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Articles 151 - 180 of 288
Full-Text Articles in Mathematics
Higher Dimensional Lattice Chains And Delannoy Numbers, John S. Caughman, Charles L. Dunn, Nancy Ann Neudauer, Colin L. Starr
Higher Dimensional Lattice Chains And Delannoy Numbers, John S. Caughman, Charles L. Dunn, Nancy Ann Neudauer, Colin L. Starr
Faculty Publications
Fix nonnegative integers n1 , . . ., nd, and let L denote the lattice of points (a1 , . . ., ad) ∈ ℤd that satisfy 0 ≤ ai ≤ ni for 1 ≤ i ≤ d. Let L be partially ordered by the usual dominance ordering. In this paper we use elementary combinatorial arguments to derive new expressions for the number of chains and the number of Delannoy paths in L. Setting ni = n (for all i) in these expressions yields a new …
Clique-Relaxed Graph Coloring, Charles Dunn, Jennifer Firkins Nordstrom, Cassandra Naymie, Erin Pitney, William Sehorn, Charlie Suer
Clique-Relaxed Graph Coloring, Charles Dunn, Jennifer Firkins Nordstrom, Cassandra Naymie, Erin Pitney, William Sehorn, Charlie Suer
Faculty Publications
We define a generalization of the chromatic number of a graph G called the k-clique-relaxed chromatic number, denoted χ(k)(G). We prove bounds on χ(k)(G) for all graphs G, including corollaries for outerplanar and planar graphs. We also define the k-clique-relaxed game chromatic number, χg(k)(G), of a graph G. We prove χg(2)(G)≤ 4 for all outerplanar graphs G, and give an example of an outerplanar graph H with χg(2)(H) ≥ 3. Finally, we prove that if H is a member …
Perspectives On Deepening Teachers’ Mathematics Content Knowledge: The Case Of The Oregon Mathematics Leadership Institute, Libby Knott, Martha Vancleave
Perspectives On Deepening Teachers’ Mathematics Content Knowledge: The Case Of The Oregon Mathematics Leadership Institute, Libby Knott, Martha Vancleave
Faculty Publications
The Oregon Mathematics Leadership Institute (OMLI) project served 180 Oregon teachers, and 90 administrators, across the K-12 grades from ten partner districts. OMLI offered a residential, three-week summer institute. Over the course of three consecutive summers, teachers were immersed in a total of six mathematics content classes– Algebra, Data & Chance, Discrete Mathematics, Geometry, Measurement & Change, and Number & Operations—along with an annual collegial leadership course. Each content class was designed and taught by a team of expert faculty from universities, community colleges, and K-12 districts. Each team chose a few “big ideas” on which to focus the course. …
Explicit Constructions Of Rip Matrices And Related Problems, Jean Bourgain, S J. Dilworth, Kevin Ford, Sergei Konyagin, Denka Kutzarova
Explicit Constructions Of Rip Matrices And Related Problems, Jean Bourgain, S J. Dilworth, Kevin Ford, Sergei Konyagin, Denka Kutzarova
Faculty Publications
We give a new explicit construction of n×N matrices satisfying the Restricted Isometry Property (RIP). Namely, for someε > 0, largeN, and any n satisfyingN1−ε ≤ n ≤ N, we construct RIP matrices of order k ≥ n1/2+ε and constant δ = n−ε. This overcomesthe natural barrier k = O(n1/2) for proofs based on small coherence, which areused in all previous explicit constructions of RIP matrices. Key ingredients in ourproof are new estimates for sumsets in product sets and for exponential sums with theproducts of sets possessing special additive structure. We also give a construction ofsets of n complex numbers whose …
Understanding Streaming In Dictyostelium Discoideum: Theory Versus Experiments, J. C. Dallon, Brittany Dalton, Chelsea Malani
Understanding Streaming In Dictyostelium Discoideum: Theory Versus Experiments, J. C. Dallon, Brittany Dalton, Chelsea Malani
Faculty Publications
Recent experimental work involving Dictyostelium discoideum seems to contradict several theoretical models. Experiments suggest that localization of the release of the chemoattractant cyclic adenosine monophosphate to the uropod of the cell is important for stream formation during aggregation. Yet several mathematical models are able to reproduce streaming as the cells aggregate without taking into account localization of the chemoattractant. A careful analysis of the experiments and the theory suggests the two major features of the system which are important to stream formation are random cell motion and chemotaxis to regions of higher cell density. Random cell motion acts to reduce …
On The Convergence Of Greedy Algorithms For Initial Segments Of The Haar Basis, S J. Dilworth, E Odell, Th Schlumprecht, Andras Zsak
On The Convergence Of Greedy Algorithms For Initial Segments Of The Haar Basis, S J. Dilworth, E Odell, Th Schlumprecht, Andras Zsak
Faculty Publications
We consider the X-Greedy Algorithm and the Dual Greedy Algorithm in a finite-dimensional Banach space with a strictly monotone basis as the dictionary. We show that when the dictionary is an initial segment of the Haar basis in Lp[0, 1] (1< p < 1) then the algorithms terminate after finitely many iterations and that the number of iterations is bounded by a function of the length of the initial segment. We also prove a more general result for a class of strictly monotone bases.
Multiscale Modeling Of Cellular Systems In Biology, J. C. Dallon
Multiscale Modeling Of Cellular Systems In Biology, J. C. Dallon
Faculty Publications
Here we review eight different multiscale modeling efforts dealing with cellular systems in biology. The first two models focus on collagen based tissue, one dealing with the biomechanical properties of the tissue and the other focusing on how the dermis is remodeled in scar tissue formation. The next two models deal with first avascular tumor growth and then the role of the vasculature in tumor growth. We then consider two models which use the Immersed Boundary method to model tissue properties and cell-cell adhesion. Finally we conclude with two models with treatments of the Cellular Potts Model. The first models …
Non-Negative Steady State Solutions To An Elliptic Biological Model, Brian Ibanez, Joon Hyuk Kang, Jungho Lee
Non-Negative Steady State Solutions To An Elliptic Biological Model, Brian Ibanez, Joon Hyuk Kang, Jungho Lee
Faculty Publications
The non-existence and existence of positive solutions for the generalized predator-prey biological model for two species of animals Δu + ug(u,v) = 0 in Ω, Δv + vh(u,v) = 0 in Ω, u = v = 0 on ∂Ω, is investigated in this paper. The techniques used in this paper are from elliptic theory, the upper-lower solution method, the maximum principles and spectrum estimates. The arguments also rely on detailed properties of solutions to logistic equations. © 2009 Academic Publications.
A Construction Of Lagrangian Submanifolds In Complex Euclidean Spaces With Legendre Curves, Yun Myung Oh
A Construction Of Lagrangian Submanifolds In Complex Euclidean Spaces With Legendre Curves, Yun Myung Oh
Faculty Publications
In [1], B. Y. Chen provided a new method to construct Lagrangian surfaces in C2 by using Legendre curves in S3(1)C2. In this paper, we investigate the similar methods to construct some Lagrangian submanifolds in complex Euclidean spaces Cn (n≥b3).
Cyclic Shifts Of The Van Der Corput Set, Dmitriy Bilyk
Cyclic Shifts Of The Van Der Corput Set, Dmitriy Bilyk
Faculty Publications
In 1980, K. Roth showed that the expected value of the L2 discrepancy of the cyclic shifts of the N-point van der Corput set is bounded by a constant multiple of √logN, thus guaranteeing the existence of a shift with asymptotically minimal L2 discrepancy. In the present paper, we construct a specific example of such a shift.
Extending The Support Theorem To Infinite Dimensions, Jeremy J. Becnel
Extending The Support Theorem To Infinite Dimensions, Jeremy J. Becnel
Faculty Publications
The Radon transform is one of the most useful and applicable tools in functional analysis. First constructed by John Radon in 1917 [9] it has now been adapted to several settings. One of the principle theorems involving the Radon transform is the Support Theorem. In this paper, we discuss how the Radon transform can be constructed in the white noise setting. We also develop a Support Theorem in this setting.
Quasi-Anosov Diffeomorphisms Of 3-Manifolds, Todd L. Fisher, Hertz M. Rodriguez
Quasi-Anosov Diffeomorphisms Of 3-Manifolds, Todd L. Fisher, Hertz M. Rodriguez
Faculty Publications
In 1969, Hirsch posed the following problem: given a diffeomorphism f:N → N and a compact invariant hyperbolic set Λ of f, describe the topology of Λ and the dynamics of f restricted to Λ. We solve the problem where Λ=M^3 is a closed 3-manifold: if M^3 is orientable, then it is a connected sum of tori and handles; otherwise it is a connected sum of tori and handles quotiented by involutions.
Health Literacy In The Mathematics Classroom: The Iowa Core Curriculum As An Opportunity To Deepen Students’ Understanding Of Mathematics, Elana Joram, Susan Roberts-Dobie, Nadene Davidson
Health Literacy In The Mathematics Classroom: The Iowa Core Curriculum As An Opportunity To Deepen Students’ Understanding Of Mathematics, Elana Joram, Susan Roberts-Dobie, Nadene Davidson
Faculty Publications
By 2012, all high schools in Iowa will be required to incorporate the new Iowa Core Curriculum, followed by elementary and middle schools in 2014 (Iowa Department of Education, 2009). The Iowa Core Curriculum addresses the question: "How is Iowa's educational system preparing our youth for successful lives in the 21st-century global environment?" (Davidson, 2009). It consists of core content standards, and identifies essential concepts and skills for content areas. The Iowa Core Curriculum also includes the ―21st Century Skills‖ of ―health, financial, technology, and civic literacy, and employability skills. These skills are to be infused into existing subject matter …
Using A Mathematical Model Of Cadherin-Based Adhesion To Understand The Function Of The Actin Cytoskeleton, J. C. Dallon, Elijah Newren, Marc Hansen
Using A Mathematical Model Of Cadherin-Based Adhesion To Understand The Function Of The Actin Cytoskeleton, J. C. Dallon, Elijah Newren, Marc Hansen
Faculty Publications
The actin cytoskeleton plays a role in cell-cell adhesion but its specific function is not clear. Actin might anchor cadherins or drive membrane protrusions in order to facilitate cell-cell adhesion. Using a mathematical model of the forces involved in cadherin-based adhesion we investigate its possible functions. The immersed boundary method is used to model the cell membrane and cortex with cadherin binding forces added as linear springs. The simulations indicate that cells in suspension can develop normal cell-cell contacts without actin-based cadherin anchoring or membrane protrusions. The cadherins can be fixed in the membrane or free to move and the …
A Review Of Fibroblast Populated Collagen Lattices, J. C. Dallon, Paul H. Ehrlich
A Review Of Fibroblast Populated Collagen Lattices, J. C. Dallon, Paul H. Ehrlich
Faculty Publications
Bellaes introduction of the fibroblast populated collagen lattice (FPCL) (1) has facilitated the study of collagen-cell interactions. As a result of the numerous modifications of the casting of FPCL's, the in vivo applications of these in vitro findings has been confusing. Here experimental FPCL contraction findings are viewed in regard to three proposed mechanisms responsible for lattice contraction. The cellular mechanisms responsible for generating FPCL contraction are: cell contraction, cell tractional forces related to cell locomotion, and initial cell elongation and spreading.
An Optimal-Order Error Estimate For A Family Of Ellam-Mfem Approximations To Porous Medium Flow, Hong Wang
An Optimal-Order Error Estimate For A Family Of Ellam-Mfem Approximations To Porous Medium Flow, Hong Wang
Faculty Publications
Mathematical models used to describe porous medium flow lead to coupled systems of time-dependent nonlinear partial differential equations, which present serious mathematical and numerical difficulties. Standard methods tend to generate numerical solutions with nonphysical oscillations or numerical dispersion along with spurious grid-orientation effect. The ELLAM-MFEM time-stepping procedure, in which an Eulerian–Lagrangian localized adjoint method (ELLAM) is used to solve the transport equation and a mixed finite element method (MFEM) is used for the pressure equation, simulates porous medium flow accurately even if large spatial grids and time steps are used. In this paper we prove an optimal-order error estimate for …
Bipartite Toughness And The K-Factors In Bipartite Graphs, Guizhen Liu, Jianbo Quan, Jonathan Z. Sun, Rui Xu
Bipartite Toughness And The K-Factors In Bipartite Graphs, Guizhen Liu, Jianbo Quan, Jonathan Z. Sun, Rui Xu
Faculty Publications
We define a new invariant tB(G) in bipartite graphs that is analogous to the toughness t(G) and we give sufficient conditions in term of tB(G) for the existence of k-factors in bipartite graphs. We also show that these results are sharp.
Delta Function For An Affine Subspace, Jeremy Becnel
Delta Function For An Affine Subspace, Jeremy Becnel
Faculty Publications
The Kubo–Yokoi and Donsker delta functions are well known generalized functions in infinite dimensional distribution theory. In this paper we develop the delta function for an affine subspace and show that it is a generalization of the Kubo–Yokoi and Donsker delta functions. The Wiener– Itˆo expansion of the delta function for an affine subspace is also given.
Constructing Subdivision Rules From Rational Maps, J. W. Cannon, W. J. Floyd, W. R. Parry
Constructing Subdivision Rules From Rational Maps, J. W. Cannon, W. J. Floyd, W. R. Parry
Faculty Publications
This paper deepens the connections between critically finite rational maps and finite subdivision rules. The main theorem is that if f is a critically finite rational map with no periodic critical points, then for any sufficiently large integer n the iterate f is the subdivision map of a finite subdivision rule. This enables one to give essentially combinatorial models for the dynamics of such iterates.
Uniform Estimates For Eulerian-Lagrangian Methods For Singularly Perturbed Time-Dependent Problems, Hong Wang, Kaixin Wang
Uniform Estimates For Eulerian-Lagrangian Methods For Singularly Perturbed Time-Dependent Problems, Hong Wang, Kaixin Wang
Faculty Publications
We prove a priori optimal-order error estimates in a weighted energy norm for several Eulerian–Lagrangian methods for singularly perturbed, time-dependent convection-diffusion equations with full regularity. The estimates depend only on certain Sobolev norms of the initial and right-hand side data, but not on ε or any norm of the true solution, and so hold uniformly with respect to ε. We use the interpolation of spaces and stability estimates to derive an ε-uniform estimate for problems with minimal or intermediate regularity, where the convergence rates are proportional to certain Besov norms of the initial and right-hand side data.
Products Of Characters With Few Irreducible Constituents, Edith Adan-Bante
Products Of Characters With Few Irreducible Constituents, Edith Adan-Bante
Faculty Publications
We study the solvable groups G that have an irreducible character χ ∈ Irr(G) such that χ--χ has at most two nonprincipal irreducible constituents.
Squares Of Characters And Finite Groups, Edith Adan-Bante
Squares Of Characters And Finite Groups, Edith Adan-Bante
Faculty Publications
Let G be a finite group and χ be an irreducible complex character. We study the character χ2 in the case that χ(1) is a prime power.
Integral And Nonnegativity Preserving Approximations Of Functions, Jiu Ding, Larry Eifler, N. H. Rhee
Integral And Nonnegativity Preserving Approximations Of Functions, Jiu Ding, Larry Eifler, N. H. Rhee
Faculty Publications
In this paper we consider the problem of approximating a function by continuous piecewise linear functions that preserve the integral and nonnegativity of the original function. (c) 2006 Elsevier Inc. All rights reserved.
The Relaxed Game Chromatic Index Of K-Degenerate Graphs, Charles Dunn
The Relaxed Game Chromatic Index Of K-Degenerate Graphs, Charles Dunn
Faculty Publications
The (r, d)-relaxed coloring game is a two-player game played on the vertex set of a graph G. We consider a natural analogue to this game on the edge set of G called the (r, d)-relaxed edge-coloring game. We consider this game on trees and more generally, on k-degenerate graphs. We show that if G is k-degenerate with ∆(G) = ∆, then the first player, Alice, has a winning strategy for this game with r = ∆+k−1 and d≥2k2 + 4k.
On Strongly Asymptotic L(P) Spaces And Minimality, S J. Dilworth, V Ferenczi, Denka Kutzarova, E Odell
On Strongly Asymptotic L(P) Spaces And Minimality, S J. Dilworth, V Ferenczi, Denka Kutzarova, E Odell
Faculty Publications
No abstract provided.
On The Kauffman Bracket Skein Module Of The Quaternionic Manifold, Patrick M. Gilmer, John M. Harris
On The Kauffman Bracket Skein Module Of The Quaternionic Manifold, Patrick M. Gilmer, John M. Harris
Faculty Publications
We use recoupling theory to study the Kauffman bracket skein module of the quaternionic manifold over Z[A(+/- 1)] localized by inverting all the cyclotomic polynomials. We prove that the skein module is spanned by five elements. Using the quantum invariants of these skein elements and the Z(2)-homology of the manifold, we determine that they are linearly independent.
Induction Of Characters And Finite P-Groups, Edith Adan-Bante
Induction Of Characters And Finite P-Groups, Edith Adan-Bante
Faculty Publications
Let G be a finite p-group, where p is an odd prime number, H be a subgroup of G and θ ∈ Irr(H) be an irreducible character of H. Assume also that | G : H | = p2. Then the character θG of G induce by θ is either a multiple of an irreducible character of G, or has at least p+1/2 distinct irreducible constituents.
Fibroblast Migration And Collagen Deposition During Dermal Wound Healing: Mathematical Modelling And Clinical Implications, S. Mcdougall, J. A. Sherratt, P. K. Maini, J. C. Dallon
Fibroblast Migration And Collagen Deposition During Dermal Wound Healing: Mathematical Modelling And Clinical Implications, S. Mcdougall, J. A. Sherratt, P. K. Maini, J. C. Dallon
Faculty Publications
The extent to which collagen alignment occurs during dermal wound healing determines the severity of scar tissue formation. We have modelled this using a multiscale approach, in which extracellular materials, for example collagen and fibrin, are modelled as continua, while fibroblasts are considered as discrete units. Within this model framework, we have explored the effects that different parameters have on the alignment process, and we have used the model to investigate how manipulation of transforming growth factor-b levels can reduce scar tissue formation. We briefly review this body of work, then extend the modelling framework to investigate the role played …
Timelike Surfaces Of Constant Mean Curvature ±1 In Anti-De Sitter 3-Space H31), Sungwook Lee
Timelike Surfaces Of Constant Mean Curvature ±1 In Anti-De Sitter 3-Space H31), Sungwook Lee
Faculty Publications
It is shown that timelike surfaces of constant mean curvature ± in anti-de Sitter 3-space H3 1(−1) can be constructed from a pair of Lorentz holomorphic and Lorentz antiholomorphic null curves in PSL2R via Bryant type representation formulae. These Bryant type representation formulae are used to investigate an explicit one-to-one correspondence, the so-called Lawson–Guichard correspondence, between timelike surfaces of constant mean curvature ± 1 and timelike minimal surfaces in Minkowski 3-space E 3 1. The hyperbolic Gauß map of timelike surfaces in H3 1(−1), which is a close analogue of the classical …
Homogeneous Products Of Conjugacy Classes, Edith Adan-Bante
Homogeneous Products Of Conjugacy Classes, Edith Adan-Bante
Faculty Publications
Let G be a finite group and a ∈G. Let a G ={g −1 a g | g ∈ G} be the conjugacy class of a in G. Assume that a G and b G are conjugacy classes of G with the property that C G (a)=C G (b). Then a G b G is a conjugacy class if and only if [a,G]=[b,G]=[ab,G] and [ab,G] is a normal subgroup of G.