Physical Sciences and Mathematics Commons^™

Modular Symbols And Hecke Operators, Paul E. Gunnells

Paul Gunnells

We survey techniques to compute the action of the Hecke operators on the cohomology of arithmetic groups. These techniques can be seen as generalizations in different directions of the classical modular symbol algorithm, due to Manin and Ash-Rudolph. Most of the work is contained in papers of the author and the author with Mark McConnell. Some results are unpublished work of Mark McConnell and Robert MacPherson.

The Structure Of Free Semigroup Algebras, Kenneth R. Davidson, Elias Katsoulis, David R. Pitts

Department of Mathematics: Faculty Publications

A free semigroup algebra is WOT-closed algebra generated by an n-tuple of isometries with pairwise orthogonal ranges. The interest in these algebras arises primarily from two of their interesting features. The first is that they provide useful information about unitary invariants of representations of the Cuntz-Toeplitz algebras. The second is that they form a class of nonself-adjoint operator algebras which are of interest in their own right. This class contains a distinguished representative, the "non-commutative Toeplitz algebra", which is generated by the left regular representation of the free semigroup on n letters and denoted . This paper provides a general …

Restricted Words By Adjacencies, Don Rawlings

Mathematics

A recurrence, a determinant formula, and generating functions are presented for enumerating words with restricted letters by adjacencies. The main theorem leads to refinements (with up to two additional parameters) of known results on compositions, polyominoes, and permutations. Among the examples considered are (1) the introduction of the ascent variation on compositions, (2) the enumeration of directed vertically convex polyominoes by upper descents, area, perimeter, relative height, and column number, (3) a tri-variate extension of MacMahon's determinant formula for permutations with prescribed descent set, and (4) a combinatorial setting for an entire sequence of bibasic Bessel functions.

Orbifold Quantum Cohomology, Weimin Chen Chen, Yongbin Ruan

Weimin Chen

This is a research announcement on a theory of Gromov-Witten invariants and quantum cohomology of symplectic or projective orbifolds. Our project started in the summer of 98 where our original motivation was to study the quantum cohomology under singular flops in complex dimension three. In this setting, we allow our three-fold to have terminal singularities which can be deformed into a symplectic orbifold. We spent the second half of 98 and most of spring of 99 to develop the foundation of Gromov-Witten invariants over orbifolds, including the key conceptual ingredient — the notion of good map. In the April of …

The Poisson Variation Of Montmort's Matching Problem, Don Rawlings

Mathematics

No abstract provided.

The Possibility Of Impossible Pyramids, Thomas Q. Sibley

Mathematics Faculty Publications

No abstract provided.

Openness Of Induced Projections, J. J. Charatonik, W. J. Charatonik, Alejandro Illanes

Mathematics and Statistics Faculty Research & Creative Works

For continua X and Y it is shown that if the projection f : X x Y ->X has its induced mapping C(f) open, then X is C*-smooth. As a corollary, a characterization of dendrites in these terms is obtained.

Euclidean Weights Of Codes From Elliptic Curves Over Rings, José Felipe Voloch, Judy L. Walker

Department of Mathematics: Faculty Publications

We construct certain error-correcting codes over finite rings and estimate their parameters. For this purpose, we need to develop some tools, notably an estimate for certain exponential sums and some results on canonical lifts of elliptic curves. These results may be of independent interest.

A code is a subset of Aⁿ, where A is a finite set (called the alphabet). Usually A is just the field of two elements and, in this case, one speaks of binary codes. Such codes are used in applications where one transmits information through noisy channels. By building redundancy into the code, transmitted …

Random Approaches To Fibonacci Identities, Arthur T. Benjamin, Gregory M. Levin, Karl Mahlburg '01, Jennifer J. Quinn

All HMC Faculty Publications and Research

No abstract provided in this article.

Phased Tilings And Generalized Fibonacci Identities, Arthur T. Benjamin, Jennifer J. Quinn, Francis E. Su

All HMC Faculty Publications and Research

Fibonacci numbers arise in the solution of many combinatorial problems. They count the number of binary sequences with no consecutive zeros, the number of sequences of 1's and 2's which sum to a given number, and the number of independent sets of a path graph. Similar interpretations exist for Lucas numbers. Using these interpretations, it is possible to provide combinatorial proofs that shed light on many interesting Fibonacci and Lucas identities (see [1], [3]). In this paper we extend the combinatorial approach to understand relationships among generalized Fibonacci numbers.

Given G₀ and G₁ a generalized Fibonacci sequence G …

Some Applications Of The Ultrapower Theorem To The Theory Of Compacta, Paul Bankston

Mathematics, Statistics and Computer Science Faculty Research and Publications

The ultrapower theorem of Keisler and Shelah allows such model-theoretic notions as elementary equivalence, elementary embedding and existential embedding to be couched in the language of categories (limits, morphism diagrams). This in turn allows analogs of these (and related) notions to be transported into unusual settings, chiefly those of Banach spaces and of compacta. Our interest here is the enrichment of the theory of compacta, especially the theory of continua, brought about by the importation of model-theoretic ideas and techniques.

Active Feedback Control Of A Wake Flow Via Forced Oscillations Based On A Reduced Model, Fu Li

Dissertations

As it is well known, the flow past a cylinder consists of a symmetric recirculation bubble of vortices at small Reynolds numbers. As Reynolds number increases, the bubble becomes unstable and develops into a Karman vortex street of alternating vortices. This instability is responsible for the occurrence of large amplitude oscillations in the lift and an increase in the mean drag. It was previously shown by numerical simulation that the mechanism driving the bubble instability is well mimicked by Foppl's four dimensional potential flow model where the bubble is represented by a saddle point. In this work, we design two …

A Study Of Droplet Burning In The Nearly Adiabatic Limit, Juan C. Gomez

Dissertations

We consider a small drop of liquid fuel that burns in an oxidizing gaseous environment and translates slowly (relative to flow 'at infinity') under the action of gravity. Practical applications include the burning of liquid fuels as sprays in domestic and industrial oil-fired burners, diesel engines, and liquid-propellant rocket motors. More relevant to the simple physical set-up of the present study are wellcharacterized laboratory experiments on the burning of a single, isolated fuel drop.

The drop burns in a nearly spherical, diffusion flame, flame sheet regime. We consider a specific example, or limit, referred to as 'nearly adiabatic burning', in …

Numerical Study Of Particle Dynamics In A Falling-Ball Viscometer, Peiwen Hou

Dissertations

The falling-ball viscometer is a device where a spherical particle falls along the axis of a circular cylinder filled with viscous fluid. The various classical results for this device are developed under the assumption that the Reynolds number of the flow is zero, i.e., Stoke's flow. Inertial effects are not taken into account. To better understand the dynamics of the particle sedimentation process and the role of inertia in this process, we implemented a numerical simulation.

The ADI (Alternating Direction Implicit) scheme is widely used to solve the vorticity-stream function formulation of the Navier-Stokes equation in axisymmetric geometries. However, a …

Superspace Geometrical Realization Of The N-Extended Super Virasoro Algebra And Its Dual, Carina Curto, James Gates Jr., V. G. J. Rodgers

Department of Mathematics: Faculty Publications

Abstract We derive properties of N-extended GR super Virasoro algebras. These include adding central extensions, identification of all primary fields and the action of the adjoint representation on its dual. The final result suggest identification with the spectrum of fields in supergravity theories and superstring/M-theory constructed from NSR N-extended supersymmetric GR Virasoro algebras.

[The version deposited with arXiv (February 2000) is also attached (below) as an additional file.]

Performance Of Bootstrap Confidence Intervals For L-Moments And Ratios Of L-Moments., Suzanne Glass

Electronic Theses and Dissertations

L-moments are defined as linear combinations of expected values of order statistics of a variable.(Hosking 1990) L-moments are estimated from samples using functions of weighted means of order statistics. The advantages of L-moments over classical moments are: able to characterize a wider range of distributions; L-moments are more robust to the presence of outliers in the data when estimated from a sample; and L-moments are less subject to bias in estimation and approximate their asymptotic normal distribution more closely.

Hosking (1990) obtained an asymptotic result specifying the sample L-moments have a multivariate normal distribution as n approaches infinity. The standard …

Adaptive Estimation And Control Method For Unstable Periodic Dynamics In Spike Trains, D. Christini, Daniel Kaplan

Daniel T. Kaplan

No abstract provided.

Σary, Moorhead State University, Mathematics Department

Math Department Newsletters

No abstract provided.

Low Seasonal Temperatures Promote Life Cycle Synchronization, Janette Lee Jenkins

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

In this paper, we discuss how seasonal temperature variation and dormancy can synchronize the development of exothermic organisms. Using a simple aging model, it is shown that minimal seasonal temperature variation and periods of dormancy during extreme temperature conditions are sufficient to establish stable, univoltine ovipositional cycles. Dormancy, in fact, promotes synchronous oviposition emergence. The mountain pine beetle, an important insect living in extreme temperature conditions and showing no evidence of diapause, invites direct application of this model. Simulations using mountain pine beetle parameters are used to determine temperature regimes for which stable, ovipositional cycles exist.

A New Perspective On Classification, Guohua Zhao

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The idea of voting multiple decision rules was introduced in to statistics by Breiman. He used bootstrap samples to build different decision rules, and then aggregated them by majority voting (bagging). In regression, bagging gives improved predictors by reducing the variance (random variation), while keeping the bias (systematic error) the same. Breiman introduced the idea of bias and variance for classification to explain how bagging works. However, Friedman showed that for the two-class situation, bias and variance influence the classification error in a very different way than they do in the regression case.

In the first part of …

Evolution Of Positive Solution Curves In Semipositone Problems With Concave Nonlinearities, Alfonso Castro, Sudhasree Gadam, Ratnasingham Shivaji

All HMC Faculty Publications and Research

We study the existence, multiplicity, and stability of positive solutions to -u''(x) = λf(u(x)) for x є (-1,1), u(-1) = 0 = u(1), where λ > 0 and f:[0,∞)→R is monotonically increasing and concave with f(0) < 0 (semipositone). We establish that f should be appropriately concave (by establishing conditions on f) to allow multiple positive solutions. For any λ > 0, we obtain the exact number of positive solutions as a function of f(t)/t. We follow several families of nonlinearities f for which f(∞) := lim t→∞ f(t) > 0 and study how the positive solution curves to the above problem evolve. Also, we give examples where our results apply. This work extends the work of A. Castro and R. Shivaji (1988, Proc. Roy. Soc. Edinburgh …

An Elliptic Equation With Spike Solutions Concentrating At Local Minima Of The Laplacian Of The Potential, Gregory S. Spradlin

Publications

We consider the equation −ԑ2∆u + V (z)u = f(u) which arises in the study of nonlinear Schrödinger equations. We seek solutions that are positive on RN and that vanish at infinity. Under the assumption that f satisfies super-linear and sub-critical growth conditions, we show that for small ԑ there exist solutions that concentrate near local minima of V. The local minima may occur in unbounded components, as long as the Laplacian of V achieves a strict local minimum along such a component. Our proofs employ vibrational mountain-pass and concentration compactness arguments. A penalization technique developed by Felmer and del …

Vertices In Total Dominating Sets., Robert Elmer Dautermann Iii

Electronic Theses and Dissertations

Fricke, Haynes, Hedetniemi, Hedetniemi, and Laskar introduced the following concept. For a graph G = (V,E), let rho denote a property of interest concerning sets of vertices. A vertex u is rho-good if u is contained in a {minimum, maximum} rho-set in G and rho-bad if u is not contained in a rho-set. Let g denote the number of rho-good vertices and b denote the number of rho-bad vertices. A graph G is called rho-excellent if every vertex in V is rho-good, rho-commendable if g > b > 0, rho-fair if g = b, and …

Mode Vertices And Mode Graphs., Jobriath Scott Kauffman

Electronic Theses and Dissertations

The eccentricity of a vertex, v, of a connected graph, G, is the distance to a furthest vertex from v. A mode vertex of a connected graph, G, is a vertex whose eccentricity occurs as often in the eccentricity sequence of G as the eccentricity of any other vertex. The mode of a graph, G, is the subgraph induced by the mode vertices of G. A mode graph is a connected graph for which each vertex is a mode vertex. Note that mode graphs are a generalization of self-centered graphs. This paper presents some …

Estimating Change Over Time From Aggregate Samples Plus Partial Transition Data, Chien-Pai Han, D. L. Hawkins

Mathematics Technical Papers

As such, the paper has two basic thrusts. The first is that to obtain efficient estimates of change measures (e.g. of transition probabilities) based on aggregate data, auxiliary data will in general be needed; several potentially useful auxiliary sampling schemes are discussed. The second thrust is the manner in which estimates from the such varied sampling schemes can be combined to achieve such efficient estimates. Since it either directly or indirectly suggests many possible longitudinal study designs, the paper necessarily cannot provide real examples of all (or even most) of the study designs considered. Indeed, the main point here is …

Pooled And Individual Bycatch Quotas: Exploring Tradeoffs Between Observer Coverage Levels, Bycatch Frequency, Pool Size, And The Precision Of Bycatch Estimates, Landon S. Jensen

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

The North Pacific Ocean is highly productive, hosting many of the world's largest groundfish populations and supporting a thriving fishing industry. Numerous regulations have been implemented to control the incidental take of non-target bycatch. Individual and Pooled Bycatch Quotas have recently been proposed as instruments that could further encourage the avoidance of such bycatch and increase enforceability of bycatch caps at less-than-entire-fishery levels of operation. The recent advent of fishing cooperatives such as the Pacific Whiting Conservation Cooperative and the Pollock Conservation Cooperatives create an additional impetus for examining the characteristics of pool and vessel specific bycatch quotas.

We have …

Banzhaf Permission Values For Games With Permission Structure, Rene Van Den Brink

Mathematics Technical Papers

A game with a permission structure describes a situation in which cooperation possibilities in a cooperative game with transferable utility are limited because there are players that need permission from other players before they are allowed to cooperate. In the conjunctive approach it is assumed that every player needs permission from all its direct superiors. In the disjunctive approach it is assumed that each player only needs permission from at least one of its direct superiors. Both approaches yield different modified games which take account of the limited cooperation possibilities. Applying the Banzhaf value to these modified games yields allocation …

Comparing Nonlinear And Nonparametric Modeling Techniques For Mapping And Stratification In Forest Inventories Of The Interior Western Usa, Gretchen Gengenbach Moisen

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Recent emphasis has been placed on merging regional forest inventory data with satellite-based information both to improve the efficiency of estimates of population totals, and to produce regional maps of forest variables. There are numerous ways in which forest class and structure variables may be modeled as functions of remotely sensed variables, yet surprisingly little work has been directed at surveying modem statistical techniques to determine which tools are best suited to the tasks given multiple objectives and logistical constraints. Here, a series of analyses to compare nonlinear and nonparametric modeling techniques for mapping a variety of forest variables, and …

Mean-Square Error Bounds And Perfect Sampling For Conditional Coding, Xiangchen Cui

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

In this dissertation, new theoretical results are obtained for bounding convergence and mean-square error in conditional coding. Further new statistical methods for the practical application of conditional coding are developed.

Criteria for the uniform convergence are first examined. Conditional coding Markov chains are aperiodic, π-irreducible, and Harris recurrent. By applying the general theories of uniform ergodicity of Markov chains on general state space, one can conclude that conditional coding Markov chains are uniformly ergodic and further, theoretical convergence rates based on Doeblin's condition can be found.

Conditional coding Markov chains can be also viewed as having finite state space. …

Positive Solutions Obtained As Local Minima Via Symmetries, For Nonlinear Elliptic Equations, Florin Catrina

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

In this dissertation, we establish existence and multiplicity of positive solutions for semilinear elliptic equations with subcritical and critical nonlinearities. We treat problems invariant under subgroups of the orthogonal group. Roughly speaking, we prove that if enough "mass " is concentrated around special orbits, then among the functions with prescribed symmetry, there is a solution for the original problem.

Our results can be regarded as a further development of the work of Z.-Q. Wang, where existence of local minima in the space of symmetric functions was studied for the Schrödinger equation. We illustrate the general theory with three examples, all …