palekar Noncommercial Software for Mixed-Integer Linear Programming, Jeff T. Linderoth and Ted K. Ralphs