Physical Sciences and Mathematics Commons^™

On The Linearity Of Certain Mapping Class Groups, Mustafa Korkmaz

Turkish Journal of Mathematics

S. Bigelow proved that the braid groups are linear. That is, there is a faithful representation of the braid group into the general linear group of some field. Using this, we deduce from previously known results that the mapping class group of a sphere with punctures and hyperelliptic mapping class groups are linear. In particular, the mapping class group of a closed orientable surface of genus $2$ is linear.

[Introduction To] Schaum's Outline Programming With C++, John R. Hubbard

Bookshelf

Tough Test Questions? Missed Lectures? Not Enough Time?

Fortunately for you, there's Schaum's Outlines. More than 40 million students have trusted Schaum's to help them succeed in the classroom and on exams. Schaum's is the key to faster learning and higher grades in every subject. Each Outline presents all the essential course information in an easy-to-follow, topic-by-topic format. You also get hundreds of examples, solved problems, and practice exercises to test your skills.

This Schaum's Outline gives you

• Practice problems with full explanations that reinforce knowledge
• Coverage of the most up-to-date developments in your course field
• In-depth review of practices …

[Introduction To] The Backward Shift On The Hardy Space, William T. Ross, Joseph A. Cima

Bookshelf

Shift operators on Hilbert spaces of analytic functions play an important role in the study of bounded linear operators on Hilbert spaces since they often serve as models for various classes of linear operators. For example, "parts" of direct sums of the backward shift operator on the classical Hardy space H2 model certain types of contraction operators and potentially have connections to understanding the invariant subspaces of a general linear operator.

This book is a thorough treatment of the characterization of the backward shift invariant subspaces of the well-known Hardy spaces Hp. The characterization of the backward shift …

Procedural Support For Cooperative Negotiations: Theoretical Design And Practical Implementation, Matthias G. Raith, Francis Su

All HMC Faculty Publications and Research

We discuss the theoretical design of algorithms for solving distributional conflicts within groups. We consider an algorithm to be procedural if the implementation of the outcome requires the participation of the players, or if it can even be conducted by the players themselves without computational assistance. We compare two procedures for multilateral problems of fair division; both establish envy-freeness, given the possibility of monetary compensations between players.

Review: Cake-Cutting Algorithms: Be Fair If You Can, Francis E. Su

All HMC Faculty Publications and Research

No abstract provided in this article.

A Leveque-Type Lower Bound For Discrepancy, Francis E. Su

All HMC Faculty Publications and Research

A sharp lower bound for discrepancy on R / Z is derived that resembles the upper bound due to LeVeque. An analogous bound is proved for discrepancy on R^k / Z^k. These are discussed in the more general context of the discrepancy of probablity measures. As applications, the bounds are applied to Kronecker sequences and to a random walk on the torus.

Translation Theorems For Fourier-Feynman Transforms And Conditional Fourier-Feynman Transforms, Seung Jun Change, Chull Park, David Skough

Department of Mathematics: Faculty Publications

Translation theorems for Wiener integrals were given by Cameron and Martin in [3] and by Cameron and Graves in [2]. Translation theorems for analytic Feynman integrals were given by Cameron and Storvick in [4], [7] and translation theorems for Feynman integrals on abstract Wiener and Hilbert spaces were given by Chung and Kang in [12].

Collected Papers Vol. Iii, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

Algebra În Exercijii Şi Probleme Pentru Liceu, Florentin Smarandache, Ion Goian, Raisa Grigor, Vasila Marin

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

A Look At Biseparating Maps From An Algebraic Point Of View, Melvin Henriksen, Frank A. Smith

All HMC Faculty Publications and Research

In [ABN], Araujo, Beckenstein, and Narici add the capstone to a series of papers by several groups of authors by showing that if ρ is a biseparating map between two algebras of all real or complex-valued functions on realcompact spaces, then it is a continuous multiple of an isomorphism between these rings. Their proof uses relatively powerful analytic and topological techniques. In what follows, the extent to which such a result can be generalized to a wider class of algebras using algebraic techniques is investigated. We are unable, however to obtain the main result of [ABN] using these techniques.

When Is |C(X X Y)| = |C(X)||C(Y)|?, O. T. Alas, W. W. Comfort, S. Garcia-Ferreira, Melvin Henriksen, R. G. Wilson, R. G. Woods

All HMC Faculty Publications and Research

Sufficient conditions on the Tychonoff spaces X and Y are found that imply that the equation in the title holds. Sufficient conditions on the Tychonoff space X are found that ensure that the equation holds for every Tychonoff space Y . A series of examples (some using rather sophisticated cardinal arithmetic) are given that witness that these results cannot be generalized much.

Steiner Systems Of The Mathieu Group M₁₂, Kristin Marie Dillard

Theses Digitization Project

A Steiner system T with parameters (5,6,12) is a collection of 6-element sets, called hexads, of a 12-element set [omega], such that any 5 of the 12 elements belong to exactly one hexad. In this project we construct a graph whose vertices are the orbits of S₁₂ on T x T, where T is the set of all Steiner systems S(5,6,12). Two vertices are joined if an orbit is taken into another under the action of a transposition. The number of hexads common to two Steiner systems are also given. We also prove that any two Steiner systems with parameters …

Boundary Controllability Of Thermoelastic Plates Via The Free Boundary Conditions, George Avalos, Irena Lasiecka

Department of Mathematics: Faculty Publications

Controllability properties of a partial differential equation (PDE) model describing a thermoelastic plate are studied. The PDE is composed of a Kirchoff plate equation coupled to a heat equation on a bounded domain, with the coupling taking place on the interior and boundary of the domain. The coupling in this PDE is parameterized by α > 0. Boundary control is exerted through the (two) free boundary conditions of the plate equation and through the Robin boundary condition of the temperature. These controls have the physical interpretation of inserted forces and moments and prescribed temperature, respectively, all of which act on the …

Estimation Of A Monotone Mean Residual Life, Subhash C. Kochar, Hari Mukerjee, Francisco J. Samaniego

Mathematics and Statistics Faculty Publications and Presentations

In survival analysis and in the analysis of life tables an important biometric function of interest is the life expectancy at age x,M(x), defined by M(x)=E[X?x|X>x], where X is a lifetime. M is called the mean residual life function. In many applications it is reasonable to assume that M is decreasing (DMRL) or increasing (IMRL); we write decreasing (increasing) for nonincreasing (non-decreasing). There is some literature on empirical estimators of M and their properties. Although tests for a monotone M are discussed in the literature, we are not aware of any estimators of M under these order restrictions. In …

Multigrid For The Mortar Finite Element Method, Jay Gopalakrishnan, Joseph E. Pasciak

Mathematics and Statistics Faculty Publications and Presentations

A multigrid technique for uniformly preconditioning linear systems arising from a mortar finite element discretization of second order elliptic boundary value problems is described and analyzed. These problems are posed on domains partitioned into subdomains, each of which is independently triangulated in a multilevel fashion. The multilevel mortar finite element spaces based on such triangulations (which need not align across subdomain interfaces) are in general not nested. Suitable grid transfer operators and smoothers are developed which lead to a variable Vcycle preconditioner resulting in a uniformly preconditioned algebraic system. Computational results illustrating the theory are also presented.

A Primer For Applying Service Learning To Computer Science, Pete Sanderson, Kenneth Vollmar

Mathematics Faculty Scholarship

Service learning is an educational philosophy that promotes active learning through community service. We have recently applied this approach in our computer science curriculum, specifically to our software engineering course. In order that other computer science departments can benefit from our experience, we have developed a primer one can follow to establish a program for service learning in the computer sciences. We also describe and assess our experience after one year of applying service learning to software engineering.

Intrinsic Equations For A Relaxed Elastic Line On An Oriented Hypersurface In The Minkowski Space R^N_1, Nevi̇n Gürbüz, Ali̇ Görgülü

Turkish Journal of Mathematics

We gived the intrinsic equations for a relaxed elastic line on an oriented surface in ${\Bbb {R}}_1^3$ ([1],[2]). In this paper, we derived the intrinsic equations for a relaxed elastic line on an oriented time-like hypersurface and space-like hypersurface in the Minkowski space ${\Bbb {R}}_1^n$ and gived additional results about relaxed elastic lines on various timelike and spacelike hypersurface in the Minkowski space ${\Bbb {R}}_1^n$.

A Simple Vaccination Model With Multiple Endemic States, Christopher Kribs, Jorge X. Velasco-Hernandez

Mathematics Faculty Publications

A simple two-dimensional SIS model with vaccination exhibits a backward bifurcation for some parameter values. A two-population version of the model leads to the consideration of vaccination policies in paired border towns. The results of our mathematical analysis indicate that a vaccination campaign φ meant to reduce a disease's reproduction number R(φ) below one may fail to control the disease. If the aim is to prevent an epidemic outbreak, a large initial number of infective persons can cause a high endemicity level to arise rather suddenly even if the vaccine-reduced reproduction number is below threshold. If the aim is to …

Non-Euclidean Geometry, Skyler W. Ross

Electronic Theses and Dissertations

In this country, the typical high school graduate has had at least some exposure to Euclidean geometry, but most lay-people are not aware that any other geometries exist. In this paper we provide an overview of the basics of hyperbolic geometry, one of many Non-Euclidean geometries, that should be accessible to anyone whose mathematical background includes geometry, trigonometry, and the calculus. We will begin with a brief history of geometry and the two hundred years of uncertainty about the independence of Euclid's fifth postulate, the resolution of which led to the development of several Non-Euclidean geometries. After an axiomatic development …

State-Based Reconstructability Modeling For Decision Analysis, Michael S. Johnson, Martin Zwick

Systems Science Faculty Publications and Presentations

Reconstructability analysis (RA) is a method for detecting and analyzing the structure of multivariate categorical data. Jones and his colleagues extended the original variable-based formulation of RA to encompass models defined in terms of system states (Jones 1982; Jones 1985; Jones 1985; Jones 1986; Jones 1989). In this paper, we demonstrate that Jones’ previous work comprises two separable ideas: the “g to k” transformation and state-based modeling. We relate the concept of state-based modeling to established variable-based RA methods (Klir 1985; Krippendorff 1986), and demonstrate that statebased modeling, when applied to event and decision tree models, is a valuable adjunct …

Rotary Honing: A Variant Of The Taylor Paint-Scraper Problem, Christopher Hills, H. Moffatt

Articles

The three-dimensional Row in a corner of fixed angle α induced by the rotation in its plane of one of the boundaries is considered. A local similarity solution valid in a neighbourhood of the centre of rotation is obtained and the streamlines are shown to be closed curves. The effects of inertia are considered and are shown to be significant in a small neighbourhood of the plane of symmetry of the flow. A simple experiment confirms that the streamlines are indeed nearly closed; their projections on planes normal to the line of intersection of the boundaries are precisely the 'Taylor' …

A Brief Biography Of Professor L.C. Hsu (Lizhi Xu), Tian-Xiao He

Scholarship

No abstract provided.

Asymptotic Behavior Of The Zero Solutions To Generalized Pipe And Rotating Shaft Equations, Ayfer Kurt

Turkish Journal of Mathematics

A non-autonomous partial differential equation describing the dynamics of a uniform pipe and a system describing the dynamics of a rotating shaft are considered.Sufficient conditions for the global asymptotic stability of the zero solution of the boundary value problem for the differential equation and the system under consideration are established by using the Lyapunov function technique.

Efficient Presentations For Some Direct Products Of Groups, Bi̇lal Vatansever, David M. Gill

Turkish Journal of Mathematics

In this paper we give efficient presentations for $A_4\times D_n$, where n is odd number, or n is even number and (n,3)=1. We also give efficient presentations for $A_5\times D_n$ where n is an even or odd number.

Zeros Of \Zeta^{''}(S) & \Zeta^{'''}(S) In \Sigma< 1/2, Cem Yalçin Yildirim

Turkish Journal of Mathematics

There is only one pair of non-real zeros of $\zeta^{''}(s)$, and of $\zeta^{'''}(s)$, in the left half-plane. The Riemann Hypothesis implies that $\zeta''(s)$ and $\zeta'''(s)$ have no zeros in the strip $0 \leq \Re\,s < {1\over 2} $.

Some Results On Derivation Groups, Murat Alp

Turkish Journal of Mathematics

In this paper we describe a share package XMOD of functions for computing with finite, permutation crossed modules, their morphisms and derivations; cat$^1$-groups, their morphisms and their sections, written using the GAP \cite{GAP} group theory programming language. We also give some mathematical results for derivations. These results are suggested by the output produced by the XMOD package.

A Generalized Trapezoid Inequality For Functions Of Bounded Variation, P. Cerone, S. S. Dragomir, C. E. M. Pearce

Turkish Journal of Mathematics

We establish a generalization of a recent trapezoid inequality for functions of bounded variation. A number of special cases are considered. Applications are made to quadrature formulae, probability theory, special means and the estimation of the beta function.

Some Commutativity Results For S -Unital Rings, Moharram A. Khan

Turkish Journal of Mathematics

In the present paper, it is shown that if $R$ is a left ( resp. right) $s$-unital ring satisfying $[f(y^mx^ry^s) \pm x^ty, x] = 0$ (resp. $[f(y^mx^ry^s) \pm yx^t, x] = 0),$ where $m, r, s, t$ are fixed non-negative integers and $f(\lambda)$ is a polynomial in ${\lambda}^2{\bf Z}[\lambda],$ then $R$ is commutative. Commutativity of $R$ has also been investigated under different sets of constraints on integral exponents.

Some Graph Type Hypersurfaces In A Semi-Euclidean Space, Ikawa Toshihiko, Honda Kyoko

Turkish Journal of Mathematics

We consider some graph type hypersurfaces in a semi-Euclidean space $\Bbb R^{n+1}_{q}$ and give conditions of the dimension $n+1$ and the index $q$ when a hypersurface is lightlike, totally geodesic and minimal.

Conjugacy Classes Of Elliptic Elements In The Picard Group, Ni̇hal Yilmaz, İsmai̇l Naci̇ Cangül

Turkish Journal of Mathematics

The Picard group $\mathbf{P}$ is a discrete subgroup of $PSL(2,\Bbb{C})$ with Gaussian integer coefficients. Here it is shown that the total number of conjugacy classes of elliptic elements of order 2 and 3 in $\mathbf{P}$, which is given as seven by B. Fine $\left[ 3\right] $, can actually be reduced to four and using this, the conditions for the maximal Fuchsian subgroups of $\mathbf{P}$ to have elliptic elements of orders 2 and 3 are found.