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Dynamical Simulation Of The Simplest Hydrides, Donald Greenspan Jan 1996

Dynamical Simulation Of The Simplest Hydrides, Donald Greenspan

Mathematics Technical Papers - Archive

In agreement with recent results of Gell-Mann and Hartle, we approximate electron motions in ground state Li7H1 and Li7H2 using an energy conserving numerical method for the solution of Newton's equations and a novel assumption about the interaction of the bonding electrons. Initial calculations for the first excited state of Li7H1 are also discussed. I. Introduction. Quantum dynamics is usually perceived through the time dependent Schrödinger equation, for which related analytical and computational problems appear to be insurmountable at the present time. There is however an alternate approach which can be implemented readily when the dynamical behavior is periodic. This …

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Conservative Motion Of Discrete, Tetrahedral Top On A Smooth Horizontal Plane, Donald Greenspan Jan 1996

Conservative Motion Of Discrete, Tetrahedral Top On A Smooth Horizontal Plane, Donald Greenspan

Mathematics Technical Papers - Archive

Tetrahedral tops are simulated as discrete, rigid bodies in rotation by introducing a molecular mechanics formulation. The contact point of the top with the XY plane is allowed to move in the plane. The conservative, dynamical differential equations are solved numerically in such a fashion that all the system invariants are preserved. Examples which include precession, nutation, cusp formation, and looping are described and discussed.

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Two Remarks On Totally Balanced Games, Juan-Enrique Martínez-Legaz Jan 1996

Two Remarks On Totally Balanced Games, Juan-Enrique Martínez-Legaz

Mathematics Technical Papers - Archive

Two results on totally balanced TU games are presented. It is first shown that the core of any subgame of a non-negative totally balanced game can be easily obtained from the maximal average value function of the game. The second result is a characterization of convex games as those games all of whose marginal games are totally balanced.

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On The Structure Of The Deflagration For The Generalized Reaction-Rate Model, William B. Bush, L. Krishnamurthy Jan 1996

On The Structure Of The Deflagration For The Generalized Reaction-Rate Model, William B. Bush, L. Krishnamurthy

Mathematics and System Engineering Faculty Publications

The structure of the deflagration is examined by means of an asymptotic analysis of the physical-plane boundary-value problem, with Lewis-Semenov number unity, in the limit of the activation-temperature ratio, β = Ta/Tb, greater than order unity, for the generalized reaction-rate-model case of (1) the heat- addition-temperature ratio, α = (Tb — Tu)/Tu, of order unity [where Ta, Tb, and Tu are the activation, adiabatic-flame (and/or burned-gas), and unburned-gas temperatures, respectively]; and (2) the exponent, a, which characterizes the pre-exponential thermal dependence of the reaction-rate term, unity. This examination indicates that the deflagration has a four-region structure. To obtain a uniformly …

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Knots About Stokes' Theorem, Michael C. Sullivan Jan 1996

Knots About Stokes' Theorem, Michael C. Sullivan

Articles and Preprints

Connections between knot theory and Stokes' Theorem as presented to students in a sophomore level vector calculus class.

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A Note On Gamma Rings, M. Sapanci, A. Nakajimaz Jan 1996

A Note On Gamma Rings, M. Sapanci, A. Nakajimaz

Turkish Journal of Mathematics

Let M be a \Gamma-ring and D a non-zero left derivation on M. We show that if there exists an element m in M such that D(m) is a right non-zero divisor, then M is commutative.

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On A Differential Analog Of The Prime-Radical And Properties Of The Lattice Of Radical Differential Ideals In Associative Differential Rings, D. Hadjiev, F. Çallialp, A. Eden Jan 1996

On A Differential Analog Of The Prime-Radical And Properties Of The Lattice Of Radical Differential Ideals In Associative Differential Rings, D. Hadjiev, F. Çallialp, A. Eden

Turkish Journal of Mathematics

In this paper we prove the following results: (1) For any assosiative differential ring with the unit we introduce a differential analog of the prime-radical and describe it; (2) any maximal differential ideal of a Ritt algebra is prime; (3) The lattice of radical differential ideals satisfies the condition of infinite \cap- distributivity.

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A Multiple-Precision Division Algorithm, David M. Smith Jan 1996

A Multiple-Precision Division Algorithm, David M. Smith

Mathematics, Statistics and Data Science Faculty Works

The classical algorithm for multiple-precision division normalizes digits during each step and sometimes makes correction steps when the initial guess for the quotient digit turns out to be wrong. A method is presented that runs faster by skipping most of the intermediate normalization and recovers from wrong guesses without separate correction steps.

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Decidability Of The Two-Quantifier Theory Of The Recursively Enumerable Weak Truth-Table Degrees And Other Distributive Upper Semi-Lattices, Klaus Ambos-Spies, Peter A. Fejer, Steffen Lempp, Manuel Lerman Jan 1996

Decidability Of The Two-Quantifier Theory Of The Recursively Enumerable Weak Truth-Table Degrees And Other Distributive Upper Semi-Lattices, Klaus Ambos-Spies, Peter A. Fejer, Steffen Lempp, Manuel Lerman

Computer Science Faculty Publication Series

We give a decision procedure for the ∀∃-theory of the weak truth-table (wtt) degrees of the recursively enumerable sets. The key to this decision procedure is a characterization of the finite lattices which can be embedded into the r.e. wtt-degrees by a map which preserves the least and greatest elements: a finite lattice has such an embedding if and only if it is distributive and the ideal generated by its cappable elements and the filter generated by its cuppable elements are disjoint. We formulate general criteria that allow one to conclude that a distributive upper semi-lattice has a decidable two-quantifier …

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Detecting Trends And Patterns In Reliability Data Over Time Using Exponentially Weighted Moving-Averages, Harry F. Martz, Paul H. Kvam Jan 1996

Detecting Trends And Patterns In Reliability Data Over Time Using Exponentially Weighted Moving-Averages, Harry F. Martz, Paul H. Kvam

Department of Math & Statistics Faculty Publications

A simple, easy-to-use graphical method is presented for use in determining if there is any statistically significant trend or pattern over time in an underlying Poisson event rate of occurrence or binomial failure on demand probability. The method is based on the combined use of both an exponentially weighted moving-average (EWMA) and a Shewhart chart. Two nuclear power plant examples are introduced and used to illustrate the method. The false alarm probability and power when using the combined procedure are also determined for both cases using Monte Carlo simulation. The results indicate that the combined procedure is quite effective in …

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Invariant Subspaces Of The Harmonic Dirichlet Space With Large Co-Dimension, William T. Ross Jan 1996

Invariant Subspaces Of The Harmonic Dirichlet Space With Large Co-Dimension, William T. Ross

Department of Math & Statistics Faculty Publications

In this paper, we comment on the complexity of the invariant subspaces (under the bilateral Dirichlet shift f → ζf) of the harmonic Dirichlet space D. Using the sampling theory of Seip and some work on invariant subspaces of Bergman spaces, we will give examples of invariant subspaces F ⊂ D with dim(F/ζF) = n, n ∈ N ∪ {∞}. We will also generalize this to the Dirichlet classes Dα, 0 <α< ∞, as well as the Besov classes Bα p , 1

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The Backward Shift Of Weighted Bergman Spaces, William T. Ross, Alexandru Aleman Jan 1996

The Backward Shift Of Weighted Bergman Spaces, William T. Ross, Alexandru Aleman

Department of Math & Statistics Faculty Publications

No abstract provided.

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A Survey Of Hadamard Difference Sets, James A. Davis, Jonathan Jedwab Jan 1996

A Survey Of Hadamard Difference Sets, James A. Davis, Jonathan Jedwab

Department of Math & Statistics Faculty Publications

A (v, k, λ) difference set is a k-element subset D of a group G of order v for which the multiset {d1d2-1 : d1, d2 ∈ D, d1 ≠ d2} contains each nonidentity element of G exactly λ times. A difference set is called abelian, nonabelian or cyclic according to the properties of the underlying group. Difference sets are important in design theory because they are equivalent to symmetric (v, k, λ) designs with a regular automorphism group [L].

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Bergman Spaces On Disconnected Domains, William T. Ross, Alexandru Aleman, Stefan Richter Jan 1996

Bergman Spaces On Disconnected Domains, William T. Ross, Alexandru Aleman, Stefan Richter

Department of Math & Statistics Faculty Publications

For a bounded region G C C and a compact set K C G, with area measure zero, we will characterize the invariant subspaces M (under f -> zf)of the Bergman space Lpa(G \ K), 1 ≤ p < ∞, which contain Lpa(G) and with dim(M/(z - λ)M) = 1 for all λϵ G \ K. When G \ K is connected, we will see that di\m(M /(z — λ)M) = 1 for all λ ϵ G \ K and thus in this case we will have a complete …

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Geometrical Modeling Of Material Aging, Alexander Chudnovsky, Serge Preston Jan 1996

Geometrical Modeling Of Material Aging, Alexander Chudnovsky, Serge Preston

Mathematics and Statistics Faculty Publications and Presentations

Material aging is understood as changes of material properties with time. The aging is usually observed as an improvement of some properties and a deterioration of others. For example an increase of rigidity and strength and reduction in toughness with time are commonly observed in engineering materials. In an attempt to model aging phenomena on a continuum (macroscopical) level one faces three major tasks. The first is to identify an adequate age parameter that represents, on a macroscopic scale, the micro and sub microscopical features, underlying the aging phenomena such as nucleation, growth and coalescence of microdefects, physico-chemical transformations etc. …

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On Transitive And Fully Transitive Abelian P-Groups, D. Carroll, Brendan Goldsmith Jan 1996

On Transitive And Fully Transitive Abelian P-Groups, D. Carroll, Brendan Goldsmith

Articles

It is a long standing problem of A.L.S. Corner as to whether there exists a non-transitive fully transitive Abelian p-group with finite Ulm subgroups. The principal result of this paper shows that no such group exists for a special class of p-groups if the Ulm subjgroup is the direct sum of two cyclic groups. Some results on summands of trnsitive and fully transitive groups are obtained.

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Finite Dimensional Attractors For A Class Of Semilinear Wave Equations, A. Eden, V. Kalantarov Jan 1996

Finite Dimensional Attractors For A Class Of Semilinear Wave Equations, A. Eden, V. Kalantarov

Turkish Journal of Mathematics

In this paper we give a self-contained survey of results related with the global attractors for a class of nonlinear wave equations with damping or viscosity terms. In particular, we prove the existence of a finite dimensional attractor and estimate its fractal dimension by imbedding it in an exponential attractor. Some results on global stability, existence of finite dimensional attractors were already partially discussed in Kalantarov [44] and in Eden et. al. [25], however we simplify the framework by introducing a unified approach to both the existence of attractors through \alpha-contractions and the construction of exponential attractors via some Lipschitzianity …

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Comparison Of Invariants For Triples Of Hilbert Spaces, P. A. Chalov Jan 1996

Comparison Of Invariants For Triples Of Hilbert Spaces, P. A. Chalov

Turkish Journal of Mathematics

In [2,3] the sequence of invariant characteristics (\mu_{m}) for the finite families of Hilbert spaces were considered. Here we make a comparison of these invariants among themselves. We construct some examples of triples of Hilbert spaces, which show that each system of the first r+1 characteristics is stronger than the system of the first r of them. Moreover we show that there exist triples of Hilbert spaces which on the one hand are not quasidiagonally isomorphic, but on the other hand they cannot be distinguished by any function \mu_{m},\,\, m\in\,\, \Bbb N.

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A Center-Unstable Manifold Theorem For Parametrically Excited Surface Waves, Larry Turyn Jan 1996

A Center-Unstable Manifold Theorem For Parametrically Excited Surface Waves, Larry Turyn

Mathematics and Statistics Faculty Publications

When fluid in a rectangular tank sits upon a platform which is oscillating with sufficient amplitude, surface waves appear in the ''Faraday resonance.'' Scientists and engineers have done bifurcation analyses which assume that there is a center manifold theory using a finite number of excited spatial modes. We establish such a center manifold theorem for Xiao-Biao Lin's model in which potential flow is assumed but an artificial dissipation term is included in the system of partial differential equations on the free surface. We use interpolation spaces developed by da Prate and Grisvard, establish maximal regularity for a family of evolution …

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On Applications Of Excess Level Processes To (N,D)-Policy Bulk Queueing Systems, Jewgeni H. Dshalalow Jan 1996

On Applications Of Excess Level Processes To (N,D)-Policy Bulk Queueing Systems, Jewgeni H. Dshalalow

Mathematics and System Engineering Faculty Publications

The paper deals with queueing systems in which N- and D-policies are combined into one. This means that an idle or vacationing server will resume his service if the queueing or workload process crosses some specified fixed level N or D, respectively. For the proposed (N,D)-policy we study the queueing processes in models with and without server vacations, with compound Poisson input, and with generally distributed service and vacation periods. The analysis of the models is essentially based on fluctuation techniques for two-dimensional marked counting processes newly developed by the author. The results enable us to arrive at stationary distributions …

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Exact Multiplicity Results For Boundary Value Problems With Nonlinearities Generalizing Cubic, Philip Korman, Yi Li, Tiancheng Ouyang Jan 1996

Exact Multiplicity Results For Boundary Value Problems With Nonlinearities Generalizing Cubic, Philip Korman, Yi Li, Tiancheng Ouyang

Mathematics and Statistics Faculty Publications

No abstract provided.

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Exponent Bounds For A Family Of Abelian Difference Sets, K. T. Arasu, James A. Davis, Jonathan Jedwab, Siu Lun Ma, Robert L. Mcfarland Jan 1996

Exponent Bounds For A Family Of Abelian Difference Sets, K. T. Arasu, James A. Davis, Jonathan Jedwab, Siu Lun Ma, Robert L. Mcfarland

Department of Math & Statistics Faculty Publications

Which groups G contain difference sets with the parameters (v, k, λ)= (q3 + 2q2 , q2 + q, q), where q is a power of a prime p? Constructions of K. Takeuchi, R.L. McFarland, and J.F. Dillon together yield difference sets with these parameters if G contains an elementary abelian group of order q2 in its center. A result of R.J. Turyn implies that if G is abelian and p is self-conjugate modulo the exponent of G, then a necessary condition for existence is that the exponent …

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Paracompact Subspaces In The Box Product Topology, Peter Nyikos, Leszek Piatkiwicz Jan 1996

Paracompact Subspaces In The Box Product Topology, Peter Nyikos, Leszek Piatkiwicz

Faculty Publications

No abstract provided.

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On Non-Holonomic Second-Order Connections With Applications To Continua With Microstructure, Marek Elźanowski, Serge Preston Jan 1996

On Non-Holonomic Second-Order Connections With Applications To Continua With Microstructure, Marek Elźanowski, Serge Preston

Mathematics and Statistics Faculty Publications and Presentations

Motivated by the theory of uniform elastic structures we try to determine the conditions for the local flatness of locally integrable connections on non-holonomic frame bundles of order 2. Utilizing the results of Yuen as well as our results for the holonomic case, we show that the locally integrable non-holonomic 2-connection is locally flat if, and only if, its projection to the bundle of linear frames is symmetric and the so-called inhomogeneity tensor vanishes. In the last section of this short paper we show how these results can be interpreted in the framework of the theory of uniformity of simple …

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Mathematical Rebuses, Florentin Smarandache Jan 1996

Mathematical Rebuses, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

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On Functions That Are Trivial Cocycles For A Set Of Irrationals. Ii, Lawrence W. Baggett, Herbert A. Medina, Kathy D. Merrill Jan 1996

On Functions That Are Trivial Cocycles For A Set Of Irrationals. Ii, Lawrence W. Baggett, Herbert A. Medina, Kathy D. Merrill

Mathematics, Statistics and Data Science Faculty Works

Two results are obtained about the topological size of the set of irrationals for which a given function is a trivial cocycle. An example of a continuous function which is a coboundary with non-L(1) cobounding function is constructed.

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An Extension Of The Binomial Theorem With Application To Stability Theory, Z. Zahreddinea Jan 1996

An Extension Of The Binomial Theorem With Application To Stability Theory, Z. Zahreddinea

Turkish Journal of Mathematics

We show how it is possible to put different stability types such as Routh-Hurwitz and Schur-Cohn on common grounds by establishing direct links between them. In the process, we obtain natural and elegant extensions of both Pascal's rule and the binomial theorem, which prove useful in establishing our main results. A M S subject classification: Primary 34D, Secondary 93D.

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The Inverse Nonstationary Scattering Problem For A Hyperbolic System Of Equations On Semi-Axis, N. Sh. Iskenderov, A. Yildiz Jan 1996

The Inverse Nonstationary Scattering Problem For A Hyperbolic System Of Equations On Semi-Axis, N. Sh. Iskenderov, A. Yildiz

Turkish Journal of Mathematics

In this paper, the direct and inverse nonstationary scattering problem for a hyperbolic system of n equations (n>3) on a semi-axis is studied. The coefficients of the system are uniquely determined according to scattering operator. The solution of the problem is generalized for an arbitrary natural number n applying the properties of separation of factors by means of operator transformations to some elements of the scattering operator and its inverse as well as reducing the scattering problem given on a semi-axis to the scattering problem on the whole-axis.

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Some Applications Of Fractional Calculus Operators To A Certain Subclass Of Analytic Functions With Negative Coefficients, Nak Eun Cho, M. K. Aouf Jan 1996

Some Applications Of Fractional Calculus Operators To A Certain Subclass Of Analytic Functions With Negative Coefficients, Nak Eun Cho, M. K. Aouf

Turkish Journal of Mathematics

The object of the present paper is to prove various distortion theorems for the fractional calculus of functions in the class T_{n}\left(\lambda,\alpha\right) consisting of analytic and univalent functions with negative coefficients. Furthermore, a distortion theorem for a fractional integral operator of functions in the class T_{n}\left(\lambda,\alpha\right) is shown.

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A Study Of The Relationship Between Use Of Technology In Math And Higher Test Scores, Mary Ann Grooters Jan 1996

A Study Of The Relationship Between Use Of Technology In Math And Higher Test Scores, Mary Ann Grooters

Masters Theses

This thesis explored the relationship of a technology enhanced curriculum to higher test scores and higher student motivation. This thesis involved two seventh grade math classes in Kentwood, Michigan. A control class received instruction including lectures, written assignments, and projects. The test group received similar assignments and projects and in addition were given technology supported exercises. A survey given to the test group examined motivation levels, and end of chapter tests compared achievement scores of both groups. The findings indicate that a technology enhanced curriculum does not lead to higher test scores but does impact student motivation to learn math.

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