Physical Sciences and Mathematics Commons^™

Tree-Based Multicasting In Wormhole-Routed Irregular Topologies, Ran Libeskind-Hadas, Dominic Mazzoni '99, Ranjith Rajagopalan '99

All HMC Faculty Publications and Research

A deadlock-free tree-based multicast routing algorithm is presented for all direct networks, regardless of interconnection topology. The algorithm delivers a message to any number of destinations using only a single startup phase. In contrast to existing tree-based schemes, this algorithm applies to all interconnection topologies, requires only fixed-sized input buffers that are independent of maximum message length, and uses a single asynchronous flit replication mechanism. The theoretical basis of the technique used here is sufficiently general to develop other tree-based multicasting algorithms for regular and irregular topologies. Simulation results demonstrate that this tree-based algorithm provides a very promising means of …

Cahit Arf's Contribution To Algebraic Number Theory And Related Fields, Masatoshi G. İkeda

Turkish Journal of Mathematics

No abstract provided.

Timelike Ruled Surfaces In The Minkowski 3-Space-Ii, A. Turgut, H. H. Hacisali̇oğlu

Turkish Journal of Mathematics

This paper is devoted to a study of timelike ruled surfaces in three dimensional Minkowski space obtained by a spacelike straight line moving along a timelike curve. The central point, the curve of striction and the distribution parameter of a timelike ruled surface in Minkowski 3-space are considered, and some theorems relating to their structure are obtained. In addition, some results about developable timelike ruled surfaces are also given.

A Berry-Esseen Bound For Empty Boxes Statistic On The Scheme An Allocations Of Several Type Balls, S.A. Mirakhmedov, O. Saidova

Turkish Journal of Mathematics

A Berry-Esseen bound for the number of empty cells in the scheme of independent and random allocation of balls of $s$ type into different cells is obtained.

Weighted Ergodic Averages, M.D. Ha

Turkish Journal of Mathematics

Let $(X, {\cal F}, \lambda)$ be the unit circle $\Bbb S^1 = \{z \in \Bbb C : z = 1\}$ with the usual $\sigma$-algebra ${\cal F}$ of Lebesgue measurable subsets and the normalized Lebesgue measure $\lambda$. Consider a sequence $\nu_n: \Bbb N \ra \Bbb R, \;\; \nu_n(k) \geq 0, \;\; \Sigma^{\infty}_{k=1} \nu_n(k) = 1$. For any measure-preserving $\tau : X \ra X$, this sequence induces a sequence $(T_n)^{\infty}_1$ of bounded, linear operators on $L^p(X), \;\; 1 \leq p \leq \infty$, by defining \[ T_n f = \sum^{\infty}_{k=1} \nu_n(k) \; f \circ \tau^k, \quad n = 1, 2, \ldots . \] …

Generalized Inverse Estimator And Comparison With Least Squares Estimator, S. Sakallıoğlu, F. Akdeniz

Turkish Journal of Mathematics

Trenkler [13] described an iteration estimator. This estimator is defined as follows: for $0 < \gamma < 1/\lambda_i \max$ \[ \hat{\beta}_{m, \gamma} = \gamma \sum^m_{i=0} (1-\gamma X'X)^i X'y , \] where $\lambda_i$ are eigenvalues of $X'X$. In this paper a new estimator (generalized inverse estimator) is introduced based on the results of Tewarson [11]. A sufficient condition for the difference of mean square error matrices of least squares estimator and generalized inverse estimator to be positive definite (p.d.) is derived.

Direct Sums And The Schur Property, Betül Tanbay

Turkish Journal of Mathematics

It is a known fact that $\ell^1$, the dual space of the null sequences $c_0$, has the Schur property, that is, weakly convergent sequences in $\ell^1$ are norm convergent. In this paper, we prove that if $(X_{\alpha})_{\alpha\in I}$ are Banach spaces and $X=(\oplus_{\alpha\in I}X_{\alpha})_1$ their $l_1$-sum, then the space $X$ has the Schur property iff each factor $X_{\alpha}$ has it.

Splitting In Locally Compact Abelian Groups, Peter Loth

Mathematics Faculty Publications

No abstract provided.

Subiecte Posibile Pentru Examenul De Admitere În Liceu Şi Examenul De Capacitate (In Romanian), Florentin Smarandache, Constantin Coanda, Gheorghe Duta

Branch Mathematics and Statistics Faculty and Staff Publications

Prezenta lucrare" încearcă să pună la dispoziţia elevilor şi profesorilor instrumente de evaluare a cunoştinţelor la toate capitolele din actuala programă de matematică. " În evoluţia adolescenţi/or din ţara noastră etapa admiterii în liceu mobilizează eforturi şi emoţii cu totul speciale. 'Actuala lucrare se doreşte a fi un sfljtuitor permanent În perioada fierbinte dintre e.;wmenul de capacitate şi admiterea În liceu. Testele cuprinse in această culegere au un caracter complementar faţă de multe materiale scrise În vederea sprijinirii celor ce se pregătesc pentru astfel de examene şi se referă la intreaga materie cuprinsă În programele analitice de aritmetică, algebră şi …

Positive Solutions For A Concave Semipositone Dirichlet Problem, Alfonso Castro, Ratnasingham Shivaji

All HMC Faculty Publications and Research

No abstract provided for this article

Average-Case Lower Bounds For Noisy Boolean Decision Trees, William Evans, Nicholas Pippenger

All HMC Faculty Publications and Research

We present a new method for deriving lower bounds to the expected number of queries made by noisy decision trees computing Boolean functions. The new method has the feature that expectations are taken with respect to a uniformly distributed random input, as well as with respect to the random noise, thus yielding stronger lower bounds. It also applies to many more functions than do previous results. The method yields a simple proof of the result (previously established by Reischuk and Schmeltz) that almost all Boolean functions of n arguments require $\Me(n \log n)$ queries, and strengthens this bound from the …

A Minmax Principle, Index Of The Critical Point, And Existence Of Sign Changing Solutions To Elliptic Boundary Value Problems, Alfonso Castro, Jorge Cossio, John M. Neuberger

All HMC Faculty Publications and Research

In this article we apply the minmax principle we developed in [6] to obtain sign-changing solutions for superlinear and asymptotically linear Dirichlet problems.

We prove that, when isolated, the local degree of any solution given by this minmax principle is +1. By combining the results of [6] with the degree-theoretic results of Castro and Cossio in [5], in the case where the nonlinearity is asymptotically linear, we provide sufficient conditions for:

i) the existence of at least four solutions (one of which changes sign exactly once),

ii) the existence of at least five solutions (two of which change sign), and …

Convergence Of Random Walks On The Circle Generated By An Irrational Rotation, Francis E. Su

All HMC Faculty Publications and Research

Fix . Consider the random walk on the circle which proceeds by repeatedly rotating points forward or backward, with probability , by an angle . This paper analyzes the rate of convergence of this walk to the uniform distribution under ``discrepancy'' distance. The rate depends on the continued fraction properties of the number . We obtain bounds for rates when is any irrational, and a sharp rate when is a quadratic irrational. In that case the discrepancy falls as (up to constant factors), where is the number of steps in the walk. This is the first example of a sharp …

Newton's Cubic Roots, Lisette G. De Pillis

All HMC Faculty Publications and Research

No abstract included in this article

Cyclic Cutwidth Of Three Dimensional Cubes, Ray N. Gregory

Theses Digitization Project

No abstract provided.

A Study Of Optimization In Hilbert Space, John Awunganyi

Theses Digitization Project

No abstract provided.

State Sum Invariants Of Three Manifolds, Sharon Angela Newman-Gomez

Theses Digitization Project

No abstract provided.

Torus Embedding And Its Applications, Rick Hung Nguyenhuu

Theses Digitization Project

No abstract provided.

Exponential Stability Of A Thermoelastic System With Free Boundary Conditions Without Mechanical Dissipation, George Avalos, Irena Lasiecka

Department of Mathematics: Faculty Publications

We show herein the uniform stability of a thermoelastic plate model with no added dissipative mechanism on the boundary (uniform stability of a thermoelastic plate with added boundary dissipation was shown in [J. Lagnese, Boundary Stabilization of Thin Plates, SIAM Stud. Appl. Math. 10, SIAM, Philadelphia, PA, 1989], as was that of the analytic case---where rotational forces are neglected---in [Z. Liu and S. Z. Heng, Quarterly Appl. Math., 55 (1997), pp. 551-564]). The proof is constructive in the sense that we make use of a multiplier with respect to the coupled system involved so as to generate a fortiori the …

Finite Direct Sums Of (D1)-Modules, Derya Keskin

Turkish Journal of Mathematics

In this paper we give necessary conditions for a finite direct sum of (D1)--modules to be a (D1)--module.

Derivation Of Separable Amplitude Equations By Multiple Scales Method, Mehmet Naci̇ Özer, Dursun Eser

Turkish Journal of Mathematics

The method of multiple scales is used to derive separable nonlinear Schrödinger equations as amplitude equation from three component 2D nonlinear Klein-Gordon Equation. We further discuss the integrability of the derived separable amplitude equations and reduce them into finite dimensional Hamiltonian systems. Finally we give first integrals for the reduced systems.

Exponential Dichotomy And Mild Solutions Of Nonautonomous Equations In Banach Spaces, Y. Latushkin, Timothy W. Randolph, R. Schnaubelt

Mathematics and Statistics Faculty Research & Creative Works

We prove that the exponential dichotomy of a strongly continuous evolution family on a Banach space is equivalent to the existence and uniqueness of continuous bounded mild solutions of the corresponding inhomogeneous equation. This result addresses nonautonomous abstract Cauchy problems with unbounded coefficients. The technique used involves evolution semigroups. Some applications are given to evolution families on scales of Banach spaces arising in center manifolds theory. © 1998 Plenum Publishing Corporation.

Some Harmonic N-Slit Mappings, Michael Dorff

Mathematics and Statistics Faculty Research & Creative Works

The class SH consists of univalent, harmonic, and sense-preserving functions f in the unit disk, Δ, such that f = h+ḡ where h(z) = z + ∑2∞ akzk g(z) = ∑1∞ bkzk. SHO will denote the subclass with b1 = 0. We present a collection of n-slit mappings (n ≥ 2) and prove that the 2-slit mappings are in SH while for n ≥ 3 the mappings are in SHO. Finally, we show that these mappings establish the sharpness of a previous theorem by Clunie and Sheil-Small while disproving a conjecture about the inner mapping radius. ©1998 American Mathematical Society.

Endomorphism Rings And Automorphism Groups Of Separable Torsion-Free Modules Over Valuation Domains, Brendan Goldsmith, P. Zanardo

Book chapter/book

No abstract provided.

Isomorphic Automorphism Groups Of Torsion-Free P-Adic Modules, Brendan Goldsmith, A. L. S. Corner

Book chapter/book

No abstract provided.

Cess-Modules, Cesim Çelik

Turkish Journal of Mathematics

In this paper, we investigate generalizations of CS-modules, namely CESS-modules, weak CS-modules and modules satisfying a condition (P). Several results are given to show the relationships between the classes of these modules.

About Some Classical Functional Equations, Nicolae Neamtu

Turkish Journal of Mathematics

The purpose of this paper is to give a new method of finding the solution of Lobashevsky's functional equation and those of other classical functional equations. At the beginning we present the properties of solution $f, \; f \neq 0$, of Lobachevsky's functional equation. Using only the boundedness property on $(-r, r)$, we deduce the continuity, convexity and differentiability properties of the solution.

A Version Of A Theorem Of Dahlberg For The Subelliptic Dirichlet Problem, Luca Capogna, Nicola Garofalo, Duy Minh Nhieu

Mathematics Sciences: Faculty Publications

No abstract provided.

The Eigenfunctions Of A Certain Composition Operator, Valentin Matache

Mathematics Faculty Publications

The composition operator on the classical Hardy space H2, induced by a hyperbolic disk automorphism is considered. It is investigated when a H2-function induces under the given operator a minimal invariant cyclic subspace. Theorems where we use the behaviour of this function in the neighbourhood of the fixed points of the hyperbolic automorphism in order to decide if the cyclic subspace mentioned above is minimal invariant or not, are obtained. The inner eigenfunctions of the operator under consideration are characterized.

Counting Cards: Combinatorics, Group Theory, And Probability In War, Angela J. Chappell

Honors Theses, 1963-2015

My project involved taking a look at the card game War, searching for patterns which develop in the game, and then looking for Mathematical explanations for those patterns. The project began when my advisor, Professor Marc Brodie, was playing War with his children and began to notice patterns and ask questions about them. The questions I set out to answer were: What is the probability of playing a game of war in which a loop develops? If we know the size of the deck we are using, can we determine what loop lengths are possible? How are cards cycling between …