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Full-Text Articles in Physical Sciences and Mathematics
On 2-Primitive Triangle Decompositions Of Cocktail Party Graphs, Ian P. Waddell
On 2-Primitive Triangle Decompositions Of Cocktail Party Graphs, Ian P. Waddell
Theses, Dissertations and Capstones
A decomposition of a graph Γ is a collection C of subgraphs, perhaps nonisomorphic, that partition the edges of Γ. Analogously, consider a group of truck drivers whose non-overlapping routes jointly cover all of the roads between a set of cities; that is, each road is traversed by precisely one driver. In this scenario, the cities are the vertices of the graph, the roads are the edges between vertices, and the drivers’ routes are the subgraphs in the decomposition. Given a graph H, we call C an H-decomposition of Γ if each subgraph in C is isomorphic to …
Many-Objective Evolutionary Algorithms: Objective Reduction, Decomposition And Multi-Modality., Monalisa Pal Dr.
Many-Objective Evolutionary Algorithms: Objective Reduction, Decomposition And Multi-Modality., Monalisa Pal Dr.
Doctoral Theses
Evolutionary Algorithms (EAs) for Many-Objective Optimization (MaOO) problems are challenging in nature due to the requirement of large population size, difficulty in maintaining the selection pressure towards global optima and inability of accurate visualization of high-dimensional Pareto-optimal Set (in decision space) and Pareto-Front (in objective space). The quality of the estimated set of Pareto-optimal solutions, resulting from the EAs for MaOO problems, is assessed in terms of proximity to the true surface (convergence) and uniformity and coverage of the estimated set over the true surface (diversity). With more number of objectives, the challenges become more profound. Thus, better strategies have …
On The Inertia Conjecture And Its Generalizations., Soumyadip Das Dr.
On The Inertia Conjecture And Its Generalizations., Soumyadip Das Dr.
Doctoral Theses
This thesis concerns problems related to the ramification behaviour of the branched Galois covers of smooth projective connected curves defined over an algebraically closed field of positive characteristic. Our first main problem is the Inertia Conjecture proposed by Abhyankar in 2001. We will show several new evidence for this conjecture. We also formulate a certain generalization of it which is our second problem, and we provide evidence for it. We give a brief overview of these problems in this introduction and reserve the details for Chapter 4.Let k be an algebraically closed field, and U be a smooth connected affine …
Commuting Isometries And Invariant Subspaces In Several Variables., Sankar T. R. Dr.
Commuting Isometries And Invariant Subspaces In Several Variables., Sankar T. R. Dr.
Doctoral Theses
A very general and fundamental problem in the theory of bounded linear operators on Hilbert spaces is to find invariants and representations of commuting families of isometries.In the case of single isometries this question has a complete and explicit answer: If V is an isometry on a Hilbert space â„‹, then there exists a Hilbert space Hu and a unitary operator U on â„‹u such that V on â„‹u and[ S ⊗ IW 0 0 U] ∈ B((l 2 (ℤ+) ⊗ W) ⊕ â„‹u),are unitarily equivalent, whereW = ker V∗ ,is the wandering subspace for V and S is the …
Lecture 09: Hierarchically Low Rank And Kronecker Methods, Rio Yokota
Lecture 09: Hierarchically Low Rank And Kronecker Methods, Rio Yokota
Mathematical Sciences Spring Lecture Series
Exploiting structures of matrices goes beyond identifying their non-zero patterns. In many cases, dense full-rank matrices have low-rank submatrices that can be exploited to construct fast approximate algorithms. In other cases, dense matrices can be decomposed into Kronecker factors that are much smaller than the original matrix. Sparsity is a consequence of the connectivity of the underlying geometry (mesh, graph, interaction list, etc.), whereas the rank-deficiency of submatrices is closely related to the distance within this underlying geometry. For high dimensional geometry encountered in data science applications, the curse of dimensionality poses a challenge for rank-structured approaches. On the other …
Functional Singular Spectrum Analysis: Nonparametric Decomposition And Forecasting Approaches For Functional Time Series, Jordan Christopher Trinka
Functional Singular Spectrum Analysis: Nonparametric Decomposition And Forecasting Approaches For Functional Time Series, Jordan Christopher Trinka
Dissertations (1934 -)
In this dissertation, we develop nonparametric decomposition methods and the subsequent forecasting techniques for functional, time-dependent data known as functional time series (FTS). We use ideas from functional data analysis (FDA) and singular spectrum analysis (SSA) to introduce the nonparametric decomposition method known as functional SSA (FSSA) and its associated forecasting techniques. We also extend these developed methodologies into multivariate FSSA (MFSSA) over different dimensional domains and its subsequent forecasting routines so that we may perform nonparametric decomposition and prediction of multivariate FTS (MFTS). The FSSA algorithm may be viewed as a signal extraction technique and we find that the …
Quantum Symmetries In Noncommutative Geometry., Suvrajit Bhattacharjee Dr.
Quantum Symmetries In Noncommutative Geometry., Suvrajit Bhattacharjee Dr.
Doctoral Theses
No abstract provided.
On Hamilton Cycle Decompositions Of Complete Multipartite Graphs Which Are Both Cyclic And Symmetric, Fatima A. Akinola
On Hamilton Cycle Decompositions Of Complete Multipartite Graphs Which Are Both Cyclic And Symmetric, Fatima A. Akinola
Theses, Dissertations and Capstones
Let G be a graph with v vertices. A Hamilton cycle of a graph is a collection of edges which create a cycle using every vertex. A Hamilton cycle decomposition is cyclic if the set of cycle is invariant under a full length permutation of the vertex set. We say a decomposition is symmetric if all the cycles are invariant under an appropriate power of the full length permutation. Such decompositions are known to exist for complete graphs and families of other graphs. In this work, we show the existence of cyclic n-symmetric Hamilton cycle decompositions of a family …
Decompositions Of Complete Symmetric Directed Graphs Into The Oriented Heptagons, Uğur Odabaşi
Decompositions Of Complete Symmetric Directed Graphs Into The Oriented Heptagons, Uğur Odabaşi
Turkish Journal of Mathematics
The complete symmetric directed graph of order $v$, denoted by $K_{v}$, is the directed graph on $v$~vertices that contains both arcs $(x,y)$ and $(y,x)$ for each pair of distinct vertices $x$ and~$y$. For a given directed graph $D$, the set of all $v$ for which $K_{v}$ admits a $D$-decomposition is called the spectrum of~$D$-decomposition. There are 10 nonisomorphic orientations of a $7$-cycle (heptagon). In this paper, we completely settled the spectrum problem for each of the oriented heptagons.
Gender Difference In Indian Consumption Expenditure., Mannu Dwivedi Dr.
Gender Difference In Indian Consumption Expenditure., Mannu Dwivedi Dr.
Doctoral Theses
The goal of any development policy is to increase the living standard of the people in the society. In any developing country, the efficiency of such policy depends on how families reallocate the resources among themselves. If the distribution is even within the family then only it can be said that the policy was fruitful. Therefore, a family is an important part of any policy and the allocation within the family should be just. But, the distribution of the resources among the family members are not always equal. Inequality always exists! Discrimination against girls or women persists in approximately all …
Regular Round Matroids, Svetlana Borissova
Regular Round Matroids, Svetlana Borissova
Electronic Theses, Projects, and Dissertations
A matroid M is a finite set E, called the ground set of M, together with a notion of what it means for subsets of E to be independent. Some matroids, called regular matroids, have the property that all elements in their ground set can be represented by vectors over any field. A matroid is called round if its dual has no two disjoint minimal dependent sets. Roundness is an important property that was very useful in the recent proof of Rota's conjecture, which remained an unsolved problem for 40 years in matroid theory. In this thesis, we …
Essays On Inequality, Polarization And Contests., Bhargav Bhattacharya Dr.
Essays On Inequality, Polarization And Contests., Bhargav Bhattacharya Dr.
Doctoral Theses
No abstract provided.
Complete And Partial Ordering Approaches In The Context Of Poverty Ordering And On The Impacts Of Growth And Inequality On Poverty., Sandip Sarkar Dr.
Complete And Partial Ordering Approaches In The Context Of Poverty Ordering And On The Impacts Of Growth And Inequality On Poverty., Sandip Sarkar Dr.
Doctoral Theses
No abstract provided.
Some Conjugacy Problems In Algebraic Groups., Anirban Bose Dr.
Some Conjugacy Problems In Algebraic Groups., Anirban Bose Dr.
Doctoral Theses
In this thesis we address two problems related to the study of algebraic groups and Lie groups. The first one deals with computation of an invariant called the genus number of a connected reductive algebraic group over an algebraically closed field and that of a compact connected Lie group. The second problem is about characterisation of real elements in exceptional groups of type F4 defined over an arbitrary field. Let G be a connected reductive algebraic group over an algebraically closed field or a compact connected Lie group. Let ZG(x) denote the centralizer of x ∈ G. Define the genus …
P_4-Decomposability In Regular Graphs And Multigraphs, David Joshua Mendell
P_4-Decomposability In Regular Graphs And Multigraphs, David Joshua Mendell
Theses and Dissertations
The main objective of this thesis is to review and expand the study of graph decomposability. An H-decomposition of a graph G=(V,E) is a partitioning of the edge set, $E$, into edge-disjoint isomorphic copies of a subgraph H. In particular we focus on the decompositions of graphs into paths. We prove that a 2,4 mutligraph with maximum multiplicity 2 admits a C_2,C_3-free Euler tour (and thus, a decomposition into paths of length 3 if it has size a multiple of 3) if and only if it avoids a set of 15 forbidden structures. We also prove that …
On Eulerian Irregularity And Decompositions In Graphs, Eric Andrews
On Eulerian Irregularity And Decompositions In Graphs, Eric Andrews
Dissertations
Abstract attached as separate file.
Packings And Coverings Of Complete Graphs With A Hole With The 4-Cycle With A Pendant Edge, Yan Xia
Packings And Coverings Of Complete Graphs With A Hole With The 4-Cycle With A Pendant Edge, Yan Xia
Electronic Theses and Dissertations
In this thesis, we consider packings and coverings of various complete graphs with the 4-cycle with a pendant edge. We consider both restricted and unrestricted coverings. Necessary and sufficient conditions are given for such structures for (1) complete graphs Kv, (2) complete bipartite graphs Km,n, and (3) complete graphs with a hole K(v,w).
Geometric Invariants For A Class Of Semi-Fredholm Hilbert Modules., Shibananda Biswas Dr.
Geometric Invariants For A Class Of Semi-Fredholm Hilbert Modules., Shibananda Biswas Dr.
Doctoral Theses
One of the basic problem in the study of a Hilbert module H over the ring of polynomials C[z] := C[z1, . . . , zm] is to find unitary invariants (cf. [15,7]) for H. It is not always possible to find invariants that are complete and yet easy to compute. There are very few instances where a set of complete invariants have been identified. Examples are Hilbert modules over continuous functions (spectral theory of normal operator), contractive modules over the disc algebra (model theory for contractive operator) and Hilbert modules in the class Bn for a bounded domain C …
Selected Aspects Of Performance Of Indian Industries: An Empirical Investigation., Anup Kumar Bhandari Dr.
Selected Aspects Of Performance Of Indian Industries: An Empirical Investigation., Anup Kumar Bhandari Dr.
Doctoral Theses
At the time of India’s independence the need of the hour was to develop the economy at a fast pace so as to achieve a reasonable standard of living for the masses within a short period of time. India’s first Industrial Policy Resolution was adopted in 1948 which put emphasis on the expansion of production of both agricultural and industrial goods to satisfy the basic needs of the masses, a large proportion of whom lived well below a subsistence level of living. Hence, emphasis was given on agricultural expansion in the First Five Year Plan and on building up the …
An Exponentially Convergent Nonpolynomial Finite Element Method For Time-Harmonic Scattering From Polygons, A. H. Barnett, T. Betcke
An Exponentially Convergent Nonpolynomial Finite Element Method For Time-Harmonic Scattering From Polygons, A. H. Barnett, T. Betcke
Dartmouth Scholarship
In recent years nonpolynomial finite element methods have received increasing attention for the efficient solution of wave problems. As with their close cousin the method of particular solutions, high efficiency comes from using solutions to the Helmholtz equation as basis functions. We present and analyze such a method for the scattering of two-dimensional scalar waves from a polygonal domain that achieves exponential convergence purely by increasing the number of basis functions in each element. Key ingredients are the use of basis functions that capture the singularities at corners and the representation of the scattered field towards infinity by a combination …
Intersection Numbers, Embedded Spheres And Geosphere Laminations For Free Groups., Suhas Pandit Dr.
Intersection Numbers, Embedded Spheres And Geosphere Laminations For Free Groups., Suhas Pandit Dr.
Doctoral Theses
Topological and geometric methods have played a major role in the study of infinite groups since the time of Poincar´e and Klein, with the work of Nielsen, Dehn, Stallings and Gromov showing particularly deep connections with the topology of surfaces and three-manifolds. This is in part because a surface or a 3-manifold is essentially determined by its fundamental group, and has a geometric structure due to the Poincar´e-K¨obe-Klein uniformisation theorem for surfaces and Thurston’s geometrisation conjecture, which is now a theorem of Perelman, for 3-manifolds.A particularly fruitful instance of such an interplay is the relation between intersection numbers of simple …
Normal Surfaces And Heegaard Splittings Of 3-Manifolds., Tejas Kalelkar Dr.
Normal Surfaces And Heegaard Splittings Of 3-Manifolds., Tejas Kalelkar Dr.
Doctoral Theses
This thesis deals with various questions regarding normal surfaces and Heegaard splittings of 3-manifolds.Chapter 1The first chapter is divided into two parts. In the first, we give an outline of normal surface theory and mention some of its important applications. The second part gives an overview of the theory of Heegaard splitting surfaces and a few of its applications. None of the material covered in this chapter is original and it is meant solely as an exposition of known results.Chapter 2In this chapter, we give a lower bound on the Euler characteristic of a normal surface, a topological invariant, in …
Isomorphism Of Schwartz Spaces Under Fourier Transform., Joydip Jana Dr.
Isomorphism Of Schwartz Spaces Under Fourier Transform., Joydip Jana Dr.
Doctoral Theses
Classical Fourier analysis derives much of its power from the fact that there are three function spaces whose images under the Fourier transform can be exactly determined. They are the Schwartz space, the L2 space and the space of all C ∞ functions of compact support. The determination of the image is obtained from the definition in the case of Schwartz space, through the Plancherel theorem for the L 2space and through the Paley-Wiener theorem for the other space.In harmonic analysis of semisimple Lie groups, function spaces on various restricted set-ups are of interest. Among the multitude of these spaces …
Homogeneous Operators In The Cowen-Douglas Class., Subrata Shyam Roy Dr.
Homogeneous Operators In The Cowen-Douglas Class., Subrata Shyam Roy Dr.
Doctoral Theses
Although, we have used techniques developed in the paper of Cowen-Douglas [18, 20], a systematic account of Hilbert space operators using a variety of tools from several different areas of mathematics is given in the book [26]. This book provides, what the authors call, a sheaf model for a large class of commuting Hilbert space operators. It is likely that these ideas will play a significant role in the future development of the topics discussed here.
Spectral Analysis And Synthesis For Radial Sections Of Homogenous Vector Bundles On Certain Noncompath Riemannian Symmetric Spaces., Sanjoy Pusti Dr.
Spectral Analysis And Synthesis For Radial Sections Of Homogenous Vector Bundles On Certain Noncompath Riemannian Symmetric Spaces., Sanjoy Pusti Dr.
Doctoral Theses
We consider two classical theorems of real analysis which deals with translation invariant subspaces of integrable and smooth functions on R respectively. The first one is a theorem of Norbert Wiener [63] which states that if the Fourier transform of a function f ∈ L 1 (R) has no real zeros then the finite linear combinations of translations f(x − a) of f with complex coefficients form a dense subspace in L 1 (R), equivalently, span{g ∗ f | g ∈ L 1 (R)} is dense in L 1 (R). This theorem is well known as the Wiener-Tauberian Theorem (WTT). …
Decompositions, Packings, And Coverings Of Complete Directed Gaphs With A 3-Circuit And A Pendent Arc., Chrys Gwellem
Decompositions, Packings, And Coverings Of Complete Directed Gaphs With A 3-Circuit And A Pendent Arc., Chrys Gwellem
Electronic Theses and Dissertations
In the study of Graph theory, there are eight orientations of the complete graph on three vertices with a pendant edge, K3 ∪ {e}. Two of these are the 3-circuit with a pendant arc and the other six are transitive triples with a pendant arc. Necessary and sufficient conditions are given for decompositions, packings, and coverings of the complete digraph with the two 3-circuit with a pendant arc orientations.
Some Geometrical Aspects Of The Cone Linear Complementarity Problem., Madhur Malik Dr.
Some Geometrical Aspects Of The Cone Linear Complementarity Problem., Madhur Malik Dr.
Doctoral Theses
Cone Linear Complementarity ProblemLet V be a finite dimensional real inner product space and K be a closed convex cone in V. Given a linear transformation L : V → V and a vector q ∈ V the cone linear complementarity problem or linear complementarity problem over K, denoted as LCP(K, L, q), is to find a vector x ∈ K such thatL(x) + q ∈ K+ and hx, L(x) + qi = 0,where h., .i denotes an inner product on V and K is the dual cone of K defined as:K∗ := {y ∈ V : hx, yi ≥ …
Uniqueness Of Coprimary Decompositions, M. Maani-Shirazi, P. F. Smith
Uniqueness Of Coprimary Decompositions, M. Maani-Shirazi, P. F. Smith
Turkish Journal of Mathematics
Uniqueness properties of coprimary decompositions of modules over non-commutative rings are presented.
On Textured Image Analysis Using Wavelets., Mausumi Acharyya Dr.
On Textured Image Analysis Using Wavelets., Mausumi Acharyya Dr.
Doctoral Theses
In image processing and computer vision research, we aim to derive better tools that give us different perspectives on the same image, allowing us to understand not only its content, but also its meaning and significance. Image processing can not compete with the human eye in terms of accuracy but it can outperform the latter easily on observational consistency, and ability to carry out detailed mathematical estimations. With time, image processing research has broadened from the basic pixel-based low- level operations to high-level analysis, that now includes the use of artificially intelligent techniques for image interpretation and understanding. These new …
Uniqueness Of Primary Decompositions, Patrick F. Smith
Uniqueness Of Primary Decompositions, Patrick F. Smith
Turkish Journal of Mathematics
Uniqueness properties of primary decompositions in modules over non-commutative rings are presented.