Asymptotic periodicity of the Volterra equation with infinite delay

For some species, hereditary factors have great effects on their population evolution, which can be described by the well-known Volterra model. A model developed is investigated in this article, considering the seasonal variation of the environment, where the diffusive effect of the population is also considered. The main approaches employed here are the upper-lower solution method and the monotone iteration technique. The results show that whether the species dies out or not depends on the relations among the birth rate, the death rate, the competition rate, the diffusivity and the hereditary effects. The evolution of the population may show asymptotic periodicity, provided a certain condition is satisfied for the above factors. (c) 2006 Elsevier Ltd. All rights reserved.

Asymptotic weighted-periodicity of the impulsive parabolic equation with time delay

The main aim of this paper is to investigate the effects of the impulse and time delay on a type of parabolic equations. In view of the characteristics of the equation, a particular iteration scheme is adopted. The results show that Under certain conditions on the coefficients of the equation and the impulse, the solution oscillates in a particular manner-called "asymptotic weighted-periodicity".

Traveling wave front for the Fisher equation on an infinite band region

Instead of discussing the existence of a one-dimensional traveling wave front solution which connects two constant steady states, the present work deals with the case connecting a constant and a nonhomogeneous steady state on an infinite band region. The corresponding model is the well-known Fisher equation with variational coefficient and Dirichlet boundary condition. (c) 2006 Elsevier Ltd. All rights reserved.

A kind of extended Korteweg-de Vries equation and solitary wave solutions for interfacial waves in a two-fluid system

This paper considers interfacial waves propagating along the interface between a two-dimensional two-fluid with a flat bottom and a rigid upper boundary. There is a light fluid layer overlying a heavier one in the system, and a small density difference exists between the two layers. It just focuses on the weakly non-linear small amplitude waves by introducing two small independent parameters: the nonlinearity ratio epsilon, represented by the ratio of amplitude to depth, and the dispersion ratio mu, represented by the square of the ratio of depth to wave length, which quantify the relative importance of nonlinearity and dispersion. It derives an extended KdV equation of the interfacial waves using the method adopted by Dullin et al in the study of the surface waves when considering the order up to O(mu(2)). As expected, the equation derived from the present work includes, as special cases, those obtained by Dullin et al for surface waves when the surface tension is neglected. The equation derived using an alternative method here is the same as the equation presented by Choi and Camassa. Also it solves the equation by borrowing the method presented by Marchant used for surface waves, and obtains its asymptotic solitary wave solutions when the weakly nonlinear and weakly dispersive terms are balanced in the extended KdV equation.

扩散波勘探方法基础及其在石油油气藏开发中的应用研究

As we know, the essence of exploration is objective body determined by getting the information. Such as seismic、electrical and electromagnetic prospecting, they are the common methods of the exploration. Therefore, They have a complete set of theory now. In fact, the effective information can also be got by the diffusion way, it is called diffusion prospecting. The diffusion way prospecting is necessary and important. The way of diffusion prospecting is studied in the paper and main works include below: (1) On the basis of studying basic law of the diffusion, the paper gives the idea of diffusion wave and the formulas of computing diffusion wave function. (2) The paper studies the way of the diffusion prospecting and the methods of data processing. At the same time, it also expounds the characteristics and the applied foreground of the diffusion prospecting. (3) The paper gives the tomography idea and the basic method of diffusion CT. Meanwhile, it also expounds the foreground that the diffusion CT is applied in oil development prospecting. (4) As the inversion of the diffusion equation is a part of the diffusion prospecting way, the methods of diffusion equation inversion are studied and the two formulas are deduced --Laplace transform and polynomial fitting inversion formulas. As the other important result of diffusion equation inversion, the inversion can offer a new analysis method for well Testing in oil development. In order to show a set of methods in the paper feasible, forward、inversion and CT numerical simulation are done in the paper.

指数矩阵近似计算在地震波场延拓中的应用

Seismic wave field numerical modeling and seismic migration imaging based on wave equation have become useful and absolutely necessarily tools for imaging of complex geological objects. An important task for numerical modeling is to deal with the matrix exponential approximation in wave field extrapolation. For small value size matrix exponential, we can approximate the square root operator in exponential using different splitting algorithms. Splitting algorithms are usually used on the order or the dimension of one-way wave equation to reduce the complexity of the question. In this paper, we achieve approximate equation of 2-D Helmholtz operator inversion using multi-way splitting operation. Analysis on Gauss integral and coefficient of optimized partial fraction show that dispersion may accumulate by splitting algorithms for steep dipping imaging. High-order symplectic Pade approximation may deal with this problem, However, approximation of square root operator in exponential using splitting algorithm cannot solve dispersion problem during one-way wave field migration imaging. We try to implement exact approximation through eigenfunction expansion in matrix. Fast Fourier Transformation (FFT) method is selected because of its lowest computation. An 8-order Laplace matrix splitting is performed to achieve a assemblage of small matrixes using FFT method. Along with the introduction of Lie group and symplectic method into seismic wave-field extrapolation, accurate approximation of matrix exponential based on Lie group and symplectic method becomes the hot research field. To solve matrix exponential approximation problem, the Second-kind Coordinates (SKC) method and Generalized Polar Decompositions (GPD) method of Lie group are of choice. SKC method utilizes generalized Strang-splitting algorithm. While GPD method utilizes polar-type splitting and symmetric polar-type splitting algorithm. Comparing to Pade approximation, these two methods are less in computation, but they can both assure the Lie group structure. We think SKC and GPD methods are prospective and attractive in research and practice.

An empirical equation for the calculation of retention time with extrapolation of temperature in gas chromatography

An empirical equation is proposed to accurately correlate isothermal data over a wide range of temperature With the equation ln k = A* + B*/T-lambda the retention times of different solutes tested on OV-101, SE-54 and PEG 20M capillary columns have been achieved even when lambda is assigned a constant value of 1.7 Comparison with ln k = A + B/T and in k = c + d/T+ h/T-2, shows that the proposed equation is of higher accuracy and is applicable to extrapolation calculation, especially from data at high temperature to those at low temperature. Parameters A* and B* as well as A and B are also discussed. The linear correlation of A* and B* is weaker than that of A and B.

The Image Irradiance Equation: Its Solution and Application

How much information about the shape of an object can be inferred from its image? In particular, can the shape of an object be reconstructed by measuring the light it reflects from points on its surface? These questions were raised by Horn [HO70] who formulated a set of conditions such that the image formation can be described in terms of a first order partial differential equation, the image irradiance equation. In general, an image irradiance equation has infinitely many solutions. Thus constraints necessary to find a unique solution need to be identified. First we study the continuous image irradiance equation. It is demonstrated when and how the knowledge of the position of edges on a surface can be used to reconstruct the surface. Furthermore we show how much about the shape of a surface can be deduced from so called singular points. At these points the surface orientation is uniquely determined by the measured brightness. Then we investigate images in which certain types of silhouettes, which we call b-silhouettes, can be detected. In particular we answer the following question in the affirmative: Is there a set of constraints which assure that if an image irradiance equation has a solution, it is unique? To this end we postulate three constraints upon the image irradiance equation and prove that they are sufficient to uniquely reconstruct the surface from its image. Furthermore it is shown that any two of these constraints are insufficient to assure a unique solution to an image irradiance equation. Examples are given which illustrate the different issues. Finally, an overview of known numerical methods for computing solutions to an image irradiance equation are presented.

Asymptotics of Perturbations to the Wave Equation

M. Hieber, I. Wood: Asymptotics of perturbations to the wave equation. In: Evolution Equations, Lecture Notes in Pure and Appl. Math., 234, Marcel Dekker, (2003), 243-252.

APPLICATION OF THE KHOKHLOV-ZABOLOTSKAYA-KUZNETSOV EQUATION TO MODELING HIGH-INTENSITY FOCUSED ULTRASOUND BEAMS

High-intensity focused ultrasound is a form of therapeutic ultrasound which uses high amplitude acoustic waves to heat and ablate tissue. HIFU employs acoustic amplitudes that are high enough that nonlinear propagation effects are important in the evolution of the sound field. A common model for HIFU beams is the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation which accounts for nonlinearity, diffraction, and absorption. The KZK equation models diffraction using the parabolic or paraxial approximation. Many HIFU sources have an aperture diameter similar to the focal length and the paraxial approximation may not be appropriate. Here, results obtained using the “Texas code,” a time-domain numerical solution to the KZK equation, were used to assess when the KZK equation can be employed. In a linear water case comparison with the O’Neil solution, the KZK equation accurately predicts the pressure field in the focal region. The KZK equation was also compared to simulations of the exact fluid dynamics equations (no paraxial approximation). The exact equations were solved using the Fourier-Continuation (FC) method to approximate derivatives in the equations. Results have been obtained for a focused HIFU source in tissue. For a low focusing gain transducer (focal length 50λ and radius 10λ), the KZK and FC models showed excellent agreement, however, as the source radius was increased to 30λ, discrepancies started to appear. Modeling was extended to the case of tissue with the appropriate power law using a relaxation model. The relaxation model resulted in a higher peak pressure and a shift in the location of the peak pressure, highlighting the importance of employing the correct attenuation model. Simulations from the code that were compared to experimental data in water showed good agreement through the focal plane.

Mapping 2-D defects in a conductive half-space by eigenfunction expansions in K-space of Fourier-Laplace transforms

info:eu-repo/semantics/published

Consistent couplings between fields with a gauge freedom and deformations of the master equation

The antibracket in the antifield-BRST formalism is known to define a map Hp × Hq → Hp + q + 1 associating with two equivalence classes of BRST invariant observables of respective ghost number p and q an equivalence class of BRST invariant observables of ghost number p + q + 1. It is shown that this map is trivial in the space of all functionals, i.e. that its image contains only the zeroth class. However, it is generically non-trivial in the space of local functionals. Implications of this result for the problem of consistent interactions among fields with a gauge freedom are then drawn. It is shown that the obstructions to constructing non-trivial such interactions lie precisely in the image of the antibracket map and are accordingly non-existent if one does not insist on locality. However consistent local interactions are severely constrained. The example of the Chern-Simons theory is considered. It is proved that the only consistent, local, Lorentz covariant interactions for the abelian models are exhausted by the non-abelian Chern-Simons extensions. © 1993.