THEORETICAL AMPLITUDE AND PERIOD OF PRECURSOR SOLITON GENERATION IN TWO-LAYER FLOW

An fKdV equation of two-layer how and an averaged fKdV equation (AfKdV equation) with respect to phase are derived to determine the theoretical amplitude and period of the precursor solitons in the present paper. In terms of the AfKdV equation derived by the authors, a new theory on the precursor soliton generation based on Lee et al.'s concept is presented. Concepts of asymptotic mean hydraulic fall and level are introduced in our analysis, and the theoretical amplitude and period both depend on the asymptotic mi-an levels and stratified parameters. From the present theoretical results, it is obtained that when the moving velocity of the topography is at the resonant points, there exist two general relations: (1) amplitude relation (A) over circle = 2F, (2) period relation <(tau)over circle> = -8m(1)m(3)(-1)root 6m(4)m(3)(-1)F, in which (A) over circle and <(tau)over circle> are the amplitude and period of the precursor solitons at the resonant points respectively, m(1), m(3) and m(4) are coefficients of the fKdV equation, and F is asymptotic mean half-hydraulic fall at subcritical cutoff points. The theoretical results of this paper are compared with experiments and numerical calculations of two-layer flow over a semicircular topography and all these results are in good agreement. Due to the canonical character of the coefficients of fKdV equations, this theory also holds for any two-dimensional system, which can be reduced to fKdV equations.

Evaluation Criteria Based on Mutual Information for Classifications Including Rejected Class

与用表演措施的常规评估标准不同，信息理论基于在场的标准在机器学习的应用的一个唯一的有益的特征。然而，我们仍然远非正在拥有熵类型标准的深入的理解，说，在与常规基于表演的标准的关系。这份报纸学习通用分类问题，它包括一拒绝，或未知，班。我们在场基本公式和分类基于信息学习的图解的图理论。一个靠近形式的方程为通用分类问题在规范的相互的信息和扩充混乱矩阵之间被导出。敏感方程的三个定理和定理集合为学习在相互的信息和常规表演索引之间的关系被给。我们也与常规标准比较举与相互的信息标准的优点和限制有关的数字例子和几讨论。

THEORETICAL MEAN WAVE RESISTANCE OF PRECURSOR SOLITON GENERATION OF SINGLE-LAYER FLOW

Theoretical mean wave resistance and regional division of the energy of single-layer flow over topogra-phy is studied at the near-resonant region in the weakly nonlinear, long wave limit. The theoretical meanwave resistance is determined in terms of the 1st and 2nd conservation laws of the fKdV equation. It isproved by the asymptotic mean method that the theoretical mean wave resistance depends only on the intensityand moving velocity of the topography. The theoretical results of this paper are in good agreement withnumerical calculations. Comparisons between the theoretical and numerical results showed that the theoryof the present paper holds for any small compact topography.

Unsteady peristaltic transport of Maxwell fluid through finite length tube:application to oesophageal swallowing

This paper analytically investigates the unsteady peristaltic transport of the Maxwell fluid in a finite tube. The walls of the tube are subjected to the contraction waves that do not cross the stationary boundaries. The analysis is carried out by a long wavelength approximation in the non-dimensional form. The expressions for the axial and radial velocities are derived. The pressures across the wavelength and the tubelength are also estimated. The reflux phenomenon is discussed, which culminates into the determination of the reflux limit. Mathematical formulations are physically interpreted for the flow of masticated food materials such as bread and white eggs in the oesophagus. It is revealed that the Maxwell fluids are favorable to flow in the oesophagus as compared with the Newtonian fluids. This endorses the experimental finding of Takahashi et al. （Takahashi, T., Ogoshi, H., Miyamoto, K., and Yao, M. L. Viscoelastic properties of commercial plain yoghurts and trial foods for swallowing disorders. Rheology, 27, 169- 172 （1999））. It is further revealed that the relaxation time does not affect the shear stress and the reflux limit. It is found that the pressure peaks are identical in the integral case while different in the non-integral case.

Analytical Solution of the Blast Wave Problem in a Non-Ideal Gas

An analytical approach is used to construct the exact solution of the blast wave problem with generalized geometries in a non-ideal medium.It is assumed that the density ahead of the shock front varies according to a power of distance from the source of the blast wave.Also,an analytical expression for the total energy in a non-ideal medium is derived.

L^2(R^n) BOUNDEDNESS FOR COMMUTATORS OF OSCILLATORY SINGULAR INTEGRAL OPERATORS

The commutators of oscillatory singular integral operators with homogeneous kernel $\frac{{\Omega (x)}}{{\left| x \right|^n }}$ are studied, where Ω is homogeneous of degree zero, has mean value zero on the unit sphere. It is proved that Ω∈L (logL)K+1(Sn-1) is a sufficient condition under which the k-th order commutator is bounded on L2(Rn).

An Approximate Analytical Solution of Imploding Strong Shocks in a Non-Ideal Gas through Lie Group Analysis

The method of Lie group transformation is used to obtain an approximate analytical solution to the system of first-order quasilinear partial differential equations that govern a one-dimensional unsteady planer, cylindrically symmetric and spherically symmetric motion in a non-ideal gas, involving strong shock waves. Invariance groups admitted by the governing system of partial differential equations, which are indeed continuous group of transformations under which the system of partial differential equations remains invariant, are determined, and the complete Lie algebra of infinitesimal symmetries is established. The infinitesimal generators are used to construct the similarity variables. These similarity variables are used to reduce the governing system of partial differential equations into a system of ordinary differential equations.

Spatially Homogeneous Bianchi Type V Cosmological Model in the Scale-Covariant Theory of Gravitation

We discuss spatially homogeneous and anisotropic Bianchi type-V spacetime filled with a perfect fluid in the framework of the seale-covariant theory of gravitation proposed by Canuto et al. By applying the law of variation for Hubble＇s parameter, exact solutions of the field equations are obtained, which correspond to the model of the universe having a big-bang type singularity at the initial time t = 0. The cosmological model, evolving from the initial singularity, expands with power-law expansion and gives essentially an empty space for a large time. The physical and dynamical properties of the model are also discussed.

SOME PROBLEMS IN THE Z-C-X SPACE

The new concepts of the Z-C-X space and excellent cone are introduced. Some problems of random semiclosed 1-set-contractive operator are investigated in the Z-C-X space. At first, an important inequality is proved. Secondly, several new conclusions are proved by means of random fixed point index in the theory of random topological degree. A random solution of a class of random operator equations under conditions of imitating the parallelogram law is obtained, famous Altman's theorem is generalized in partially ordered Z-C-X space. Therefore, some new results are obtained.

Stokes flow of micro-polar fluids by peristaltic pumping through tube with slip boundary condition

This paper studies the Stokes flow of micro-polar fluids by peristaltic pumping through the cylindrical tube under the effect of the slip boundary condition. The motion of the wall is governed by the sinusoidal wave equation. The analytical and numerical solutions for the axial velocity, the micro-polar vector, the stream function, the pressure gradient, the friction force, and the mechanical efficiency are obtained by using the lu- brication theory under the low Reynolds number and long wavelength approximations. The impacts of the emerging parameters, such as the coupling number, the micro-polar parameter, the slip parameter on pumping characteristics, the friction force, the velocity profile, the mechanical efficiency, and the trapping phenomenon are depicted graphically. The numerical results infer that large pressure is required for peristaltic pumping when the coupling number is large, while opposite behaviors are found for the micro-polar parameter and the slip parameter. The size of the trapped bolus reduces with the increase in the coupling number and the micro-polar parameter, whereas it blows up with the increase in the slip parameter.

Adaptive Algorithm for Accelerating Direct Isosurface Rendering on GPU

Direct isosurface volume rendering is the most prominent modern method for medical data visualization.It is based on finding intersection points between the rays corresponding to pixels on the screen and isosurface. This article describes a two-pass algorithm for accelerating the method on the graphic processing unit(GPU). On the first pass, the intersections with the isosurface are found only for a small number of rays, which is done by rendering into a lower-resolution texture. On the second pass, the obtained information is used to efficiently calculate the intersection points of all the other. The number of rays to use during the first pass is determined by using an adaptive algorithm, which runs on the central processing unit(CPU) in parallel with the second pass of the rendering. The proposed approach allows to significantly speed up isosurface visualization without quality loss. Experiments show acceleration up to 10 times in comparison with a common ray casting method implemented on GPU. To the authors’ knowledge, this is the fastest approach for ray casting which does not require any preprocessing and could be run on common GPUs.

Landau–Stanyukovich Rule and the Similarity Parameter of Converging Shock Waves in Magnetogasdynamics

Second-kind self-similar solutions to a problem of converging cylindrical shock waves in magnetogasdynamics are investigated.Two trial functions suggested by Chisnell and the shooting method of Landau–Stanyukovich are used to determine the similarity exponent for different values of specific heat ratioγand the parameter k,where kın(0,1].Detailed analyses of flow patterns for different values of adiabatic heat exponent and magnetic field strength are carried out.It is observed that the general behavior of the velocity and density profiles is not affected in a magnetogasdynamics regime whereas there is an increase in the absolute value of the flow parameters with an increase in the magnetic field strength.However,the pressure profiles are greatly affected by the magnetic field interaction.

A Non-Conventional Coloring of the Edges of a Graph

Coloring the nodes of a graph is a commonly used technique to speed up clique search algorithms. Coloring the edges of the graph as a preconditioning method can also be used to speed up computations. In this paper we will show that an unconventional coloring scheme of the edges leads to an NP-complete problem when one intends to determine the optimal number of colors.

Three-Dimensional Thermal-Stress Analysis of Semi-infinite Transversely Isotropic Composites

By making use of the direct integration method,an exact analysis of the general three-dimensional thermoelasticity problem is performed for the case of a transversely isotropic homogeneous half-space subject to local thermal and force loadings.The material plane of isotropy is assumed to be parallel to the limiting surface of the halfspace.By reducing the original thermoelasticity equations to the governing ones for individual stress-tensor components,the effect of material anisotropy in the stress field is analyzed with regard to the feasibility requirement,i.e.,the finiteness of the stress field at a distance from the disturbed area.As a result,the solution is constructed in the form of explicit analytical dependencies on the force and thermal loadings for various kinds of transversely isotropic materials and agrees with the basic principles of the continua mechanics.The solution can be efficiently used as a benchmark one for the direct computation of temperature and thermal stresses in transversely isotropic semi-infinite domains,as well as for the verification of solutions constructed by different means.

Handwritten Character Recognition Using Multiresolution Technique and Euclidean Distance Metric

In the present paper, the problem of handwritten character recognition has been tackled with multiresolution technique using discrete wavelet transform (DWT) and Euclidean distance metric (EDM). The technique has been tested and found to be more accurate and faster. Characters is classified into 26 pattern classes based on appropriate properties. Features of the handwritten character images are extracted by DWT used with appropriate level of multiresolution technique, and then each pattern class is characterized by a mean vector. Distances from input pattern vector to all the mean vectors are computed by EDM. Minimum distance determines the class membership of input pattern vector. The proposed method provides good recognition accuracy of 90% for handwritten characters even with fewer samples.

An interacting two-fluid scenario for dark energy in a Bianchi type-I cosmological model

We study the evolution of the dark energy parameter within a Bianchi type-I cosmological model filled with barotropic fluid and dark energy. The solutions have been obtained for power law and exponential forms of the expansion parameter （they correspond to a constant deceleration parameter in general relativity）. After a long time, the models tend to be isotropic under certain conditions.

Bianchi-Type VI_(0) Bulk Viscous Fluid Models with Variable Gravitational and Cosmological Constants

This paper deals with Bianchi type VI0 anisotropic cosmological models filled with a bulk viscous cosmic fluid in the presence of time-varying gravitational and cosmological constant. Physically realistic solutions of Einstein's field equations are obtained by assuming the conditions 1) the expansion scalar is proportional to shear scalar 2) the coefficient of the bulk viscosity is a power function of the energy density and 3) the cosmic fluid obeys the barotropic equation of state. We observe that the corresponding models retain the well established features of the standard cosmology and in addition, are in accordance with recent type Ia supernovae observations. Physical behaviours of the cosmological models are also discussed.

BOUNDEDNESS CRITERION FOR SOME COMMUTATORS OF LINEAR OPERATORS

The paper is to establish a boundedness criterion for some commutators of linear operators when these linear operators don't satisfy the general Ap weight estimates but satisfy some radial weight estimates.

Physical universals in problem of precursor soliton generation

Six physical universals and two general relations in the problem of locally forced precursor soliton generation are found theoretically in terms of the AfKdV equation derived by authors. These six universals and two general relations are examined by experiment and numerical calculation of two-layer flow based on the canonical character of the coefficients of the fKdV equations. From comparisons among the theoretical, numerical and experimental results, it is shown that they are in good agreement. There is not any free parameter in this theory, so the theory of the present paper can be used to predict the wave properties of locally forced precursor soliton generation.

Steinberg triality groups acting on 2-(v,k,1)designs

A 2 - (υ, k, 1) design D = (?,?, ?) is a system consisting of a finite set ? of υ points and a collection ? of ?-subsets of ?, called blocks, such that each 2-subset of ? is contained in precisely one block. Let G be an automorphism group of a 2-(υ, k, 1) design. Delandtsheer proved that if G is block-primitive and D is not a projective plane, then G is almost simple, that is, T ? G ? Aut(T), where T is a non-abelian simple group. In this paper, we prove that T is not isomorphic to 3 D 4(q). This paper is part of a project to classify groups and designs where the group acts primitively on the blocks of the design.