Unique continuation property for the Kadomtsev-Petviashvili (KP-II equation
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Mahendra Panthee
2005-06-01
Full Text Available We generalize a method introduced by Bourgain in cite{Borg} based on complex analysis to address two spatial dimensional models and prove that if a sufficiently smooth solution to the initial value problem associated with the Kadomtsev-Petviashvili (KP-II equation $$ (u_t+u_{xxx}+uu_{x}_{x} +u_{yy}=0, quad (x, y in mathbb{R}^2, ;tinmathbb{R}, $$ is supported compactly in a nontrivial time interval then it vanishes identically.
On elliptic cylindrical Kadomtsev-Petviashvili equation for surface waves
Khusnutdinova, K R; Matveev, V B; Smirnov, A O
2012-01-01
The `elliptic cylindrical Kadomtsev-Petviashvili equation' is derived for surface gravity waves with nearly-elliptic front, generalising the cylindrical KP equation for nearly-concentric waves. We discuss transformations between the derived equation and two existing versions of the KP equation, for nearly-plane and nearly-concentric waves. The transformations are used to construct important classes of exact solutions of the derived equation and corresponding approximate solutions for surface waves.
Whitham modulation theory for the Kadomtsev- Petviashvili equation.
Ablowitz, Mark J; Biondini, Gino; Wang, Qiao
2017-08-01
The genus-1 Kadomtsev-Petviashvili (KP)-Whitham system is derived for both variants of the KP equation; namely the KPI and KPII equations. The basic properties of the KP-Whitham system, including symmetries, exact reductions and its possible complete integrability, together with the appropriate generalization of the one-dimensional Riemann problem for the Korteweg-de Vries equation are discussed. Finally, the KP-Whitham system is used to study the linear stability properties of the genus-1 solutions of the KPI and KPII equations; it is shown that all genus-1 solutions of KPI are linearly unstable, while all genus-1 solutions of KPII are linearly stable within the context of Whitham theory.
A splitting approach for the Kadomtsev--Petviashvili equation
Einkemmer, Lukas
2014-01-01
We consider a splitting approach for the Kadomtsev--Petviashvili equation with periodic boundary conditions and show that the necessary interpolation procedure can be efficiently implemented. The error made by this numerical scheme is compared to exponential integrators which have been shown in Klein and Roidot (SIAM J. Sci. Comput., 2011) to perform best for stiff solutions of the Kadomtsev--Petviashvili equation. Since splitting methods are limited to order two in this case, we propose a stable extrapolation method in order to construct a numerical scheme of order four. In addition, the conservation properties of the numerical schemes under consideration are investigated.
Solving Kadomtsev-Petviashvili Equation via a New Decomposition and Darboux Transformation
Institute of Scientific and Technical Information of China (English)
FAN En-Gui
2002-01-01
Recently, a new decomposition of the (2+1)-dimensional Kadomtsev Petviashvili (KP) equation to a (1+1 )-dimensional Broer-Kaup (BK) equation and a (1+1)-dimensional high-order BK equation was presented by Lou andHu. In our paper, a unified Darboux transformation for both the BK equation and high-order BK equation is derivedwith the help of a gauge transformation of their spectral problems. As application, new explicit soliton-like solutionswith five arbitrary parameters for the BK equation, high-order BK equation and KP equation are obtained.
Quantisation of Kadomtsev-Petviashvili equation
Kozlowski, Karol K; Torrielli, Alessandro
2016-01-01
A quantisation of the KP equation on a cylinder is proposed that is equivalent to an infinite system of non-relativistic one-dimensional bosons carrying masses $m=1,2,\\ldots$ The Hamiltonian is Galilei-invariant and includes the split $\\Psi^\\dagger_{m_1}\\Psi^\\dagger_{m_2}\\Psi_{m_1+m_2}$ and merge $\\Psi^\\dagger_{m_1+m_2}\\Psi_{m_1}\\Psi_{m_2}$ terms for all combinations of particles with masses $m_1$, $m_2$ and $m_1+m_2$, with a special choice of coupling constants. The Bethe eigenfunctions for the model are constructed. The consistency of the coordinate Bethe Ansatz, and therefore, the quantum integrability of the model is verified up to the mass $M=8$ sector.
Matrix Kadomtsev-Petviashvili equation: matrix identities and explicit non-singular solutions
Energy Technology Data Exchange (ETDEWEB)
Sakhnovich, A L [Branch of Hydroacoustics, Marine Institute of Hydrophysics, National Academy of Sciences of Ukraine (Ukraine)
2003-05-09
A new version of the Baecklund-Darboux transformation for the matrix Kadomtsev-Petviashvili (KP) equation is used to construct and study explicit multi-parameter solutions and wavefunctions (in terms of the matrix exponents). A class of the self-adjoint non-singular solutions of KP I is introduced using the controllability notion from the system theory. A subclass of the rationally decaying self-adjoint non-singular solutions is studied, in particular. Several results prove new in the scalar case also.
Stationary Solutions for a Generalized Kadomtsev-Petviashvili Equation in Bounded Domain
Institute of Scientific and Technical Information of China (English)
Zhang Ke-yu; Xu Jia-fa; Li Yong(Communicated)
2014-01-01
In this work, we are mainly concerned with the existence of stationary solutions for a generalized Kadomtsev-Petviashvili equation in bounded domain of Rn. We utilize variational method and critical point theory to establish our main results.
Institute of Scientific and Technical Information of China (English)
Mao Jie-Jian; Yang Jian-Rong
2006-01-01
Using the solution of general Korteweg-de Vries (KdV) equation, the solutions of the generalized wriable coefficient Kadomtsev-Petviashvili (KP) equation are constructed, and then its new solitary wave-like solution and Jacobi clliptic function solution are obtained.
Leblond, Hervé; Mihalache, Dumitru; 10.1103/PHYSREVA.81.033824
2011-01-01
By using a reductive perturbation method, we derive from Maxwell-Bloch equations a cubic generalized Kadomtsev-Petviashvili equation for ultrashort spatiotemporal optical pulse propagation in cubic (Kerr-like) media without the use of the slowly varying envelope approximation. We calculate the collapse threshold for the propagation of few-cycle spatiotemporal pulses described by the generic cubic generalized Kadomtsev-Petviashvili equation by a direct numerical method and compare it to analytic results based on a rigorous virial theorem. Besides, typical evolution of the spectrum (integrated over the transverse spatial coordinate) is given and a strongly asymmetric spectral broadening of ultrashort spatiotemporal pulses during collapse is evidenced.
Lump Solutions for the (3+1)-Dimensional Kadomtsev-Petviashvili Equation
Liu, De-Yin; Tian, Bo; Xie, Xi-Yang
2016-12-01
In this article, we investigate the lump solutions for the Kadomtsev-Petviashvili equation in (3+1) dimensions that describe the dynamics of plasmas or fluids. Via the symbolic computation, lump solutions for the (3+1)-dimensional Kadomtsev-Petviashvili equation are derived based on the bilinear forms. The conditions to guarantee analyticity and rational localisation of the lump solutions are presented. The lump solutions contain eight parameters, two of which are totally free, and the other six of which need to satisfy the presented conditions. Plots with particular choices of the involved parameters are made to show the lump solutions and their energy distributions.
CTE method and interaction solutions for the Kadomtsev-Petviashvili equation
Ren, Bo
2017-02-01
The consistent tanh expansion method is applied to the Kadomtsev-Petviashvili equation. The interaction solutions among one soliton and other types of solitary waves, such as multiple resonant soliton solutions and cnoidal waves, are explicitly given. Some special concrete interaction solutions are discussed both in analytical and graphical ways.
Dispersive shock waves in the Kadomtsev-Petviashvili and two dimensional Benjamin-Ono equations
Ablowitz, Mark J.; Demirci, Ali; Ma, Yi-Ping
2016-10-01
Dispersive shock waves (DSWs) in the Kadomtsev-Petviashvili (KP) equation and two dimensional Benjamin-Ono (2DBO) equation are considered using step like initial data along a parabolic front. Employing a parabolic similarity reduction exactly reduces the study of such DSWs in two space one time (2 + 1) dimensions to finding DSW solutions of (1 + 1) dimensional equations. With this ansatz, the KP and 2DBO equations can be exactly reduced to the cylindrical Korteweg-de Vries (cKdV) and cylindrical Benjamin-Ono (cBO) equations, respectively. Whitham modulation equations which describe DSW evolution in the cKdV and cBO equations are derived and Riemann type variables are introduced. DSWs obtained from the numerical solutions of the corresponding Whitham systems and direct numerical simulations of the cKdV and cBO equations are compared with very good agreement obtained. In turn, DSWs obtained from direct numerical simulations of the KP and 2DBO equations are compared with the cKdV and cBO equations, again with good agreement. It is concluded that the (2 + 1) DSW behavior along self similar parabolic fronts can be effectively described by the DSW solutions of the reduced (1 + 1) dimensional equations.
Directory of Open Access Journals (Sweden)
Shaolin Li
2014-01-01
Full Text Available The bilinear operator and F-expansion method are applied jointly to study (2+1-dimensional Kadomtsev-Petviashvili (KP equation. An exact cusped solitary wave solution is obtained by using the extended single-soliton test function and its mechanical feature which blows up periodically in finite time for cusped solitary wave is investigated. By constructing the extended double-soliton test function, a new type of exact traveling wave solution describing the assimilation of solitary wave and periodic traveling wave is also presented. Our results validate the effectiveness for joint application of the bilinear operator and F-expansion method.
Bilinear B(a)cklund Transformation for a Variable-Coefficient Kadomtsev-Petviashvili Equation
Institute of Scientific and Technical Information of China (English)
WU Jian-Ping
2011-01-01
Resorting to the Hirota bilinear form, a bilinear Backlund transformation (BT) is obtained for a variable-coefficient Kadomtsev-Petviashvili equation. As applications, based on the resulting bilinear BT, single-soliton solutions and two-soliton solutions together with their soliton characteristics are presented for the equation. Furthermore, starting from the bilinear BT, a Lax pair and a new variable-coefficient (2+l)-dimensional nonlinear evolution equation is derived.%@@ Resorting to the Hirota bilinear form, a bilinear B(a)cklund transformation (BT) is obtained for a variable-coefficient Kadomtsev-Petviashvili equation.As applications, based on the resulting bilinear BT, singie-soliton solutions and two-soliton solutions together with their soliton characteristics are presented for the equation.Furthermore, starting from the bilinear BT, a Lax pair and a new variable-coefficient (2+1)-dimensional nonlinear evolution equation is derived.
Grammian Solutions to a Non-Isospectral Kadomtsev-Petviashvili Equation
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ZHANG Da-Jun
2006-01-01
@@ Solutions in the Grammian form for a non-isospectral Kadomtsev-Petviashvili equation are derived by means of Pfaffian derivative formulae. Explicit entries of the Grammian are given. Non-isospectral dynamics of the solutions generated from the Grammian are investigated in an analytic way. The solutions obtained can describe line solitons in non-uniform media travelling with time-dependent amplitude and time-dependent direction. In addition, some other solutions have singularities.
The Kadomtsev-Petviashvili equation for dust ion-acoustic solitons in pair-ion plasmas
Institute of Scientific and Technical Information of China (English)
Hafeez Ur-Rehman
2013-01-01
Using the reductive perturbation method,we have derived the Kadomtsev-Petviashvili (KP) equation to study the nonlinear properties of electrostatic collisionless dust ion-acoustic solitons in pair-ion (p-i) plasmas.We have chosen the fluid model for the positive ions,the negative ions,and a fraction of static charged (both positively and negatively) dust particles.Numerical solutions of these dust ion-acoustic solitons are plotted and their characteristics are discussed.It is found that only the amplitudes of the electrostatic dust ion-acoustic solitons vary when the dust is introduced in the pair-ion plasma.It is also noticed that the amplitude and the width of these solitons both vary when the thermal energy of the positive or negative ions is varied.It is shown that potential hump structures are formed when the temperature of the negative ions is higher than that of the positive ions,and potential dip structures are observed when the temperature of the positive ions supersedes that of the negative ions.As the pair-ion plasma mimics the electron-positron plasma,thus our results might be helpful in understanding the nonlinear dust ion acoustic solitary waves in super dense astronomical bodies.
Santini, P M
2011-01-01
Vector fields naturally arise in many branches of mathematics and physics. Recently it was discovered that Lax pairs for many important multidimensional integrable partial differential equations (PDEs) of hydrodynamic type (also known as dispersionless PDEs) consist of vector field equations. These vector fields have complex coefficients and their analytic, in the spectral parameter, eigenfunctions play an important role in the formulations of the direct and inverse spectral transforms. In this paper we prove existence of eigenfunctions of the basic vector field associated with the celebrated dispersionless Kadomtsev-Petviashvili equation, which are holomorphic in the spectral parameter $\\lambda$ in the strips $|\\Im\\lambda|> C_0$.
Institute of Scientific and Technical Information of China (English)
LI Ye-Zhou; LIU Jian-Guo; WEI Guang-Mei; GAO Yi-Tian
2007-01-01
A spherical Kadomtsev-Petviashvili (SKP) equation for dust acoustic or ion-acoustic waves is studied. Similarity reductions of the SKP equation are obtained with the one-parameter (e) Lie group of infinitesimal transformations and Clarkson-Kruskal direct method. The SKP equation is also solved with a generalized tanh function method.
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Ma Hong-Cai
2013-01-01
Full Text Available The simple direct method is adopted to find Non-Auto-Backlund transformation for variable coefficient non-linear systems. The (2+1-dimensional generalized Kadomtsev-Petviashvili equation with variable coefficients is used as an example to elucidate the solution procedure, and its symmetry transformation and exact solutions are obtained.
Alves, Claudianor O.; Miyagaki, Olímpio H.
2017-08-01
In this paper, we establish some results concerning the existence, regularity, and concentration phenomenon of nontrivial solitary waves for a class of generalized variable coefficient Kadomtsev-Petviashvili equation. Variational methods are used to get an existence result, as well as, to study the concentration phenomenon, while the regularity is more delicate because we are leading with functions in an anisotropic Sobolev space.
El-Shiekh, Rehab M.
2015-06-01
In this paper, the generalized (3+1)-dimensional variable-coefficient Kadomtsev-Petviashvili equation (VCKPE), which can describe nonlinear phenomena in fluids or plasmas, is studied by using two different Clarkson and Kruskal (CK) direct methods, namely, the classical CK and the modified enlarged CK method. A similarity reduction to a (2+1)-dimensional nonlinear partial differential equation and a direct similarity reduction to a nonlinear ordinary differential equation are obtained, respectively. By solving the reduced ordinary differential equation, new solitary, periodic, and singular solutions for the VCKPE are obtained. Some figures for the soliton and periodic wave solutions are given to reflect the effect of the variable coefficients on the solution propagation. Finally, the comparison between the two different CK techniques indicates that the modified enlarged CK technique is clearly more powerful and simple than the classical CK technique.
Das, Amiya; Ganguly, Asish
2017-07-01
The paper deals with Kadomtsev-Petviashvili (KP) equation in presence of a small dispersion effect. The nature of solutions are examined under the dispersion effect by using Lyapunov function and dynamical system theory. We prove that when dispersion is added to the KP equation, in certain regions, yet there exist bounded traveling wave solutions in the form of solitary waves, periodic and elliptic functions. The general solution of the equation with or without the dispersion effect are obtained in terms of Weirstrass ℘ functions and Jacobi elliptic functions. New form of kink-type solutions are established by exploring a new technique based on factorization method, use of functional transformation and the Abel's first order nonlinear equation. Furthermore, the stability analysis of the dispersive solutions are examined which shows that the traveling wave velocity is a bifurcation parameter which governs between different classes of waves. We use the phase plane analysis and show that at a critical velocity, the solution has a transcritical bifurcation.
Institute of Scientific and Technical Information of China (English)
WEI Guang-Mei; GAO Yi-Tian; XU Tao; MENG Xiang-Hua; ZHANG Chun-Yi
2008-01-01
A variable-coefficient Kadomtsev-Petviashvili equation is investigated.The Painlevé analysis leads to its explicit Painlevé-integrable conditions.An auto-B(a)cklund transformation and the bilinear form are presented via the truncated Painlevé expansion and symbolic computation.Several families of new analytic solutions axe presented,including the soliton-like and periodic solutions.
Indian Academy of Sciences (India)
ZHENHUI XU; HANLIN CHEN; ZHENGDE DAI
2016-08-01
In this paper, we obtained the exact breather-type kink soliton and breather-type periodic soliton solutions for the (3+1)-dimensional B-type Kadomtsev--Petviashvili (BKP) equation using the extended homoclinic test technique. Some new nonlinear phenomena, such as kink and periodic degeneracies, are investigated. Using the homoclinic breather limit method, some new rational breather solutions are found as well. Meanwhile, we also obtained the rational potential solution which is found to be just a rogue wave. These results enrich thevariety of the dynamics of higher-dimensional nonlinear wave field.
Santucci, F.; Santini, P. M.
2016-10-01
We study the generalization of the dispersionless Kadomtsev-Petviashvili (dKP) equation in n+1 dimensions and with nonlinearity of degree m+1, a model equation describing the propagation of weakly nonlinear, quasi one-dimensional waves in the absence of dispersion and dissipation, and arising in several physical contexts, like acoustics, plasma physics, hydrodynamics and nonlinear optics. In 2 + 1 dimensions and with quadratic nonlinearity, this equation is integrable through a novel inverse scattering transform, and it has been recently shown to be a prototype model equation in the description of the two-dimensional wave breaking of localized initial data. In higher dimensions and with higher nonlinearity, the generalized dKP equations are not integrable, but their invariance under motions on the paraboloid allows one to construct in this paper a family of exact solutions describing waves constant on their paraboloidal wave front and breaking simultaneously in all points of it, developing after breaking either multivaluedness or single-valued discontinuous profiles (shocks). Then such exact solutions are used to build the longtime behavior of the solutions of the Cauchy problem, for small and localized initial data, showing that wave breaking of small initial data takes place in the longtime regime if and only if m(n-1)≤slant 2. Lastly, the analytic aspects of such wave breaking are investigated in detail in terms of the small initial data, in both cases in which the solution becomes multivalued after breaking or it develops a shock. These results, contained in the 2012 master’s thesis of one of the authors (FS) [1], generalize those obtained in [2] for the dKP equation in n+1 dimensions with quadratic nonlinearity, and are obtained following the same strategy.
Institute of Scientific and Technical Information of China (English)
HUANGDing-Jiang; ZHANGHong-Qing
2004-01-01
By using the extended homogeneous balance method, a new auto-Baecklund transformation(BT) to the generalized Kadomtsew-Petviashvili equation with variable coefficients (VCGKP) are obtained. And making use of the auto-BT and choosing a special seed solution, we get many families of new exact solutions of the VCGKP equations, which include single soliton-like solutions, multi-soliton-like solutions, and special-soliton-like solutions. Since the KP equation and cylindrical KP equation are all special cases of the VCGKP equation, and the corresponding results of these equations are also given respectively.
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Hafeez-Ur-Rehman; Mahmood, S. [Theoretical Plasma Physics Division, PINSTECH, P.O. Nilore, Islamabad (Pakistan); Department of Physics and Applied Mathematics, PIEAS, Nilore, 44000 Islamabad (Pakistan); Shah, Asif; Haque, Q. [Theoretical Plasma Physics Division, PINSTECH, P.O. Nilore, Islamabad (Pakistan)
2011-12-15
Two dimensional (2D) solitons are studied in a plasma system comprising of relativistically streaming ions, kappa distributed electrons, and positrons. Kadomtsev-Petviashvili (KP) equation is derived through the reductive perturbation technique. Analytical solution of the KP equation has been studied numerically and graphically. It is noticed that kappa parameters of electrons and positrons as well as the ions relativistic streaming factor have an emphatic influence on the structural as well as propagation characteristics of two dimensional solitons in the considered plasma system. Our results may be helpful in the understanding of soliton propagation in astrophysical and laboratory plasmas, specifically the interaction of pulsar relativistic wind with supernova ejecta and the transfer of energy to plasma by intense electric field of laser beams producing highly energetic superthermal and relativistic particles [L. Arons, Astrophys. Space Sci. Lib. 357, 373 (2009); P. Blasi and E. Amato, Astrophys. Space Sci. Proc. 2011, 623; and A. Shah and R. Saeed, Plasma Phys. Controlled Fusion 53, 095006 (2011)].
New Interaction Solutions of (3+1-Dimensional KP and (2+1-Dimensional Boussinesq Equations
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Bo Ren
2015-01-01
Full Text Available The consistent tanh expansion (CTE method has been succeeded to apply to the nonintegrable (3+1-dimensional Kadomtsev-Petviashvili (KP and (2+1-dimensional Boussinesq equations. The interaction solution between one soliton and one resonant soliton solution for the (3+1-dimensional KP equation is obtained with CTE method. The interaction solutions among one soliton and cnoidal waves for these two equations are also explicitly given. These interaction solutions are investigated in both analytical and graphical ways. It demonstrates that the interactions between one soliton and cnoidal waves are elastic with phase shifts.
Exact periodic wave solutions for some nonlinear partial differential equations
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El-Wakil, S.A. [Theoretical Physics Research Group, Department of Physics, Faculty of Science, Mansoura University, Mansoura 35516 (Egypt); Elgarayhi, A. [Theoretical Physics Research Group, Department of Physics, Faculty of Science, Mansoura University, Mansoura 35516 (Egypt)]. E-mail: elgarayhi@yahoo.com; Elhanbaly, A. [Theoretical Physics Research Group, Department of Physics, Faculty of Science, Mansoura University, Mansoura 35516 (Egypt)
2006-08-15
The periodic wave solutions for some nonlinear partial differential equations, including generalized Klein-Gordon equation, Kadomtsev-Petviashvili (KP) equation and Boussinesq equations, are obtained by using the solutions of Jacobi elliptic equation. Under limit conditions, exact solitary wave solutions, shock wave solutions and triangular periodic wave solutions have been recovered.
Alam, Md Nur; Akbar, M Ali
2013-01-01
The new approach of the generalized (G'/G)-expansion method is an effective and powerful mathematical tool in finding exact traveling wave solutions of nonlinear evolution equations (NLEEs) in science, engineering and mathematical physics. In this article, the new approach of the generalized (G'/G)-expansion method is applied to construct traveling wave solutions of the Kadomtsev-Petviashvili-Benjamin-Bona-Mahony (KP-BBM) equation. The solutions are expressed in terms of the hyperbolic functions, the trigonometric functions and the rational functions. By means of this scheme, we found some new traveling wave solutions of the above mentioned equation.
Phase dynamics of periodic wavetrains leading to the 5th order KP equation
Ratliff, Daniel J.
2017-09-01
Using the previous approach outlined in Ratliff and Bridges (2016, 2015), a novel method is presented to derive the fifth order Kadomtsev-Petviashvili(KP) equation from periodic wavetrains. As a result, the coefficients and criterion for the fifth order KP to emerge take a universal form that can be determined a-priori, relating to the system's conservation laws and the termination of a Jordan chain. Moreover, the analysis reveals that generically a mixed dispersive term qXXXY appears within the final phase equation. The theory presented here is complimented by an example from the context of flexural gravity waves in shallow water and a higher order Nonlinear Schrödinger model relevant in plasma physics, demonstrating how the coefficients in this model are determined via elementary calculations.
Derivation of a viscous KP including surface tension, and related equations
Meur, Hervé Le
2015-01-01
The aim of this article is to derive surface wave models in the presence of surface tension and viscosity. Using the Navier-Stokes equations with a free surface, flat bottom and surface tension, we derive the viscous 2D Boussinesq system with a weak transverse variation. The assumed transverse variation is on a larger scale than along the main propagation direction. This Boussinesq system is only an intermediate result that enables us to derive the Kadomtsev-Petviashvili (KP) equation which is a 2D generalization of the KdV equation. In addition, we get the 1D KdV equation, and lastly the Boussinesq equation. All these equations are derived for non-vanishing initial conditions.
Destrade, M.
2010-12-08
We study the propagation of two-dimensional finite-amplitude shear waves in a nonlinear pre-strained incompressible solid, and derive several asymptotic amplitude equations in a simple, consistent and rigorous manner. The scalar Zabolotskaya (Z) equation is shown to be the asymptotic limit of the equations of motion for all elastic generalized neo-Hookean solids (with strain energy depending only on the first principal invariant of Cauchy-Green strain). However, we show that the Z equation cannot be a scalar equation for the propagation of two-dimensional shear waves in general elastic materials (with strain energy depending on the first and second principal invariants of strain). Then, we introduce dispersive and dissipative terms to deduce the scalar Kadomtsev-Petviashvili (KP), Zabolotskaya-Khokhlov (ZK) and Khokhlov- Zabolotskaya-Kuznetsov (KZK) equations of incompressible solid mechanics. © 2010 The Royal Society.
Numerical study of the KP equation for non-periodic waves
Kao, Chiu-Yen
2010-01-01
The Kadomtsev-Petviashvili (KP) equation describes weakly dispersive and small amplitude waves propagating in a quasi-two dimensional situation. Recently a large variety of exact soliton solutions of the KP equation has been found and classified. Those soliton solutions are localized along certain lines in a two-dimensional plane and decay exponentially everywhere else, and they are called line-soliton solutions in this paper. The classification is based on the far-field patterns of the solutions which consist of a finite number of line-solitons. In this paper, we study the initial value problem of the KP equation with V- and X-shape initial waves consisting of two distinct line-solitons by means of the direct numerical simulation. We then show that the solution converges asymptotically to some of those exact soliton solutions. The convergence is in a locally defined $L^2$-sense. The initial wave patterns considered in this paper are related to the rogue waves generated by nonlinear wave interactions in shall...
Integrable hierarchies of Heisenberg ferromagnet equation
Nugmanova, G.; Azimkhanova, A.
2016-08-01
In this paper we consider the coupled Kadomtsev-Petviashvili system. From compatibility conditions we obtain the form of matrix operators. After using a gauge transformation, obtained a new type of Lax representation for the hierarchy of Heisenberg ferromagnet equation, which is equivalent to the gauge coupled Kadomtsev-Petviashvili system.
Wang, Ning; Zhang, Xiao Wen
2006-07-01
We propose a dispersionless limit of the NC Kadomtsev Petviashvili hierarchy. Multi-Hamiltonian formulation, l-reductions and relevant W-algebras are investigated. As examples, Gelfand Dickey (GD) Poisson brackets for dispersionless NCKdV and NC Boussinesq hierarchies are constructed explicitly. The associated GD Poisson algebras are shown large N-like analogs of classical V-algebras.
Lump solutions to the BKP equation by symbolic computation
Yang, Jing-Yun; Ma, Wen-Xiu
2016-09-01
Lump solutions are rationally localized in all directions in the space. A general class of lump solutions to the (2+1)-dimensional B-Kadomtsev-Petviashvili (BKP) equation is presented through symbolic computation with Maple. The Hirota bilinear form of the equation is the starting point in the computation process. Like the KP equation, the resulting lump solutions contain six arbitrary parameters. Two of the parameters are due to the translation invariances of the BKP equation with the independent variables, and the other four need to satisfy a nonzero determinant condition and the positivity condition, which guarantee analyticity and rational localization of the solutions.
A procedure to construct exact solutions of nonlinear evolution equations
Indian Academy of Sciences (India)
Adem Cengiz Çevikel; Ahmet Bekir; Mutlu Akar; Sait San
2012-09-01
In this paper, we implemented the functional variable method for the exact solutions of the Zakharov-Kuznetsov-modified equal-width (ZK-MEW), the modified Benjamin-Bona-Mohany (mBBM) and the modified kdV-Kadomtsev-Petviashvili (kdV-KP) equation. By using this scheme, we found some exact solutions of the above-mentioned equation. The obtained solutions include solitary wave solutions, periodic wave solutions and combined formal solutions. The functional variable method presents a wider-applicability for handling nonlinear wave equations.
Directory of Open Access Journals (Sweden)
M. G. Hafez
2016-01-01
Full Text Available Two-dimensional three-component plasma system consisting of nonextensive electrons, positrons, and relativistic thermal ions is considered. The well-known Kadomtsev-Petviashvili-Burgers and Kadomtsev-Petviashvili equations are derived to study the basic characteristics of small but finite amplitude ion acoustic waves of the plasmas by using the reductive perturbation method. The influences of positron concentration, electron-positron and ion-electron temperature ratios, strength of electron and positrons nonextensivity, and relativistic streaming factor on the propagation of ion acoustic waves in the plasmas are investigated. It is revealed that the electrostatic compressive and rarefactive ion acoustic waves are obtained for superthermal electrons and positrons, but only compressive ion acoustic waves are found and the potential profiles become steeper in case of subthermal positrons and electrons.
Generalized Kudryashov method for solving some (3+1-dimensional nonlinear evolution equations
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Md. Shafiqul Islam
2015-06-01
Full Text Available In this work, we have applied the generalized Kudryashov methods to obtain the exact travelling wave solutions for the (3+1-dimensional Jimbo-Miwa (JM equation, the (3+1-dimensional Kadomtsev-Petviashvili (KP equation and the (3+1-dimensional Zakharov-Kuznetsov (ZK. The attained solutions show distinct physical configurations. The constraints that will guarantee the existence of specific solutions will be investigated. These solutions may be useful and desirable for enlightening specific nonlinear physical phenomena in genuinely nonlinear dynamical systems.
Solitary Wave Solutions of KP equation, Cylindrical KP Equation and Spherical KP Equation
Li, Xiang-Zheng; Zhang, Jin-Liang; Wang, Ming-Liang
2017-02-01
Three (2+1)-dimensional equations-KP equation, cylindrical KP equation and spherical KP equation, have been reduced to the same KdV equation by different transformation of variables respectively. Since the single solitary wave solution and 2-solitary wave solution of the KdV equation have been known already, substituting the solutions of the KdV equation into the corresponding transformation of variables respectively, the single and 2-solitary wave solutions of the three (2+1)-dimensional equations can be obtained successfully. Supported by the National Natural Science Foundation of China under Grant No. 11301153 and the Doctoral Foundation of Henan University of Science and Technology under Grant No. 09001562, and the Science and Technology Innovation Platform of Henan University of Science and Technology under Grant No. 2015XPT001
Integrable nonlinear evolution partial differential equations in 4 + 2 and 3 + 1 dimensions.
Fokas, A S
2006-05-19
The derivation and solution of integrable nonlinear evolution partial differential equations in three spatial dimensions has been the holy grail in the field of integrability since the late 1970s. The celebrated Korteweg-de Vries and nonlinear Schrödinger equations, as well as the Kadomtsev-Petviashvili (KP) and Davey-Stewartson (DS) equations, are prototypical examples of integrable evolution equations in one and two spatial dimensions, respectively. Do there exist integrable analogs of these equations in three spatial dimensions? In what follows, I present a positive answer to this question. In particular, I first present integrable generalizations of the KP and DS equations, which are formulated in four spatial dimensions and which have the novelty that they involve complex time. I then impose the requirement of real time, which implies a reduction to three spatial dimensions. I also present a method of solution.
The KP and ZK equations for electrostatic waves with grain charge fluctuation
Institute of Scientific and Technical Information of China (English)
Xue Ju-Kui; Lang He
2004-01-01
@@ The propagation of three-dimensional nonlinear dust-acoustic and dust-Coulomb waves in unmagnetized/magnetized dusty plasmas consisting of electrons, ions, and charged dust particles is investigated. The grain charge fluctuation effect is also incorporated through the current balance equation. By using the perturbation method,a Kadomtsev-Petviashvili equation and a Zakharov-Kuznetsov equation governing the nonlinear waves in the unmagnetized and magnetized systems are obtained respectively. It has been shown that with the combined effects of grain charge fluctuation, the transverse perturbation, and the external magnetic field would modify the wave structures.Waves in those systems are unstable to the high-order long-wave perturbations.
Method of Squared Eigenfunction Potentials in Integrable Hierarchies of KP Type
Aratyn, H; Pacheva, S
1997-01-01
The method of squared eigenfunction potentials (SEP) is developed systematically to describe and gain new information about Kadomtsev-Petviashvili (KP) hierarchy and its reductions. Interrelation to the tau-function method is discussed in detail. The principal result, which forms the basis of our SEP method, is the proof that any eigenfunction of the general KP hierarchy can be represented as a spectral integral over the Baker-Akhiezer (BA) wave function with a spectral density expressed in terms of SEP. In fact, the spectral representations of the (adjoint) BA functions can, in turn, be considered as defining equations for the KP hierarchy. The SEP method is subsequently used to show how the reduction of the full KP hierarchy to the constrained KP hierarchies can be given entirely in terms of linear constraint equations on the pertinent tau-functions. The concept of SEP turns out to be crucial in providing a description of constrained KP hierarchies in the language of universal Sato Grassmannian and finding ...
Wen, Xiao-Yong; Yan, Zhenya
2017-02-01
The novel generalized perturbation (n, M)-fold Darboux transformations (DTs) are reported for the (2 + 1)-dimensional Kadomtsev-Petviashvili (KP) equation and its extension by using the Taylor expansion of the Darboux matrix. The generalized perturbation (1 , N - 1) -fold DTs are used to find their higher-order rational solitons and rogue wave solutions in terms of determinants. The dynamics behaviors of these rogue waves are discussed in detail for different parameters and time, which display the interesting RW and soliton structures including the triangle, pentagon, heptagon profiles, etc. Moreover, we find that a new phenomenon that the parameter (a) can control the wave structures of the KP equation from the higher-order rogue waves (a ≠ 0) into higher-order rational solitons (a = 0) in (x, t)-space with y = const . These results may predict the corresponding dynamical phenomena in the models of fluid mechanics and other physically relevant systems.
New Exact Solutions of Ion-Acoustic Wave Equations by (G′/G-Expansion Method
Directory of Open Access Journals (Sweden)
Wafaa M. Taha
2013-01-01
Full Text Available The (G′/G-expansion method is used to study ion-acoustic waves equations in plasma physic for the first time. Many new exact traveling wave solutions of the Schamel equation, Schamel-KdV (S-KdV, and the two-dimensional modified KP (Kadomtsev-Petviashvili equation with square root nonlinearity are constructed. The traveling wave solutions obtained via this method are expressed by hyperbolic functions, the trigonometric functions, and the rational functions. In addition to solitary waves solutions, a variety of special solutions like kink shaped, antikink shaped, and bell type solitary solutions are obtained when the choice of parameters is taken at special values. Two- and three-dimensional plots are drawn to illustrate the nature of solutions. Moreover, the solution obtained via this method is in good agreement with previously obtained solutions of other researchers.
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DOU Fu-Quan; SUN Jian-An; DUAN Wen-Shan; SHI Yu-Ren; L(U) Ke-Pu; HONG Xue-Ren
2006-01-01
With the aid of computerized symbolic computation, the new modified Jacobi elliptic function expansion method for constructing exact periodic solutions of nonlinear mathematical physics equation is presented by a new general ansatz. The proposed method is more powerful than most of the existing methods. By use of the method, we not only can successfully recover the previously known formal solutions but also can construct new and more general formal solutions for some nonlinear evolution equations. We choose the (3+1)-dimensional Kadomtsev-Petviashvili equation to illustrate our method. As a result, twenty families of periodic solutions are obtained. Of course, more solitary wave solutions, shock wave solutions or triangular function formal solutions can be obtained at their limit condition.
On the solutions of the second heavenly and Pavlov equations
Manakov, S. V.; Santini, P. M.
2009-10-01
We have recently solved the inverse scattering problem for one-parameter families of vector fields, and used this result to construct the formal solution of the Cauchy problem for a class of integrable nonlinear partial differential equations connected with the commutation of multidimensional vector fields, such as the heavenly equation of Plebanski, the dispersionless Kadomtsev-Petviashvili (dKP) equation and the two-dimensional dispersionless Toda (2ddT) equation, as well as with the commutation of one-dimensional vector fields, such as the Pavlov equation. We also showed that the associated Riemann-Hilbert inverse problems are powerful tools to establish if the solutions of the Cauchy problem break at finite time, to construct their long-time behaviour and characterize classes of implicit solutions. In this paper, using the above theory, we concentrate on the heavenly and Pavlov equations, (i) establishing that their localized solutions evolve without breaking, unlike the cases of dKP and 2ddT; (ii) constructing the long-time behaviour of the solutions of their Cauchy problems; (iii) characterizing a distinguished class of implicit solutions of the heavenly equation.
Directory of Open Access Journals (Sweden)
Elsayed Mohamed Elsayed ZAYED
2014-07-01
Full Text Available In this article, many new exact solutions of the (2+1-dimensional nonlinear Boussinesq-Kadomtsev-Petviashvili equation and the (1+1-dimensional nonlinear heat conduction equation are constructed using the Riccati equation mapping method. By means of this method, many new exact solutions are successfully obtained. This method can be applied to many other nonlinear evolution equations in mathematical physics.doi:10.14456/WJST.2014.14
Extended (Super-) KP-hierarchies and generalised String equations
Maroufi, B; Sedra, M B
2000-01-01
We propose a consistently algebraic formulation of the extended KP (supersymmetric) integrable -hierarchy systems. We exploit the results already established in [14] and which consist in a framework suspected to unify in a fascinating way all the possible supersymmetric KP-hierarchies and then their underlying supergravity theories . This construction leads among other to built explicit non standard integrable Lax evolution equations suspected to reduce to the well known KP integrable equation. We present also a contribution of our construction to the subject of string equation and solitons. Other algebraic properties are also presented
``Riemann equations'' in bidifferential calculus
Chvartatskyi, O.; Müller-Hoissen, F.; Stoilov, N.
2015-10-01
We consider equations that formally resemble a matrix Riemann (or Hopf) equation in the framework of bidifferential calculus. With different choices of a first-order bidifferential calculus, we obtain a variety of equations, including a semi-discrete and a fully discrete version of the matrix Riemann equation. A corresponding universal solution-generating method then either yields a (continuous or discrete) Cole-Hopf transformation, or leaves us with the problem of solving Riemann equations (hence an application of the hodograph method). If the bidifferential calculus extends to second order, solutions of a system of "Riemann equations" are also solutions of an equation that arises, on the universal level of bidifferential calculus, as an integrability condition. Depending on the choice of bidifferential calculus, the latter can represent a number of prominent integrable equations, like self-dual Yang-Mills, as well as matrix versions of the two-dimensional Toda lattice, Hirota's bilinear difference equation, (2+1)-dimensional Nonlinear Schrödinger (NLS), Kadomtsev-Petviashvili (KP) equation, and Davey-Stewartson equations. For all of them, a recent (non-isospectral) binary Darboux transformation result in bidifferential calculus applies, which can be specialized to generate solutions of the associated "Riemann equations." For the latter, we clarify the relation between these specialized binary Darboux transformations and the aforementioned solution-generating method. From (arbitrary size) matrix versions of the "Riemann equations" associated with an integrable equation, possessing a bidifferential calculus formulation, multi-soliton-type solutions of the latter can be generated. This includes "breaking" multi-soliton-type solutions of the self-dual Yang-Mills and the (2+1)-dimensional NLS equation, which are parametrized by solutions of Riemann equations.
The multicomponent KP hierarchy: differential Fay identities and Lax equations
Teo, Lee Peng
2011-06-01
In this paper, we show that four sets of differential Fay identities of an N-component KP hierarchy derived from the bilinear relation satisfied by the tau function of the hierarchy are sufficient to derive the auxiliary linear equations for the wavefunctions. From this, we derive the Lax representation for the N-component KP hierarchy, which are equations satisfied by some pseudo-differential operators with matrix coefficients. Besides the Lax equations with respect to the time variables proposed in Date et al (1981 J. Phys. Soc. Japan 50 3806-12), we also obtain a set of equations relating different charge sectors, which can be considered as a generalization of the modified KP hierarchy proposed in Takebe (2002 Lett. Math. Phys. 59 157-72).
CONDITIONAL SIMILARITY REDUCTION APPROACH:JIMBO-MIWA EQUATION
Institute of Scientific and Technical Information of China (English)
楼森岳; 唐晓艳
2001-01-01
The direct method developed by Clarkson and Kruskal (1989 J. Math. Phys. 30 2201) for finding the symmetryreductions of a nonlinear system is extended to find the conditional similarity solutions. Using the method of the JimboMiwa (JM) equation, we find that three well-known (2+1)-dimensional models-the asymmetric Nizhnik-NovikovVeselov equation, the breaking soliton equation and the Kadomtsev-Petviashvili equation-can all be obtained as the conditional similarity reductions of the JM equation.
High-Dimensional Integrable Models with Conformal Invariance
Institute of Scientific and Technical Information of China (English)
LIN Ji; QIAN Xian-Ming
2003-01-01
Using the (2+1)-dimensional Schwartz derivative, the usual (2+1)-dimensional Schwartz Kadomtsev-Petviashvili (KP) equation is extended to (n+1)-dimensional conformal invariance equation. The extension possessestwo spatial-plane solitons solutions of a (3+1)-dimensional equation are obtained.
Rational solutions to the KPI equation and multi rogue waves
Gaillard, Pierre
2016-04-01
We construct here rational solutions to the Kadomtsev-Petviashvili equation (KPI) as a quotient of two polynomials in x, y and t depending on several real parameters. This method provides an infinite hierarchy of rational solutions written in terms of polynomials of degrees 2 N(N + 1) in x, y and t depending on 2 N - 2 real parameters for each positive integer N. We give explicit expressions of the solutions in the simplest cases N = 1 and N = 2 and we study the patterns of their modulus in the (x , y) plane for different values of time t and parameters.
Virasoro Constraints and Topological Recursion for Grothendieck's Dessin Counting
Kazarian, Maxim; Zograf, Peter
2015-08-01
We compute the number of coverings of with a given monodromy type over and given numbers of preimages of 0 and 1. We show that the generating function for these numbers enjoys several remarkable integrability properties: it obeys the Virasoro constraints, an evolution equation, the KP (Kadomtsev-Petviashvili) hierarchy and satisfies a topological recursion in the sense of Eynard-Orantin.
Fredholm and Wronskian representations of solutions to the KPI equation and multi-rogue waves
Gaillard, Pierre
2016-06-01
We construct solutions to the Kadomtsev-Petviashvili equation (KPI) in terms of Fredholm determinants. We deduce solutions written as a quotient of Wronskians of order 2N. These solutions, called solutions of order N, depend on 2N - 1 parameters. When one of these parameters tends to zero, we obtain N order rational solutions expressed as a quotient of two polynomials of degree 2N(N + 1) in x, y, and t depending on 2N - 2 parameters. So we get with this method an infinite hierarchy of solutions to the KPI equation.
Institute of Scientific and Technical Information of China (English)
ZHAO Qiang; LIU Shi-Kuo; FU Zun-Tao
2004-01-01
The (2+ 1)-dimensional Boussinesq equation and (3+ 1)-dimensional KP equation are studied by using the extended Jacobi elliptic-function method. The exact periodic-wave solutions for the two equations are obtained.
Properties of Solutions of the KPI Equation
Boiti, M; Pogrebkov, A K; Boiti, Marco
1993-01-01
Abstract: The Kadomtsev--Petviashvili I (KPI) is considered as a useful laboratory for experimenting new theoretical tools able to handle the specific features of integrable models in $2+1$ dimensions. The linearized version of the KPI equation is first considered by solving the initial value problem for different classes of initial data. Properties of the solutions in different cases are analyzed in details. The obtained results are used as a guideline for studying the properties of the solution $u(t,x,y)$ of the Kadomtsev--Petviashvili I (KPI) equation with given initial data $u(0,x,y)$ belonging to the Schwartz space. The spectral theory associated to KPI is studied in the space of the Fourier transform of the solutions. The variables $p=\\{p_1,p_2\\}$ of the Fourier space are shown to be the most convenient spectral variables to use for spectral data. Spectral data are shown to decay rapidly at large $p$ but to be discontinuous at $p=0$. Direct and inverse problems are solved with special attention to the b...
Aratyn, H; Pacheva, S
1996-01-01
This paper provides a systematic description of the interplay between a specific class of reductions denoted as \\cKPrm ($r,m \\geq 1$) of the primary continuum integrable system -- the Kadomtsev-Petviashvili ({\\sf KP}) hierarchy and discrete multi-matrix models. The relevant integrable \\cKPrm structure is a generalization of the familiar $r$-reduction of the full {\\sf KP} hierarchy to the $SL(r)$ generalized KdV hierarchy ${\\sf cKP}_{r, 0}$. The important feature of \\cKPrm hierarchies is the presence of a discrete symmetry structure generated by successive Darboux-Bãcklund (DB) transformations. This symmetry allows for expressing the relevant tau-functions as Wronskians within a formalism which realizes the tau-functions as DB orbits of simple initial solutions. In particular, it is shown that any DB orbit of a ${\\sf cKP}_{r,1}$ defines a generalized 2-dimensional Toda lattice structure. Furthermore, we consider the class of truncated {\\sf KP} hierarchies ({\\sl i.e.}, those defined via Wilson-Sato dressing op...
Determinant Solutions to a (3+1)-Dimensional Generalized KP Equation with Variable Coefficients
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Alrazi ABDELJABBAR; Wenxiu MA; Ahmet YILDIRIM
2012-01-01
A system of linear conditions is presented for Wronskian and Grammian solutions to a (3+1)-dimensional generalized vcKP equation. The formulations of these solutions require a constraint on variable coefficients.
Parabola solitons for the nonautonomous KP equation in fluids and plasmas
Energy Technology Data Exchange (ETDEWEB)
Yu, Xin, E-mail: yuxin@buaa.edu.cn; Sun, Zhi-Yuan
2016-04-15
Under investigation in this paper is a nonautonomous Kadomtsev–Petviashvili (KP) equation in fluids and plasmas. The integrability of this equation is examined via the Painlevé analysis and its multi-soliton solutions are constructed. A constraint is proposed to ensure the existence of parabola solitons for such KP equation. Based on the constructed solutions, the solitonic propagation and interaction, including the elastic interaction, inelastic interaction and soliton resonance for parabola solitons, are discussed. The results might be useful for shallow water wave and rogue wave.
A new method to the(2+1)-dimensional modified KP equation
Institute of Scientific and Technical Information of China (English)
无
2011-01-01
By means of the auxiliary ordinary differential equation method,we have obtained many solitary wave solutions,periodic wave solutions and variable separation solutions for the (2+1)-dimensional KP equation.Using a mixed method,many exact solutions have been obtained.
Hungry Volterra equation, multi boson KP hierarchy and Two Matrix Models
Hisakado, M
1998-01-01
We consider the hungry Volterra hierarchy from the view point of the multi boson KP hierarchy. We construct the hungry Volterra equation as the ``fractional '' BT. We also study the relations between the (discrete time) hungry Volterra equation and two matrix models. From this point of view we study the reduction from (discrete time) 2d Toda lattice to the (discrete time) hungry Volterra equation.
High-Dimensional Integrable Models with Conformal Invariance
Institute of Scientific and Technical Information of China (English)
LINJi; QIANXian-Ming
2003-01-01
Using the (2+1)-dimensional Schwartz dcrivative, the usual (2+1)-dimensional Schwartz Kadomtsev-Petviashvili (KP) equation is extended to (n+1)-dimensional conformal invariance equation. The extension possesses Painlcvc property. Some (3+1)-dimensional examples are given and some single three-dimensional camber soliton and two spatial-plane solitons solutions of a (3+1)-dimensional equation are obtained.
Periodic Wave Solutions and Their Limits for the Generalized KP-BBM Equation
Ming Song; Zhengrong Liu
2012-01-01
We use the bifurcation method of dynamical systems to study the periodic wave solutions and their limits for the generalized KP-BBM equation. A number of explicit periodic wave solutions are obtained. These solutions contain smooth periodic wave solutions and periodic blow-up solutions. Their limits contain periodic wave solutions, kink wave solutions, unbounded wave solutions, blow-up wave solutions, and solitary wave solutions.
Energy Technology Data Exchange (ETDEWEB)
Ibragimov, Nail H [Department of Mathematics and Science, Blekinge Institute of Technology, SE-371 79 Karlskrona (Sweden); Meleshko, Sergey V [School of Mathematics, Institute of Science, Suranaree University of Technology, Nakhon Ratchasima 30000 (Thailand); Rudenko, Oleg V, E-mail: nib@bth.se, E-mail: sergey@math.sut.ac.th, E-mail: rudenko@acs366.phys.msu.ru [Department of Physics, Moscow State University, 119991 Moscow (Russian Federation)
2011-08-05
The paper deals with an evolutionary integro-differential equation describing nonlinear waves. A particular choice of the kernel in the integral leads to well-known equations such as the Khokhlov-Zabolotskaya equation, the Kadomtsev-Petviashvili equation and others. Since the solutions of these equations describe many physical phenomena, the analysis of the general model studied in this paper is important. One of the methods for obtaining solutions of differential equations is provided by the Lie group analysis. However, this method is not applicable to integro-differential equations. Therefore, we discuss new approaches developed in modern group analysis and apply them to the general model considered in this paper. Reduced equations and exact solutions are also presented.
Energy Technology Data Exchange (ETDEWEB)
Verhoeven, C; Musette, M [Dienst Theoretische Natuurkunde, Vrije Universiteit Brussel, Pleinlaan 2, B-1050 Brussels (Belgium)
2003-02-28
In this letter, we analyse two bidirectional sixth-order partial differential equations, which are reductions in (1 + 1) dimensions of equations belonging to the KP hierarchy. They have fourth-order and fifth-order Lax pairs, respectively. We derive their Baecklund transformations and, from the nonlinear superposition formula, we can build their soliton solutions like a Grammian. The interesting dynamics of these solitons is that they may describe not only the overtaking collision but also the head-on collision of solitary waves of different type and shape. (letter to the editor)
Dispersive deformations of hydrodynamic reductions of (2 + 1)D dispersionless integrable systems
Ferapontov, E. V.; Moro, A.
2009-01-01
We demonstrate that hydrodynamic reductions of dispersionless integrable systems in 2 + 1 dimensions, such as the dispersionless Kadomtsev-Petviashvili (dKP) and dispersionless Toda lattice (dTl) equations, can be deformed into reductions of the corresponding dispersive counterparts. Modulo the Miura group, such deformations are unique. The requirement that any hydrodynamic reduction possesses a deformation of this kind imposes strong constraints on the structure of dispersive terms, suggesting an alternative approach to the integrability in 2 + 1 dimensions.
Solutions of the KPI equation with smooth initial data
Boiti, M; Pogrebkov, A K
1993-01-01
Abstract: The solution $u(t,x,y)$ of the Kadomtsev--Petviashvili I (KPI) equation with given initial data $u(0,x,y)$ belonging to the Schwartz space is considered. No additional special constraints, usually considered in literature, as $\\int\\!dx\\,u(0,x,y)=0$ are required to be satisfied by the initial data. The problem is completely solved in the framework of the spectral transform theory and it is shown that $u(t,x,y)$ satisfies a special evolution version of the KPI equation and that, in general, $\\partial_t u(t,x,y)$ has different left and right limits at the initial time $t=0$. The conditions of the type $\\int\\!dx\\,u(t,x,y)=0$, are dynamically generated by the evolution equation for $t\
Conservation Laws and Web-Solutions for the Benney--Luke Equation
Ablowitz, Mark
2012-01-01
A long wave multi-dimensional approximation of shallow water waves is the bi-directional Benney-Luke equation. It yields the well-known Kadomtsev-Petviashvili equation in a quasi one-directional limit. A direct perturbation method is developed; it uses the underlying conservation laws to determine the slow evolution of parameters of two space dimensional, non-decaying web-type solutions to the Benney-Luke equation. New numerical simulations, based on windowing methods which are effective for non-decaying data, are presented. These simulations support the analytical results and elucidate the relationship between the Kadomtsev-Petviashvilli and the Benney-Luke equations and are also used to obtain amplitude information regarding particular web solutions. Additional dissipative perturbations to the Benney-Luke equation are also studied.
Institute of Scientific and Technical Information of China (English)
ZHANG Li-Hua; LIU Xi-Qiang; BAI Cheng-Lin
2006-01-01
In this paper, the generalized tanh function method is extended to (2+1)-dimensional canonical generalized KP (CGKP) equation with variable coefficients. Taking advantage of the Riccati equation, many explicit exact solutions,which contain multiple soliton-like and periodic solutions, are obtained for the (2+1)-dimensional CGKP equation with variable coefficients.
Multi-rogue waves solutions: from the NLS to the KP-I equation
Dubard, P.; Matveev, V. B.
2013-12-01
Our discovery of multi-rogue wave (MRW) solutions in 2010 completely changed the viewpoint on the links between the theory of rogue waves and integrable systems, and helped explain many phenomena which were never understood before. It is enough to mention the famous Three Sister waves observed in oceans, the creation of a regular approach to studying higher Peregrine breathers, and the new understanding of 2 + 1 dimensional rogue waves via the NLS-KP correspondence. This article continues the study of the MRW solutions of the NLS equation and their links with the KP-I equation started in a previous series of articles (Dubard et al 2010 Eur. Phys. J. 185 247-58, Dubard and Matveev 2011 Natural Hazards Earth Syst. Sci. 11 667-72, Matveev and Dubard 2010 Proc. Int. Conf. FNP-2010 (Novgorod, St Petersburg) pp 100-101, Dubard 2010 PhD Thesis). In particular, it contains a discussion of the large parametric asymptotics of these solutions, which has never been studied before.
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ZHANG Xiao-Xian; WEN Xiao-Yong; SUN Ye-Peng
2008-01-01
With the aid of symbolic computation system Maple, many exact solutions for the (3+1)-dimensional KP equation axe constructed by introducing an auxiliary equation and using its new Jacobi elliptic function solutions, where the new solutions are also constructed. When the modulus m → 1 and m → 0, these solutions reduce to the corresponding solitary evolution solutions and trigonometric function solutions.
Interaction and resonance phenomena of multi-soliton
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YANG Hong-juan; SHI Yu-ren; DUAN Wen-shan
2006-01-01
As is well known,Korteweg-de Vries equation is a typical one which has planar solitary wave.By considering higher order transverse disturbance to planar solitary waves,we study a Kadomtsev-Petviashvili (KP) equation and find some interesting results.In this letter we investigate the three soliton interaction and their resonance phenomena of KP equation,and theoretically find that the maximum amplitude is 9 times of the initial interacting soliton for three same amplitude solitons.Three arbitrary amplitude soliton interaction of KP equation is also studied by numerical simulation,which can also results in resonance phenomena.
Institute of Scientific and Technical Information of China (English)
陈怀堂; 张鸿庆
2003-01-01
A new generalized Jacobi elliptic function method is used to construct the exact travelling wave solutions of nonlinear partial differential equations (PDEs) in a unified way. The main idea of this method is to take full advantage of the elliptic equation which has more new solutions. More new doubly periodic and multiple soliton solutions are obtained for the generalized (3+1)-dimensional Kronig-Penny (KP) equation with variable coefficients. This method can be applied to other equations with variable coefficients.
Koch, Herbert; Vişan, Monica
2014-01-01
The first part of the book provides an introduction to key tools and techniques in dispersive equations: Strichartz estimates, bilinear estimates, modulation and adapted function spaces, with an application to the generalized Korteweg-de Vries equation and the Kadomtsev-Petviashvili equation. The energy-critical nonlinear Schrödinger equation, global solutions to the defocusing problem, and scattering are the focus of the second part. Using this concrete example, it walks the reader through the induction on energy technique, which has become the essential methodology for tackling large data critical problems. This includes refined/inverse Strichartz estimates, the existence and almost periodicity of minimal blow up solutions, and the development of long-time Strichartz inequalities. The third part describes wave and Schrödinger maps. Starting by building heuristics about multilinear estimates, it provides a detailed outline of this very active area of geometric/dispersive PDE. It focuses on concepts and ide...
Indian Academy of Sciences (India)
Hamid Reza Pakzad
2010-04-01
In this work, the propagation of nonlinear waves in warm dusty plasmas with variable dust charge, two-temperature ion and nonthermal electron is studied. By using the reductive perturbation theory, the Kadomstev–Petviashvili (KP) equation is derived. The energy of the soliton and the linear dispersion relation are obtained. The effects of variable dust charge on the energy of soliton and the angular frequency of linear wave are also discussed.
Relativistic Magnetosonic Soliton in a Negative-Ion-Rich Magnetized Plasma
Institute of Scientific and Technical Information of China (English)
WANG Yun-Liang; ZHOU Zhong-Xiang; LU Yan-Zhen; NI Xiao-Dong; SHEN Jiang; ZHANG Yu
2008-01-01
@@ Two-dimensional (2D) relativistic magnetosonic solitons in the negative-ion-rich plasma consisting of positive ions Ar+, negative ions SF6- and electrons are investigated in the presence of an applied magnetic field Bo and can be described by a Kadomtsev-Petviashvili (KP) equation in the weakly relativistic limit. The ratio of positive ion density to negative ion density has a marked influence on the amplitude φm and width W of the steady-state KP soliton. The interaction law of the nontrivial solitons with rich web structure is studied by the Wronskian determinant method.
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BAI Cheng-Jie; BAI Cheng-Lin; HAN Ji-Guang; ZHAO Hong
2005-01-01
By the application of the extended homogeneous balance method, we derive an auto-Backlund transformation (BT) for (2+1)-dimensional variable coefficient generalized KP equations. Based on the BT, in which there are two homogeneity equations to be solved, we obtain some exact solutions containing single solitary waves.
Exact Solutions of the (3+1)-Dimensional KP and KdV-Type Equations
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LI De-Sheng; Lü Zhuo-Sheng; ZHANG Hong-Qing
2003-01-01
Abundant new soliton-like and period form solutions for certain (3+1)-dimensional physically important nonlinear evolution equations are obtained by using a further extended tanh method and symbolic computation system, Maple.
Dark solitons, dispersive shock waves, and transverse instabilities
Hoefer, M A
2011-01-01
The nature of transverse instabilities to dark solitons and dispersive shock waves for the (2+1)-dimensional defocusing nonlinear Schrodinger equation / Gross-Pitaevskii (NLS / GP) equation is considered. Special attention is given to the small (shallow) amplitude regime, which limits to the Kadomtsev-Petviashvili (KP) equation. We study analytically and numerically the eigenvalues of the linearized NLS / GP equation. The dispersion relation for shallow solitons is obtained asymptotically beyond the KP limit. This yields 1) the maximum growth rate and associated wavenumber of unstable perturbations; and 2) the separatrix between convective and absolute instabilities. The latter result is used to study the transition between convective and absolute instabilities of oblique dispersive shock waves (DSWs). Stationary and nonstationary oblique DSWs are constructed analytically and investigated numerically by direct simulations of the NLS / GP equation. The instability properties of oblique DSWs are found to be dir...
KP hierarchy for Hodge integrals
Kazarian, M.
2008-01-01
Starting from the ELSV formula, we derive a number of new equations on the generating functions for Hodge integrals over the moduli space of complex curves. This gives a new simple and uniform treatment of certain known results on Hodge integrals like Witten's conjecture, Virasoro constrains, Faber's lambda_g conjecture etc. Among other results we show that a properly arranged generating function for Hodge integrals satisfies the equations of the KP hierarchy.
Light Meets Water in Nonlocal Media: Surface Tension Analogue in Optics
Horikis, Theodoros P.; Frantzeskakis, Dimitrios J.
2017-06-01
Shallow water wave phenomena find their analogue in optics through a nonlocal nonlinear Schrödinger (NLS) model in 2 +1 dimensions. We identify an analogue of surface tension in optics, namely, a single parameter depending on the degree of nonlocality, which changes the sign of dispersion, much like surface tension does in the shallow water wave problem. Using multiscale expansions, we reduce the NLS model to a Kadomtsev-Petviashvili (KP) equation, which is of the KPII (KPI) type, for strong (weak) nonlocality. We demonstrate the emergence of robust optical antidark solitons forming Y -, X -, and H -shaped wave patterns, which are approximated by colliding KPII line solitons, similar to those observed in shallow waters.
An extended integrable fractional-order KP soliton hierarchy
Energy Technology Data Exchange (ETDEWEB)
Li Li, E-mail: li07099@163.co [College of Maths and Systematic Science, Shenyang Normal University, Shenyang 110034 (China)
2011-01-17
In this Letter, we consider the modified derivatives and integrals of fractional-order pseudo-differential operators. A sequence of Lax KP equations hierarchy and extended fractional KP (fKP) hierarchy are introduced, and the fKP hierarchy has Lax presentations with the extended Lax operators. In the case of the extension with the half-order pseudo-differential operators, a new integrable fKP hierarchy is obtained. A few particular examples of fractional order will be listed, together with their Lax pairs.
Nonlinear ion acoustic waves scattered by vortexes
Ohno, Yuji; Yoshida, Zensho
2016-09-01
The Kadomtsev-Petviashvili (KP) hierarchy is the archetype of infinite-dimensional integrable systems, which describes nonlinear ion acoustic waves in two-dimensional space. This remarkably ordered system resides on a singular submanifold (leaf) embedded in a larger phase space of more general ion acoustic waves (low-frequency electrostatic perturbations). The KP hierarchy is characterized not only by small amplitudes but also by irrotational (zero-vorticity) velocity fields. In fact, the KP equation is derived by eliminating vorticity at every order of the reductive perturbation. Here, we modify the scaling of the velocity field so as to introduce a vortex term. The newly derived system of equations consists of a generalized three-dimensional KP equation and a two-dimensional vortex equation. The former describes 'scattering' of vortex-free waves by ambient vortexes that are determined by the latter. We say that the vortexes are 'ambient' because they do not receive reciprocal reactions from the waves (i.e., the vortex equation is independent of the wave fields). This model describes a minimal departure from the integrable KP system. By the Painlevé test, we delineate how the vorticity term violates integrability, bringing about an essential three-dimensionality to the solutions. By numerical simulation, we show how the solitons are scattered by vortexes and become chaotic.
Self-focusing instability of two-dimensional solitons and vortices
DEFF Research Database (Denmark)
Kuznetsov, E.A.; Juul Rasmussen, J.
1995-01-01
The instability of two-dimensional solitons and vortices is demonstrated in the framework of the three-dimensional nonlinear Schrodinger equation (NLSE). The instability can be regarded as the analog of the Kadomtsev-Petviashvili instability [B. B. Kadomtsev and V. I. Petviashvili, Sov. Phys. Dokl...
The $n$-component KP hierarchy and representation theory
Kac, V G
1993-01-01
Starting from free charged fermions we give equivalent definitions of the $n\\/$-component KP hierarchy, in terms of $\\tau\\/$-functions $\\tau_\\alpha\\/$ (where $\\alpha \\in M =\\/$ root lattice of $sl_n\\/$), in terms of $n \\times n\\/$ matrix valued wave functions $W_\\alpha(\\alpha\\in M)\\/$, and in terms of pseudodifferential wave operators $P_\\alpha(\\alpha\\in M)\\/$. These imply the deformation and the zero curvature equations. We show that the 2-component KP hierarchy contains the Davey-Stewartson system and the $n\\geq3\\/$ component KP hierarchy continues the $n\\/$-wave interaction equations. This allows us to construct theis solutions.
Nonlinear ion acoustic waves scattered by vortexes
Ohno, Yuji
2015-01-01
The Kadomtsev--Petviashvili (KP) hierarchy is the archetype of infinite-dimensional integrable systems, which describes nonlinear ion acoustic waves in two-dimensional space. This remarkably ordered system resides on a singular submanifold (leaf) embedded in a larger phase space of more general ion acoustic waves (low-frequency electrostatic perturbations). The KP hierarchy is characterized not only by small amplitudes but also by irrotational (zero-vorticity) velocity fields. In fact, the KP equation is derived by eliminating vorticity at every order of the reductive perturbation. Here we modify the scaling of the velocity field so as to introduce a vortex term. The newly derived system of equations consists of a generalized three-dimensional KP equation and a two-dimensional vortex equation. The former describes `scattering' of vortex-free waves by ambient vortexes that are determined by the latter. We say that the vortexes are `ambient' because they do not receive reciprocal reactions from the waves (i.e.,...
Addition Formulae of Discrete KP, q-KP and Two-Component BKP Systems
Gao, Xu; Li, Chuan-Zhong; He, Jing-Song
2016-04-01
In this paper, we construct the addition formulae for several integrable hierarchies, including the discrete KP, the q-deformed KP, the two-component BKP and the D type Drinfeld-Sokolov hierarchies. With the help of the Hirota bilinear equations and τ functions of different kinds of KP hierarchies, we prove that these addition formulae are equivalent to these hierarchies. These studies show that the addition formula in the research of the integrable systems has good universality. Supported by the Zhejiang Provincial Natural Science Foundation under Grant No. LY15A010004, the National Natural Science Foundation of China under Grant Nos. 11201251, 11571192 and the Natural Science Foundation of Ningbo under Grant No. 2015A610157. Jingsong He is supported by the National Natural Science Foundation of China under Grant No. 11271210, K.C. Wong Magna Fund in Ningbo University
Third Order Reconstruction of the KP Scheme for Model of River Tinnelva
Directory of Open Access Journals (Sweden)
Susantha Dissanayake
2017-01-01
Full Text Available The Saint-Venant equation/Shallow Water Equation is used to simulate flow of river, flow of liquid in an open channel, tsunami etc. The Kurganov-Petrova (KP scheme which was developed based on the local speed of discontinuity propagation, can be used to solve hyperbolic type partial differential equations (PDEs, hence can be used to solve the Saint-Venant equation. The KP scheme is semi discrete: PDEs are discretized in the spatial domain, resulting in a set of Ordinary Differential Equations (ODEs. In this study, the common 2nd order KP scheme is extended into 3rd order scheme while following the Weighted Essentially Non-Oscillatory (WENO and Central WENO (CWENO reconstruction steps. Both the 2nd order and 3rd order schemes have been used in simulation in order to check the suitability of the KP schemes to solve hyperbolic type PDEs. The simulation results indicated that the 3rd order KP scheme shows some better stability compared to the 2nd order scheme. Computational time for the 3rd order KP scheme for variable step-length ode solvers in MATLAB is less compared to the computational time of the 2nd order KP scheme. In addition, it was confirmed that the order of the time integrators essentially should be lower compared to the order of the spatial discretization. However, for computation of abrupt step changes, the 2nd order KP scheme shows a more accurate solution.
具有物理背景的高维Painlevé可积模型%HIGHER DIMENSIONAL PAINLEV? INTEGRABLE MODELS WITH REAL PHYSICAL SIGNIFICATION
Institute of Scientific and Technical Information of China (English)
阮航宇; 陈一新
2001-01-01
提出了一种求解任意维数非线性模型的“Mbious”变换下不变的渐进展开方法，并可同时获得许多新的与原模型有着相同维数的Painlevé可积模型.取(2+1)维KdV-Burgers(KdVB)方程和Kadomtsev-Petviashvili(KP)方程为具体例子，获得了一些新的具有Painlevé性质的高维“Mbious”变换下不变的方程及原模型的近似解.在某些特殊情况下，某些近似解可以成为精确解.%A “Mbius” invariant asymptotic expansion approach to solve any nonlinear integrable and nonintegrable models with any dimension is proposed. Many new Painlevé integrable models with the same dimension can be obtained at the same time. Taking the (2+1)-dimensional KdV-Burgers(KdVB) equation, (3+1)-dimensional Kudomtsev-Petviashvili (KP) equation as concrete examples, we obtain some new higher dimensional “Mbius” invariant models with Painlevé property and the approximate solutions of these models. In some special case, some approximate solutions become exact.
Generating Quadrilateral and Circular Lattices in KP Theory
Doliwa, A; Alonso, L M; Doliwa, Adam; Manas, Manuel; Alonso, Luis Martinez
1998-01-01
The bilinear equations of the $N$-component KP and BKP hierarchies and a corresponding extended Miwa transformation allow us to generate quadrilateral and circular lattices from conjugate and orthogonal nets, respectively. The main geometrical objects are expressed in terms of Baker functions.
Foda, O; Zuparic, M
2009-01-01
Using a Jacobi-Trudi-type identity, we show that the scalar product of a general state and a Bethe eigenstate in a finite-length XXZ spin-1/2 chain is (a restriction of) a KP tau function. This leads to a correspondence between the eigenstates and points on Sato's Grassmannian. Each of these points is a function of the rapidities of the corresponding eigenstate, the inhomogeneity variables of the spin chain and the crossing parameter.
Energy Technology Data Exchange (ETDEWEB)
Foda, O. [Department of Mathematics and Statistics, University of Melbourne, Parkville, Victoria 3010 (Australia)], E-mail: foda@ms.unimelb.edu.au; Wheeler, M. [Department of Mathematics and Statistics, University of Melbourne, Parkville, Victoria 3010 (Australia)], E-mail: mwheeler@ms.unimelb.edu.au; Zuparic, M. [Department of Mathematics and Statistics, University of Melbourne, Parkville, Victoria 3010 (Australia)], E-mail: mzup@ms.unimelb.edu.au
2009-10-21
Using a Jacobi-Trudi-type identity, we show that the scalar product of a general state and a Bethe eigenstate in a finite-length XXZ spin-1/2 chain is (a restriction of) a KP {tau} function. This leads to a correspondence between the eigenstates and points on Sato's Grassmannian. Each of these points is a function of the rapidities of the corresponding eigenstate, the inhomogeneity variables of the spin chain and the crossing parameter.
Gidel, Floriane; Bokhove, Onno; Kalogirou, Anna
2017-01-01
In this work, we model extreme waves that occur due to Mach reflection through the intersection of two obliquely incident solitary waves. For a given range of incident angles and amplitudes, the Mach stem wave grows linearly in length and amplitude, reaching up to 4 times the amplitude of the incident waves. A variational approach is used to derive the bidirectional Benney-Luke equations, an asymptotic equivalent of the three-dimensional potential-flow equations modelling water waves. This nonlinear and weakly dispersive model has the advantage of allowing wave propagation in two horizontal directions, which is not the case with the unidirectional Kadomtsev-Petviashvili (KP) equation used in most previous studies. A variational Galerkin finite-element method is applied to solve the system numerically in Firedrake with a second-order Störmer-Verlet temporal integration scheme, in order to obtain stable simulations that conserve the overall mass and energy of the system. Using this approach, we are able to get close to the 4-fold amplitude amplification predicted by Miles.
Slavnov determinants, Yang-Mills structure constants, and discrete KP
Foda, O
2012-01-01
Using Slavnov's scalar product of a Bethe eigenstate and a generic state in closed XXZ spin-1/2 chains, with possibly twisted boundary conditions, we obtain determinant expressions for tree-level structure constants in 1-loop conformally-invariant sectors in various planar (super) Yang-Mills theories. When certain rapidity variables are allowed to be free rather than satisfy Bethe equations, these determinants become discrete KP tau-functions.
The KP4 killer protein gene family
Killer protein 4 (KP4) is a well studied toxin secreted by the maize smut fungus Ustilago maydis that kills sensitive Ustilago strains as well as inhibits Fusarium and plant root growth. This small, cysteine rich protein is encoded by a virus that depends on host survival for replication. KP4 functi...
Singh, Manpreet; Singh Saini, Nareshpal; Ghai, Yashika; Kaur, Nimardeep
2016-07-01
Dusty plasma is a fully or partially ionized gas which contain micron or sub-micron sized dust particles. These dust particles can be positively or negatively charged, depending upon the mechanism of charging . Dusty plasma is often observed in most of the space and astrophysical plasma environments. Presence of these dust particles can modify the dispersion properties of waves in the plasma and can introduce several new wave modes, e.g., dust acoustic (DA) waves, dust-ion acoustic (DIA) waves, dust-acoustic shock waves etc. In this investigation we have studied the small amplitude dust acoustic waves in an unmagnetized plasma comprising of electrons, positively charged ions, negatively charged hot as well as cold dust. Electrons and ions are described by superthermal distribution which is more appropriate for modeling space and astrophysical plasmas. Kadomtsev- Petviashvili (KP) equation has been derived using reductive perturbation technique. Positive as well as negative potential structures are observed, depending upon some critical values of parameters. Amplitude and width of dust acoustic solitary waves are modified by varying these parameters such as superthermality of electrons and ions, direction of propagation of the wave, relative concentration of hot and cold dust particles etc. This study may be helpful in understanding the formation and dynamics of nonlinear structures in various space and astrophysical plasma environments such Saturn's F-rings.
Growth of fat slits and dispersionless KP hierarchy
Zabrodin, A
2008-01-01
A "fat slit" is a compact domain in the upper half plane bounded by a curve with endpoints on the real axis and a segment of the real axis between them. We consider conformal maps of the upper half plane to the exterior of a fat slit parameterized by harmonic moments of the latter and show that they obey an infinite set of Lax equations for the dispersionless KP hierarchy. Deformation of a fat slit under changing a particular harmonic moment can be treated as a growth process similar to the Laplacian growth of domains in the whole plane. This construction extends the well known link between solutions to the dispersionless KP hierarchy and conformal maps of slit domains in the upper half plane and provides a new, large family of solutions.
Integrable KP Coupling and Its Exact Solution
Institute of Scientific and Technical Information of China (English)
彭凌; 杨旭东; 楼森岳
2012-01-01
The integrable coupling is one of the most important topics in the nonlinear physics. This paper creates a novel integrable KP coupling and solves it via a recently-developed dark parameterization procedure.
Planetary Kp index forecast using autoregressive models
Gonzalez, Arian Ojeda; Odriozola, Siomel Savio; Rosa, Reinaldo Roberto; Mendes, Odim
2014-01-01
The geomagnetic Kp index is derived from the K index measurements obtained from thirteen stations located around the Earth geomagnetic latitudes between $48^\\circ$ and $63^\\circ$. This index is processed every three hours, is quasi-logarithmic and estimates the geomagnetic activity. The Kp values fall within a range of 0 to 9 and are organized as a set of 28 discrete values. The data set is important because it is used as one of the many input parameters of magnetospheric and ionospheric models. The objective of this work is to use historical data from the Kp index to develop a methodology to make a prediction in a time interval of at least three hours. Five different models to forecast geomagnetic indices Kp and ap are tested. Time series of values of Kp index from 1932 to 15/12/2012 at 21:00 UT are used as input to the models. The purpose of the model is to predict the three measured values after the last measured value of the Kp index (it means the next 9 hours values). The AR model provides the lowest com...
Cohomology of real Grassmann manifold and KP flow
Casian, Luis
2010-01-01
We consider a realization of the real Grassmann manifold Gr(k,n) based on a particular flow defined by the corresponding (singular) solution of the KP equation. Then we show that the KP flow can provide an explicit and simple construction of the incidence graph for the integral cohomology of Gr(k,n). It turns out that there are two types of graphs, one for the trivial coefficients and other for the twisted coefficients, and they correspond to the homology groups of the orientable and non-orientable cases of Gr(k,n) via the Poincare-Lefschetz duality. We also derive an explicit formula of the Poincare polynomial for Gr(k,n) and show that the Poincare polynomial is also related to the number of points on a suitable version of Gr(k,n) over a finite field $\\F_q$ with q being a power of a prime. In particular, we find that the number of $\\F_q$ points on Gr(k,n) can be computed by counting the number of singularities along the KP flow.
Domain wall partition functions and KP
Foda, O; Zuparic, M
2009-01-01
We observe that the partition function of the six vertex model on a finite square lattice with domain wall boundary conditions is (a restriction of) a KP tau function and express it as an expectation value of charged free fermions (up to an overall normalization).
The master T-operator for inhomogeneous XXX spin chain and mKP hierarchy
Zabrodin, A
2014-01-01
Following the approach of [1], we show how to construct the master T-operator for the quantum GL(N)-invariant inhomogeneous XXX spin chain with twisted boundary conditions. It satisfiesthe bilinear identity and Hirota equations for the classical mKP hierarchy. We also characterize the class of solutions to the mKP hierarchy that correspond to eigenvalues of the master T-operator and study dynamics of their zeros as functions of the spectral parameter. This implies a remarkable connection between the quantum spin chain and the classical Ruijsenaars-Schneider system of particles.
Matrix integral solutions to the discrete KP hierarchy and its Pfaffianized version
Lafortune, Stéphane; Li, Chun-Xia
2016-11-01
Matrix integrals used in random matrix theory for the study of eigenvalues of Hermitian ensembles have been shown to provide τ-functions for several hierarchies of integrable equations. In this article, we extend this relation by showing that such integrals can also provide τ-functions for the discrete KP hierarchy and a coupled version of the same hierarchy obtained through the process of Pfaffianization. To do so, we consider the first equation of the discrete KP hierarchy, the Hirota-Miwa equation. We write the Wronskian determinant solutions to the Hirota-Miwa equation and consider a particular form of matrix integrals, which we show is an example of those Wronskian solutions. The argument is then generalized to the whole hierarchy. A similar strategy is used for the Pfaffianized version of the hierarchy except that in that case, the solutions are written in terms of Pfaffians rather than determinants.
On the Recursive Sequence xn=A+xn−kp/xn−1r
Directory of Open Access Journals (Sweden)
Fangkuan Sun
2009-01-01
Full Text Available This paper studies the dynamic behavior of the positive solutions to the difference equation xn=A+xn−kp/xn−1r, n=1,2,…, where A,p, and r are positive real numbers, and the initial conditions are arbitrary positive numbers. We establish some results regarding the stability and oscillation character of this equation for p∈(0,1.
Linear and Nonlinear Surface Waves in Electrohydrodynamics
Hunt, Matthew; Vanden-broeck, Jean-Marc; Papageorgiou, Demetrios
2015-01-01
The problem of interest in this article are waves on a layer of finite depth governed by the Euler equations in the presence of gravity, surface tension, and vertical electric fields. Perturbation theory is used to identify canonical scalings and to derive a Kadomtsev-Petviashvili equation withan additional non-local term arising in interfacial electrohydrodynamics.When the Bond number is equal to 1/3, dispersion disappears and shock waves could potentially form. In the additional limit of vanishing electric fields, a new evolution equation is obtained which contains third and fifth-order dispersion as well as a non-local electric field term.
KP solitons and the Grassmannians combinatorics and geometry of two-dimensional wave patterns
Kodama, Yuji
2017-01-01
This is the first book to treat combinatorial and geometric aspects of two-dimensional solitons. Based on recent research by the author and his collaborators, the book presents new developments focused on an interplay between the theory of solitons and the combinatorics of finite-dimensional Grassmannians, in particular, the totally nonnegative (TNN) parts of the Grassmannians. The book begins with a brief introduction to the theory of the Kadomtsev–Petviashvili (KP) equation and its soliton solutions, called the KP solitons. Owing to the nonlinearity in the KP equation, the KP solitons form very complex but interesting web-like patterns in two dimensions. These patterns are referred to as soliton graphs. The main aim of the book is to investigate the detailed structure of the soliton graphs and to classify these graphs. It turns out that the problem has an intimate connection with the study of the TNN part of the Grassmannians. The book also provides an elementary introduction to the recent development of ...
Indian Academy of Sciences (India)
Wang Zhen-Li; Liu Qiang
2015-07-01
In this paper, the classical Lie group method is employed to obtain exact travelling wave solutions of the generalized Camassa–Holm Kadomtsev–Petviashvili (g-CH–KP) equation. We give the conservation laws of the g-CH–KP equation. Using the symmetries, we find six classical similarity reductions of g-CH–KP equation. Many types of exact solutions of the g-CH–KP equation are derived by solving the reduced equations.
KP-LAB Knowledge Practices Laboratory -- Stakeholders analysis
Delrio, Claudio; Ami, Zvi Ben; De Groot, Reuma; Drachman, Raul; Ilomäki, Liisa
2006-01-01
deliverables; The aim of this report is, first of all, to present the KP-Lab approach toward stakeholders in the wider framework of European policies. Secondly, the KP-Lab definition of stakeholders and the strategy to address different stakeholders needs, concerns and expectations is presented in the following paragraphs. The second chapter presents concrete examples of stakeholders involvement in the KP-Lab project. The third chapter proposes a tool for self-assessing stakeholders awarene...
Charged free fermions, vertex operators and the classical theory of conjugate nets
Energy Technology Data Exchange (ETDEWEB)
Doliwa, Adam [Istituto Nazionale di Fisica Nucleare, Sezione di Roma, Rome (Italy); Instytut Fizyki Teoretycznej, Uniwersytet Warszawski, Warsaw (Poland); Manas, Manuel [Departamento de Matematica Aplicada y Estadistica, EUIT Aeronautica, Universidad Politecnica de Madrid, Madrid (Spain); Departamento de Fisica Teorica, Universidad Complutense, Madrid (Spain); Martinez Alonso, Luis; Medina, Elena [Departamento de Matematicas, Universidad de Cadiz, Cadiz (Spain); Santini, Paolo Maria [Istituto Nazionale di Fisica Nucleare, Sezione di Roma, Rome (Italy); Dipartimento di Fisica, Universita di Catania, Catania (Italy)
1999-02-19
We show that the quantum field theoretical formulation of the {tau}-function theory has a geometrical interpretation within the classical transformation theory of conjugate nets. In particular, we prove that (i) the partial charge transformations preserving the neutral sector are Laplace transformations, (ii) the basic vertex operators are Levy and adjoint Levy transformations and (iii) the diagonal soliton vertex operators generate fundamental transformations. We also show that the bilinear identity for the multicomponent Kadomtsev-Petviashvili hierarchy becomes, through a generalized Miwa map, a bilinear identity for the multidimensional quadrilateral lattice equations. (author)
Leblond, Hervé; Mihalache, Dumitru; 10.1103/PHYSREVA.80.053812
2011-01-01
By using a powerful reductive perturbation technique, or a multiscale analysis, a generic Kadomtsev-Petviashvili evolution equation governing the propagation of femtosecond spatiotemporal optical solitons in quadratic nonlinear media beyond the slowly varying envelope approximation is put forward. Direct numerical simulations show the formation, from adequately chosen few-cycle input pulses, of both stable line solitons (in the case of a quadratic medium with normal dispersion) and of stable lumps (for a quadratic medium with anomalous dispersion). Besides, a typical example of the decay of the perturbed unstable line soliton into stable lumps for a quadratic nonlinear medium with anomalous dispersion is also given.
Instability of two-dimensional solitons and vortices in defocusing media
Kuznetsov, E. A.; Rasmussen, J. Juul
1995-05-01
In the framework of the three-dimensional nonlinear Schrödinger equation the instability of two-dimensional solitons and vortices is demonstrated. The soliton instability can be considered as the analog of the Kadomtsev-Petviashvili instability (Dokl. Akad. Nauk SSSR 192, 753 (1970) [Sov. Phys. Dokl. 15, 539 (1970)]) of one-dimensional acoustic solitons in media with positive dispersion. For large distances between the vortices, this instability transforms into the Crow instability [AIAA J. 8, 2172 (1970)] of two vortex filaments with opposite circulations.
Dark Lump Excitations in Bose-Einstein Condensates
Institute of Scientific and Technical Information of China (English)
黄国翔; 朱善华
2002-01-01
Key Laboratory for Optical and Magnetic Resonance Spectroscopy and Department of Physics, East China Normal University, Shanghai 200062We investigate the dynamics of two-dimensional matter-wave pulses in a Bose-Einstein condensate with diskshaped traps. For the case ofrepulsive atom-atom interactions, a Kadomtsev-Petviashvili equation with positive dispersion is derived using the method of multiple scales. The results show that it is possible to excite dark lump-like two-dimensional nonlinear excitations in the Bose-Einstein condensate.
XXZ scalar products, Miwa variables and discrete KP
Foda, O
2010-01-01
We revisit the quantum/classical integrable model correspondence in the context of inhomogeneous finite length XXZ spin-1/2 chains with periodic boundary conditions and show that the Bethe scalar product of an arbitrary state and a Bethe eigenstate is a discrete KP tau-function. The continuous Miwa variables of discrete KP are the rapidities of the arbitrary state.
The Master T-Operator for Inhomogeneous XXX Spin Chain and mKP Hierarchy
Zabrodin, Anton
2014-01-01
Following the approach of [Alexandrov A., Kazakov V., Leurent S., Tsuboi Z., Zabrodin A., J. High Energy Phys. 2013 (2013), no. 9, 064, 65 pages, arXiv:1112.3310], we show how to construct the master T-operator for the quantum inhomogeneous GL(N) XXX spin chain with twisted boundary conditions. It satisfies the bilinear identity and Hirota equations for the classical mKP hierarchy. We also characterize the class of solutions to the mKP hierarchy that correspond to eigenvalues of the master T-operator and study dynamics of their zeros as functions of the spectral parameter. This implies a remarkable connection between the quantum spin chain and the classical Ruijsenaars-Schneider system of particles.
Rogue wave variational modelling through the interaction of two solitary waves
Gidel, Floriane; Bokhove, Onno
2016-04-01
The extreme and unexpected characteristics of Rogue waves have made them legendary for centuries. It is only on the 1st of January 1995 that these mariners' tales started to raise scientist's curiosity, when such a wave was recorded in the North Sea; a sudden wall of water hit the Draupner offshore platform, more than twice higher than the other waves, providing evidence of the existence of rogue or freak waves. Since then, studies have shown that these surface gravity waves of high amplitude (at least twice the height of the other sea waves [Dyste et al., 2008]) appear in non-linear dispersive water motion [Drazin and Johnson, 1989], at any depth, and have caused a lot of damage in recent years [Nikolkina and Didenkulova, 2011 ]. So far, most of the studies have tried to determine their probability of occurrence, but no conclusion has been achieved yet, which means that we are currently unenable to predict or avoid these monster waves. An accurate mathematical and numerical water-wave model would enable simulation and observation of this external forcing on boats and offshore structures and hence reduce their threat. In this work, we aim to model rogue waves through a soliton splash generated by the interaction of two solitons coming from different channels at a specific angle. Kodama indeed showed that one way to produce extreme waves is through the intersection of two solitary waves, or one solitary wave and its oblique reflection on a vertical wall [Yeh, Li and Kodama, 2010 ]. While he modelled Mach reflection from Kadomtsev-Petviashvili (KP) theory, we aim to model rogue waves from the three-dimensional potential flow equations and/or their asymptotic equivalent described by Benney and Luke [Benney and Luke, 1964]. These theories have the advantage to allow wave propagation in several directions, which is not the case with KP equations. The initial solitary waves are generated by removing a sluice gate in each channel. The equations are derived through a
Centrally extended W$_{1+\\infty}$ and the KP hierarchy
Martínez-Moras, F; Martinez-Moras, Fernando; Mas, Javier
1994-01-01
It is well known that the centerless \\W_{1+\\infty} algebra provides a hamiltonian structure for the KP hierarchy. In this letter we address the question whether the centerfull version plays a similar r\\^ole in any related integrable system. We find that, surprisingly enough the centrally extended W_{1+\\infty} algebra yields another Poisson structure for the same standard KP hierarchy. This is proven by explicit construction of the infinitely many new hamiltonians in closed form.
Directory of Open Access Journals (Sweden)
Xinzhi Liu
1998-01-01
Full Text Available This paper studies a class of high order delay partial differential equations. Employing high order delay differential inequalities, several oscillation criteria are established for such equations subject to two different boundary conditions. Two examples are also given.
KP and Toda tau functions in Bethe ansatz
Takasaki, Kanehisa
2010-01-01
Recent work of Foda and his group on a connection between classical integrable hierarchies (the KP and 2D Toda hierarchies) and some quantum integrable systems (the 6-vertex model with DWBC, the finite XXZ chain of spin 1/2, the phase model on a finite chain, etc.) is reviewed. Some additional information on this issue is also presented.
Kp and Toda Tau Functions in Bethe Ansatz
Takasaki, Kanehisa
2011-10-01
Recent work of Foda and his group on a connection between classical integrable hierarchies (the KP and 2D Toda hierarchies) and some quantum integrable systems (the 6-vertex model with DWBC, the finite XXZ chain of spin 1/2, the phase model on a finite chain, etc.) is reviewed. Some additional information on this issue is also presented.
Hasse-Schmidt derivations on Grassmann algebras with applications to vertex operators
Gatto, Letterio
2016-01-01
This book provides a comprehensive advanced multi-linear algebra course based on the concept of Hasse-Schmidt derivations on a Grassmann algebra (an analogue of the Taylor expansion for real-valued functions), and shows how this notion provides a natural framework for many ostensibly unrelated subjects: traces of an endomorphism and the Cayley-Hamilton theorem, generic linear ODEs and their Wronskians, the exponential of a matrix with indeterminate entries (Putzer's method revisited), universal decomposition of a polynomial in the product of two monic polynomials of fixed smaller degree, Schubert calculus for Grassmannian varieties, and vertex operators obtained with the help of Schubert calculus tools (Giambelli's formula). Significant emphasis is placed on the characterization of decomposable tensors of an exterior power of a free abelian group of possibly infinite rank, which then leads to the celebrated Hirota bilinear form of the Kadomtsev-Petviashvili (KP) hierarchy describing the Plücker embedding of ...
Well-posedness for the fifth order KP-II initial data problem in H s , 0 (R × T)
Li, Junfeng; Li, Xia
2017-02-01
The well-posed properties for the fifth order KP-II initial value problem for x ∈ R, y ∈ T are considered. It is proved to be locally well posed in H s , 0 (R × T) for s ≥ -3/4 with small initial data and s > -3/4 with general initial data. By the L2 conservation law of KP equation, the L2 global well-posedness is also obtained. The crucial ingredient of the argument is the L2 estimates of a bilinear operator which was introduced in recent works [14] and [13]. This operator is Galilean invariant in the content of T2 and R2 but not in the content R × T.
A New (2+1)-Dimensional Integrable Equation
Institute of Scientific and Technical Information of China (English)
PEN Bo; LIN Ji
2009-01-01
A new nonlinear partial differential equation (PDE) in 2+1 dimensions is obtained from the mKP equation by means of an asymptotically exact reduction method based on Fourier expansion and spatio-temporal rescaling. In order to demonstrate integrability property of the new equation, the corresponding Lax pair is obtained by applying the reduction technique to the Lax pair of the mKP equation.
Kp,q-factorization of complete bipartite graphs
Institute of Scientific and Technical Information of China (English)
DU; Beiliang; WANG; Jian
2004-01-01
Let Km,n be a completebipartite graph with two partite sets having m and n vertices,respectively. A Kp,q-factorization of Km,n is a set ofedge-disjoint Kp,q-factors of Km,n which partition theset of edges of Km,n. When p=1 and q is a prime number,Wang, in his paper "On K1,k-factorizations of a completebipartite graph" (Discrete Math, 1994, 126: 359-364),investigated the K1,q-factorization of Km,n and gave asufficient condition for such a factorization to exist. In the paper"K1,k-factorizations of complete bipartite graphs" (DiscreteMath, 2002, 259: 301-306), Du and Wang extended Wang's resultto the case that q is any positive integer. In this paper, we give a sufficient condition for Km,n to have aKp,q-factorization. As a special case, it is shown that theMartin's BAC conjecture is true when p:q=k:(k+1) for any positiveinteger k.
A Revocable KP-ABE Scheme%一种可撤销的KP-ABE方案①
Institute of Scientific and Technical Information of China (English)
胡海英; 商威
2013-01-01
This paper proposes a Key Policy Attribute-Based Encryption (KP-ABE) scheme supporting user's private key revocation under the direct revocation model, without affecting the public key and any user's private key, so the cost of the revocation is small. Based on the access tree, the construction of our scheme is simpler than the construction proposed by Attrapadung which is based on linear Secret Sharing Schemes(LSSS). Its security can be reduced to the q-Bilinear Diffie-Hellman Exponent (q-BDHE) assumption under the standard model.%提出了一个支持私钥撤销的KP-ABE(Key Policy Attribute Based Encryption)方案，该方案以直接撤销模式对用户进行撤销，能够在不更新系统公钥和任何一个用户的私钥的情况下完成对用户的撤销，更新代价较小。同时该方案基于访问树实现与 Attrapadung 等人基于 LSSS(Linear Secret Sharing Schemes)的支持用户撤销的KP-ABE 方案相比，构造更为简单。该方案的安全性可以规约到标准模型下的判定性 q-BDHE(q-Bilinear Diffie-Hellman Exponent)假设。
Loewner equations and dispersionless hierarchies
Energy Technology Data Exchange (ETDEWEB)
Takebe, Takashi [Department of Mathematics, Ochanomizu University, Otsuka 2-1-1, Bunkyo-ku, Tokyo, 112-8610 (Japan); Teo, Lee-Peng [Faculty of Information Technology, Multimedia University, Jalan Multimedia, Cyberjaya, 63100, Selangor Darul Ehsan (Malaysia); Zabrodin, Anton [Institute of Biochemical Physics, Kosygina str. 4, 119991 Moscow, Russia and ITEP, Bol. Cheremushkinskaya str. 25, 117259 Moscow (Russian Federation)
2006-09-15
Using the Hirota representation of dispersionless dKP and dToda hierarchies, we show that the chordal Loewner equations and radial Loewner equations respectively serve as consistency conditions for one-variable reductions of these integrable hierarchies. We also clarify the geometric meaning of this result by relating it to the eigenvalue distribution of normal random matrices in the large N limit.
Quijano, Carolina Diaz; Wichmann, Fabienne; Schlaich, Thomas; Fammartino, Alessandro; Huckauf, Jana; Schmidt, Kerstin; Unger, Christoph; Broer, Inge; Sautter, Christof
2016-09-01
Ustilago tritici causes loose smut, which is a seed-borne fungal disease of wheat, and responsible for yield losses up to 40%. Loose smut is a threat to seed production in developing countries where small scale farmers use their own harvest as seed material. The killer protein 4 (KP4) is a virally encoded toxin from Ustilago maydis and inhibits growth of susceptible races of fungi from the Ustilaginales. Enhanced resistance in KP4 wheat to stinking smut, which is caused by Tilletia caries, had been reported earlier. We show that KP4 in genetically engineered wheat increased resistance to loose smut up to 60% compared to the non-KP4 control under greenhouse conditions. This enhanced resistance is dose and race dependent. The overexpression of the transgene kp4 and its effect on fungal growth have indirect effects on the expression of endogenous pathogen defense genes.
Directory of Open Access Journals (Sweden)
Carolina Diaz Quijano
2016-09-01
Full Text Available Ustilago tritici causes loose smut, which is a seed-borne fungal disease of wheat, and responsible for yield losses up to 40%. Loose smut is a threat to seed production in developing countries where small scale farmers use their own harvest as seed material. The killer protein 4 (KP4 is a virally encoded toxin from Ustilago maydis and inhibits growth of susceptible races of fungi from the Ustilaginales. Enhanced resistance in KP4 wheat to stinking smut, which is caused by Tilletia caries, had been reported earlier. We show that KP4 in genetically engineered wheat increased resistance to loose smut up to 60% compared to the non-KP4 control under greenhouse conditions. This enhanced resistance is dose and race dependent. The overexpression of the transgene kp4 and its effect on fungal growth have indirect effects on the expression of endogenous pathogen defense genes.
AtKP1, a kinesin-like protein, mainly localizes to mitochondria in Arabidopsis thaliana
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
Kinesins and kinesin-like proteins (KLPs) constitute a large family of microtubule-based motors that play important roles in many fundamental cellular and developmental processes. To date, a number of kinesins or KLPs have been identified in plants including Arabidopsis thaliana. Here, a polyclonal antibody against AtKP1 (kinesin-like protein 1 in A.thaliana) was raised by injection the expressed AtKP1 specific C-terminal polypeptides in rabbits, and immunoblot analysis was conducted with the affinity-purified anti-AtKP1 antibody. The results indicated that this antibody recognized the AtKP1 fusion proteins expressed in E. coli and proteins of ～125 kDa in the soluble fractions of Arabidopsis extracts. The molecular weight was consistent with the calculated molecular weight based on deduced amino acids sequence of AtKP1. To acquire the subcellular localization of the protein, AtKP1 in Arabidopsis root cells was observed by indirect immunofluorescence microscopy. AtKP1 was localized to particle-like organelles in interphase or dividing cells, but not to mitotic microtubule arrays. Relatively more AtKP1 was found in isolated mitochondria fraction on immunoblot of the subcellular fractions. The AtKP1 protein could not be released following a 0.6 M KI washing,indicating that AtKP1 is tightly bind to mitochondria and might function associated with this kind of organelles.
Block Toeplitz Determinants, Constrained KP and Gelfand-Dickey Hierarchies
Energy Technology Data Exchange (ETDEWEB)
Cafasso, M. [SISSA-International School for Advanced Studies (Italy)], E-mail: cafasso@sissa.it
2008-02-15
We propose a method for computing any Gelfand-Dickey {tau} function defined on the Segal-Wilson Grassmannian manifold as the limit of block Toeplitz determinants associated to a certain class of symbols W(t,z). Also truncated block Toeplitz determinants associated to the same symbols are shown to be {tau} functions for rational reductions of KP. Connection with Riemann-Hilbert problems is investigated both from the point of view of integrable systems and block Toeplitz operator theory. Examples of applications to algebro-geometric solutions are given.
THE HAMILTONIAN EQUATIONS IN SOME MATHEMATICS AND PHYSICS PROBLEMS
Institute of Scientific and Technical Information of China (English)
陈勇; 郑宇; 张鸿庆
2003-01-01
Some new Hamiltonian canonical system are discussed for a series of partialdifferential equations in Mathematics and Physics. It includes the Hamiltonian formalism forthe symmetry second-order equation with the variable coefficients, the new nonhomogeneousHamiltonian representation for fourth-order symmetry equation with constant coefficients,the one of MKdV equation and KP equation.
A nonlinear kp-εp particle two-scale turbulence model and its application
Institute of Scientific and Technical Information of China (English)
Zhuoxiong Zeng; Zhuozhi Zeng; Yihua Xu
2007-01-01
A particle nonlinear two-scale Kp-εp turbulence model is proposed for simulating the anisotropic turbulent two-phase flow. The particle kinetic energy equation for two-scale fluctuation, particle energy transfer rate equation for large-scale fluctuation, and particle turbulent kinetic energy dissipation rate equation for small-scale fluctuation are deri-ved and closed. This model is used to simulate gas-particle flows in a sudden-expansion chamber. The simulation is com-pared with the experiment and with those obtained by using another two kinds of tow-phase turbulence model, such as the single-scale k-ε two-phase turbulence model and the particle two-scale second-order moment (USM) two-phase turbulence model. It is shown that the present model gives simulation in much better agreement with the experiment than the single-scale k-ε two-phase turbulence model does and is almost as good as the particle two-scale USM turbu-lence model.
Institute of Scientific and Technical Information of China (English)
杜北梁; 王建
2004-01-01
如果完全二部图Km,n的边集可以划分为Km,n的Kp,q-因子,则称Km,n存在Kp,q-因子分解.给出Km,n存在Kp,q-因子分解的一个充分条件.同时证明:对于任意正整数k,当p:q=k:(k+1)时,Km,n存在Kp,q-因子分解,即Martin的BAC猜想成立.
Finite Dimensional KP \\tau-functions I. Finite Grassmannians
Balogh, F; Harnad, J
2014-01-01
We study \\tau-functions of the KP hierarchy in terms of abelian group actions on finite dimensional Grassmannians, viewed as subquotients of the Hilbert space Grassmannians of Sato, Segal and Wilson. A determinantal formula of Gekhtman and Kasman involving exponentials of finite dimensional matrices is shown to follow naturally from such reductions. All reduced flows of exponential type generated by matrices with arbitrary nondegenerate Jordan forms are derived, both in the Grassmannian setting and within the fermionic operator formalism. A slightly more general determinantal formula involving resolvents of the matrices generating the flow, valid on the big cell of the Grassmannian, is also derived. An explicit expression is deduced for the Pl\\"ucker coordinates appearing as coefficients in the Schur function expansion of the \\tau-function.
The constrained KP hierarchy and the generalised Miura transformation
Mas, J; Mas, Javier; Ramos, Eduardo
1995-01-01
Recently much attention has been paid to the restriction of KP to the submanifold of operators which can be represented as a ratio of two purely differential operators L=AB^{-1}. Whereas most of the aspects concerning this reduced hierarchy, like the Lax flows and the Hamiltonians, are by now well understood, there still lacks a clear and conclusive statement about the associated Poisson structure. We fill this gap by placing the problem in a more general framework and then showing how the required result follows from an interesting property of the second Gelfand-Dickey brackets under multiplication and inversion of Lax operators. As a byproduct we give an elegant and simple proof of the generalised Kupershmidt-Wilson theorem.
Topological theories from Virasoro constraints on the KP hierarchy
Gato-Rivera, Beatriz; Gato-Rivera, Beatriz; Rosado, Jose Ignacio
1994-01-01
A conformal field theory can be recovered, via the Kontsevich-Miwa transform, as a solution to the Virasoro constraints on the KP tau function. That theory, which we call KM CFT, consists of d \\leq 1 matter plus a scalar and a dressing prescription: \\Delta = 0 for every primary field. By adding a spin-1 bc system the KM CFT provides a realization of the N=2 twisted topological algebra. The other twist of the corresponding untwisted N=2 superconformal theory is a DDK realization of the N=2 twisted topological algebra. Talk given by Beatriz Gato-Rivera at the "28th International Symposium on the Theory of Elementary Particles", Wendisch-Rietz (Germany), August 30 - September 3, 1994.
Ion acoustic shock waves in plasmas with warm ions and kappa distributed electrons and positrons
Energy Technology Data Exchange (ETDEWEB)
Hussain, S.; Mahmood, S.; Hafeez Ur-Rehman [Theoretical Plasma Physics Division, PINSTECH, P.O. Nilore, Islamabad 44000, Pakistan and Department of Physics and Applied Mathematics, PIEAS, P.O. Nilore, Islamabad 44000 (Pakistan)
2013-06-15
The monotonic and oscillatory ion acoustic shock waves are investigated in electron-positron-ion plasmas (e-p-i) with warm ions (adiabatically heated) and nonthermal kappa distributed electrons and positrons. The dissipation effects are included in the model due to kinematic viscosity of the ions. Using reductive perturbation technique, the Kadomtsev-Petviashvili-Burgers (KPB) equation is derived containing dispersion, dissipation, and diffraction effects (due to perturbation in the transverse direction) in e-p-i plasmas. The analytical solution of KPB equation is obtained by employing tangent hyperbolic (Tanh) method. The analytical condition for the propagation of oscillatory and monotonic shock structures are also discussed in detail. The numerical results of two dimensional monotonic shock structures are obtained for graphical representation. The dependence of shock structures on positron equilibrium density, ion temperature, nonthermal spectral index kappa, and the kinematic viscosity of ions are also discussed.
Wave system and its approximate similarity solutions
Institute of Scientific and Technical Information of China (English)
Liu Ping; Fu Pei-Kai
2011-01-01
Recently,a new (2+1)-dimensional shallow water wave system,the (2+1)-dimensional displacement shallow water wave system (2DDSWWS),was constructed by applying the variational principle of the analytic mechanics in the Lagrange coordinates. The disadvantage is that fluid viscidity is not considered in the 2DDSWWS,which is the same as the famous Kadomtsev-Petviashvili equation and Korteweg-de Vries equation. Applying dimensional analysis,we modify the 2DDSWWS and add the term related to the fluid viscidity to the 2DDSWWS. The approximate similarity solutions of the modified 2DDSWWS (M2DDSWWS) is studied and four similarity solutions are obtained. For the perfect fluids,the coefficient of kinematic viscosity is zero,then the M2DDSWWS will degenerate to the 2DDSWWS.
N'tcha, Christine; Sina, Haziz; Kayodé, Adéchola Pierre Polycarpe; Gbenou, Joachim D.
2017-01-01
The aim of this study was to investigate the antibacterial effect of the crude starter “kpètè-kpètè” and lactic acid bacteria used during the production of “tchoukoutou.” To achieve this, a total of 11 lactic acid bacteria and 40 starter samples were collected from four communes. The samples were tested on 29 gram + and − strains by disk diffusion method. The minimum inhibitory and bactericidal concentrations of starter and lactic acid bacteria were determined by conventional methods. Organic acids, sugar, and volatile compounds were determined using the HPLC method. The “kpètè-kpètè” displays a high antibacterial activity against the tested strains. The most sensitive strain was S. epidermidis (12.5 mm) whereas the resistance strain was Proteus mirabilis (8 mm). All the tested ferment has not any inhibitory effect on Enterococcus faecalis. The lactic acid bacteria isolates of Parakou showed the highest (17.48 mm) antibacterial activity whereas the smallest diameter was obtained with the ferment collected from Boukoumbé (9.80 mm). The starters' chemical screening revealed the presence of tannins, anthocyanin flavonoids, triterpenes, steroids, reducing compounds, and mucilage O-glycosides. These compounds are probably the source of recorded inhibition effect. The lactic acid bacteria of the “kpètè-kpètè” could be used to develop a food ingredient with probiotic property. PMID:28367445
The algebra of q-pseudodifferential symbols and the q-W$_{KP}^{n}$ algebra
Mas, J; Mas, Javier; Seco, Marcos
1995-01-01
We construct q-deformations of the W_KP and related W-type algebras. These algebras arise as Gelfand-Dickey brackets on the space of q-pseudodifferential symbols. The construction establishes a continuous correspondence between the Toda lattice and the KP hierarchy at the level of their hamiltonian structures
Remarks on dispersionless KP, KdV, and 2D gravity
Carroll, R.
1994-12-01
We use the SDiff(2) framework of Takasaki and Takebe and the ( L, M) program ( L is the Lax operator and Mω=ωλ) to show thatmathfrak{M}=semiclassical limit of M ishat ξ + sumnolimits_2^infty {T'_n } λ ^{n - 1} , where (λ , - hat ξ ) are action angle variables in the Gibbons-Kodama theory of Hamilton-Jacobi type for dispersionless KP. We also showhat ξ is the semiclassical limit of WxW -1 ( W is the gauge operator), where G=WxW -1 is a quantity studied by the author in an earlier paper in connection with symmetries. We give then a semiclassical version of the Jevicki-Yoneya action principle for 2D gravity, where againhat ξ arises in calculations, and this yields directly the Landau-Ginsburg equation that corresponds to the semiclassical limit of an integrated string equation. For KdV we also show how inverse scattering data are connected to Hamiltonians for dispersionless KdV. We also discuss Hirota bilinear formulas relative to the dispersionless hierarchies and establish various limiting formulas.
Deka, Manoj Kr.
2016-12-01
In this report, a detailed investigation on the study of dust acoustics solitary waves solution with negatively dust charge fluctuation in dusty plasma corresponding to lower and higher temperature nonthermal ions with trapped electrons is presented. We consider temporal variation of dust charge as a source of dissipation term to derive the lower order modified Kadomtsev-Petviashvili equation by using the reductive perturbation technique. Solitary wave solution is obtained with the help of sech method in presence of trapped electrons and low (and high) temperature nonthermal ions. Both nonthermality of ions and trapped state of the electrons are found to have an imperative control on the nonlinear coefficient, dissipative coefficient as well as height of the wave potential.
Dark lump excitations in superfluid Fermi gases
Institute of Scientific and Technical Information of China (English)
Xu Yan-Xia; Duan Wen-Shan
2012-01-01
We study the linear and nonlinear properties of two-dimensional matter-wave pulses in disk-shaped superfluid Fermi gases.A Kadomtsev Petviashvili I (KPI) solitary wave has been realized for superfluid Fermi gases in the limited cases of Bardeen-Cooper-Schrieffer (BCS) regime,Bose-Einstein condensate (BEC) regime,and unitarity regime.Onelump solution as well as one-line soliton solutions for the KPI equation are obtained,and two-line soliton solutions with the same amplitude are also studied in the limited cases.The dependence of the lump propagating velocity and the sound speed of two-dimensional superfluid Fermi gases on the interaction parameter are investigated for the limited cases of BEC and unitarity.
Indian Academy of Sciences (India)
ALY R SEADAWY
2017-09-01
Nonlinear two-dimensional Kadomtsev–Petviashvili (KP) equation governs the behaviour of nonlinear waves in dusty plasmas with variable dust charge and two temperature ions. By using the reductive perturbation method, the two-dimensional dust-acoustic solitary waves (DASWs) in unmagnetized cold plasma consisting of dust fluid, ions and electrons lead to a KP equation. We derived the solitary travelling wave solutions of the twodimensional nonlinear KP equation by implementing sech–tanh, sinh–cosh, extended direct algebraic and fraction direct algebraicmethods. We found the electrostatic field potential and electric field in the form travellingwave solutions for two-dimensional nonlinear KP equation. The solutions for the KP equation obtained by using these methods can be demonstrated precisely and efficiency. As an illustration, we used the readymade package of $\\it{Mathematica}$ program 10.1 to solve the original problem. These solutions are in good agreement with the analytical one.
The (K-,p) reaction on C12 at KEK
Magas, V K; Hirenzaki, S; Oset, E; Ramos, A
2009-01-01
We study the (K-,p) reaction on C12 with a kaon beam of 1 GeV momentum, paying a special attention to the region of emitted protons having kinetic energy above 600 MeV, which was used to claim a deep kaon nucleus optical potential [1]. The experiment looks for fast protons emitted from the absorption of in flight kaons by nuclei, but in coincidence with at least one charged particle in the decay counters sandwiching the target. The analysis of the data is done in [1] assuming that the coincidence requirement does not change the shape of the final spectra. However our detailed calculations show that this assumption doesn't hold, and, thus, the final conclusion of this experiment is doubtful. We perform Monte Carlo simulation of this reaction. The advantage of our method with respect to Green's function method used in [1] is that it allows to account not only for quasi-elastic K- p scattering, but also for the other processes which contribute to the proton spectra. We investigated the effect of the multi-scatte...
The determinant representation of the gauge transformation for the discrete KP hierarchy
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
A successive gauge transformation operator Tn+k for the discrete KP(dKP) hierarchy is defined,which is involved with two types of gauge transformations operators.The determinant representation of the Tn+k is established and it is used to get a new τ function τ(n+k) of the dKP hierarchy from an initial τ.In this process,we introduce a generalized discrete Wronskian determinant and some useful properties of discrete difference operators.
Directory of Open Access Journals (Sweden)
Christine N’tcha
2017-01-01
Full Text Available The aim of this study was to investigate the antibacterial effect of the crude starter “kpètè-kpètè” and lactic acid bacteria used during the production of “tchoukoutou.” To achieve this, a total of 11 lactic acid bacteria and 40 starter samples were collected from four communes. The samples were tested on 29 gram + and − strains by disk diffusion method. The minimum inhibitory and bactericidal concentrations of starter and lactic acid bacteria were determined by conventional methods. Organic acids, sugar, and volatile compounds were determined using the HPLC method. The “kpètè-kpètè” displays a high antibacterial activity against the tested strains. The most sensitive strain was S. epidermidis (12.5 mm whereas the resistance strain was Proteus mirabilis (8 mm. All the tested ferment has not any inhibitory effect on Enterococcus faecalis. The lactic acid bacteria isolates of Parakou showed the highest (17.48 mm antibacterial activity whereas the smallest diameter was obtained with the ferment collected from Boukoumbé (9.80 mm. The starters’ chemical screening revealed the presence of tannins, anthocyanin flavonoids, triterpenes, steroids, reducing compounds, and mucilage O-glycosides. These compounds are probably the source of recorded inhibition effect. The lactic acid bacteria of the “kpètè-kpètè” could be used to develop a food ingredient with probiotic property.
Infinitely-many conservation laws for two (2+1)-dimensional nonlinear evolution equations in fluids
Indian Academy of Sciences (India)
Yan Jiang; Bo Tian; Pan Wang; Kun Su
2014-07-01
In this paper, a method that can be used to construct the infinitely-many conservation laws with the Lax pair is generalized from the (1+1)-dimensional nonlinear evolution equations (NLEEs) to the (2+1)-dimensional ones. Besides, we apply that method to the Kadomtsev– Petviashvili (KP) and Davey–Stewartson equations in fluids, and respectively obtain their infinitelymany conservation laws with symbolic computation. Based on that method, we can also construct the infinitely-many conservation laws for other multidimensional NLEEs possessing the Lax pairs, including the cylindrical KP, modified KP and (2+1)-dimensional Gardner equations, in fluids, plasmas, optical fibres and Bose–Einstein condensates.
Algebraic Approaches to Partial Differential Equations
Xu, Xiaoping
2012-01-01
Partial differential equations are fundamental tools in mathematics,sciences and engineering. This book is mainly an exposition of the various algebraic techniques of solving partial differential equations for exact solutions developed by the author in recent years, with emphasis on physical equations such as: the Calogero-Sutherland model of quantum many-body system in one-dimension, the Maxwell equations, the free Dirac equations, the generalized acoustic system, the Kortweg and de Vries (KdV) equation, the Kadomtsev and Petviashvili (KP) equation, the equation of transonic gas flows, the short-wave equation, the Khokhlov and Zabolotskaya equation in nonlinear acoustics, the equation of geopotential forecast, the nonlinear Schrodinger equation and coupled nonlinear Schrodinger equations in optics, the Davey and Stewartson equations of three-dimensional packets of surface waves, the equation of the dynamic convection in a sea, the Boussinesq equations in geophysics, the incompressible Navier-Stokes equations...
Effect of Lactococcin BZ and Enterocin KP on the Activity of Yoghurt Cultures
Directory of Open Access Journals (Sweden)
Nilgün Öncül
2015-02-01
Full Text Available In this study, the effects of lactococcin BZ from Lactococcus lactis ssp. lactis BZ and enterocin KP from Enterococcus faecalis KP (1600 AU/mL on the activities of three different yoghurt cultures (Y1 and Y2: CHR Hansen, Denmark; Y3: Sacco, Italy were investigated. Lactic acid bacteria counts and pH values of the samples were determined during the incubation period (at 42°C for 24 h. It was found that lactococcin BZ had bactericidal effect against only one yoghurt culture whereas enterocin KP was effective against two yoghurt cultures. When lactococcin BZ and enterosin KP were used in combination (1:1, they showed bactericidal effect against two yoghurt cultures.
Simple equation method for nonlinear partial differential equations and its applications
Directory of Open Access Journals (Sweden)
Taher A. Nofal
2016-04-01
Full Text Available In this article, we focus on the exact solution of the some nonlinear partial differential equations (NLPDEs such as, Kodomtsev–Petviashvili (KP equation, the (2 + 1-dimensional breaking soliton equation and the modified generalized Vakhnenko equation by using the simple equation method. In the simple equation method the trial condition is the Bernoulli equation or the Riccati equation. It has been shown that the method provides a powerful mathematical tool for solving nonlinear wave equations in mathematical physics and engineering problems.
Integrability of two coupled Kadomtsev–Petviashvili equations
Indian Academy of Sciences (India)
Abdul-Majid Wazwaz
2011-08-01
The integrability of two coupled KP equations is studied. The simpliﬁed Hereman form of Hirota’s bilinear method is used to examine the integrability of each coupled equation. Multiplesoliton solutions and multiple singular soliton solutions are formally derived for each coupled KdV equation.
Directory of Open Access Journals (Sweden)
Suryanata Rahardja
2001-01-01
Full Text Available Fiber glass products are widely used in the industry. High quality fiberglass product requires a composition and to obtain the optimal composition, an experiment needs to be done. In this project, experimental designs in 2k-p fractional factorial design and Taguchi method were carried out to obtain the optimal composition. According to the impact test results based on the model by the JIS (Japanese Industrial Standard for fiber glass, it was found that the 2k-p fractional factorial design method and Taguchi methods are the same. Abstract in Bahasa Indonesia : Produk fiber glass banyak digunakan di dunia industri saat ini. Produk fiber glass berkualitas tinggi dibutuhkan suatu komposisi, dimana untuk komposisi yang tepat diperlukan eksperimen. Desain eksperimen 2k-p fractional factorial design dengan metode Taguchi telah digunakan untuk mendapatkan komposisi yang optimal. Hasil pengujian kekuatan impak dengan bentuk dan pengujian sesuai JIS (Japanese Industrial Standard pada fiber glass didapatkan bahwa metode 2k-p fractional factorial design dengan metode Taguchi tidak berbeda. Kata kunci : 2k-p fractional factorial design, Taguchi, JIS
Directory of Open Access Journals (Sweden)
Harald Eriksson
2015-04-01
Full Text Available Klebsiella pneumoniae phages vB_KpnP_SU503 (SU503 and vB_KpnP_SU552A (SU552A are virulent viruses belonging to the Autographivirinae subfamily of Podoviridae that infect and kill multi-resistant K. pneumoniae isolates. Phages SU503 and SU552A show high pairwise nucleotide identity to Klebsiella phages KP34 (NC_013649, F19 (NC_023567 and NTUH-K2044-K1-1 (NC_025418. Bioinformatic analysis of these phage genomes show high conservation of gene arrangement and gene content, conserved catalytically active residues of their RNA polymerase, a common and specific lysis cassette, and form a joint cluster in phylogenetic analysis of their conserved genes. Also, we have performed biological characterization of the burst size, latent period, host specificity (together with KP34 and NTUH-K2044-K1-1, morphology, and structural genes as well as sensitivity testing to various conditions. Based on the analyses of these phages, the creation of a new phage genus is suggested within the Autographivirinae, called “Kp34likevirus” after their type phage, KP34. This genus should encompass the recently genome sequenced Klebsiella phages KP34, SU503, SU552A, F19 and NTUH-K2044-K1-1.
KP Cyg: an Unusual Metal-rich RR Lyr Type Star of Long Period
Andrievsky, S M; Wallerstein, George; Korotin, S A; Huang, Wenjin
2010-01-01
We present the results of a detailed spectroscopic study of the long period ($P=0.856$ days) RR Lyrae star, KP Cyg. We derived abundances of many chemical elements including the light species, iron-group elements and elements of the s-processes. Most RR Lyrae stars with periods longer than 0.7 days are metal-deficient objects. Surprisingly, our results show that KP Cyg is very metal rich ([Fe/H] $= +0.18\\pm 0.23$). By comparison with a number of short period ($P=1\\sim 6$ days), metal-rich CWB stars, we suggest that KP Cyg may be a very short period CWB star (BL Her star) rather than an RR Lyrae star. As seen in some CWB stars, KP Cyg shows strong excesses of carbon and nitrogen in its atmosphere. This indicates that the surface of KP Cyg has been polluted by material that has undergone helium burning (to enhance carbon) and proton capture (to transform carbon into nitrogen). We also note that UY CrB, whose period is 0.929 days, also shows an enhancement of C and N, and that two carbon cepheids of short period...
DETERMINATION OF THE PRIMALITY OF 2kp+1%形如2kp+1的数的素性检验
Institute of Scientific and Technical Information of China (English)
张韶华; 陈恭亮; 周光明; 杨金凤
2005-01-01
In this paper, we preliminarily explore how to determine quickly whether a large number n is prime, where n-1 has a large prime factor, and how to generate a large prime p such that p-1 has a large prime divisor q. We give a deterministic polynomial-time algorithm that determines whether n=2kp+ 1 is prime, where p is a given odd prime and k is a positive integer satisfying 22k ＜2kp. The algorithm we present runs in O(log32n) time. Then we give algorithms for generating a prime p such that p- 1 has a large prime divisor q, where q satisfies q＞(p-1)/log2 (p-1). Especially, we give the algorithm that determines and generates a safe prime p.%本文初步探讨了如何快速检验一个大数n是素数(这里n-1含有大的素因子)的算法问题以及如何生成一个大素数p使得p-1有大的素因子q的算法问题.我们给出了形如n=2kp+1的数的素性检验的多项式时间算法,这里p是一个给定的大素数,k是正整数满足22k＜2kp.该算法的计算量为O(log32n).然后我们给出了生成一个大素数p使得p-1有大的素因子q的算法,其中q满足q＞(p-1)/log2(p-1).特别地,我们给出了判定并生成一个安全素数p的算法.
Directory of Open Access Journals (Sweden)
Yusuf Pandir
2012-01-01
Full Text Available We obtain the classification of exact solutions, including soliton, rational, and elliptic solutions, to the one-dimensional general improved Camassa Holm KP equation and KdV equation by the complete discrimination system for polynomial method. In discussion, we propose a more general trial equation method for nonlinear partial differential equations with generalized evolution.
Asymptotic reductions and solitons of nonlocal nonlinear Schr\\"{o}dinger equations
Horikis, Theodoros P
2016-01-01
Asymptotic reductions of a defocusing nonlocal nonlinear Schr\\"{o}dinger model in $(3+1)$-dimensions, in both Cartesian and cylindrical geometry, are presented. First, at an intermediate stage, a Boussinesq equation is derived, and then its far-field, in the form of a variety of Kadomtsev-Petviashvilli (KP) equations for right- and left-going waves, is found. KP models include versions of the KP-I and KP-II equations, in Cartesian and cylindrical geometry. Solitary waves solutions, planar or ring-shaped, and of dark or anti-dark type, are also predicted to occur. Their nature and stability is determined by a parameter defined by the physical parameters of the original nonlocal system. It is thus found that (dark) anti-dark solitary waves are only supported by a weak (strong) nonlocality, and are unstable (stable) in higher-dimensions. Our analytical predictions are corroborated by direct numerical simulations.
Institute of Scientific and Technical Information of China (English)
LI XuYan; WANG HaiQing; XU Tao; CAO QinHong; REN DongTao; LIU GuoQin
2007-01-01
Kinesins are common in a variety of eukaryotic cells with diverse functions.A cDNA encoding a member of the Kinesin-14B subfamily is obtained using 3'-RACE technology and named AtKP1 (for Arabidopsis kinesin protein 1).This cDNA has a maximum open reading frame of 3.3 kb encoding a polypeptide of 1087 aa.Protein domain analysis shows that AtKP1 contains the motor domain and the calponin homology domain in the central and amino-terminal regions,respectively.The carboxyl-terminal region with 202 aa residues is diverse from other known kinesins.Northern blot analysis shows that AtKP1 is widely expressed at a higher level in seedlings than in mature plants.2808 bp of the AtKP1 promoter region is cloned and fused to GUS.GUS expression driven by the AtKP1 promoter region shows that AtKP1 is mainly expressed in vasculature of young organs and young leaf trichomes,indicating that AtKP1 may participate in the differentiation or development of Arabidopsis thaliana vascular bundles and trichomes.A truncated AtKP1 protein containing the putative motor domain is expressed in E.coll and affinity-purified.In vitro characterizations indicate that the polypeptide has nucleotide-dependent microtubule-binding ability and microtubule-stimulated ATPase activity.
Late onset neonatal anaemia due to maternal anti-Kp(b) induced haemolytic disease of the newborn.
Elhence, Priti; Sachan, Deepti; Verma, Anupam; Kumar, Archana; Chaudhary, Rajendra
2012-12-01
Alloanti-Kp(b) is a rare, clinically significant antibody against high frequency red cell antigen Kp(b) of Kell blood group system. We report here a case of Haemolytic disease of newborn (HDN) due to anti-Kp(b), which manifested as severe anaemia at the age of 1 month. To diagnose and successfully manage anti-Kp(b) induced HDN. Direct antiglobulin test (DAT), antigen typing, irregular antibody screening and identification were done by polyspecific LISS Coombs Gel card and standard methods. At presentation the neonate had severe anemia with reticulocytopenia. Blood group was B, Rh D positive and DAT was 2+. Anti-Kp(b) was detected in mother's serum. Due to unavailability of Kp(b) negative red cells and incompatible blood group of mother (A(1)B Rh D positive) infant was transfused group B Rh D, Kp(b) positive PRBCs under steroid cover. He was symptom free at 4 months of age and DAT became negative at 6 months. Anti-Kp(b) is capable of causing severe late HDN. Infants born to irregular antibody positive mothers should be investigated and closely monitored for several weeks after birth for immune HDN even if asymptomatic at birth. Copyright © 2012 Elsevier Ltd. All rights reserved.
τ-Functions for a two-point version of the KP-hierarchy
Helminck, G.F.
2003-01-01
In this paper a multipoint version of the linearization of the KP-hierarchy is described. Solutions of this system in the form of wave functions are constructed starting from a suitable Grassmann manifold and a group of commuting flows corresponding to the configuration of n points in C. The failure
$\\tau$-Functions for a two-point version of the $KP$-hierarchy
Helminck, G.F.
2003-01-01
In this paper a multipoint version of the linearization of the $KP$-hierarchy is described. Solutions of this system in the form of wave functions are constructed starting from a suitable Grassmann manifold and a group of commuting flows corresponding to the configuration of $n$ points in
Nanoformulation improves activity of the (pre)clinical anticancer ruthenium complex KP1019.
Heffeter, P; Riabtseva, A; Senkiv, Y; Kowol, C R; Körner, W; Jungwith, U; Mitina, N; Keppler, B K; Konstantinova, T; Yanchuk, I; Stoika, R; Zaichenko, A; Berger, W
2014-05-01
Ruthenium anticancer drugs belong to the most promising non-platinum anticancer metal compounds in clinical evaluation. However, although the clinical results are promising regarding both activity and very low adverse effects, the clinical application is currently hampered by the limited solubility and stability of the drug in aqueous solution. Here, we present a new nanoparticle formulation based on polymer-based micelles loaded with the anticancer lead ruthenium compound KP1019. Nanoprepared KP1019 was characterised by enhanced stability in aqueous solutions. Moreover, the nanoparticle formulation facilitated cellular accumulation of KP1019 (determined by ICP-MS measurements) resulting in significantly lowered IC50 values. With regard to the mode of action, increased cell cycle arrest in G2/M phase (PI-staining), DNA damage (Comet assay) as well as enhanced levels of apoptotic cell death (caspase 7 and PARP cleavage) were found in HCT116 cells treated with the new nanoformulation of KP1019. Summarizing, we present for the first time evidence that nanoformulation is a feasible strategy for improving the stability as well as activity of experimental anticancer ruthenium compounds.
Symmetric polynomials, quantum Jacobi-Trudi identities and \\tau-functions
Harnad, J
2013-01-01
An element [\\Phi] of the Grassmannian of n-dimensional subspaces of the Hardy space H^2, extended over the field C(x_1,..., x_n), may be associated to any polynomial basis {\\phi} for C(x). The Pl\\"ucker coordinates S^\\phi_{\\lambda,n}(x_1,..., x_n) of \\Phi, labelled by partitions \\lambda, provide an analog of Jacobi's bi-alternant formula, defining a generalization of Schur polynomials. Applying the recursion relations satisfied by the polynomial system to the analog of the complete symmetric functions generates a doubly infinite matrix of symmetric polynomials that determine an element [H] of the Grasmannian. This is shown to coincide with [\\Phi], implying a set of {\\it quantum Jacobi-Trudi identities} that generalize a result obtained by Sergeev and Veselov for the case of orthogonal polynomials. The symmetric polynomials S^\\phi_{\\lambda,n}(x_1,..., x_n) are shown to be KP (Kadomtsev-Petviashvili) tau-functions in terms of the monomial sums in the parameters x_a, viewed as KP flow variables. A fermionic oper...
Lienard Equation and Exact Solutions for Some Soliton-Producing Nonlinear Equations
Institute of Scientific and Technical Information of China (English)
ZHANG Wei-Guo; CHANG Qian-Shun; ZHANG Qi-Ren
2004-01-01
In this paper, we first consider exact solutions for Lienard equation with nonlinear terms of any order. Then,explicit exact bell and kink profile solitary-wave solutions for many nonlinear evolution equations are obtained by means of results of the Lienard equation and proper deductions, which transform original partial differential equations into the Lienard one. These nonlinear equations include compound KdV, compound KdV-Burgers, generalized Boussinesq,generalized KP and Ginzburg-Landau equation. Some new solitary-wave solutions are found.
Institute of Scientific and Technical Information of China (English)
CHEN Jiang; HE Hong-Sheng; YANG Kong-Qing
2005-01-01
A generalized F-expansion method is introduced and applied to (3+ 1)-dimensional Kadomstev-Petviashvili(KP) equation. As a result, some new Jacobi elliptic function solutions of the equation are found, from which the trigonometric function solutions and the solitary wave solutions can be obtained. The method can also be extended to other types of nonlinear evolution equations in mathematical physics.
Kubista, Bernd; Schoefl, Thomas; Mayr, Lisa; van Schoonhoven, Sushilla; Heffeter, Petra; Windhager, Reinhard; Keppler, Bernhard K; Berger, Walter
2017-04-12
Osteosarcoma is the most frequent primary malignant bone tumor. Although survival has distinctly increased due to neoadjuvant chemotherapy in the past, patients with metastatic disease and poor response to chemotherapy still have an adverse prognosis. Hence, development of new therapeutic strategies is still of utmost importance. Anticancer activity of KP46 against osteosarcoma cell models was evaluated as single agent and in combination approaches with chemotherapeutics and Bcl-2 inhibitors using MTT assay. Underlying mechanisms were tested by cell cycle, apoptosis and autophagy assays. KP46 exerted exceptional anticancer activity at the nanomolar to low micromolar range, depending on the assay format, against all osteosarcoma cell models with minor but significant differences in IC50 values. KP46 treatment of osteosarcoma cells caused rapid loss of cell adhesion, weak cell cycle accumulation in S-phase and later signs of apoptotic cell death. Furthermore, already at sub-cytotoxic concentrations KP46 reduced the migratory potential of osteosarcoma cells and exerted synergistic effects with cisplatin, a standard osteosarcoma chemotherapeutic. Moreover, the gallium compound induced signs of autophagy in osteosarcoma cells. Accordingly, blockade of autophagy by chloroquine but also by the Bcl-2 inhibitor obatoclax increased the cytotoxic activity of KP46 treatment significantly, suggesting autophagy induction as a protective mechanism against KP46. Together, our results identify KP46 as a new promising agent to supplement standard chemotherapy and possible future targeted therapy in osteosarcoma.
Removal of Ca2+ and Zn2+ from aqueous solutions by zeolites NaP and KP.
Yusof, Alias Mohd; Malek, Nik Ahmad Nizam Nik; Kamaruzaman, Nurul Asyikin; Adil, Muhammad
2010-01-01
Zeolites P in sodium (NaP) and potassium (KP) forms were used as adsorbents for the removal of calcium (Ca2+) and zinc (Zn2+) cations from aqueous solutions. Zeolite KP was prepared by ion exchange of K+ with Na+ which neutralizes the negative charge of the zeolite P framework structure. The ion exchange capacity of K+ on zeolite NaP was determined through the Freundlich isotherm equilibrium study. Characterization of zeolite KP was determined using infrared spectroscopy and X-ray diffraction (XRD) techniques. From the characterization, the structure of zeolite KP was found to remain stable after the ion exchange process. Zeolites KP and NaP were used for the removal of Ca and Zn from solution. The amount of Ca2+ and Zn2+ in aqueous solution before and after the adsorption by zeolites was analysed using the flame atomic absorption spectroscopy method. The removal of Ca2+ and Zn2+ followed the Freundlich isotherm rather than the Langmuir isotherm model. This result also revealed that zeolite KP adsorbs Ca2+ and Zn2+ more than zeolite NaP and proved that modification of zeolite NaP with potassium leads to an increase in the adsorption efficiency of the zeolite. Therefore, the zeolites NaP and KP can be used for water softening (Ca removal) and reducing water pollution/toxicity (Zn removal).
Directory of Open Access Journals (Sweden)
Zeliha Yıldırım
2014-01-01
Full Text Available In this study, the effects of food preservative p-hydroxybenzoic acid and propyl-paraben on the inhibitory activity of enterocin KP produced by Enterococcus faecalis KP were determined. Staphylococcus aureus, Escherichia coli O157:H7 and Salmonella Typhimurium, resistant to enterocin KP bacteriocin, were used as target organisms. The inhibitor activity of enterosin KP (1600 AU/ml alone or in combination with p-hydroxybenzoic acid (%0.1-0.3 and propyl-paraben (%0.008-0.16 on the growth of Staphylococcus aureus, Escherichia coli O157:H7 and Salmonella Typhimurium were determined. The inhibitory activity of enterocin KP was increased when used in combination with p-hydroxybenzoic acid and propyl-paraben at concentrations of 0.1-0.3% and 0.008-0.016%, respectively. Furthermore, Staphylococcus aureus, E. coli O157:H7 and Salmonella Typhimurium became sensitive to enterocin KP. In conclusion, the use of enterocin KP in combination with other food preservatives principles resulted in an increase in its inhibitory activity and spectrum.
Allen, Aron; Islamovic, Emir; Kaur, Jagdeep; Gold, Scott; Shah, Dilip; Smith, Thomas J
2011-10-01
The corn smut fungus, Ustilago maydis, is a global pathogen responsible for extensive agricultural losses. Control of corn smut using traditional breeding has met with limited success because natural resistance to U. maydis is organ specific and involves numerous maize genes. Here, we present a transgenic approach by constitutively expressing the Totivirus antifungal protein KP4, in maize. Transgenic maize plants expressed high levels of KP4 with no apparent negative impact on plant development and displayed robust resistance to U. maydis challenges to both the stem and ear tissues in the greenhouse. More broadly, these results demonstrate that a high level of organ independent fungal resistance can be afforded by transgenic expression of this family of antifungal proteins.
Schur function expansions of KP tau functions associated to algebraic curves
Enolski, V
2010-01-01
The Schur function expansion of Sato-Segal-Wilson KP tau-functions is reviewed. The case of tau-functions related to algebraic curves of arbitrary genus is studied in detail. Explicit expressions for the Pl\\"ucker coordinate coefficients appearing in the expansion are obtained in terms of directional derivatives of the Riemann theta function or Klein sigma function along the KP flow directions. Using the fundamental bi-differential, it is shown how the coefficients can be expressed as polynomials in terms of Klein's higher genus generalizations of Weierstrass' zeta and P functions. The cases of genus two hyperelliptic and genus three trigonal curves are detailed as illustrations of the approach developed here.
Verification of short lead time forecast models: applied to Kp and Dst forecasting
Wintoft, Peter; Wik, Magnus
2016-04-01
In the ongoing EU/H2020 project PROGRESS models that predicts Kp, Dst, and AE from L1 solar wind data will be used as inputs to radiation belt models. The possible lead times from L1 measurements are shorter (10s of minutes to hours) than the typical duration of the physical phenomena that should be forecast. Under these circumstances several metrics fail to single out trivial cases, such as persistence. In this work we explore metrics and approaches for short lead time forecasts. We apply these to current Kp and Dst forecast models. This project has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No 637302.
Structure and Properties of `Steel 08kp + ChNMSh Iron' Bimetal Obtained by Explosion Welding
Denisov, I. V.
2017-05-01
The structure of a bimetal from structural steel 08kp and low-alloy iron ChNMSh obtained by explosion welding is studied. The effect of different heat treatments on the structure and properties of the bimetal is determined, and expedient modes of heat treatment for reliving the internal stresses in the zone of joining, which do not worsen the operating properties of the welded materials, are suggested.
Paralič, Ján; Babič, František
This paper presents a collaborative working and learning environment called KP-Lab System. It provides a complex and multifunctional application built on principles of semantic web, exploiting also some web2.0 approaches as Google Apps or mashups. This system offers virtual user environment with different, necessary and advanced features for collaborative learning or working knowledge intensive activities. This paper briefly presents the whole system with special emphasis on its semantic-based aspects and analytical tools.
Defending against Key Abuse Attacks in KP-ABE Enabled Broadcast Systems
Yu, Shucheng; Ren, Kui; Lou, Wenjing; Li, Jin
Key-Policy Attribute-Based Encryption (KP-ABE) is a promising cryptographic primitive which enables fine-grained access control over sensitive data. However, key abuse attacks in KP-ABE may impede its wide application especially in copyright-sensitive systems. To defend against this kind of attacks, this paper proposes a novel KP-ABE scheme which is able to disclose any illegal key distributor’s ID when key abuse is detected. In our scheme, each bit of user ID is defined as an attribute and the user secret key is associated with his unique ID. The tracing algorithm fulfills its task by tricking the pirate device into decrypting the ciphertext associated with the corresponding bits of his ID. Our proposed scheme has the salient property of black box tracing, i.e., it traces back to the illegal key distributor’s ID only by observing the pirate device’s outputs on certain inputs. In addition, it does not require the pirate device’s secret keys to be well-formed as compared to some previous work. Our proposed scheme is provably secure under the Decisional Bilinear Diffie-Hellman (DBDH) assumption and the Decisional Linear (DL) assumption.
Mutation of HIV-1 genomes in a clinical population treated with the mutagenic nucleoside KP1461.
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James I Mullins
Full Text Available The deoxycytidine analog KP1212, and its prodrug KP1461, are prototypes of a new class of antiretroviral drugs designed to increase viral mutation rates, with the goal of eventually causing the collapse of the viral population. Here we present an extensive analysis of viral sequences from HIV-1 infected volunteers from the first "mechanism validation" phase II clinical trial of a mutagenic base analog in which individuals previously treated with antiviral drugs received 1600 mg of KP1461 twice per day for 124 days. Plasma viral loads were not reduced, and overall levels of viral mutation were not increased during this short-term study, however, the mutation spectrum of HIV was altered. A large number (N = 105 per sample of sequences were analyzed, each derived from individual HIV-1 RNA templates, after 0, 56 and 124 days of therapy from 10 treated and 10 untreated control individuals (>7.1 million base pairs of unique viral templates were sequenced. We found that private mutations, those not found in more than one viral sequence and likely to have occurred in the most recent rounds of replication, increased in treated individuals relative to controls after 56 (p = 0.038 and 124 (p = 0.002 days of drug treatment. The spectrum of mutations observed in the treated group showed an excess of A to G and G to A mutations (p = 0.01, and to a lesser extent T to C and C to T mutations (p = 0.09, as predicted by the mechanism of action of the drug. These results validate the proposed mechanism of action in humans and should spur development of this novel antiretroviral approach.
Mutation of HIV-1 genomes in a clinical population treated with the mutagenic nucleoside KP1461.
Mullins, James I; Heath, Laura; Hughes, James P; Kicha, Jessica; Styrchak, Sheila; Wong, Kim G; Rao, Ushnal; Hansen, Alexis; Harris, Kevin S; Laurent, Jean-Pierre; Li, Deyu; Simpson, Jeffrey H; Essigmann, John M; Loeb, Lawrence A; Parkins, Jeffrey
2011-01-14
The deoxycytidine analog KP1212, and its prodrug KP1461, are prototypes of a new class of antiretroviral drugs designed to increase viral mutation rates, with the goal of eventually causing the collapse of the viral population. Here we present an extensive analysis of viral sequences from HIV-1 infected volunteers from the first "mechanism validation" phase II clinical trial of a mutagenic base analog in which individuals previously treated with antiviral drugs received 1600 mg of KP1461 twice per day for 124 days. Plasma viral loads were not reduced, and overall levels of viral mutation were not increased during this short-term study, however, the mutation spectrum of HIV was altered. A large number (N = 105 per sample) of sequences were analyzed, each derived from individual HIV-1 RNA templates, after 0, 56 and 124 days of therapy from 10 treated and 10 untreated control individuals (>7.1 million base pairs of unique viral templates were sequenced). We found that private mutations, those not found in more than one viral sequence and likely to have occurred in the most recent rounds of replication, increased in treated individuals relative to controls after 56 (p = 0.038) and 124 (p = 0.002) days of drug treatment. The spectrum of mutations observed in the treated group showed an excess of A to G and G to A mutations (p = 0.01), and to a lesser extent T to C and C to T mutations (p = 0.09), as predicted by the mechanism of action of the drug. These results validate the proposed mechanism of action in humans and should spur development of this novel antiretroviral approach.
Pathogenicity ofKlebsiella pneumonia(KpC4) infecting maize and mice
Institute of Scientific and Technical Information of China (English)
HUANG Min; HE Yue-qiu; LIN Li; WU Yi-xin; Honhing Ho; HE Peng-fei; LI Guo-zhi; HE Peng-bo; XIONG Guo-ru; YUAN Yuan
2016-01-01
Recently, a new bacterial top rot disease of maize has frequently appeared in many areas of Yunnan Province, China. The pathogen of the disease was identiifed asKlebsiela pneumoniae(KpC4), which is wel known to cause pulmonary and urinary diseases in humans and animals and occasionaly exists as a harmless endophyte in plants. To evaluate the viru-lence of the maize pathogen to maize and mice, we inoculated maize and mice with routine inoculation and intraperitoneal injection respectively according to Koch’s postulates. The results showed that KpC4 and the clinical strainK. pneumoniae 138 (Kp138) were al highly pathogenic to maize and mice and the strain re-isolated from diseased mice also caused typical top rot symptoms on maize by artiifcial inoculation. It is highlighting that a seemingly dedicated human/animal pathogen could cause plant disease. This is the ifrst report ofK. pneumoniae, an opportunistic pathogen of human/animal , could infect maize and mice. The ifndings serve as an alert to plant, medical and veterinarian scientists regarding a potentialy dangerous bacterial pathogen infecting both plants and animals/humans. The maize plants in the ifeld could serve as a reservoir forK. pneumoniae which might infect animals and probably humans when conditions are favorable. The new ifndings not only are signiifcant in the developing control strategy for the new disease in Yunnan, but also serve as a starting point for further studies on the mechanism of pathogenesis and epidemiology ofK. pneumoniae.
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Yozi Aulia Rahman
2015-12-01
Full Text Available Poverty is a serious problem, it’s happened in all the world, such as Indonesia. In September 2006, BPS announced that the poverty rate in Indonesiahad increased during the period February 2005 to march 2006 from 16.0 percent to 17.75 percent contrast to steady declines in the poverty rate since the crisis. Number of Poverty in Indonesiain 2006 have been reached 35,5 milion people. Government of Indonesiahas implemented programs to reduce poverty until village level. These programs such as IDT, PPK, BLT, etc. But, that programs just a short run programs, not long run programs. As long run program, P2KP has many programs, such as micro credits, infrastructure, and training. In Pepedan and Linggapura village implemented infrastructure programs. Its first priority programs because there many roads in that village are broken and disturbs local economic activities. BKM and KSM managed this program so that is success. Based on SWOT analysis, appropriate strategy to improve the function of P2KP is by intregrated horizontal strategy. It means, Local Government (Brebes Regency Goverment must have policy strategic and must cooperation with BKM, KSM and people in village. Project evaluate (Inputs, Outputs, Outcames, Benefits, Impact needs to know programs running.
Akaishi, Yoshinori
2016-01-01
We propose and examine a new high-density composite of Lambda* equiv K-p = (s ubar) times (uud), which may be called Kaonic Proton Matter (KPM), or simply, Lambda*-Matter (Lambda*-M}, where substantial shrinkage of baryonic bound systems originating from the strong attraction of the (KbarN) I=0 interaction takes place, providing a ground-state neutral baryonic system with a huge energy gap. The mass of an ensemble of (K-p) m, where m, the number of the K-p pair, is larger than m approx 10, is predicted to drop down below its corresponding neutron ensemble, (n) m, since the attractive interaction is further increased by the Heitler-London type molecular covalency, as well as by chiral symmetry restoration of the QCD vacuum. Since the seed clusters K-p, K-pp and K-K-pp) are short-lived, the formation of such a stabilized relic ensemble, (K-p) m, may only be conceived during the Big-Bang Quark Gluon Plasma (QGP) period in the early universe before the hadronization and quark-anti-quark annihilation proceed. At t...
Self-Consistent Sources for Integrable Equations Via Deformations of Binary Darboux Transformations
Chvartatskyi, Oleksandr; Dimakis, Aristophanes; Müller-Hoissen, Folkert
2016-08-01
We reveal the origin and structure of self-consistent source extensions of integrable equations from the perspective of binary Darboux transformations. They arise via a deformation of the potential that is central in this method. As examples, we obtain in particular matrix versions of self-consistent source extensions of the KdV, Boussinesq, sine-Gordon, nonlinear Schrödinger, KP, Davey-Stewartson, two-dimensional Toda lattice and discrete KP equation. We also recover a (2+1)-dimensional version of the Yajima-Oikawa system from a deformation of the pKP hierarchy. By construction, these systems are accompanied by a hetero binary Darboux transformation, which generates solutions of such a system from a solution of the source-free system and additionally solutions of an associated linear system and its adjoint. The essence of all this is encoded in universal equations in the framework of bidifferential calculus.
Kuhn, Paul-Steffen
2014-10-20
A one-electron reduction of osmium(IV) complexes trans-[OsIVCl4(Hazole)2], where Hazole = 1H-pyrazole ([1]0), 2H-indazole ([2]0), 1H-imidazole ([3]0), and 1H-benzimidazole ([4]0), afforded a series of eight new complexes as osmium analogues of KP1019, a lead anticancer drug in clinical trials, with the general formula (cation)[trans-OsIIICl4(Hazole)2], where cation = H2pz+ (H2pz[1]), H2ind+ (H2ind[2]), H2im+ (H2im[3]), Ph4P+ (Ph4P[3]), nBu4N+ (nBu4N[3]), H2bzim+ (H2bzim[4]), Ph4P+ (Ph4P[4]), and nBu4N+ (nBu4N[4]). All complexes were characterized by elemental analysis, 1H NMR spectroscopy, electrospray ionization mass spectrometry, UV-vis spectroscopy, cyclic voltammetry, while H2pz[1], H2ind[2], and nBu4[3], in addition, by X-ray diffraction. The reduced species [1]- and [4]- are stable in aqueous media in the absence of air oxygen and do not react with small biomolecules such as amino acids and the nucleotide 5′-dGMP. Cell culture experiments in five different human cancer cell lines (HeLa, A549, FemX, MDA-MB-453, and LS-174) and one noncancerous cell line (MRC-5) were performed, and the results were discussed and compared to those for KP1019 and cisplatin. Benzannulation in complexes with similar structure enhances antitumor activity by several orders of magnitude, implicating different mechanisms of action of the tested compounds. In particular, complexes H2ind[2] and H2bzim[4] exhibited significant antiproliferative activity in vitro when compared to H2pz[1] and H2im[3]. (Chemical Equation Presented).
Indian Academy of Sciences (India)
Ahmet Bekir; Özkan Güner
2013-08-01
In this paper, we obtain the 1-soliton solutions of the (3 + 1)-dimensional generalized Kadomtsev–Petviashvili (gKP) equation and the generalized Benjamin equation. By using two solitary wave ansatz in terms of sech$^{p}$ and tanh$^{p}$ functions, we obtain exact analytical bright and dark soliton solutions for the considered model. These solutions may be useful and desirable for explaining some nonlinear physical phenomena in genuinely nonlinear dynamical systems.
Institute of Scientific and Technical Information of China (English)
张辉; 贾桂娟; 李忠正
2004-01-01
文中对皇竹草KP-AQ浆的CEpH漂白条件、漂白浆特性及其打浆性能进行了研究,并与芦苇浆作了比较.实验结果表明,皇竹草浆CEpH漂白较佳条件为:总用氯量11%,C、H段用氯比为7:3;E段H2O2用量1.3%,漂白浆得率89.4%,白度84.9%ISO,返黄值2.5,粘度863mL/g,卡伯值1.7;打浆度为41～42°SR时,皇竹草漂白浆主要物理指标为:紧度0 58g/cm3,耐破指数2.92kPa·m2/g,耐折度16次,撕裂度指数8.16mN·m2/g,裂断长4070m;皇竹草漂白浆白度、得率、返黄值、卡伯值等综合性能优于芦苇浆,粘度低于芦苇浆;芦苇浆比皇竹草浆更易打浆;芦苇漂白浆强度指数稍高于皇竹草浆.
Chen, Liang; Chavda, Kalyan D.; Melano, Roberto G.; Jacobs, Michael R.; Koll, Brian; Hong, Tao; Rojtman, Albert D.; Levi, Michael H.; Bonomo, Robert A.
2014-01-01
The global spread of Klebsiella pneumoniae carbapenemase (KPC) is predominately associated with K. pneumoniae strains genotyped as sequence type 258 (ST258). The first ST258-associated plasmid, pKpQIL, was described in Israel in 2006, but its history in the northeastern United States remains unknown. Six pKpQIL-like plasmids from four K. pneumoniae isolates (three ST258 and one ST234), one Escherichia coli isolate, and one Enterobacter aerogenes isolate, collected from 2003 to 2010 in New York (NY) and New Jersey (NJ) hospitals, were completely sequenced. The sequences and overall sizes of the six plasmids are highly similar to those of pKpQIL; the major difference is that five of six NJ/NY strains harbor blaKPC-2, while pKpQIL contains blaKPC-3. Moreover, a 26.7-kb fragment was inverted in pKpQIL-234 (from ST234 K. pneumoniae), while a 14.5-kb region was deleted in pKpQIL-Ec (from ST131 E. coli). PCR screening of 284 other clinical K. pneumoniae isolates identified 101 (35.6%) harboring pKpQIL-like plasmids from 9 of 10 surveyed hospitals, demonstrating the wide dissemination of pKpQIL in this region of endemicity. Among the positive isolates, 87.1% were typed as ST258 and 88.1% carried blaKPC-2. The finding of pKpQIL-like plasmid in this study from strains that predate the initial report of KPC in Israel provides evidence that pKpQIL may have originated in the United States. Our findings demonstrate that pKpQIL plasmids are both spreading clonally in ST258 strains and spreading horizontally to different sequence types and species, further highlighting the clinical and public health concerns associated with carbapenem resistance. PMID:24614371
First Hα and Revised Photometric Studies of Contact Binary KP101231
Indian Academy of Sciences (India)
Shanti Priya Devarapalli; Rukmini Jagirdar
2016-09-01
This paper reports the first spectroscopic observations in the $\\rm{H}\\alpha$ region at different orbital phases and the revised photometric solutions, for the contact binary KP101231 (V1) in the direction of the open cluster Praesepe. The photometric solutions obtained for the data in V and R passbands using the Wilson--Devinney (WD) method suggest that both components were in good thermal contact. The equivalent widths (EW) of ${\\rm H}\\alpha$ and Na lines were studied at various phases and a filled-in absorption profile around phase 0.58--0.68 was observed and compared with other phases. A correlation was observed between the profiles of ${\\rm H}\\alpha$ and Na lines at various phases.
Energy Technology Data Exchange (ETDEWEB)
Ramirez-Nicolas, M.
2011-07-01
The structure of the Earth is characterized by a number of regions which have different physical properties. For their study one uses models such PREM or IASPEI91. These models describe the internal structure of the Earth providing us the theoretical values of the velocity of the waves that pass through each of these regions. In this paper we focus on the waves that cross the inner core (PKIKP), and the reflected waves on the surface of the inner core (PKiKP). The aim of this study is to identify the PKiKP and PKIKP phases in a seismogram and compare them with the theoretical values obtained from the models. Another objective of this work is to propose an expression for the propagation velocity of seismic waves at the discontinuity between the outer and inner core from the minimization of waste of time (time difference between the arrival of the wave PKIKP and PKiKP). For this study we have selected two earthquakes, one occurred in Colombia, 04/26/1999 (Mw 5.9) and the other in Peru-Ecuador 16/11/2007 (Mw = 6.8). We have analyzed only the seismograms from stations with epicentral distances between 130 degree centigrade and 140 degree centigrade, because of the interference phenomena between the PKIKP and the PKiKP for epicentral distances less than 130 degree centigrade. (Author) 14 refs.
Values of Kp Indices, Ap Indices, Cp Indices, C9 Indices, Sunspot Number, and 10.7 cm Flux
National Oceanic and Atmospheric Administration, Department of Commerce — This data file consists of Kp indices, Ap indices, Cp indices, C9 indices, sunspot number, and 10.7 cm flux. The most often requested parameter of this file are the...
Genome Sequence of Klebsiella pneumoniae KpQ3, a DHA-1 β-Lactamase-Producing Nosocomial Isolate
Tobes, Raquel; Codoñer, Francisco M.; López-Camacho, Elena; Salanueva, Iñigo J.; Manrique, Marina; Brozynska, Marta; Gómez-Gil, Rosa; Martínez-Blanch, Juan F.; Álvarez-Tejado, Miguel; Pareja, Eduardo
2013-01-01
Klebsiella pneumoniae KpQ3 is a multidrug-resistant isolate obtained from a blood culture of a patient in a burn unit in the Hospital Universitario La Paz (Madrid, Spain) in 2008. The genome contains multiple antibiotic resistance genes, including a plasmid-mediated DHA-1 cephalosporinase gene. PMID:23469341
Dynamical mass generation in unquenched QED using the Dyson--Schwinger equations
Kizilersu, Ayse; Sizer, Tom; Williams, Anthony G; Williams, Richard
2014-01-01
We present a comprehensive numerical study of dynamical mass generation for unquenched QED in four dimensions, in the absence of four-fermion interactions, using the Dyson--Schwinger approach. We begin with an overview of previous investigations of criticality in the quenched approximation. To this we add an analysis using a new fermion-antifermion-boson interaction ansatz, the Kizilersu-Pennington (KP) vertex, developed for an unquenched treatment. After surveying criticality in previous unquenched studies, we investigate the performance of the KP vertex in dynamical mass generation using a renormalized fully unquenched system of equations. This we compare with the results for two hybrid vertices incorporating the Curtis--Pennington vertex in the fermion equation. We conclude that the KP vertex is as yet incomplete, and its relative gauge-variance is due to its lack of massive transverse components in its design.
基于代理的即时属性撤销KP-ABE方案%Proxy-based Immediate Attribute Revocation KP-ABE Scheme
Institute of Scientific and Technical Information of China (English)
林娟; 薛庆水; 曹珍富
2014-01-01
Attribute revocation is crucial to the practical use of Attribute-based Encryption( ABE) . Most of the existing revocable ABE schemes under the indirect revocation model suffer in terms of delaying in revocation or updating keys and ciphertexts. To address this,this paper proposes a proxy-based immediate attribute revocation Key Policy( KP) attribute-based encryption under the indirect model without issuing new keys or re-encrypting existing ciphertexts. It achieves attribute revocation by introducing a proxy in the decryption process and reduces the burden for the key authority. The proxy is semi-trusted which revokes user access privileges and cannot decrypt ciphertexts. Analysis results show that the scheme supports fine-grained access control policies and achieves three kinds of revocation including system attribute revocation,user revocation and user attribute revocation.%属性撤销是属性基加密方案在实际应用中亟须解决的问题，已有支持间接撤销模式的可撤销属性基加密方案存在撤销延时或需要更新密钥及密文等问题。为此，提出一种间接模式下基于代理的支持属性即时撤销的密钥策略属性基加密方案，该方案不需要用户更新密钥及重加密密文，通过在解密过程中引入代理实现撤销管理，减轻了授权机构的工作量，其要求代理为半可信，不支持为撤销用户提供访问权限及解密密文。分析结果表明，该方案支持细粒度访问控制策略，并且可以实现系统属性的撤销、用户的撤销及用户的部分属性撤销。
Directory of Open Access Journals (Sweden)
Mukesh Kumar
2015-09-01
Full Text Available A novel tannase producing bacterial strain was isolated from rhizospheric soil of Acacia species and identified as Klebsiella pneumoniae KP715242. A 3.25-fold increase in tannase production was achieved upon optimization with central composite design using response surface methodology. Four variables namely pH, temperature, incubation period, and agitation speed were used to optimize significant correlation between the effects of these variables on tannase production. A second-order polynomial was fitted to data and validated by ANOVA. The results showed a complex relationship between variables and response given that all factors were significant and could explain 99.6% of the total variation. The maximum production was obtained at 5.2 pH, 34.97 °C temperature, 103.34 rpm agitation speed and 91.34 h of incubation time. The experimental values were in good agreement with the predicted ones and the models were highly significant with a correlation coefficient (R2 of 0.99 and a highly significant F-value of 319.37.
Robo-AO KP: A new era in robotic adaptive optics
Riddle, Reed L.; Baranec, Christoph; Law, Nicholas M.; Kulkarni, Shrinivas R.; Duev, Dmitry; Ziegler, Carl; Jensen-Clem, Rebecca M.; Atkinson, Dani Eleanor; Tanner, Angelle M.; Zhang, Celia; Ray, Amy
2016-01-01
Robo-AO is the first and only fully automated adaptive optics laser guide star AO instrument. It was developed as an instrument for 1-3m robotic telescopes, in order to take advantage of their availability to pursue large survey programs and target of opportunity observations that aren't possible with other AO systems. Robo-AO is currently the most efficient AO system in existence, and it can achieve an observation rate of 20+ science targets per hour. In more than three years of operations at Palomar Observatory, it has been quite successful, producing technology that is being adapted by other AO systems and robotic telescope projects, as well as several high impact scientific publications. Now, Robo-AO has been selected to take over operation of the Kitt Peak National Observatory 2.1m telescope. This will give Robo-AO KP the opportunity to pursue multiple science programs consisting of several thousand targets each during the three years it will be on the telescope. One-sixth of the observing time will be allocated to the US community through the NOAO TAC process. This presentation will discuss the process adapting Robo-AO to the KPNO 2.1m telescope, the plans for integration and initial operations, and the science operations and programs to be pursued.
Directory of Open Access Journals (Sweden)
Hye Jung Ihn
Full Text Available Abnormally elevated formation and activation of osteoclasts are primary causes for a majority of skeletal diseases. In this study, we found that KP-A159, a newly synthesized thiazolopyridine derivative, inhibited osteoclast differentiation and function in vitro, and inflammatory bone loss in vivo. KP-A159 did not cause a cytotoxic response in bone marrow macrophages (BMMs, but significantly inhibited the formation of multinucleated tartrate-resistant acid phosphatase (TRAP-positive osteoclasts induced by macrophage colony-stimulating factor (M-CSF and receptor activator of nuclear factor-κB ligand (RANKL. KP-A159 also dramatically inhibited the expression of marker genes related to osteoclast differentiation, including TRAP (Acp5, cathepsin K (Ctsk, dendritic cell-specific transmembrane protein (Dcstamp, matrix metallopeptidase 9 (Mmp9, and nuclear factor of activated T-cells, cytoplasmic 1 (Nfatc1. Moreover, actin ring and resorption pit formation were inhibited by KP-A159. Analysis of the signaling pathway involved showed that KP-A159 inhibited RANKL-induced activation of extracellular signal-regulated kinase (ERK, c-Jun N-terminal kinase (JNK, and mitogen-activated protein kinase kinase1/2 (MEK1/2. In a mouse inflammatory bone loss model, KP-A159 significantly rescued lipopolysaccharide (LPS-induced bone loss by suppressing osteoclast numbers. Therefore, KP-A159 targets osteoclasts, and may be a potential candidate compound for prevention and/or treatment of inflammatory bone loss.
Nishino, Hitoshi
2012-01-01
We present a system of a self-dual Yang-Mills field and a self-dual vector-spinor field with nilpotent fermionic symmetry (but not supersymmetry) in 2+2 dimensions, that generates supersymmetric integrable systems in lower dimensions. Our field content is (A_\\mu{}^I, \\psi_\\mu{}^I, \\chi^{I J}), where I and J are the adjoint indices of arbitrary gauge group. The \\chi^{I J} is a Stueckelberg field for consistency. The system has local nilpotent fermionic symmetry with the algebra \\{N_\\alpha{}^I, N_\\beta{}^J \\} = 0. This system generates supersymmetric Kadomtsev-Petviashvili equations in D=2+1, and supersymmetric Korteweg-de Vries equations in D=1+1 after appropriate dimensional reductions. We also show that a similar self-dual system in seven dimensions generates self-dual system in four dimensions. Based on our results we conjecture that lower-dimensional supersymmetric integral models can be generated by non-supersymmetric self-dual systems in higher dimensions only with nilpotent fermionic symmetries.
Leyton, Felipe; Koper, Keith D.
2007-05-01
Previous seismic studies have reported evidence of scattered seismic energy coming from the inner core (IC). This implies that the IC has lateral variations in structure or composition with a scale length of tens of kilometers. In the present study, we focus on synthesizing the coda following precritical PKiKP and try to determine the location of the heterogeneities that produce this coda, using previously reported observations as a guide. Using a single-scattering approximation and ray theory, we generate synthetic PKiKP coda envelopes from six distinctive places inside the Earth: within the lower mantle on the source and receiver side, along the core-mantle boundary on the source and receiver side, along the inner core boundary, and within the inner core. We use two approaches to generate synthetic coda from topography on a boundary surface and one that is appropriate for volumetric scattering. In our computations we calculate the arrival time, ray parameter, and amplitude of the seismic waves and take into account errors in the back azimuth, as well as source and receiver effects. We find that previously reported "spindle"-shaped or growing coda can only be produced from volumetric heterogeneities located in the shallowest 350 km of the IC; however, strong trade-offs between the different parameters describing the volumetric heterogeneities (i.e., characteristic wavelengths, RMS velocity or impedance contrast, and total volume) preclude the determination of a unique model. Additionally, we find that reasonable models of topography at the core-mantle boundary can produce large variations of the PKiKP amplitude due to focusing and defocusing effects. Therefore complexity at the inner core boundary is not necessarily required to account for dramatic amplitude variations in the direct PKiKP amplitudes.
Strongly-Coupled Unquenched QED4 Propagators Using Schwinger-Dyson Equations
Kizilersu, Ayse; Williams, Anthony G
2013-01-01
We study unquenched QED in four dimensions using renormalised Schwinger-Dyson equations and focus on the behaviour of the fermion and photon propagators. For this purpose we use an improved Kizilersu-Pennington (KP) vertex which respects gauge invariance, multiplicative renormalizability for the massless case, agrees with perturbation theory in the weak coupling regime and is free of kinematic singularities. We find that the KP vertex performs very well as expected specially in comparison with other vertex choices. We find that the Landau pole problem familiar from perturbative QED persists in the nonperturbative case with the renormalised inverse photon propagator having zero crossing.
Paseiro-Cerrato, Rafael; Tongchat, Chinawat; Franz, Roland
2016-05-01
This study evaluated the influence of parameters such as temperature and type of low-density polyethylene (LDPE) film on the log Kp/f values of seven model migrants in food simulants. Two different types of LDPE films contaminated by extrusion and immersion were placed in contact with three food simulants including 20% ethanol, 50% ethanol and olive oil under several time-temperature conditions. Results suggest that most log Kp/f values are little affected by these parameters in this study. In addition, the relation between log Kp/f and log Po/w was established for each food simulant and regression lines, as well as correlation coefficients, were calculated. Correlations were compared with data from real foodstuffs. Data presented in this study could be valuable in assigning certain foods to particular food simulants as well as predicting the mass transfer of potential migrants into different types of food or food simulants, avoiding tedious and expensive laboratory analysis. The results could be especially useful for regulatory agencies as well as for the food industry.
k.p theory of freestanding narrow band gap semiconductor nanowires
Luo, Ning; Liao, Gaohua; Xu, H. Q.
2016-12-01
We report on a theoretical study of the electronic structures of freestanding nanowires made from narrow band gap semiconductors GaSb, InSb and InAs. The nanowires are described by the eight-band k.p Hamiltonians and the band structures are computed by means of the finite element method in a mixture basis consisting of linear triangular elements inside the nanowires and constrained Hermite triangular elements near the boundaries. The nanowires with two crystallographic orientations, namely the [001] and [111] orientations, and with different cross-sectional shapes are considered. For each orientation, the nanowires of the three narrow band gap semiconductors are found to show qualitatively similar characteristics in the band structures. However, the nanowires oriented along the two different crystallographic directions are found to show different characteristics in the valence bands. In particular, it is found that all the conduction bands show simple, good parabolic dispersions in both the [001]- and [111]-oriented nanowires, while the top valence bands show double-maximum structures in the [001]-oriented nanowires, but single-maximum structures in the [111]-oriented nanowires. The wave functions and spinor distributions of the band states in these nanowires are also calculated. It is found that significant mixtures of electron and hole states appear in the bands of these narrow band gap semiconductor nanowires. The wave functions exhibit very different distribution patterns in the nanowires oriented along the [001] direction and the nanowires oriented along the [111] direction. It is also shown that single-band effective mass theory could not reproduce all the band state wave functions presented in this work.
Long-term evolution of strongly nonlinear internal solitary waves in a rotating channel
Directory of Open Access Journals (Sweden)
J. C. Sánchez-Garrido
2009-09-01
Full Text Available The evolution of internal solitary waves (ISWs propagating in a rotating channel is studied numerically in the framework of a fully-nonlinear, nonhydrostatic numerical model. The aim of modelling efforts was the investigation of strongly-nonlinear effects, which are beyond the applicability of weakly nonlinear theories. Results reveal that small-amplitude waves and sufficiently strong ISWs evolve differently under the action of rotation. At the first stage of evolution an initially two-dimensional ISW transforms according to the scenario described by the rotation modified Kadomtsev-Petviashvili equation, namely, it starts to evolve into a Kelvin wave (with exponential decay of the wave amplitude across the channel with front curved backwards. This transition is accompanied by a permanent radiation of secondary Poincaré waves attached to the leading wave. However, in a strongly-nonlinear limit not all the energy is transmitted to secondary radiated waves. Part of it returns to the leading wave as a result of nonlinear interactions with secondary Kelvin waves generated in the course of time. This leads to the formation of a slowly attenuating quasi-stationary system of leading Kelvin waves, capable of propagating for several hundreds hours as a localized wave packet.
Dispersive mudslide-induced tsunamis
Directory of Open Access Journals (Sweden)
A. Rubino
1998-01-01
Full Text Available A nonlinear nested model for mudslide-induced tsunamis is proposed in which three phases of the life of the wave, i.e. the generation, far-field propagation and costal run-up are described by means of different mathematical models, that are coupled through appropriate matching procedures. The generation and run-up dynamics are simulated through a nonlinear shallow-water model with movable lateral boundaries: in the generation region two active layers are present, the lower one describing the slide descending on a sloping topography. For the intermediate phase, representing wave propagation far from the generation region, the hydrostatic assumption is not assumed as appropriate in general and, therefore, a nonlinear model allowing for weak phase dispersion, namely a Kadomtsev-Petviashvili equation, is used. This choice is made in order to assess the relevance of dispersive features such as solitary waves and dispersive tails. It is shown that in some realistic circumstances dispersive mudslide-induced tsunami waves can be produced over relatively short, distances. In such cases the use of a hydrostatic model throughout the whole tsunami history turns out to give erroneous results. In particular, when solitary waves are generated during the tsunami propagation in the open sea, the resulting run-up process yields peculiar wave forms leading to amplified coastal inundations with respect to a mere hydrostatic context.
Kondo, Kenichi
2013-11-01
Ultradiscretization with negative values is a long-standing problem and several attempts have been made to solve it. Among others, we focus on the symmetrized max-plus algebra, with which we ultradiscretize the discrete sine-Gordon equation. Another ultradiscretization of the discrete sine-Gordon equation has already been proposed by previous studies, but the equation and the solutions obtained here are considered to directly correspond to the discrete counterpart. We also propose a noncommutative discrete analogue of the sine-Gordon equation, reveal its relations to other integrable systems including the noncommutative discrete KP equation, and construct multisoliton solutions by a repeated application of Darboux transformations. Moreover, we derive a noncommutative ultradiscrete analogue of the sine-Gordon equation and its 1-soliton and 2-soliton solutions, using the symmetrized max-plus algebra. As a result, we have a complete set of commutative and noncommutative versions of continuous, discrete, and ultradiscrete sine-Gordon equations.
Directory of Open Access Journals (Sweden)
Kenichi Kondo
2013-11-01
Full Text Available Ultradiscretization with negative values is a long-standing problem and several attempts have been made to solve it. Among others, we focus on the symmetrized max-plus algebra, with which we ultradiscretize the discrete sine-Gordon equation. Another ultradiscretization of the discrete sine-Gordon equation has already been proposed by previous studies, but the equation and the solutions obtained here are considered to directly correspond to the discrete counterpart. We also propose a noncommutative discrete analogue of the sine-Gordon equation, reveal its relations to other integrable systems including the noncommutative discrete KP equation, and construct multisoliton solutions by a repeated application of Darboux transformations. Moreover, we derive a noncommutative ultradiscrete analogue of the sine-Gordon equation and its 1-soliton and 2-soliton solutions, using the symmetrized max-plus algebra. As a result, we have a complete set of commutative and noncommutative versions of continuous, discrete, and ultradiscrete sine-Gordon equations.
Directory of Open Access Journals (Sweden)
Grażyna Majkowska-Skrobek
2016-12-01
Full Text Available The rise of antibiotic-resistant Klebsiella pneumoniae, a leading nosocomial pathogen, prompts the need for alternative therapies. We have identified and characterized a novel depolymerase enzyme encoded by Klebsiella phage KP36 (depoKP36, from the Siphoviridae family. To gain insights into the catalytic and structural features of depoKP36, we have recombinantly produced this protein of 93.4 kDa and showed that it is able to hydrolyze a crude exopolysaccharide of a K. pneumoniae host. Using in vitro and in vivo assays, we found that depoKP36 was also effective against a native capsule of clinical K. pneumoniae strains, representing the K63 type, and significantly inhibited Klebsiella-induced mortality of Galleria mellonella larvae in a time-dependent manner. DepoKP36 did not affect the antibiotic susceptibility of Klebsiella strains. The activity of this enzyme was retained in a broad range of pH values (4.0–7.0 and temperatures (up to 45 °C. Consistently, the circular dichroism (CD spectroscopy revealed a highly stability with melting transition temperature (Tm = 65 °C. In contrast to other phage tailspike proteins, this enzyme was susceptible to sodium dodecyl sulfate (SDS denaturation and proteolytic cleavage. The structural studies in solution showed a trimeric arrangement with a high β-sheet content. Our findings identify depoKP36 as a suitable candidate for the development of new treatments for K. pneumoniae infections.
Majkowska-Skrobek, Grażyna; Łątka, Agnieszka; Berisio, Rita; Maciejewska, Barbara; Squeglia, Flavia; Romano, Maria; Lavigne, Rob; Struve, Carsten; Drulis-Kawa, Zuzanna
2016-01-01
The rise of antibiotic-resistant Klebsiella pneumoniae, a leading nosocomial pathogen, prompts the need for alternative therapies. We have identified and characterized a novel depolymerase enzyme encoded by Klebsiella phage KP36 (depoKP36), from the Siphoviridae family. To gain insights into the catalytic and structural features of depoKP36, we have recombinantly produced this protein of 93.4 kDa and showed that it is able to hydrolyze a crude exopolysaccharide of a K. pneumoniae host. Using in vitro and in vivo assays, we found that depoKP36 was also effective against a native capsule of clinical K. pneumoniae strains, representing the K63 type, and significantly inhibited Klebsiella-induced mortality of Galleria mellonella larvae in a time-dependent manner. DepoKP36 did not affect the antibiotic susceptibility of Klebsiella strains. The activity of this enzyme was retained in a broad range of pH values (4.0–7.0) and temperatures (up to 45 °C). Consistently, the circular dichroism (CD) spectroscopy revealed a highly stability with melting transition temperature (Tm) = 65 °C. In contrast to other phage tailspike proteins, this enzyme was susceptible to sodium dodecyl sulfate (SDS) denaturation and proteolytic cleavage. The structural studies in solution showed a trimeric arrangement with a high β-sheet content. Our findings identify depoKP36 as a suitable candidate for the development of new treatments for K. pneumoniae infections. PMID:27916936
Ihn, Hye Jung; Lee, Doohyun; Lee, Taeho; Shin, Hong-In; Bae, Yong Chul; Kim, Sang-Hyun; Park, Eui Kyun
2015-12-01
The triazole family of compounds has been implicated in modulating various biological processes such as inflammation, tumorigenesis, and infection. To our knowledge, this is the first study to demonstrate the effects of 1,2,3-triazole substituted biarylacrylonitrile compounds, including KP-A021, on the differentiation and function of osteoclasts. KP-A021 and its triazole derivatives, at a concentration that does not cause a cytotoxic response in bone marrow macrophages (BMMs), significantly inhibited osteoclast differentiation induced by receptor activator of nuclear factor-κB ligand (RANKL) and macrophage colony-stimulating factor (M-CSF) as assessed by tartrate-resistant acid phosphatase (TRAP) staining. KP-A021 also dramatically inhibited the expression of marker genes associated with osteoclast differentiation, such as TRAP, cathepsin K (Cat K), dendritic cell-specific transmembrane protein (DC-STAMP), and nuclear factor of activated T-cells, cytoplasmic 1 (NFATc1). Furthermore, KP-A021 inhibited actin ring formation in osteoclasts as well as resorption pit formation induced by osteoclasts. Analysis of the signaling pathway for KP-A021 indicated that this triazole compound inhibited the RANKL-induced activation of extracellular signal-regulated kinase (ERK) and its upstream signaling molecule, mitogen-activated protein kinase kinase1/2 (MEK1/2). Taken together, these results demonstrate that KP-A021 has an inhibitory effect on the differentiation and function of osteoclasts via modulation of the RANKL-induced activation of the MEK-ERK pathway.
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
The main reason why the application of nuclear technology in petroleum exploration has not yet been accepted by most exploration workers is that they are not clear about the homologous distribution features of oil and gas fields and radioactive radiation. The authors hold that the disequilibrium of uranium, radium and radon as a natural radioactive series is the basic feature in the use of this technology in petroleum exploration. The invention Gamma-ray Spectral Measurement of the Equilibium Coefficient Kp and Its Embodiment of the senior author now can readily solve that problem and replace the impedient measure of normalization of uranium and potassium to thorium that had to be proposed before. Application of this impedient measure has some limitations. In areas where the surface is covered by beach or river sands, thorium minerals such as monazite may be concentrated by placering. This could result in local thorium highs that would yield local uranium and potassium lows after normalization to thorium, and these would constitute false anomalies.This paper elucidates the relation between the equilibrium coefficient Kp and petroleum exploration and points out that immediately over petroleum the radioactive equilibrium is biased with uranium, while at peripheries of the petroleum reservoir the equilibrium is biased with radium; therefore, the true uranium content immediately over petroleum is not lower but higher, and by constrast the uranium content at peripheries of the petroleum reservoir is not higher but lower. This paper further introduces the main technical requirements for the instrument used in petroleum exploration with nuclear technology and the design basis and work procedure of the petroleum-field effective equilibrium coefficient ground detector and finally introduces the applicability of the detector in petroleum exploration through the distribution features of the equilibrium coefficient Kp of five types of trap-type petroleum deposits.
A three-dimensional k-ε-kp model in curvilinear coordinates for sediment movement and bed evolution
Institute of Scientific and Technical Information of China (English)
SHEN YongMing; LIU Cheng
2009-01-01
To aim at the substitution of the magnitude and direction of water flow movement near bed for those of bed load transport in solid-liquid two-phase one-fluid model, and to simulate the effect of secondary flow on transverse bed load transport in channel bends and the effect of bed slope on bed load transport in a better way, a three-dimensional k-ε-kp solid-liquid two-phase two-fluid model in curvilinear coordinates is solved numerically with a finite-volume method on an adaptive grid for studying water-sediment movements and bed evolution in a 120° channel bend. Numerical results show that the trajectories of solid-phase deviate from those of liquid-phase in the channel bend, and the deviation increases with the increase of the particle diameters. The calculated bed deformation by the k-ε-kpmodel is in better agreement with measured bed deformation than those by one-fluid model. It is proved that the k-ε-kp model can simulate the effect of secondary flow on lateral bed load transport with the higher accuracy than the one-fluid model.
Md Sidek, Nurul Lyana; Tan, Joo Shun; Abbasiliasi, Sahar; Wong, Fadzlie Wong Faizal; Mustafa, Shuhaimi; Ariff, Arbakariya B
2016-08-01
An aqueous two-phase flotation (ATPF) system based on polyethylene glycol (PEG) and sodium citrate (NaNO3C6H5O7·2H2O) was considered for primary recovery of bacteriocin-like inhibitory substance (BLIS) from Pediococcus acidilactici Kp10. The effects of ATPF parameters namely phase composition, tie-line length (TLL), volume ratio between the two phases (VR), amount of crude load (CL), pH, nitrogen gas flow rate (FR) and flotation time (FT) on the performance of recovery were evaluated. BLIS was mainly concentrated into the upper PEG-rich phase in all systems tested so far. The optimum conditions for BLIS purification, which composed of PEG 8000/sodium citrate, were: TLL of 42.6, VR of 0.4, CL of 22% (w/w), pH 7, average FT of 30min and FR of 20mL/min. BLIS was partially purified up to 5.9-fold with a separation efficiency of 99% under this optimal conditions. A maximum yield of BLIS activity of about 70.3% was recovered in the PEG phase. The BLIS from the top phase was successfully recovered with a single band in SDS-gel with molecular weight of about 10-15kDa. ATPF was found to be an effective technique for the recovery of BLIS from the fermentation broth of P. acidilactici Kp10.
Abenda, Simonetta
2017-09-01
We continue the program started in Abenda and Grinevich (2015) of associating rational degenerations of M-curves to points in GrTNN(k , n) using KP theory for real finite gap solutions. More precisely, we focus on the inverse problem of characterizing the soliton data which produce Krichever divisors compatible with the KP reality condition when Γ is a certain rational degeneration of a hyperelliptic M-curve. Such choice is motivated by the fact that Γ is related to the curves associated to points in GrTP(1 , n) and in GrTP(n - 1 , n) in Abenda and Grinevich (2015). We prove that the reality condition on the Krichever divisor on Γ singles out a special family of KP multi-line solitons (T-hyperelliptic solitons) in GrTP(k , n) , k ∈ [ n - 1 ] , naturally connected to the finite non-periodic Toda hierarchy. We discuss the relations between the algebraic-geometric description of KP T-hyperelliptic solitons and of the open Toda system. Finally, we also explain the effect of the space-time transformation which conjugates soliton data in GrTP(k , n) to soliton data in GrTP(n - k , n) on the Krichever divisor for such KP solitons.
Institute of Scientific and Technical Information of China (English)
黄杜煜; 张振峰; 张立武
2012-01-01
User's private key revocation is crucial to the practical use of ABE. The existing ABE schemes supporting user's private key revocation could revoke user's private key by introducing the concept of the user's identity and revoking user's identity. But the security of these schemes could only reach selective security. Based on the idea of the existing schemes, we construct an adaptively secure KP-ABE scheme supporting user's private key revocation on composite order bilinear groups by combining Lewko's adaptively secure ABE scheme and Leyou Zhang's adaptively secure identity-based broadcast encryption scheme.%用户私钥撤销是基于属性的加密(Attribute Based Encryption,ABE)方案在实际应用中所必需解决的问题.现有的支持用户私钥撤销的ABE方案通过引入用户身份的概念,以撤销用户身份的方式实现了对用户私钥的撤销,但其安全性只能达到选择性安全.本文借鉴已有方案的思想,通过将Lewko等人提出的适应性安全ABE方案与Leyou Zhang提出的适应性安全基于身份的组播加密方案相结合,利用双系统加密技术,在合数阶双线性群上实现了一个适应性安全的支持对用户私钥进行撤销的KP-ABE方案.
Inclusive production of π0-mesons in π p, Kp and γ p collisions at energies around 100 GeV
Apsimon, R. J.; Atkinson, M.; Baake, M.; Bagdasarian, L. S.; Barberis, D.; Brodbeck, T. J.; Brook, N.; Charity, T.; Clegg, A. B.; Coyle, P.; Danaher, S.; Danagulian, S.; Davenport, M.; Dickinson, B.; Diekmann, B.; Donnachie, A.; Doyle, A. T.; Eades, J.; Ellison, R. J.; Flower, P. S.; Foster, J. M.; Galbraith, W.; Galumian, P. I.; Gapp, C.; Gebert, F.; Hallewell, G.; Heinloth, K.; Henderson, R. C. W.; Hickman, M. T.; Hoeger, C.; Holzkamp, A.; Holzkamp, S.; Hughes-Jones, R. E.; Ibbotson, M.; Jakob, H. P.; Joseph, D.; Keemer, N. R.; Kingler, J.; Koersgen, G.; Kolya, S. D.; Lafferty, G. D.; McCann, H.; McClatchey, R.; McManus, C.; Mercer, D.; Morris, J. A. G.; Morris, J. V.; Newton, D.; O'Connor, A.; Oedingen, R.; Oganesian, A. G.; Ottewell, P. J.; Paterson, C. N.; Paul, E.; Reid, D.; Rotscheidt, H.; Sharp, P. H.; Soeldner-Rembold, S.; Thacker, N. A.; Thompson, L.; Thompson, R. J.; Waterhouse, J.; Weigend, A. S.; Wilson, G. W.
1991-09-01
Measurements are reported of inclusive production of π0-mesons in the beam fragmentation region in γ p, π p and Kp collisions. Results include the ratio of π0 production in Kp and π p collisions, showing reduced production from fragmentation of the K-meson, and the ratio of π0 production in photon and hadron collisions which shows agreement with modified Vector Meson Dominance at low P T , and departures at higher P T signalling the onset of direct photon reactions. The pattern of departure from Feynman scaling at high P T points to a contribution of hard parton-parton collisions in both γ p and π p collisions.
Energy Technology Data Exchange (ETDEWEB)
Anjan Kumar, V., E-mail: anjankumar.nitw@gmail.com; Pendyala, Naresh Babu; Banerjee, Arup [Sensor Development Area, Space Applications Centre, ISRO, Ahmedabad 380015, Gujarat (India)
2014-11-28
Conduction band energy levels in quantum-dot-in-a-well structures are computed by eight band k.p method (Burt-Foreman Hamiltonian) using finite element software. Optical absorption spectrum due to intersubband transitions is simulated using Fermi golden rule. The use of contact pair boundary condition in strain calculation and criteria for choosing band mixing parameter (E{sub p}) to avoid the spurious solutions are examined in this paper. The simulated intersubband optical absorption spectrum of different structures reported in the literature is in close agreement with the experimentally measured photoconductive absorption region and shows that the method can be used as an effective modeling for quick design of the heterostructures based infrared photodetectors for various wavelengths.
Magnus, Wilhelm
2004-01-01
The hundreds of applications of Hill's equation in engineering and physics range from mechanics and astronomy to electric circuits, electric conductivity of metals, and the theory of the cyclotron. New applications are continually being discovered and theoretical advances made since Liapounoff established the equation's fundamental importance for stability problems in 1907. Brief but thorough, this volume offers engineers and mathematicians a complete orientation to the subject.""Hill's equation"" connotes the class of homogeneous, linear, second order differential equations with real, period
Numerical solution of multiband k.p model for tunnelling in type-II heterostructures
Directory of Open Access Journals (Sweden)
A.E. Botha
2010-01-01
Full Text Available A new and very general method was developed for calculating the charge and spin-resolved electron tunnelling in type-II heterojunctions. Starting from a multiband k.p description of the bulk energy-band structure, a multiband k.p Riccati equation was derived. The reflection and transmission coefficients were obtained for each channel by integrating the Riccati equation over the entire heterostructure. Numerical instability was reduced through this method, in which the multichannel log-derivative of the envelope function matrix, rather than the envelope function itself, was propagated. As an example, a six-band k.p Hamiltonian was used to calculate the current-voltage characteristics of a 10-nm wide InAs/ GaSb/InAs single quantum well device which exhibited negative differential resistance at room temperature. The calculated current as a function of applied (bias voltage was found to be in semiquantitative agreement with the experiment, a result which indicated that inelastic transport mechanisms do not contribute significantly to the valley currents measured in this particular device.
Albers-Wolthers, C H J; de Gier, J; Rutten, V P M G; van Kooten, P J S; Leegwater, P A J; Schaefers-Okkens, A C; Kooistra, H S
2016-01-01
Kisspeptin (KP) plays a key role in the regulation of the hypothalamic-pituitary-gonadal axis via the release of GnRH. As normal KP signaling is essential for reproductive function, it could be an interesting new target for therapeutic interventions, e.g., nonsurgical contraception in dogs. The aims
Inclusive production of η-mesons in π p, Kp and γ p collisions at energies around 100 GeV
Apsimon, R. J.; Atkinson, M.; Baake, M.; Bagdasarian, L. S.; Barberis, D.; Brodbeck, T. J.; Brook, N.; Charity, T.; Clegg, A. B.; Coyle, P.; Danaher, S.; Danagulian, S.; Davenport, M.; Dickinson, B.; Diekmann, B.; Donnachie, A.; Doyle, A. T.; Eades, J.; Ellison, R. J.; Flower, P. S.; Foster, J. M.; Galbraith, W.; Galumian, P. I.; Gapp, C.; Gebert, F.; Hallewell, G.; Heinloth, K.; Henderson, R. C. W.; Hickman, M. T.; Hoeger, C.; Holzkamp, A.; Holzkamp, S.; Hughes-Jones, R. E.; Ibbotson, M.; Jakob, H. P.; Joseph, D.; Keemer, N. R.; Kingler, J.; Koersgen, G.; Kolya, S. D.; Lafferty, G. D.; McCann, H.; McClatchey, R.; McManus, C.; Mercer, D.; Morris, J. A. G.; Morris, J. V.; Newton, D.; O'Connor, A.; Oedingen, R.; Oganesian, A. G.; Ottewell, P. J.; Paterson, C. N.; Paul, E.; Reid, D.; Rotscheidt, H.; Sharp, P. H.; Soeldner-Rembold, S.; Thacker, N. A.; Thompson, L.; Thompson, R. J.; Waterhouse, J.; Weigend, A. S.; Wilson, G. W.
1992-06-01
Measurements are reported of inclusive production of η-mesons in the beam fragmentation region in γ p, π p and Kp collisions. Results include a small but significant departure from VMD, and a pronounced rise in the η/ π 0 ratio with increasing p T .
Directory of Open Access Journals (Sweden)
Abbasiliasi Sahar
2012-11-01
Full Text Available Abstract Background Lactic acid bacteria (LAB can be isolated from traditional milk products. LAB that secrete substances that inhibit pathogenic bacteria and are resistant to acid, bile, and pepsin but not vancomycin may have potential in food applications. Results LAB isolated from a range of traditional fermented products were screened for the production of bacteriocin-like inhibitory substances. A total of 222 LAB strains were isolated from fermented milk products in the form of fresh curds, dried curds, and ghara (a traditional flavor enhancer prepared from whey, and fermented cocoa bean. Eleven LAB isolates that produced antimicrobial substances were identified as Lactococcus lactis, Lactobacillus plantarum, and Pediococcus acidilactici strains by biochemical methods and 16S rDNA gene sequencing. Of these, the cell-free supernatant of Kp10 (P. acidilactici most strongly inhibited Listeria monocytogenes. Further analysis identified the antimicrobial substance produced by Kp10 as proteinaceous in nature and active over a wide pH range. Kp10 (P. acidilactici was found to be catalase-negative, able to produce β-galactosidase, resistant to bile salts (0.3% and acidic conditions (pH 3, and susceptible to most antibiotics. Conclusion Traditionally prepared fermented milk products are good sources of LAB with characteristics suitable for industrial applications. The isolate Kp10 (P. acidilactici shows potential for the production of probiotic and functional foods.
Indian Academy of Sciences (India)
M Mirzazadeh; M Eslami
2013-12-01
Studying compactons, solitons, solitary patterns and periodic solutions is important in nonlinear phenomena. In this paper we study nonlinear variants of the Kadomtsev–Petviashvili (KP) and the Korteweg–de Vries (KdV) equations with positive and negative exponents. The functional variable method is used to establish compactons, solitons, solitary patterns and periodic solutions for these variants. This method is a powerful tool for searching exact travelling solutions in closed form.
Indian Academy of Sciences (India)
Aiyong Chen; Zhongjun Ma
2008-07-01
By applying the bifurcation theory of dynamical system to the generalized KP-BBM equation, the phase portraits of the travelling wave system are obtained. It can be shown that singular straight line in the travelling wave system is the reason why smooth periodic waves converge to periodic cusp waves. Under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are given. Some exact explicit parametric representations of the above waves are obtained.
Moiseiwitsch, B L
2005-01-01
Two distinct but related approaches hold the solutions to many mathematical problems--the forms of expression known as differential and integral equations. The method employed by the integral equation approach specifically includes the boundary conditions, which confers a valuable advantage. In addition, the integral equation approach leads naturally to the solution of the problem--under suitable conditions--in the form of an infinite series.Geared toward upper-level undergraduate students, this text focuses chiefly upon linear integral equations. It begins with a straightforward account, acco
Directory of Open Access Journals (Sweden)
Lloyd K. Williams
1987-01-01
Full Text Available In this paper we find closed form solutions of some Riccati equations. Attention is restricted to the scalar as opposed to the matrix case. However, the ones considered have important applications to mathematics and the sciences, mostly in the form of the linear second-order ordinary differential equations which are solved herewith.
Prentis, Jeffrey J.
1996-05-01
One of the most challenging goals of a physics teacher is to help students see that the equations of physics are connected to each other, and that they logically unfold from a small number of basic ideas. Derivations contain the vital information on this connective structure. In a traditional physics course, there are many problem-solving exercises, but few, if any, derivation exercises. Creating an equation poem is an exercise to help students see the unity of the equations of physics, rather than their diversity. An equation poem is a highly refined and eloquent set of symbolic statements that captures the essence of the derivation of an equation. Such a poetic derivation is uncluttered by the extraneous details that tend to distract a student from understanding the essential physics of the long, formal derivation.
Energy Technology Data Exchange (ETDEWEB)
Young, C.W. [Applied Research Associates, Inc., Albuquerque, NM (United States)
1997-10-01
In 1967, Sandia National Laboratories published empirical equations to predict penetration into natural earth materials and concrete. Since that time there have been several small changes to the basic equations, and several more additions to the overall technique for predicting penetration into soil, rock, concrete, ice, and frozen soil. The most recent update to the equations was published in 1988, and since that time there have been changes in the equations to better match the expanding data base, especially in concrete penetration. This is a standalone report documenting the latest version of the Young/Sandia penetration equations and related analytical techniques to predict penetration into natural earth materials and concrete. 11 refs., 6 tabs.
Kamano, Hiroyuki
2016-01-01
We report our recent effort for the extraction of resonance parameters (complex pole mass and residues etc.) associated with Lambda* and Sigma* hyperons. This was accomplished via a comprehensive partial-wave analysis of the data for K^- p --> barK N, pi Sigma, pi Lambda, eta Lambda, K Xi reactions from the thresholds up to W=2.1 GeV within a dynamical coupled-channels approach. The results suggest a possible existence of new narrow J^P=3/2^+ \\Lambda resonance with pole mass 1671^{+2}_{-8} -i(5^{+11}_{-2}) MeV, located close to the eta Lambda threshold. This resonance is found to be responsible for reproducing the data for K^-p --> eta Lambda differential cross sections near the threshold, and thus the data seem favor its existence. The extracted poles for J^P=1/2^- Lambda resonances below the barK N threshold, including Lambda(1405), are also presented.
Energy Technology Data Exchange (ETDEWEB)
Sivakumar, B.; Mohan, R. [Preidency College, Bangalore (India); Raj, S. Gokul [RR and Dr. SR Technical Univ., Avadi (India); Kumar, G. Ramesh [Anna Univ., Arni (India)
2012-11-15
Single crystals of lithium potassium phthalate (LiKP) were successfully grown from aqueous solution by solvent evaporation technique. The grown crystals were characterized by single crystal X-ray diffraction. The lithium potassium phthalate C{sub 16} H{sub 12} K Li{sub 3} O{sub 11} belongs to triclinic system with the following unit-cell dimensions at 298(2) K; a = 7.405(5) A; b = 9.878(5) A; c = 13.396(5) A; α = 71.778(5) .deg.; β = 87.300(5) .deg.; γ = 85.405(5) .deg.; having a space group P1. Mass spectrometric analysis provides the molecular weight of the compound and possible ways of fragmentations occurs in the compound. Thermal stability of the crystal was also studied by both simultaneous TGA/DTA analyses. The UV-Vis-NIR spectrum shows a good transparency in the whole of Visible and as well as in the near IR range. Third order nonlinear optical studies have also been studied by Z-scan technique. Nonlinear absorption and nonlinear refractive index were found out and the third order bulk susceptibility of compound was also estimated.
Tricomi, FG
2013-01-01
Based on his extensive experience as an educator, F. G. Tricomi wrote this practical and concise teaching text to offer a clear idea of the problems and methods of the theory of differential equations. The treatment is geared toward advanced undergraduates and graduate students and addresses only questions that can be resolved with rigor and simplicity.Starting with a consideration of the existence and uniqueness theorem, the text advances to the behavior of the characteristics of a first-order equation, boundary problems for second-order linear equations, asymptotic methods, and diff
Barbu, Viorel
2016-01-01
This textbook is a comprehensive treatment of ordinary differential equations, concisely presenting basic and essential results in a rigorous manner. Including various examples from physics, mechanics, natural sciences, engineering and automatic theory, Differential Equations is a bridge between the abstract theory of differential equations and applied systems theory. Particular attention is given to the existence and uniqueness of the Cauchy problem, linear differential systems, stability theory and applications to first-order partial differential equations. Upper undergraduate students and researchers in applied mathematics and systems theory with a background in advanced calculus will find this book particularly useful. Supplementary topics are covered in an appendix enabling the book to be completely self-contained.
Institute of Scientific and Technical Information of China (English)
张辉; 蔡兆斌
2006-01-01
研究并比较了皇竹草Soda-AQ与KP-AQ法蒸煮制浆综合性能,得出了两种蒸煮方法主要蒸煮工艺参数用碱量A、最高温度C、保温时间T、硫化度S与浆料得率Y和卡伯价K间的回归方程.较佳蒸煮条件和结果分别为A17%、C158℃、T20min、Y49.96%、K15.2和A18%、C160℃、T30min、S15%、Y51.54%、K13.9;两种浆CEpH法均能漂至白度＞82%ISO;蒸煮、漂白浆料纤维长度分布小于等于100目的＞80%～85%;打浆度43、42°SR时,撕裂指数7.5、7.2mN·m2/g,耐破指数3.28、3.10kPa·m2/g,裂断长5.22、5.17km;两种蒸煮方法均较好地适用于皇竹草,但综合前者更优.
Shen, Zhongyin; Ai, Yinshuang; He, Yumei; Jiang, Mingming
2016-03-01
We collected 177 pre-critical PKiKP-PcP records, assembling a wealth of traveltime and amplitude data. These observations sample the inner core boundary (ICB) beneath East Asia with good spatial coverage. Combined with previous studies, our results demonstrate a 100-km-wide anomaly with positive PKiKP-PcP traveltime residuals surrounded by negatives beneath the Yellow Sea area (123°E, 33°N) (Yellow Sea anomaly). After correcting the elliptic effects and mantle Vp heterogeneities based on the tomography models, the residuals of the Yellow Sea anomaly remain at least 0.6 s faster than those of the surrounding areas, suggesting a thickening of 2-3 km between the ICB and core mantle boundary (CMB). Due to the negative CMB topography along the western Pacific rim, we attribute this anomaly mainly to negative ICB topography. Across the northern border of the Yellow Sea anomaly, PKiKP/PcP amplitude ratios increase by approximately 50% from north to south, which can be explained by an approximately 0.6 g/cm3 raise in ICB density contrast. These traveltime and amplitude features suggest a mosaic structure at the ICB beneath the Yellow Sea areas.
On tau-functions of Zakharov-Shabat and other matrix hierarchies of integrable equations
Dickey, L A
1995-01-01
Matrix hierarchies are: multi-component KP, general Zakharov-Shabat (ZS) and its special cases, e.g., AKNS. The ZS comprises all integrable systems having a form of zero-curvature equations with rational dependence of matrices on a spectral parameter. The notion of a \\tau-function is introduced here in the most general case along with formulas linking \\tau-functions with wave Baker functions. The method originally invented by Sato et al. for the KP hierarchy is used. This method goes immediately from definitions and does not require any assumption about the character of a solution, being the most general. Applied to the matrix hierarchies, it involves considerable sophistication. The paper is self-contained and does not expect any special prerequisite from a reader.
Brick, D H; Shapiro, A M; Widgoff, M; Ansorge, Rainer E; Carter, J R; Neale, William W; Rushbrooke, John G; Ward, D R; Whyman, B M; Burnstein, R A; Rubin, H A; Cooper, J W; Snyder, A; Alyea, E D; Bachman, L; Chien, C Y; Lucas, P; Pevsner, A; Bober, J T; Elahi, M; Frank, T; Hafen, E S; Haridas, P; Hochman, D; Huang, D; Hulsizer, R I; Kistiakowsky, V; Levy, A; Lutz, P; Oh, S; Pless, I A; Stoughton, T B; Suchorebrow, V; Tether, S; Trepagnier, P C; Wu, Y; Yamamoto, R K; Grard, F; Hanton, J; Henri, V; Herquet, P; Lesceux, J M; Windmolders, R; Crijns, F; De Bock, H; Kittel, E W; Metzger, W J; Pols, C L A; Schouten, M M; Van de Walle, R T; Cohn, H O
1980-01-01
Double pomeron exchange in the reactions pp --> pppi$^{+}$pi$^{-}$, K$^{+}$p --> K$^{+}$ppi$^{+}$pi$^{-}$, pi$^{+}$p --> pi$^{+}$ppi$^{+}$pi$^{-}$ and pi$^{-}$p --> pi$^{-}$ppi$^{+}$pi$^{-}$ at 147 GeV/c
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
A generalized variable-coefficient algebraic method is applied to construct several new families of exact solutions of physical interestfor (3+1)-dimensional Kadomtsev-Petviashvilli (KP) equation. Among them, the Jacobi elliptic periodic solutions exactly degenerate to the soliton solutions at a certain limit condition. Compared with the existing tanh method, the extended tanh method, the Jacobi elliptic function method, and the algebraic method, the proposed method gives new and more general solutions.
National Oceanic and Atmospheric Administration, Department of Commerce — METAR is a routine scheduled observation and is the primary observation code used in the United States to satisfy requirements for reporting surface meteorological...
National Oceanic and Atmospheric Administration, Department of Commerce — METAR is a routine scheduled observation and is the primary observation code used in the United States to satisfy requirements for reporting surface meteorological...
National Oceanic and Atmospheric Administration, Department of Commerce — METAR is a routine scheduled observation and is the primary observation code used in the United States to satisfy requirements for reporting surface meteorological...
National Oceanic and Atmospheric Administration, Department of Commerce — METAR is a routine scheduled observation and is the primary observation code used in the United States to satisfy requirements for reporting surface meteorological...
Institute of Scientific and Technical Information of China (English)
陶玉杰; 王宏志; 王贵君
2015-01-01
Researching on the approximation of fuzzy system to integrable function class by means of the integral norm (a metric)is one method of common concern to the people.The Kp-integral norm induced by the K-quasi-arithmetic operations is not only a generalization for a one dimensional integral norm,but also an important tool to describe the p-integrable function classes.In this paper,the Kp-integral norm is redefined by introducing the quasi-subtraction operator.In the sense of the Kp-integral norm,the approximation of the piecewise linear functions to a kind of ^μp-integrable functions is discussed.Then,we prove constructively that the generalized Mamdani fuzzy system has the approximation to a class of ^μp-integrable functions.Finally,by a practical example the approximation effect of the generalized Mamdani fuzzy systems is illustrated.The results show that the generalized Mamdani fuzzy system can approximate a kind of ^μp-integrable functions to arbitrary accuracy.%利用积分模（度量）研究模糊系统对可积函数类的逼近性是人们普遍关注的方法，而基于 K-拟算术运算诱导的 Kp-积分模不仅是一维积分模的推广，而且是刻画 p-次可积函数类的重要工具。本文通过引入拟减运算重新定义 Kp-积分模，且在 Kp-积分模意义下讨论分片线性函数对一类＾μp-可积函数的逼近性，进而构造性地证明广义Mamdani 模糊系统对＾μp-可积函数类仍有逼近性。最后通过实例分析说明广义 Mamdani 模糊系统的逼近效果。结果表明广义 Mamdani 模糊系统可以按任意精度逼近一类＾μp-可积函数。
Tricomi, Francesco Giacomo
1957-01-01
This classic text on integral equations by the late Professor F. G. Tricomi, of the Mathematics Faculty of the University of Turin, Italy, presents an authoritative, well-written treatment of the subject at the graduate or advanced undergraduate level. To render the book accessible to as wide an audience as possible, the author has kept the mathematical knowledge required on the part of the reader to a minimum; a solid foundation in differential and integral calculus, together with some knowledge of the theory of functions is sufficient. The book is divided into four chapters, with two useful
Stochastic partial differential equations
Chow, Pao-Liu
2014-01-01
Preliminaries Introduction Some Examples Brownian Motions and Martingales Stochastic Integrals Stochastic Differential Equations of Itô Type Lévy Processes and Stochastic IntegralsStochastic Differential Equations of Lévy Type Comments Scalar Equations of First Order Introduction Generalized Itô's Formula Linear Stochastic Equations Quasilinear Equations General Remarks Stochastic Parabolic Equations Introduction Preliminaries Solution of Stochastic Heat EquationLinear Equations with Additive Noise Some Regularity Properties Stochastic Reaction-Diffusion Equations Parabolic Equations with Grad
Ferrari, Luca; Borghetti, Paolo; Ferrarini, Giulia; De Angelis, Elena; Canelli, Elena; Ogno, Giulia; Catella, Alessia; Ciociola, Tecla; Magliani, Walter; Martelli, Paolo
2016-12-01
An engineered killer peptide (KP) based on a recombinant anti-idiotypic antibody representing the functional image of a yeast killer toxin (KT) was demonstrated to mediate antimicrobial effects against fungi and viruses. KP binds to murine dendritic cells and macrophages and up-regulate co-receptor expression, thus sustaining CD4+ lymphocyte activation. No immunological data are available in domestic animals thus KP-induced immunomodulation was evaluated in porcine monocyte and lymphocyte subsets. PBMC from healthy adult pigs were stimulated with KP or a scramble peptide (SP), or kept unstimulated for 24, 48 and 72h, and subsequently analyzed by flow cytometry. In monocytes, KP induced a strong dose-dependent shift from a major fraction of CD172α+CD14+(low) cells to a predominant fraction of CD172α+CD14+(high) cells, known to sustain leukocyte activation/differentiation and inflammatory responses. The CD16+ cell percentages, specifically the CD3+CD16+ natural killer T (NKT) cell fraction and CD16 expression showed an intense and stable dose-dependent increase while the CD3-CD16+ NK cell fraction decreased. CD4+ and CD8+ T cells increased and CD8α and CD8β expression were up-regulated. CD8β+ cytotoxic T cells and CD16+ cells comparably increased. A marked stimulation of activated CD16+CD25+ and CD8β+CD25+ cells was observed at 24h. The increase of CD8α+ cells and CD8α expression were due to increased CD4+CD8α+ (memory T helper) cells, also showing a CD8α+(high) phenotype. Concomitantly, the CD4+CD8α- T helper lymphocyte fraction significantly decreased. Overall, KP induced a wide modulation of innate immune and T cells that can exert regulatory and cytotoxic functions, which are fundamental for an efficient Th1 response. Copyright © 2016 Elsevier Ltd. All rights reserved.
Institute of Scientific and Technical Information of China (English)
bibi
2010-01-01
LG机群中有不少经典产品，其中的一些也许没有特别的功能，但是在外观设计方面却往往为人们所称道，其中最著名的就是“巧克力”系列。而KP500是最近一年多LG最受关注的机型之一，它同样继承了LG手机的特点，比较照顾用户的视觉感受，同时它打破了人们对LG热门手机一向价高的印象，成为一款“平易近人”的机型。
Institute of Scientific and Technical Information of China (English)
戴晓明
2016-01-01
基于Gorbunov等人的电路结构下的基于属性的加密(ABE)方案,提出"反复重编码技术".结合该方案与技术,利用Gentry等提出的同态转化机制,设计了一个基于LWE的密钥策略全同态ABE(KP-ABFHE)方案.该方案解决了传统的ABE方案不能够对密文直接进行计算这一功能上的缺陷,在访问结构对应的布尔电路上应用"反复重编码技术",使得电路层结构更清晰.探索了该方案在云存储领域的应用.
KP泥浆在八面石矿区的实际应用与改进%Application and improvement of KP mud of the Bamianshi mining area
Institute of Scientific and Technical Information of China (English)
王坚
2012-01-01
八面石矿区的地层比较复杂,在钻孔施工中,易发生坍塌、掉块、缩径等现象,我们通过对KP泥浆的不断改进,在保证钻孔质量的前提下,有效地控制了孔内事故,提高钻进效率、降低钻进成本。%Stratum of Bamianshi mining area is relative complex,during the drilling construction,it can be collapse,loss,shrinkage phenomenon.We continuously improved the KP mud,with the condition to ensure the borehole quality,effectively controlled the drilling accident,improved the drilling efficiency,and reduced the cost of drilling.
O'Hara, Jessica A.; Hu, Fupin; Ahn, Chulsoo; Nelson, Jeremy; Rivera, Jesabel I.; Pasculle, Anthony W.
2014-01-01
Of 20 Klebsiella pneumoniae carbapenemase (KPC)-producing Escherichia coli isolates identified at hospitals in western Pennsylvania, 60% belonged to the epidemic ST131-fimH30 subclone. IncFIIk was the most common replicon type for the blaKPC-carrying plasmids (n = 8). All IncFIIk plasmids possessed a scaffold similar to that of pKpQIL, and seven of them were borne by ST131-fimH30 isolates. IncN plasmids conferred resistance to trimethoprim-sulfamethoxazole, and IncA/C plasmids conferred resistance to gentamicin. Three blaKPC-carrying plasmids (IncA/C and IncN) possessed blaSHV-7/12 and qnrA1 or qnrS1. PMID:24820082
AyalaÂ Solares, Jose Roberto; Wei, Hua-Liang; Boynton, R. J.; Walker, Simon N.; Billings, Stephen A.
2016-10-01
Severe geomagnetic disturbances can be hazardous for modern technological systems. The reliable forecast of parameters related to the state of the magnetosphere can facilitate the mitigation of adverse effects of space weather. This study is devoted to the modeling and forecasting of the evolution of the Kp index related to global geomagnetic disturbances. Throughout this work the Nonlinear Autoregressive with Exogenous inputs (NARX) methodology is applied. Two approaches are presented: (i) a recursive sliding window approach and (ii) a direct approach. These two approaches are studied separately and are then compared to evaluate their performances. It is shown that the direct approach outperforms the recursive approach, but both tend to produce predictions slightly biased from the true values for low and high disturbances.
Kuhn, Paul-Steffen; Büchel, Gabriel E; Jovanović, Katarina K; Filipović, Lana; Radulović, Siniša; Rapta, Peter; Arion, Vladimir B
2014-10-20
A one-electron reduction of osmium(IV) complexes trans-[Os(IV)Cl4(Hazole)2], where Hazole = 1H-pyrazole ([1](0)), 2H-indazole ([2](0)), 1H-imidazole ([3](0)), and 1H-benzimidazole ([4](0)), afforded a series of eight new complexes as osmium analogues of KP1019, a lead anticancer drug in clinical trials, with the general formula (cation)[trans-Os(III)Cl4(Hazole)2], where cation = H2pz(+) (H2pz[1]), H2ind(+) (H2ind[2]), H2im(+) (H2im[3]), Ph4P(+) (Ph4P[3]), nBu4N(+) (nBu4N[3]), H2bzim(+) (H2bzim[4]), Ph4P(+) (Ph4P[4]), and nBu4N(+) (nBu4N[4]). All complexes were characterized by elemental analysis, (1)H NMR spectroscopy, electrospray ionization mass spectrometry, UV-vis spectroscopy, cyclic voltammetry, while H2pz[1], H2ind[2], and nBu4[3], in addition, by X-ray diffraction. The reduced species [1](-) and [4](-) are stable in aqueous media in the absence of air oxygen and do not react with small biomolecules such as amino acids and the nucleotide 5'-dGMP. Cell culture experiments in five different human cancer cell lines (HeLa, A549, FemX, MDA-MB-453, and LS-174) and one noncancerous cell line (MRC-5) were performed, and the results were discussed and compared to those for KP1019 and cisplatin. Benzannulation in complexes with similar structure enhances antitumor activity by several orders of magnitude, implicating different mechanisms of action of the tested compounds. In particular, complexes H2ind[2] and H2bzim[4] exhibited significant antiproliferative activity in vitro when compared to H2pz[1] and H2im[3].
Modulus-Pressure Equation for Confined Fluids
Gor, Gennady Y; Shen, Vincent K; Bernstein, Noam
2016-01-01
Ultrasonic experiments allow one to measure the elastic modulus of bulk solid or fluid samples. Recently such experiments have been carried out on fluid-saturated nanoporous glass to probe the modulus of a confined fluid. In our previous work [J. Chem. Phys., (2015) 143, 194506], using Monte Carlo simulations we showed that the elastic modulus $K$ of a fluid confined in a mesopore is a function of the pore size. Here we focus on modulus-pressure dependence $K(P)$, which is linear for bulk materials, a relation known as the Tait-Murnaghan equation. Using transition-matrix Monte Carlo simulations we calculated the elastic modulus of bulk argon as a function of pressure and argon confined in silica mesopores as a function of Laplace pressure. Our calculations show that while the elastic modulus is strongly affected by confinement and temperature, the slope of the modulus versus pressure is not. Moreover, the calculated slope is in a good agreement with the reference data for bulk argon and experimental data for ...
Partial Differential Equations
1988-01-01
The volume contains a selection of papers presented at the 7th Symposium on differential geometry and differential equations (DD7) held at the Nankai Institute of Mathematics, Tianjin, China, in 1986. Most of the contributions are original research papers on topics including elliptic equations, hyperbolic equations, evolution equations, non-linear equations from differential geometry and mechanics, micro-local analysis.
Dolgikh, Elena; Watson, Ian A; Desai, Prashant V; Sawada, Geri A; Morton, Stuart; Jones, Timothy M; Raub, Thomas J
2016-11-28
We report development and prospective validation of a QSAR model of the unbound brain-to-plasma partition coefficient, Kp,uu,brain, based on the in-house data set of ∼1000 compounds. We discuss effects of experimental variability, explore the applicability of both regression and classification approaches, and evaluate a novel, model-within-a-model approach of including P-glycoprotein efflux prediction as an additional variable. When tested on an independent test set of 91 internal compounds, incorporation of P-glycoprotein efflux information significantly improves the model performance resulting in an R(2) of 0.53, RMSE of 0.57, Spearman's Rho correlation coefficient of 0.73, and qualitative prediction accuracy of 0.8 (kappa = 0.6). In addition to improving the performance, one of the key advantages of this approach is the larger chemical space coverage provided indirectly through incorporation of the in vitro, higher throughput data set that is 4 times larger than the in vivo data set.
Kinetic energy equations for the average-passage equation system
Johnson, Richard W.; Adamczyk, John J.
1989-01-01
Important kinetic energy equations derived from the average-passage equation sets are documented, with a view to their interrelationships. These kinetic equations may be used for closing the average-passage equations. The turbulent kinetic energy transport equation used is formed by subtracting the mean kinetic energy equation from the averaged total instantaneous kinetic energy equation. The aperiodic kinetic energy equation, averaged steady kinetic energy equation, averaged unsteady kinetic energy equation, and periodic kinetic energy equation, are also treated.
Kinetic energy equations for the average-passage equation system
Johnson, Richard W.; Adamczyk, John J.
1989-01-01
Important kinetic energy equations derived from the average-passage equation sets are documented, with a view to their interrelationships. These kinetic equations may be used for closing the average-passage equations. The turbulent kinetic energy transport equation used is formed by subtracting the mean kinetic energy equation from the averaged total instantaneous kinetic energy equation. The aperiodic kinetic energy equation, averaged steady kinetic energy equation, averaged unsteady kinetic energy equation, and periodic kinetic energy equation, are also treated.
Solving Nonlinear Wave Equations by Elliptic Equation
Institute of Scientific and Technical Information of China (English)
FU Zun-Tao; LIU Shi-Da; LIU Shi-Kuo
2003-01-01
The elliptic equation is taken as a transformation and applied to solve nonlinear wave equations. It is shown that this method is more powerful to give more kinds of solutions, such as rational solutions, solitary wave solutions,periodic wave solutions and so on, so it can be taken as a generalized method.
Institute of Scientific and Technical Information of China (English)
高晶; 徐彬; 郭晓奎; 秦金红
2016-01-01
Multiple drug-resistant Klebsiella pneumonia strains collected from several hospitals in Shanghai were used as the host bacteria to isolate phages in the wastewater .A novel phage KP002 was isolated and analyzed in details .The morphology and size of the bacteriophage was observed by electron microscope with negative staining .The results indicated that it was a tailed phage with head diameter about 70 nm , tail length about 80 nm and tail width about 20 nm . This phage had high activity at pH from 3 to 9 and temperature from 4 to 50 ℃ .The adsorption rate was above 95% within 6 min .Its incubation period was 10 min and burst period was 50 min .The burst size reached 172 pfu/cell .The whole genome sequence showed that it contained a circular double-stranded DNA with a full-length of 47 173 bp and GC content of 48% . KP002 is a new phage against drug-resistant bacteria and could be served as a potential resource for clinical treatment of multiple-drug resistant bacterial infection .%以上海某些医院临床分离到的多重耐药肺炎克雷伯菌为宿主菌 ,从不同环境的污水中分离获得1株肺炎克雷伯菌噬菌体KP002.电子显微镜显示其为有尾噬菌体 ,头部直径约70 nm ,尾长约80 nm ,尾宽约20 nm.对其生物学特性进行研究 ,结果显示此株噬菌体在pH 3~9及4~50 ℃的环境中具有较高活性 ;6 min吸附率达95% 以上 ;潜伏期为10 min ,爆发期为50 min;裂解量为172 pfu/cell.结果表明 ,该噬菌体对pH值和温度适应范围较宽.对其全基因组进行测序分析 ,结果显示其基因组为环状双链 DNA ,全长47 173 bp , GC含量为48% .本研究筛选获得1株对 pH值和温度适应范围较宽的耐药肺炎克雷伯菌烈性噬菌体KP002 ,为建立耐药肺炎克雷伯菌的噬菌体库以用于治疗临床多重耐药菌感染提供了新的思路.
Papagiannitsis, Costas C; Dolejska, Monika; Izdebski, Radoslaw; Dobiasova, Hana; Studentova, Vendula; Esteves, Francisco J; Derde, Lennie P G; Bonten, Marc J M; Hrabák, Jaroslav; Gniadkowski, Marek
2015-08-01
IMP-8 metallo-β-lactamase was identified in Klebsiella pneumoniae sequence type 252 (ST252), isolated in a Portuguese hospital in 2009. blaIMP-8 was the first gene cassette of a novel class 3 integron, In1144, also carrying the blaGES-5, blaBEL-1, and aacA4 cassettes. In1144 was located on a ColE1-like plasmid, pKP-M1144 (12,029 bp), with a replication region of limited nucleotide similarity to those of other RNA-priming plasmids, such as pJHCMW1. In1144 and pKP-M1144 represent an interesting case of evolution of resistance determinants in Gram-negative bacteria.
Introduction to differential equations
Taylor, Michael E
2011-01-01
The mathematical formulations of problems in physics, economics, biology, and other sciences are usually embodied in differential equations. The analysis of the resulting equations then provides new insight into the original problems. This book describes the tools for performing that analysis. The first chapter treats single differential equations, emphasizing linear and nonlinear first order equations, linear second order equations, and a class of nonlinear second order equations arising from Newton's laws. The first order linear theory starts with a self-contained presentation of the exponen
The Modified Magnetohydrodynamical Equations
Institute of Scientific and Technical Information of China (English)
EvangelosChaliasos
2003-01-01
After finding the really self-consistent electromagnetic equations for a plasma, we proceed in a similar fashion to find how the magnetohydrodynamical equations have to be modified accordingly. Substantially this is done by replacing the "Lorentz" force equation by the correct (in our case) force equation. Formally we have to use the vector potential instead of the magnetic field intensity. The appearance of the formulae presented is the one of classical vector analysis. We thus find a set of eight equations in eight unknowns, as previously known concerning the traditional MHD equations.
Indian Academy of Sciences (India)
George F R Ellis
2007-07-01
The Raychaudhuri equation is central to the understanding of gravitational attraction in astrophysics and cosmology, and in particular underlies the famous singularity theorems of general relativity theory. This paper reviews the derivation of the equation, and its significance in cosmology.
Directory of Open Access Journals (Sweden)
Daniella Barreto-Santana
2015-03-01
Materiales y métodos. Se seleccionaron treinta ninfas de cada especie después de xenodiagnóstico artificial en sangre infectada con T. rangeli. Se examinaron periódicamente muestras de heces y hemolinfa. Los insectos con hemolinfas infectadas fueron alimentados en ratones a fin de comprobar la transmisión por picadura y posteriormente disecados para confirmar la infección de las glándulas salivales. Resultados. En Rhodnius pictipes se encontró un mayor porcentaje de infección intestinal que en las otras especies. Se detectaron epimastigotes y tripomastigotes en la hemolinfa de las cuatro especies, y se encontró que el parasitismo fue menor en las especies del linaje R. robustus. Rhodnius robustus y R. neglectus no transmitían T. rangeli a ratones por picadura: después de la disección, sus glándulas no estaban infectadas. Solo un espécimen de R. nasutus y dos de R. pictipes transmitieron el parásito por la picadura. La tasa de infección glandular fue de 16 % para R. pictipes y de 4 % para R. nasutus. Conclusiones. La capacidad infecciosa (hemolinfática, intestinal y glandular y la transmisión de T. rangeli (SC-58/KP1- fueron mayores y más eficientes en R. pictipes. Estos resultados refuerzan la hipótesis de que estos triatominos actúan como filtros biológicos en la transmisión de T. rangeli.
Beginning partial differential equations
O'Neil, Peter V
2014-01-01
A broad introduction to PDEs with an emphasis on specialized topics and applications occurring in a variety of fields Featuring a thoroughly revised presentation of topics, Beginning Partial Differential Equations, Third Edition provides a challenging, yet accessible,combination of techniques, applications, and introductory theory on the subjectof partial differential equations. The new edition offers nonstandard coverageon material including Burger's equation, the telegraph equation, damped wavemotion, and the use of characteristics to solve nonhomogeneous problems. The Third Edition is or
Renormalizing Partial Differential Equations
Bricmont, J.; Kupiainen, A.
1994-01-01
In this review paper, we explain how to apply Renormalization Group ideas to the analysis of the long-time asymptotics of solutions of partial differential equations. We illustrate the method on several examples of nonlinear parabolic equations. We discuss many applications, including the stability of profiles and fronts in the Ginzburg-Landau equation, anomalous scaling laws in reaction-diffusion equations, and the shape of a solution near a blow-up point.
Ordinary differential equations
Greenberg, Michael D
2014-01-01
Features a balance between theory, proofs, and examples and provides applications across diverse fields of study Ordinary Differential Equations presents a thorough discussion of first-order differential equations and progresses to equations of higher order. The book transitions smoothly from first-order to higher-order equations, allowing readers to develop a complete understanding of the related theory. Featuring diverse and interesting applications from engineering, bioengineering, ecology, and biology, the book anticipates potential difficulties in understanding the various solution steps
Energy Technology Data Exchange (ETDEWEB)
Gladysiewicz, M.; Wartak, M. S. [Faculty of Fundamental Problems of Technology, Wroclaw University of Technology, Wybrzeze Wyspianskiego 27, 50-370 Wroclaw (Poland); Department of Physics and Computer Science, Wilfrid Laurier University, Waterloo, Ontario N2L 3C5 (Canada); Kudrawiec, R. [Faculty of Fundamental Problems of Technology, Wroclaw University of Technology, Wybrzeze Wyspianskiego 27, 50-370 Wroclaw (Poland)
2015-08-07
The electronic band structure and material gain have been calculated for GaAsBi/GaAs quantum wells (QWs) with various bismuth concentrations (Bi ≤ 15%) within the 8-band and 14-band kp models. The 14-band kp model was obtained by extending the standard 8-band kp Hamiltonian by the valence band anticrossing (VBAC) Hamiltonian, which is widely used to describe Bi-related changes in the electronic band structure of dilute bismides. It has been shown that in the range of low carrier concentrations n < 5 × 10{sup 18 }cm{sup −3}, material gain spectra calculated within 8- and 14-band kp Hamiltonians are similar. It means that the 8-band kp model can be used to calculate material gain in dilute bismides QWs. Therefore, it can be applied to analyze QWs containing new dilute bismides for which the VBAC parameters are unknown. Thus, the energy gap and electron effective mass for Bi-containing materials are used instead of VBAC parameters. The electronic band structure and material gain have been calculated for 8 nm wide GaInAsBi QWs on GaAs and InP substrates with various compositions. In these QWs, Bi concentration was varied from 0% to 5% and indium concentration was tuned in order to keep the same compressive strain (ε = 2%) in QW region. For GaInAsBi/GaAs QW with 5% Bi, gain peak was determined to be at about 1.5 μm. It means that it can be possible to achieve emission at telecommunication windows (i.e., 1.3 μm and 1.55 μm) for GaAs-based lasers containing GaInAsBi/GaAs QWs. For GaInAsBi/Ga{sub 0.47}In{sub 0.53}As/InP QWs with 5% Bi, gain peak is predicted to be at about 4.0 μm, i.e., at the wavelengths that are not available in current InP-based lasers.
The Modified Magnetohydrodynamical Equations
Institute of Scientific and Technical Information of China (English)
Evangelos Chaliasos
2003-01-01
After finding the really self-consistent electromagnetic equations for a plasma, we proceed in a similarfashion to find how the magnetohydrodynamical equations have to be modified accordingly. Substantially this is doneby replacing the "Lorentz" force equation by the correct (in our case) force equation. Formally we have to use the vectorpotential instead of the magnetic field intensity. The appearance of the formulae presented is the one of classical vectoranalysis. We thus find a set of eight equations in eight unknowns, as previously known concerning the traditional MHDequations.
Singular stochastic differential equations
Cherny, Alexander S
2005-01-01
The authors introduce, in this research monograph on stochastic differential equations, a class of points termed isolated singular points. Stochastic differential equations possessing such points (called singular stochastic differential equations here) arise often in theory and in applications. However, known conditions for the existence and uniqueness of a solution typically fail for such equations. The book concentrates on the study of the existence, the uniqueness, and, what is most important, on the qualitative behaviour of solutions of singular stochastic differential equations. This is done by providing a qualitative classification of isolated singular points, into 48 possible types.
Fractional Differential Equations
Directory of Open Access Journals (Sweden)
Jianping Zhao
2012-01-01
Full Text Available An extended fractional subequation method is proposed for solving fractional differential equations by introducing a new general ansätz and Bäcklund transformation of the fractional Riccati equation with known solutions. Being concise and straightforward, this method is applied to the space-time fractional coupled Burgers’ equations and coupled MKdV equations. As a result, many exact solutions are obtained. It is shown that the considered method provides a very effective, convenient, and powerful mathematical tool for solving fractional differential equations.
PREFACE: Symmetries and Integrability of Difference Equations
Doliwa, Adam; Korhonen, Risto; Lafortune, Stéphane
2007-10-01
to integrability. The first section contains a paper by T Hamamoto and K Kajiwara on hypergeometric solutions to the q-Painlevé equation of type A4(1). Discrete geometry. In this category there are three papers. J Cielinski offers a geometric definition and a spectral approach on pseudospherical surfaces on time scales, while A Doliwa considers generalized isothermic lattices. The paper by U Pinkall, B Springborn and S Weiss mann is concerned with a new doubly discrete analogue of smoke ring flow and the real time simulation of fluid flow. Integrable systems in statistical physics. Under this heading there is a paper by R J Baxter on corner transfer matrices in statistical mechanics, and a paper by S Boukraa, S Hassani, J-M Maillard, B M McCoy, J-A Weil and N Zenine where the authors consider Fuchs-Painlevé elliptic representation of the Painlevé VI equation. KP lattices and differential-difference hierarchies. In this section we have seven articles. C R Gilson, J J C Nimmo and Y Ohta consider quasideterminant solutions of a non-Abelian Hirota-Miwa equation, while B Grammaticos, A Ramani, V Papageorgiou, J Satsuma and R Willox discuss the construction of lump-like solutions of the Hirota-Miwa equation. J Hietarinta and C Viallet analyze the factorization process for lattice maps searching for integrable cases, the paper by X-B Hu and G-F Yu is concerned with integrable discretizations of the (2+1)-dimensional sinh-Gordon equation, and K Kajiwara, M Mazzocco and Y Ohta consider the Hankel determinant formula of the tau-functions of the Toda equation. Finally, V G Papageorgiou and A G Tongas study Yang-Baxter maps and multi-field integrable lattice equations, and H-Y Wang, X-B Hu and H-W Tam consider the two-dimensional Leznov lattice equation with self-consistent sources. Quantum integrable systems. This category contains a paper on q-extended eigenvectors of the integral and finite Fourier transforms by N M Atakishiyev, J P Rueda and K B Wolf, and an article by S
Differential equations for dummies
Holzner, Steven
2008-01-01
The fun and easy way to understand and solve complex equations Many of the fundamental laws of physics, chemistry, biology, and economics can be formulated as differential equations. This plain-English guide explores the many applications of this mathematical tool and shows how differential equations can help us understand the world around us. Differential Equations For Dummies is the perfect companion for a college differential equations course and is an ideal supplemental resource for other calculus classes as well as science and engineering courses. It offers step-by-step techniques, practical tips, numerous exercises, and clear, concise examples to help readers improve their differential equation-solving skills and boost their test scores.
Directory of Open Access Journals (Sweden)
Wei Khim Ng
2009-02-01
Full Text Available We construct nonlinear extensions of Dirac's relativistic electron equation that preserve its other desirable properties such as locality, separability, conservation of probability and Poincaré invariance. We determine the constraints that the nonlinear term must obey and classify the resultant non-polynomial nonlinearities in a double expansion in the degree of nonlinearity and number of derivatives. We give explicit examples of such nonlinear equations, studying their discrete symmetries and other properties. Motivated by some previously suggested applications we then consider nonlinear terms that simultaneously violate Lorentz covariance and again study various explicit examples. We contrast our equations and construction procedure with others in the literature and also show that our equations are not gauge equivalent to the linear Dirac equation. Finally we outline various physical applications for these equations.
Partial differential equations
Evans, Lawrence C
2010-01-01
This text gives a comprehensive survey of modern techniques in the theoretical study of partial differential equations (PDEs) with particular emphasis on nonlinear equations. The exposition is divided into three parts: representation formulas for solutions; theory for linear partial differential equations; and theory for nonlinear partial differential equations. Included are complete treatments of the method of characteristics; energy methods within Sobolev spaces; regularity for second-order elliptic, parabolic, and hyperbolic equations; maximum principles; the multidimensional calculus of variations; viscosity solutions of Hamilton-Jacobi equations; shock waves and entropy criteria for conservation laws; and, much more.The author summarizes the relevant mathematics required to understand current research in PDEs, especially nonlinear PDEs. While he has reworked and simplified much of the classical theory (particularly the method of characteristics), he primarily emphasizes the modern interplay between funct...
Fractional Chemotaxis Diffusion Equations
Langlands, T A M
2010-01-01
We introduce mesoscopic and macroscopic model equations of chemotaxis with anomalous subdiffusion for modelling chemically directed transport of biological organisms in changing chemical environments with diffusion hindered by traps or macro-molecular crowding. The mesoscopic models are formulated using Continuous Time Random Walk master equations and the macroscopic models are formulated with fractional order differential equations. Different models are proposed depending on the timing of the chemotactic forcing. Generalizations of the models to include linear reaction dynamics are also derived. Finally a Monte Carlo method for simulating anomalous subdiffusion with chemotaxis is introduced and simulation results are compared with numerical solutions of the model equations. The model equations developed here could be used to replace Keller-Segel type equations in biological systems with transport hindered by traps, macro-molecular crowding or other obstacles.
Directory of Open Access Journals (Sweden)
K. Banoo
1998-01-01
equation in the discrete momentum space. This is shown to be similar to the conventional drift-diffusion equation except that it is a more rigorous solution to the Boltzmann equation because the current and carrier densities are resolved into M×1 vectors, where M is the number of modes in the discrete momentum space. The mobility and diffusion coefficient become M×M matrices which connect the M momentum space modes. This approach is demonstrated by simulating electron transport in bulk silicon.
Developmental Partial Differential Equations
Duteil, Nastassia Pouradier; Rossi, Francesco; Boscain, Ugo; Piccoli, Benedetto
2015-01-01
In this paper, we introduce the concept of Developmental Partial Differential Equation (DPDE), which consists of a Partial Differential Equation (PDE) on a time-varying manifold with complete coupling between the PDE and the manifold's evolution. In other words, the manifold's evolution depends on the solution to the PDE, and vice versa the differential operator of the PDE depends on the manifold's geometry. DPDE is used to study a diffusion equation with source on a growing surface whose gro...
Differential equations I essentials
REA, Editors of
2012-01-01
REA's Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Differential Equations I covers first- and second-order equations, series solutions, higher-order linear equations, and the Laplace transform.
Ordinary differential equations
Pontryagin, Lev Semenovich
1962-01-01
Ordinary Differential Equations presents the study of the system of ordinary differential equations and its applications to engineering. The book is designed to serve as a first course in differential equations. Importance is given to the linear equation with constant coefficients; stability theory; use of matrices and linear algebra; and the introduction to the Lyapunov theory. Engineering problems such as the Watt regulator for a steam engine and the vacuum-tube circuit are also presented. Engineers, mathematicians, and engineering students will find the book invaluable.
Hazewinkel, M.
1995-01-01
Dedication: I dedicate this paper to Prof. P.C. Baayen, at the occasion of his retirement on 20 December 1994. The beautiful equation which forms the subject matter of this paper was invented by Wouthuysen after he retired. The four complex variable Wouthuysen equation arises from an original space-
Shabat, A. B.
2016-12-01
We consider the class of entire functions of exponential type in relation to the scattering theory for the Schrödinger equation with a finite potential that is a finite Borel measure. These functions have a special self-similarity and satisfy q-difference functional equations. We study their asymptotic behavior and the distribution of zeros.
Dissipative Boussinesq equations
Dutykh, D; Dias, Fr\\'{e}d\\'{e}ric; Dutykh, Denys
2007-01-01
The classical theory of water waves is based on the theory of inviscid flows. However it is important to include viscous effects in some applications. Two models are proposed to add dissipative effects in the context of the Boussinesq equations, which include the effects of weak dispersion and nonlinearity in a shallow water framework. The dissipative Boussinesq equations are then integrated numerically.
Directory of Open Access Journals (Sweden)
Hannelore Breckner
2000-01-01
Full Text Available We consider a stochastic equation of Navier-Stokes type containing a noise part given by a stochastic integral with respect to a Wiener process. The purpose of this paper is to approximate the solution of this nonlinear equation by the Galerkin method. We prove the convergence in mean square.
Differential Equation of Equilibrium
African Journals Online (AJOL)
user
than the classical method in the solution of the aforementioned differential equation. Keywords: ... present a successful approximation of shell ... displacement function. .... only applicable to cylindrical shell subject to ..... (cos. 4. 4. 4. 3 β. + β. + β. -. = β. - β x x e ex. AL. xA w. Substituting equations (29); (30) and (31) into.
Directory of Open Access Journals (Sweden)
Topouchian J
2014-01-01
Full Text Available Jirar Topouchian,1 Davide Agnoletti,1 Jacques Blacher,1 Ahmed Youssef,1 Mirna N Chahine,2,3 Isabel Ibanez,3 Nathalie Assemani,3 Roland Asmar1–31Centre de Diagnostic, Hôpital Hôtel-Dieu, Paris, France; 2Faculty of Medicine of the Lebanese University, 3Foundation-Medical Research Institutes, Beirut, LebanonBackground: Four oscillometric devices, including the Omron M6 Comfort, Omron HEM-7420, Withings BP-800, and Polygreen KP-7670, designed for self-blood pressure measurement (SBPM were evaluated according to the European Society of Hypertension (ESH International Protocol Revision 2010 in four separate studies.Methods: The four devices measure brachial blood pressure (BP using the oscillometric method. The Withings BP-800 has to be connected to an Apple® iOS device such as an iPhone®, iPad®, or iPod®. The ESH International Protocol Revision 2010 includes a total number of 33 subjects. The difference between observer and device BP values was calculated for each measure. Ninety-nine pairs of BP differences were classified into three categories (≤5 mmHg, ≤10 mmHg, ≤15 mmHg. The protocol procedures were followed precisely in each of the four studies.Results: All four tested devices passed the validation process. The mean differences between the device and mercury readings were: −1.8±5.1 mmHg and −0.4±2.8 mmHg for systolic and diastolic BP, respectively, using the Omron M6 Comfort device; 2.5±4.6 mmHg and −1.2±4.3 mmHg for the Omron HEM-7420 device; −0.2±5.0 mmHg and 0.4±4.2 mmHg for the Withings BP-800 device; and 3.0±5.3 mmHg and 0.3±5.2 mmHg for the Polygreen KP-7670 device.Conclusion: Omron M6 Comfort, Omron HEM-7420, Withings BP-800, and Polygreen KP-7670 readings differing by less than 5 mmHg, 10 mmHg, and 15 mmHg fulfill the ESH International Protocol Revision 2010 requirements, and therefore are suitable for use by patients for SBPM, if used correctly.Keywords: Omron M6 Comfort, Omron HEM-7420, Withings BP-800
Applied partial differential equations
Logan, J David
2004-01-01
This primer on elementary partial differential equations presents the standard material usually covered in a one-semester, undergraduate course on boundary value problems and PDEs. What makes this book unique is that it is a brief treatment, yet it covers all the major ideas: the wave equation, the diffusion equation, the Laplace equation, and the advection equation on bounded and unbounded domains. Methods include eigenfunction expansions, integral transforms, and characteristics. Mathematical ideas are motivated from physical problems, and the exposition is presented in a concise style accessible to science and engineering students; emphasis is on motivation, concepts, methods, and interpretation, rather than formal theory. This second edition contains new and additional exercises, and it includes a new chapter on the applications of PDEs to biology: age structured models, pattern formation; epidemic wave fronts, and advection-diffusion processes. The student who reads through this book and solves many of t...
Kuksin, Sergei; Maiocchi, Alberto
In this chapter we present a general method of constructing the effective equation which describes the behavior of small-amplitude solutions for a nonlinear PDE in finite volume, provided that the linear part of the equation is a hamiltonian system with a pure imaginary discrete spectrum. The effective equation is obtained by retaining only the resonant terms of the nonlinearity (which may be hamiltonian, or may be not); the assertion that it describes the limiting behavior of small-amplitude solutions is a rigorous mathematical theorem. In particular, the method applies to the three- and four-wave systems. We demonstrate that different possible types of energy transport are covered by this method, depending on whether the set of resonances splits into finite clusters (this happens, e.g. in case of the Charney-Hasegawa-Mima equation), or is connected (this happens, e.g. in the case of the NLS equation if the space-dimension is at least two). For equations of the first type the energy transition to high frequencies does not hold, while for equations of the second type it may take place. Our method applies to various weakly nonlinear wave systems, appearing in plasma, meteorology and oceanography.
Differential equations problem solver
Arterburn, David R
2012-01-01
REA's Problem Solvers is a series of useful, practical, and informative study guides. Each title in the series is complete step-by-step solution guide. The Differential Equations Problem Solver enables students to solve difficult problems by showing them step-by-step solutions to Differential Equations problems. The Problem Solvers cover material ranging from the elementary to the advanced and make excellent review books and textbook companions. They're perfect for undergraduate and graduate studies.The Differential Equations Problem Solver is the perfect resource for any class, any exam, and
Ordinary differential equations
Miller, Richard K
1982-01-01
Ordinary Differential Equations is an outgrowth of courses taught for a number of years at Iowa State University in the mathematics and the electrical engineering departments. It is intended as a text for a first graduate course in differential equations for students in mathematics, engineering, and the sciences. Although differential equations is an old, traditional, and well-established subject, the diverse backgrounds and interests of the students in a typical modern-day course cause problems in the selection and method of presentation of material. In order to compensate for this diversity,
Pierret, Frédéric
2016-02-01
We derived the equations of Celestial Mechanics governing the variation of the orbital elements under a stochastic perturbation, thereby generalizing the classical Gauss equations. Explicit formulas are given for the semimajor axis, the eccentricity, the inclination, the longitude of the ascending node, the pericenter angle, and the mean anomaly, which are expressed in term of the angular momentum vector H per unit of mass and the energy E per unit of mass. Together, these formulas are called the stochastic Gauss equations, and they are illustrated numerically on an example from satellite dynamics.
Beginning partial differential equations
O'Neil, Peter V
2011-01-01
A rigorous, yet accessible, introduction to partial differential equations-updated in a valuable new edition Beginning Partial Differential Equations, Second Edition provides a comprehensive introduction to partial differential equations (PDEs) with a special focus on the significance of characteristics, solutions by Fourier series, integrals and transforms, properties and physical interpretations of solutions, and a transition to the modern function space approach to PDEs. With its breadth of coverage, this new edition continues to present a broad introduction to the field, while also addres
Hyperbolic partial differential equations
Witten, Matthew
1986-01-01
Hyperbolic Partial Differential Equations III is a refereed journal issue that explores the applications, theory, and/or applied methods related to hyperbolic partial differential equations, or problems arising out of hyperbolic partial differential equations, in any area of research. This journal issue is interested in all types of articles in terms of review, mini-monograph, standard study, or short communication. Some studies presented in this journal include discretization of ideal fluid dynamics in the Eulerian representation; a Riemann problem in gas dynamics with bifurcation; periodic M
Wu Zhuo Qun; Li Hui Lai; Zhao Jun Ning
2001-01-01
Nonlinear diffusion equations, an important class of parabolic equations, come from a variety of diffusion phenomena which appear widely in nature. They are suggested as mathematical models of physical problems in many fields, such as filtration, phase transition, biochemistry and dynamics of biological groups. In many cases, the equations possess degeneracy or singularity. The appearance of degeneracy or singularity makes the study more involved and challenging. Many new ideas and methods have been developed to overcome the special difficulties caused by the degeneracy and singularity, which
Partial differential equations
Friedman, Avner
2008-01-01
This three-part treatment of partial differential equations focuses on elliptic and evolution equations. Largely self-contained, it concludes with a series of independent topics directly related to the methods and results of the preceding sections that helps introduce readers to advanced topics for further study. Geared toward graduate and postgraduate students of mathematics, this volume also constitutes a valuable reference for mathematicians and mathematical theorists.Starting with the theory of elliptic equations and the solution of the Dirichlet problem, the text develops the theory of we
Introduction to functional equations
Sahoo, Prasanna K
2011-01-01
Introduction to Functional Equations grew out of a set of class notes from an introductory graduate level course at the University of Louisville. This introductory text communicates an elementary exposition of valued functional equations where the unknown functions take on real or complex values. In order to make the presentation as manageable as possible for students from a variety of disciplines, the book chooses not to focus on functional equations where the unknown functions take on values on algebraic structures such as groups, rings, or fields. However, each chapter includes sections hig
Uncertain differential equations
Yao, Kai
2016-01-01
This book introduces readers to the basic concepts of and latest findings in the area of differential equations with uncertain factors. It covers the analytic method and numerical method for solving uncertain differential equations, as well as their applications in the field of finance. Furthermore, the book provides a number of new potential research directions for uncertain differential equation. It will be of interest to researchers, engineers and students in the fields of mathematics, information science, operations research, industrial engineering, computer science, artificial intelligence, automation, economics, and management science.
A Comparison of IRT Equating and Beta 4 Equating.
Kim, Dong-In; Brennan, Robert; Kolen, Michael
Four equating methods were compared using four equating criteria: first-order equity (FOE), second-order equity (SOE), conditional mean squared error (CMSE) difference, and the equipercentile equating property. The four methods were: (1) three parameter logistic (3PL) model true score equating; (2) 3PL observed score equating; (3) beta 4 true…
Applied partial differential equations
Logan, J David
2015-01-01
This text presents the standard material usually covered in a one-semester, undergraduate course on boundary value problems and PDEs. Emphasis is placed on motivation, concepts, methods, and interpretation, rather than on formal theory. The concise treatment of the subject is maintained in this third edition covering all the major ideas: the wave equation, the diffusion equation, the Laplace equation, and the advection equation on bounded and unbounded domains. Methods include eigenfunction expansions, integral transforms, and characteristics. In this third edition, text remains intimately tied to applications in heat transfer, wave motion, biological systems, and a variety other topics in pure and applied science. The text offers flexibility to instructors who, for example, may wish to insert topics from biology or numerical methods at any time in the course. The exposition is presented in a friendly, easy-to-read, style, with mathematical ideas motivated from physical problems. Many exercises and worked e...
Frédéric, Pierret
2014-01-01
The equations of celestial mechanics that govern the variation of the orbital elements are completely derived for stochastic perturbation which generalized the classic perturbation equations which are used since Gauss, starting from Newton's equation and it's solution. The six most understandable orbital element, the semi-major axis, the eccentricity, the inclination, the longitude of the ascending node, the pericenter angle and the mean motion are express in term of the angular momentum vector $\\textbf{H}$ per unit of mass and the energy $E$ per unit of mass. We differentiate those expressions using It\\^o's theory of differential equations due to the stochastic nature of the perturbing force. The result is applied to the two-body problem perturbed by a stochastic dust cloud and also perturbed by a stochastic dynamical oblateness of the central body.
Kinetic equations: computation
Pareschi, Lorenzo
2013-01-01
Kinetic equations bridge the gap between a microscopic description and a macroscopic description of the physical reality. Due to the high dimensionality the construction of numerical methods represents a challenge and requires a careful balance between accuracy and computational complexity.
Saaty, Thomas L
1981-01-01
Covers major types of classical equations: operator, functional, difference, integro-differential, and more. Suitable for graduate students as well as scientists, technologists, and mathematicians. "A welcome contribution." - Math Reviews. 1964 edition.
Geometry of differential equations
Khovanskiĭ, A; Vassiliev, V
1998-01-01
This volume contains articles written by V. I. Arnold's colleagues on the occasion of his 60th birthday. The articles are mostly devoted to various aspects of geometry of differential equations and relations to global analysis and Hamiltonian mechanics.
Regularized Structural Equation Modeling.
Jacobucci, Ross; Grimm, Kevin J; McArdle, John J
A new method is proposed that extends the use of regularization in both lasso and ridge regression to structural equation models. The method is termed regularized structural equation modeling (RegSEM). RegSEM penalizes specific parameters in structural equation models, with the goal of creating easier to understand and simpler models. Although regularization has gained wide adoption in regression, very little has transferred to models with latent variables. By adding penalties to specific parameters in a structural equation model, researchers have a high level of flexibility in reducing model complexity, overcoming poor fitting models, and the creation of models that are more likely to generalize to new samples. The proposed method was evaluated through a simulation study, two illustrative examples involving a measurement model, and one empirical example involving the structural part of the model to demonstrate RegSEM's utility.
Institute of Scientific and Technical Information of China (English)
A.I.Arbab
2013-01-01
A unified complex model of Maxwell's equations is presented.The wave nature of the electromagnetic field vector is related to the temporal and spatial distributions and the circulation of charge and current densities.A new vacuum solution is obtained,and a new transformation under which Maxwell's equations are invariant is proposed.This transformation extends ordinary gauge transformation to include charge-current as well as scalar-vector potential.An electric dipole moment is found to be related to the magnetic charges,and Dirac's quantization is found to determine an uncertainty relation expressing the indeterminacy of electric and magnetic charges.We generalize Maxwell's equations to include longitudinal waves.A formal analogy between this formulation and Dirac's equation is also discussed.
Applied partial differential equations
DuChateau, Paul
2012-01-01
Book focuses mainly on boundary-value and initial-boundary-value problems on spatially bounded and on unbounded domains; integral transforms; uniqueness and continuous dependence on data, first-order equations, and more. Numerous exercises included.
Singular Renormalization Group Equations
Minoru, HIRAYAMA; Department of Physics, Toyama University
1984-01-01
The possible behaviour of the effective charge is discussed in Oehme and Zimmermann's scheme of the renormalization group equation. The effective charge in an example considered oscillates so violently in the ultraviolet limit that the bare charge becomes indefinable.
Problems in differential equations
Brenner, J L
2013-01-01
More than 900 problems and answers explore applications of differential equations to vibrations, electrical engineering, mechanics, and physics. Problem types include both routine and nonroutine, and stars indicate advanced problems. 1963 edition.
Relativistic Guiding Center Equations
Energy Technology Data Exchange (ETDEWEB)
White, R. B. [PPPL; Gobbin, M. [Euratom-ENEA Association
2014-10-01
In toroidal fusion devices it is relatively easy that electrons achieve relativistic velocities, so to simulate runaway electrons and other high energy phenomena a nonrelativistic guiding center formalism is not sufficient. Relativistic guiding center equations including flute mode time dependent field perturbations are derived. The same variables as used in a previous nonrelativistic guiding center code are adopted, so that a straightforward modifications of those equations can produce a relativistic version.
Asymptotics for dissipative nonlinear equations
Hayashi, Nakao; Kaikina, Elena I; Shishmarev, Ilya A
2006-01-01
Many of problems of the natural sciences lead to nonlinear partial differential equations. However, only a few of them have succeeded in being solved explicitly. Therefore different methods of qualitative analysis such as the asymptotic methods play a very important role. This is the first book in the world literature giving a systematic development of a general asymptotic theory for nonlinear partial differential equations with dissipation. Many typical well-known equations are considered as examples, such as: nonlinear heat equation, KdVB equation, nonlinear damped wave equation, Landau-Ginzburg equation, Sobolev type equations, systems of equations of Boussinesq, Navier-Stokes and others.
Functional Equations and Fourier Analysis
2010-01-01
By exploring the relations among functional equations, harmonic analysis and representation theory, we give a unified and very accessible approach to solve three important functional equations -- the d'Alembert equation, the Wilson equation, and the d'Alembert long equation, on compact groups.
Scaling Equation for Invariant Measure
Institute of Scientific and Technical Information of China (English)
LIU Shi-Kuo; FU Zun-Tao; LIU Shi-Da; REN Kui
2003-01-01
An iterated function system (IFS) is constructed. It is shown that the invariant measure of IFS satisfies the same equation as scaling equation for wavelet transform (WT). Obviously, IFS and scaling equation of WT both have contraction mapping principle.
Directory of Open Access Journals (Sweden)
Florian Ion Tiberiu Petrescu
2015-09-01
Full Text Available This paper presents the dynamic, original, machine motion equations. The equation of motion of the machine that generates angular speed of the shaft (which varies with position and rotation speed is deduced by conservation kinetic energy of the machine. An additional variation of angular speed is added by multiplying by the coefficient dynamic D (generated by the forces out of mechanism and or by the forces generated by the elasticity of the system. Kinetic energy conservation shows angular speed variation (from the shaft with inertial masses, while the dynamic coefficient introduces the variation of w with forces acting in the mechanism. Deriving the first equation of motion of the machine one can obtain the second equation of motion dynamic. From the second equation of motion of the machine it determines the angular acceleration of the shaft. It shows the distribution of the forces on the mechanism to the internal combustion heat engines. Dynamic, the velocities can be distributed in the same way as forces. Practically, in the dynamic regimes, the velocities have the same timing as the forces. Calculations should be made for an engine with a single cylinder. Originally exemplification is done for a classic distribution mechanism, and then even the module B distribution mechanism of an Otto engine type.
Introduction to partial differential equations
Greenspan, Donald
2000-01-01
Designed for use in a one-semester course by seniors and beginning graduate students, this rigorous presentation explores practical methods of solving differential equations, plus the unifying theory underlying the mathematical superstructure. Topics include basic concepts, Fourier series, second-order partial differential equations, wave equation, potential equation, heat equation, approximate solution of partial differential equations, and more. Exercises appear at the ends of most chapters. 1961 edition.
Xiang, Dai-Rong; Li, Jun-Jie; Sheng, Zi-Ke; Yu, Hai-Ying; Deng, Mei; Bi, Sheng; Hu, Fei-Shu; Chen, Wei; Xue, Xiao-Wei; Zhou, Zhi-Bo; Doi, Yohei; Li, Lan-Juan
2015-01-01
A high fosfomycin resistance rate was observed in Klebsiella pneumoniae carbapenemase (KPC)-producing K. pneumoniae (KPC-KP) in our previous study, but little is known about its mechanisms. In this study, we explored the prevalence of plasmid-mediated fosfomycin resistance determinants among fosfomycin-resistant KPC-KP strains from a Chinese university hospital and determined the complete sequence of a novel fosA3-carrying plasmid isolated from an epidemic K. pneumoniae sequence type (ST) 11 strain. A total of 97 KPC-KP strains were studied, of which 57 (58.8%) were resistant to fosfomycin, including 44 (45.4%) harboring fosA3 and 1 harboring fosA. All fosA3-positive strains belonged to the dominant ST11-pulse type (PT) A clone according to multilocus sequence typing and pulsed-field gel electrophoresis, suggesting clonal dissemination. The fosA-positive isolate belonged to ST11-PTE. The fosA3-carrying plasmid pKP1034 is 136,848 bp in length and is not self-transmissible. It is a multireplicon plasmid belonging to IncR-F33:A−: B−. Besides fosA3, a variety of other resistance determinants, including blaKPC-2, rmtB, blaCTX-M-65, and blaSHV-12, are identified in pKP1034, which would allow for coselection of fosA3 by most β-lactams and/or aminoglycosides and facilitate its dissemination despite limited use of fosfomycin in China. Detailed comparisons with related plasmids revealed that pKP1034 is highly mosaic and might have evolved from alarming recombination of the blaKPC-2-carrying plasmid pKPC-LK30 from Taiwan and the epidemic fosA3-carrying plasmid pHN7A8 from mainland China. PMID:26666939
Generalization of Hopf Functional Equation
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
This paper generalizes the Hopf functional equation in order to apply it to a wider class of not necessarily incompressible fluid flows. We start by defining characteristic functionals of the velocity field, the density field and the temperature field of a compressible field. Using the continuity equation, the Navier-Stokes equations and the equation of energy we derive a functional equation governing the motion of an ideal gas flow and a van der Waals gas flow, and then give some general methods of deriving a functional equation governing the motion of any compressible fluid flow. These functional equations can be considered as the generalization of the Hopf functional equation.
Stochastic porous media equations
Barbu, Viorel; Röckner, Michael
2016-01-01
Focusing on stochastic porous media equations, this book places an emphasis on existence theorems, asymptotic behavior and ergodic properties of the associated transition semigroup. Stochastic perturbations of the porous media equation have reviously been considered by physicists, but rigorous mathematical existence results have only recently been found. The porous media equation models a number of different physical phenomena, including the flow of an ideal gas and the diffusion of a compressible fluid through porous media, and also thermal propagation in plasma and plasma radiation. Another important application is to a model of the standard self-organized criticality process, called the "sand-pile model" or the "Bak-Tang-Wiesenfeld model". The book will be of interest to PhD students and researchers in mathematics, physics and biology.
Quasirelativistic Langevin equation.
Plyukhin, A V
2013-11-01
We address the problem of a microscopic derivation of the Langevin equation for a weakly relativistic Brownian particle. A noncovariant Hamiltonian model is adopted, in which the free motion of particles is described relativistically while their interaction is treated classically, i.e., by means of action-to-a-distance interaction potentials. Relativistic corrections to the classical Langevin equation emerge as nonlinear dissipation terms and originate from the nonlinear dependence of the relativistic velocity on momentum. On the other hand, similar nonlinear dissipation forces also appear as classical (nonrelativistic) corrections to the weak-coupling approximation. It is shown that these classical corrections, which are usually ignored in phenomenological models, may be of the same order of magnitude, if not larger than, relativistic ones. The interplay of relativistic corrections and classical beyond-the-weak-coupling contributions determines the sign of the leading nonlinear dissipation term in the Langevin equation and thus is qualitatively important.
Boussinesq evolution equations
DEFF Research Database (Denmark)
Bredmose, Henrik; Schaffer, H.; Madsen, Per A.
2004-01-01
This paper deals with the possibility of using methods and ideas from time domain Boussinesq formulations in the corresponding frequency domain formulations. We term such frequency domain models "evolution equations". First, we demonstrate that the numerical efficiency of the deterministic...... Boussinesq evolution equations of Madsen and Sorensen [Madsen, P.A., Sorensen, O.R., 1993. Bound waves and triad interactions in shallow water. Ocean Eng. 20 359-388] can be improved by using Fast Fourier Transforms to evaluate the nonlinear terms. For a practical example of irregular waves propagating over...... a submerged bar, it is demonstrated that evolution equations utilising FFT can be solved around 100 times faster than the corresponding time domain model. Use of FFT provides an efficient bridge between the frequency domain and the time domain. We utilise this by adapting the surface roller model for wave...
Nonlocal electrical diffusion equation
Gómez-Aguilar, J. F.; Escobar-Jiménez, R. F.; Olivares-Peregrino, V. H.; Benavides-Cruz, M.; Calderón-Ramón, C.
2016-07-01
In this paper, we present an analysis and modeling of the electrical diffusion equation using the fractional calculus approach. This alternative representation for the current density is expressed in terms of the Caputo derivatives, the order for the space domain is 0numerical methods based on Fourier variable separation. The case with spatial fractional derivatives leads to Levy flight type phenomena, while the time fractional equation is related to sub- or super diffusion. We show that the mathematical concept of fractional derivatives can be useful to understand the behavior of semiconductors, the design of solar panels, electrochemical phenomena and the description of anomalous complex processes.
Equations of mathematical physics
Tikhonov, A N
2011-01-01
Mathematical physics plays an important role in the study of many physical processes - hydrodynamics, elasticity, and electrodynamics, to name just a few. Because of the enormous range and variety of problems dealt with by mathematical physics, this thorough advanced-undergraduate or graduate-level text considers only those problems leading to partial differential equations. The authors - two well-known Russian mathematicians - have focused on typical physical processes and the principal types of equations deailing with them. Special attention is paid throughout to mathematical formulation, ri
Gas Dynamics Equations: Computation
Chen, Gui-Qiang G
2012-01-01
Shock waves, vorticity waves, and entropy waves are fundamental discontinuity waves in nature and arise in supersonic or transonic gas flow, or from a very sudden release (explosion) of chemical, nuclear, electrical, radiation, or mechanical energy in a limited space. Tracking these discontinuities and their interactions, especially when and where new waves arise and interact in the motion of gases, is one of the main motivations for numerical computation for the gas dynamics equations. In this paper, we discuss some historic and recent developments, as well as mathematical challenges, in designing and formulating efficient numerical methods and algorithms to compute weak entropy solutions for the Euler equations for gas dynamics.
Theory of differential equations
Gel'fand, I M
1967-01-01
Generalized Functions, Volume 3: Theory of Differential Equations focuses on the application of generalized functions to problems of the theory of partial differential equations.This book discusses the problems of determining uniqueness and correctness classes for solutions of the Cauchy problem for systems with constant coefficients and eigenfunction expansions for self-adjoint differential operators. The topics covered include the bounded operators in spaces of type W, Cauchy problem in a topological vector space, and theorem of the Phragmén-Lindelöf type. The correctness classes for the Cau
Systematic Equation Formulation
DEFF Research Database (Denmark)
Lindberg, Erik
2007-01-01
A tutorial giving a very simple introduction to the set-up of the equations used as a model for an electrical/electronic circuit. The aim is to find a method which is as simple and general as possible with respect to implementation in a computer program. The “Modified Nodal Approach”, MNA, and th......, and the “Controlled Source Approach”, CSA, for systematic equation formulation are investigated. It is suggested that the kernel of the P Spice program based on MNA is reprogrammed....
Generalized estimating equations
Hardin, James W
2002-01-01
Although powerful and flexible, the method of generalized linear models (GLM) is limited in its ability to accurately deal with longitudinal and clustered data. Developed specifically to accommodate these data types, the method of Generalized Estimating Equations (GEE) extends the GLM algorithm to accommodate the correlated data encountered in health research, social science, biology, and other related fields.Generalized Estimating Equations provides the first complete treatment of GEE methodology in all of its variations. After introducing the subject and reviewing GLM, the authors examine th
Institute of Scientific and Technical Information of China (English)
Ding Yi
2009-01-01
In this article, the author derives a functional equation η(s)=［(π/4)s-1/2√2/πг(1-s)sin(πs/2)]η(1-s) of the analytic function η(s) which is defined by η(s)=1-s-3-s-5-s+7-s…for complex variable s with Re s>1, and is defined by analytic continuation for other values of s. The author proves (1) by Ramanujan identity (see [1], [3]). Her method provides a new derivation of the functional equation of Riemann zeta function by using Poisson summation formula.
Comparison of Kernel Equating and Item Response Theory Equating Methods
Meng, Yu
2012-01-01
The kernel method of test equating is a unified approach to test equating with some advantages over traditional equating methods. Therefore, it is important to evaluate in a comprehensive way the usefulness and appropriateness of the Kernel equating (KE) method, as well as its advantages and disadvantages compared with several popular item…
Test equating methods and practices
Kolen, Michael J
1995-01-01
In recent years, many researchers in the psychology and statistical communities have paid increasing attention to test equating as issues of using multiple test forms have arisen and in response to criticisms of traditional testing techniques This book provides a practically oriented introduction to test equating which both discusses the most frequently used equating methodologies and covers many of the practical issues involved The main themes are - the purpose of equating - distinguishing between equating and related methodologies - the importance of test equating to test development and quality control - the differences between equating properties, equating designs, and equating methods - equating error, and the underlying statistical assumptions for equating The authors are acknowledged experts in the field, and the book is based on numerous courses and seminars they have presented As a result, educators, psychometricians, professionals in measurement, statisticians, and students coming to the subject for...
The Statistical Drake Equation
Maccone, Claudio
2010-12-01
We provide the statistical generalization of the Drake equation. From a simple product of seven positive numbers, the Drake equation is now turned into the product of seven positive random variables. We call this "the Statistical Drake Equation". The mathematical consequences of this transformation are then derived. The proof of our results is based on the Central Limit Theorem (CLT) of Statistics. In loose terms, the CLT states that the sum of any number of independent random variables, each of which may be ARBITRARILY distributed, approaches a Gaussian (i.e. normal) random variable. This is called the Lyapunov Form of the CLT, or the Lindeberg Form of the CLT, depending on the mathematical constraints assumed on the third moments of the various probability distributions. In conclusion, we show that: The new random variable N, yielding the number of communicating civilizations in the Galaxy, follows the LOGNORMAL distribution. Then, as a consequence, the mean value of this lognormal distribution is the ordinary N in the Drake equation. The standard deviation, mode, and all the moments of this lognormal N are also found. The seven factors in the ordinary Drake equation now become seven positive random variables. The probability distribution of each random variable may be ARBITRARY. The CLT in the so-called Lyapunov or Lindeberg forms (that both do not assume the factors to be identically distributed) allows for that. In other words, the CLT "translates" into our statistical Drake equation by allowing an arbitrary probability distribution for each factor. This is both physically realistic and practically very useful, of course. An application of our statistical Drake equation then follows. The (average) DISTANCE between any two neighboring and communicating civilizations in the Galaxy may be shown to be inversely proportional to the cubic root of N. Then, in our approach, this distance becomes a new random variable. We derive the relevant probability density
Variation principle of piezothermoelastic bodies, canonical equation and homogeneous equation
Institute of Scientific and Technical Information of China (English)
LIU Yan-hong; ZHANG Hui-ming
2007-01-01
Combining the symplectic variations theory, the homogeneous control equation and isoparametric element homogeneous formulations for piezothermoelastic hybrid laminates problems were deduced. Firstly, based on the generalized Hamilton variation principle, the non-homogeneous Hamilton canonical equation for piezothermoelastic bodies was derived. Then the symplectic relationship of variations in the thermal equilibrium formulations and gradient equations was considered, and the non-homogeneous canonical equation was transformed to homogeneous control equation for solving independently the coupling problem of piezothermoelastic bodies by the incensement of dimensions of the canonical equation. For the convenience of deriving Hamilton isoparametric element formulations with four nodes, one can consider the temperature gradient equation as constitutive relation and reconstruct new variation principle. The homogeneous equation simplifies greatly the solution programs which are often performed to solve nonhomogeneous equation and second order differential equation on the thermal equilibrium and gradient relationship.
Calculus & ordinary differential equations
Pearson, David
1995-01-01
Professor Pearson's book starts with an introduction to the area and an explanation of the most commonly used functions. It then moves on through differentiation, special functions, derivatives, integrals and onto full differential equations. As with other books in the series the emphasis is on using worked examples and tutorial-based problem solving to gain the confidence of students.
Standardized Referente Evapotranspiration Equation
Directory of Open Access Journals (Sweden)
M.D. Mundo–Molina
2009-04-01
Full Text Available In this paper is presented a discussion on the necessity to standardize the Penman–Monteith equations in order to estimate ETo. The proposal is to define an accuracy and standarize equation based in Penman–Monteith. The automated weather station named CIANO (27° 22 ' 144 North latitude and 109" 55' west longitude it was selected tomake comparisons. The compared equations we re: a CIANO weat her station, b Penman–Monteith ASCE (PMA, Penman–Monteith FAO 56 (PM FAO 56, Penman–Monteith estandarizado ASCE (PM Std. ASCE. The results were: a There are important differences between PMA and CIANO weather station. The differences are attributed to the nonstandardization of the equation CIANO weather station, b The coefficient of correlation between both methods was of 0,92, with a standard deviation of 1,63 mm, an average quadratic error of 0,60 mm and one efficiency in the estimation of ETo with respect to the method pattern of 87%.
Modified differential equations
Chartier, Philippe; Hairer, Ernst; Vilmart, Gilles
2007-01-01
Motivated by the theory of modified differential equations (backward error analysis) an approach for the construction of high order numerical integrators that preserve geometric properties of the exact flow is developed. This summarises a talk presented in honour of Michel Crouzeix.
Equational binary decision diagrams
Groote, J.F.; Pol, J.C. van de
2000-01-01
We incorporate equations in binary decision diagrams (BDD). The resulting objects are called EQ-BDDs. A straightforward notion of ordered EQ-BDDs (EQ-OBDD) is defined, and it is proved that each EQ-BDD is logically equivalent to an EQ-OBDD. Moreover, on EQ-OBDDs satisfiability and tautology checkin
Directory of Open Access Journals (Sweden)
Garkavenko A. S.
2011-08-01
Full Text Available The rate equations of the exciton laser in the system of interacting excitons have been obtained and the inverted population conditions and generation have been derived. The possibility of creating radically new gamma-ray laser has been shown.
Equational binary decision diagrams
J.F. Groote (Jan Friso); J.C. van de Pol (Jaco)
2000-01-01
textabstractWe incorporate equations in binary decision diagrams (BDD). The resulting objects are called EQ-BDDs. A straightforward notion of ordered EQ-BDDs (EQ-OBDD) is defined, and it is proved that each EQ-BDD is logically equivalent to an EQ-OBDD. Moreover, on EQ-OBDDs satisfiability and
Structural Equation Model Trees
Brandmaier, Andreas M.; von Oertzen, Timo; McArdle, John J.; Lindenberger, Ulman
2013-01-01
In the behavioral and social sciences, structural equation models (SEMs) have become widely accepted as a modeling tool for the relation between latent and observed variables. SEMs can be seen as a unification of several multivariate analysis techniques. SEM Trees combine the strengths of SEMs and the decision tree paradigm by building tree…
Generalized reduced magnetohydrodynamic equations
Energy Technology Data Exchange (ETDEWEB)
Kruger, S.E.
1999-02-01
A new derivation of reduced magnetohydrodynamic (MHD) equations is presented. A multiple-time-scale expansion is employed. It has the advantage of clearly separating the three time scales of the problem associated with (1) MHD equilibrium, (2) fluctuations whose wave vector is aligned perpendicular to the magnetic field, and (3) those aligned parallel to the magnetic field. The derivation is carried out without relying on a large aspect ratio assumption; therefore this model can be applied to any general configuration. By accounting for the MHD equilibrium and constraints to eliminate the fast perpendicular waves, equations are derived to evolve scalar potential quantities on a time scale associated with the parallel wave vector (shear-Alfven wave time scale), which is the time scale of interest for MHD instability studies. Careful attention is given in the derivation to satisfy energy conservation and to have manifestly divergence-free magnetic fields to all orders in the expansion parameter. Additionally, neoclassical closures and equilibrium shear flow effects are easily accounted for in this model. Equations for the inner resistive layer are derived which reproduce the linear ideal and resistive stability criterion of Glasser, Greene, and Johnson. The equations have been programmed into a spectral initial value code and run with shear flow that is consistent with the equilibrium input into the code. Linear results of tearing modes with shear flow are presented which differentiate the effects of shear flow gradients in the layer with the effects of the shear flow decoupling multiple harmonics.
Directory of Open Access Journals (Sweden)
Hatem Mejjaoli
2008-12-01
Full Text Available We introduce and study the Dunkl symmetric systems. We prove the well-posedness results for the Cauchy problem for these systems. Eventually we describe the finite speed of it. Next the semi-linear Dunkl-wave equations are also studied.
Equational binary decision diagrams
J.F. Groote (Jan Friso); J.C. van de Pol (Jaco)
2000-01-01
textabstractWe incorporate equations in binary decision diagrams (BDD). The resulting objects are called EQ-BDDs. A straightforward notion of ordered EQ-BDDs (EQ-OBDD) is defined, and it is proved that each EQ-BDD is logically equivalent to an EQ-OBDD. Moreover, on EQ-OBDDs satisfiability and tauto
Large nonlinear w$_{\\infty}$ algebras from nonlinear integrable deformations of self dual gravity
Castro, C
1994-01-01
A proposal for constructing a universal nonlinear {\\hat W}_{\\infty} algebra is made as the symmetry algebra of a rotational Killing-symmetry reduction of the nonlinear perturbations of Moyal-Integrable deformations of D=4 Self Dual Gravity (IDSDG). This is attained upon the construction of a nonlinear bracket based on nonlinear gauge theories associated with infinite dimensional Lie algebras. A Quantization and supersymmetrization program can also be carried out. The relevance to the Kadomtsev-Petviashvili hierarchy, 2D dilaton gravity, quantum gravity and black hole physics is discussed in the concluding remarks.
Abdelwahab, N M; Adkins, J K; Agakishiev, G; Aggarwal, M M; Ahammed, Z; Alekseev, I; Alford, J; Anson, C D; Aparin, A; Arkhipkin, D; Aschenauer, E C; Averichev, G S; Banerjee, A; Beavis, D R; Bellwied, R; Bhasin, A; Bhati, A K; Bhattarai, P; Bielcik, J; Bielcikova, J; Bland, L C; Bordyuzhin, I G; Borowski, W; Bouchet, J; Brandin, A V; Brovko, S G; Bültmann, S; Bunzarov, I; Burton, T P; Butterworth, J; Caines, H; Sánchez, M Calderón de la Barca; Campbell, J M; Cebra, D; Cendejas, R; Cervantes, M C; Chaloupka, P; Chang, Z; Chattopadhyay, S; Chen, H F; Chen, J H; Chen, L; Cheng, J; Cherney, M; Chikanian, A; Christie, W; Chwastowski, J; Codrington, M J M; Contin, G; Cramer, J G; Crawford, H J; Cui, X; Das, S; Leyva, A Davila; De Silva, L C; Debbe, R R; Dedovich, T G; Deng, J; Derevschikov, A A; de Souza, R Derradi; di Ruzza, B; Didenko, L; Dilks, C; Ding, F; Djawotho, P; Dong, X; Drachenberg, J L; Draper, J E; Du, C M; Dunkelberger, L E; Dunlop, J C; Efimov, L G; Engelage, J; Engle, K S; Eppley, G; Esha, R; Eun, L; Evdokimov, O; Eyser, O; Fatemi, R; Fazio, S; Fedorisin, J; Filip, P; Fisyak, Y; Flores, C E; Gagliardi, C A; Gangadharan, D R; Garand, D; Geurts, F; Gibson, A; Girard, M; Gliske, S; Greiner, L; Grosnick, D; Gunarathne, D S; Guo, Y; Gupta, A; Gupta, S; Guryn, W; Haag, B; Hamad, A; Hamed, A; Han, L-X; Haque, R; Harris, J W; Heppelmann, S; Hirsch, A; Hoffmann, G W; Hofman, D J; Horvat, S; Huang, B; Huang, H Z; Huang, X; Huck, P; Humanic, T J; Igo, G; Jacobs, W W; Jang, H; Judd, E G; Kabana, S; Kalinkin, D; Kang, K; Kauder, K; Ke, H W; Keane, D; Kechechyan, A; Kesich, A; Khan, Z H; Kikola, D P; Kisel, I; Kisiel, A; Koetke, D D; Kollegger, T; Konzer, J; Koralt, I; Kosarzewski, L K; Kotchenda, L; Kraishan, A F; Kravtsov, P; Krueger, K; Kulakov, I; Kumar, L; Kycia, R A; Lamont, M A C; Landgraf, J M; Landry, K D; Lauret, J; Lebedev, A; Lednicky, R; Lee, J H; Li, C; Li, W; Li, X; Li, Y; Li, Z M; Lisa, M A; Liu, F; Ljubicic, T; Llope, W J; Lomnitz, M; Longacre, R S; Luo, X; Ma, G L; Ma, Y G; Mahapatra, D P; Majka, R; Margetis, S; Markert, C; Masui, H; Matis, H S; McDonald, D; McShane, T S; Minaev, N G; Mioduszewski, S; Mohanty, B; Mondal, M M; Morozov, D A; Mustafa, M K; Nandi, B K; Nasim, Md; Nayak, T K; Nelson, J M; Nigmatkulov, G; Nogach, L V; Noh, S Y; Novak, J; Nurushev, S B; Odyniec, G; Ogawa, A; Oh, K; Ohlson, A; Okorokov, V; Oldag, E W; Olvitt, D L; Page, B S; Pan, Y X; Pandit, Y; Panebratsev, Y; Pawlak, T; Pawlik, B; Pei, H; Perkins, C; Pile, P; Planinic, M; Pluta, J; Poljak, N; Poniatowska, K; Porter, J; Poskanzer, A M; Pruthi, N K; Przybycien, M; Putschke, J; Qiu, H; Quintero, A; Ramachandran, S; Raniwala, R; Raniwala, S; Ray, R L; Riley, C K; Ritter, H G; Roberts, J B; Rogachevskiy, O V; Romero, J L; Ross, J F; Roy, A; Ruan, L; Rusnak, J; Rusnakova, O; Sahoo, N R; Sahu, P K; Sakrejda, I; Salur, S; Sandacz, A; Sandweiss, J; Sangaline, E; Sarkar, A; Schambach, J; Scharenberg, R P; Schmah, A M; Schmidke, W B; Schmitz, N; Seger, J; Seyboth, P; Shah, N; Shahaliev, E; Shanmuganathan, P V; Shao, M; Sharma, B; Shen, W Q; Shi, S S; Shou, Q Y; Sichtermann, E P; Simko, M; Skoby, M J; Smirnov, D; Smirnov, N; Solanki, D; Sorensen, P; Spinka, H M; Srivastava, B; Stanislaus, T D S; Stevens, J R; Stock, R; Strikhanov, M; Stringfellow, B; Sumbera, M; Sun, X; Sun, X M; Sun, Y; Sun, Z; Surrow, B; Svirida, D N; Symons, T J M; Szelezniak, M A; Takahashi, J; Tang, A H; Tang, Z; Tarnowsky, T; Thomas, J H; Timmins, A R; Tlusty, D; Tokarev, M; Trentalange, S; Tribble, R E; Tribedy, P; Trzeciak, B A; Tsai, O D; Turnau, J; Ullrich, T; Underwood, D G; Van Buren, G; van Nieuwenhuizen, G; Vandenbroucke, M; Vanfossen,, J A; Varma, R; Vasconcelos, G M S; Vasiliev, A N; Vertesi, R; Videbæk, F; Viyogi, Y P; Vokal, S; Voloshin, S A; Vossen, A; Wada, M; Wang, F; Wang, G; Wang, H; Wang, J S; Wang, X L; Wang, Y; Webb, G; Webb, J C; Wen, L; Westfall, G D; Wieman, H; Wissink, S W; Wu, Y F; Xiao, Z; Xie, W; Xin, K; Xu, H; Xu, J; Xu, N; Xu, Q H; Xu, Y; Xu, Z; Yan, W; Yang, C; Yang, Y; Ye, Z; Yepes, P; Yi, L; Yip, K; Yoo, I-K; Yu, N; Zbroszczyk, H; Zha, W; Zhang, J B; Zhang, J L; Zhang, S; Zhang, X P; Zhang, Y; Zhang, Z P; Zhao, F; Zhao, J; Zhong, C; Zhu, X; Zhu, Y H; Zoulkarneeva, Y; Zyzak, M
2014-01-01
A search for the quantum chromodynamics (QCD) critical point was performed by the STAR experiment at the Relativistic Heavy Ion Collider, using dynamical fluctuations of unlike particle pairs. Heavy-ion collisions were studied over a large range of collision energies with homogeneous acceptance and excellent particle identification, covering a significant range in the QCD phase diagram where a critical point may be located. Dynamical $K/\\pi$, $p/\\pi$, and $K/p$ fluctuations as measured by the STAR experiment in central 0-5% Au+Au collisions from center-of-mass collision energies $\\rm \\sqrt{s_{NN}}$ = 7.7 to 200 GeV are presented. The observable $\\rm \
Klimenko, Maxim; Klimenko, Vladimir; Ratovsky, Konstantin; Goncharenko, Larisa
Earlier by Klimenko et al., 2009 under carrying out the calculations of the ionospheric effects of storm sequence on September 9-14, 2005 the model input parameters (potential difference through polar caps, field-aligned currents of the second region and particle precipitation fluxes and energy) were set as function of Kp-index of geomagnetic activity. The analyses of obtained results show that the reasons of quantitative distinctions of calculation results and observations can be: the use of 3 hour Kp-index at the setting of time dependence of model input parameters; the dipole approach of geomagnetic field; the absence in model calculations the effects of the solar flares, which were taken place during the considered period. In the given study the model input parameters were set as function of AE-and Kp-indices of geomagnetic activity according to different empirical models and morphological representations Feshchenko and Maltsev, 2003; Cheng et al., 2008; Zhang and Paxton, 2008. At that, we taken into account the shift of field-aligned currents of the second region to the lower latitudes as by Sojka et al., 1994 and 30 min. time delay of variations of the field-aligned currents of second region relative to the variations of the potential difference through polar caps at the storm sudden commencement phase. Also we taken into account the ionospheric effects of solar flares. Calculation of ionospheric effects of storm sequence has been carried out with use of the Global Self-Consistent Model of the Thermosphere, Ionosphere and Protonosphere (GSM TIP) developed in WD IZMIRAN (Nam-galadze et al., 1988). We carried out the comparison of calculation results with experimental data. This study is supported by RFBR grant 08-05-00274. References Cheng Z.W., Shi J.K., Zhang T.L., Dunlop M. and Liu Z.X. Relationship between FAC at plasma sheet boundary layers and AE index during storms from August to October, 2001. Sci. China Ser. E-Tech. Sci., 2008, Vol. 51, No. 7, 842
Lie Symmetries of Ishimori Equation
Institute of Scientific and Technical Information of China (English)
SONG Xu-Xia
2013-01-01
The Ishimori equation is one of the most important (2+1)-dimensional integrable models,which is an integrable generalization of (1+1)-dimensional classical continuous Heisenberg ferromagnetic spin equations.Based on importance of Lie symmetries in analysis of differential equations,in this paper,we derive Lie symmetries for the Ishimori equation by Hirota's direct method.
Lectures on partial differential equations
Petrovsky, I G
1992-01-01
Graduate-level exposition by noted Russian mathematician offers rigorous, transparent, highly readable coverage of classification of equations, hyperbolic equations, elliptic equations and parabolic equations. Wealth of commentary and insight invaluable for deepening understanding of problems considered in text. Translated from the Russian by A. Shenitzer.
Elements of partial differential equations
Sneddon, Ian N
2006-01-01
Geared toward students of applied rather than pure mathematics, this volume introduces elements of partial differential equations. Its focus is primarily upon finding solutions to particular equations rather than general theory.Topics include ordinary differential equations in more than two variables, partial differential equations of the first and second orders, Laplace's equation, the wave equation, and the diffusion equation. A helpful Appendix offers information on systems of surfaces, and solutions to the odd-numbered problems appear at the end of the book. Readers pursuing independent st
Spatial and temporal compact equations for water waves
Dyachenko, Alexander; Kachulin, Dmitriy; Zakharov, Vladimir
2016-04-01
complex normal variable c(x,t) which is analytic function in the upper half-planeHamiltonians both for temporal and spatial equations are very simple It can be easily implemented for numerical simulation The equations can be generalized for "almost" 2-D waves like KdV is generalized to KP. This work was supported by was Grant "Wave turbulence: theory, numerical simulation, experiment" #14-22-00174 of Russian Science Foundation.
Methods for Equating Mental Tests.
1984-11-01
1983) compared conventional and IRT methods for equating the Test of English as a Foreign Language ( TOEFL ) after chaining. Three conventional and...three IRT equating methods were examined in this study; two sections of TOEFL were each (separately) equated. The IRT methods included the following: (a...group. A separate base form was established for each of the six equating methods. Instead of equating the base-form TOEFL to itself, the last (eighth
Differential Equations with Linear Algebra
Boelkins, Matthew R; Potter, Merle C
2009-01-01
Linearity plays a critical role in the study of elementary differential equations; linear differential equations, especially systems thereof, demonstrate a fundamental application of linear algebra. In Differential Equations with Linear Algebra, we explore this interplay between linear algebra and differential equations and examine introductory and important ideas in each, usually through the lens of important problems that involve differential equations. Written at a sophomore level, the text is accessible to students who have completed multivariable calculus. With a systems-first approach, t
SPECIFIC SOLUTIONS GROUNDWATER FLOW EQUATION
Syahruddin, Muhammad Hamzah
2014-01-01
Geophysic publication Groundwater flow under surface, its usually slow moving, so that in laminer flow condition can find analisys using the Darcy???s law. The combination between Darcy law and continuity equation can find differential Laplace equation as general equation groundwater flow in sub surface. Based on Differential Laplace Equation is the equation that can be used to describe hydraulic head and velocity flow distribution in porous media as groundwater. In the modeling Laplace e...
Stochastic differential equations and applications
Friedman, Avner
2006-01-01
This text develops the theory of systems of stochastic differential equations, and it presents applications in probability, partial differential equations, and stochastic control problems. Originally published in two volumes, it combines a book of basic theory and selected topics with a book of applications.The first part explores Markov processes and Brownian motion; the stochastic integral and stochastic differential equations; elliptic and parabolic partial differential equations and their relations to stochastic differential equations; the Cameron-Martin-Girsanov theorem; and asymptotic es
DEFF Research Database (Denmark)
Dyre, Jeppe
1995-01-01
energies chosen randomly according to a Gaussian. The random-walk model is here derived from Newton's laws by making a number of simplifying assumptions. In the second part of the paper an approximate low-temperature description of energy fluctuations in the random-walk modelthe energy master equation...... (EME)is arrived at. The EME is one dimensional and involves only energy; it is derived by arguing that percolation dominates the relaxational properties of the random-walk model at low temperatures. The approximate EME description of the random-walk model is expected to be valid at low temperatures...... of the random-walk model. The EME allows a calculation of the energy probability distribution at realistic laboratory time scales for an arbitrarily varying temperature as function of time. The EME is probably the only realistic equation available today with this property that is also explicitly consistent...
Classical Diophantine equations
1993-01-01
The author had initiated a revision and translation of "Classical Diophantine Equations" prior to his death. Given the rapid advances in transcendence theory and diophantine approximation over recent years, one might fear that the present work, originally published in Russian in 1982, is mostly superseded. That is not so. A certain amount of updating had been prepared by the author himself before his untimely death. Some further revision was prepared by close colleagues. The first seven chapters provide a detailed, virtually exhaustive, discussion of the theory of lower bounds for linear forms in the logarithms of algebraic numbers and its applications to obtaining upper bounds for solutions to the eponymous classical diophantine equations. The detail may seem stark--- the author fears that the reader may react much as does the tourist on first seeing the centre Pompidou; notwithstanding that, Sprind zuk maintainsa pleasant and chatty approach, full of wise and interesting remarks. His emphases well warrant, ...
Numerical Solution of Heun Equation Via Linear Stochastic Differential Equation
Directory of Open Access Journals (Sweden)
Hamidreza Rezazadeh
2014-05-01
Full Text Available In this paper, we intend to solve special kind of ordinary differential equations which is called Heun equations, by converting to a corresponding stochastic differential equation(S.D.E.. So, we construct a stochastic linear equation system from this equation which its solution is based on computing fundamental matrix of this system and then, this S.D.E. is solved by numerically methods. Moreover, its asymptotic stability and statistical concepts like expectation and variance of solutions are discussed. Finally, the attained solutions of these S.D.E.s compared with exact solution of corresponding differential equations.
Dissipative Boussinesq equations
2007-01-01
40 pages, 15 figures, published in C. R. Mecanique 335 (2007) Other author's papers can be downloaded at http://www.cmla.ens-cachan.fr/~dutykh; International audience; The classical theory of water waves is based on the theory of inviscid flows. However it is important to include viscous effects in some applications. Two models are proposed to add dissipative effects in the context of the Boussinesq equations, which include the effects of weak dispersion and nonlinearity in a shallow water fr...
Differential equations with Mathematica
Abell, Martha L
2004-01-01
The Third Edition of the Differential Equations with Mathematica integrates new applications from a variety of fields,especially biology, physics, and engineering. The new handbook is also completely compatible with recent versions of Mathematica and is a perfect introduction for Mathematica beginners.* Focuses on the most often used features of Mathematica for the beginning Mathematica user* New applications from a variety of fields, including engineering, biology, and physics* All applications were completed using recent versions of Mathematica
Arithmetic partial differential equations
Buium, Alexandru; Simanca, Santiago R.
2006-01-01
We develop an arithmetic analogue of linear partial differential equations in two independent ``space-time'' variables. The spatial derivative is a Fermat quotient operator, while the time derivative is the usual derivation. This allows us to ``flow'' integers or, more generally, points on algebraic groups with coordinates in rings with arithmetic flavor. In particular, we show that elliptic curves have certain canonical ``flows'' on them that are the arithmetic analogues of the heat and wave...
Stability in Neutral Equations
1976-02-04
Martinez-Amores Division of Applied Mathematics Brown University Providence, Rhode Island 02912 and Universidad de Granada, Seccion de Matematicas , Spain S...XG w)1- 0 ~t)- >~~~ 0 suc ht j~<kIp, Ii 2 ~ o ~~~ X~ G (t) , y’ip X= 0 y 20 since equation (3.16) is satisfied. Since F = col(f,0), only the col
Trzetrzelewski, Maciej
2016-11-01
Starting with a Nambu-Goto action, a Dirac-like equation can be constructed by taking the square-root of the momentum constraint. The eigenvalues of the resulting Hamiltonian are real and correspond to masses of the excited string. In particular there are no tachyons. A special case of radial oscillations of a closed string in Minkowski space-time admits exact solutions in terms of wave functions of the harmonic oscillator.
Directory of Open Access Journals (Sweden)
D. Diederen
2015-06-01
Full Text Available We present a new equation describing the hydrodynamics in infinitely long tidal channels (i.e., no reflection under the influence of oceanic forcing. The proposed equation is a simple relationship between partial derivatives of water level and velocity. It is formally derived for a progressive wave in a frictionless, prismatic, tidal channel with a horizontal bed. Assessment of a large number of numerical simulations, where an open boundary condition is posed at a certain distance landward, suggests that it can also be considered accurate in the more natural case of converging estuaries with nonlinear friction and a bed slope. The equation follows from the open boundary condition and is therefore a part of the problem formulation for an infinite tidal channel. This finding provides a practical tool for evaluating tidal wave dynamics, by reconstructing the temporal variation of the velocity based on local observations of the water level, providing a fully local open boundary condition and allowing for local friction calibration.
Quantum molecular master equations
Brechet, Sylvain D.; Reuse, Francois A.; Maschke, Klaus; Ansermet, Jean-Philippe
2016-10-01
We present the quantum master equations for midsize molecules in the presence of an external magnetic field. The Hamiltonian describing the dynamics of a molecule accounts for the molecular deformation and orientation properties, as well as for the electronic properties. In order to establish the master equations governing the relaxation of free-standing molecules, we have to split the molecule into two weakly interacting parts, a bath and a bathed system. The adequate choice of these systems depends on the specific physical system under consideration. Here we consider a first system consisting of the molecular deformation and orientation properties and the electronic spin properties and a second system composed of the remaining electronic spatial properties. If the characteristic time scale associated with the second system is small with respect to that of the first, the second may be considered as a bath for the first. Assuming that both systems are weakly coupled and initially weakly correlated, we obtain the corresponding master equations. They describe notably the relaxation of magnetic properties of midsize molecules, where the change of the statistical properties of the electronic orbitals is expected to be slow with respect to the evolution time scale of the bathed system.
Directory of Open Access Journals (Sweden)
M. Paul Gough
2008-07-01
Full Text Available LandauerÃ¢Â€Â™s principle is applied to information in the universe. Once stars began forming there was a constant information energy density as the increasing proportion of matter at high stellar temperatures exactly compensated for the expanding universe. The information equation of state was close to the dark energy value, w = -1, for a wide range of redshifts, 10 > z > 0.8, over one half of cosmic time. A reasonable universe information bit content of only 1087 bits is sufficient for information energy to account for all dark energy. A time varying equation of state with a direct link between dark energy and matter, and linked to star formation in particular, is clearly relevant to the cosmic coincidence problem. In answering the Ã¢Â€Â˜Why now?Ã¢Â€Â™ question we wonder Ã¢Â€Â˜What next?Ã¢Â€Â™ as we expect the information equation of state to tend towards w = 0 in the future.c
Reduction operators of Burgers equation.
Pocheketa, Oleksandr A; Popovych, Roman O
2013-02-01
The solution of the problem on reduction operators and nonclassical reductions of the Burgers equation is systematically treated and completed. A new proof of the theorem on the special "no-go" case of regular reduction operators is presented, and the representation of the coefficients of operators in terms of solutions of the initial equation is constructed for this case. All possible nonclassical reductions of the Burgers equation to single ordinary differential equations are exhaustively described. Any Lie reduction of the Burgers equation proves to be equivalent via the Hopf-Cole transformation to a parameterized family of Lie reductions of the linear heat equation.
Bitsadze, A V
1963-01-01
Equations of the Mixed Type compiles a series of lectures on certain fundamental questions in the theory of equations of mixed type. This book investigates the series of problems concerning linear partial differential equations of the second order in two variables, and possessing the property that the type of the equation changes either on the boundary of or inside the considered domain. Topics covered include general remarks on linear partial differential equations of mixed type; study of the solutions of second order hyperbolic equations with initial conditions given along the lines of parab
New application to Riccati equation
Taogetusang; Sirendaoerji; Li, Shu-Min
2010-08-01
To seek new infinite sequence of exact solutions to nonlinear evolution equations, this paper gives the formula of nonlinear superposition of the solutions and Bäcklund transformation of Riccati equation. Based on the tanh-function expansion method and homogenous balance method, new infinite sequence of exact solutions to Zakharov-Kuznetsov equation, Karamoto-Sivashinsky equation and the set of (2+1)-dimensional asymmetric Nizhnik-Novikov-Veselov equations are obtained with the aid of symbolic computation system Mathematica. The method is of significance to construct infinite sequence exact solutions to other nonlinear evolution equations.
Evaluating Equating Results: Percent Relative Error for Chained Kernel Equating
Jiang, Yanlin; von Davier, Alina A.; Chen, Haiwen
2012-01-01
This article presents a method for evaluating equating results. Within the kernel equating framework, the percent relative error (PRE) for chained equipercentile equating was computed under the nonequivalent groups with anchor test (NEAT) design. The method was applied to two data sets to obtain the PRE, which can be used to measure equating…
Auxiliary equation method for solving nonlinear partial differential equations
Energy Technology Data Exchange (ETDEWEB)
Sirendaoreji,; Jiong, Sun
2003-03-31
By using the solutions of an auxiliary ordinary differential equation, a direct algebraic method is described to construct several kinds of exact travelling wave solutions for some nonlinear partial differential equations. By this method some physically important nonlinear equations are investigated and new exact travelling wave solutions are explicitly obtained with the aid of symbolic computation.
New Exact Solutions to NLS Equation and Coupled NLS Equations
Institute of Scientific and Technical Information of China (English)
FU Zun-Tao; LIU Shi-Da; LIU Shi-Kuo
2004-01-01
A transformation is introduced on the basis of the projective Riccati equations, and it is applied as an intermediate in expansion method to solve nonlinear Schrodinger (NLS) equation and coupled NLS equations. Many kinds of envelope travelling wave solutions including envelope solitary wave solution are obtained, in which some are found for the first time.
The compressible adjoint equations in geodynamics: equations and numerical assessment
Ghelichkhan, Siavash; Bunge, Hans-Peter
2016-04-01
The adjoint method is a powerful means to obtain gradient information in a mantle convection model relative to past flow structure. While the adjoint equations in geodynamics have been derived for the conservation equations of mantle flow in their incompressible form, the applicability of this approximation to Earth is limited, because density increases by almost a factor of two from the surface to the Core Mantle Boundary. Here we introduce the compressible adjoint equations for the conservation equations in the anelastic-liquid approximation. Our derivation applies an operator formulation in Hilbert spaces, to connect to recent work in seismology (Fichtner et al (2006)) and geodynamics (Horbach et al (2014)), where the approach was used to derive the adjoint equations for the wave equation and incompressible mantle flow. We present numerical tests of the newly derived equations based on twin experiments, focusing on three simulations. A first, termed Compressible, assumes the compressible forward and adjoint equations, and represents the consistent means of including compressibility effects. A second, termed Mixed, applies the compressible forward equation, but ignores compressibility effects in the adjoint equations, where the incompressible equations are used instead. A third simulation, termed Incompressible, neglects compressibility effects entirely in the forward and adjoint equations relative to the reference twin. The compressible and mixed formulations successfully restore earlier mantle flow structure, while the incompressible formulation yields noticeable artifacts. Our results suggest the use of a compressible formulation, when applying the adjoint method to seismically derived mantle heterogeneity structure.
Elliptic Equation and New Solutions to Nonlinear Wave Equations
Institute of Scientific and Technical Information of China (English)
FU Zun-Tao; LIU Shi-Kuo; LIU Shi-Da
2004-01-01
The new solutions to elliptic equation are shown, and then the elliptic equation is taken as a transformationand is applied to solve nonlinear wave equations. It is shown that more kinds of solutions are derived, such as periodicsolutions of rational form, solitary wave solutions of rational form, and so on.
Partial differential equations
Sloan, D; Süli, E
2001-01-01
/homepage/sac/cam/na2000/index.html7-Volume Set now available at special set price ! Over the second half of the 20th century the subject area loosely referred to as numerical analysis of partial differential equations (PDEs) has undergone unprecedented development. At its practical end, the vigorous growth and steady diversification of the field were stimulated by the demand for accurate and reliable tools for computational modelling in physical sciences and engineering, and by the rapid development of computer hardware and architecture. At the more theoretical end, the analytical insight in
Hyperbolic partial differential equations
Lax, Peter D
2006-01-01
The theory of hyperbolic equations is a large subject, and its applications are many: fluid dynamics and aerodynamics, the theory of elasticity, optics, electromagnetic waves, direct and inverse scattering, and the general theory of relativity. This book is an introduction to most facets of the theory and is an ideal text for a second-year graduate course on the subject. The first part deals with the basic theory: the relation of hyperbolicity to the finite propagation of signals, the concept and role of characteristic surfaces and rays, energy, and energy inequalities. The structure of soluti
Dimensional Equations of Entropy
Sparavigna, Amelia Carolina
2015-01-01
Entropy is a quantity which is of great importance in physics and chemistry. The concept comes out of thermodynamics, proposed by Rudolf Clausius in his analysis of Carnot cycle and linked by Ludwig Boltzmann to the number of specific ways in which a physical system may be arranged. Any physics classroom, in its task of learning physics, has therefore to face this crucial concept. As we will show in this paper, the lectures can be enriched by discussing dimensional equations linked to the entropy of some physical systems.
Partial differential equations
Levine, Harold
1997-01-01
The subject matter, partial differential equations (PDEs), has a long history (dating from the 18th century) and an active contemporary phase. An early phase (with a separate focus on taut string vibrations and heat flow through solid bodies) stimulated developments of great importance for mathematical analysis, such as a wider concept of functions and integration and the existence of trigonometric or Fourier series representations. The direct relevance of PDEs to all manner of mathematical, physical and technical problems continues. This book presents a reasonably broad introductory account of the subject, with due regard for analytical detail, applications and historical matters.
Ordinary differential equations
Cox, William
1995-01-01
Building on introductory calculus courses, this text provides a sound foundation in the underlying principles of ordinary differential equations. Important concepts, including uniqueness and existence theorems, are worked through in detail and the student is encouraged to develop much of the routine material themselves, thus helping to ensure a solid understanding of the fundamentals required.The wide use of exercises, problems and self-assessment questions helps to promote a deeper understanding of the material and it is developed in such a way that it lays the groundwork for further
Savvidy, G K
1998-01-01
We discuss the basic properties of the gonihedric string and the problem of its formulation in continuum. We propose a generalization of the Dirac equation and of the corresponding gamma matrices in order to describe the gonihedric string. The wave function and the Dirac matrices are infinite-dimensional. The spectrum of the theory consists of particles and antiparticles of increasing half-integer spin lying on quasilinear trajectories of different slope. Explicit formulas for the mass spectrum allow to compute the string tension and thus demonstrate the string character of the theory.
Generalized estimating equations
Hardin, James W
2013-01-01
Generalized Estimating Equations, Second Edition updates the best-selling previous edition, which has been the standard text on the subject since it was published a decade ago. Combining theory and application, the text provides readers with a comprehensive discussion of GEE and related models. Numerous examples are employed throughout the text, along with the software code used to create, run, and evaluate the models being examined. Stata is used as the primary software for running and displaying modeling output; associated R code is also given to allow R users to replicat
The Arrhenius equation revisited.
Peleg, Micha; Normand, Mark D; Corradini, Maria G
2012-01-01
The Arrhenius equation has been widely used as a model of the temperature effect on the rate of chemical reactions and biological processes in foods. Since the model requires that the rate increase monotonically with temperature, its applicability to enzymatic reactions and microbial growth, which have optimal temperature, is obviously limited. This is also true for microbial inactivation and chemical reactions that only start at an elevated temperature, and for complex processes and reactions that do not follow fixed order kinetics, that is, where the isothermal rate constant, however defined, is a function of both temperature and time. The linearity of the Arrhenius plot, that is, Ln[k(T)] vs. 1/T where T is in °K has been traditionally considered evidence of the model's validity. Consequently, the slope of the plot has been used to calculate the reaction or processes' "energy of activation," usually without independent verification. Many experimental and simulated rate constant vs. temperature relationships that yield linear Arrhenius plots can also be described by the simpler exponential model Ln[k(T)/k(T(reference))] = c(T-T(reference)). The use of the exponential model or similar empirical alternative would eliminate the confusing temperature axis inversion, the unnecessary compression of the temperature scale, and the need for kinetic assumptions that are hard to affirm in food systems. It would also eliminate the reference to the Universal gas constant in systems where a "mole" cannot be clearly identified. Unless proven otherwise by independent experiments, one cannot dismiss the notion that the apparent linearity of the Arrhenius plot in many food systems is due to a mathematical property of the model's equation rather than to the existence of a temperature independent "energy of activation." If T+273.16°C in the Arrhenius model's equation is replaced by T+b, where the numerical value of the arbitrary constant b is substantially larger than T and T
Differential Equations as Actions
DEFF Research Database (Denmark)
Ronkko, Mauno; Ravn, Anders P.
1997-01-01
We extend a conventional action system with a primitive action consisting of a differential equation and an evolution invariant. The semantics is given by a predicate transformer. The weakest liberal precondition is chosen, because it is not always desirable that steps corresponding to differential...... actions shall terminate. It is shown that the proposed differential action has a semantics which corresponds to a discrete approximation when the discrete step size goes to zero. The extension gives action systems the power to model real-time clocks and continuous evolutions within hybrid systems....
Conservational PDF Equations of Turbulence
Shih, Tsan-Hsing; Liu, Nan-Suey
2010-01-01
Recently we have revisited the traditional probability density function (PDF) equations for the velocity and species in turbulent incompressible flows. They are all unclosed due to the appearance of various conditional means which are modeled empirically. However, we have observed that it is possible to establish a closed velocity PDF equation and a closed joint velocity and species PDF equation through conditions derived from the integral form of the Navier-Stokes equations. Although, in theory, the resulted PDF equations are neither general nor unique, they nevertheless lead to the exact transport equations for the first moment as well as all higher order moments. We refer these PDF equations as the conservational PDF equations. This observation is worth further exploration for its validity and CFD application
Program Transformation by Solving Equations
Institute of Scientific and Technical Information of China (English)
朱鸿
1991-01-01
Based on the theory of orthogonal program expansion[8-10],the paper proposes a method to transform programs by solving program equations.By the method,transformation goals are expressed in program equations,and achieved by solving these equations.Although such equations are usually too complicated to be solved directly,the orthogonal expansion of programs makes it possible to reduce such equations into systems of equations only containing simple constructors of programs.Then,the solutions of such equations can be derived by a system of solving and simplifying rules,and algebraic laws of programs.The paper discusses the methods to simplify and solve equations and gives some examples.
On the supercritical KdV equation with time-oscillating nonlinearity
Panthee, M
2011-01-01
For the initial value problem (IVP) associated the generalized Korteweg-de Vries (gKdV) equation with supercritical nonlinearity, u_{t}+\\partial_x^3u+\\partial_x(u^{k+1}) =0,\\qquad k\\geq 5, numerical evidence \\cite{BDKM1, BSS1} shows that there are initial data $\\phi\\in H^1(\\mathbb{R})$ such that the corresponding solution may blow-up in finite time. Also, with the evidence from numerical simulation \\cite{ACKM, KP}, the physicists claim that a periodic time dependent term in factor of the nonlinearity would disturb the blow-up solution, either accelerating or delaying it. In this work, we investigate the IVP associated to the gKdV equation u_{t}+\\partial_x^3u+g(\\omega t)\\partial_x(u^{k+1}) =0, where $g$ is a periodic function and $k\\geq 5$ is an integer. We prove that, for given initial data $\\phi \\in H^1(\\R)$, as $|\\omega|\\to \\infty$, the solution $u_{\\omega}$ converges to the solution $U$ of the initial value problem associated to U_{t}+\\partial_x^3U+m(g)\\partial_x(U^{k+1}) =0, with the same initial data, wh...
Equation with the many fathers
DEFF Research Database (Denmark)
Kragh, Helge
1984-01-01
In this essay I discuss the origin and early development of the first relativistic wave equation, known as the Klein-Gordon equation. In 1926 several physicists, among them Klein, Fock, Schrödinger, and de Broglie, announced this equation as a candidate for a relativistic generalization of the us...
An Extented Wave Action Equation
Institute of Scientific and Technical Information of China (English)
左其华
2003-01-01
Based on the Navier-Stokes equation, an average wave energy equation and a generalized wave action conservation equation are presented in this paper. The turbulence effects on water particle velocity ui and wave surface elavation ξ as well as energy dissipation are included. Some simplified forms are also given.
Successfully Transitioning to Linear Equations
Colton, Connie; Smith, Wendy M.
2014-01-01
The Common Core State Standards for Mathematics (CCSSI 2010) asks students in as early as fourth grade to solve word problems using equations with variables. Equations studied at this level generate a single solution, such as the equation x + 10 = 25. For students in fifth grade, the Common Core standard for algebraic thinking expects them to…
Successfully Transitioning to Linear Equations
Colton, Connie; Smith, Wendy M.
2014-01-01
The Common Core State Standards for Mathematics (CCSSI 2010) asks students in as early as fourth grade to solve word problems using equations with variables. Equations studied at this level generate a single solution, such as the equation x + 10 = 25. For students in fifth grade, the Common Core standard for algebraic thinking expects them to…
Prolongation structures for supersymmetric equations
Roelofs, G.H.M.; Hijligenberg, van den N.W.
1990-01-01
The well known prolongation technique of Wahlquist and Estabrook (1975) for nonlinear evolution equations is generalized for supersymmetric equations and applied to the supersymmetric extension of the KdV equation of Manin-Radul. Using the theory of Kac-Moody Lie superalgebras, the explicit form of
Solution of Finite Element Equations
DEFF Research Database (Denmark)
Krenk, Steen
An important step in solving any problem by the finite element method is the solution of the global equations. Numerical solution of linear equations is a subject covered in most courses in numerical analysis. However, the equations encountered in most finite element applications have some special...
Discovering evolution equations with applications
McKibben, Mark
2011-01-01
Most existing books on evolution equations tend either to cover a particular class of equations in too much depth for beginners or focus on a very specific research direction. Thus, the field can be daunting for newcomers to the field who need access to preliminary material and behind-the-scenes detail. Taking an applications-oriented, conversational approach, Discovering Evolution Equations with Applications: Volume 2-Stochastic Equations provides an introductory understanding of stochastic evolution equations. The text begins with hands-on introductions to the essentials of real and stochast
A generalized advection dispersion equation
Indian Academy of Sciences (India)
Abdon Atangana
2014-02-01
This paper examines a possible effect of uncertainties, variability or heterogeneity of any dynamic system when being included in its evolution rule; the notion is illustrated with the advection dispersion equation, which describes the groundwater pollution model. An uncertain derivative is defined; some properties of the operator are presented. The operator is used to generalize the advection dispersion equation. The generalized equation differs from the standard equation in four properties. The generalized equation is solved via the variational iteration technique. Some illustrative figures are presented.
Integral equations and their applications
Rahman, M
2007-01-01
For many years, the subject of functional equations has held a prominent place in the attention of mathematicians. In more recent years this attention has been directed to a particular kind of functional equation, an integral equation, wherein the unknown function occurs under the integral sign. The study of this kind of equation is sometimes referred to as the inversion of a definite integral. While scientists and engineers can already choose from a number of books on integral equations, this new book encompasses recent developments including some preliminary backgrounds of formulations of in
Reduction of infinite dimensional equations
Directory of Open Access Journals (Sweden)
Zhongding Li
2006-02-01
Full Text Available In this paper, we use the general Legendre transformation to show the infinite dimensional integrable equations can be reduced to a finite dimensional integrable Hamiltonian system on an invariant set under the flow of the integrable equations. Then we obtain the periodic or quasi-periodic solution of the equation. This generalizes the results of Lax and Novikov regarding the periodic or quasi-periodic solution of the KdV equation to the general case of isospectral Hamiltonian integrable equation. And finally, we discuss the AKNS hierarchy as a special example.
Differential equations extended to superspace
Energy Technology Data Exchange (ETDEWEB)
Torres, J. [Instituto de Fisica, Universidad de Guanajuato, A.P. E-143, Leon, Guanajuato (Mexico); Rosu, H.C. [Instituto Potosino de Investigacion Cientifica y Tecnologica, A.P. 3-74, Tangamanga, San Luis Potosi (Mexico)
2003-07-01
We present a simple SUSY Ns = 2 superspace extension of the differential equations in which the sought solutions are considered to be real superfields but maintaining the common derivative operators and the coefficients of the differential equations unaltered. In this way, we get self consistent systems of coupled differential equations for the components of the superfield. This procedure is applied to the Riccati equation, for which we obtain in addition the system of coupled equations corresponding to the components of the general superfield solution. (Author)
Yehorchenko, Irina
2010-01-01
We study possible Lie and non-classical reductions of multidimensional wave equations and the special classes of possible reduced equations - their symmetries and equivalence classes. Such investigation allows to find many new conditional and hidden symmetries of the original equations.
Institute of Scientific and Technical Information of China (English)
黄虎; 丁平兴; 吕秀红
2001-01-01
The Hamiltonian formalism for surface waves and the mild-slope approximation were empolyed in handling the case of slowly varying three-dimensional currents and an uneven bottom, thus leading to an extended mild-slope equation. The bottom topography consists of two components: the slowly varying component whose horizontal length scale is longer than the surface wave length, and the fast varying component with the amplitude being smaller than that of the surface wave. The frequency of the fast varying depth component is, however, comparable to that of the surface waves. The extended mild- slope equation is more widely applicable and contains as special cases famous mild-slope equations below: the classical mild-slope equation of Berkhoff , Kirby' s mild-slope equation with current, and Dingemans' s mild-slope equation for rippled bed. The extended shallow water equations for ambient currents and rapidly varying topography are also obtained.
Scaling of differential equations
Langtangen, Hans Petter
2016-01-01
The book serves both as a reference for various scaled models with corresponding dimensionless numbers, and as a resource for learning the art of scaling. A special feature of the book is the emphasis on how to create software for scaled models, based on existing software for unscaled models. Scaling (or non-dimensionalization) is a mathematical technique that greatly simplifies the setting of input parameters in numerical simulations. Moreover, scaling enhances the understanding of how different physical processes interact in a differential equation model. Compared to the existing literature, where the topic of scaling is frequently encountered, but very often in only a brief and shallow setting, the present book gives much more thorough explanations of how to reason about finding the right scales. This process is highly problem dependent, and therefore the book features a lot of worked examples, from very simple ODEs to systems of PDEs, especially from fluid mechanics. The text is easily accessible and exam...
Energy Technology Data Exchange (ETDEWEB)
Cardona, Carlos [Physics Division, National Center for Theoretical Sciences, National Tsing-Hua University,Hsinchu, Taiwan 30013 (China); Gomez, Humberto [Instituto de Fisica - Universidade de São Paulo,Caixa Postal 66318, 05315-970 São Paulo, SP (Brazil); Facultad de Ciencias Basicas, Universidad Santiago de Cali,Calle 5 62-00 Barrio Pampalinda, Cali, Valle (Colombia)
2016-06-16
Recently the CHY approach has been extended to one loop level using elliptic functions and modular forms over a Jacobian variety. Due to the difficulty in manipulating these kind of functions, we propose an alternative prescription that is totally algebraic. This new proposal is based on an elliptic algebraic curve embedded in a ℂP{sup 2} space. We show that for the simplest integrand, namely the n−gon, our proposal indeed reproduces the expected result. By using the recently formulated Λ−algorithm, we found a novel recurrence relation expansion in terms of tree level off-shell amplitudes. Our results connect nicely with recent results on the one-loop formulation of the scattering equations. In addition, this new proposal can be easily stretched out to hyperelliptic curves in order to compute higher genus.
$\\Lambda$ Scattering Equations
Gomez, Humberto
2016-01-01
The CHY representation of scattering amplitudes is based on integrals over the moduli space of a punctured sphere. We replace the punctured sphere by a double-cover version. The resulting scattering equations depend on a parameter $\\Lambda$ controlling the opening of a branch cut. The new representation of scattering amplitudes possesses an enhanced redundancy which can be used to fix, modulo branches, the location of four punctures while promoting $\\Lambda$ to a variable. Via residue theorems we show how CHY formulas break up into sums of products of smaller (off-shell) ones times a propagator. This leads to a powerful way of evaluating CHY integrals of generic rational functions, which we call the $\\Lambda$ algorithm.
The Riccati Differential Equation and a Diffusion-Type Equation
Suazo, Erwin; Vega-Guzman, Jose M
2008-01-01
We construct an explicit solution of the Cauchy initial value problem for certain diffusion-type equation with variable coefficients on the entire real line. The corresponding Green function (heat kernel) is given in terms of elementary functions and certain integrals involving a characteristic function, which should be found as an analytic or numerical solution of the second order linear differential equation with time-dependent coefficients. Some special and limiting cases are outlined. Solution of the corresponding nonhomogeneous equation is also found.
Comparison between characteristics of mild slope equations and Boussinesq equations
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
Boussinesq-type equations and mild-slope equations are compared in terms of their basic forms and characteristics. It is concluded that linear mild-slope equations on dispersion relation are better than non-linear Boussinesq equations. In addition, Berkhoff experiments are computed and compared by the two models, and agreement between model results and available experimental data is found to be quite reasonable, which demonstrates the two models' capacity to simulate wave transformation. However they can deal with different physical processes respectively, and they have their own characteristics.
Mode decomposition evolution equations.
Wang, Yang; Wei, Guo-Wei; Yang, Siyang
2012-03-01
Partial differential equation (PDE) based methods have become some of the most powerful tools for exploring the fundamental problems in signal processing, image processing, computer vision, machine vision and artificial intelligence in the past two decades. The advantages of PDE based approaches are that they can be made fully automatic, robust for the analysis of images, videos and high dimensional data. A fundamental question is whether one can use PDEs to perform all the basic tasks in the image processing. If one can devise PDEs to perform full-scale mode decomposition for signals and images, the modes thus generated would be very useful for secondary processing to meet the needs in various types of signal and image processing. Despite of great progress in PDE based image analysis in the past two decades, the basic roles of PDEs in image/signal analysis are only limited to PDE based low-pass filters, and their applications to noise removal, edge detection, segmentation, etc. At present, it is not clear how to construct PDE based methods for full-scale mode decomposition. The above-mentioned limitation of most current PDE based image/signal processing methods is addressed in the proposed work, in which we introduce a family of mode decomposition evolution equations (MoDEEs) for a vast variety of applications. The MoDEEs are constructed as an extension of a PDE based high-pass filter (Europhys. Lett., 59(6): 814, 2002) by using arbitrarily high order PDE based low-pass filters introduced by Wei (IEEE Signal Process. Lett., 6(7): 165, 1999). The use of arbitrarily high order PDEs is essential to the frequency localization in the mode decomposition. Similar to the wavelet transform, the present MoDEEs have a controllable time-frequency localization and allow a perfect reconstruction of the original function. Therefore, the MoDEE operation is also called a PDE transform. However, modes generated from the present approach are in the spatial or time domain and can be
Introduction to partial differential equations
Borthwick, David
2016-01-01
This modern take on partial differential equations does not require knowledge beyond vector calculus and linear algebra. The author focuses on the most important classical partial differential equations, including conservation equations and their characteristics, the wave equation, the heat equation, function spaces, and Fourier series, drawing on tools from analysis only as they arise.Within each section the author creates a narrative that answers the five questions: (1) What is the scientific problem we are trying to understand? (2) How do we model that with PDE? (3) What techniques can we use to analyze the PDE? (4) How do those techniques apply to this equation? (5) What information or insight did we obtain by developing and analyzing the PDE? The text stresses the interplay between modeling and mathematical analysis, providing a thorough source of problems and an inspiration for the development of methods.
Differential equations methods and applications
Said-Houari, Belkacem
2015-01-01
This book presents a variety of techniques for solving ordinary differential equations analytically and features a wealth of examples. Focusing on the modeling of real-world phenomena, it begins with a basic introduction to differential equations, followed by linear and nonlinear first order equations and a detailed treatment of the second order linear equations. After presenting solution methods for the Laplace transform and power series, it lastly presents systems of equations and offers an introduction to the stability theory. To help readers practice the theory covered, two types of exercises are provided: those that illustrate the general theory, and others designed to expand on the text material. Detailed solutions to all the exercises are included. The book is excellently suited for use as a textbook for an undergraduate class (of all disciplines) in ordinary differential equations. .
Energy Conservation Equations of Motion
Vinokurov, Nikolay A
2015-01-01
A conventional derivation of motion equations in mechanics and field equations in field theory is based on the principle of least action with a proper Lagrangian. With a time-independent Lagrangian, a function of coordinates and velocities that is called energy is constant. This paper presents an alternative approach, namely derivation of a general form of equations of motion that keep the system energy, expressed as a function of generalized coordinates and corresponding velocities, constant. These are Lagrange equations with addition of gyroscopic forces. The important fact, that the energy is defined as the function on the tangent bundle of configuration manifold, is used explicitly for the derivation. The Lagrangian is derived from a known energy function. A development of generalized Hamilton and Lagrange equations without the use of variational principles is proposed. The use of new technique is applied to derivation of some equations.
Stochastic partial differential equations
Lototsky, Sergey V
2017-01-01
Taking readers with a basic knowledge of probability and real analysis to the frontiers of a very active research discipline, this textbook provides all the necessary background from functional analysis and the theory of PDEs. It covers the main types of equations (elliptic, hyperbolic and parabolic) and discusses different types of random forcing. The objective is to give the reader the necessary tools to understand the proofs of existing theorems about SPDEs (from other sources) and perhaps even to formulate and prove a few new ones. Most of the material could be covered in about 40 hours of lectures, as long as not too much time is spent on the general discussion of stochastic analysis in infinite dimensions. As the subject of SPDEs is currently making the transition from the research level to that of a graduate or even undergraduate course, the book attempts to present enough exercise material to fill potential exams and homework assignments. Exercises appear throughout and are usually directly connected ...
Energy Technology Data Exchange (ETDEWEB)
Menikoff, Ralph [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2015-12-15
The JWL equation of state (EOS) is frequently used for the products (and sometimes reactants) of a high explosive (HE). Here we review and systematically derive important properties. The JWL EOS is of the Mie-Grueneisen form with a constant Grueneisen coefficient and a constants specific heat. It is thermodynamically consistent to specify the temperature at a reference state. However, increasing the reference state temperature restricts the EOS domain in the (V, e)-plane of phase space. The restrictions are due to the conditions that P ≥ 0, T ≥ 0, and the isothermal bulk modulus is positive. Typically, this limits the low temperature regime in expansion. The domain restrictions can result in the P-T equilibrium EOS of a partly burned HE failing to have a solution in some cases. For application to HE, the heat of detonation is discussed. Example JWL parameters for an HE, both products and reactions, are used to illustrate the restrictions on the domain of the EOS.
The generalized Airy diffusion equation
Directory of Open Access Journals (Sweden)
Frank M. Cholewinski
2003-08-01
Full Text Available Solutions of a generalized Airy diffusion equation and an associated nonlinear partial differential equation are obtained. Trigonometric type functions are derived for a third order generalized radial Euler type operator. An associated complex variable theory and generalized Cauchy-Euler equations are obtained. Further, it is shown that the Airy expansions can be mapped onto the Bessel Calculus of Bochner, Cholewinski and Haimo.
Hyperbolic Methods for Einstein's Equations
Directory of Open Access Journals (Sweden)
Reula Oscar
1998-01-01
Full Text Available I review evolutionary aspects of general relativity, in particular those related to the hyperbolic character of the field equations and to the applications or consequences that this property entails. I look at several approaches to obtaining symmetric hyperbolic systems of equations out of Einstein's equations by either removing some gauge freedoms from them, or by considering certain linear combinations of a subset of them.
Partial Differential Equations of Physics
Geroch, Robert
1996-01-01
Apparently, all partial differential equations that describe physical phenomena in space-time can be cast into a universal quasilinear, first-order form. In this paper, we do two things. First, we describe some broad features of systems of differential equations so formulated. Examples of such features include hyperbolicity of the equations, constraints and their roles (e.g., in connection with the initial-value formulation), how diffeomorphism freedom is manifest, and how interactions betwee...
Integrable Equations on Time Scales
Gurses, Metin; Guseinov, Gusein Sh.; Silindir, Burcu
2005-01-01
Integrable systems are usually given in terms of functions of continuous variables (on ${\\mathbb R}$), functions of discrete variables (on ${\\mathbb Z}$) and recently in terms of functions of $q$-variables (on ${\\mathbb K}_{q}$). We formulate the Gel'fand-Dikii (GD) formalism on time scales by using the delta differentiation operator and find more general integrable nonlinear evolutionary equations. In particular they yield integrable equations over integers (difference equations) and over $q...
Delay equations and radiation damping
Chicone, C.; Kopeikin, S. M.; Mashhoon, B.; Retzloff, D. G.
2001-06-01
Starting from delay equations that model field retardation effects, we study the origin of runaway modes that appear in the solutions of the classical equations of motion involving the radiation reaction force. When retardation effects are small, we argue that the physically significant solutions belong to the so-called slow manifold of the system and we identify this invariant manifold with the attractor in the state space of the delay equation. We demonstrate via an example that when retardation effects are no longer small, the motion could exhibit bifurcation phenomena that are not contained in the local equations of motion.
Correct Linearization of Einstein's Equations
Directory of Open Access Journals (Sweden)
Rabounski D.
2006-06-01
Full Text Available Regularly Einstein's equations can be reduced to a wave form (linearly dependent from the second derivatives of the space metric in the absence of gravitation, the space rotation and Christoffel's symbols. As shown here, the origin of the problem is that one uses the general covariant theory of measurement. Here the wave form of Einstein's equations is obtained in the terms of Zelmanov's chronometric invariants (physically observable projections on the observer's time line and spatial section. The obtained equations depend on solely the second derivatives even if gravitation, the space rotation and Christoffel's symbols. The correct linearization proves: the Einstein equations are completely compatible with weak waves of the metric.
Solutions of relativistic radial quasipotential equations
Energy Technology Data Exchange (ETDEWEB)
Minh, V.X.; Kadyshevskii, V.G.; Zhidkov, E.P.
1985-11-01
A systematic approach to the investigation of relativistic radial quasipotential equations is developed. The quasipotential equations can be interpreted either as linear equations in finite differences of fourth and second orders, respectively, or as differential equations of infinite order.
The generalized Kolmogorov-Petrovskii-Piskunov equation
Adomian, G.
1995-02-01
Nonlinear nonlocal equations of mathematical physics such as the K.P.P. equation, the generalized nonlinear Schrödinger equation, the Witham equation for water waves et al. are solved by decomposition.
Anomalous Fractional Diffusion Equation for Transport Phenomena
Institute of Scientific and Technical Information of China (English)
QiuhuaZENG; HouqiangLI; 等
1999-01-01
We derive the standard diffusion equation from the continuity equation and by discussing the defectiveness of earlier proposed equations,we get the generalized fractional diffusion equation for anomalous diffusion.
Institute of Scientific and Technical Information of China (English)
王正艳; 李锐; 王成国; 刘瑾; 许淑云; 薛克营
2009-01-01
目的:研究细胞外基质(ECM)对哮喘大鼠气道平滑肌细胞(ASMCs)磷脂酰肌醇-3-激酶p85(PI3Kp85)表达的影响.方珐:卵白蛋白(OVA)致敏法复制大鼠哮喘模型,将培养后的大鼠叶支气管ASMCs分别种植在涂覆有纤维连接蛋白、Ⅰ型胶原及层粘蛋白的培养瓶中培养,Western blot检测各组ASMCs中PI3Kp85蛋白表达,Realtime PCR检测其mRNA.另取12只正常大鼠做对照.结果:哮喘纤维连接蛋白组、层粘蛋白组、Ⅰ型胶原蛋白组ASMCs中PI3Kp85 mRNA的表达分别是(7.63±0.61)、(9.73±0.68)、(16.22±0.88),均明显高于对照组(5.93±0.75)(P<0.01);蛋白表达情况与mRNA趋势一致.结论:纤维连接蛋白、Ⅰ型胶原及层粘蛋白可以上调哮喘大鼠气道平滑肌细胞中PI3Kp85表达.
ANALYTICAL SOLUTIONS FOR SOME NONLINEAR EVOLUTION EQUATIONS
Institute of Scientific and Technical Information of China (English)
胡建兰; 张汉林
2003-01-01
The following partial differential equations are studied: generaliz ed fifth-orderKdV equation, water wave equation, Kupershmidt equation, couples KdV equation. Theanalytical solutions to these problems via using various ansaiz es by introducing a second-order ordinary differential equation are found out.
Conservation Laws of Differential Equations in Finance
Institute of Scientific and Technical Information of China (English)
QIN Mao-Chang; MEI Feng-Xiang; SHANG Mei
2005-01-01
Conservation laws of some differential equations in fiance are studied in this paper. This method does not involve the use or existence of a variational principle. As an alternative, linearize the given equation and find adjoint equation of the linearized equation, the conservation laws can be constructed directly from the symmetries and adjoint symmetries of the associated linearized equation and its adjoint equation.
Introduction to nonlinear dispersive equations
Linares, Felipe
2015-01-01
This textbook introduces the well-posedness theory for initial-value problems of nonlinear, dispersive partial differential equations, with special focus on two key models, the Korteweg–de Vries equation and the nonlinear Schrödinger equation. A concise and self-contained treatment of background material (the Fourier transform, interpolation theory, Sobolev spaces, and the linear Schrödinger equation) prepares the reader to understand the main topics covered: the initial-value problem for the nonlinear Schrödinger equation and the generalized Korteweg–de Vries equation, properties of their solutions, and a survey of general classes of nonlinear dispersive equations of physical and mathematical significance. Each chapter ends with an expert account of recent developments and open problems, as well as exercises. The final chapter gives a detailed exposition of local well-posedness for the nonlinear Schrödinger equation, taking the reader to the forefront of recent research. The second edition of Introdu...
Singularity: Raychaudhuri equation once again
Indian Academy of Sciences (India)
Naresh Dadhich
2007-07-01
I first recount Raychaudhuri's deep involvement with the singularity problem in general relativity. I then argue that precisely the same situation has arisen today in loop quantum cosmology as obtained when Raychaudhuri discovered his celebrated equation. We thus need a new analogue of the Raychaudhuri equation in quantum gravity.
Directory of Open Access Journals (Sweden)
Vijay K. Garg
1998-01-01
reason for the discrepancy on the pressure surface could be the presence of unsteady effects due to stator-rotor interaction in the experiments which are not modeled in the present computations. Prediction using the two-equation model is in general poorer than that using the zero-equation model, while the former requires at least 40% more computational resources.
Differential equations a concise course
Bear, H S
2011-01-01
Concise introduction for undergraduates includes, among other topics, a survey of first order equations, discussions of complex-valued solutions, linear differential operators, inverse operators and variation of parameters method, the Laplace transform, Picard's existence theorem, and an exploration of various interpretations of systems of equations. Numerous clearly stated theorems and proofs, examples, and problems followed by solutions.
On Degenerate Partial Differential Equations
Chen, Gui-Qiang G.
2010-01-01
Some of recent developments, including recent results, ideas, techniques, and approaches, in the study of degenerate partial differential equations are surveyed and analyzed. Several examples of nonlinear degenerate, even mixed, partial differential equations, are presented, which arise naturally in some longstanding, fundamental problems in fluid mechanics and differential geometry. The solution to these fundamental problems greatly requires a deep understanding of nonlinear degenerate parti...
Enclosing Solutions of Integral Equations
DEFF Research Database (Denmark)
Madsen, Kaj; NA NA NA Caprani, Ole; Stauning, Ole
1996-01-01
We present a method for enclosing the solution of an integral equation. It is assumed that a solution exists and that the corresponding integral operator T is a contraction near y. When solving the integral equation by iteration we obtain a result which is normally different from y because...
Institute of Scientific and Technical Information of China (English)
M. Ko(c)ak; B. G(o)nül
2007-01-01
The solutions, in terms of orthogonal polynomials, of Dirac equation with analytically solvable potentials are investigated within a novel formalism by transforming the relativistic equation into a Schr(o)dinger-like one. Earlier results are discussed in a unified framework, and some solutions of a large class of potentials are given.
Stochastic integral equations without probability
Mikosch, T; Norvaisa, R
2000-01-01
A pathwise approach to stochastic integral equations is advocated. Linear extended Riemann-Stieltjes integral equations driven by certain stochastic processes are solved. Boundedness of the p-variation for some 0
Solving equations by topological methods
Directory of Open Access Journals (Sweden)
Lech Górniewicz
2005-01-01
Full Text Available In this paper we survey most important results from topological fixed point theory which can be directly applied to differential equations. Some new formulations are presented. We believe that our article will be useful for analysts applying topological fixed point theory in nonlinear analysis and in differential equations.
Enclosing Solutions of Integral Equations
DEFF Research Database (Denmark)
Madsen, Kaj; NA NA NA Caprani, Ole; Stauning, Ole
1996-01-01
We present a method for enclosing the solution of an integral equation. It is assumed that a solution exists and that the corresponding integral operator T is a contraction near y. When solving the integral equation by iteration we obtain a result which is normally different from y because...
Moro, J.; Denardini, C. M.; Resende, L. C. A.; Chen, S. S.; Schuch, N. J.
2016-10-01
In this work, the seasonal dependency of the E region electric field (EEF) at the dip equator is examined. The eastward zonal (Ey) and the daytime vertical (Ez) electric fields are responsible for the overall phenomenology of the equatorial and low-latitude ionosphere, including the equatorial electrojet (EEJ) and its plasma instability. The electric field components are studied based on long-term backscatter radars soundings (348 days for both systems) collected during geomagnetic quiet days (Kp ≤ 3+), from 2001 to 2010, at the São Luís Space Observatory (SLZ), Brazil (2.33°S, 44.20°W), and at the Jicamarca Radio Observatory (JRO), Peru (11.95°S, 76.87°W). Among the results, we observe, for the first time, a seasonal difference between the EEF in these two sectors in South America based on coherent radar measurements. The EEF is more intense in summer at SLZ, in equinox at JRO, and has been highly variable with season in the Brazilian sector compared to the Peruvian sector. In addition, the secular variation on the geomagnetic field and its effect on the EEJ over Brazil resulted that as much farther away is the magnetic equator from SLZ, later more the EEJ is observed (10 h LT) and sooner it ends (16 h LT). Moreover, the time interval of type II occurrence decreased significantly after the year 2004, which is a clear indication that SLZ is no longer an equatorial station due to the secular variation of the geomagnetic field.
A Generalized Cubic Functional Equation
Institute of Scientific and Technical Information of China (English)
P. K. SAHOO
2005-01-01
In this paper, we determine the general solution of the functional equation f1 (2x + y) +f2(2x - y) ＝ f3(x + y) + f4(x - y) + f5(x) without assuming any regularity condition on the unknown functions f1,f2,f3, f4,f5: R → R. The general solution of this equation is obtained by finding the general solution of the functional equations f(2x + y) + f(2x - y) = g(x + y) + g(x - y) + h(x) and f(2x + y) - f(2x - y) ＝ g(x + y) - g(x - y). The method used for solving these functional equations is elementary but exploits an important result due to Hosszu. The solution of this functional equation can also be determined in certain type of groups using two important results due to Székelyhidi.
Directory of Open Access Journals (Sweden)
Hernández Olivares, F.
1998-12-01
Full Text Available Silica fume (SF or microsilica is related mainly with preparation of High Resistance Concrete. This has justified its use -together with portland cement (I-42'5/SR,MR and an superfiuidifying additive- in the preparation of a concrete whose value for compressive mechanical resistance at early ages (only 5 to 10 hours is higher than 40 kp/cm2, instead of preparing it with the portland cement plus a setting accelerator or "model" dosage. The experimental techniques used to reach that objective have been: ultrasound energy and a press for breaking 30 x 15 mm specimens, and a maximum load of 2001. With the first technique, in only 25 days, 13 different dossages were prepared, which were compared to the "model" dosage, and two more that did not contain neither setting accelerator nor SF, this means that they had been prepared with the same portland cement, same fine and coarse aggregates and the same consistency, and that they would act as "reference" for all previous ones. In such a way the dosage was found: E, in this case, that was the same as the "model" as for the amount of fine and coarse aggregates, but not as for the amount of the portland cement used which this time was 360 kg/m3 instead of 400kg/m3 SF content 40 kg/m3 and water 144 l/m3Al humo de sílice(HSE o microsílice, se le relaciona, principalmente, con la preparación de hormigones de alta resistencia. Esta peculiar característica, ha justificado su utilización -junto a cemento portland (un I-42,5/SR,MR y un aditivo superfluidificante- en la preparación de un hormigón cuyo valor de resistencia mecánica a compresión a edades iniciales (5 a 10 horas, solamente fuera superior a 40 kp/cm2, en lugar de prepararlo con dicho cemento portland y un acelerador de fraguado o dosificación "patrón”. Las técnicas experimentales utilizadas para alcanzar dicho objetivo han sido: la energía de ultrasonido y una prensa para la rotura de probetas de 30x15 cm, de 200 t de carga m
Upper bounds for parabolic equations and the Landau equation
Silvestre, Luis
2017-02-01
We consider a parabolic equation in nondivergence form, defined in the full space [ 0 , ∞) ×Rd, with a power nonlinearity as the right-hand side. We obtain an upper bound for the solution in terms of a weighted control in Lp. This upper bound is applied to the homogeneous Landau equation with moderately soft potentials. We obtain an estimate in L∞ (Rd) for the solution of the Landau equation, for positive time, which depends only on the mass, energy and entropy of the initial data.
Energy equation, the dissipation function and the Euler turbine equation
Energy Technology Data Exchange (ETDEWEB)
Mobarak, A. (Cairo Univ. (Egypt). Faculty of Engineering)
1978-01-01
The derivation of the energy equation for a rotating frame of coordinates is presented. The link between the thermodynamics and the fluid dynamics of viscous flow and which is generally given by the dissipation function is discussed in more detail. This work shows, that the published definition of the dissipation function is an improper one, and leads in connection with the energy equation to contradictory results when considering the principle of energy conservation. Further, the Euler turbine equation is discussed, and it is shown that the present form is only valid, if the flow condition in the rotor (the relative system) is steady.
COMPARISON BETWEEN BOUSSINESQ EQUATIONS AND MILD-SLOPE EQUATIONS MODEL
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
In this paper, the Boussinesq equations and mild-slope equation of wave transformation in near-shore shallow water were introduced and the characteristics of the two forms of equations were compared and analyzed. Meanwhile, a Boussinesq wave model which includes effects of bottom friction, wave breaking and subgrid turbulent mixing is established, slot technique dealing with moving boundary and damping layer dealing with absorbing boundary were established. By adopting empirical nonlinear dispersion relation and including nonlinear term, the mild-slope equation model was modified to take nonlinear effects into account. The two types of models were validated with the experiment results given by Berkhoff and their accuracy was analysed and compared with that of correlated methods.
Higher derivative gravity: Field equation as the equation of state
Dey, Ramit; Liberati, Stefano; Mohd, Arif
2016-08-01
One of the striking features of general relativity is that the Einstein equation is implied by the Clausius relation imposed on a small patch of locally constructed causal horizon. The extension of this thermodynamic derivation of the field equation to more general theories of gravity has been attempted many times in the last two decades. In particular, equations of motion for minimally coupled higher-curvature theories of gravity, but without the derivatives of curvature, have previously been derived using a thermodynamic reasoning. In that derivation the horizon slices were endowed with an entropy density whose form resembles that of the Noether charge for diffeomorphisms, and was dubbed the Noetheresque entropy. In this paper, we propose a new entropy density, closely related to the Noetheresque form, such that the field equation of any diffeomorphism-invariant metric theory of gravity can be derived by imposing the Clausius relation on a small patch of local causal horizon.
Higher derivative gravity: field equation as the equation of state
Dey, Ramit; Mohd, Arif
2016-01-01
One of the striking features of general relativity is that the Einstein equation is implied by the Clausius relation imposed on a small patch of locally constructed causal horizon. Extension of this thermodynamic derivation of the field equation to more general theories of gravity has been attempted many times in the last two decades. In particular, equations of motion for minimally coupled higher curvature theories of gravity, but without the derivatives of curvature, have previously been derived using a thermodynamic reasoning. In that derivation the horizon slices were endowed with an entropy density whose form resembles that of the Noether charge for diffeomorphisms, and was dubbed the Noetheresque entropy. In this paper, we propose a new entropy density, closely related to the Noetheresque form, such that the field equation of any diffeomorphism invariant metric theory of gravity can be derived by imposing the Clausius relation on a small patch of local causal horizon.
Extended Trial Equation Method for Nonlinear Partial Differential Equations
Gepreel, Khaled A.; Nofal, Taher A.
2015-04-01
The main objective of this paper is to use the extended trial equation method to construct a series of some new solutions for some nonlinear partial differential equations (PDEs) in mathematical physics. We will construct the solutions in many different functions such as hyperbolic function solutions, trigonometric function solutions, Jacobi elliptic function solutions, and rational functional solutions for the nonlinear PDEs when the balance number is a real number via the Zhiber-Shabat nonlinear differential equation. The balance number of this method is not constant as we shown in other methods, but it is changed by changing the trial equation derivative definition. This method allowed us to construct many new types of solutions. It is shown by using the Maple software package that all obtained solutions satisfy the original PDEs.
Stochastic differential equations, backward SDEs, partial differential equations
Pardoux, Etienne
2014-01-01
This research monograph presents results to researchers in stochastic calculus, forward and backward stochastic differential equations, connections between diffusion processes and second order partial differential equations (PDEs), and financial mathematics. It pays special attention to the relations between SDEs/BSDEs and second order PDEs under minimal regularity assumptions, and also extends those results to equations with multivalued coefficients. The authors present in particular the theory of reflected SDEs in the above mentioned framework and include exercises at the end of each chapter. Stochastic calculus and stochastic differential equations (SDEs) were first introduced by K. Itô in the 1940s, in order to construct the path of diffusion processes (which are continuous time Markov processes with continuous trajectories taking their values in a finite dimensional vector space or manifold), which had been studied from a more analytic point of view by Kolmogorov in the 1930s. Since then, this topic has...
Wave equations for pulse propagation
Shore, B. W.
1987-06-01
Theoretical discussions of the propagation of pulses of laser radiation through atomic or molecular vapor rely on a number of traditional approximations for idealizing the radiation and the molecules, and for quantifying their mutual interaction by various equations of propagation (for the radiation) and excitation (for the molecules). In treating short-pulse phenomena it is essential to consider coherent excitation phenomena of the sort that is manifest in Rabi oscillations of atomic or molecular populations. Such processes are not adequately treated by rate equations for excitation nor by rate equations for radiation. As part of a more comprehensive treatment of the coupled equations that describe propagation of short pulses, this memo presents background discussion of the equations that describe the field. This memo discusses the origin, in Maxwell's equations, of the wave equation used in the description of pulse propagation. It notes the separation into lamellar and solenoidal (or longitudinal and transverse) and positive and negative frequency parts. It mentions the possibility of separating the polarization field into linear and nonlinear parts, in order to define a susceptibility or index of refraction and, from these, a phase and group velocity.
Extension of the Schrodinger equation
Somsikov, Vyacheslav
2017-03-01
Extension of the Schrodinger equation is submitted by removing its limitations appearing due to the limitations of the formalism of Hamilton, based on which this equation was obtained. For this purpose the problems of quantum mechanics arising from the limitations of classical mechanics are discussed. These limitations, in particular, preclude the use of the Schrodinger equation to describe the time symmetry violation. The extension of the Schrodinger equation is realized based on the principle of duality symmetry. According to this principle the dynamics of the systems is determined by the symmetry of the system and by the symmetry of the space. The extension of the Schrodinger equation was obtained from the dual expression of energy, represented in operator form. For this purpose the independent micro - and macro-variables that determine respectively the dynamics of quantum particle system relative to its center of mass and the movement of the center of mass in space are used. The solution of the extended Schrodinger equation for the system near equilibrium is submitted. The main advantage of the extended Schrodinger equation is that it is applicable to describe the interaction and evolution of quantum systems in inhomogeneous field of external forces.
Equational theories of tropical sernirings
DEFF Research Database (Denmark)
Aceto, Luca; Esik, Zoltan; Ingolfsdottir, Anna
2003-01-01
of these commutative idempotent weak semirings, the paper offers characterizations of the equations that hold in them, decidability results for their equational theories, explicit descriptions of the free algebras in the varieties they generate, and relative axiomatization results. Udgivelsesdato: APR 11......This paper studies the equational theories of various exotic semirings presented in the literature. Exotic semirings are semirings whose underlying carrier set is some subset of the set of real numbers equipped with binary operations of minimum or maximum as sum, and addition as product. Two prime...
Lectures on ordinary differential equations
Hurewicz, Witold
2014-01-01
Hailed by The American Mathematical Monthly as ""a rigorous and lively introduction,"" this text explores a topic of perennial interest in mathematics. The author, a distinguished mathematician and formulator of the Hurewicz theorem, presents a clear and lucid treatment that emphasizes geometric methods. Topics include first-order scalar and vector equations, basic properties of linear vector equations, and two-dimensional nonlinear autonomous systems. Suitable for senior mathematics students, the text begins with an examination of differential equations of the first order in one unknown funct
Integral equation methods for electromagnetics
Volakis, John
2012-01-01
This text/reference is a detailed look at the development and use of integral equation methods for electromagnetic analysis, specifically for antennas and radar scattering. Developers and practitioners will appreciate the broad-based approach to understanding and utilizing integral equation methods and the unique coverage of historical developments that led to the current state-of-the-art. In contrast to existing books, Integral Equation Methods for Electromagnetics lays the groundwork in the initial chapters so students and basic users can solve simple problems and work their way up to the mo
Loop equations from differential systems
Eynard, Bertrand; Marchal, Olivier
2016-01-01
To any differential system $d\\Psi=\\Phi\\Psi$ where $\\Psi$ belongs to a Lie group (a fiber of a principal bundle) and $\\Phi$ is a Lie algebra $\\mathfrak g$ valued 1-form on a Riemann surface $\\Sigma$, is associated an infinite sequence of "correlators" $W_n$ that are symmetric $n$-forms on $\\Sigma^n$. The goal of this article is to prove that these correlators always satisfy "loop equations", the same equations satisfied by correlation functions in random matrix models, or the same equations as Virasoro or W-algebra constraints in CFT.
Friedmann equation and Hubble condition
Baumgaertel, Hellmut
2014-01-01
The note presents results on the solutions of the Friedmann equation, which satisfy the Hubble condition, where the radiation term is taken into account. For these solutions the equation $\\sigma=\\sigma_{cr}$, where $\\sigma$ is the radiation invariant of the Friedmann equation and $\\sigma_{cr}$ the "critical radiation parameter", introduced in [5], is an analytic relation between the matter density and the radiation density at the present time and the cosmological constant which can be represented by two function branches, expressing the cosmological constant as unique functions of the matter and radiation density. These functions are the "frontier lines" between regions of constant type.
General Theory of Algebraic Equations
Bezout, Etienne
2008-01-01
This book provides the first English translation of Bezout's masterpiece, the General Theory of Algebraic Equations. It follows, by almost two hundred years, the English translation of his famous mathematics textbooks. Here, Bézout presents his approach to solving systems of polynomial equations in several variables and in great detail. He introduces the revolutionary notion of the "polynomial multiplier," which greatly simplifies the problem of variable elimination by reducing it to a system of linear equations. The major result presented in this work, now known as "Bézout's theorem," is stat
Soliton equations and Hamiltonian systems
Dickey, L A
2002-01-01
The theory of soliton equations and integrable systems has developed rapidly during the last 30 years with numerous applications in mechanics and physics. For a long time, books in this field have not been written but the flood of papers was overwhelming: many hundreds, maybe thousands of them. All this output followed one single work by Gardner, Green, Kruskal, and Mizura on the Korteweg-de Vries equation (KdV), which had seemed to be merely an unassuming equation of mathematical physics describing waves in shallow water. Besides its obvious practical use, this theory is attractive also becau
Fokker-Planck-Kolmogorov equations
Bogachev, Vladimir I; Röckner, Michael; Shaposhnikov, Stanislav V
2015-01-01
This book gives an exposition of the principal concepts and results related to second order elliptic and parabolic equations for measures, the main examples of which are Fokker-Planck-Kolmogorov equations for stationary and transition probabilities of diffusion processes. Existence and uniqueness of solutions are studied along with existence and Sobolev regularity of their densities and upper and lower bounds for the latter. The target readership includes mathematicians and physicists whose research is related to diffusion processes as well as elliptic and parabolic equations.
Reflection algebra and functional equations
Energy Technology Data Exchange (ETDEWEB)
Galleas, W., E-mail: w.galleas@uu.nl; Lamers, J., E-mail: j.lamers@uu.nl
2014-09-15
In this work we investigate the possibility of using the reflection algebra as a source of functional equations. More precisely, we obtain functional relations determining the partition function of the six-vertex model with domain-wall boundary conditions and one reflecting end. The model's partition function is expressed as a multiple-contour integral that allows the homogeneous limit to be obtained straightforwardly. Our functional equations are also shown to give rise to a consistent set of partial differential equations satisfied by the partition function.
Manufactured Turbulence with Langevin equations
Mishra, Aashwin
2016-01-01
By definition, Manufactured turbulence(MT) is purported to mimic physical turbulence rather than model it. The MT equations are constrained to be simple to solve and provide an inexpensive surrogate to Navier-Stokes based Direct Numerical Simulations (DNS) for use in engineering applications or theoretical analyses. In this article, we investigate one approach in which the linear inviscid aspects of MT are derived from a linear approximation of the Navier-Stokes equations while the non-linear and viscous physics are approximated via stochastic modeling. The ensuing Langevin MT equations are used to compute planar, quadratic turbulent flows. While much work needs to be done, the preliminary results appear promising.
Applications of KP Nuclear Parton Distributions
Kulagin, Sergey
2016-01-01
We review the nuclear parton distribution functions computed on the basis of our microscopic model taking into account a number of nuclear effects including Fermi motion and nuclear binding, nuclear meson-exchange currents, off-shell corrections to bound nucleon distributions and nuclear shadowing. We discuss applications to a number of different processes including lepton-nucleus deep inelastic scattering, proton-nucleus Drell-Yan lepton pair production at Fermilab, as well as $W^\\pm$ and $Z^0$ boson production in proton-lead collisions at the LHC.
Solutions of Nonlocal -Laplacian Equations
Directory of Open Access Journals (Sweden)
Mustafa Avci
2013-01-01
Full Text Available In view of variational approach we discuss a nonlocal problem, that is, a Kirchhoff-type equation involving -Laplace operator. Establishing some suitable conditions, we prove the existence and multiplicity of solutions.
Derivation of the Simon equation
Fedorov, P. P.
2016-09-01
The form of the empirical Simon equation describing the dependence of the phase-transition temperature on pressure is shown to be asymptotically strict when the system tends to absolute zero of temperature, and then only for crystalline phases.
ATTRACTORS OF NONAUTONOMOUS SCHRODINGER EQUATIONS
Institute of Scientific and Technical Information of China (English)
刘玉荣; 刘曾荣; 郑永爱
2001-01-01
The long-time behaviour of a two-dimensional nonautonomous nonlinear SchrOdinger equation is considered. The existence of uniform attractor is proved and the up per bound of the uniform attractor' s Hausdorff dimension is given.
Diophantine approximations and Diophantine equations
Schmidt, Wolfgang M
1991-01-01
"This book by a leading researcher and masterly expositor of the subject studies diophantine approximations to algebraic numbers and their applications to diophantine equations. The methods are classical, and the results stressed can be obtained without much background in algebraic geometry. In particular, Thue equations, norm form equations and S-unit equations, with emphasis on recent explicit bounds on the number of solutions, are included. The book will be useful for graduate students and researchers." (L'Enseignement Mathematique) "The rich Bibliography includes more than hundred references. The book is easy to read, it may be a useful piece of reading not only for experts but for students as well." Acta Scientiarum Mathematicarum
Field equations or conservation laws?
Francaviglia, Mauro; Winterroth, Ekkehart
2013-01-01
We explicate some epistemological implications of stationary principles and in particular of Noether Theorems. Noether's contribution to the problem of covariance, in fact, is epistemologically relevant, since it moves the attention from equations to conservation laws.
Correct Linearization of Einstein's Equations
Directory of Open Access Journals (Sweden)
Rabounski D.
2006-04-01
Full Text Available Routinely, Einstein’s equations are be reduced to a wave form (linearly independent of the second derivatives of the space metric in the absence of gravitation, the space rotation and Christoffel’s symbols. As shown herein, the origin of the problem is the use of the general covariant theory of measurement. Herein the wave form of Einstein’s equations is obtained in terms of Zelmanov’s chronometric invariants (physically observable projections on the observer’s time line and spatial section. The equations so obtained depend solely upon the second derivatives, even for gravitation, the space rotation and Christoffel’s symbols. The correct linearization proves that the Einstein equations are completely compatible with weak waves of the metric.
Relativistic effects and quasipotential equations
Ramalho, G; Peña, M T
2002-01-01
We compare the scattering amplitude resulting from the several quasipotential equations for scalar particles. We consider the Blankenbecler-Sugar, Spectator, Thompson, Erkelenz-Holinde and Equal-Time equations, which were solved numerically without decomposition into partial waves. We analyze both negative-energy state components of the propagators and retardation effects. We found that the scattering solutions of the Spectator and the Equal-Time equations are very close to the nonrelativistic solution even at high energies. The overall relativistic effect increases with the energy. The width of the band for the relative uncertainty in the real part of the scattering $T$ matrix, due to different dynamical equations, is largest for backward-scattering angles where it can be as large as 40%.
Invariant foliations for parabolic equations
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
It is proved for parabolic equations that under certain conditions the weak (un-)stable manifolds possess invariant foliations, called strongly (un-)stable foliations. The relevant results on center manifolds are generalized to weak hyperbolic manifolds.
Geophysical interpretation using integral equations
Eskola, L
1992-01-01
Along with the general development of numerical methods in pure and applied to apply integral equations to geophysical modelling has sciences, the ability improved considerably within the last thirty years or so. This is due to the successful derivation of integral equations that are applicable to the modelling of complex structures, and efficient numerical algorithms for their solution. A significant stimulus for this development has been the advent of fast digital computers. The purpose of this book is to give an idea of the principles by which boundary-value problems describing geophysical models can be converted into integral equations. The end results are the integral formulas and integral equations that form the theoretical framework for practical applications. The details of mathematical analysis have been kept to a minimum. Numerical algorithms are discussed only in connection with some illustrative examples involving well-documented numerical modelling results. The reader is assu med to have a back...
The quasilinear parabolic kirchhoff equation
Directory of Open Access Journals (Sweden)
Dawidowski Łukasz
2017-04-01
Full Text Available In this paper the existence of solution of a quasilinear generalized Kirchhoff equation with initial – boundary conditions of Dirichlet type will be studied using the Leray – Schauder principle.
Comment on "Quantum Raychaudhuri equation"
Lashin, E. I.; Dou, Djamel
2017-03-01
We address the validity of the formalism and results presented in S. Das, Phys. Rev. D 89, 084068 (2014), 10.1103/PhysRevD.89.084068 with regard to the quantum Raychaudhuri equation. The author obtained the so-called quantum Raychaudhuri equation by replacing classical geodesics with quantal trajectories arising from Bhommian mechanics. The resulting modified equation was used to draw some conclusions about the inevitability of focusing and the formation of conjugate points and therefore singularity. We show that the whole procedure is full of problematic points, on both physical relevancy and mathematical correctness. In particular, we illustrate the problems associated with the technical derivation of the so-called quantum Raychaudhuri equation, as well as its invalid physical implications.
Saha equation in Rindler space
Indian Academy of Sciences (India)
SANCHARI DE; SOMENATH CHAKRABARTY
2017-06-01
The Saha equations for the photoionization process of hydrogen atoms and the creation of electron–positron pairs at high temperature are investigated in a reference frame undergoing a uniform accelerated motion. It is known as the Rindler space.
A New Unified Evolution Equation
1998-01-01
WE propose a new unified evolution equation for parton distribution functions appropriate for both large and small Bjorken x. Compared with the Ciafaloni- Catani-Fiorani-Marchesini equation, the cancellation of soft poles between virtual and real gluon emissions is made explicitly without introducing infrared cutoffs, next-to-leading contributions to the Sudakov resummation can be included systematically, and the scales of the running coupling constants are determined unambiguously.
Partial Differential Equations An Introduction
Choudary, A. D. R.; Parveen, Saima; Varsan, Constantin
2010-01-01
This book encompasses both traditional and modern methods treating partial differential equation (PDE) of first order and second order. There is a balance in making a selfcontained mathematical text and introducing new subjects. The Lie algebras of vector fields and their algebraic-geometric representations are involved in solving overdetermined of PDE and getting integral representation of stochastic differential equations (SDE). It is addressing to all scientists using PDE in treating mathe...
Symmetries of partial differential equations
Gaussier, Hervé; Merker, Joël
2004-01-01
We establish a link between the study of completely integrable systems of partial differential equations and the study of generic submanifolds in C^n. Using the recent developments of Cauchy-Riemann geometry we provide the set of symmetries of such a system with a Lie group structure. Finally we determine the precise upper bound of the dimension of this Lie group for some specific systems of partial differential equations.
Hidden Statistics of Schroedinger Equation
Zak, Michail
2011-01-01
Work was carried out in determination of the mathematical origin of randomness in quantum mechanics and creating a hidden statistics of Schr dinger equation; i.e., to expose the transitional stochastic process as a "bridge" to the quantum world. The governing equations of hidden statistics would preserve such properties of quantum physics as superposition, entanglement, and direct-product decomposability while allowing one to measure its state variables using classical methods.
Partial Differential Equations An Introduction
Choudary, A D R; Varsan, Constantin
2010-01-01
This book encompasses both traditional and modern methods treating partial differential equation (PDE) of first order and second order. There is a balance in making a selfcontained mathematical text and introducing new subjects. The Lie algebras of vector fields and their algebraic-geometric representations are involved in solving overdetermined of PDE and getting integral representation of stochastic differential equations (SDE). It is addressing to all scientists using PDE in treating mathematical methods.
Wave equations for pulse propagation
Energy Technology Data Exchange (ETDEWEB)
Shore, B.W.
1987-06-24
Theoretical discussions of the propagation of pulses of laser radiation through atomic or molecular vapor rely on a number of traditional approximations for idealizing the radiation and the molecules, and for quantifying their mutual interaction by various equations of propagation (for the radiation) and excitation (for the molecules). In treating short-pulse phenomena it is essential to consider coherent excitation phenomena of the sort that is manifest in Rabi oscillations of atomic or molecular populations. Such processes are not adequately treated by rate equations for excitation nor by rate equations for radiation. As part of a more comprehensive treatment of the coupled equations that describe propagation of short pulses, this memo presents background discussion of the equations that describe the field. This memo discusses the origin, in Maxwell's equations, of the wave equation used in the description of pulse propagation. It notes the separation into lamellar and solenoidal (or longitudinal and transverse) and positive and negative frequency parts. It mentions the possibility of separating the polarization field into linear and nonlinear parts, in order to define a susceptibility or index of refraction and, from these, a phase and group velocity. The memo discusses various ways of characterizing the polarization characteristics of plane waves, that is, of parameterizing a transverse unit vector, such as the Jones vector, the Stokes vector, and the Poincare sphere. It discusses the connection between macroscopically defined quantities, such as the intensity or, more generally, the Stokes parameters, and microscopic field amplitudes. The material presented here is a portion of a more extensive treatment of propagation to be presented separately. The equations presented here have been described in various books and articles. They are collected here as a summary and review of theory needed when treating pulse propagation.
Nonlinear evolution equations in QCD
Stasto, A. M.
2004-01-01
The following lectures are an introduction to the phenomena of partonic saturation and nonlinear evolution equations in Quantum Chromodynamics. After a short introduction to the linear evolution, the problems of unitarity bound and parton saturation are discussed. The nonlinear Balitsky-Kovchegov evolution equation in the high energy limit is introduced, and the progress towards the understanding of the properties of its solution is reviewed. We discuss the concepts of the saturation scale, g...
On basic equation of statistical physics
Institute of Scientific and Technical Information of China (English)
邢修三
1996-01-01
Considering that thermodynamic irreversibility, the principle of entropy increase and hydrodynamic equations cannot be derived rigorously and in a unified way from the Liouville equations, the anomalous Langevin equation in Liouville space or its equivalent generalized Liouville equation is proposed as a basic equation of statistical physics. This equation reflects the fact that the law of motion of statistical thermodynamics is stochastic, but not deterministic. From that the nonequilibrium entropy, the principle of entropy increase, the theorem of minimum entropy production and the BBGKY diffusion equation hierarchy have been derived. The hydrodynamic equations, such as the generalized Navier-Stokes equation and the mass drift-diffusion equation, etc. have been derived from the BBGKY diffusion equation hierarchy. This equation has the same equilibrium solution as that of the Liouville equation. All these are unified and rigorous without adding any extra assumption. But it is difficult to prove that th
Revisiting the Simplified Bernoulli Equation
Heys, Jeffrey J; Holyoak, Nicole; Calleja, Anna M; Belohlavek, Marek; Chaliki, Hari P
2010-01-01
Background: The assessment of the severity of aortic valve stenosis is done by either invasive catheterization or non-invasive Doppler Echocardiography in conjunction with the simplified Bernoulli equation. The catheter measurement is generally considered more accurate, but the procedure is also more likely to have dangerous complications. Objective: The focus here is on examining computational fluid dynamics as an alternative method for analyzing the echo data and determining whether it can provide results similar to the catheter measurement. Methods: An in vitro heart model with a rigid orifice is used as a first step in comparing echocardiographic data, which uses the simplified Bernoulli equation, catheterization, and echocardiographic data, which uses computational fluid dynamics (i.e., the Navier-Stokes equations). Results: For a 0.93cm2 orifice, the maximum pressure gradient predicted by either the simplified Bernoulli equation or computational fluid dynamics was not significantly different from the experimental catheter measurement (p > 0.01). For a smaller 0.52cm2 orifice, there was a small but significant difference (p < 0.01) between the simplified Bernoulli equation and the computational fluid dynamics simulation, with the computational fluid dynamics simulation giving better agreement with experimental data for some turbulence models. Conclusion: For this simplified, in vitro system, the use of computational fluid dynamics provides an improvement over the simplified Bernoulli equation with the biggest improvement being seen at higher valvular stenosis levels. PMID:21625471
Computational partial differential equations using Matlab
Li, Jichun
2008-01-01
Brief Overview of Partial Differential Equations The parabolic equations The wave equations The elliptic equations Differential equations in broader areasA quick review of numerical methods for PDEsFinite Difference Methods for Parabolic Equations Introduction Theoretical issues: stability, consistence, and convergence 1-D parabolic equations2-D and 3-D parabolic equationsNumerical examples with MATLAB codesFinite Difference Methods for Hyperbolic Equations IntroductionSome basic difference schemes Dissipation and dispersion errors Extensions to conservation lawsThe second-order hyperbolic PDE
Equationally Compact Acts : Coproducts / Peeter Normak
Normak, Peeter
1998-01-01
In this article equational compactness of acts and its generalizations are discussed. As equational compactness does not carry over to coproducts a slight generalization of c-equational campactness is introduced. It is proved that a coproduct of acts is c-equationally compact if and only if all components are c-equationally campact
Equationally Compact Acts : Coproducts / Peeter Normak
Normak, Peeter
1998-01-01
In this article equational compactness of acts and its generalizations are discussed. As equational compactness does not carry over to coproducts a slight generalization of c-equational campactness is introduced. It is proved that a coproduct of acts is c-equationally compact if and only if all components are c-equationally campact
Fredholm's equations for subwavelength focusing
Velázquez-Arcos, J. M.
2012-10-01
Subwavelength focusing (SF) is a very useful tool that can be carried out with the use of left hand materials for optics that involve the range of the microwaves. Many recent works have described a successful alternative procedure using time reversal methods. The advantage is that we do not need devices which require the complicated manufacture of left-hand materials; nevertheless, the theoretical mathematical bases are far from complete because before now we lacked an adequate easy-to-apply frame. In this work we give, for a broad class of discrete systems, a solid support for the theory of electromagnetic SF that can be applied to communications and nanotechnology. The very central procedure is the development of vector-matrix formalism (VMF) based on exploiting both the inhomogeneous and homogeneous Fredholm's integral equations in cases where the last two kinds of integral equations are applied to some selected discrete systems. To this end, we first establish a generalized Newmann series for the Fourier transform of the Green's function in the inhomogeneous Fredholm's equation of the problem. Then we go from an integral operator equation to a vector-matrix algebraic one. In this way we explore the inhomogeneous case and later on also the very interesting one about the homogeneous equation. Thus, on the one hand we can relate in a simple manner the arriving electromagnetic signals with those at their sources and we can use them to perform a SF. On the other hand, we analyze the homogeneous version of the equations, finding resonant solutions that have analogous properties to their counterparts in quantum mechanical scattering, that can be used in a proposed very powerful way in communications. Also we recover quantum mechanical operator relations that are identical for classical electromagnetics. Finally, we prove two theorems that formalize the relation between the theory of Fredholm's integral equations and the VMF we present here.
Abstract methods in partial differential equations
Carroll, Robert W
2012-01-01
Detailed, self-contained treatment examines modern abstract methods in partial differential equations, especially abstract evolution equations. Suitable for graduate students with some previous exposure to classical partial differential equations. 1969 edition.
Equivalent boundary integral equations for plane elasticity
Institute of Scientific and Technical Information of China (English)
胡海昌; 丁皓江; 何文军
1997-01-01
Indirect and direct boundary integral equations equivalent to the original boundary value problem of differential equation of plane elasticity are established rigorously. The unnecessity or deficiency of some customary boundary integral equations is indicated by examples and numerical comparison.
ON THE EQUIVALENCE OF THE ABEL EQUATION
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
This article uses the reflecting function of Mironenko to study some complicated differential equations which are equivalent to the Abel equation. The results are applied to discuss the behavior of solutions of these complicated differential equations.
How to obtain the covariant form of Maxwell's equations from the continuity equation
Energy Technology Data Exchange (ETDEWEB)
Heras, Jose A [Departamento de Ciencias Basicas, Universidad Autonoma Metropolitana, Unidad Azcapotzalco, Av. San Pablo No. 180, Col. Reynosa, 02200, Mexico D. F. (Mexico); Departamento de Fisica y Matematicas, Universidad Iberoamericana, Prolongacion Paseo de la Reforma 880, Mexico D. F. 01210 (Mexico)
2009-07-15
The covariant Maxwell equations are derived from the continuity equation for the electric charge. This result provides an axiomatic approach to Maxwell's equations in which charge conservation is emphasized as the fundamental axiom underlying these equations.
Quasi self-adjoint nonlinear wave equations
Energy Technology Data Exchange (ETDEWEB)
Ibragimov, N H [Department of Mathematics and Science, Blekinge Institute of Technology, SE-371 79 Karlskrona (Sweden); Torrisi, M; Tracina, R, E-mail: nib@bth.s, E-mail: torrisi@dmi.unict.i, E-mail: tracina@dmi.unict.i [Dipartimento di Matematica e Informatica, University of Catania (Italy)
2010-11-05
In this paper we generalize the classification of self-adjoint second-order linear partial differential equation to a family of nonlinear wave equations with two independent variables. We find a class of quasi self-adjoint nonlinear equations which includes the self-adjoint linear equations as a particular case. The property of a differential equation to be quasi self-adjoint is important, e.g. for constructing conservation laws associated with symmetries of the differential equation. (fast track communication)
First-order partial differential equations
Rhee, Hyun-Ku; Amundson, Neal R
2001-01-01
This first volume of a highly regarded two-volume text is fully usable on its own. After going over some of the preliminaries, the authors discuss mathematical models that yield first-order partial differential equations; motivations, classifications, and some methods of solution; linear and semilinear equations; chromatographic equations with finite rate expressions; homogeneous and nonhomogeneous quasilinear equations; formation and propagation of shocks; conservation equations, weak solutions, and shock layers; nonlinear equations; and variational problems. Exercises appear at the end of mo
Fractional complex transform for fractional differential equations
National Research Council Canada - National Science Library
Lİ, Zheng Biao; HE, Ji Huan
2010-01-01
Fractional complex transform is proposed to convert fractional differential equations into ordinary differential equations, so that all analytical methods devoted to advanced calculus can be easily...
Differential Equations for Morphological Amoebas
Welk, Martin; Breuß, Michael; Vogel, Oliver
This paper is concerned with amoeba median filtering, a structure-adaptive morphological image filter. It has been introduced by Lerallut et al. in a discrete formulation. Experimental evidence shows that iterated amoeba median filtering leads to segmentation-like results that are similar to those obtained by self-snakes, an image filter based on a partial differential equation. We investigate this correspondence by analysing a space-continuous formulation of iterated median filtering. We prove that in the limit of vanishing radius of the structuring elements, iterated amoeba median filtering indeed approximates a partial differential equation related to self-snakes and the well-known (mean) curvature motion equation. We present experiments with discrete iterated amoeba median filtering that confirm qualitative and quantitative predictions of our analysis.
Dynamics of partial differential equations
Wayne, C Eugene
2015-01-01
This book contains two review articles on the dynamics of partial differential equations that deal with closely related topics but can be read independently. Wayne reviews recent results on the global dynamics of the two-dimensional Navier-Stokes equations. This system exhibits stable vortex solutions: the topic of Wayne's contribution is how solutions that start from arbitrary initial conditions evolve towards stable vortices. Weinstein considers the dynamics of localized states in nonlinear Schrodinger and Gross-Pitaevskii equations that describe many optical and quantum systems. In this contribution, Weinstein reviews recent bifurcations results of solitary waves, their linear and nonlinear stability properties, and results about radiation damping where waves lose energy through radiation. The articles, written independently, are combined into one volume to showcase the tools of dynamical systems theory at work in explaining qualitative phenomena associated with two classes of partial differential equ...
Numerical Solution of Parabolic Equations
DEFF Research Database (Denmark)
Østerby, Ole
These lecture notes are designed for a one-semester course on finite-difference methods for parabolic equations. These equations which traditionally are used for describing diffusion and heat-conduction problems in Geology, Physics, and Chemistry have recently found applications in Finance Theory....... Among the special features of this book can be mentioned the presentation of a practical approach to reliable estimates of the global error, including warning signals if the reliability is questionable. The technique is generally applicable for estimating the discretization error in numerical...... approximations which depend on a step size, such as numerical integration and solution of ordinary and partial differential equations. An integral part of the error estimation is the estimation of the order of the method and can thus satisfy the inquisitive mind: Is the order what we expect it to be from theopry...
Introductory course on differential equations
Gorain, Ganesh C
2014-01-01
Introductory Course on DIFFERENTIAL EQUATIONS provides an excellent exposition of the fundamentals of ordinary and partial differential equations and is ideally suited for a first course of undergraduate students of mathematics, physics and engineering. The aim of this book is to present the elementary theories of differential equations in the forms suitable for use of those students whose main interest in the subject are based on simple mathematical ideas. KEY FEATURES: Discusses the subject in a systematic manner without sacrificing mathematical rigour. A variety of exercises drill the students in problem solving in view of the mathematical theories explained in the book. Worked out examples illustrated according to the theories developed in the book with possible alternatives. Exhaustive collection of problems and the simplicity of presentation differentiate this book from several others. Material contained will help teachers as well as aspiring students of different competitive examinations.
The respiratory system in equations
Maury, Bertrand
2013-01-01
The book proposes an introduction to the mathematical modeling of the respiratory system. A detailed introduction on the physiological aspects makes it accessible to a large audience without any prior knowledge on the lung. Different levels of description are proposed, from the lumped models with a small number of parameters (Ordinary Differential Equations), up to infinite dimensional models based on Partial Differential Equations. Besides these two types of differential equations, two chapters are dedicated to resistive networks, and to the way they can be used to investigate the dependence of the resistance of the lung upon geometrical characteristics. The theoretical analysis of the various models is provided, together with state-of-the-art techniques to compute approximate solutions, allowing comparisons with experimental measurements. The book contains several exercises, most of which are accessible to advanced undergraduate students.
Quantum corrections for Boltzmann equation
Institute of Scientific and Technical Information of China (English)
M.; Levy; PETER
2008-01-01
We present the lowest order quantum correction to the semiclassical Boltzmann distribution function,and the equation satisfied by this correction is given. Our equation for the quantum correction is obtained from the conventional quantum Boltzmann equation by explicitly expressing the Planck constant in the gradient approximation,and the quantum Wigner distribution function is expanded in pow-ers of Planck constant,too. The negative quantum correlation in the Wigner dis-tribution function which is just the quantum correction terms is naturally singled out,thus obviating the need for the Husimi’s coarse grain averaging that is usually done to remove the negative quantum part of the Wigner distribution function. We also discuss the classical limit of quantum thermodynamic entropy in the above framework.
Students' understanding of quadratic equations
López, Jonathan; Robles, Izraim; Martínez-Planell, Rafael
2016-05-01
Action-Process-Object-Schema theory (APOS) was applied to study student understanding of quadratic equations in one variable. This required proposing a detailed conjecture (called a genetic decomposition) of mental constructions students may do to understand quadratic equations. The genetic decomposition which was proposed can contribute to help students achieve an understanding of quadratic equations with improved interrelation of ideas and more flexible application of solution methods. Semi-structured interviews with eight beginning undergraduate students explored which of the mental constructions conjectured in the genetic decomposition students could do, and which they had difficulty doing. Two of the mental constructions that form part of the genetic decomposition are highlighted and corresponding further data were obtained from the written work of 121 undergraduate science and engineering students taking a multivariable calculus course. The results suggest the importance of explicitly considering these two highlighted mental constructions.
Integration of quantum hydrodynamical equation
Ulyanova, Vera G.; Sanin, Andrey L.
2007-04-01
Quantum hydrodynamics equations describing the dynamics of quantum fluid are a subject of this report (QFD).These equations can be used to decide the wide class of problem. But there are the calculated difficulties for the equations, which take place for nonlinear hyperbolic systems. In this connection, It is necessary to impose the additional restrictions which assure the existence and unique of solutions. As test sample, we use the free wave packet and study its behavior at the different initial and boundary conditions. The calculations of wave packet propagation cause in numerical algorithm the division. In numerical algorithm at the calculations of wave packet propagation, there arises the problem of division by zero. To overcome this problem we have to sew together discrete numerical and analytical continuous solutions on the boundary. We demonstrate here for the free wave packet that the numerical solution corresponds to the analytical solution.
Numerical optimization using flow equations.
Punk, Matthias
2014-12-01
We develop a method for multidimensional optimization using flow equations. This method is based on homotopy continuation in combination with a maximum entropy approach. Extrema of the optimizing functional correspond to fixed points of the flow equation. While ideas based on Bayesian inference such as the maximum entropy method always depend on a prior probability, the additional step in our approach is to perform a continuous update of the prior during the homotopy flow. The prior probability thus enters the flow equation only as an initial condition. We demonstrate the applicability of this optimization method for two paradigmatic problems in theoretical condensed matter physics: numerical analytic continuation from imaginary to real frequencies and finding (variational) ground states of frustrated (quantum) Ising models with random or long-range antiferromagnetic interactions.
Integration Rules for Scattering Equations
Baadsgaard, Christian; Bourjaily, Jacob L; Damgaard, Poul H
2015-01-01
As described by Cachazo, He and Yuan, scattering amplitudes in many quantum field theories can be represented as integrals that are fully localized on solutions to the so-called scattering equations. Because the number of solutions to the scattering equations grows quite rapidly, the contour of integration involves contributions from many isolated components. In this paper, we provide a simple, combinatorial rule that immediately provides the result of integration against the scattering equation constraints for any M\\"obius-invariant integrand involving only simple poles. These rules have a simple diagrammatic interpretation that makes the evaluation of any such integrand immediate. Finally, we explain how these rules are related to the computation of amplitudes in the field theory limit of string theory.
Integration rules for scattering equations
Baadsgaard, Christian; Bjerrum-Bohr, N. E. J.; Bourjaily, Jacob L.; Damgaard, Poul H.
2015-09-01
As described by Cachazo, He and Yuan, scattering amplitudes in many quantum field theories can be represented as integrals that are fully localized on solutions to the so-called scattering equations. Because the number of solutions to the scattering equations grows quite rapidly, the contour of integration involves contributions from many isolated components. In this paper, we provide a simple, combinatorial rule that immediately provides the result of integration against the scattering equation constraints fo any Möbius-invariant integrand involving only simple poles. These rules have a simple diagrammatic interpretation that makes the evaluation of any such integrand immediate. Finally, we explain how these rules are related to the computation of amplitudes in the field theory limit of string theory.
Stability Analysis of Ecomorphodynamic Equations
Bärenbold, Fabian; Perona, Paolo
2014-01-01
Although riparian vegetation is present in or along many water courses of the world, its active role resulting from the interaction with flow and sediment processes has only recently become an active field of research. Especially, the role of vegetation in the process of river pattern formation has been explored and demonstrated mostly experimentally and numerically until now. In the present work, we shed light on this subject by performing a linear stability analysis on a simple model for riverbed vegetation dynamics coupled with the set of classical river morphodynamic equations. The vegetation model only accounts for logistic growth, local positive feedback through seeding and resprouting, and mortality by means of uprooting through flow shear stress. Due to the simplicity of the model, we can transform the set of equations into an eigenvalue problem and assess the stability of the linearized equations when slightly perturbated away from a spatially homogeneous solution. If we couple vegetation dynamics wi...
Directory of Open Access Journals (Sweden)
E. M. E. Zayed
2014-01-01
Full Text Available We apply the generalized projective Riccati equations method to find the exact traveling wave solutions of some nonlinear evolution equations with any-order nonlinear terms, namely, the nonlinear Pochhammer-Chree equation, the nonlinear Burgers equation and the generalized, nonlinear Zakharov-Kuznetsov equation. This method presents wider applicability for handling many other nonlinear evolution equations in mathematical physics.
Integral equations on time scales
Georgiev, Svetlin G
2016-01-01
This book offers the reader an overview of recent developments of integral equations on time scales. It also contains elegant analytical and numerical methods. This book is primarily intended for senior undergraduate students and beginning graduate students of engineering and science courses. The students in mathematical and physical sciences will find many sections of direct relevance. The book contains nine chapters and each chapter is pedagogically organized. This book is specially designed for those who wish to understand integral equations on time scales without having extensive mathematical background.
Group analysis of differential equations
Ovsiannikov, L V
1982-01-01
Group Analysis of Differential Equations provides a systematic exposition of the theory of Lie groups and Lie algebras and its application to creating algorithms for solving the problems of the group analysis of differential equations.This text is organized into eight chapters. Chapters I to III describe the one-parameter group with its tangential field of vectors. The nonstandard treatment of the Banach Lie groups is reviewed in Chapter IV, including a discussion of the complete theory of Lie group transformations. Chapters V and VI cover the construction of partial solution classes for the g
Radar equations for modern radar
Barton, David K
2012-01-01
Based on the classic Radar Range-Performance Analysis from 1980, this practical volume extends that work to ensure applicability of radar equations to the design and analysis of modern radars. This unique book helps you identify what information on the radar and its environment is needed to predict detection range. Moreover, it provides equations and data to improve the accuracy of range calculations. You find detailed information on propagation effects, methods of range calculation in environments that include clutter, jamming and thermal noise, as well as loss factors that reduce radar perfo
Hamiltonian systems as selfdual equations
Institute of Scientific and Technical Information of China (English)
2008-01-01
Hamiltonian systems with various time boundary conditions are formulated as absolute minima of newly devised non-negative action func-tionals obtained by a generalization of Bogomolnyi's trick of 'completing squares'. Reminiscent of the selfdual Yang-Mills equations, they are not derived from the fact that they are critical points (i.e., from the correspond- ing Euler-Lagrange equations) but from being zeroes of the corresponding non-negative Lagrangians. A general method for resolving such variational problems is also described and applied to the construction of periodic solutions for Hamiltonian systems, but also to study certain Lagrangian intersections.
Partial differential equations an introduction
Colton, David
2004-01-01
Intended for a college senior or first-year graduate-level course in partial differential equations, this text offers students in mathematics, engineering, and the applied sciences a solid foundation for advanced studies in mathematics. Classical topics presented in a modern context include coverage of integral equations and basic scattering theory. This complete and accessible treatment includes a variety of examples of inverse problems arising from improperly posed applications. Exercises at the ends of chapters, many with answers, offer a clear progression in developing an understanding of
Energy Technology Data Exchange (ETDEWEB)
Kahana, S.
1986-01-01
The role of the nuclear equation of state in determining the fate of the collapsing cores of massive stars is examined in light of both recent theoretical advances in this subject and recent experimental measurements with relativistic heavy ions. The difficulties existing in attempts to bring the softer nuclear matter apparently required by the theory of Type II supernovae into consonance with the heavy ion data are discussed. Relativistic mean field theory is introduced as a candidate for derivation of the equation of state, and a simple form for the saturation compressibility is obtained. 28 refs., 4 figs., 1 tab.