Mathematics Commons^™

Kernels Of Directed Graph Laplacians, John S. Caughman Iv, J. J. P. Veerman

Mathematics and Statistics Faculty Publications and Presentations

Let G denote a directed graph with adjacency matrix Q and in- degree matrix D. We consider the Kirchhoff matrix L = D − Q, sometimes referred to as the directed Laplacian. A classical result of Kirchhoff asserts that when G is undirected, the multiplicity of the eigenvalue 0 equals the number of connected components of G. This fact has a meaningful generalization to directed graphs, as was observed by Chebotarev and Agaev in 2005. Since this result has many important applications in the sciences, we offer an independent and self-contained proof of their theorem, showing in this paper …

Generalised E-Algebras Over Valuation Domains, Brendan Goldsmith, P. Zanardo

Articles

Let R be a valuation domain. We investigate the notions of E(R)- algebra and generalized E(R)-algebra and show that for wide classes of maximal valuation domains R, all generalized E(R)-algebras have rank one. As a by-product we prove if R is a maximal valuation domain of finite Krull dimension, then the two notions coincide. We give some examples of E(R)-algebras of finite rank that are decomposable, but show that over Nagata domains of small degree, the E(R)-algebras are, with one exception, the indecomposable finite rank algebras.

Extended Camassa-Holm Hierarchy And Conserved Quantities, Rossen Ivanov

Articles

An extension of the Camassa-Holm hierarchy is constructed in this letter. The conserved quantities of the hierarchy are studied and a recurrent formula for the integrals of motion is derived.

On Finitary Permutation Groups, Ali̇ Osman Asar

Turkish Journal of Mathematics

In this work we give some sufficient conditions under which the structure of a transitive group of finitary permutations on an infinite set can be determined from the structure of a point stabilizer. Also, we give some sufficient conditions for the existence of a proper subgroup having an infinite orbit in a totally imprimitive p-group of finitary permutations. These results, with the help of some known results, give sufficient conditions for the nonexistence of a perfect locally finite minimal non FC - (p-group).

On Uniform Hermitian P-Normed Algebras, A. El-Kinani

Turkish Journal of Mathematics

We show that the completion of a uniform hermitian p-normed algebra is a commutative C^*-algebra.

A Survey On The Distribution Of B-Free Numbers, Emre Alkan, Alexandru Zaharescu

Turkish Journal of Mathematics

In this paper we present a survey of recent progress on the distribution of B-free numbers in short intervals and some of its applications.

Diagonal Lift In The Tangent Bundle Of Order Two And Its Applications, Fouzi Hathout, H. M. Dida

Turkish Journal of Mathematics

In this paper we define a diagonal lift ^{D}g of Riemannian metric g of manifold M_n to the tangent bundle of order two denoted by T^{2}M_n of M_n, we associate to ^{D}g its Levi-civita connection of T^2 M and we investigate applications of the diagonal lifts in the killing vectors and geodesics.

Note On Generalized Jordan Derivations Associate With Hochschild 2-Cocycles Of Rings, Atsushi Nakajima

Turkish Journal of Mathematics

We introduce a new type of generalized derivations associate with Hochschild 2-cocycles and prove that every generalized Jordan derivation of this type is a generalized derivation under certain conditions. This result contains the results of I. N. Herstein [6, Theorem 3.1] and M. Ashraf and N-U. Rehman [1, Theorem].

Differential Inclusions On Proximate Retracts Of Separable Hilbert Spaces, Ravi P. Agarwal, Donal O'Regan

Mathematics and System Engineering Faculty Publications

New existence results are presented which guarantee the existence of viable solutions to differential inclusions in separable Hilbert spaces. Our results rely on the existence of maximal solutions for an appropriate differential equation in the real case. Copyright ©2006 Rocky Mountain Mathematics Consortium.

Generalized Flow Invariance For Differential Inclusions, Tarun Gnana Bhaskar, V. Lakshmikantham

Mathematics and System Engineering Faculty Publications

We introduce a generalized notion of invariance for differential inclusions, using a proximal aiming condition in terms of proximal normals. A set of sufficient conditions for the weak and strong invariance in the generalized sense are presented.

Random Effects And Spatial Autocorrelations With Equal Weights, Badi H. Baltagi

Center for Policy Research

This note considers a panel data regression model with spatial autoregressive disturbances and random effects where the weight matrix is normalized and has equal elements. This is motivated by Kelejian et al. (2005), who argue that such a weighting matrix, having blocks of equal elements, might be considered when units are equally distant within certain neighborhoods but unrelated between neighborhoods. We derive a simple weighted least squares transformation that obtains GLS on this model as a simple OLS. For the special case of a spatial panel model with no random effects, we obtain two sufficient conditions where GLS on this …

Estimating Heterogeneous Capacity And Capacity Utilization In A Multi-Species Fishery, Ronald G. Felthoven, William C. Horrace, Kurt E. Schnier

Center for Policy Research

We use a stochastic production frontier model to investigate the presence of heterogeneous production and its impact on fleet capacity and capacity utilization in a multi-species fishery. Furthermore, we propose a new fleet capacity estimate that incorporates complete information on the stochastic differences between each vessel-specific technical efficiency distribution. Results indicate that ignoring heterogeneity in production technologies within a multi-species fishery, as well as the complete distribution of a vessel's technical efficiency score, may yield erroneous fleet-wide production profiles and estimates of capacity. Furthermore, our new estimate of capacity enables out-of-sample production predictions predicated on either homogeneity or heterogeneity modeling …

Algebraic Characterizations Of Graph Imbeddability In Surfaces And Pseudosurfaces, Lowell Abrams, Dan Slilaty

Mathematics and Statistics Faculty Publications

Given a finite connected graph G and specifications for a closed, connected pseudosurface, we characterize when G can be imbedded in a closed, connected pseudosurface with the given specifications. The specifications for the pseudosurface are: the number of face-connected components, the number of pinches, the number of crosscaps and handles, and the dimension of the first Z2-homology group. The characterizations are formulated in terms of the existence of a dual graph G ∗ on the same set of edges as G which satisfies algebraic conditions inspired by homology groups and their intersection products.

Restricted Signed Permutations Counted By The Schröder Numbers, Eric S. Egge

Mathematics and Statistics Faculty Work

Gire, West, and Kremer have found ten classes of restricted permutations counted by the large Schröder numbers, no two of which are trivially Wilf-equivalent. In this paper we enumerate eleven classes of restricted signed permutations counted by the large Schröder numbers, no two of which are trivially Wilf-equivalent. We obtain five of these enumerations by elementary methods, five by displaying isomorphisms with the classical Schröder generating tree, and one by giving an isomorphism with a new Schröder generating tree. When combined with a result of Egge and a computer search, this completes the classification of restricted signed permutations counted by …

On Adaptive Testing In Orthogonal Saturated Designs, Daniel T. Voss, Weizhen Wang

Mathematics and Statistics Faculty Publications

Adaptive, size-a step-down tests are provided for the analysis of orthogonal saturated designs. The tests work effectively under effect sparsity, and include as special cases the individual nonadaptive tests of Berk and Picard (1991) and the simultaneous nonadaptive tests of Voss (1988). The approach is similar to that used by Wang and Voss (2003) to construct adaptive confidence intervals, but testing is simpler because one can use the same denominator for all statistics. Step-down tests also have a clear power advantage over simultaneous confidence intervals and analogous single-step tests, as is demonstrated theoretically and assessed via simulation.

The Classical Dirichlet Space, William T. Ross

Department of Math & Statistics Faculty Publications

In this survey paper, we will present a selection of results concerning the class of analytic functions f on the open unit disk D := {z ϵ C : │z│ < 1} which have finite Dirichlet integral.

A Logistic Regression/Markov Chain Model For Ncaa Basketball, Paul H. Kvam, Joel Sokol

Department of Math & Statistics Faculty Publications

Each year, more than $3 billion is wagered on the NCAA Division I men’s basketball tournament. Most of that money is wagered in pools where the object is to correctly predict winners of each game, with emphasis on the last four teams remaining (the Final Four). In this paper, we present a combined logistic regression/Markov chain model for predicting the outcome of NCAA tournament games given only basic input data. Over the past 6 years, our model has been significantly more successful than the other common methods such as tournament seedings, the AP and ESPN/USA Today polls, the RPI, and …

Temporal Processing In The Exponential Integrate-And-Fire Model Is Nonlinear, Joanna R. Wares, Todd W. Troyer

Department of Math & Statistics Faculty Publications

The exponential integrate-and-fire (EIF) model was introduced by Fourcaud-Trocme et al. (2003) as an extension of the standard leaky integrate-and-fire model (LIF). Here, the nonlinearity in the EIF model’s temporal response to square-wave inputs is investigated. Comparing the time course of onset and offset responses revealed that offset responses have a steeper initial slope, but a slower approach to equilibrium. A linear systems analysis performed for these square-wave inputs indicates that at frequencies above ~40 Hz, gain was slightly smaller for square-wave inputs, but phase did not change significantly relative to simulations in which the corresponding sinusoids were presented in …

Use Of Pen-Based Technology In Calculus Courses, John R. Hubbard

Department of Math & Statistics Faculty Publications

The author and his students used Tablet computers in Calculus I and Calculus II classes, providing students with dynamic digital transcripts that they could replay at their convenience. He and his students agreed that these graphic replays provide an effective alternative to the static explanations found in textbooks and in traditional course notes. Two specific examples are given in this paper.

Reliability Modeling In Spatially Distributed Logistics System, Ni Wang, Jye-Chyi Lu, Paul H. Kvam

Department of Math & Statistics Faculty Publications

This article proposes methods for modeling service reliability in a supply chain. The logistics system in a supply chain typically consists of thousands of retail stores along with multiple distribution centers (DC). Products are transported between DC & stores through multiple routes. The service reliability depends on DC location layouts, distances from DC to stores, time requirements for product replenishing at stores, DC's capability for supporting store demands, and the connectivity of transportation routes. Contingent events such as labor disputes, bad weather, road conditions, traffic situations, and even terrorist threats can have great impacts on a system's reliability. Given the …

Statistical Reliability With Applications, Paul H. Kvam, Jye-Chyi Lu

Department of Math & Statistics Faculty Publications

This chapter reviews fundamental ideas in reliability theory and inference. The first part of the chapter accounts for lifetime distributions that are used in engineering reliability analyis, including general properties of reliability distributions that pertain to lifetime for manufactured products. Certain distributions are formulated on the basis of simple physical properties, and other are more or less empirical. The first part of the chapter ends with a description of graphical and analytical methods to find appropriate lifetime distributions for a set of failure data.

The second part of the chapter describes statistical methods for analyzing reliability data, including maximum likelihood …

Counting Coffee Combinations: An Example Of The Fundamental Principle Of Counting, David R. Duncan, Bonnie H. Litwiller

Faculty Work

Teachers in courses which involve probability and statistics are always looking for situations in which the Fundamental Principle of Counting (FPC) can be exemplified. We shall present an example involving a coffee vending machine at a highway rest stop.

The Homological Theory Of Degree Of Fql-Mappings, Aki̇f Abbasov

Turkish Journal of Mathematics

In this article the homological theory is specially worked out, ìadaptedî for definition of the degree of mapping from one of the classes of infinite-dimensional mappings, exactly FQL-mappings, introduced in [7].

The Range Of Angles In The Euler-Gergonne-Soddy Triangle, David J. Gisch

Dissertations and Theses @ UNI

For any triangle one can construct its Euler-Gergonne-Soddy triangle (EGST). In 1996 it was shown that the EGST is always a right triangle. In this work we compute the range of the other angles of the EGST by calculating the maximum angle of the EGST at the de Longchamps point.

Writing Projective Representations Over Subfields, Stephen P. Glasby, C. R. Leedham-Green, E. A. O'Brien

All Faculty Scholarship for the College of the Sciences

Let G=〈X〉be an absolutely irreducible subgroup of GL(d, K), and let F be a proper subfield of the finite field K. We present a practical algorithm to decide constructively whether or not G is conjugate to a subgroup of GL(d, F).K×, where K× denotes the centre of GL(d, K). If the derived group of G also acts absolutely irreducibly, then the algorithm is Las Vegas and costs O(|X|d³+d²log|F|) arithmetic operations in K. This work forms part of a recognition project based on Aschbacher’s classification of maximal subgroups of GL(d, K).

Infinitely Often Dense Bases And Geometric Structure Of Sumsets, Jaewoo Lee

Dissertations, Theses, and Capstone Projects

We'll discuss two problems related to sumsets.

Nathanson constructed bases of integers with prescribed representation functions, then asked how dense bases for integers can be in such cases. Let A(-x, x) be the number of elements of A whose absolute value is less than or equal to x, then it's easy to see that A(-x, x) << x1/2 if its representation function is bounded, giving us a general upper bound. Chen constructed unique representation bases for integers with A(-x, x) ≥ x1/2-epsilon infinitely often. In the first chapter, we'll construct bases for integers with a prescribed representation function with A(-x, x) > x1/2/&phis;(x) infinitely often where &phis;(x) is any nonnegative real-valued function which tends to infinity.

In the second chapter, we'll see how sumsets appear geometrically. Assume A is a finite set of lattice points and h*D=h˙x:x∈conv A is a full dimensional polytope. Then we'll see …

The Pitch And The Pseudo Angle Of Pitch Of A Closed Piece Of (K+1)-Dimensional Ruled Surface In R_\Nu^N, Ayşe Altin

Turkish Journal of Mathematics

In this paper, we define the closed piece of ruled surface, the pitch and the pseudo angle of pitch of a closed piece of ruled surface and calculate these values in Minkowski space R_\nu^n= (R ^n,-\sum^{\nu}_{i=1}dx_i+\sum^n_{i=\nu+1}dx_i).

Quasi Separation Axioms, Mohammad S. Sarsak

Turkish Journal of Mathematics

In [5], Maheshwari et al. introduced and studied some new separation axioms, namely, quasi semi T_i axioms where i \in {0, 1, 2}, the quasi semi T_{1/2} axiom was then introduced and investigated by Gyu-Ihn et al. in [2]. In the present paper we introduce and study quasi T_i axioms, i \in {0, 1 / 2, 1, 2} as a special variety of quasi semi T_i axioms, the class of quasi T_{1/2} (respectively, quasi T_1) bitopological spaces is placed between quasi T_0 (respectively, quasi T_{1/2}) bitopological spaces and quasi T_1 (respectively, quasi T_2) bitopological spaces. Among several counter examples we …

P-Elastica In The 3-Dimensional Lorentzian Space Forms, Nevi̇n Gürbüz

Turkish Journal of Mathematics

R Huang worked the p-elastic in a Riemannian manifold with constant sectional curvature [1]. In this work, we solve the Euler-Lagrange equation by quadrature and study the Frenet equation of the p-elastica by using the Killing field in the three dimensional Lorentzian space forms

Second-Order Nonlinear Three Point Boundary-Value Problems On Time Scales, S. Gülşan Topal

Turkish Journal of Mathematics

We consider a second order three point boundary value problem for dynamic equations on time scales and establish criteria for the existence of at least two positive solutions of an eigenvalue problem by an application of a fixed point theorem in cones. Existence result for non-eigenvalue problem is also given by the monotone method.