Digital Commons Network^™

A Mathematical Model Of The Dynamics Of An Optically Pumped Four-Level Solid State Laser System, Lila Freeman Roberts

Mathematics & Statistics Theses & Dissertations

This is a study of a mathematical model of the dynamics of an optically pumped four-level solid state laser system. A general mathematical model that describes the spatial and temporal evolution of the electron populations in the laser rod as well as the development of the left and right traveling photon fluxes in the cavity is developed. The model consists of a coupled set of first order semilinear partial differential equations. While the model was developed for Titanium-doped sapphire lasers, it is applicable to three and four level lasers in general.

The analysis of the model is conducted in two …

No Antitwins In Minimal Imperfect Graphs, Stephan Olariu

Computer Science Faculty Publications

It is customary to call vertices x and y twins if every vertex distinct from x and y is adjacent either to both of them or to neither of them. By analogy, we shall call vertices x and yantitwins if every vertex distinct from x and y is adjacent to precisely one of them. Lovász proved that no minimal imperfect graph has twins. The purpose of this note is to prove the analogous statement for antitwins.

The Twentieth Fermat Number Is Composite, Jeff Young, Duncan A. Buell

Faculty Publications

The twentieth Fermat number, F₂₀ = 2^{2^20} +1, has been proven composite by machine computation.

Caustics And Virtual Cathodes In Electron Beams, Evangelos A. Coutsias

Branch Mathematics and Statistics Faculty and Staff Publications

A simplified model is discussed that captures the basic physics of the phenomenon of oscillatory virtual cathodes in electron beams. A monoenergetic non-relativistic one-dimensional electron beam is injected through a conducting grid into a semi-infinite drift space. Attraction from image charges (and, possibly, an adverse externally applied electric field) cause particle reflection and the formation of a caustic where the charge density has an integrable singularity. The steady-state solution of the Vlasov equation describing the flow is known from numerical simulation to be unstable, but analytical demonstration of this instability has proved intractable. Here we derive an integral-delay equation describing …

Dual Pricing: Theory And Applications., Shikha Jha Dr.

Doctoral Theses

Even after thirty five yaara of planned economic develogment a large fraction of people in India cannot afford to have the basic necessities Like food, clothing and shelter. To quote from the Econonic Survey [1984-85), Buoyant agricultural parformance thus far has dependad mainly upon production gains in wheat and rice. Performance with raspect to other critical crops, such as pulser and oilseeds, and dryland farning generally, remains veak. The rate of growth of industry, although somewhat higher than in the ten years preceding the sixth Plan, remains low... population continues to grow at about 2 percent per year. At this …

A Proposed C Language Binding For The Graphical Kernel System 3-D, M. G. Bolten, C. Y. Ho

Computer Science Technical Reports

This thesis introduces a proposed C language binding definition for the International standards Organization's draft international standard of the Graphical Kernel System-JD. This work augments the earlier C language binding of the two-dimensional version of the Graphical Kernel System commonly known as GKS. The proposed function interface will provide a basis for, if not a final, C language binding for the three-dimensional version of the Graphical Kernel System.

Some Applications Of The Bounded Convergence Theorem For An Introductory Course In Analysis, Jonathan W. Lewin

Faculty Articles

The Arzela bounded convergence theorem is the special case of the Lebesgue dominated convergence theorem in which the functions are assumed to be Riemann integrable.

Competing Risks In Parallel And Series Systems, Lloyd R. Jaisingh

Morehead State Theses and Dissertations

A research paper written by Lloyd R. Jaisingh of the Department of Mathematical Sciences at Morehead State University on November 24, 1987.

The Bisection Method: Which Root?, Arthur T. Benjamin

All HMC Faculty Publications and Research

No abstract provided in this article.

Quasi F-Covers Of Tychonoff Spaces, Melvin Henriksen, J. Vermeer, R. G. Woods

All HMC Faculty Publications and Research

A Tychonoff topological space is called a quasi F-space if each dense cozero-set of X is C*-embedded in X. In Canad. J. Math. 32 (1980), 657-685 Dashiell, Hager, and Henriksen construct the "minimal quasi F-cover" QF(X) of a compact space X as an inverse limit space, and identify the ring C(QF(X)) as the order-Cauchy completion of the ring C*(X). In On perfect irreducible preimages, Topology Proc. 9 (1984), 173-189, Vermeer constructed the minimal quasi F-cover of an arbitrary Tychonoff space. In this paper the minimal quasi F-cover of a compact space X is constructed as the space of ultrafilters …

Integer Squares With Constant Second Difference, Duncan A. Buell

Faculty Publications

The problem addressed is this: Do there exist nonconsecutive integers n₀, n₁, n₂, . . ., such that the second differences of the squares of the n_i are constant? Specifically, can that constant be equal to 2? A complete characterization of sequences of length four can be given. The question of whether or not sequences of length five exist is still open but the existence or nonexistence of such sequences can be described in a more algorithmic way than the simple statement of the problem.

Model Of Hot-Film Sensor With Substrate Effects, David Mcalpine Judge

Electrical & Computer Engineering Theses & Dissertations

A detailed mathematical model is constructed to investigate the frequency response of a hot-film anemometer system. Since several diverse factors affect the frequency response, the analysis is broken down into three main parts. Each part is a detailed mathematical model. The first model consists of the ordinary differential equations which govern the electronics of the feedback system and heat transfer of the sensor. An important simplification in this model is that the rate of heat conduction from the sensor to its substrate is constant.

In the second model the unsteady state heat transfer properties of the substrate are examined by …

An Application Of Global Optimization Algorithm For Modal Parameter Identification, Chung-Men Chen

Mechanical & Aerospace Engineering Theses & Dissertations

Single-mode projection filters for modal parameter identification for flexible structures are introduced. An effective two-dimensional global optimization method using interval analysis is combined with the projection filters to facilitate identification for modal frequency and damping. A numerical simulation of a ten-mode structure is presented to illustrate the feasibility of the new method. The projection filters are practical for parallel processing implementation.

Ordered Products Of Topological Groups, Melvin Henriksen, Ralph Kopperman, Frank A. Smith

All HMC Faculty Publications and Research

The topology most often used on a totally ordered group (G, <) is the interval topology. There are usually many ways to totally order G x G (e.g., the lexicographic order) but the interval topology induced by such a total order is rarely used since the product topology has obvious advantages. Let ℝ(+) denote the real line with its usual order and Q(+) the subgroup of rational numbers. There is an order on Q x Q whose associated interval topology is the product topology, but no such order on ℝ x ℝ can be found. In this paper we characterize those pairs G, H of totally ordered groups such that there is a total order on G x H for which the interval topology is the product topology.

Infinitely Many Radially Symmetric Solutions To A Superlinear Dirichlet Problem In A Ball, Alfonso Castro, Alexandra Kurepa

All HMC Faculty Publications and Research

In this paper we show that a radially symmetric superlinear Dirichlet problem in a ball has infinitely many solutions. This result is obtained even in cases of rapidly growing nonlinearities, that is, when the growth of the nonlinearity surpasses the critical exponent of the Sobolev embedding theorem. Our methods rely on the energy analysis and the phase-plane angle analysis of the solutions for the associated singular ordinary differential equation.

Sequentially Compact, Franklin-Rajagopalan Spaces, Peter J. Nyikos, J. E. Vaughan

Faculty Publications

No abstract provided.

Improving The Lower Bound For The Reliability When The Strength Distribution Is Gamma And The Stress Distribution In Chi-Square, Lloyd R. Jaisingh

Morehead State Theses and Dissertations

A research paper written by Lloyd R. Jaisingh of the Department of Mathematical Sciences at Morehead State University in August of 1987.

The Persistence Of Universal Formulae In Free Algebras, Anthony M. Gaglione, Dennis Spellman

Mathematics Faculty Publications

Gilbert Baumslag, B.H. Neumann, Hanna Neumann, and Peter M. Neumann successfully exploited their concept of discrimination to obtain generating groups of product varieties via the wreath product construction. We have discovered this same underlying concept in a somewhat different context. Specifically, let V be a non-trivial variety of algebras. For each cardinal α let Fα(V) be a V-free algebra of rank α. Then for a fixed cardinal r one has the equivalence of the following two statements ...

A Quantitative Analysis Of Poverty, Inequality And Consumer Behaviour: The Case Of The Schedule Casts And Tribes Of Karnataka., Shailaja Raghuprasad Dr.

Doctoral Theses

The concept of growth with social justice is basic to the philosophy of development underlying Indian economic Planning. This philosophy is reflected in our former Prime Minister Mrs Indira Gandhi's foreword to the sixth Plan (1980-85) document where she wrote, Economic Growth must be balanced, it must ensure self - reliance, stability and social justice. All sections should be assured that there will be no discrimination'.It is with those weaker sections - rather a segment of them that this study is concerned, Our study is an attempt to look closely at the levels of living and the consumer behaviour of …

Cyclic Operators, Commutators, And Absolutely Continuous Measures, Joanne Dombrowski

Mathematics and Statistics Faculty Publications

Commutator equations are used to study the relationship between the tridiagonal matrix structure of an unbounded cyclic selfadjoint operator and its spectrum. Sufficient conditions are given for absolute continuity. Results are related to the study of systems of orthogonal polyomials for which the measure of orthogonality is supported on an unbounded subset of the real line.

Teaching With A Humanist, David Meredith

Humanistic Mathematics Network Journal

This paper is a report about a team-taught course at San Francisco State University, and what the author learned having taught it over 11 years with faculty in the humanities. As part of an interdisciplinary curriculum called NEXA, which explored the boundaries between science and the humanities, the course revealed to the author several ways mathematics and humanities pedagogies can reciprocally learn from each other and emphasize similar goals.

Patterns Of Emotion Within Mathematics Problem-Solving, Frances A. Rosamond

Humanistic Mathematics Network Journal

There is often a divide between the experience of positive emotions toward math on the part of mathematical educators and negative emotions toward math on the part of students. This paper utilizes psychologist Richard Lazarus's work on the effects of positive emotions in order to highlight their benefits for mathematical pedagogy, to explain the author's experiment applying Lazarus's theory, and to suggest ways this application might support and foster positive emotions in students.

Gresham's Law: Algorithm Drives Out Thought, Sherman K. Stein

Humanistic Mathematics Network Journal

Gresham's law in economics states, "Bad money drives good money out of circulation." An application of this law in mathematical pedagogy states that "Algorithm drives out thought." While universities are ideally places where classes are meant to develop students' independence and critical thinking skills, often mathematics courses reflect this altered version of Gresham's law. This paper demonstrates the ways traditional mathematical pedagogy has held up Gresham's law and presents several suggestions for ways to change this approach to mathematical education to focus more on critical thinking without sacrificing the necessity of algorithm.

Letter From The Editor, Issue 1, 1987, Alvin White

Humanistic Mathematics Network Journal

No abstract provided.

Applied Mathematics As Social Contract, Philip J. Davis

Humanistic Mathematics Network Journal

The author takes the position that mathematical education must redefine its goals so as to create a citizenry with sufficient knowledge to provide social backpressure on future mathematizations. This can be accomplished by increasing the part of mathematical education that is devoted to the description and interpretation of the processes of mathematization and by allowing the technicalities of the formal operations within mathematics itself to be deemphasized or automated out by computer.

Appendix

Humanistic Mathematics Network Journal

No abstract provided.

A Rank Correlation Coefficient Resistant To Outliers, Rudy Gideon, Robert Ashley Hollister

Mathematical Sciences Faculty Publications

In this article, a nonparametric correlation coefficient is defined that is based on the principle of maximum deviations. This new correlation coefficient, RgB is easy to compute by hand for small to medium sample sizes. In comparing it with existing correlation coefficients, it was found to be superior in a sampling situation that we call "biased outliers," and hence appears to be more resistant to outliers than the Pearson, Spear- man, and Kendall correlation coefficients. In a correlational study not included in this article of some social data consisting of five variables for each of 51 observations, Rg was compared …

Dynamics Of Large Eddies In Turbulent Channel Flows, F. R. Payne, S. K. Hong

Mathematics Technical Papers - Archive

A turbulence model that describes dynamics of large, characteristic eddies in inhomogeneous flows is proposed; two closure parameters are initially undetermined. To determine the optimum values of these parameters, the present model is applied to channel flows at two Reynolds numbers. The nature of the closure parameters and their effects upon predicted Reynolds stresses and other turbulence structural quantities are examined and optimum values are suggested. It is demonstrated that the current Large-Eddy Interaction Model not only predicts Reynolds stresses reasonably but also presents an opportunity to illuminate typical characteristic motions of large-scale turbulence and the phenomenological aspects of engineering …

Problems, Lawrence Stout

Scholarship

No abstract provided.

Reduced Coproducts Of Compact Hausdorff Spaces, Paul Bankston

Mathematics, Statistics and Computer Science Faculty Research and Publications

By analyzing how one obtains the Stone space of the reduced product of an indexed collection of Boolean algebras from the Stone spaces of those algebras, we derive a topological construction, the "reduced coproduct", which makes sense for indexed collections of arbitrary Tichonov spaces. When the filter in question is an ultrafilter, we show how the "ultracoproduct" can be obtained from the usual topological ultraproduct via a compactification process in the style of Wallman and Frink. We prove theorems dealing with the topological structure of reduced coproducts (especially ultracoproducts) and show in addition how one may use this construction to …