A general method for numerical Green''''s function in arbitrarily layered soils

A straightforward approach is developed to calculate Green's function of a point current source in horizontal multi-layersoils. The sampling value of the coefficient of Green's function is obtained in an iterative way in terms of the equation group satisfying thepertinent boundary value problem. Further, the closed-form expression of multilayered soil Green's function can be given by the vectormatrix pencil technology. The numerical results are in agreement with those by using other softwares. The approach proposed here is ap-plicable to grounding problems with the structure of arbitrarily layered soil without needing the analytical expression of Green's function.     

THE BOUNDARY VALUE PROBLEM OF DEGENERATE ELLIPTIC EQUATION IN FOUR-DIMENSION SPACE

If G is a bounded domain in the plane R~2, Its boundary consists of a line segment [0,1] in x-axis anda smooth curve which lies upper half plane. Tian Maoying studied the following non-linear degenerate ellip-tic equation of second orderand proved that some boundary value problems of equation (1) and (2) have a unique solution.Wen Guochun discussed some boundary value problem for elliptic system of first order equations in thedomainThis paper makes a deeper study about the degenerate elliptic equation. Utilizing the qualities of four-     

Large range step method for acoustic waveguide with two layer media

A numerical method is developed for solving the two-dimensional Helmholtz equation in a two-layer region bounded by a flat top, a flat bottom and a curved interface. A better local orthogonal transformation is used to flatten the curved interface of the waveguide. The one-way re-formulation based on the Dirichlet-to-Neumann (DtN) map is then used to reduce the boundary value problem to an initial value problem. Numerical implemetation of the resulting operator Riccati equation uses a large range step method for discretizing the range variable and a truncated local eigenfunction expansion for approximating the operators. This method is particularly useful for solving long range wave propagation problems in slowly varying waveguides.     

Wave Damping and Refraction-Diffraction Due to Variable Depth Porous Bottom

The refraction-diffraction of surface waves due to porous variable depth has been the subject of many investigations. In the present study, we extend the boundary-value problem of impermeable varying topography to that of a variable depth porous seabed, which is the situation most likely to be encountered in practical problems of coastal engineering. A wave-induced fluid motion is applied to the porous bottom, while the well-known linear potential theory is applied to the free-water above the bottom. Eigenfunction expansions are employed to derive the matching condition and the so-caUed modified dispersion relation. As a result of the porous bottom, the wavenumber becomes a complex value, of which the real part represents the spatial periodicity while the imaginary part refers to the energy dissipation. The characteristics of water waves over a porous bottom are studied in detail. By neglecting the non-propagating modes which only have a local effect and damp exponentially with distance, we derive a mathematical model to represent the characteristics of both the wave refraction-diffraction and wave-damping. The developed model is applied to the damping problem of waves over submerged porous breakwaters.     

Introduction to game theory

The basic ideas of game theory were originated from the problems of maximum and minimum given by J. von Neumann in 1928. Later, wars accelerated the study of game theory, there are many developments that contributed to the advancement of game theory, many problems of optimum appeared in economic development process. Scientists applied mathematic methods to studying game theory to make the theory more profound and perfect. The axiomatic structure of game theory was nearly complete in 1944. The path of the development of game theory started from finite to infinite, from two players to many players, from expressing gains with quantity to showing the ending of game theory with abstract result, and from certainty problems to random problems, Thus development of game theory is closely related to the economic development. In recent years, the research on the non-differentiability of Shapley value posed by Belgian Mertens is one of the advanced studies in game theory.     

Bounds of Spectral Radii of Weighted Trees

Graphs for the design of networks or electronic circuits are usually weighted and the spectrum of weighted graphs are often analyzed to solve problems. This paper discusses the spectrum and the spectral radii of trees with edge weights. We derive expressions for the spectrum and the spectral radius of a weighted star,together with the boundary limits of the spectral radii for weighted paths and weighted trees. The analysis uses the theory of nonnogative matrices and applies the “moving edge” technique. Some simple examples of weighted paths and trees are presented to explain the results. Then, we propose some open problems in this area.     

Counting Problems in Parameterized Complexity

Parameterized complexity is a multivariate theory for the analysis of computational problems. It leads to practically efficient algorithms for many NP-hard problems and also provides a much finer complexity classification for other intractable problems. Although the theory is mostly on decision problems, parameterized complexity naturally extends to counting problems as well. The purpose of this article is to survey a few aspects of parameterized counting complexity, with a particular emphasis on some general frameworks in which parameterized complexity proves to be indispensable.     

Reaction diffusion equations for nonlinear boundary conditions

A class of singularly perturbed initial boundary value problems of reaction diffusion equations for nonlinear boundary conditions is considered.Under suitable conditions,by using the theory of differential inequalities,the existence and asymptotic behavior of solution for initial boundary value problem are studied.Moreover,the obtained solution indicates that there are initial and boundary layers,and the thickness of the initial layer is less than that of the boundary layer.     

Quasilinear singularly perturbed problem with boundary perturbation

A class of quasilinear singularly perturbed problems with boundary perturbation is considered. Under suitable conditions, using theory of differential inequalities we studied the asymptotic behavior of the solution for the boundary value problem.     

Similarity solutions to a laminar boundary layer problem in power law fluids

A suitable similarity transformation is introduced to reduce the laminar boundary layer equations of power law fluids to a class of singular nonlinear two-point boundary value problems. The kin friction and shear stress distributions for boundary layer flow over amoving flat plate are investigated by utilizing the shooting technique. Results indicate that for each fixed value of the power law exponent n or the velocity ratio parameter xi, the skin frictionand shear stress decrease with the increasing of n or ξ respectively.     

Boundary Integral Equations and A Posteriori Error Estimates

Adaptive methods have been rapidly developed and applied in many fields of scientific and engineering computing, Reliable and efficient a posteriori error estimates play key roles for both adaptive finite element and boundary element methods. The aim of this paper is to develop a posteriori error estimates for boundary element methods. The standard a posteriori error estimates for boundary element methods are obtained from the classical boundary integral equations. This paper presents hyper-singular a posteriori error estimates based on the hyper-singular integral equations, Three kinds of residuals are used as the estimates for boundary element errors. The theoretical analysis and numerical examples show that the hypersingular residuals are good a posteriori error indicators in many adaptive boundary element computations.     

Manufacturing Oriented Fuzzy Function - Feature Mapping

The mechanism of the Concurrent Engineering(CE)and the methods of the manufacturing consultation are discussed. CE-oriented computer aided manufacture consulting methods are one of the key issues in concurrent design. The problems are settled in part function-feature mapping in concurrent design. The fuzzy set theory is applied to the function-feature mapping. A method for part function-feature mapping based on fuzzy theory is presented.     

Nonlinear predator-prey singularly perturbed Robin Problems for reaction diffusion systems

The nonlinear predator-prey reaction diffusion systems for singularly perturbed Robin Problems are considered. Under suitable conditions, the theory of differential inequalities can be used to study the asymptotic behavior of the solution for initial boundary value problems.     

Prediction of end-roll strength and rapid adjustment of the on-the-spot composition in automobile cross-beam steel

According to the hot working technology, the calculating formulas of the end-roll strength in the automobile cross-beam steel have been given in theory with electron structure parameters of the alloying phase and the biphase interface. The relationships among the chemical composition, the end-roll grain size and the strength, achieved by calculations, are applied to predetermine the optimal end-roll grain size and chemical composition range to satisfy the technical requirements. In the productive process, according to the on-the-spot result analyzed, the computer can calculate the value of end-roll strength quickly, and the on-the-spot composition can also be adjusted in accordance with the demand until the composition is up to the technical requirements. The forecast is fit for all the non-quenched-tempered steels.     

Variation-difference method for solving boundary value problems for linear elliptic complex equations

This paper deals with boundary value problems for linear uniformly elliptic systems. First the general linear uniformly elliptic system of the first order equations is reduced to complex form, and then the compound boundary value problem for the complex equations of the first order is discussed. The approximate solutions of the boundary value problem are found by the variation-difference method, and the error estimates for the approximate solutions are derived.Finally the approximate method of the oblique derivative problem for linear uniformly elliptic equations of the second or der is introduced.     

Agents and Lattice-valued Logic

In fuzzy set theory, instead of the underlying membership set being a two -valued set it is a multi-valued set that generally has the structure of a lattice L with a minimal element O and the maximal element I. Furthermore if ∧, ∨, → and ┐ are defined in the set L, then we can use these operations to define, as in the ordinary set theory, operations on fuzzy subsets. In this paper we give a model of the Lattice-Valued Logic with set of agents.Any agents know the logic value of a sentence p. The logic value is compatible with all of the accessible conceptual models or worlds of p inside the agent. Agent can be rational or irrational in the use of the logic operation.Every agent of n agents can have the same set of conceptual models for p and know the same logic for p in this case the agents form a consistent group of agents.When agents have different conceptual models for p,different subgroup of agents know different logic value for p. In this case the n agents are inconsistent in the expression of the logic value for p. The valuation structure of set of agents can be used as a semantic model for the Lattice-valued Logic and fuzzy logic.     

Similarity solution to a heat equation with convection in an infinite medium

A second order heat equation with convection in an infinite medium is studied. Suitable similarity transformations are used to reduce the parabolic heat equation to a class of singular nonlinear boundary value problems. Numerical solutions are presented for different representations of heat conduction, heat convection, heat flux, and power law parameters by utilizing the shooting technique. The results reveal the heat transfer characteristic and the effect of parameters on the solutions.     

Online support vector regression for reinforcement learning

The goal in reinforcement learning is to learn the value of state-action pair in order to maximize the total reward. For continuous states and actions in the real world, the representation of value functions is critical. Furthermore, the samples in value functions are sequentially obtained. Therefore, an online sup-port vector regression （OSVR） is set up, which is a function approximator to estimate value functions in reinforcement learning. OSVR updates the regression function by analyzing the possible variation of sup-port vector sets after new samples are inserted to the training set. To evaluate the OSVR learning ability, it is applied to the mountain-car task. The simulation results indicate that the OSVR has a preferable con- vergence speed and can solve continuous problems that are infeasible using lookup table.     

Block Cipher Design:Generalized Single-Use-Algorithm Based on Chaos

The idea of using a one-time-one-key design has been widely applied in conventional cryptography.With the security theory of conventional cryptology,encryption algorithms are made public while all the secrets are encoded only in the keys.This paper applies chaos theory to conventional cryptography to develop a one-time-one-algorithm design.A general theory is given to generate the clock key,substitution box,permutation box and operational sign functions for a one-time-one-algorithm scheme.This scheme is then implemented in a system to manage the tradeoff between speed and the security of the encryption algorithm.     

Displacement Pump Evolution Theories and the Innovative Design of the Pump with a Half-Sphere Rotor

Some mechanisms evolve from other mechanisms to fulfil a new function. It follows that there is cognation between certain mechanisms. Addressed in the present paper are innovative design methods for displacement machinery. According to the design of the changeable displacement pump, it may be a closed pair of components in the mechanism that possesses periodically relative movement to form a periodically changeable and closed cavity. To this can be adapted design methods based on innovative theories, such as the Scotch Cousin theory in evolution venations, the theory of Cognation, the theory of “Nodes“ among generations and so on. Thus innovative designs for them can be produced by imaginative thinking. Illustrated here is an innovative design for a pump a with half-sphere rotor, developed from a typical 4-bar mechanism in accordance with the principle of Precession Evolution, which is to be applied to the recovery of oil spillage at sea.