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Articles 20941 - 20970 of 27475
Full-Text Articles in Physical Sciences and Mathematics
Characterizations In Domination Theory, Andrew Robert Plummer
Characterizations In Domination Theory, Andrew Robert Plummer
Mathematics Theses
Let G = (V,E) be a graph. A set R is a restrained dominating set (total restrained dominating set, resp.) if every vertex in V − R (V) is adjacent to a vertex in R and (every vertex in V −R) to a vertex in V −R. The restrained domination number of G (total restrained domination number of G), denoted by gamma_r(G) (gamma_tr(G)), is the smallest cardinality of a restrained dominating set (total restrained dominating set) of G. If T is a tree of order n, then gamma_r(T) is greater than or equal to (n+2)/3. We show that gamma_tr(T) is …
Spectrally Arbitrary Tree Sign Pattern Matrices, Krishna Kaphle
Spectrally Arbitrary Tree Sign Pattern Matrices, Krishna Kaphle
Mathematics Theses
A sign pattern (matrix) is a matrix whose entries are from the set {+,–, 0}. A sign pattern matrix A is a spectrally arbitrary pattern if for every monic real polynomial p(x) of degree n there exists a real matrix B whose entries agree in sign with A such that the characteristic polynomial of B is p(x). All 3 × 3 SAP's, as well as tree sign patterns with star graphs that are SAP's, have already been characterized. We investigate tridiagonal sign patterns of order 4. All irreducible tridiagonal SAP's are identified. Necessary and sufficient conditions for an irreducible tridiagonal …
Generalized Differentiation Of Parameter-Dependent Sets And Mappings, Boris S. Mordukhovich, Bingwu Wang
Generalized Differentiation Of Parameter-Dependent Sets And Mappings, Boris S. Mordukhovich, Bingwu Wang
Mathematics Research Reports
The paper concerns new aspects of generalized differentiation theory that plays a crucial role in many areas of modern variational analysis, optimization, and their applications. In contrast to the majority of previous developments, we focus here on generalized differentiation of parameter-dependent objects (sets, set-valued mappings, and nonsmooth functions), which naturally appear, e.g., in parametric optimization and related topics. The basic generalized differential constructions needed in this case are different for those known in parameter-independent settings, while they still enjoy comprehensive calculus rules developed in this paper.
Optimal Control Of Nonconvex Differential Inclusions, Boris S. Mordukhovich
Optimal Control Of Nonconvex Differential Inclusions, Boris S. Mordukhovich
Mathematics Research Reports
The paper concerns new aspects of generalized differentiation theory that plays a crucial role in many areas of modern variational analysis, optimization, and their applications. In contrast to the majority of previous developments, we focus here on generalized differentiation of parameter-dependent objects (sets, set-valued mappings, and nonsmooth functions), which naturally appear, e.g., in parametric optimization and related topics. The basic generalized differential constructions needed in this case are different for those known in parameter-independent settings, while they still enjoy comprehensive calculus rules developed in this paper.
Toral Algebraic Sets And Function Theory On Polydisks, Jim Agler, John E. Mccarthy, Mark Stankus
Toral Algebraic Sets And Function Theory On Polydisks, Jim Agler, John E. Mccarthy, Mark Stankus
Mathematics
A toral algebraic set A is an algebraic set in Cn whose intersection with Tn is sufficiently large to determine the holomorphic functions on A. We develop the theory of these sets, and give a number of applications to function theory in several variables and operator theoretic model theory. In particular, we show that the uniqueness set for an extremal Pick problem on the bidisk is a toral algebraic set, that rational inner functions have zero sets whose irreducible components are not toral, and that the model theory for a commuting pair of contractions with finite defect …
Epi-Convergent Discretization Of The Generalizaed Bolza Problem In Dynamic Optimization, Boris S. Mordukhovich, Teemu Pennanen
Epi-Convergent Discretization Of The Generalizaed Bolza Problem In Dynamic Optimization, Boris S. Mordukhovich, Teemu Pennanen
Mathematics Research Reports
The paper is devoted to well-posed discrete approximations of the so-called generalized Bolza problem of minimizing variational functionals defined via extended-real-valued functions. This problem covers more conventional Bolza-type problems in the calculus of variations and optimal control of differential inclusions as well of parameterized differential equations. Our main goal is find efficient conditions ensuring an appropriate epi-convergence of discrete approximations, which plays a significant role in both the qualitative theory and numerical algorithms of optimization and optimal control. The paper seems to be the first attempt to study epi-convergent discretizations of the generalized Bolza problem; it establishes several rather general …
Efficient Domination In Knights Graphs, Anne Sinko, Peter J. Slater
Efficient Domination In Knights Graphs, Anne Sinko, Peter J. Slater
Mathematics Faculty Publications
The influence of a vertex set S ⊆V(G) is I(S) = Σv∈S(1 + deg(v)) = Σv∈S |N[v]|, which is the total amount of domination done by the vertices in S. The efficient domination number F(G) of a graph G is equal to the maximum influence of a packing, that is, F(G) is the maximum number of vertices one can dominate under the restriction that no vertex gets dominated more than once.
In …
Wavelet-Based Functional Mixed Models To Characterize Population Heterogeneity In Accelerometer Profiles: A Case Study. , Jeffrey S. Morris, Cassandra Arroyo, Brent A. Coull, Louise M. Ryan, Steven L. Gortmaker
Wavelet-Based Functional Mixed Models To Characterize Population Heterogeneity In Accelerometer Profiles: A Case Study. , Jeffrey S. Morris, Cassandra Arroyo, Brent A. Coull, Louise M. Ryan, Steven L. Gortmaker
Jeffrey S. Morris
We present a case study illustrating the challenges of analyzing accelerometer data taken from a sample of children participating in an intervention study designed to increase physical activity. An accelerometer is a small device worn on the hip that records the minute-by-minute activity levels of the child throughout the day for each day it is worn. The resulting data are irregular functions characterized by many peaks representing short bursts of intense activity. We model these data using the wavelet-based functional mixed model. This approach incorporates multiple fixed effects and random effect functions of arbitrary form, the estimates of which are …
Some Issues In The Art Image Database Systems, Peter L. Stanchev, David Green Jr., Boyan N. Dimitrov
Some Issues In The Art Image Database Systems, Peter L. Stanchev, David Green Jr., Boyan N. Dimitrov
Mathematics Publications
In this paper we illustrate several aspects of art databases, such as: the spread of the multimedia art images; the main characteristics of art images; main art images search models; unique characteristics for art image retrieval; the importance of the sensory and semantic gaps. In addition, we present several interesting features of an art image database, such as: image indexing; feature extraction; analysis on various levels of precision; style classification. We stress color features and their base, painting analysis and painting styles. We study also which MPEG-7 descriptors are best for fine painting images retrieval. An experimental system is developed …
Asymptotic Sign-Solvability, Multiple Objective Linear Programming, And The Nonsubstitution Theorem, L Clayton, R Herring, Allen G. Holder, J Holzer, C Nightingale, T Stohs
Asymptotic Sign-Solvability, Multiple Objective Linear Programming, And The Nonsubstitution Theorem, L Clayton, R Herring, Allen G. Holder, J Holzer, C Nightingale, T Stohs
Mathematics Faculty Research
In this paper we investigate the asymptotic stability of dynamic, multiple-objective linear programs. In particular, we show that a generalization of the optimal partition stabilizes for a large class of data functions. This result is based on a new theorem about asymptotic sign-solvable systems. The stability properties of the generalized optimal partition are used to extend a dynamic version of the Nonsubstitution Theorem.
Partitioning Multiple Objective Optimal Solutions With Applications In Radiotherapy Design, Allen G. Holder
Partitioning Multiple Objective Optimal Solutions With Applications In Radiotherapy Design, Allen G. Holder
Mathematics Faculty Research
The optimal partition for linear programming is induced by any strictly complementary solution, and this partition is important because it characterizes the optimal set. However, constructing a strictly complementary solution in the presence of degeneracy was not practical until interior point algorithms became viable alternatives to the simplex algorithm. We develop analogs of the optimal partition for linear programming in the case of multiple objectives and show that these new partitions provide insight into the optimal set (both pareto optimality and lexicographic ordering are considered). Techniques to produce these optimal partitions are provided, and examples from the design of radiotherapy …
Explicit Symmetries Of Strict Feedforward Control Systems, Issa Amadou Tall, Witold Respondek
Explicit Symmetries Of Strict Feedforward Control Systems, Issa Amadou Tall, Witold Respondek
Miscellaneous (presentations, translations, interviews, etc)
We show that any symmetry of a smooth strict feedforward system is conjugated to a scaling translation and any 1-parameter family of symmetries to a family of scaling translations along the first variable. We compute explicitly those symmetries by finding the conjugating diffeomorphism. We deduce, in accordance with our previous work, that a smooth system is feedback equivalent to a strict feedforward form if and only if it gives rise to a sequence of systems, such that each element of the sequence, firstly, possesses an infinitesimal symmetry whose flow is conjugated to a 1- parameter families of scaling translations and, …
Teaching Time Savers: Some Advice On Giving Advice, Michael E. Orrison Jr.
Teaching Time Savers: Some Advice On Giving Advice, Michael E. Orrison Jr.
All HMC Faculty Publications and Research
There are always a lot of questions that need to be answered at the beginning of a course. When are office hours? What are the grading policies? How many exams will there be? Will late homework be accepted? We have all seen the answers to these sorts of questions form the bulk of a standard course syllabus, and most of us feel an obligation (and rightly so) to provide such information.
Ahlfors Type Estimates For Perimeter Measures In Carnot-Carathéodory Spaces, Luca Capogna, Nicola Garofalo
Ahlfors Type Estimates For Perimeter Measures In Carnot-Carathéodory Spaces, Luca Capogna, Nicola Garofalo
Mathematics Sciences: Faculty Publications
We study the relationship between the geometry of hypersurfaces in a Carnot-Carathéodory (CC) space and the Ahlfors regularity of the corresponding perimeter measure. To this end we establish comparison theorems for perimeter estimates between an hypersurface and its tangent space, and between a CC geometry and its "tangent" Carnot group structure.
Simple Braids For Surface Homeomorphisms, Kamlesh Parwani
Simple Braids For Surface Homeomorphisms, Kamlesh Parwani
Faculty Research and Creative Activity
Let S be a compact, oriented surface with negative Euler characteristic and f:S→S be a homeomorphism isotopic to the identity. If there exists a periodic orbit with a non-zero rotation vector (p→,q), then there exists a simple braid with the same rotation vector.
Simple Braids For Surface Homeomorphisms, Kamlesh Parwani
Simple Braids For Surface Homeomorphisms, Kamlesh Parwani
Faculty Research and Creative Activity
Let S be a compact, oriented surface with negative Euler characteristic and f:S→S be a homeomorphism isotopic to the identity. If there exists a periodic orbit with a non-zero rotation vector (p→,q), then there exists a simple braid with the same rotation vector.
Linear Conditions Imposed On Flag Varieties, Julianna S. Tymoczko
Linear Conditions Imposed On Flag Varieties, Julianna S. Tymoczko
Mathematics Sciences: Faculty Publications
We study subvarieties of the flag variety called Hessenberg varieties, defined by certain linear conditions. These subvarieties arise naturally in applications including geometric representation theory, number theory, and numerical analysis. We describe completely the homology of Hessenberg varieties over GLn(ℂ) and show that they have no odd-dimensional homology. We provide an explicit geometric construction which partitions each Hessenberg variety into pieces homeomorphic to affine space. We characterize these affine pieces by fillings of Young tableaux and show that the dimension of the affine piece can be computed by combinatorial rules generalizing the Eulerian numbers. We give an equivalent formulation of …
Conformality And Q-Harmonicity In Carnot Groups, Luca Capogna, Michael Cowling
Conformality And Q-Harmonicity In Carnot Groups, Luca Capogna, Michael Cowling
Mathematics Sciences: Faculty Publications
We show that if f is a 1-quasiconformal map defined on an open subset of a Carnot group G, then composition with f preserves Q-harmonic functions. We combine this with a regularity theorem for Q-harmonic functions and an algebraic regularity theorem for maps between Carnot groups to show that f is smooth. We give some applications to the study of rigidity.
Local Energy Decay For Solutions Of Multi-Dimensional Isotropic Symmetric Hyperbolic Systems, Thomas C. Sideris, Becca Thomases
Local Energy Decay For Solutions Of Multi-Dimensional Isotropic Symmetric Hyperbolic Systems, Thomas C. Sideris, Becca Thomases
Mathematics Sciences: Faculty Publications
The local decay of energy is established for solutions to certain linear, multidimensional symmetric hyperbolic systems, with constraints. The key assumptions are isotropy and nondegeneracy of the associated symbols. Examples are given, including Maxwell's equations and linearized elasticity. Such estimates prove useful in treating nonlinear perturbations.
Solutions For The Cell Cycle In Cell Lines Derived From Human Tumors, B. Zubik-Kowal
Solutions For The Cell Cycle In Cell Lines Derived From Human Tumors, B. Zubik-Kowal
Mathematics Faculty Publications and Presentations
The goal of the paper is to compute efficiently solutions for model equations that have the potential to describe the growth of human tumor cells and their responses to radiotherapy or chemotherapy. The mathematical model involves four unknown functions of two independent variables: the time variable t and dimensionless relative DNA content x. The unknown functions can be thought of as the number density of cells and are solutions of a system of four partial differential equations. We construct solutions of the system, which allow us to observe the number density of cells for different t and x values. …
Les For Wing Tip Vortex Around An Airfoil, Jiangang Cai
Les For Wing Tip Vortex Around An Airfoil, Jiangang Cai
Mathematics Dissertations
The wing tip vortex is very important because of its effects on the noise generation, blade/vortex interactions on helicopter blades, propeller cavitations on ships, and other fields. The objective of this work is to use the numerical simulation with high order accuracy and high resolution to investigate the formation and the near field evolution of a wing tip vortex at high Reynolds number. The computational domain includes a rectangular half-wing with a NACA 0012 airfoil section, a rounded wing tip and the surrounding boundaries. The wing has an aspect ratio of 0.75. The angle of attack is 10 degrees. The …
Simple Braids For Surface Homeomorphisms, Kamlesh Parwani
Simple Braids For Surface Homeomorphisms, Kamlesh Parwani
Kamlesh Parwani
Let S be a compact, oriented surface with negative Euler characteristic and f:S→S be a homeomorphism isotopic to the identity. If there exists a periodic orbit with a non-zero rotation vector (p→,q), then there exists a simple braid with the same rotation vector.
The Relationship Between The Minimal Rank Of A Tree And The Rank-Spreads Of The Vertices And Edges, John Henry Sinkovic
The Relationship Between The Minimal Rank Of A Tree And The Rank-Spreads Of The Vertices And Edges, John Henry Sinkovic
Theses and Dissertations
Let F be a field, G = (V,E) be an undirected graph on n vertices, and let S(F,G) be the set of all symmetric n × n matrices whose nonzero off-diagonal entries occur in exactly the positions corresponding to the edges of G. Let mr(F,G)be the minimum rank over all matrices in S(F,G). We give a field independent proof of a well-known result that for a tree the sum of its path cover number and minimal rank is equal to the number of vertices in the tree. The rank-spread of a vertex v of G is the difference between the …
Variational And Partial Differential Equation Models For Color Image Denoising And Their Numerical Approximations Using Finite Element Methods, Miun Yoon
Masters Theses
Image processing has been a traditional engineering field, which has a broad range of applications in science, engineering and industry. Not long ago, statistical and ad hoc methods had been main tools for studying and analyzing image processing problems. In the past decade, a new approach based on variational and partial differential equation (PDE) methods has emerged as a more powerful approach. Compared with old approaches, variational and PDE methods have remarkable advantages in both theory and computation. It allows to directly handle and process visually important geometric features such as gradients, tangents and curvatures, and to model visually meaningful …
Overinterpolation, Dan Coman, Evgeny A. Poletsky
Overinterpolation, Dan Coman, Evgeny A. Poletsky
Mathematics - All Scholarship
In this paper we study the consequences of overinterpolation, i.e., the situation when a function can be interpolated by polynomial, or rational, or algebraic functions in more points that normally expected. We show that in many cases such a function has specific forms.
Properties Of Some Matrix Classes In Linear Complementarity Theory., Arup Kumar Das Dr.
Properties Of Some Matrix Classes In Linear Complementarity Theory., Arup Kumar Das Dr.
Doctoral Theses
The linear complementarity problem is a fundamental problem that arises in optimization, game theory, economics, and engineering. It can be stated as follows:Given a square matrix A of order n with real entries and an n dimensional vector q, find n dimensional vectors w and z satisfying w − Az = q, w ≥ 0, z ≥ 0 (1.1.1) w t z = 0. (1.1.2)This problem is denoted as LCP(q, A). The name comes from the condition (1.1.2), the complementarity condition which requires that at least one variable in the pair (wj , zj ) should be equal to 0 …
A New Integrable Equation With Cuspons And W/M-Shape-Peaks Solitons, Zhijun Qiao
A New Integrable Equation With Cuspons And W/M-Shape-Peaks Solitons, Zhijun Qiao
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
In this paper, we propose a new completely integrable wave equation: mt+mx u2 −ux 2 +2m2ux=0, m=u−uxx. The equation is derived from the two dimensional Euler equation and is proven to have Lax pair and bi-Hamiltonian structures. This equation possesses new cusp solitons—cuspons, instead of regular peakons ce− −ct with speed c. Through investigating the equation, we develop a new kind of soliton solutions—“W/M”-shape-peaks solitons. There exist no smooth solitons for this integrable water wave equation.
Changepoint Analysis Of Hiv Marker Responses, Joy Michelle Rogers
Changepoint Analysis Of Hiv Marker Responses, Joy Michelle Rogers
Mathematics Theses
We will propose a random changepoint model for the analysis of longitudinal CD4 and CD8 T-cell counts, as well as viral RNA loads, for HIV infected subjects following highly active antiretroviral treatment. The data was taken from two studies, one of the Aids Clinical Group Trial 398 and one performed by the Terry Beirn Community Programs for Clinical Research on AIDS. Models were created with the changepoint following both exponential and truncated normal distributions. The estimation of the changepoints was performed in a Bayesian analysis, with implementation in the WinBUGS software using Markov Chain Monte Carlo methods. For model selection, …
Criticality For The Gehring Link Problem, Jason Cantarella, Joseph H.G. Fu, Robert Kusner, John M. Sullivan, Nancy C. Wrinkle
Criticality For The Gehring Link Problem, Jason Cantarella, Joseph H.G. Fu, Robert Kusner, John M. Sullivan, Nancy C. Wrinkle
Robert Kusner
In 1974, Gehring posed the problem of minimizing the length of two linked curves separated by unit distance. This constraint can be viewed as a measure of thickness for links, and the ratio of length over thickness as the ropelength. In this paper we refine Gehring’s problem to deal with links in a fixed link-homotopy class: we prove ropelength minimizers exist and introduce a theory of ropelength criticality.
Our balance criterion is a set of necessary and sufficient conditions for criticality, based on a strengthened, infinite-dimensional version of the Kuhn–Tucker theorem. We use this to prove that every critical link …
Balanced Biorthogonal Scaling Vectors Using Fractal Function Macroelements On [0,1], Bruce Kessler
Balanced Biorthogonal Scaling Vectors Using Fractal Function Macroelements On [0,1], Bruce Kessler
Mathematics Faculty Publications
Geronimo, Hardin, et al have previously constructed orthogonal and biorthogonal scaling vectors by extending a spline scaling vector with functions supported on $[0,1]$. Many of these constructions occurred before the concept of balanced scaling vectors was introduced. This paper will show that adding functions on $[0,1]$ is insufficient for extending spline scaling vectors to scaling vectors that are both orthogonal and balanced. We are able, however, to use this technique to extend spline scaling vectors to balanced, biorthogonal scaling vectors, and we provide two large classes of this type of scaling vector, with approximation order two and three, respectively, with …