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FullText 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
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 nonSTEM 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 crossdisciplinary ...
Spacetime Groups, Ian M. Anderson, Charles G. Torre
Spacetime Groups, Ian M. Anderson, Charles G. Torre
Publications
A spacetime group is a connected 4dimensional 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 NewmanPenrose 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 4dimensional 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
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
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 realworld 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 MeanRisk Mixed Integer Nonlinear Program For Transportation Network Protection, Jie Lu, Akshay Gupte, Yongxi Huang
A MeanRisk 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 twostage stochastic programming has been widely adopted to obtain solutions under a riskneutral preference through the use of expectations in the recourse function. In reality, decision makers hold different risk preferences. We develop a meanrisk twostage 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 valueatrisk (CVaR) is included as the risk measure ...
AlmostBps Solutions In MultiCenter TaubNut, C. Rugina, A. Ludu
AlmostBps Solutions In MultiCenter TaubNut, C. Rugina, A. Ludu
Publications
Microstates of multiple collinear black holes embedded in a noncollinear twocenter TaubNUT spacetime are sought in 4 dimensions. A set of coupled partial differential equations are obtained and solved for almostBPS 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 timelike curves) are present. The larger framework is that of 11dimensional N = 2 supergravity, and the current theory is obtained by compactifying it down to 4 dimensions. This work is a generalization (to three noncollinear centers) of a previous ...
Elliptic Solutions And Solitary Waves Of A Higher Order KdvBbm Long Wave Equation, Stefan C. Mancas, Ronald Adams
Elliptic Solutions And Solitary Waves Of A Higher Order KdvBbm 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 fifthorder KdV–BBM (Kortewegde Vries–Benjamin, Bona & Mahony) regularized long wave equation. An analysis for the initial value problem is developed together with a local and global wellposedness theory for the thirdorder 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 fifthorder KdV–BBM equation we show that a parameter γ = 1 ...
Generalized ThomasFermi Equations As The Lampariello Class Of EmdenFowler Equations, Haret C. Rosu, Stefan C. Mancas
Generalized ThomasFermi Equations As The Lampariello Class Of EmdenFowler Equations, Haret C. Rosu, Stefan C. Mancas
Publications
A oneparameter family of EmdenFowler equations defined by Lampariello’s parameter p which, upon using ThomasFermi boundary conditions, turns into a set of generalized ThomasFermi equations comprising the standard ThomasFermi 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 ThomasFermi equation and perform its phaseplane 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
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 LArabinose Operon In Escherichia Coli, Andy Jenkins, Matthew Macauley
Synchrony In A Boolean Network Of The LArabinose 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 VelizCuba 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 wellknown 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 RubinsteinSalzedo
Noncrossing Partitions, Toggles, And Homomesies, David Einstein, Miriam Farber, Emily Gunawan, Michael Joseph, Matthew Macauley, James Propp, Simon RubinsteinSalzedo
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 CamassaHolm Waves, Haret C. Rosu, Stefan C. Mancas
Ermakov Equation And CamassaHolm 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 CamassaHolm 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 CamassaHolm equation.
Morphisms And Order Ideals Of Toric Posets, Matthew Macauley
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 orderpreserving 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 UshijimaMwesigwa
What Moser Could Have Asked: Counting Hamilton Cycles In Tournaments, Neil J. Calkin, Beth Novick, Hayato UshijimaMwesigwa
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
Relaxations And Discretizations For The Pooling Problem, Akshay Gupte, Shabbir Ahmed, Santanu S. Dey, Myun Seok Cheon
Publications
The pooling problem is a folklore NPhard 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 highdimensional 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
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 EmdenFowler Form, Stefan C. Mancas, Haret C. Rosu
Existence Of Periodic Orbits In Nonlinear Oscillators Of EmdenFowler Form, Stefan C. Mancas, Haret C. Rosu
Publications
The nonlinear pseudooscillator recently tackled by Gadella and Lara is mapped to an Emden–Fowler (EF) equation that is written as an autonomous twodimensional ODE system for which we provide the phasespace 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. GutierrezRuiz, S. C. Mancas, H. C. Rosu
Nongauge Bright Soliton Of The Nonlinear Schrodinger (Nls) Equation And A Family Of Generalized Nls Equations, M. A. Reyes, D. GutierrezRuiz, 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
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 ThreeDimensional Surface Waves On DeepWater Using Elliptic Solutions Of Nonlinear Schrödinger Equation, Shahrdad G. Sajjadi, Stefan C. Mancas, Frederique Drullion
Formation Of ThreeDimensional Surface Waves On DeepWater Using Elliptic Solutions Of Nonlinear Schrödinger Equation, Shahrdad G. Sajjadi, Stefan C. Mancas, Frederique Drullion
Publications
A review of threedimensional waves on deepwater is presented. Three forms of threedimensionality, namely oblique, forced and spontaneous types, are identified. An alternative formulation for these threedimensional 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 GinzburgLandau Equation, Stefan C. Mancas, Roy S. Choudhury
Pulses And Snakes In GinzburgLandau 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 cubicquintic Ginzburg–Landau equation (CGLE). In contrast to the regular solitary waves investigated in numerous integrable and nonintegrable systems over the last three decades, these dissipative solitons are not stationary in time. Rather, they are spatially confined pulsetype 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
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.
OneParameter Families Of Supersymmetric Isospectral Potentials From Riccati Solutions In Function Composition Form, Haret C. Rosu, Stefan C. Mancas, Pisin Chen
OneParameter 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 oneparameter 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 ...
SelfAdjoint Extension And Spectral Theory Of A Linear Relation In A Hilbert Space, Keshav R. Acharya
SelfAdjoint 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 selfadjoint extensions in terms of defect indices and discuss some spectral theory of such linear relation.
A Regression Model To Investigate The Performance Of BlackScholes Using Macroeconomic Predictors, Timothy A. Smith, Ersoy Subasi, Aliraza M. Rattansi
A Regression Model To Investigate The Performance Of BlackScholes 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
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
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 sourcetosink 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, CharlesJulien Vandamme, Stefan C. Mancas
2d Novel Structures Along An Opitcal Fiber, CharlesJulien 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 creepingvortex (propellers), spinning rings and spinning “beanshape” 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
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
Vortex Patterns Beyond Hypergeometric, Andrei Ludu
Publications
We prove that loop vortices are created by a pointlike magnetic dipole in an infinite superconductor space. The geometry of the vortex system is obtained through analytic solutions of the linearized GinzburgLandau equation described in terms of Heun functions, generalizing the traditional hypergeometric behavior of such magnetic singularity.