Physical Sciences and Mathematics Commons^™

Mixed Sublinear, Superlinear, And Singular Systems Of Functional Differential Equations, William Trench

William F. Trench

No abstract provided.

On Conformal Scalar Curvature Equations In Rn, Yi Li, Wei-Ming Ni

Yi Li

No abstract provided.

On Conformal Scalar Curvature Equations In Rn, Yi Li, Wei-Ming Ni

Mathematics and Statistics Faculty Publications

No abstract provided.

On A Duality Principle In Processes Of Servicing Machines With Double Control, Jewgeni H. Dshalalow

Mathematics and System Engineering Faculty Publications

This paper examines a doubly controlled process of servicing machines. The classical system treated by Takács is equipped with m+1 unreliable machines served by one repairman. In the present modification of this model, the failure rates and the repair time may be controlled with respect to the state of the system. The process describing the number of intact machines is considered. To derive its steady state distribution in the form of a simple explicit formula, the author introduces an auxiliary model with m unreliable machines and a single repairman who keeps working even when all machines are intact. This result …

De Re And De Dicto, Thomas Jager

University Faculty Publications and Creative Works

No abstract provided.

Periodic Solutions Of Volterra Integral Equations, Muhammad Islam

Mathematics Faculty Publications

Consider the system of equations

x(t)=f(t)+∫−∞tk(t,s)x(s)ds,           (1)

and

x(t)=f(t)+∫−∞tk(t,s)g(s,x(s))ds.        (2)

Existence of continuous periodic solutions of (1) is shown using the resolvent function of the kernel k. Some important properties of the resolvent function including its uniqueness are obtained in the process. In obtaining periodic solutions of (1) it is necessary that the resolvent of k is integrable in some sense. For a scalar convolution kernel k some explicit conditions are derived to determine whether or not the resolvent of k is integrable. Finally, the existence and uniqueness of continuous periodic solutions of (1) and (2) are obtained using the …

Fault Tolerance In Networks Of Bounded Degree, Cynthia Dwork, David Peleg, Nicholas Pippenger, Eli Upfal

All HMC Faculty Publications and Research

Achieving processor cooperation in the presence of faults is a major problem in distributed systems. Popular paradigms such as Byzantine agreement have been studied principally in the context of a complete network. Indeed, Dolev [J. Algorithms, 3 (1982), pp. 14–30] and Hadzilacos [Issues of Fault Tolerance in Concurrent Computations, Ph.D. thesis, Harvard University, Cambridge, MA, 1984] have shown that Ω(t) connectivity is necessary if the requirement is that all nonfaulty processors decide unanimously, where t is the number of faults to be tolerated. We believe that in forseeable technologies the number of faults will grow with the size of the …

Nonnegative Solutions For A Class Of Nonpositone Problems, Alfonso Castro, Ratnasingham Shivaji

All HMC Faculty Publications and Research

In the recent past many results have been established on non-negative solutions to boundary value problems of the form

-u''(x) = λf(u(x)); 0 < x < 1,

u(0) = 0 = u(1)

where λ>0, f(0)>0 (positone problems). In this paper we consider the impact on the non-negative solutions when f(0)<0. We find that we need f(u) to be convex to guarantee uniqueness of positive solutions, and f(u) to be appropriately concave for multiple positive solutions. This is in contrast to the case of positone problems, where the roles of convexity and concavity were interchanged to obtain similar results. We further establish the existence of non-negative solutions with interior zeros, which did not exist in positone problems.

Wide-Sense Nonblocking Networks, Paul Feldman, Joel Friedman, Nicholas Pippenger

All HMC Faculty Publications and Research

A new method for constructing wide-sense nonblocking networks is presented. Application of this method yields (among other things) wide-sense nonblocking generalized connectors with n inputs and outputs and size O( n log n ), and with depth k and size O( n^{1 + 1/k} ( log n )^{1 - 1/k} ).

Reliable Computation By Formulas In The Presence Of Noise, Nicholas Pippenger

All HMC Faculty Publications and Research

It is shown that if formulas are used to compute Boolean functions in the presence of randomly occurring failures then: (1) there is a limit strictly less than 1/2 to the failure probability per gate that can be tolerated, and (2) formulas that tolerate failures must be deeper (and, therefore, compute more slowly) than those that do not. The heart of the proof is an information-theoretic argument that deals with computation and errors in very general terms. The strength of this argument is that it applies with equal ease no matter what types of gate are available. Its weaknesses is …

Finite Dimensional Complement Theorems: Examples And Results, R. B. Sher, Gerard A. Venema

University Faculty Publications and Creative Works

Examples are given which show the necessity of various hypotheses in the known finite dimensional complement theorems. In addition, several positive results are presented which improve one direction of such theorems.

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.

Equations Of Variation For Ordinary Differential Equations On Manifolds, J. B. Bennett

Journal of the Arkansas Academy of Science

No abstract provided.

Dredging Management: A Comparative Analysis Of Mid-Sized U.S. North Atlantic Ports, Matthew H. Masters

Marine Affairs Theses and Major Papers

Dredging management within the states of Rhode Island, Maine and Connecticut is examined through an analysis of the ports of Providence, Portland, and New Haven. These ports were selected from a field of 30 Atlantic Coast ports through a multivariate statistical analysis, based on similarities in size, function and geography. Each port's dredging history was compiled to illustrate the frequency and magnitude of dredging activity among the three states. Pertinent state laws, regulations and policies regarding dredging and dredged material disposal were reviewed in an attempt to identify similarities and differences. It was believed that differences among each state's regulatory …

The Relationship Between Perceptions Of Gentrification And Waterfront Revitalization Policies, Noreen Merainer

Marine Affairs Theses and Major Papers

This thesis examines the waterfront revitalization experience in Jersey City, N.J. In particular, the issue of gentrification, as perceived by the city administration, was examined to determine its impact on current city policies. A direct relationship between perceptions of gentrification and waterfront revitalization policies is suggested based on data obtained from detailed interviews and city documents.

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 …

Test Generation By Fault Sampling, Vishwani Agrawal, Hassan Farhat, Sharad C. Seth

Mathematics Faculty Publications

This paper presents a novel technique of generating tests from a random sample of faults. The entire fault population of the circuit is randomly divided into two groups. Only one group, usually the smaller one, is used for test generation by the test-generator and fault-simulator programs. This group is known as the sample and its coverage is deterministic. The coverage of faults in the remaining group is similar to that of random vectors and is estimated from the distribution of fault detection probabilities in the circuit. As the sample size increases, the fraction of unsampled faults reduces. At the same …

Involutions On Banach Spaces And Reflexivity, S J. Dilworth

Faculty Publications

No abstract provided.

Supercomputer, Simulation Of Liquid Drop Formation, Fall, And Collision, Donald Greenspan

Mathematics Technical Papers

A generic molecular type model of liquid drops is developed and studied. Drop formation, fall, and collision are simulated on a CRAY X-MP/24 and associated modes of oscillation are described. Methods for application to particular fluids with known Lennard-Jones parameters are given.

Covariant Computation In Special Relativistic Dynamics, Donald Greenspan

Mathematics Technical Papers

The motion of a particle in a special relativistic framework is studied numerically. Difference equations which are covariant are developed first. It is then shown how computations can be done in both the lab and rocket frames so that the numerical results are related by the Lorentz transformation. Finally, assuming the usual force formula for harmonic oscillation, it is shown that the dynamical equation is necessarily nonlinear and trajectories are studied numerically for various initial data.

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 …

Quasilinear Evolution Equations In Nonclassical Diffusion, Kenneth Kuttler, Elias Aifantis

Faculty Publications

After describing the motivation leading to some nonclassical diffusion equations, we formulate a general abstract nonlinear evolution equation and establish existence of solutions. Then we return to the original equation and discuss particular initial-boundary value problems.

Essentially Indecomposable Modules Which Are Almost Free, Brendan Goldsmith, R. Gobel

Articles

No abstract provided

A Note On Coslender Groups, R. Dimitric, Brendan Goldsmith

Articles

The notion of a coslender group has been introduced previously by the first author. This work continues the investigation of such groups, defines coslender part of a group, proves embeddability results, gives a characterization of finite rank coslender grops, and proves a result on smooth ascending chains of coslender groups with a conjecture that every countable coslender torsion free group is a smooth ascending union of finite rank coslender pure subgroups.

Interpolation Of Besov-Spaces, Ronald A. Devore, Vasil A. Popova

Faculty Publications

We investigate Besov spaces and their connection with dyadic spline approximation in Lp(Omega), 0 < p (less than or equal to) infinity. Our main results are: the determination of the interpolation spaces between a pair of Besov spaces; an atomic decomposition for functions in a Besov space; the characterization of the class of functions which have certain prescribed degree of approximation by dyadic splines.

Particle Simulation Of Biological Sorting On A Supercomputer, Donald Greenspan

Mathematics Technical Papers

Cell sorting, or, self reorganization, is modelled by means of particles which obey classical molecular dynamical equations. A system of N second order, nonlinear, ordinary differential equations results when the number of particles is N. Applications and examples are described and discussed, with N > 1000, for both double layer and triple layer self reorganization.

Conservative Difference Formulations Of Calogero And Toda Hamiltonian Systems, Donald Greenspan

Mathematics Technical Papers

Calogero and Toda Hamiltonian systems are reformulated using only differences. The formulations prove to have the same fundamental invariants as the continuous systems and, in addition, are readily implementable on modern digital computers.

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.

A Mathematical Model Of Tumor Growth By Diffusion, John A. Adam

Mathematics & Statistics Faculty Publications

A diffusion model of the prevascular stage of tumor growth is presented. The basic feature of such a model is the diffusion of growth inhibitor, which is produced at a spatially non-uniform rate within the tissue. Regimes of limited and unlimited tissue growth are determined, and the consistency of this and simpler models is discussed in the light of observational results.

On A General Class Of Multivariate Linear Smoothing Operators, Tian-Xiao He

Tian-Xiao He

No abstract provided.