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Articles 1 - 25 of 25
Full-Text Articles in Physical Sciences and Mathematics
Multiple Soliton Solutions Of (2+1)-Dimensional Potential Kadomtsev-Petviashvili Equation, Mohammad Najafi M.Najafi, Ali Jamshidi
Multiple Soliton Solutions Of (2+1)-Dimensional Potential Kadomtsev-Petviashvili Equation, Mohammad Najafi M.Najafi, Ali Jamshidi
mohammad najafi
We employ the idea of Hirota’s bilinear method, to obtain some new exact soliton solutions for high nonlinear form of (2+1)-dimensional potential Kadomtsev-Petviashvili equation. Multiple singular soliton solutions were obtained by this method. Moreover, multiple singular soliton solutions were also derived.
Highly Connected Multicoloured Subgraphs Of Multicoloured Graphs, H. Liu, R. Morris, N. Prince
Highly Connected Multicoloured Subgraphs Of Multicoloured Graphs, H. Liu, R. Morris, N. Prince
Hua Kun Liu
Suppose the edges of the complete graph on n vertices, E(Kn), are coloured using r colours; how large a k-connected subgraph are we guaranteed to find, which uses only at most s of the colours? This question is due to Bollobás, and the case s=1 was considered in Liu et al. [Highly connected monochromatic subgraphs of multicoloured graphs, J. Graph Theory, to appear]. Here we shall consider the case s is greater than or equal to 2, proving in particular that when s=2 and r+1 is a power of 2 then the answer lies between 4n/(r+1)-17kr(r+2k+1) and 4n/(r+1)+4 and that …
Counter-Propagating Two-Soliton Solutions In The Fermi–Pasta–Ulam Lattice, Aaron Hoffman, C.E. Wayne
Counter-Propagating Two-Soliton Solutions In The Fermi–Pasta–Ulam Lattice, Aaron Hoffman, C.E. Wayne
Aaron Hoffman
We study the interaction of small amplitude, long-wavelength solitary wavesin the Fermi–Pasta–Ulam model with general nearest-neighbour interactionpotential. We establish global-in-time existence and stability of counterpropagatingsolitary wave solutions. These solutions are close to the linearsuperposition of two solitary waves for large positive and negative values oftime; for intermediate values of time these solutions describe the interactionof two counter-propagating pulses. These solutions are stable with respectto perturbations in L2 and asymptotically stable with respect to perturbationswhich decay exponentially at spatial ±∞.
Boundary Effects In Large-Aspect-Ratio Lasers, G.K. Harkness, W.J. Firth, John B. Geddes, J.V Moloney, E.M. Wright
Boundary Effects In Large-Aspect-Ratio Lasers, G.K. Harkness, W.J. Firth, John B. Geddes, J.V Moloney, E.M. Wright
John B. Geddes
We study theoretically the effect of transverse boundary conditions on the traveling waves foundin infinitely extended and positively detuned laser systems. We find that for large-aspect-ratiosystems, well above threshold and away from the boundaries, the traveling waves persist. Sourceand sink defects are observed on the boundaries, and in very-large-aspect-ratio systems these defectscan also exist away from the boundaries. The transverse size of the sink defect, relative to the sizeof the transverse domain, is important in determining the final pattern observed, and so, close tothreshold, standing waves are always observed.
Constructing Large Numbers With Cheap Computers, Andrew Shallue, Steven Hayman
Constructing Large Numbers With Cheap Computers, Andrew Shallue, Steven Hayman
Andrew Shallue
No abstract provided.
How To Study Mathematics, Lawrence N. Stout
How To Study Mathematics, Lawrence N. Stout
Lawrence N. Stout
In high school mathematics much of your time was spent learning algorithms and manipulative techniques which you were expected to be able to apply in certain well-defined situations. This limitation of material and expectations for your performance has probably led you to develop study habits which were appropriate for high school mathematics but may be insufficient for college mathematics. This can be a source of much frustration for you and for your instructors. My object in writing this essay is to help ease this frustration by describing some study strategies which may help you channel your abilities and energies in …
A High-Resolution Finite-Difference Method For Simulating Two-Fluid, Viscoelastic Gel Dynamics, Grady Wright, Robert D. Guy, Jian Du, Aaron L. Fogelson
A High-Resolution Finite-Difference Method For Simulating Two-Fluid, Viscoelastic Gel Dynamics, Grady Wright, Robert D. Guy, Jian Du, Aaron L. Fogelson
Grady Wright
An important class of gels are those composed of a polymer network and fluid solvent. The mechanical and rheological properties of these two-fluid gels can change dramatically in response to temperature, stress, and chemical stimulus. Because of their adaptivity, these gels are important in many biological systems, e.g. gels make up the cytoplasm of cells and the mucus in the respiratory and digestive systems, and they are involved in the formation of blood clots. In this study we consider a mathematical model for gels that treats the network phase as a viscoelastic fluid with spatially and temporally varying material parameters …
Change Point Estimation Of Bilevel Functions, Leming Qu, Yi-Cheng Tu
Change Point Estimation Of Bilevel Functions, Leming Qu, Yi-Cheng Tu
Leming Qu
Reconstruction of a bilevel function such as a bar code signal in a partially blind deconvolution problem is an important task in industrial processes. Existing methods are based on either the local approach or the regularization approach with a total variation penalty. This article reformulated the problem explicitly in terms of change points of the 0-1 step function. The bilevel function is then reconstructed by solving the nonlinear least squares problem subject to linear inequality constraints, with starting values provided by the local extremas of the derivative of the convolved signal from discrete noisy data. Simulation results show a considerable …
Inversion For Non-Smooth Models With Physical Bounds, Partha S. Routh, Leming Qu, Mrinal K. Sen, Phil D. Anno
Inversion For Non-Smooth Models With Physical Bounds, Partha S. Routh, Leming Qu, Mrinal K. Sen, Phil D. Anno
Leming Qu
Geological processes produce structures at multiple scales. A discontinuity in the subsurface can occur due to layering, tectonic activities such as faulting, folding and fractures. Traditional approaches to invert geophysical data employ smoothness constraints. Such methods produce smooth models and thefore sharp contrasts in the medium such as lithological boundaries are not easily discernible. The methods that are able to produce non-smooth models, can help interpret the geological discontinuity. In this paper we examine various approaches to obtain non-smooth models from a finite set of noisy data. Broadly they can be categorized into approaches: (1) imposing non-smooth regularization in the …
Rayleigh Wave Dispersion Curve Inversion: Occam Versus The L1-Norm, Matthew M. Haney, Leming Qu
Rayleigh Wave Dispersion Curve Inversion: Occam Versus The L1-Norm, Matthew M. Haney, Leming Qu
Leming Qu
We compare inversions of Rayleigh wave dispersion curves for shear wave velocity depth profiles based on the L2-norm (Occam's Inversion) and L1-norm (TV Regularization). We forward model Rayleigh waves using a finite-element method instead of the conventional technique based on a recursion formula and root-finding. The forward modeling naturally leads to an inverse problem that is overparameterized in depth. Solving the inverse problem with Occam's Inversion gives the smoothest subsurface model that satisfies the data. However, the subsurface need not be smooth and we therefore also solve the inverse problem with TV Regularization, a procedure that does not penalize discontinuities. …
Bayesian Wavelet Estimation Of Long Memory Parameter, Leming Qu
Bayesian Wavelet Estimation Of Long Memory Parameter, Leming Qu
Leming Qu
A Bayesian wavelet estimation method for estimating parameters of a stationary I(d) process is represented as an useful alternative to the existing frequentist wavelet estimation methods. The effectiveness of the proposed method is demonstrated through Monte Carlo simulations. The sampling from the posterior distribution is through the Markov Chain Monte Carlo (MCMC) easily implemented in the WinBUGS software package.
Copula Density Estimation By Total Variation Penalized Likelihood With Linear Equality Constraints, Leming Qu, Wotao Yin
Copula Density Estimation By Total Variation Penalized Likelihood With Linear Equality Constraints, Leming Qu, Wotao Yin
Leming Qu
A copula density is the joint probability density function (PDF) of a random vector with uniform marginals. An approach to bivariate copula density estimation is introduced that is based on a maximum penalized likelihood estimation (MPLE) with a total variation (TV) penalty term. The marginal unity and symmetry constraints for copula density are enforced by linear equality constraints. The TV-MPLE subject to linear equality constraints is solved by an augmented Lagrangian and operator-splitting algorithm. It offers an order of magnitude improvement in computational efficiency over another TV-MPLE method without constraints solved by log-barrier method for second order cone program. A …
Wavelet Reconstruction Of Nonuniformly Sampled Signals, Leming Qu, Partha S. Routh, Phil D. Anno
Wavelet Reconstruction Of Nonuniformly Sampled Signals, Leming Qu, Partha S. Routh, Phil D. Anno
Leming Qu
For the reconstruction of a nonuniformly sampled signal based on its noisy observations, we propose a level dependent l1 penalized wavelet reconstruction method. The LARS/Lasso algorithm is applied to solve the Lasso problem. The data adaptive choice of the regularization parameters is based on the AIC and the degrees of freedom is estimated by the number of nonzero elements in the Lasso solution. Simulation results conducted on some commonly used 1_D test signals illustrate that the proposed method possesses good empirical properties.
Wavelet Deconvolution In A Periodic Setting Using Cross-Validation, Leming Qu, Partha S. Routh, Kyungduk Ko
Wavelet Deconvolution In A Periodic Setting Using Cross-Validation, Leming Qu, Partha S. Routh, Kyungduk Ko
Leming Qu
The wavelet deconvolution method WaveD using band-limited wavelets offers both theoretical and computational advantages over traditional compactly supported wavelets. The translation-invariant WaveD with a fast algorithm improves further. The twofold cross-validation method for choosing the threshold parameter and the finest resolution level in WaveD is introduced. The algorithm’s performance is compared with the fixed constant tuning and the default tuning in WaveD.
Wavelet-Based Bayesian Estimation Of Partially Linear Regression Models With Long Memory Errors, Kyungduk Ko, Leming Qu, Marina Vannucci
Wavelet-Based Bayesian Estimation Of Partially Linear Regression Models With Long Memory Errors, Kyungduk Ko, Leming Qu, Marina Vannucci
Leming Qu
In this paper we focus on partially linear regression models with long memory errors, and propose a wavelet-based Bayesian procedure that allows the simultaneous estimation of the model parameters and the nonparametric part of the model. Employing discrete wavelet transforms is crucial in order to simplify the dense variance-covariance matrix of the long memory error. We achieve a fully Bayesian inference by adopting a Metropolis algorithm within a Gibbs sampler. We evaluate the performances of the proposed method on simulated data. In addition, we present an application to Northern hemisphere temperature data, a benchmark in the long memory literature.
The Onset Of Oscillations In Microvascular Blood Flow, John B. Geddes, Russell T. Carr, Nathaniel J. Karst, Fan Wu
The Onset Of Oscillations In Microvascular Blood Flow, John B. Geddes, Russell T. Carr, Nathaniel J. Karst, Fan Wu
John B. Geddes
We explore the stability of equilibrium solution(s) of a simple model of microvascular blood flow in a two-node network. The model takes the form of convection equations for red blood cell concentration, and contains two important rheological effects—the Fåhræus–Lindqvist effect, which governs viscosity of blood flow in a single vessel, and the plasma skimming effect, which describes the separation of red blood cells at diverging nodes. We show that stability is governed by a linear system of integral equations, and we study the roots of the associated characteristic equation in detail. We demonstrate using a combination of analytical and numerical …
Fractional Trigonometric Functions In Complex-Valued Space: Applications Of Complex Number To Local Fractional Calculus Of Complex Function, Yang Xiao-Jun
Xiao-Jun Yang
This paper presents the fractional trigonometric functions in complex-valued space and proposes a short outline of local fractional calculus of complex function in fractal spaces.
Linear Algebra, Lawrence Stout
Linear Algebra, Lawrence Stout
Lawrence N. Stout
This book is designed to deal with all of the concepts of linear algebra first in R2, a simple context where algorithmic concerns are minimized and geometric intuition can be brought to bear. Then those same concepts are dealt with in full generality. I find that this conceptual front loading helps in the understanding of the rest of the material. Students can see easily what aspects of the plane are focused on when we think of it as a vector space; linear transformations can be understood as deformations of the plane of a very special type. Nothing more complicated than …
Characterizations Of Orthogonal Generalized Gegenbauer-Humbert Polynomials And Orthogonal Sheffer-Type Polynomials, Tian-Xiao He
Characterizations Of Orthogonal Generalized Gegenbauer-Humbert Polynomials And Orthogonal Sheffer-Type Polynomials, Tian-Xiao He
Tian-Xiao He
We present characterizations of the orthogonal generalized Gegen-bauer-Humbert polynomial sequences and the orthogonal Sheffer-type polynomial sequences. Using a new polynomial sequence transformation technique presented in [12], we give a method to evaluate the measures and their supports of some orthogonal generalized Gegenbauer-Humbert polynomial sequences.
How Do Mathematicians Make Sense Of Definitions?, Laurie O. Cavey, Margaret T. Kinzel, Thomas A. Kinzel, Kathleen L. Rohrig, Sharon B. Walen
How Do Mathematicians Make Sense Of Definitions?, Laurie O. Cavey, Margaret T. Kinzel, Thomas A. Kinzel, Kathleen L. Rohrig, Sharon B. Walen
Margaret T. Kinzel
It seems clear that students’ activity while working with definitions differs from that of mathematicians. The constructs of concept definition and concept image have served to support analyses of both mathematicians’ and students’ work with definitions (c.f. Edwards & Ward, 2004; Tall & Vinner, 1981). As part of an ongoing study, we chose to look closely at how mathematicians make sense of definitions in hopes of informing the ways in which we interpret students’ activity and support their understanding of definitions. We conducted interviews with mathematicians in an attempt to reveal their process when making sense of definitions. A striking …
Student Surveys: What Do They Think?, Holly Zullo, Kelly Cline, Mark Parker, Ron Buckmire, John George, Katharine Gurski, Jakob J. Larsen, Blake Mellor, Jack Oberweiser, Dennis Peterson, Richard Spindler, Ann Stewart, Christopher Storm
Student Surveys: What Do They Think?, Holly Zullo, Kelly Cline, Mark Parker, Ron Buckmire, John George, Katharine Gurski, Jakob J. Larsen, Blake Mellor, Jack Oberweiser, Dennis Peterson, Richard Spindler, Ann Stewart, Christopher Storm
Ron Buckmire
No abstract provided.
Asymptotic Preconditioning Of Linear Homogeneous Systems Of Differential Equations, William F. Trench
Asymptotic Preconditioning Of Linear Homogeneous Systems Of Differential Equations, William F. Trench
William F. Trench
No abstract provided.
Riordan Arrays Associated With Laurent Series And Generalized Sheffer-Type Groups, Tian-Xiao He
Riordan Arrays Associated With Laurent Series And Generalized Sheffer-Type Groups, Tian-Xiao He
Tian-Xiao He
A relationship between a pair of Laurent series and Riordan arrays is formulated. In addition, a type of generalized Sheffer groups is defined using Riordan arrays with respect to power series with non-zero coefficients. The isomorphism between a generalized Sheffer group and the group of the Riordan arrays associated with Laurent series is established. Furthermore, Appell, associated, Bell, and hitting-time subgroups of the groups are defined and discussed. A relationship between the generalized Sheffer groups with respect to different power series is presented. The equivalence of the defined Riordan array pairs and generalized Stirling number pairs is given. A type …
The Relationship Between Trench's Toeplitz Inversion Algorithm And The Gohberg-Semencul Formula, William F. Trench
The Relationship Between Trench's Toeplitz Inversion Algorithm And The Gohberg-Semencul Formula, William F. Trench
William F. Trench
No abstract provided.
Closing The Loop: Involving Faculty In The Assessment Of Scientific And Quantitative Reasoning Skills Of Biology Majors, C. A. Hurney, J. Brown, H. P. Griscom, E. Kancler, C. J. Wigtil, Donna L. Sundre
Closing The Loop: Involving Faculty In The Assessment Of Scientific And Quantitative Reasoning Skills Of Biology Majors, C. A. Hurney, J. Brown, H. P. Griscom, E. Kancler, C. J. Wigtil, Donna L. Sundre
Donna L. Sundre
No abstract provided.