Physical Sciences and Mathematics Commons^™

Linked Exact Triples Of Triangulated Categories And A Calculus Of T-Structures, Michael Berg

Mathematics, Statistics and Data Science Faculty Works

We introduce a new formalism of exact triples of triangulated categories arranged in certain types of diagrams. We prove that these arrangements are well-behaved relative to the process of gluing and ungluing t-structures defined on the indicated categories and we connect our con. structs to· a problem (from number theory) involving derived categories. We also briefly address a possible connection with a result of R. Thomason.

Maldi-Tof Baseline Drift Removal Using Stochastic Bernstein Approximation, Joseph Kolibal, Daniel Howard

Faculty Publications

Stochastic Bernstein (SB) approximation can tackle the problem of baseline drift correction of instrumentation data. This is demonstrated for spectral data: matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOF) data. Two SB schemes for removing the baseline drift are presented: iterative and direct. Following an explanation of the origin of the MALDI-TOF baseline drift that sheds light on the inherent difficulty of its removal by chemical means, SB baseline drift removal is illustrated for both proteomics and genomics MALDI-TOF data sets. SB is an elegant signal processing method to obtain a numerically straightforward baseline shift removal method as it includes a …

A Connected Sum Of Knots And Fintushel-Stern Knot Surgery On 4-Manifolds, Manabu Akaho

Turkish Journal of Mathematics

We give some new examples of smooth 4-manifolds which are diffeomorphic although they are obtained by Fintushel-Stern knot surgeries on a smooth 4-manifold with different knots; the first such examples are given by Akbulut [1]. In the proof we essentially use the monodromy of a cusp.

A Fractal Example Of A Continuous Monotone Function With Vanishing Derivatives On A Dense Set And Infinite Derivatives On Another Dense Set, Bünyami̇n Demi̇r, Vakif Dzhafarov, Şahi̇n Koçak, Mehmet Üreyen

Turkish Journal of Mathematics

Inspired by the theory of analysis on fractals, we construct an example of a continuous, monotone function on an interval, which has vanishing derivatives on a dense set and infinite derivatives on another dense set. Although such examples could be constructed by classical means of probability and measure theory, this one is more elementary and emerges naturally as a byproduct of some new fractal constructions.

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.

Adaptive Finite Element Methods For Elliptic Pdes Based On Conforming Centroidal Voronoi-Delaunay Triangulations, Lili Ju, Max Gunzburger, Weidong Zhao

Faculty Publications

A new triangular mesh adaptivity algorithm for elliptic PDEs that combines a posteriori error estimation with centroidal Voronoi–Delaunay tessellations of domains in two dimensions is proposed and tested. The ability of the first ingredient to detect local regions of large error and the ability of the second ingredient to generate superior unstructured grids result in a mesh adaptivity algorithm that has several very desirable features, including the following. Errors are very well equidistributed over the triangles; at all levels of refinement, the triangles remain very well shaped, even if the grid size at any particular refinement level, when viewed globally, …

The Restriction And The Continuity Properties Of Potentials Depending On \Lambda-Distance, M. Zeki̇ Sarikaya, Hüseyi̇n Yildirim

Turkish Journal of Mathematics

In this study we establish theorems on the restriction and continuity of the generalized Riesz potentials with the non-isotropic kernels depending on \lambda-distance.

The Radius Of Starlikeness P-Valently Analytic Functions In The Unit Disc, Yaşar Polatoğlu, Meti̇n Bolcal, Arzu Şen, H. Esra Özkan

Turkish Journal of Mathematics

In the present paper we shall give the radius of starlikeness for the classes of p-valent analytic functions in the unit disc D = { z z < 1 }.

Pure Extensions Of Locally Compact Abelian Groups, Peter Loth

Mathematics Faculty Publications

In this paper, we study the group Pext(C,A) for locally compact abelian (LCA) groups A and C. Sufficient conditions are established for Pext(C,A) to coincide with the first Ulm subgroup of Ext(C,A). Some structural information on pure injectives in the category of LCA groups is obtained. Letting K denote the class of LCA groups which can be written as the topological direct sum of a compactly generated group and a discrete group, we determine the groups G in K which are pure injective in the category of LCA groups. Finally we describe those groups G in K such that every …

Unfolding The Labyrinth: Open Problems In Physics, Mathematics, Astrophysics, And Other Areas Of Science, Florentin Smarandache, Victor Christianto, Fu Yuhua, Radi Khrapko, John Hutchison

Branch Mathematics and Statistics Faculty and Staff Publications

The reader will find herein a collection of unsolved problems in mathematics and the physical sciences. Theoretical and experimental domains have each been given consideration. The authors have taken a liberal approach in their selection of problems and questions, and have not shied away from what might otherwise be called speculative, in order to enhance the opportunities for scientific discovery. Progress and development in our knowledge of the structure, form and function of the Universe, in the true sense of the word, its beauty and power, and its timeless presence and mystery, before which even the greatest intellect is awed …

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 …

Enumerations Of The Kolmogorov Function, Richard Beigel, Harry Buhrman, Peter Fejer, Lance Fortnow, Piotr Grabowski, Luc Longpré, Andrej Muchnik, Frank Stephan, Leen Torenvliet

Computer Science Faculty Publication Series

A recursive enumerator for a function h is an algorithm f which enumerates for an input x finitely many elements including h(x). f is a k(n)-enumerator if for every input x of length n, h(x) is among the first k(n) elements enumerated by f. If there is a k(n)-enumerator for h then h is called k(n)-enumerable. We also consider enumerators which are only A-recursive for some oracle A.

We determine exactly how hard it is to enumerate the Kolmogorov function, which assigns to each string x its Kolmogorov complexity:

• For every underlying universal machine U, there is a constant a …

Introduction To N-Adaptive Fuzzy Models To Analyze Public Opinion On Aids, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

“AIDS is not simply a physical malady, it is also an artifact of social and sexual transgression, violated taboo, fractured identity—political and personal projections. Its key words are primarily the property of the powerful. AIDS: Keywords – is my attempt to identify and contest some of the assumptions underlying our current ‘knowledge’. In this effort I am joined by many AIDS activists including people living with AIDS— Acquired Immuno Deficiency Syndrome. “A syndrome is a pattern of symptoms pointing to a “morbid state” which may or may not be caused by infectious agents; a disease, on the other hand is, …

The Formal Laplace-Borel Transform Of Fliess Operators And The Composition Product, Yaqin Li, W. Steven Gray

Electrical & Computer Engineering Faculty Publications

The formal Laplace-Borel transform of an analytic integral operator, known as a Fliess operator, is defined and developed. Then, in conjunction with the composition product over formal power series, the formal Laplace-Borel transform is shown to provide an isomorphism between the semigroup of all Fliess operators under operator composition and the semigroup of all locally convergent formal power series under the composition product. Finally, the formal Laplace-Borel transform is applied in a systems theory setting to explicitly derive the relationship between the formal Laplace transform of the input and output functions of a Fliess operator. This gives a compact interpretation …

Interdependency Of Pharmacokinetic Parameters: A Chicken-And-Egg Problem? Not!, Reza Mehvar

Pharmacy Faculty Articles and Research

Pharmacokinetic (PK) software packages are widely used by scientists in different disciplines to estimate PK parameters. However, their use without a clear understanding of physiological parameters affecting the PK parameters and how different PK parameters are related to each other may result in erroneous interpretation of data. Often, mathematical relationships used for the estimation of PK parameters obscure the true physiological relationships among these parameters, prompting a discussion of which parameter came first and giving the appearance of the-chicken-and-the-egg dilemma. In this article, the author attempts to show how different PK parameters are related to physiological parameters and each other …

The Kronecker Product, Bobbi Jo Broxson

UNF Graduate Theses and Dissertations

This paper presents a detailed discussion of the Kronecker product of matrices. It begins with the definition and some basic properties of the Kronecker product. Statements will be proven that reveal information concerning the eigenvalues, singular values, rank, trace, and determinant of the Kronecker product of two matrices. The Kronecker product will then be employed to solve linear matrix equations. An investigation of the commutativity of the Kronecker product will be carried out using permutation matrices. The Jordan - Canonical form of a Kronecker product will be examined. Variations such as the Kronecker sum and generalized Kronecker product will be …

Mathematically Modeling The Effects Of Counting Factor (Cf) In Dictyostelium Discoideum, J. C. Dallon, W. Jang, R. H. Gomer

Faculty Publications

Size regulation is a crucial feature in many biological systems, with misregulation leading to dysplasia or hyperplasia. The recent discovery of counting factor (CF) in Dictyostelium discoideum will lead to a greater understanding of how the system regulates the size of a group of cells. In this paper we mathematically model the known effects of CF using two different models: a cellular automata model and a discrete continuum hybrid model. With the use of these models we are able to understand how modulation of adhesion and motile forces by CF can facilitate stream breakup. In addition, the modelling suggests a …

Bass Series For Small Witt Rings, Robert W. Fitzgerald

Articles and Preprints

No abstract provided.

Factoring Positive Braids Via Branched Manifolds, Michael C. Sullivan

Articles and Preprints

We show that a positive braid is composite if and only if the factorization is "visually obvious" by placing the braid k in a specially constructed smooth branched 2- manifold B(k) and studying how a would-be cutting sphere meets B(k). This gives an elementary proof of a theorem due to Peter Cromwell.

New Families Of Embedded Triply Periodic Minimal Surfaces Of Genus Three In Euclidean Space, Adam G. Weyhaupt

All Theses, Dissertations, and Capstone Projects

Until 1970, all known examples of embedded triply periodic minimal surfaces (ETPMS) contained either straight lines or curves of planar symmetry. In 1970, Alan Schoen discovered the gyroid, an ETPMS that contains neither straight lines nor planar symmetry curves. Meeks discovered in 1975 a 5-parameter family of genus 3 ETPMS that contained all known examples of genus 3 ETPMS except the gyroid. A second example lying outside the Meeks family was proposed by Lidin in 1990. Große-Brauckmann and Wohlgemuth showed in 1996 the existence and embeddedness of the gyroid and “Lidinoid”. In a series of investigations the scientists, Lidin, et. …

Hamiltonian Formulation And Integrability Of A Complex Symmetric Nonlinear System, Rossen Ivanov

Articles

The integrability of a complex generalisation of the ’elegant’ system, proposed by D. Fairlie and its relation to the Nahm equation and the Manakov top is discussed.

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.

$H$-Vectors Of Generalized Associahedra And Noncrossing Partitions, Colum Watt, Thomas Brady, Christos A. Athanasiadis, Jon Mccammond

Articles

A uniform proof is given that the entries of the $h$-vector of the cluster complex $\Delta (\Phi)$, associated by S. Fomin and A. Zelevinsky to a finite root system $\Phi$, count elements of the lattice $\mathbf{L}$ of noncrossing partitions of corresponding type by rank. Similar interpretations for the $h$-vector of the positive part of $\Delta (\Phi)$ are provided. The proof utilizes the appearance of the complex $\Delta (\Phi)$ in the context of the lattice $\mathbf{L}$ in recent work of two of the authors, as well as an explicit shelling of $\Delta (\Phi)$.

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 …

Prediction In The Panel Data Model With Spatial Correlation: The Case Of Liquor, Badi H. Baltagi, Dong Li

Center for Policy Research

This paper considers the problem of prediction in a panel data regression model with spatial autocorrelation in the context of a simple demand equation for liquor. This is based on a panel of 43 states over the period 1965-1994. The spatial autocorrelation due to neighboring states and the individual heterogeneity across states is taken explicitly into account. We compare the performance of several predictors of the states demand for liquor for one year and five years ahead. The estimators whose predictions are compared include OLS, fixed effects ignoring spatial correlation, fixed effects with spatial correlation, random effects GLS estimator ignoring …

Testing For Cointegrating Rank Via Model Selection: Evidence From 165 Data Sets, Badi H. Baltagi, Zijun Wang

Center for Policy Research

The model selection approach has been proposed as an alternative to the popular tests for cointegration such as the residual-based ADF test and the system-based trace test. Using information criteria, we conduct cointegration tests on 165 data sets used in published studies. The empirical results demonstrate the usefulness of the model selection approach for applied researchers.

A Solidification Phenomenon In Random Packings, L. Bowen, R. Lyons, C. Radin, P. Winkler

Dartmouth Scholarship

We prove that uniformly random packings of copies of a certain simply connected figure in the plane exhibit global connectedness at all sufficiently high densities, but not at low densities.

The Chang-Los-Suszko Theorem In A Topological Setting, Paul Bankston

Mathematics, Statistics and Computer Science Faculty Research and Publications

The Chang-Łoś-Suszko theorem of first-order model theory characterizes universal-existential classes of models as just those elementary classes that are closed under unions of chains. This theorem can then be used to equate two model-theoretic closure conditions for elementary classes; namely unions of chains and existential substructures. In the present paper we prove a topological analogue and indicate some applications.

Specific Antibodies To Recombinant Allergens Of Aspergillus Fumigatus In Cystic Fibrosis Patients With Abpa, Viswanath P. Kurup, Alan P. Knutsen, Richard B. Moss, Naveen K. Bansal

Mathematics, Statistics and Computer Science Faculty Research and Publications

Background

Aspergillus fumigatus, a widely distributed fungus, has been implicated in causing life threatening infections as well as severe asthma and allergic diseases in man. Allergic affliction like allergic bronchopulmonary aspergillosis (ABPA) is a disabling lung disease frequently seen in patients with asthma and cystic fibrosis. Immunodiagnosis of the former is comparatively easier due to the availability of purified antigens and sensitive methods. However, this is not true with cystic fibrosis patients where the prevalence of ABPA is fairly high and the morbidity and mortality are significant.

Methods

In the present study, we have evaluated purified recombinant allergens from …