Mathematics Commons^™

Identifying Almost Invariant Sets In Stochastic Dynamical Systems, Lora Billings, Ira Schwartz

Department of Mathematics Faculty Scholarship and Creative Works

We consider the approximation of fluctuation induced almost invariant sets arising from stochastic dynamical systems. The dynamical evolution of densities is derived from the stochastic Frobenius– Perron operator. Given a stochastic kernel with a known distribution, approximate almost invariant sets are found by translating the problem into an eigenvalue problem derived from reversible Markov processes. Analytic and computational examples of the methods are used to illustrate the technique, and are shown to reveal the probability transport between almost invariant sets in nonlinear stochastic systems. Both small and large noise cases are considered. © 2008 American Institute of Physics.

Frobenius Number, Covering Radius, And Well-Rounded Lattices, Lenny Fukshansky, Sinai Robins

CMC Faculty Publications and Research

Lecture given at the Joint Mathematics Meeting in San Diego, January 2008.

Characterization Of Digraphs With Equal Domination Graphs And Underlying Graphs, Kim A. S. Factor, Larry L. Langley

College of the Pacific Faculty Articles

A domination graph of a digraph D, dom(D), is created using the vertex set of D and edge {u,v}∈E[dom(D)] whenever (u,z)∈A(D) or (v,z)∈A(D) for every other vertex z∈V(D). The underlying graph of a digraph D, UG(D), is the graph for which D is a biorientation. We completely characterize digraphs whose underlying graphs are identical to their domination graphs, UG(D)=dom(D). The maximum and minimum number of single arcs in these digraphs, and their characteristics, is given.

Illustrating The Use Of The Nine Chapters In The Classroom, Joel K. Haack

Faculty Work

No abstract provided.

Optimal Control Of Delay-Differential Inclusions With Multivalued Initial Conditions In Infinite Dimensions, Boris S. Mordukhovich, Dong Wang, Lianwen Wang

Mathematics Research Reports

This paper is devoted to the study of a general class of optimal control problems described by delay-differential inclusions with infinite-dimensional state spaces, endpoints constraints, and multivalued initial conditions. To the best of our knowledge, problems of this type have not been considered in the literature, except some particular cases when either the state space is finite-dimensional or there is no delay in the dynamics. We develop the method of discrete approximations to derive necessary optimality conditions in the extended Euler-Lagrange form by using advanced tools of variational analysis and generalized differentiation in infinite dimensions. This method consists of the …

Highly Connected Multicoloured Subgraphs Of Multicoloured Graphs, H. Liu, R. Morris, N. Prince

Faculty Publications & Research

Suppose the edges of the complete graph on n vertices, E(Kn), are coloured using r colours; how large a k-connected subgraph are we guaranteed to find, which uses only at most s of the colours? This question is due to Bollobás, and the case s=1 was considered in Liu et al. [Highly connected monochromatic subgraphs of multicoloured graphs, J. Graph Theory, to appear]. Here we shall consider the case s is greater than or equal to 2, proving in particular that when s=2 and r+1 is a power of 2 then the answer lies between 4n/(r+1)-17kr(r+2k+1) and 4n/(r+1)+4 and that …

Lectures On Computational Numerical Analysis Of Partial Differential Equations, James M. Mcdonough

Mechanical Engineering Textbook Gallery

From Chapter 1:

The purpose of these lectures is to present a set of straightforward numerical methods with applicability to essentially any problem associated with a partial differential equation (PDE) or system of PDEs independent of type, spatial dimension or form of nonlinearity.

Dynamic Web Tools For Trigonometry, Steven J. Wilson

Innovations in Math Technology

In the last 20 years, computer technology having mathematical capability has been developed, improved, and become widely available, but textbook presentations are still largely free of any discussion that might require technology. Technology could be used in mathematical instruction for student drill and practice, for instructor demonstrations that promote conceptual understanding, or for the exploration of mathematical ideas, but software is often designed to be pedagogically generic, leaving its use to the creativity of the instructor. Technological solutions for local machines can be quite extensive, but cost and time constraints then limit availability for student use. The internet has the …

K-Dependence And Domination In Kings Graphs., Eugen J. Ionascu

Faculty Bibliography

No abstract provided.

The Probability Of Winning A High School Football Game., Jennifer Brown

Faculty Bibliography

No abstract provided.

Twin Problems On Non-Periodic Functions, Eugen J. Ionascu

Faculty Bibliography

No abstract provided.

A Classification Of Certain Maximal Subgroups Of Alternating Groups, Bret Benesh

Mathematics Faculty Publications

This paper addresses and extension of Problem 12.82 of the Kourovka notebook, which asks for all ordered pairs (n,m) such that the symmetric groups S_n embeds in S_m as a maximal subgroup. Problem 12.82 was answered in a previous paper by the author and Benjamin Newton. In this paper, we will consider the extension problem where we allow either or both of the groups from the ordered pair to be an alternating group.

On Powers Associated With Sierpiński Numbers, Riesel Numbers And Polignac's Conjecture, Mark Kozek, Michael Filaseta, Carrie Finch

Mathematics

We address conjectures of P. Erdős and conjectures of Y.-G. Chen concerning the numbers in the title. We obtain a variety of related results, including a new smallest positive integer that is simultaneously a Sierpiński number and a Riesel number and a proof that for every positive integer r, there is an integer k such that the numbers k,k2, k3,...,kr are simultaneously Sierpiński numbers.

Property Of Kelley For The Cartesian Products And Hyperspaces, W. J. Charatonik, J. J. Charatonik

Mathematics and Statistics Faculty Research & Creative Works

A continuum X having the property of Kelley is constructed such that neither X × [0, 1], nor the hyperspace C(X), nor small Whitney levels in C(X) have the property of Kelley. This answers several questions asked in the literature.

Iterated Oscillation Criteria For Delay Dynamic Equations Of First Order, B. Karpuz, O. Öcalan, Martin Bohner

Mathematics and Statistics Faculty Research & Creative Works

We obtain new sufficient conditions for the oscillation of all solutions of first-order delay dynamic equations on arbitrary time scales, hence combining and extending results for corresponding differential and difference equations. Examples, some of which coincide with well-known results on particular time scales, are provided to illustrate the applicability of our results.

The Dublin Institute Of Technology And University Status: A Case Study Of The Application By Dit For Designation As A University (1996-99), Colm Garvey

Other resources

Section 9 of the Universities Act 1997 set out, for the first time, a statutory mechanism for the establishment of a new university in Ireland. The Dublin Institute of Technology (DIT) was the first institution to be granted a review under this legislation. This thesis presents an account and analysis of how the application for university title was handled by an international review group, by the Higher Education Authority (HEA) and by the Irish Government. This case study is based on access to files held by the HEA and on interviews with some of the leading players in the Review …

A Characterization Of All Equilateral Triangles In Z³, Eugen J. Ionascu

Faculty Bibliography

This paper is a continuation of the work started by the second author in a series of papers. We extend to the general case the characterization previously found for those equilateral triangles in R3 whose vertices have integer coordinates. In this earlier work, we made use of the hypothesis that (a, b, c) is a non-degenerate primitive solution of a2 +b2 +c2 = 3d2. This condition is now eliminated. Although degenerate solutions present less interest as a result, we state a conjecture which gives a characterization for the existence of such solutions. An approximate extrapolation formula for the sequence ET(n) …

Counting All Equilateral Triangles In {0, 1, …, N}³, Eugen J. Ionascu

Faculty Bibliography

Abstract. We describe a procedure of counting all equilateral triangles in the three dimensional space whose coordinates are allowed only in the set {0, 1, ..., n}. This sequence is denoted here by ET(n) and it has the entry A102698 in “The On-Line Encyclopedia of Integer Sequences”. The procedure is implemented in Maple and its main idea is based on the results in [3]. Using this we calculated the values ET(n) for n = 1 . . . 55 extending previous calculations known for n ≤ 34. Some facts and conjectures about this sequence are stated. The main conjecture raised …

Non-Preemptive Shunting In M/M/1 And Dynamic Service Queueing Systems, Steven Lacek

Theses, Dissertations and Capstones

We provide a study of two queueing systems, namely, an M/M/1 queueing system in which an incoming customer shunts, or skips line, and a dynamic server in an infinite capacity system moving among service nodes. In the former, we explore various aspects of the system, including waiting time, and the relationships between shunting and position in queue and rate of service. Through use of global balance equations, we find the probability that an arriving non-priority customer, finding customers waiting in the system, will shunt to a position other than behind the queue. In the latter, we explore a system in …

A Study Of Present Value Maximization For The Monopolist Problem In Time Scales, Keshav Prasad Pokhrel

Theses, Dissertations and Capstones

There are some mathematical characters in the abstract that will not transfer. Refer to the download to read full abstract.

General results for time scales with right dense points are established. A study of issues that arise when unifying (C) and (D) is included in the analysis

Elliptic Complexes And Generalized Poincaré Inequalities, Derek Gustafson

Mathematics - All Scholarship

We study first order differential operators with constant coefficients. The main question is under what conditions a generalized Poincar\'e inequality holds. We show that the constant rank condition is sufficient. The concept of the Moore-Penrose generalized inverse of a matrix comes into play.

Review: Lie Structure In Semiprime Superalgebras With Superinvolution, Gizem Karaali

Pomona Faculty Publications and Research

No abstract provided.

Number Fields Ramified At One Prime, John W. Jones, David P. Roberts

Mathematics Publications

For G a finite group and p a prime, a G-p field is a Galois number field K with Gal(K/Q)≅G and disc(K)=±p^a for some a. We study the existence of G-p fields for fixed G and varying p.

Intersection Numbers Of Heegner Divisors On Shimura Curves, Kevin Keating, David P. Roberts

Mathematics Publications

In foundational papers, Gross, Zagier, and Kohnen established two formulas for arithmetic intersection numbers of certain Heegner divisors on integral models of modular curves. In [GZ1], only one imaginary quadratic discriminant plays a role. In [GZ2] and [GKZ], two quadratic discriminants play a role. In this paper we generalize the two-discriminant formula from the modular curves X₀(N) to certain Shimura curves defined over Q. Our intersection formula was stated in [Ro], but the proof was only outlined there. Independently, the general formula was given, in a weaker and less explicit form, in [Ke2]; there it was proved completely. …

Maximum Likelihood Estimation Methodology Comparison For The Three-Parameter Weibull Distribution With Applications To Offshore Oil Spills In The Gulf Of Mexico, William V. Harper, Thomas R. James, Ted G. Eschenbach, Leigh Slauson

Mathematics Faculty Scholarship

Maximum Likelihood estimation of the two-parameter Weibull distribution is straightforward; however, there are multiple methods for maximum likelihood estimation of the three-parameter Weibull. This paper presents an evaluation of these methods using four data sets including oil spill data from the Gulf of Mexico. Highlighted are fairly major differences in the estimated parameters between nine statistical packages. A VBA routine has been developed allowing practitioners to implement three-parameter Weibull maximum likelihood estimate within Excel. The code and support documentation are available free at http:faculty.otterbein.edu/WHarper.

The Two Variable Substitution Problem For Free Products Of Groups, Leo Comerford, Charles Edmunds

Faculty Research and Creative Activity

We consider equations of the form W(x,y) = U with U an element of a free product G of groups. We show that with suitable algorithmic conditions on the free factors of G, one can effectively determine whether or not the equations have solutions in G. We also show that under certain hypotheses on the free factors of G and the equation itself, the equation W(x,y) = U has only finitely many solutions, up to the action of the stabilizer of W(x,y) in Aut().

Intrinsic Linking And Knotting Are Arbitrarily Complex, Erica Flapan, Blake Mellor, Ramin Naimi

Pomona Faculty Publications and Research

We show that, given any n and alpha, any embedding of any sufficiently large complete graph in R³ contains an oriented link with components Q₁,...,Q_n such that for every i not equal to j, Ilk(Q_i,Q_j)I greater than or equal to alpha and la₂(Q_i)l greater than or equal to alpha, where a₂(Q_i) denotes the second coefficient of the Conway polynomial of Q_i.

Review: Some Remarks On Quantized Lie Superalgebras Of Classical Type, Gizem Karaali

Pomona Faculty Publications and Research

No abstract provided.

Review: Degenerate Series Representations Of The Q-Deformed Algebra Soq′(R,S), Gizem Karaali

Pomona Faculty Publications and Research

No abstract provided.

Distribution Of The Number Of Encryptions In Revocation Schemes For Stateless Receivers, Christopher Eagle, Zhicheng Gao, Mohamed Omar, Daniel Panario, Bruce Richmond

All HMC Faculty Publications and Research

We study the number of encryptions necessary to revoke a set of users in the complete subtree scheme (CST) and the subset-difference scheme (SD). These are well-known tree based broadcast encryption schemes. Park and Blake in: Journal of Discrete Algorithms, vol. 4, 2006, pp. 215--238, give the mean number of encryptions for these schemes. We continue their analysis and show that the limiting distribution of the number of encryptions for these schemes is normal. This implies that the mean numbers of Park and Blake are good estimates for the number of necessary encryptions used by these schemes.