A more general form of lump solution,lumpoff,and instanton/rogue wave solutions of a reduced (3+1)-dimensional nonlinear evolution equation

In this manuscript,a reduced(3+1)-dimensional nonlinear evolution equation is studied.We first construct the bilinear formalism of the equation by using the binary Bell polynomials theory,then explore a lump solution to the special case for z=x.Furthermore,a more general form of lump solution of the equation is found which possesses seven arbitrary parameters and four constraint conditions.By cutting the lump by the induced soliton(s),lumpoff and instanton/rogue wave solutions are also constructed by the more general form of lump solution.

A GENERAL FORM OF THE INCREMENTS OF TWO-PARAMETER FRACTIONAL WIENER PROCESS

A general form of the increments of two-parameter fractional Wiener process is given. The results of Csoergo-Révész increments are a special case,and it also implies the results of the increments of the two-parameter Wiener process.

Strong/weak limits and strong/weak differentials of multi-variable indeterminate forms. I: Deduction and geometric illustration

Strong and weak limits as well as strong and weak differentials of multi-variable indeterminate forms are discussed based on the thorough exploration of differentiation to solve the strong and weak limits and differentials of unitary indeterminate forms. The fruit of this work is going to be reported in three parts. The first part presents the standard analysis on this subject which supplements, systematizes and advances L. Hospital抯 principles on differential calculus by applying special ,general, and limit guaranteeing theories together with K(t) and XhK0 theories. The combination of theoretical analysis and geometric signification makes the derivation intuitional, visual and easy to perceive.

On General Mller Transformation

We give a study on the general Moiler transformation and emphatically introduce its differential form. In this paper, a definition of acceleration is given in spacetime language and the inertial reference frame is also settled. With a discussion of the geodesic equations of motion, the differential form of the general MФller transformation at arbitrary direction is presented.

On the two-layer high-level Green-Naghdi model in a general form

The traditional high-level Green-Naghdi(HLGN)model,which uses the polynomial as the shape function to approximate the variation of the horizontal-and vertical-velocity components along the vertical direction for each-fluid layer,can accurately describe the large-amplitude internal waves in a two-layer system for the shallow configuration(h_(2)/λ■1,h_(1)/λ■1).However,for the cases of the deep configuration(h_(2)/λ■1,h_(1)/λ=O(1)),higher-order polynomial is needed to approximate the variation of the velocity components along the vertical direction for the lower-fluid layer.This,however,introduces additional unknowns,leading to a significant increase in computational time.This paper,for the first time,derives a general form of the HLGN model for a two-layer fluid system,where the general form of the shape function is used during the derivation.After obtaining the general form of the two-layer HLGN equations,corresponding solutions can be obtained by determining the reasonable shape function.Large-amplitude internal solitary waves in a deep configuration are studied by use of two different HLGN models.Comparison of the two HLGN models shows that the polynomial as the shape function for the upper-fluid layer and the production of exponential and polynomial as the shape function for the lower-fluid layer is a good choice.By comparing with Euler’s solutions and the laboratory measurements,the accuracy of the two-layer HLGN model is verified.

A reaction-difusion model with nonlinearity driven difusion

In this paper, we deal with the model with a very general growth law and an M- driven diffusion For the general case of time dependent functions M and #, the existence and uniqueness for positive solution is obtained. If M and # are T0-periodic functions in t, then there is an attractive positive periodic solution. Furthermore, if M and # are time-independent, then the non-constant stationary solution M（x） is globally stable. Thus, we can easily formulate the conditions deriving the above behaviors for specific population models with the logistic growth law, Gilpin-Ayala growth law and Gompertz growth law, respectively. We answer an open problem proposed by L. Korobenko and E. Braverman in [Can. Appl. Math. Quart. 17（2009） 85-104].

Study on General Governing Equations of Computational Heat Transfer and Fluid Flow

The governing equations for heat transfer and fluid flow are often formulated in a general formfor the simplification of discretization and programming,which has achieved great success in thermal science and engineering.Based on the analysis of the popular general form of governing equations,we found that energy conservation cannot be guaranteed when specific heat capacity is not constant,which may lead to unreliable results.A new concept of generalized density is put forward,based on which a new general form of governing equations is proposed to guarantee energy conservation.A number of calculation examples have been employed to verify validation and feasibility.