The Bernstein Problem For Embedded Surfaces In The Heisenberg Group H,
2010
Purdue University
The Bernstein Problem For Embedded Surfaces In The Heisenberg Group H, Donatella Danielli, Nicola Garofalo, Duy-Minh Nhieu, Scott D. Pauls
Dartmouth Scholarship
In the paper [13] we proved that the only stable C 2 minimal surfaces in the first Heisenberg group H 1 which are graphs over some plane and have empty characteristic locus must be vertical planes. This result represents a sub-Riemannian version of the celebrated theorem of Bernstein. In this paper we extend the result in [13] to C 2 complete em-bedded minimal surfaces in H 1 with empty characteristic locus. We prove that every such a surface without boundary must be a vertical plane. This result represents a sub-Riemannian coun-terpart of the classical theorems of Fischer-Colbrie and Schoen, [16], …
On The Convergence Of An Implicit Iterative Process For Generalized Asymptotically Quasi-Nonexpansive Mappings,
2010
Florida Institute of Technology
On The Convergence Of An Implicit Iterative Process For Generalized Asymptotically Quasi-Nonexpansive Mappings, Ravi P. Agarwal, Xiaolong Qin, Shinmin Kang
Mathematics and System Engineering Faculty Publications
The purpose of this paper is to introduce and consider a general implicit iterative process which includes Schu's explicit iterative processes and Sun's implicit iterative processes as special cases for a finite family of generalized asymptotically quasi-nonexpansive mappings. Strong convergence of the purposed iterative process is obtained in the framework of real Banach spaces.
Quantification Of Artistic Style Through Sparse Coding Analysis In The Drawings Of Pieter Bruegel The Elder,
2010
Dartmouth College
Quantification Of Artistic Style Through Sparse Coding Analysis In The Drawings Of Pieter Bruegel The Elder, James M. Hughes, Daniel J. Graham, Daniel N. Rockmore
Dartmouth Scholarship
Recently, statistical techniques have been used to assist art historians in the analysis of works of art. We present a novel technique for the quantification of artistic style that utilizes a sparse coding model. Originally developed in vision research, sparse coding models can be trained to represent any image space by maximizing the kurtosis of a representation of an arbitrarily selected image from that space. We apply such an analysis to successfully distinguish a set of authentic drawings by Pieter Bruegel the Elder from another set of well-known Bruegel imitations. We show that our approach, which involves a direct comparison …
Harmonic Mapping Problem And Affine Capacity,
2010
Syracuse University and University of Helsinki
Harmonic Mapping Problem And Affine Capacity, Tadeusz Iwaniec, Leonid V. Kovalev, Jani Onninen
Mathematics - All Scholarship
The Harmonic Mapping Problem asks when there exists a harmonic homeomorphism between two given domains. It arises in the theory of minimal surfaces and in calculus of variations, specifically in hyperelasticity theory. We investigate this problem for doubly connected domains in the plane, where it already presents considerable challenge and leads to several interesting open questions.
Cryptography: A History In Mathematics, An Application In The Classroom,
2010
Bemidji State University
Cryptography: A History In Mathematics, An Application In The Classroom, Brian Olmanson
Honors Capstones
Capstone submitted as a graduation requirement for the BSU Honors Program.
On The Interlace Polynomials Of Forests,
2010
University of Nebraska
On The Interlace Polynomials Of Forests, C. Anderson, Jonathan Cutler, A. J. Radcliffe, L. Traldi
Department of Mathematics Faculty Scholarship and Creative Works
The interlace polynomials were introduced by Arratia, Bollobás and Sorkin (2004) [3-5]. These invariants generalize to arbitrary graphs some special properties of the Euler circuits of 2-in, 2-out digraphs. Among many other results, Arratia, Bollobás and Sorkin (2004) [3-5] give explicit formulas for the interlace polynomials of certain types of graphs, including paths; it is natural to wonder whether or not it is possible to extend these formulas to larger classes of graphs. We give a combinatorial description of the interlace polynomials of trees and forests.
Singular Points Of Real Sextic Curves I,
2010
George Fox University
Singular Points Of Real Sextic Curves I, David A. Weinberg, Nicholas J. Willis
Faculty Publications - Department of Mathematics
A complete classification of the individual types of singular points is given for irreducible real sextic curves. This classification is derived by using the computer algebra system Maple. There are 191 types of singular points for real irreducible sextic curves. We clarify that the classification is based on computing just enough of the Puiseux expansion to separate the branches. A significant portion of the proof consists of a sequence of large symbolic computations that can be done nicely using Maple.
Covariant Quantum Fields On Noncommutative Spacetimes,
2010
Syracuse University
Covariant Quantum Fields On Noncommutative Spacetimes, A. P. Balachandran, A. Ibort, G. Marmo, M. Martone
Physics - All Scholarship
A spinless covariant field $\phi$ on Minkowski spacetime $\M^{d+1}$ obeys the relation $U(a,\Lambda)\phi(x)U(a,\Lambda)^{-1}=\phi(\Lambda x+a)$ where $(a,\Lambda)$ is an element of the Poincar\'e group $\Pg$ and $U:(a,\Lambda)\to U(a,\Lambda)$ is its unitary representation on quantum vector states. It expresses the fact that Poincar\'e transformations are being unitary implemented. It has a classical analogy where field covariance shows that Poincar\'e transformations are canonically implemented. Covariance is self-reproducing: products of covariant fields are covariant. We recall these properties and use them to formulate the notion of covariant quantum fields on noncommutative spacetimes. In this way all our earlier results on dressing, statistics, etc. for …
Numerical Investigation Of Aeroelastic Mode Distribution For Aircraft Wing Model In Subsonic Air Flow,
2010
University of New Hampshire
Numerical Investigation Of Aeroelastic Mode Distribution For Aircraft Wing Model In Subsonic Air Flow, Marianna A. Shubov, Stephen B. Wineberg, Robert Holt
Mathematics & Statistics
In this paper, the numerical results on two problems originated in aircraft wing modeling have been presented. The first problem is concerned with the approximation to the set of the aeroelastic modes, which are the eigenvalues of a certain boundary-value problem. The affirmative answer is given to the following question: can the leading asymptotical terms in the analytical formulas be used as reasonably accurate description of the aeroelastic modes? The positive answer means that these leading terms can be used by engineers for practical calculations. The second problem is concerned with the flutter phenomena in aircraft wings in a subsonic, …
An F4-Style Involutive Basis Algorithm,
2010
University of Southern Mississippi
An F4-Style Involutive Basis Algorithm, Miao Yu
Mathematics Student Presentations
This paper introduces a new algorithm for computing Gröbner bases. To avoid as much ambiguity as possible, this algorithm combines the F4 algorithm and basic algorithm of involutive bases and it replaces the symbolic precomputation of S-polynomials and ordinary division in F4 by a new symbolic precomputation of non-multiplicative prolongations and involutive division. This innovation makes the sparse matrix of F4 in a deterministic way. As an example the Cyclic-4 problem is presented.
Parallelization Of The Wolff Single-Cluster Algorithm,
2010
University of Latvia
Parallelization Of The Wolff Single-Cluster Algorithm, Jevgenijs Kaupužs, Jānis Rimšāns, Roderick V.N. Melnik
Mathematics Faculty Publications
A parallel [open multiprocessing (OpenMP)] implementation of the Wolff single-cluster algorithm has been developed and tested for the three-dimensional (3D) Ising model. The developed procedure is generalizable to other lattice spin models and its effectiveness depends on the specific application at hand. The applicability of the developed methodology is discussed in the context of the applications, where a sophisticated shuffling scheme is used to generate pseudorandom numbers of high quality, and an iterative method is applied to find the critical temperature of the 3D Ising model with a great accuracy. For the lattice with linear size L=1024, we have …
On Independent Sets In Purely Atomic Probability Spaces With Geometric Distribution.,
2010
Columbus State University
On Independent Sets In Purely Atomic Probability Spaces With Geometric Distribution., Eugen J. Ionascu, Alin A. Stancu
Faculty Bibliography
We are interested in constructing concrete independent events in purely atomic probability spaces with geometric distribution. Among other facts we prove that there are uncountable many sequences of independent events.
A Predator-Prey Model In The Chemostat With Time Delay,
2010
Columbus State University
A Predator-Prey Model In The Chemostat With Time Delay, Guihong Fan
Faculty Bibliography
No abstract provided.
Solution To Problem 11366,
2010
Columbus State University
Solution To Problem 11366, Eugen J. Ionascu
Faculty Bibliography
No abstract provided.
The Probabilistic Zeta Function,
2010
College of Saint Benedict/Saint John's University
The Probabilistic Zeta Function, Bret Benesh
Mathematics Faculty Publications
This paper is a summary of results on the PG(s) function, which is the reciprocal of the probabilistic zeta function for finite groups. This function gives the probability that s randomly chosen elements generate a group G, and information about the structure of the group G is embedded in it.
Ozsváth-Szabó And Rasmussen Invariants Of Cable Knots,
2010
University of San Francisco
Ozsváth-Szabó And Rasmussen Invariants Of Cable Knots, Cornelia A. Van Cott
Mathematics
We study the behavior of the Ozsváth–Szabó and Rasmussen knot concordance invariants τ and s on Km,n, the (m,n)–cable of a knot K where m and n are relatively prime. We show that for every knot K and for any fixed positive integer m, both of the invariants evaluated on Km,n differ from their value on the torus knot Tm,n by fixed constants for all but finitely many n>0. Combining this result together with Hedden’s extensive work on the behavior of τ on (m,mr+1)–cables yields bounds on the value of τ on any (m,n)–cable of K. In addition, several …
Reply To "Comment On 'Cooperation In An Evolutionary Prisoner's Dilemma On Networks With Degree-Degree Correlations' ",
2010
University of San Francisco
Reply To "Comment On 'Cooperation In An Evolutionary Prisoner's Dilemma On Networks With Degree-Degree Correlations' ", Stephen Devlin, T Treloar
Mathematics
We respond to the comment of Zhu et al. [Phys. Rev. E 82, 038101 (2010)] and show that the results in question are not misleading.
Augmented Measurement System Assessment,
2010
University of San Francisco
Augmented Measurement System Assessment, Nathaniel Stevens, R Browne, S H. Steiner, R J. Mackay
Mathematics
The standard plan for the assessment of the variation due to a measurement system involves a number of operators repeatedly measuring a number of parts in a balanced design. In this article, we consider the performance of two types of (unbalanced) assessment plans. In each type, we use a standard plan augmented with a second component. In type A augmentation, each operator measures a different set of parts once each. In type B augmentation, each operator measures the same set of parts once each. The goal of the paper is to identify good augmented plans for estimating the gauge repeatability …
The Ro(G)-Graded Serre Spectral Sequence,
2010
Whittier College
The Ro(G)-Graded Serre Spectral Sequence, William C. Kronholm
Mathematics
In this paper the Serre spectral sequence of Moerdijk and Svensson is extended from Bredon cohomology to RO(G)RO(G)-graded cohomology for finite groups GG. Special attention is paid to the case G=Z/2G=Z/2 where the spectral sequence is used to compute the cohomology of certain projective bundles and loop spaces.
Analysis Of The Consistency Of A Mixed Integer Programming-Based Multi-Category Constrained Discriminant Model,
2010
Virginia Commonwealth University
Analysis Of The Consistency Of A Mixed Integer Programming-Based Multi-Category Constrained Discriminant Model, J. Paul Brooks, Eva K. Lee
Statistical Sciences and Operations Research Publications
Classification is concerned with the development of rules for the allocation of observations to groups, and is a fundamental problem in machine learning. Much of previous work on classification models investigates two-group discrimination. Multi-category classification is less-often considered due to the tendency of generalizations of two-group models to produce misclassification rates that are higher than desirable. Indeed, producing “good” two-group classification rules is a challenging task for some applications, and producing good multi-category rules is generally more difficult. Additionally, even when the “optimal” classification rule is known, inter-group misclassification rates may be higher than tolerable for a given classification model. …
