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Full-Text Articles in Physical Sciences and Mathematics

Infusing Humanities In Stem Education: Student Opinions Of Disciplinary Connections In An Introductory Chemistry Course, Emily K. Faulconer, Beverly Wood, John C. Griffith Mar 2020

Infusing Humanities In Stem Education: Student Opinions Of Disciplinary Connections In An Introductory Chemistry Course, Emily K. Faulconer, Beverly Wood, John C. Griffith

Publications

The Next Generation Science Standards and other educational reforms support the formation of deep connections across the STEM disciplines. Integrated STEM is considered as a best practice by the educational communities of the disparate disciplines. However, the integration of non-STEM disciplines is understudied and generally limited to the integration of art (STEAM). Humanistic STEM blends the study of STEM with interest in and concern for human affairs, welfare, values, or culture. This study looks at an infusion of the humanities into an online chemistry course to see if there is an influence on student connection between course content and cross-disciplinary ...


Spacetime Groups, Ian M. Anderson, Charles G. Torre Jan 2019

Spacetime Groups, Ian M. Anderson, Charles G. Torre

Publications

A spacetime group is a connected 4-dimensional Lie group G endowed with a left invariant Lorentz metric h and such that the connected component of the isometry group of h is G itself. The Newman-Penrose formalism is used to give an algebraic classification of spacetime groups, that is, we determine a complete list of inequivalent spacetime Lie algebras, which are pairs (g,η), with g being a 4-dimensional Lie algebra and η being a Lorentzian inner product on g. A full analysis of the equivalence problem for spacetime Lie algebras is given which leads to a completely algorithmic solution to ...


Weighted Composition Operators On Analytic Function Spaces: Some Recent Progress, Dip Acharyya Oct 2018

Weighted Composition Operators On Analytic Function Spaces: Some Recent Progress, Dip Acharyya

Publications

Theory of Composition Operators is a steady point of interest for almost 100 years. While studying these operators, our general goal is to describe their operator theoretic properties in terms of the associated function symbols. In this talk, I will discuss some recent results concerning linear combinations (sums, differences, etc.) of weighted composition operators in certain spaces of Analytic functions.


Weighted Composition Operators On Spaces Of Analytic Functions: A Survey, Soumyadip Acharyya Sep 2018

Weighted Composition Operators On Spaces Of Analytic Functions: A Survey, Soumyadip Acharyya

Publications

“Pure mathematics is, in its way, the poetry of logical ideas.” - Albert Einstein. Pure mathematicians study abstract entities and structures that underlie mathematics. Although their general perspective is “math for math’s sake”, sometimes even the most abstract mathematics can have unexpected applications! Come learn some of these astonishing discoveries in the history of science and mathematics! They might make you thrilled but keep in mind real-world usage is rarely the goal behind developing a new mathematical theory.

Welcome to the world of pure mathematics! In this talk, we will focus on the theory of composition operators which is a ...


A Mean-Risk Mixed Integer Nonlinear Program For Transportation Network Protection, Jie Lu, Akshay Gupte, Yongxi Huang Feb 2018

A Mean-Risk Mixed Integer Nonlinear Program For Transportation Network Protection, Jie Lu, Akshay Gupte, Yongxi Huang

Publications

This paper focuses on transportation network protection to hedge against extreme events such as earthquakes. Traditional two-stage stochastic programming has been widely adopted to obtain solutions under a risk-neutral preference through the use of expectations in the recourse function. In reality, decision makers hold different risk preferences. We develop a mean-risk two-stage stochastic programming model that allows for greater flexibility in handling risk preferences when allocating limited resources. In particular, the first stage minimizes the retrofitting cost by making strategic retrofit decisions whereas the second stage minimizes the travel cost. The conditional value-at-risk (CVaR) is included as the risk measure ...


Almost-Bps Solutions In Multi-Center Taub-Nut, C. Rugina, A. Ludu Oct 2017

Almost-Bps Solutions In Multi-Center Taub-Nut, C. Rugina, A. Ludu

Publications

Microstates of multiple collinear black holes embedded in a non-collinear two-center Taub-NUT spacetime are sought in 4 dimensions. A set of coupled partial differential equations are obtained and solved for almost-BPS states, where some supersymmetry is preserved in the context of N = 2 supergravity in 4 dimensions. The regularity of solutions is carefully considered, and we ensure that no CTC (closed time-like curves) are present. The larger framework is that of 11-dimensional N = 2 supergravity, and the current theory is obtained by compactifying it down to 4 dimensions. This work is a generalization (to three non-collinear centers) of a previous ...


Elliptic Solutions And Solitary Waves Of A Higher Order Kdv-Bbm Long Wave Equation, Stefan C. Mancas, Ronald Adams Aug 2017

Elliptic Solutions And Solitary Waves Of A Higher Order Kdv-Bbm Long Wave Equation, Stefan C. Mancas, Ronald Adams

Publications

We provide conditions for existence of hyperbolic, unbounded periodic and elliptic solutions in terms of Weierstrass ℘ functions of both third and fifth-order KdV–BBM (Korteweg-de Vries–Benjamin, Bona & Mahony) regularized long wave equation. An analysis for the initial value problem is developed together with a local and global well-posedness theory for the third-order KdV–BBM equation. Traveling wave reduction is used together with zero boundary conditions to yield solitons and periodic unbounded solutions, while for nonzero boundary conditions we find solutions in terms of Weierstrass elliptic ℘ functions. For the fifth-order KdV–BBM equation we show that a parameter γ = 1 ...


Generalized Thomas-Fermi Equations As The Lampariello Class Of Emden-Fowler Equations, Haret C. Rosu, Stefan C. Mancas Apr 2017

Generalized Thomas-Fermi Equations As The Lampariello Class Of Emden-Fowler Equations, Haret C. Rosu, Stefan C. Mancas

Publications

A one-parameter family of Emden-Fowler equations defined by Lampariello’s parameter p which, upon using Thomas-Fermi boundary conditions, turns into a set of generalized Thomas-Fermi equations comprising the standard Thomas-Fermi equation for p = 1 is studied in this paper. The entire family is shown to be non integrable by reduction to the corresponding Abel equations whose invariants do not satisfy a known integrability condition. We also discuss the equivalent dynamical system of equations for the standard Thomas-Fermi equation and perform its phase-plane analysis. The results of the latter analysis are similar for the whole class.


Difference Of Two Weighted Composition Operators On Bergman Spaces, S. Acharyya, Z. Wu Mar 2017

Difference Of Two Weighted Composition Operators On Bergman Spaces, S. Acharyya, Z. Wu

Publications

Following the techniques developed by Moorhouse and Saukko, the authors characterize the compactness of the difference of two weighted composition operators acting between different weighted Bergman spaces, under certain restrictions on the weights.


Synchrony In A Boolean Network Of The L-Arabinose Operon In Escherichia Coli, Andy Jenkins, Matthew Macauley Nov 2016

Synchrony In A Boolean Network Of The L-Arabinose Operon In Escherichia Coli, Andy Jenkins, Matthew Macauley

Publications

The lactose operon in Escherichia coli was the first known gene regulatory network, and it is frequently used as a prototype for new modeling paradigms. Historically, many of these modeling frameworks use differential equations. More recently, Stigler and Veliz-Cuba proposed a Boolean network model that captures the bistability of the system and all of the biological steady states. In this paper, we model the well-known arabinose operon in E. coli with a Boolean network. This has several complex features not found in the lac operon, such as a protein that is both an activator and repressor, a DNA looping mechanism ...


Noncrossing Partitions, Toggles, And Homomesies, David Einstein, Miriam Farber, Emily Gunawan, Michael Joseph, Matthew Macauley, James Propp, Simon Rubinstein-Salzedo Sep 2016

Noncrossing Partitions, Toggles, And Homomesies, David Einstein, Miriam Farber, Emily Gunawan, Michael Joseph, Matthew Macauley, James Propp, Simon Rubinstein-Salzedo

Publications

We introduce n(n−1)/2 natural involutions (“toggles”) on the set S of noncrossing partitions π of size n, along with certain composite operations obtained by composing these involutions. We show that for many operations T of this kind, a surprisingly large family of functions f on S (including the function that sends π to the number of blocks of π) exhibits the homomesy phenomenon: the average of f over the elements of a T -orbit is the same for all T -orbits. We can apply our method of proof more broadly to toggle operations back on the collection ...


Ermakov Equation And Camassa-Holm Waves, Haret C. Rosu, Stefan C. Mancas Sep 2016

Ermakov Equation And Camassa-Holm Waves, Haret C. Rosu, Stefan C. Mancas

Publications

From the works of authors of this article, it is known that the solution of the Ermakov equation is an important ingredient in the spectral problem of the Camassa-Holm equation. Here, we review this interesting issue and consider in addition more features of the Ermakov equation which have an impact on the behavior of the shallow water waves as described by the Camassa-Holm equation.


Morphisms And Order Ideals Of Toric Posets, Matthew Macauley Jun 2016

Morphisms And Order Ideals Of Toric Posets, Matthew Macauley

Publications

Toric posets are in some sense a natural “cyclic” version of finite posets in that they capture the fundamental features of a partial order but without the notion of minimal or maximal elements. They can be thought of combinatorially as equivalence classes of acyclic orientations under the equivalence relation generated by converting sources into sinks, or geometrically as chambers of toric graphic hyperplane arrangements. In this paper, we define toric intervals and toric order-preserving maps, which lead to toric analogues of poset morphisms and order ideals. We develop this theory, discuss some fundamental differences between the toric and ordinary cases ...


What Moser Could Have Asked: Counting Hamilton Cycles In Tournaments, Neil J. Calkin, Beth Novick, Hayato Ushijima-Mwesigwa Apr 2016

What Moser Could Have Asked: Counting Hamilton Cycles In Tournaments, Neil J. Calkin, Beth Novick, Hayato Ushijima-Mwesigwa

Publications

Moser asked for a construction of explicit tournaments on n vertices having at least Hamilton cycles. We show that he could have asked rather more.


Relaxations And Discretizations For The Pooling Problem, Akshay Gupte, Shabbir Ahmed, Santanu S. Dey, Myun Seok Cheon Apr 2016

Relaxations And Discretizations For The Pooling Problem, Akshay Gupte, Shabbir Ahmed, Santanu S. Dey, Myun Seok Cheon

Publications

The pooling problem is a folklore NP-hard global optimization problem that finds applications in industries such as petrochemical refining, wastewater treatment and mining. This paper assimilates the vast literature on this problem that is dispersed over different areas and gives new insights on prevalent techniques. We also present new ideas for computing dual bounds on the global optimum by solving high-dimensional linear programs. Finally, we propose discretization methods for inner approximating the feasible region and obtaining good primal bounds. Valid inequalities are derived for the discretized models, which are formulated as mixed integer linear programs. The strength of our relaxations ...


Integrable Abel Equations And Vein's Abel Equation, Stefan C. Mancas, Haret C. Rosu Apr 2016

Integrable Abel Equations And Vein's Abel Equation, Stefan C. Mancas, Haret C. Rosu

Publications

We first reformulate and expand with several novel findings some of the basic results in the integrability of Abel equations. Next, these results are applied to Vein’s Abel equation whose solutions are expressed in terms of the third order hyperbolic functions and a phase space analysis of the corresponding nonlinear oscillator is also provided.


Existence Of Periodic Orbits In Nonlinear Oscillators Of Emden-Fowler Form, Stefan C. Mancas, Haret C. Rosu Jan 2016

Existence Of Periodic Orbits In Nonlinear Oscillators Of Emden-Fowler Form, Stefan C. Mancas, Haret C. Rosu

Publications

The nonlinear pseudo-oscillator recently tackled by Gadella and Lara is mapped to an Emden–Fowler (EF) equation that is written as an autonomous two-dimensional ODE system for which we provide the phase-space analysis and the parametric solution. Through an invariant transformation we find periodic solutions to a certain class of EF equations that pass an integrability condition. We show that this condition is necessary to have periodic solutions and via the ODE analysis we also find the sufficient condition for periodic orbits. EF equations that do not pass integrability conditions can be made integrable via an invariant transformation which also ...


Nongauge Bright Soliton Of The Nonlinear Schrodinger (Nls) Equation And A Family Of Generalized Nls Equations, M. A. Reyes, D. Gutierrez-Ruiz, S. C. Mancas, H. C. Rosu Jan 2016

Nongauge Bright Soliton Of The Nonlinear Schrodinger (Nls) Equation And A Family Of Generalized Nls Equations, M. A. Reyes, D. Gutierrez-Ruiz, S. C. Mancas, H. C. Rosu

Publications

We present an approach to the bright soliton solution of the nonlinear Schrödinger (NLS) equation from the standpoint of introducing a constant potential term in the equation. We discuss a “nongauge” bright soliton for which both the envelope and the phase depend only on the traveling variable. We also construct a family of generalized NLS equations with solitonic sechpsechp solutions in the traveling variable and find an exact equivalence with other nonlinear equations, such as the Korteveg–de Vries (KdV) and Benjamin–Bona–Mahony (BBM) equations when p=2.


Toric Partial Orders, Mike Develin, Matthew Macauley, Victor Reiner Jul 2015

Toric Partial Orders, Mike Develin, Matthew Macauley, Victor Reiner

Publications

We define toric partial orders, corresponding to regions of graphic toric hyperplane arrangements, just as ordinary partial orders correspond to regions of graphic hyperplane arrangements. Combinatorially, toric posets correspond to finite posets under the equivalence relation generated by converting minimal elements into maximal elements, or sources into sinks. We derive toric analogues for several features of ordinary partial orders, such as chains, antichains, transitivity, Hasse diagrams, linear extensions, and total orders.


Formation Of Three-Dimensional Surface Waves On Deep-Water Using Elliptic Solutions Of Nonlinear Schrödinger Equation, Shahrdad G. Sajjadi, Stefan C. Mancas, Frederique Drullion Jul 2015

Formation Of Three-Dimensional Surface Waves On Deep-Water Using Elliptic Solutions Of Nonlinear Schrödinger Equation, Shahrdad G. Sajjadi, Stefan C. Mancas, Frederique Drullion

Publications

A review of three-dimensional waves on deep-water is presented. Three forms of three-dimensionality, namely oblique, forced and spontaneous types, are identified. An alternative formulation for these three-dimensional waves is given through cubic nonlinear Schrödinger equation. The periodic solutions of the cubic nonlinear Schrödinger equation are found using Weierstrass elliptic ℘ functions. It is shown that the classification of solutions depends on the boundary conditions, wavenumber and frequency. For certain parameters, Weierstrass ℘ functions are reduced to periodic, hyperbolic or Jacobi elliptic functions. It is demonstrated that some of these solutions do not have any physical significance. An analytical solution of cubic nonlinear ...


Pulses And Snakes In Ginzburg-Landau Equation, Stefan C. Mancas, Roy S. Choudhury Jan 2015

Pulses And Snakes In Ginzburg-Landau Equation, Stefan C. Mancas, Roy S. Choudhury

Publications

Using a variational formulation for partial differential equations combined with numerical simulations on ordinary differential equations (ODEs), we find two categories (pulses and snakes) of dissipative solitons, and analyze the dependence of both their shape and stability on the physical parameters of the cubic-quintic Ginzburg–Landau equation (CGLE). In contrast to the regular solitary waves investigated in numerous integrable and non-integrable systems over the last three decades, these dissipative solitons are not stationary in time. Rather, they are spatially confined pulse-type structures whose envelopes exhibit complicated temporal dynamics. Numerical simulations reveal very interesting bifurcations sequences as the parameters of the ...


An Alternate Proof Of The De Branges Theorem On Canonical Systems, Keshav R. Acharya Apr 2014

An Alternate Proof Of The De Branges Theorem On Canonical Systems, Keshav R. Acharya

Publications

The aim of this paper is to show that, in the limit circle case, the defect index of a symmetric relation induced by canonical systems, is constant on ₵. This provides an alternative proof of the De Branges theorem that the canonical systems with trH1 imply the limit point case. To this end, we discuss the spectral theory of a linear relation induced by a canonical system.


One-Parameter Families Of Supersymmetric Isospectral Potentials From Riccati Solutions In Function Composition Form, Haret C. Rosu, Stefan C. Mancas, Pisin Chen Apr 2014

One-Parameter Families Of Supersymmetric Isospectral Potentials From Riccati Solutions In Function Composition Form, Haret C. Rosu, Stefan C. Mancas, Pisin Chen

Publications

In the context of supersymmetric quantum mechanics, we define a potential through a particular Riccati solution of the composition form (F∘f)(x)=F(f(x)) and obtain a generalized Mielnik construction of one-parameter isospectral potentials when we use the general Riccati solution. Some examples for special cases of F and f are given to illustrate the method. An interesting result is obtained in the case of a parametric double well potential generated by this method, for which it is shown that the parameter of the potential controls the heights of the localization probability in the two wells, and for ...


Self-Adjoint Extension And Spectral Theory Of A Linear Relation In A Hilbert Space, Keshav R. Acharya Mar 2014

Self-Adjoint Extension And Spectral Theory Of A Linear Relation In A Hilbert Space, Keshav R. Acharya

Publications

The aim of this paper is to develop the conditions for a symmetric relation in a Hilbert space ℋ to have self-adjoint extensions in terms of defect indices and discuss some spectral theory of such linear relation.


A Regression Model To Investigate The Performance Of Black-Scholes Using Macroeconomic Predictors, Timothy A. Smith, Ersoy Subasi, Aliraza M. Rattansi Jan 2014

A Regression Model To Investigate The Performance Of Black-Scholes Using Macroeconomic Predictors, Timothy A. Smith, Ersoy Subasi, Aliraza M. Rattansi

Publications

As it is well known an option is defined as the right to buy sell a certain asset, thus, one can look at the purchase of an option as a bet on the financial instrument under consideration. Now while the evaluation of options is a completely different mathematical topic than the prediction of future stock prices, there is some relationship between the two. It is worthy to note that henceforth we will only consider options that have a given fixed expiration time T, i.e., we restrict the discussion to the so called European options. Now, for a simple illustration ...


Not All Traces On The Circle Come From Functions Of Least Gradient In The Disk, Gregory S. Spradlin, Alexandru Tamasan Jan 2014

Not All Traces On The Circle Come From Functions Of Least Gradient In The Disk, Gregory S. Spradlin, Alexandru Tamasan

Publications

We provide an example of an L¹ function on the circle, which cannot be the trace of a function of bounded variation of least gradient in the disk.


On The Cyclically Fully Commutative Elements Of Coxeter Groups, T. Boothby, J. Burket, M. Eichwald, D. C. Ernst, R. M. Green, Matthew Macauley Aug 2012

On The Cyclically Fully Commutative Elements Of Coxeter Groups, T. Boothby, J. Burket, M. Eichwald, D. C. Ernst, R. M. Green, Matthew Macauley

Publications

Let W be an arbitrary Coxeter group. If two elements have expressions that are cyclic shifts of each other (as words), then they are conjugate (as group elements) in W. We say that w is cyclically fully commutative (CFC) if every cyclic shift of any reduced expression for w is fully commutative (i.e., avoids long braid relations). These generalize Coxeter elements in that their reduced expressions can be described combinatorially by acyclic directed graphs, and cyclically shifting corresponds to source-to-sink conversions. In this paper, we explore the combinatorics of the CFC elements and enumerate them in all Coxeter groups ...


2d Novel Structures Along An Opitcal Fiber, Charles-Julien Vandamme, Stefan C. Mancas Jun 2012

2d Novel Structures Along An Opitcal Fiber, Charles-Julien Vandamme, Stefan C. Mancas

Publications

By using spectral methods, we present seven classes of stable and unstable structures that occur in a dissipative media. By varying parameters and initial conditions we find ranges of existence of stable structures (spinning elliptic, pulsating, stationary, organized exploding), and unstable structures (filament, disorganized exploding, creeping). By varying initial conditions, vorticity, and parameters of the equation, we find a reacher behavior of solutions in the form of creeping-vortex (propellers), spinning rings and spinning “bean-shape” solitons. Each class differentiates from the other by distinctive features of their shape and energy evolution, as well as domain of existence.


Nested Canalyzing Depth And Network Stability, Lori Layne, Elena Dimitrova, Matthew Macauley Feb 2012

Nested Canalyzing Depth And Network Stability, Lori Layne, Elena Dimitrova, Matthew Macauley

Publications

We introduce the nested canalyzing depth of a function, which measures the extent to which it retains a nested canalyzing structure. We characterize the structure of functions with a given depth and compute the expected activities and sensitivities of the variables. This analysis quantifies how canalyzation leads to higher stability in Boolean networks. It generalizes the notion of nested canalyzing functions (NCFs), which are precisely the functions with maximum depth. NCFs have been proposed as gene regulatory network models, but their structure is frequently too restrictive and they are extremely sparse. We find that functions become decreasingly sensitive to input ...


Vortex Patterns Beyond Hypergeometric, Andrei Ludu Jan 2012

Vortex Patterns Beyond Hypergeometric, Andrei Ludu

Publications

We prove that loop vortices are created by a point-like magnetic dipole in an infinite superconductor space. The geometry of the vortex system is obtained through analytic solutions of the linearized Ginzburg-Landau equation described in terms of Heun functions, generalizing the traditional hypergeometric behavior of such magnetic singularity.