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Articles 751 - 779 of 779

Full-Text Articles in Mathematics

Integrable Equations With Non-Smooth Solitons, Xianqi Li Aug 2009

Integrable Equations With Non-Smooth Solitons, Xianqi Li

Theses and Dissertations - UTB/UTPA

In this thesis, we present a class of integrable equations with non-smooth soliton solutions. In particular, we derive the bi-Hamiltonian structure and Lax pair of the equation pt = bux + \[{u2 — u1)p]x,p = u — uxx, which guarantee its integrability. Another interesting integrable equation we study is (=Jff!i)t = 2uux, which is exactly the first member of the negative KdV hierarchy. Through traveling wave setting arid phase step analysis, we obtain non-smooth soliton solutions of these integrable equations under different boundary condition at infinities. These equations were shown to have peaked soliton (peakon), "W/M-shape" peakon or cusped soliton …

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Two-Dimensional Wigner-Ville Transforms And Their Basic Properties, Bheemaiah Veena Shankara Narayana Rao Aug 2009

Two-Dimensional Wigner-Ville Transforms And Their Basic Properties, Bheemaiah Veena Shankara Narayana Rao

Theses and Dissertations - UTB/UTPA

This thesis deals with Wigner-Ville transforms and their basic properties. The Wigner-Ville transforms are a non-linear transform which constitute an important tool in nonstationary signal analysis. Wigner-Ville transforms in one dimension and their basic properties are discussed here. Special attention is given to formulation of two dimensional Wigner-Ville transform, its inversion formula and some of their basic properties. Some applications of Wigner-Ville transforms are also briefly discussed.

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Reaction-Diffusion Systems With A Nonlinear Rate Of Growth, Yubing Wan Aug 2009

Reaction-Diffusion Systems With A Nonlinear Rate Of Growth, Yubing Wan

Theses and Dissertations - UTB/UTPA

In the literature there are quite a few elegant approaches which have been proposed to find (he first integrals of nonlinear differential equations. Recently, the modified Prelle-Singer method for finding the first integrals of second-order nonlinear ordinary differential equations (ODEs) has attracted considerable attention. Many researchers used this method to derive the first integrals to various systems. In this thesis, we are concerned with the first integrals for reaction-diffusion systems with a nonlinear rate of growth. Under certain parametric conditions we express the first integrals explicitly by applying an analytical method as well as the modified Prelle-Singer method.

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Analytical And Computational Studies Of Magneto-Convection In Solidifying Mushy Layer, Mallikarjunaiah Siddapura Muddamallappa Aug 2009

Analytical And Computational Studies Of Magneto-Convection In Solidifying Mushy Layer, Mallikarjunaiah Siddapura Muddamallappa

Theses and Dissertations - UTB/UTPA

Natural convection in solidifying binary media is of great interest due to it's applications in material processing and crystal growth industries. Convective flows between the layers of melt during alloy solidification is known to produce mechanical imperfections such as freckle's. Hence it is important to investigate the criterion for freckling and discover the means of suppressing it. A mushy layer, which has both solid and fluid components and is formed between underlying solid and overlying liquid, is known to produce chimneys, which are narrow, vertical vents, devoid of solid. We consider the problem of magneto-convection in a horizontal mushy layer …

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A Dna Approach To The Road-Coloring Problem, Arindam Roy Aug 2009

A Dna Approach To The Road-Coloring Problem, Arindam Roy

Theses and Dissertations - UTB/UTPA

The Road-Coloring Problem in graph theory can be stated as follows: Is any irreducible aperiodic directed graph with constant outdegree 2 road-colorable? In other words, does such a graph have a synchronizing instruction? That is to say: can we label (or color) the two outgoing edges at each vertex, one with “b” or blue color and the other with “r” or red color, in such a manner that there will be an instruction in the form of a finite sequence in “b”s and “r”s (example: rrbrbbbr) such that this instruction will lead each vertex to the same “target” vertex? This …

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Analysis Of Rotating Flow Around A Growing Protein Crystal, Daniel N. Riahi, Charles W. Obare Jun 2009

Analysis Of Rotating Flow Around A Growing Protein Crystal, Daniel N. Riahi, Charles W. Obare

School of Mathematical & Statistical Sciences Faculty Publications

We consider the problem of steady flow around a growing protein crystal in a medium of its solution in a normal gravity environment. The whole flow system is assumed to be rotating with a constant angular velocity about a vertical axis which is anti-parallel to the gravity vector. Convective flow takes place due to the solute depletion around the growing crystal which leads to a buoyancy driven flow. Such convective flow can produce inhomogeneous solute concentration, which subsequently generate non-uniformities in the crystal’s structure finalizing lower quality protein crystal. Using scaling analysis within a diffusion boundary layer around the crystal, …

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A Comparative Study Of Risk Factors Involved In Diabetes Between Texas And Other States, Andres Padilla Oviedo May 2009

A Comparative Study Of Risk Factors Involved In Diabetes Between Texas And Other States, Andres Padilla Oviedo

Theses and Dissertations - UTB/UTPA

Diabetes is a serious concern in the United States and Texas is a state with high percentage of diabetes. The risk factors contributing to diabetes are current smoking, high blood cholesterol, hypertension, physical inactivity etc. In this thesis, we would like to identify the crucial risk factors for Texas. This motivates us to use the online data resources for a comparative study between Texas and other states. Looking at the data, we decide to use independent sample t-tests and independent sample non parametric tests [Wilcoxon Mann Whitney] for such comparative studies. This analysis has two parts – in the first …

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Locality And Stability Of The Cascades Of Two-Dimensional Turbulence, Eleftherios Gkioulekas Dec 2008

Locality And Stability Of The Cascades Of Two-Dimensional Turbulence, Eleftherios Gkioulekas

School of Mathematical & Statistical Sciences Faculty Publications

We investigate and clarify the notion of locality as it pertains to the cascades of two-dimensional turbulence. The mathematical framework underlying our analysis is the infinite system of balance equations that govern the generalized unfused structure functions, first introduced by L’vov and Procaccia. As a point of departure we use a revised version of the system of hypotheses that was proposed by Frisch for three-dimensional turbulence. We show that both the enstrophy cascade and the inverse energy cascade are local in the sense of nonperturbative statistical locality. We also investigate the stability conditions for both cascades. We have shown that …

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Some Applications Of Dirac's Delta Function In Statistics For More Than One Random Variable, Santanu Chakraborty Jun 2008

Some Applications Of Dirac's Delta Function In Statistics For More Than One Random Variable, Santanu Chakraborty

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, we discuss some interesting applications of Dirac's delta function in Statistics. We have tried to extend some of the existing results to the more than one variable case. While doing that, we particularly concentrate on the bivariate case.

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Winterberg’S Conjectured Breaking Of The Superluminal Quantum Correlations Over Large Distances, Eleftherios Gkioulekas May 2008

Winterberg’S Conjectured Breaking Of The Superluminal Quantum Correlations Over Large Distances, Eleftherios Gkioulekas

School of Mathematical & Statistical Sciences Faculty Publications

We elaborate further on a hypothesis by Winterberg that turbulent fluctuations of the zero point field may lead to a breakdown of the superluminal quantum correlations over very large distances. A phenomenological model that was proposed by Winterberg to estimate the transition scale of the conjectured breakdown, does not lead to a distance that is large enough to be agreeable with recent experiments. We consider, but rule out, the possibility of a steeper slope in the energy spectrum of the turbulent fluctuations, due to compressibility, as a possible mechanism that may lead to an increased lower-bound for the transition scale. …

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Quantum Phases For A Generalized Harmonic Oscillator, Paul Bracken Jan 2008

Quantum Phases For A Generalized Harmonic Oscillator, Paul Bracken

School of Mathematical & Statistical Sciences Faculty Publications

An effective Hamiltonian for the generalized harmonic oscillator is determined by using squeezed state wavefunctions. The equations of motion over an extended phase space are determined and then solved perturbatively for a specific choice of the oscillator parameters. These results are used to calculate the dynamic and geometric phases for the generalized oscillator with this choice of parameters.

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An Action For A Classical String, The Equation Of Motion And Group Invariant Classical Solutions, Paul Bracken Jan 2008

An Action For A Classical String, The Equation Of Motion And Group Invariant Classical Solutions, Paul Bracken

School of Mathematical & Statistical Sciences Faculty Publications

A string action which is essentially a Willmore functional is presented and studied. This action determines the physics of a surface in Euclidean three space which can be used to model classical string configurations. By varying this action an equation of motion for the mean curvature of the surface is obtained which is shown to govern certain classical string configurations. Several classes of classical solutions for this equation are discussed from the symmetry group point of view and an application is presented.

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A Fragment On Euler's Constant In Ramanujan's Lost Notebook, Bruce C. Berndt, Timothy Huber Jan 2008

A Fragment On Euler's Constant In Ramanujan's Lost Notebook, Bruce C. Berndt, Timothy Huber

School of Mathematical & Statistical Sciences Faculty Publications

A formula for Euler’s constant found in Ramanujan’s lost notebook and also in a problem he submitted to the Journal of the Indian Mathematical Society is proved and discussed.

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On Mathematical Modeling, Nonlinear Properties And Stability Of Secondary Flow In A Dendrite Layer, Daniel N. Riahi Dec 2007

On Mathematical Modeling, Nonlinear Properties And Stability Of Secondary Flow In A Dendrite Layer, Daniel N. Riahi

School of Mathematical & Statistical Sciences Faculty Publications

This paper studies instabilities in the flow of melt within a horizontal dendrite layer with deformed upper boundary and in the presence or absence of rotation during the solidification of a binary alloy. In the presence of rotation, it is assumed that the layer is rotating about a vertical axis at a constant angular velocity. Linear and weakly nonlinear stability analyses provide results about various flow features such as the critical mode of convection, neutral stability curve, preferred flow pattern and the solid fraction distribution within the dendrite layer. The preferred shape of the deformed upper boundary of the layer, …

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Is The Subdominant Part Of The Energy Spectrum Due To Downscale Energy Cascade Hidden In Quasi-Geostrophic Turbulence?, Eleftherios Gkioulekas, Ka Kit Tung Sep 2007

Is The Subdominant Part Of The Energy Spectrum Due To Downscale Energy Cascade Hidden In Quasi-Geostrophic Turbulence?, Eleftherios Gkioulekas, Ka Kit Tung

School of Mathematical & Statistical Sciences Faculty Publications

In systems governing two-dimensional turbulence, surface quasi-geostrophic turbulence, (more generally $\alpha$-turbulence), two-layer quasi-geostrophic turbulence, etc., there often exist two conservative quadratic quantities, one "energy''-like and one "enstrophy''-like. In a finite inertial range there are in general two spectral fluxes, one associated with each conserved quantity. We derive here an inequality comparing the relative magnitudes of the "energy'' and "enstrophy'' fluxes for finite or infinitesimal dissipations, and for hyper or hypo viscosities. When this inequality is satisfied, as is the case of 2D turbulence,where the energy flux contribution to the energy spectrum is small, the subdominant part will be effectively hidden. …

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New Integrable Hierarchy, Its Parametric Solutions, Cuspons, One-Peak Solitons, And M/W-Shape Peak Solitons, Zhijun Qiao Aug 2007

New Integrable Hierarchy, Its Parametric Solutions, Cuspons, One-Peak Solitons, And M/W-Shape Peak Solitons, Zhijun Qiao

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, we propose a new completely integrable hierarchy. Particularly in the hierarchy we draw two new soliton equations: 1 mt= 1 2 1/m2xxx− 1 2 1/m2 x; 2 mt+mx u2−ux 2+2m2ux=0, m=u−uxx. The first one is the second positive member in the hierarchy while the second one is the second negative member in the hierarchy. Both equations can be derived from the two-dimensional Euler equation by using the approximation procedure. All equations in the hierarchy are proven to have bi-Hamiltonian operators and Lax pairs through solving a crucial matrix equation. Moreover, we develop parametric solutions of the entire …

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On The Elimination Of The Sweeping Interactions From Theories Of Hydrodynamic Turbulence, Eleftherios Gkioulekas Feb 2007

On The Elimination Of The Sweeping Interactions From Theories Of Hydrodynamic Turbulence, Eleftherios Gkioulekas

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, we revisit the claim that the Eulerian and quasi-Lagrangian same time correlation tensors are equal. This statement allows us to transform the results of an MSR quasi-Lagrangian statistical theory of hydrodynamic turbulence back to the Eulerian representation. We define a hierarchy of homogeneity symmetries between incremental homogeneity and global homogeneity. It is shown that both the elimination of the sweeping interactions and the derivation of the 4/5-law require a homogeneity assumption stronger than incremental homogeneity but weaker than global homogeneity. The quasi-Lagrangian transformation, on the other hand, requires an even stronger homogeneity assumption which is many-time rather …

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Solving Ramanujan's Differential Equations For Eisenstein Series Via A First Order Riccati Equation, James M. Hill, Bruce C. Berndt, Timothy Huber Jan 2007

Solving Ramanujan's Differential Equations For Eisenstein Series Via A First Order Riccati Equation, James M. Hill, Bruce C. Berndt, Timothy Huber

School of Mathematical & Statistical Sciences Faculty Publications

In this paper we prove that Ramanujan's differential equations for the Eisenstein series P, Q, and R are invariant under a simple one-parameter stretching group of transformations. Using this, we show that the three differential equations may be reduced to a first order Riccati differential equation, the solution of which may be represented in terms of hypergeometric functions. The resulting formulas allow for the derivation of parametric representations of P, Q, and R, analogous to representations in Ramanujan's second notebook. In contrast, in the classical approach, one first needs to derive the fundamental formula connecting theta functions with elliptic integrals. …

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A New Integrable Equation With Cuspons And W/M-Shape-Peaks Solitons, Zhijun Qiao Nov 2006

A New Integrable Equation With Cuspons And W/M-Shape-Peaks Solitons, Zhijun Qiao

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, we propose a new completely integrable wave equation: mt+mx u2 −ux 2 +2m2ux=0, m=u−uxx. The equation is derived from the two dimensional Euler equation and is proven to have Lax pair and bi-Hamiltonian structures. This equation possesses new cusp solitons—cuspons, instead of regular peakons ce− −ct with speed c. Through investigating the equation, we develop a new kind of soliton solutions—“W/M”-shape-peaks solitons. There exist no smooth solitons for this integrable water wave equation.

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Recent Developments In Understanding Two-Dimensional Turbulence And The Nastrom-Gage Spectrum, Eleftherios Gkioulekas, Ka Kit Tung Nov 2006

Recent Developments In Understanding Two-Dimensional Turbulence And The Nastrom-Gage Spectrum, Eleftherios Gkioulekas, Ka Kit Tung

School of Mathematical & Statistical Sciences Faculty Publications

Two-dimensional turbulence appears to be a more formidable problem than three-dimensional turbulence despite the numerical advantage of working with one less dimension. In the present paper we review recent numerical investigations of the phenomenology of two-dimensional turbulence as well as recent theoretical breakthroughs by various leading researchers. We also review efforts to reconcile the observed energy spectrum of the atmosphere (the spectrum) with the predictions of two-dimensional turbulence and quasigeostrophic turbulence.

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Recent Applications Of Fractional Calculus To Science And Engineering, Lokenath Debnath Jan 2003

Recent Applications Of Fractional Calculus To Science And Engineering, Lokenath Debnath

School of Mathematical & Statistical Sciences Faculty Publications

This paper deals with recent applications of fractional calculus to dynamical systems in control theory, electrical circuits with fractance, generalized voltage divider, viscoelasticity, fractional-order multipoles in electromagnetism, electrochemistry, tracer in fluid flows, and model of neurons in biology. Special attention is given to numerical computation of fractional derivatives and integrals.

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Category Of Nonlinear Evolution Equations, Algebraic Structure, And R-Matrix, Zhijun Qiao, Cewen Cao, Walter Strampp Jan 2003

Category Of Nonlinear Evolution Equations, Algebraic Structure, And R-Matrix, Zhijun Qiao, Cewen Cao, Walter Strampp

School of Mathematical & Statistical Sciences Faculty Publications

In this paper we deal with the category of nonlinear evolution equations ~NLEEs! associated with the spectral problem and provide an approach for constructing their algebraic structure and r-matrix. First we introduce the category of NLEEs, which is composed of various positive order and negative order hierarchies of NLEEs both integrable and nonintegrable. The whole category of NLEEs possesses a generalized Lax representation. Next, we present two different Lie algebraic structures of the Lax operator: one of them is universal in the category, i.e., independent of the hierarchy, while the other one is nonuniversal in the hierarchy, i.e., dependent on …

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The Weierstrass–Enneper System For Constant Mean Curvature Surfaces And The Completely Integrable Sigma Model, Paul Bracken, A. M. Grundland, L. Martina Jun 1999

The Weierstrass–Enneper System For Constant Mean Curvature Surfaces And The Completely Integrable Sigma Model, Paul Bracken, A. M. Grundland, L. Martina

School of Mathematical & Statistical Sciences Faculty Publications

The integrability of a system which describes constant mean curvature surfaces by means of the adapted Weierstrass–Enneper inducing formula is studied. This is carried out by using a specific transformation which reduces the initial system to the completely integrable two-dimensional Euclidean nonlinear sigma model. Through the use of the apparatus of differential forms and Cartan theory of systems in involution, it is demonstrated that the general analytic solutions of both systems possess the same degree of freedom. Furthermore, a new linear spectral problem equivalent to the initial Weierstrass–Enneper system is derived via the method of differential constraints. A new procedure …

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On Different Integrable Systems Sharing The Same Nondynamical R-Matrix, Zhijun Qiao, Walter Strampp May 1998

On Different Integrable Systems Sharing The Same Nondynamical R-Matrix, Zhijun Qiao, Walter Strampp

School of Mathematical & Statistical Sciences Faculty Publications

In a recent paper @Zhijun Qiao and Ruguang Zhou, Phys. Lett. A 235, 35 ~1997!#, the amazing fact was reported that a discrete and a continuous integrable system share the same r-matrix with the interesting property of being nondynamical. Now, we present three further pairs of different continuous integrable systems sharing the same r-matrix again being nondynamical. The first pair is the finite-dimensional constrained system ~FDCS! of the famous AKNS hierarchy and the Dirac hierarchy; the second pair is the FDCS of the well-known geodesic flows on the ellipsoid and the Heisenberg spin chain hierarchy; and the third pair is …

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Effective Characteristic Polynomials And Two-Point Pade Approximants As Summation Techniques For The Strongly Divergent Perturbation Expansions Of The Ground State Energies Of Anharmonic Oscillators, Jiri Cizek, Ernst Joachim Weniger, Paul Bracken, Vladimir Spirko Mar 1996

Effective Characteristic Polynomials And Two-Point Pade Approximants As Summation Techniques For The Strongly Divergent Perturbation Expansions Of The Ground State Energies Of Anharmonic Oscillators, Jiri Cizek, Ernst Joachim Weniger, Paul Bracken, Vladimir Spirko

School of Mathematical & Statistical Sciences Faculty Publications

Pade approximants are able to sum effectively the Rayleigh-Schrodinger perturbation series for the ground state energy of the quartic anharmonic oscillator, as well as the corresponding renormalized perturbation expansion [E.J. Weniger, J. Cizek, and F. Vinette, J. Math. Phys. 34, 571 (1993)]. In the sextic case, Pade approximants are still able to sum these perturbation series, but convergence is so slow that they are computationally useless. In the octic case, Pade approximants are not powerful enough and fail. On the other hand, the inclusion of only a few additional data from the strong coupling domain [E.J. Weniger, Ann. Phys. (N.Y.) …

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A Completely Integrable System And Parametric Representation Of Solutions Of The Wadati-Konno-Ichikawa Hierarchy, Zhijun Qiao Jan 1995

A Completely Integrable System And Parametric Representation Of Solutions Of The Wadati-Konno-Ichikawa Hierarchy, Zhijun Qiao

School of Mathematical & Statistical Sciences Faculty Publications

A finite-dimensional involutive system is presented, and the Wadati-Konno- Ichikawa (WKI) hierarchy of nonlinear evolution equations and their commutator representations are discussed in this article. By this finite-dimensional involutive system, it is proven that under the so-called Bargmann constraint between the potentials and the eigenfunctions, the eigenvalue problem (called the WKI eigenvalue problem) studied by Wadati, Konno, and Ichikawa [J. Phys. Sot. Jpn. 47, 1698 (1979)] is nonlinearized as a completely integrable Hamiltonian system in the Liouville sense. Moreover, the parametric representation of the solution of each equation in the WKI hierarchy is obtained by making use of the solution …

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A Hierarchy Of Nonlinear Evolution Equations And Finite-Dimensional Involutive Systems, Zhijun Qiao Jun 1994

A Hierarchy Of Nonlinear Evolution Equations And Finite-Dimensional Involutive Systems, Zhijun Qiao

School of Mathematical & Statistical Sciences Faculty Publications

A spectral problem and an associated hierarchy of nonlinear evolution equations are presented in this article. In particular, the reductions of the two representative equations in this hierarchy are given: one is the nonlinear evolution equation rl= - ar,- 2icu/3] r2] r which looks like the nonlinear Schrijdinger equation, the other is the generalized derivative nonlinear Schrijdinger equation rt= $ar,,- ialr12r- a/3(lr12r),- a j3I r I 2r,-2iap21r14r which is just a combination of the nonlinear Schrijdinger equation and two different derivative nonlinear Schrodinger equations [D. J. Kaup and A. C. Newell, J. Math. Phys. 19, 789 (1978); M. J. Ablowitz, …

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An Involutive System And Integrable C. Neumann System Associated With The Modified Korteweg-De Vries Hierarchy, Zhijun Qiao Feb 1994

An Involutive System And Integrable C. Neumann System Associated With The Modified Korteweg-De Vries Hierarchy, Zhijun Qiao

School of Mathematical & Statistical Sciences Faculty Publications

In this article, a system of finite-dimensional involutive functions is presented and proven to be integrable in the Liouville sense. By using the nonlinearization method, the C. Neumann system associated with the modified Korteweg-de Vries (mKdV) hierarchy is obtained. Thus, the C. Neumann system is shown to be completely integrable via a gauge transformation between it and an integrable Hamiltonian system. Finally, the solution of a stationary mKdV equation and the involutive solutions of the mKdV hierarchy are secured. As two examples, the involutive solutions are given for the mKdV equation: u,+ ;uXXX- $u2u,=0 and the 5th mKdV equation v,- …

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A New Completely Integrable Liouville's System Produced By The Kaup-Newell Elgenvalue Problem, Zhijun Qiao Jan 1993

A New Completely Integrable Liouville's System Produced By The Kaup-Newell Elgenvalue Problem, Zhijun Qiao

School of Mathematical & Statistical Sciences Faculty Publications

Under the constraint between the potentials and eigenfunctions, the Kaup–Newell eigenvalue problem is nonlinearized as a new completely integrable Hamiltonian system (R2N,dpΛdq,H): H=i〈Λ2p,q〉+1/2〈Λq,q〉〈Λp,p〉. Furthermore, the involutive solution of the high‐order Kaup–Newell equation is obtained. Specifically, the involutive solution of the well‐known derivative Schrödinger equation ut=1/2iuxx+1/2(u‖u‖2)x is developed.

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