for linear bounded operators on Hilbert spaces, where X is the unknown operator. This solution is expressed in terms of the Moore-Penrose inverse of the operator A. Thus, results of J. H. Hodges [Some matrix equations over a finite field, Ann. Mat. Pura Appl. 44 (1957) 245–550] are extended to the infinite dimensional settings.  相似文献   

3.
Explicit solution of a Kolmogorov equation     
S. -T. Yau  S. S. -T. Yau 《Applied Mathematics and Optimization》1996,34(3):231-266
Ever since the technique of the Kalman-Bucy filter was popularized, there has been an intense interest in finding new classes of finite-dimensional recursive filters. In the late seventies, the concept of the estimation algebra of a filtering system was introduced. It has been the major tool in studying the Duncan-Mortensen-Zakai equation. Recently the second author has constructed general finite-dimensional filters which contain both Kalman-Bucy filters and Benes filter as special cases. In this paper we consider a filtering system with arbitrary nonlinear driftf(x) which satisfies some regularity assumption at infinity. This is a natural assumption in view of Theorem 10 of [DTWY] in a special case. Under the assumption on the observation h(x)=constant, we propose writing down the solution of the Duncan-Mortensen-Zakai equation explicitly.This research was supported by Army Grant DAAH-04-93G-0006.  相似文献   

4.
Explicit block iterative method for the solution of the biharmonic equation     
W. S. Yousif  D. J. Evans 《Numerical Methods for Partial Differential Equations》1993,9(1):1-12
We develop an iterative algorithm for the solution of a finite difference approximation of the biharmonic equation over a rectangular region by using the explicit block iterative method, i.e., box over relaxation scheme. The 4- and 9-point explicit blocks were considered and performance results for the two algorithms are presented.© 1993 John Wiley & Sons, Inc.  相似文献   

5.
Explicit solutions of the viscous model vorticity equation     
Steven Schochet 《纯数学与应用数学通讯》1986,39(4):531-537
Explicit solutions are found for the viscous version of the model vorticity equation recently proposed by P. Constantin, P. D. Lax, and A. Majda: where H(w) is the Hilbert transform of w, and v is a positive constant. Various properties of these solutions, including the fact that they blow up after a finite time, are discussed.  相似文献   

6.
Explicit determinantal representation formulas for the solution of the two-sided restricted quaternionic matrix equation     
Ivan I. Kyrchei 《Journal of Applied Mathematics and Computing》2018,58(1-2):335-365
Weighted singular value decomposition of a quaternion matrix and with its help determinantal representations of the quaternion weighted Moore–Penrose inverse have been derived recently by the author. In this paper, using these determinantal representations, explicit determinantal representation formulas for the solution of the restricted quaternionic matrix equations, \(\mathbf{A}{} \mathbf{X}{} \mathbf{B}=\mathbf{D}\), and consequently, \(\mathbf{A}{} \mathbf{X}=\mathbf{D}\) and \(\mathbf{X}{} \mathbf{B}=\mathbf{D}\) are obtained within the framework of the theory of column–row determinants. We consider all possible cases depending on weighted matrices.  相似文献   

7.
Semirotors in the Josephson junction equations     
D. G. Aronson  M. Krupa  P. Ashwin 《Journal of Nonlinear Science》1996,6(1):85-103
Summary We consider the dynamics of arrays ofN-series coupled Josephson junctions, under pure resistive and capacitive loads. In the limit of the junction capacitance becoming large, we prove the existence of semirotor solutions. These are periodic solutions in which the phase difference across the gap ink of the junctions oscillates with small amplitude while the remainingN—k phase differences increase by 2π radians per period. We investigate the stability of these solutions and report observations of chaotic behavior associated with these solutions.  相似文献   

8.
Explicit series solution of travelling waves with a front of Fisher equation     
《Chaos, solitons, and fractals》2007,31(2):462-472
In this paper, an analytic technique, namely the homotopy analysis method, is employed to solve the Fisher equation, which describes a family of travelling waves with a front. The explicit series solution for all possible wave speeds 0 < c < +∞ is given. Such kind of explicit series solution has never been reported, to the best of author’s knowledge. Our series solution indicates that the solution contains an oscillation part when 0 < c < 2. The proposed analytic approach is general, and can be applied to solve other similar nonlinear travelling wave problems.  相似文献   

9.
10.
Explicit solutions of the Bogoyavlensky-Konoplechenko equation     
Xiang-peng Xin  Xi-qiang Liu  Lin-lin Zhang 《Applied mathematics and computation》2010,215(10):3669-3673
By means of the generalized direct method, a relationship is constructed between the new solutions and the old ones of the Bogoyavlensky-Konoplechenko equation. Based on the relationship, a new solution is obtained by using a given solution of the equation. The symmetry is also obtained for the BK equation. Then we get the reductions using the symmetry and give some exact solutions of the BK equation.  相似文献   

11.
Explicit expression for the transition density of the solution of a stochastic diffusion equation with piecewise-constant drift coefficient     
M. Almazov 《Journal of Mathematical Sciences》1993,63(4):484-489
The explicit form of the transition density is determined for the solution (t) of the stochastic diffusion equation d(t)=a((t))dt+dw(t), where a(z)= for x [a, b] and a(x)=0 for x [a, b], w(t) is a Wiener process.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 61, pp. 99–105, 1987.  相似文献   

12.
Laguerre polynomial solution of the nonlinear Boltzmann equation for the hard-sphere model     
G. Kügerl 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1989,40(6):816-827
We consider a spatially homogeneous and isotropic gas consisting of hard-sphere molecules. A vector representation of the scattering kernel is used to adapt the original Boltzmann equation to the idealized geometrical situation. By means of an expansion of the distribution function in terms of Laguerre polynomials this scalar Boltzmann equation is transformed to a set of moment equations. All algebraized collision integrals can be evaluated analytically. We discuss the truncation of the moment equations necessary for the practical application of this method. The eigenvalues of the linearized relaxation problem show a good convergence with respect to the truncation index.
Zusammenfassung Wir betrachten ein räumlich homogenes Gas harter Kugeln mit isotroper Geschwindigkeitsverteilung. Mit Hilfe einer Vektordarstellung des Streukerns wird die nichtlineare Boltzmanngleichung den vereinfachten geometrischen Verhältnissen angepaßt. Die entstehende skalare kinetische Gleichung wird durch eine Laguerre-Reihenentwicklung der Teilchenverteilungsdichte in ein System von Momentegleichungen übergeführt. Sämtliche algebraisierten Stoßintegrale erweisen sich als analytisch lösbar. Wir diskutieren den für den praktischen Gebrauch der Methode notwendigen Abbruch des Systems der Momentegleichungen. Die Eigenwerte des linearisierten Relaxationsproblems zeigen eine rasche Konvergenz bezüglich einer Steigerung des Abbruchindex.
  相似文献   

13.
组合Zakharov-Kuznetsov方程的显式孤波解   总被引:6,自引:0,他引:6  
闫振亚  张鸿庆 《纯粹数学与应用数学》2000,16(2):31-35
借助于Mathematica是吴消元法,本文通过用一个新的假设,获得了组合Za-kharov-Kuznetsov方程的12种孤波解,其中包括钟状与扭状组合型孤波解和周期型孤波解。这种假设也能用于其他的非线性演化方程(组)。  相似文献   

14.
Explicit solutions of the reduced Ostrovsky equation     
《Chaos, solitons, and fractals》2007,31(3):602-610
It is shown that the Vakhnenko equation (VE) and the Ostrovsky–Hunter equation (OHE) are particular forms of the reduced Ostrovsky equation, and that they are related by a simple transformation. Explicit analytical periodic and solitary travelling-wave solutions of the OHE are derived by using a method used previously by Vakhnenko and the present author to solve the VE. These exact solutions of the OHE are related to some approximate solutions obtained by Boyd [Boyd JP. Ostrovsky and Hunter’s generic wave equation for weakly dispersive waves: matched asymptotic and pseudospectral study of the paraboidal travelling waves (corner and near-corner waves). Eur J Appl Math 2005;15:1–17].  相似文献   

15.
Explicit solutions of the inhomogeneous dirac equation     
Frank Sommen  Bernard Jancewicz 《Journal d'Analyse Mathématique》1997,71(1):59-74
In this paper we establish a general principle which may be used to construct many explicit solutions to special inhomogeneous Dirac equations with distributional right-hand side. These solutions are presented as series of products of Clifford algebra valued functions which themselves satisfy Dirac equations in a lower dimension. We also present several special examples, including plane waves, zonal functions, Cauchy kernels and electromagnetic fields.  相似文献   

16.
Explicit solution of the Carlson problem     
Marija Dodig  Marko Stošić 《Linear algebra and its applications》2012,436(1):190-201
In this paper we give new, explicit and direct proof of the classical Carlson problem, by using only elementary matrix completion tools and combinatorics.  相似文献   

17.
Asymptotic analysis of the current-voltage characteristic of the Josephson junction     
A. Ya. Kazakov 《Journal of Mathematical Sciences》1995,73(3):361-365
The current-voltage characteristic of the Josephson junction placed in a high-frequency electromagnetic field is obtained. Bibliography: 7 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 186, pp. 101–106, 1990. Translated by A. Ya. Kazakov.  相似文献   

18.
19.
An algebraic method for solving the KdV equation (III). N-parameter solution family     
《Chaos, solitons, and fractals》2000,11(11):1753-1757
By direct solving Hirota's τ-equation, we obtain the explicit expressions of N-parameter solution family which include known N-soliton solution. The transformation relations among the N-parameter solution family and the results obtained by using the IST method, Hirota method and Backlund transformation, respectively, are given. Thus the complete pattern of the soliton theory is revealed.  相似文献   

20.
Explicit rational solutions of Knizhnik-Zamolodchikov equation     
Lev Sakhnovich 《Central European Journal of Mathematics》2008,6(1):179-187
We consider the Knizhnik-Zamolodchikov system of linear differential equations. The coefficients of this system are rational functions generated by elements of the symmetric group n . We assume that parameter ρ = ±1. In previous paper [5] we proved that the fundamental solution of the corresponding KZ-equation is rational. Now we construct this solution in the explicit form.   相似文献   

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1.
In this work we study dynamical systems on the torus modeling Josephson junctions in the theory of superconductivity, and also perturbations of these systems. We show that, in the family of equations that describe resistively shunted Josephson junctions, phase lock occurs only for integer rotation numbers and propose a simple method for calculating the boundaries of the corresponding Arnold tongues. This part is a simplification of known results about the quantization of rotation number [4]. Moreover, we show that the quantization of rotation number only at integer points is a phenomenon of infinite codimension. Namely, there is an infinite set of independent perturbations of systems that give rise to countably many nondiscretely located phase-locking regions.  相似文献   

2.
In this paper we find the explicit solution of the equation
A*X+X*A=B
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