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Articles 1 - 30 of 79
Full-Text Articles in Physical Sciences and Mathematics
The Impact Of Neighborhood Socioeconomic Disadvantage On Operative Outcomes After Single-Level Lumbar Fusion, Grace Y. Ng, Ritesh Karsalia, Ryan S. Gallagher, Austin J. Borja, Jianbo Na, Scott Mcclintock, Neil R. Malhotra
The Impact Of Neighborhood Socioeconomic Disadvantage On Operative Outcomes After Single-Level Lumbar Fusion, Grace Y. Ng, Ritesh Karsalia, Ryan S. Gallagher, Austin J. Borja, Jianbo Na, Scott Mcclintock, Neil R. Malhotra
Mathematics Faculty Publications
INTRODUCTION: The relationship between socioeconomic status and neurosurgical outcomes has been investigated with respect to insurance status or median household income, but few studies have considered more comprehensive measures of socioeconomic status. This study examines the relationship between Area Deprivation Index (ADI), a comprehensive measure of neighborhood socioeconomic disadvantage, and short-term postoperative outcomes after lumbar fusion surgery. METHODS: 1861 adult patients undergoing single-level, posterior-only lumbar fusion at a single, multihospital academic medical center were retrospectively enrolled. An ADI matching protocol was used to identify each patient's 9-digit zip code and the zip code-associated ADI data. Primary outcomes included 30- and …
A Natural Pseudometric On Homotopy Groups Of Metric Spaces, Jeremy Brazas, Paul Fabel
A Natural Pseudometric On Homotopy Groups Of Metric Spaces, Jeremy Brazas, Paul Fabel
Mathematics Faculty Publications
For a path-connected metric space (X, d), the n-th homotopy group π n ( X) inherits a natural pseudometric from the n-th iterated loop space with the uniform metric. This pseudometric gives π n ( X) the structure of a topological group and when X is compact, the induced pseudometric topology is independent of the metric d. In this paper, we study the properties of this pseudometric and how it relates to previously studied structures on π n ( X). Our main result is that the pseudometric topology agrees with the shape topology on π n ( X) if X …
On Maps With Continuous Path Lifting, Jeremy Brazas, Atish Mitra
On Maps With Continuous Path Lifting, Jeremy Brazas, Atish Mitra
Mathematics Faculty Publications
We study a natural generalization of covering projections defined in terms of unique lifting properties. A map p : E -+ X has the continuous path-covering property if all paths in X lift uniquely and continuously (rel. basepoint) with respect to the compactopen topology. We show that maps with this property are closely related to fibrations with totally path-disconnected fibers and to the natural quotient topology on the homotopy groups. In particular, the class of maps with the continuous path-covering property lies properly between Hurewicz fibrations and Serre fibrations with totally path-disconnected fibers. We extend the usual classification of covering …
Free Quasitopological Groups, Jeremy Brazas, Sarah Emery
Free Quasitopological Groups, Jeremy Brazas, Sarah Emery
Mathematics Faculty Publications
In this paper, we study the topological structure of a universal construction related to quasitopological groups: the free quasitopological group F-q(X) on a space X. We show that free quasitopological groups may be constructed directly as quotient spaces of free semitopological monoids, which are themselves constructed by iterating product spaces equipped with the "cross topology." Using this explicit description of F-q(X), we show that for any T-1 space X, F-q(X) is the direct limit of closed subspaces F-q(X)(n) of words of length at most n. We also prove that the natural map i(n): (sic)(n)(i=0)(X boolean OR X-1)(circle times i) - …
Elements Of Higher Homotopy Groups Undetectable By Polyhedral Approximation, John K. Aceti, Jeremy Brazas
Elements Of Higher Homotopy Groups Undetectable By Polyhedral Approximation, John K. Aceti, Jeremy Brazas
Mathematics Faculty Publications
When nontrivial local structures are present in a topological space X, a common approach to characterizing the isomorphism type of the n-th homotopy group πn(X, x0) is to consider the image of πn(X, x0) in the nth Cˇ ech homotopy group πˇ n(X, x0) under the canonical homomorphism 9n : πn(X, x0) → πˇ n(X, x0). The subgroup ker(9n) is the obstruction to this tactic as it consists of precisely those elements of πn(X, x0), which cannot be detected by polyhedral approximations to X. In this paper, we use higher dimensional analogues of Spanier groups to characterize ker(9n). In particular, …
Tennis Anyone? Teaching Experimental Design By Designing And Executing A Tennis Ball Experiment, Laura Pyott
Tennis Anyone? Teaching Experimental Design By Designing And Executing A Tennis Ball Experiment, Laura Pyott
Mathematics Faculty Publications
Understanding the abstract principles of statistical experimental design can challenge undergraduate students, especially when learned in a lecture setting. This article presents a concrete and easily replicated example of experimental design principles in action through a hands-on learning activity for students enrolled in an experimental design course. The activity, conducted during five 50-min classes, requires the students to work as a team to design and execute a simple and safe factorial experiment and collect and analyze the data. During three in-class design meetings, the students design and plan all aspects of the experiment, including choosing the response variable and factors, …
On Generating Functions In Additive Number Theory, Ii: Lower-Order Terms And Applications To Pdes, J. Brandes, Scott T. Parsell, C. Poulias, G. Shakan, R. C. Vaughn
On Generating Functions In Additive Number Theory, Ii: Lower-Order Terms And Applications To Pdes, J. Brandes, Scott T. Parsell, C. Poulias, G. Shakan, R. C. Vaughn
Mathematics Faculty Publications
We obtain asymptotics for sums of the form
Sigma(p)(n=1) e(alpha(k) n(k) + alpha(1)n),
involving lower order main terms. As an application, we show that for almost all alpha(2) is an element of [0, 1) one has
sup(alpha 1 is an element of[0,1)) | Sigma(1 <= n <= P) e(alpha(1)(n(3) + n) + alpha(2)n(3))| << P3/4+epsilon,
and that in a suitable sense this is best possible. This allows us to improve bounds for the fractal dimension of solutions to the Schrodinger and Airy equations.
Infinite Sets Of Solutions And Almost Solutions Of The Equation N∙M = Reversal(N∙M) Ii, Viorel Nitica, Cem Ekinci
Infinite Sets Of Solutions And Almost Solutions Of The Equation N∙M = Reversal(N∙M) Ii, Viorel Nitica, Cem Ekinci
Mathematics Faculty Publications
Motivated by their intrinsic interest and by applications to the study of numeric palindromes and other sequences of integers, we discover a method for producing infinite sets of solutions and almost solutions of the equation N M reversal N M ⋅= ⋅ ( ) , our results are valid in a general numeration base b > 2 .
A Generalization Of Schroter's Formula To George Andrews, On His 80th Birthday, James Mclaughlin
A Generalization Of Schroter's Formula To George Andrews, On His 80th Birthday, James Mclaughlin
Mathematics Faculty Publications
We prove a generalization of Schroter's formula to a product of an arbitrary number of Jacobi triple products. It is then shown that many of the well-known identities involving Jacobi triple products (for example the Quintuple Product Identity, the Septuple Product Identity, and Winquist's Identity) all then follow as special cases of this general identity. Various other general identities, for example certain expansions of (q; q)(infinity) and (q; q)(infinity)(k), k >= 3, as combinations of Jacobi triple products, are also proved.
A Randomized Controlled Trial: Attachment-Based Family And Nondirective Supportive Treatments For Youth Who Are Suicidal, Guy S. Diamond, Roger R. Kobak, E. Stephanie Krauthamer Ewing, Suzanne A. Levy, Joanna L. Herres, Jody M. Russon, Robert J. Gallop
A Randomized Controlled Trial: Attachment-Based Family And Nondirective Supportive Treatments For Youth Who Are Suicidal, Guy S. Diamond, Roger R. Kobak, E. Stephanie Krauthamer Ewing, Suzanne A. Levy, Joanna L. Herres, Jody M. Russon, Robert J. Gallop
Mathematics Faculty Publications
Objective: To evaluate the efficacy of attachment-based family therapy (ABFT) compared with a family-enhanced nondirective supportive therapy (FE-NST) for decreasing adolescents’ suicide ideation and depressive symptoms. Method: A randomized controlled trial of 129 adolescents who are suicidal ages 12- to 18-years-old (49% were African American) were randomized to ABFT (n ¼ 66) or FE-NST (n ¼ 63) for 16 weeks of treatment. Assessments occurred at baseline and 4, 8, 12, and 16 weeks. Trajectory of change and clinical recovery were calculated for suicidal ideation and depressive symptoms. Results: There was no significant between-group difference in the rate of change in …
Applications Of The Heine And Bauer-Muir Transformations To Rogers-Ramanujan Type Continued Fractions, Jongsil Lee, James Mclaughlin, Jaebum Sohn
Applications Of The Heine And Bauer-Muir Transformations To Rogers-Ramanujan Type Continued Fractions, Jongsil Lee, James Mclaughlin, Jaebum Sohn
Mathematics Faculty Publications
In this paper we show that various continued fractions for the quotient of general Ramanujan functions G(aq, b, λq)/G(a, b, λ) may be derived from each other via Bauer-Muir transformations. The separate convergence of numerators and denominators play a key part in showing that the continued fractions and their Bauer-Muir transformations converge to the same limit. We also show that these continued fractions may be derived from either Heine’s continued fraction for a ratio of 2φ1 functions, or other similar continued fraction expansions of ratios of 2φ1 functions. Further, by employing essentially the same methods, a new continued fraction for …
Mock Theta Function Identities Deriving From Bilateral Basic Hypergeometric Series, James Mclaughlin
Mock Theta Function Identities Deriving From Bilateral Basic Hypergeometric Series, James Mclaughlin
Mathematics Faculty Publications
The bilateral series corresponding to many of the third-, fifth-, sixth- and eighth order mock theta functions may be derived as special cases of 2ψ2 series ∞ ∑n=−∞ (a, c;q)n (b,d;q)n z n . Three transformation formulae for this series due to Bailey are used to derive various transformation and summation formulae for both these mock theta functions and the corresponding bilateral series. New and existing summation formulae for these bilateral series are also used to make explicit in a number of cases the fact that for a mock theta function, say χ(q), and a root of unity in a …
On Approximately Controlled Systems, Nazim I. Mahmudov, Mark A. Mckibben
On Approximately Controlled Systems, Nazim I. Mahmudov, Mark A. Mckibben
Mathematics Faculty Publications
No abstract provided.
General Existence Results For Abstract Mckean-Vlasov Stochastic Equations With Variable Delay, Mark A. Mckibben
General Existence Results For Abstract Mckean-Vlasov Stochastic Equations With Variable Delay, Mark A. Mckibben
Mathematics Faculty Publications
Results concerning the global existence and uniqueness of mild solutions for a class of first-order abstract stochastic integro-differential equations with variable delay in a real separable Hilbert space in which we allow the nonlinearities at a given time t to depend not only on the state of the solution at time t, but also on the corresponding probability distribution at time t are established. The classical Lipschitz is replaced by a weaker so-called Caratheodory condition under which we still maintain uniqueness. The time-dependent case is discussed, as well as an extension of the theory to the case of a nonlocal …
General Multi-Sum Transformations And Some Implications, James Mclaughlin
General Multi-Sum Transformations And Some Implications, James Mclaughlin
Mathematics Faculty Publications
We give two general transformations that allows certain quite general basic hypergeometric multi-sums of arbitrary depth (sums that involve an arbitrary sequence {g(k)}), to be reduced to an infinite q-product times a single basic hypergeometric sum. Various applications are given, including summation formulae for some q orthogonal polynomials, and various multisums that are expressible as infinite products.
Controllability Of Neutral Stochastic Integro-Differential Evolution Equations Driven By A Fractional Brownian Motion, El Hassan Lakhel, Mark A. Mckibben
Controllability Of Neutral Stochastic Integro-Differential Evolution Equations Driven By A Fractional Brownian Motion, El Hassan Lakhel, Mark A. Mckibben
Mathematics Faculty Publications
We establish sufficient conditions for the controllability of a certain class of neutral stochastic functional integro-differential evolution equations in Hilbert spaces. The results are obtained using semigroup theory, resolvent operators and a fixed-point technique. An application to neutral partial integro-differential stochastic equations perturbed by fractional Brownian motion is given.
A Discontinuous Galerkin Method For Unsteady Two-Dimensional Convective Flows, Andreas C. Aristotelous, N. C. Papanicolaou
A Discontinuous Galerkin Method For Unsteady Two-Dimensional Convective Flows, Andreas C. Aristotelous, N. C. Papanicolaou
Mathematics Faculty Publications
We develop a High-Order Symmetric Interior Penalty (SIP) Discontinuous Galerkin (DG) Finite Element Method (FEM) to investigate two-dimensional in space natural convective flows in a vertical cavity. The physical problem is modeled by a coupled nonlinear system of partial differential equations and admits various solutions including stable and unstable modes in the form of traveling and/or standing waves, depending on the governing parameters. These flows are characterized by steep boundary and internal layers which evolve with time and can be well-resolved by high-order methods that also are adept to adaptive meshing. The standard no-slip boundary conditions which apply on the …
Refinements Of Some Partition Inequalities, James Mclaughlin
Refinements Of Some Partition Inequalities, James Mclaughlin
Mathematics Faculty Publications
In the present paper we initiate the study of a certain kind of partition inequality, by showing, for example, that if M ≥ 5 is an integer and the integers a and b are relatively prime to M and satisfy 1 ≤ a < b < M/2, and the c(m, n) are defined by 1 (sqa, sqM−a; qM)∞ − 1 (sqb , sqM−b ; qM)∞ := X m,n≥0 c(m, n)s mq n , then c(m, Mn) ≥ 0 for all integers m ≥ 0, n ≥ 0. A similar result is proved for the integers d(m, n) defined by (−sqa , −sqM−a ; q M)∞ − (−sqb , −sqM−b ; q M)∞ := X m,n≥0 d(m, n)s mq n . In each case there are obvious interpretations in terms of integer partitions. For example, if p1,5(m, n) (respectively p2,5(m, n)) denotes the number of partitions of n into exactly m parts ≡ ±1( mod 5) (respectively ≡ ±2( mod 5)), then for each integer n ≥ 1, p1,5(m, 5n) ≥ p2,5(m, 5n), 1 ≤ m ≤ 5n.
Dialectical Behavior Therapy For High Suicide Risk In Individuals With Borderline Personality Disorder: A Randomized Clinical Trial And Component Analysis, Marsha M. Linehan, Kathryn E. Korslund, Melanie S. Harned, Robert J. Gallop, Anita Lungu, Andrada D. Neacsiu, Joshua Mcdavid, Katherine Anne Comtois, Angela M. Murray-Gregory
Dialectical Behavior Therapy For High Suicide Risk In Individuals With Borderline Personality Disorder: A Randomized Clinical Trial And Component Analysis, Marsha M. Linehan, Kathryn E. Korslund, Melanie S. Harned, Robert J. Gallop, Anita Lungu, Andrada D. Neacsiu, Joshua Mcdavid, Katherine Anne Comtois, Angela M. Murray-Gregory
Mathematics Faculty Publications
No abstract provided.
Open And Dense Topological Transitivity Of Extensions By Non-Compact Fiber Of Hyperbolic Systems: A Review, Viorel Nitica, Andrei Török
Open And Dense Topological Transitivity Of Extensions By Non-Compact Fiber Of Hyperbolic Systems: A Review, Viorel Nitica, Andrei Török
Mathematics Faculty Publications
Currently, there is great renewed interest in proving the topological transitivity of various classes of continuous dynamical systems. Even though this is one of the most basic dynamical properties that can be investigated, the tools used by various authors are quite diverse and are strongly related to the class of dynamical systems under consideration. The goal of this review article is to present the state of the art for the class of Hölder extensions of hyperbolic systems with non-compact connected Lie group fiber. The hyperbolic systems we consider are mostly discrete time. In particular, we address the stability and genericity …
Control, Stability, And Qualitative Theory Of Dynamical Systems 2014, Nazim I. Mahmudov, Mark A. Mckibben, Sakthivel Rathinasamy, Yong Ren
Control, Stability, And Qualitative Theory Of Dynamical Systems 2014, Nazim I. Mahmudov, Mark A. Mckibben, Sakthivel Rathinasamy, Yong Ren
Mathematics Faculty Publications
No abstract provided.
Further Results On Vanishing Coefficients In Infinite Product Expansions, James Mclaughlin
Further Results On Vanishing Coefficients In Infinite Product Expansions, James Mclaughlin
Mathematics Faculty Publications
We extend results of Andrews and Bressoud on the vanishing of coefficients in the series expansions of certain infinite products. These results have the form that if (q r−tk, qmk−(r−tk) ; q mk)∞ (q r, qmk−r; qmk)∞ =: X∞ n=0 cnq n , for certain integers k, m s and t, where r = sm+t, then ckn−rs is always zero. Our theorems also partly give a simpler reformulation of results of Alladi and Gordon, but also give results for cases not covered by the theorems of Alladi and Gordon. We also give some interpretations of the analytic results in terms …
Predictors And Moderators Of Outcomes Of Hiv/Std Sex Risk Reduction Interventions In Substance Abuse Treatment Programs: A Pooled Analysis Of Two Randomized Controlled Trials, Paul Crits-Christoph, Robert Gallop, Jaclyn S. Sadicario, Hannah M. Markell, Donald A. Calsyn, Wan Tang, Hua He, Xin Tu, George Woody
Predictors And Moderators Of Outcomes Of Hiv/Std Sex Risk Reduction Interventions In Substance Abuse Treatment Programs: A Pooled Analysis Of Two Randomized Controlled Trials, Paul Crits-Christoph, Robert Gallop, Jaclyn S. Sadicario, Hannah M. Markell, Donald A. Calsyn, Wan Tang, Hua He, Xin Tu, George Woody
Mathematics Faculty Publications
No abstract provided.
Abstract Functional Stochastic Evolution Equations Driven By Fractional Brownian Motion, Mark A. Mckibben, Micah Webster
Abstract Functional Stochastic Evolution Equations Driven By Fractional Brownian Motion, Mark A. Mckibben, Micah Webster
Mathematics Faculty Publications
We investigate a class of abstract functional stochastic evolution equations driven by a fractional Brownianmotion in a real separable Hilbert space.Global existence results concerningmild solutions are formulated under various growth and compactness conditions. Continuous dependence estimates and convergence results are also established. Analysis of three stochastic partial differential equations, including a second-order stochastic evolution equation arising in the modeling of wave phenomena and a nonlinear diffusion equation, is provided to illustrate the applicability of the general theory.
A Metric On Max-Min Algebra, Jonathan Eskeldson, Miriam Jaffe, Viorel Nitica
A Metric On Max-Min Algebra, Jonathan Eskeldson, Miriam Jaffe, Viorel Nitica
Mathematics Faculty Publications
No abstract provided.
Tropical Convexity Over Max-Min Semiring, Viorel Nitica, Sergei Sergeev
Tropical Convexity Over Max-Min Semiring, Viorel Nitica, Sergei Sergeev
Mathematics Faculty Publications
No abstract provided.
Measure-Dependent Stochastic Nonlinear Beam Equations Driven By Fractional Brownian Motion, Mark A. Mckibben
Measure-Dependent Stochastic Nonlinear Beam Equations Driven By Fractional Brownian Motion, Mark A. Mckibben
Mathematics Faculty Publications
We study a class of nonlinear stochastic partial differential equations arising in themathematicalmodeling of the transverse motion of an extensible beam in the plane. Nonlinear forcing terms of functional-type and those dependent upon a family of probability measures are incorporated into the initial-boundary value problem (IBVP), and noise is incorporated into the mathematical description of the phenomenon via a fractional Brownian motion process. The IBVP is subsequently reformulated as an abstract second-order stochastic evolution equation driven by a fractional Brownian motion (fBm) dependent upon a family of probability measures in a real separableHilbert space and is studied using the tools …
Control, Stability, And Qualitative Theory Of Dynamical Systems, Nazim Idrisoglu Mahmudov, Mark A. Mckibben, Sakthivel Rathinasamy, Yong Ren
Control, Stability, And Qualitative Theory Of Dynamical Systems, Nazim Idrisoglu Mahmudov, Mark A. Mckibben, Sakthivel Rathinasamy, Yong Ren
Mathematics Faculty Publications
No abstract provided.
A Reciprocity Relation For Wp-Bailey Pairs, James Mclaughlin, Peter Zimmer
A Reciprocity Relation For Wp-Bailey Pairs, James Mclaughlin, Peter Zimmer
Mathematics Faculty Publications
We derive a new general transformation for WP-Bailey pairs by considering the a certain limiting case of a WP-Bailey chain previously found by the authors, and examine several consequences of this new transformation. These consequences include new summation formulae involving WP-Bailey pairs. Other consequences include new proofs of some classical identities due to Jacobi, Ramanujan and others, and indeed extend these identities to identities involving particular specializations of arbitrary WP-Bailey pairs.
A Hardy-Ramanujan-Rademacher-Type Formula For (R,S)-Regular Partitions, James Mclaughlin, Scott Parsell
A Hardy-Ramanujan-Rademacher-Type Formula For (R,S)-Regular Partitions, James Mclaughlin, Scott Parsell
Mathematics Faculty Publications
Let pr,s(n) denote the number of partitions of a positive integer n into parts containing no multiples of r or s, where r > 1 and s > 1 are square-free, relatively prime integers. We use classical methods to derive a Hardy-Ramanujan-Rademacher-type infinite series for pr,s(n).