An extended functional transformation method and its application in some evolution equations

In this paper, an extended functional transformation is given to solve some nonlinear evolution equations. This function, in fact, is a solution of the famous KdV equation, so this transformation gives a transformation between KdV equation and other soliton equations. Then many new exact solutions can be given by virtue of the solutions of KdV equation.

A callus transformation system for gene functional studies in soybean

Obtaining transgenic plants is a common method for analyzing gene function. Unfortunately, stable genetic transformation is difficult to achieve, especially for plants（e.g., soybean）, which are recalcitrant to genetic transformation. Transient expression systems, such as Arabidopsis protoplast, Nicotiana leaves, and onion bulb leaves are widely used for gene functional studies. A simple method for obtaining transgenic soybean callus tissues was reported recently. We extend this system with simplified culture conditions to gene functional studies, including promoter analysis, expression and subcellular localization of the target protein, and protein-protein interaction. We also evaluate the plasticity of this system with soybean varieties, different vector constructs, and various Agrobacterium strains. The results indicated that the callus transformation system is efficient and adaptable for gene functional investigation in soybean genotype-, vector-, and Agrobacterium strain-independent modes. We demonstrated an easy set-up and practical homologous strategy for soybean gene functional studies.

Function Combined Method for Design Innovation of Children's Bike

As children mature, bike products for children in the market develop at the same time, and the conditions are frequently updated. Certain problems occur when using a bike, such as cycle overlapping, repeating function, and short life cycle, which go against the principles of energy conservation and the environmental protection intensive design concept. In this paper, a rational multi-function method of design through functional superposition, transformation, and technical implementation is proposed. An organic combination of frog-style scooter and children’s tricycle is developed using the multi-function method. From the ergonomic perspective, the paper elaborates on the body size of children aged 5 to 12 and effectively extracts data for a multi-function children’s bike, which can be used for gliding and riding. By inverting the body, parts can be interchanged between the handles and the pedals of the bike. Finally, the paper provides a detailed analysis of the components and structural design, body material, and processing technology of the bike. The study of Industrial Product Innovation Design provides an effective design method to solve the bicycle problems, extends the function problems, improves the product market situation, and enhances the energy saving feature while implementing intensive product development effectively at the same time.

Comprehensive Reliability Allocation Method for CNC Lathes Based on Cubic Transformed Functions of Failure Mode and Effects Analysis

Reliability allocation of computerized numerical controlled（CNC）lathes is very important in industry.Traditional allocation methods only focus on high-failure rate components rather than moderate failure rate components,which is not applicable in some conditions.Aiming at solving the problem of CNC lathes reliability allocating,a comprehensive reliability allocation method based on cubic transformed functions of failure modes and effects analysis（FMEA）is presented.Firstly,conventional reliability allocation methods are introduced.Then the limitations of direct combination of comprehensive allocation method with the exponential transformed FMEA method are investigated.Subsequently,a cubic transformed function is established in order to overcome these limitations.Properties of the new transformed functions are discussed by considering the failure severity and the failure occurrence.Designers can choose appropriate transform amplitudes according to their requirements.Finally,a CNC lathe and a spindle system are used as an example to verify the new allocation method.Seven criteria are considered to compare the results of the new method with traditional methods.The allocation results indicate that the new method is more flexible than traditional methods.By employing the new cubic transformed function,the method covers a wider range of problems in CNC reliability allocation without losing the advantages of traditional methods.

A whole-space transform formula of cylindrical wave functions for scattering problems

The theory of elastic wave scattering is a fundamental concept in the study of elastic dynamics and wave motion,and the wave function expansion technique has been widely used in many subjects.To supply the essential tools for solving wave scattering problems induced by an eccentric source or multi-sources as well as multi-scatters,a whole-space transform formula of cylindrical wave functions is presented and its applicability to some simple cases is demonstrated in this study.The transforms of wave functions in cylindrical coordinates can be classifi ed into two basic types: interior transform and exterior transform,and the existing Graf’s addition theorem is only suitable for the former.By performing a new replacement between the two coordinates,the exterior transform formula is fi rst deduced.It is then combined with Graf’s addition theorem to establish a whole-space transform formula.By using the whole-space transform formula,the scattering solutions by the sources outside and inside a cylindrical cavity are constructed as examples of its application.The effectiveness and advantages of the whole-space transform formula is illustrated by comparison with the approximate model based on a large cycle method.The whole-space transform formula presented herein can be used to perform the transform between two different cylindrical coordinates in the whole space.In addition,its concept and principle are universal and can be further extended to establish the coordinate transform formula of wave functions in other coordinate systems.

On the generalized Cauchy function and new Conjecture on its exterior singularities

This article studies on Cauchy’s function f （z） and its integral, （2πi）J[ f （z）] ≡ ■C f （t）dt/（t z） taken along a closed simple contour C, in regard to their comprehensive properties over the entire z = x ＋ iy plane consisted of the simply connected open domain D ＋ bounded by C and the open domain D outside C. （1） With f （z） assumed to be C n （n ∞-times continuously differentiable） z ∈ D ＋ and in a neighborhood of C, f （z） and its derivatives f （n） （z） are proved uniformly continuous in the closed domain D ＋ = [D ＋ ＋ C]. （2） Cauchy’s integral formulas and their derivatives z ∈ D ＋ （or z ∈ D ） are proved to converge uniformly in D ＋ （or in D = [D ＋C]）, respectively, thereby rendering the integral formulas valid over the entire z-plane. （3） The same claims （as for f （z） and J[ f （z）]） are shown extended to hold for the complement function F（z）, defined to be C n z ∈ D and about C. （4） The uniform convergence theorems for f （z） and F（z） shown for arbitrary contour C are adapted to find special domains in the upper or lower half z-planes and those inside and outside the unit circle ｜z｜ = 1 such that the four general- ized Hilbert-type integral transforms are proved. （5） Further, the singularity distribution of f （z） in D is elucidated by considering the direct problem exemplified with several typ- ical singularities prescribed in D . （6） A comparative study is made between generalized integral formulas and Plemelj’s formulas on their differing basic properties. （7） Physical sig- nificances of these formulas are illustrated with applicationsto nonlinear airfoil theory. （8） Finally, an unsolved inverse problem to determine all the singularities of Cauchy function f （z） in domain D , based on the continuous numerical value of f （z） z ∈ D ＋ = [D ＋ ＋ C], is presented for resolution as a conjecture.

A NOTE ON DERIVATIVES OF FUNCTION AND THEIR FOURIER TRANSFORMS IN L_2

The purpose of this article is to indicate the shortcomings of a few theorems of[1]. Moreover, some interesting results are detluced.

Biofilm formation under high temperature causes the commensal bacteria Bacillus cereus WPySW2 to shift from friend to foe in Neoporphyra haitanensis in vitro model

Although biofilm formation may promote growth,biofilms are not always beneficial to their hosts.The biofilm formation characteristics of Bacillus cereus WPySW2 and its changes at different temperatures were studied.Results show that B.cereus WPySW2 promoted the growth of Neoporphyra haitanensis(an economically cultivated seaweed)at 20℃ but accelerated algal rot at 28℃.Thicker B.cereus WPySW2 biofilms covered the surface of N.haitanensis thalli at 28℃,which hindered material exchange between the algae and surrounding environment,inhibited algal photosynthesis and respiration,and accelerated algal decay.Compared with planktonic bacteria,mature biofilm cells had lower energy consumption and metabolic levels.The biofilm metabolic characteristics of B.cereus WPySW2 changed significantly with temperature.High temperature accelerated biofilm maturation,which made it thicker and more stable,allowing the bacteria to easily adapt to environmental changes and obtain greater benefits from their host.High temperature did not affect the production or increased the abundance of toxic metabolites,indicating that the negative effects of B.cereus WPySW2 on algae were not caused by toxins.This study shows that increased temperature can transform a harmless bacterium into a detrimental one,demonstrating that temperature may change the ecological function of phycospheric bacteria by affecting their morphology and metabolism.

An Efficient Method of N-D FIR Digital Filter Designs and Implementation

All efficient method of N-D FIR digital filter designs and implementation is presented in the peper.The most interesting aspects of the work in the paper are divided into three parts:First,an efficient transformation functions which have good properties are proposed.Second,the essential properties for spherically or hyperspherically symmetric filters are given.Finally,the most efficient implementatiou which exploits the structure inherent in the design is discussed.

Synthetic Aperture Radar Raw Signals Simulation of Extended Scenes

A synthetic aperture radar (SAR) raw signal simulation algorithm for extended scenes is presented. This algorithm is based on the SAR two-dimensional system transform function (STF). To cope with range-variant nature of SAR STF and increase the speed of this algorithms, new formulas for range-variant phase corrections in range-Doppler (RD) domain are developed. In this way, many azimuth lines can be simulated with the same SAR STF. It only needs two-dimensional fast Fourier transform code and complex multiplications. Comparing with time-domain simulation algorithm, it is very simple and thus efficient. Simulation results have shown that this algorithm is accurate and efficient. Key words synthetic aperture radar - raw signal simulation - system transform function CLC number TP 751. 1 Foundation item: Supported by the National Natural Science Foundation of China (40376051)Biography: Sun Jin-yao (1967-), female, Ph. D. candidate, research direction: SAR image simulation and 3D recover for SAR image.

An analytical model for evaluating the dynamic response of a tunnel embedded in layered foundation soil with different saturations

This paper proposes an analytical model for evaluating the dynamic response of an underground railway tunnel in layered foundation soil with different saturations.The soil is modeled as layered media,and the circular tunnel lining is modeled as an infinite Flügge cylindrical shell.The separation of variables method is used to solve the motion equation of the shell,and the wave equation of the soil is solved using the Helmholtz decomposition theorem.A dynamic matrix reflecting the wave vectors of soil layers is established using the transfer matrix method.Based on boundary conditions,the tunnel-soil model is coupled using the transformation method of plane wave functions and cylindrical wave functions.The proposed model is validated by comparison with existing tunnel models,and the effects of saturation and the layered properties of soil on the dynamic response of a layered tunnel-soil system is demonstrated via case studies.

A Class of General Transformation of Characteristic Functions in Dynamic Games

The transformation of characteristic functions is an effective way to avoid time-inconsistency of cooperative solutions in dynamic games.There are several forms on the transformation of characteristic functions.In this paper,a class of general transformation of characteristic functions is proposed.It can lead to the time-consistency of cooperative solutions and guarantee that the irrational-behaviorproof conditions hold true.To illustrate the theory,an example of dynamic game on a tree is given.

Travelling Wave Solutions to the m-KdV-Sine-Gordon Equation and the m-KdV-Sinh-Gordon Equation

By using the function transformation and proper Sub-ODE, exact travelling wave solutions of the m-KdV-Sine-Gordon and the m-KdV-Sinh-Gordon equation are obtained, from which exact travelling wave solutions of the m-KdV equation, the Sine-Gordon equation and the Sinh-Gordon equation are derived.

Promoting the Transformation of Government Function for Achieving the Coordinated Urban-Rural Development of Resources and Environment: Practice of “MultiPlan Integration” in Xiamen

This paper analyzes the main problems in China's urban planning and construction, including conf licts among various spatial plans, the lack of a unified spatial planning management system, the inefficiency of examination and approval administration, and the social contradictions caused by unclear information. It articulates the significance of multi-plan integration from the viewpoints of implementing the national strategies issued by the central government, meeting the underlying demand of development transition of cities, and promoting the modernization of a city governance system and city governance capacity, etc. It introduces in detail the practice of multi-plan integration in Xiamen, which takes the urban development strategies in consensus as the top-level design, establishes a spatial planning system through the "strict control based on one blueprint" and the "coordinated management on one platform," promotes the transformation of the government function via reforming the examination and approval administration system, and builds up a guarantee mechanism through the direct inspection by the top leader of the government and the joint efforts from the top to the bottom. It finally summarizes the effects of the practice of multi-plan integration in Xiamen and proposes some suggestions on further completing the spatial planning system, improving the examination and approval administration system, and accelerating the transformation of the government function, etc., in hope of serving as a reference for other Chinese cities.

THE EXTENDED JORDAN'S LEMMA AND THE RELATION BETWEEN LAPLACE TRANSFORM AND FOURIER TRANSFORM

Jordan's lemma can be used for a wider range than the original one. The extended Jordan's lemma can be described as follows. Let f(z) be analytic in the upper half of the z plane (Imz≥0), with the exception of a finite number of isolated singularities, and for P>o, if then where z=Rei and CR is the open semicircle in the upper half of the z plane.With the extended Jordan's lemma one can find that Laplace transform and Fourier transform are a pair of integral transforms which relate to each other.

耦合KdV方程组的复合型新解

In this paper,new infinite sequence complex solutions of the coupled Kd V equations are constructed with the help of function transformation and the second kind of elliptic equation.First of all,according to the function transformation,the coupled Kd V equations are changed into the second kind of elliptic equation.Secondly,the new solutions and Bäcklund transformation of the second kind of elliptic equation are applied to search for new infinite sequence complex solutions of the coupled Kd V equations.These solutions include new infinite sequence complex solutions composed by Jacobi elliptic function,hyperbolic function and triangular function.

NON-ORTHOGONAL P-WAVELET PACKETS ON THE HALF-LINE

In this paper, the notion of p-wavelet packets on the positive half-line P＋ is introduced. A new method for constructing non-orthogonal wavelet packets related to Walsh functions is developed by splitting the wavelet subspaces directly instead of using the lowpass and high-pass filters associated with the multiresolution analysis as used in the classical theory of wavelet packets. Further, the method overcomes the difficulty of constructing non-orthogonal wavelet packets of the dilation factor p 〉 2.

Correlation between large-and small-scale velocity components under Fourier filters

By introducing the Fourier filters, we analyse the correlation between large- and small-scale velocity components in homogeneous isotropic turbulence theoretically. We show that different Fourier filters act similarly on this multiscale correlation with a ＂natural＂ mechanism of removing the physical correlations between large- and small-scale velocity components. This conclusion calls for the further investigation on the Hilbert-Huang decomposition to investigate the mechanism of Marusic et al （2008）.

Interpretation of the short period variations in geomagnetic anomalies of Shaanxi region

A temporary profile from Shiquan in the southern part of Shaanxi Province to Ningxian in Gansu Province for observation of geomagnetic short period variations was set up. The characteristics of geomagnetic short period variations in the profile region was analyzed through geomagnetic transfer functions at measurement sites (Fan, et al, 1998). According to the theory of multi-scale analysis of wavelet transform, the components affected by regional origin in the region is extracted in this paper. The components of regional origin is used as original data in the inversion study for investigation of 2-D conductivity structure corresponding to the regional origin. The inversion method (Zhdanov, Traynin, 1997) which is based on the minimum of the total energy of the residual field between observational electro-magnetic field and the calculated theoretical field of conductivity model and the conception of migrated residual field is introduced into our inversion of the data of magneto-variation sounding. The result of the inversion gives the underground conductivity structure in depth range of 100 km beneath the profile, and shows that a high conductivity area is located under Wugong and Qianling. The main characteristics of the inversion method is briefly discussed, that is, it can reflect the depth and the distribution of anomalous conductivity area comparatively well, and large number of parameters of inversion model is allowed to be used in the Inversion.

Some Kinds of New Composite Solutions of a Kind of Coupled Schrodinger Equation

With the help of the method that combines the first kind of elliptic equation with the function transformation, some kinds of new composite solutions of a kind of coupled Schr?dinger equation are constructed. First, a kind of function transformation is presented, and then the problem of solving solutions of a kind of coupled Schr?dinger equation can be changed to the problem of solving solutions of the first kind of elliptic equation. Then, with the help of the conclusions of the B?cklund transformation and so on of the first kind of elliptic equation, the new infinite sequence composite solutions of a kind of coupled Schr?dinger equation are constructed. These solutions are consisting of two-soliton solutions and two-period solutions and so on.