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.

Improved Particle Swarm Optimization for Parameter Identification of Permanent Magnet Synchronous Motor

In the process of identifying parameters for a permanent magnet synchronous motor,the particle swarm optimization method is prone to being stuck in local optima in the later stages of iteration,resulting in low parameter accuracy.This work proposes a fuzzy particle swarm optimization approach based on the transformation function and the filled function.This approach addresses the topic of particle swarmoptimization in parameter identification from two perspectives.Firstly,the algorithm uses a transformation function to change the form of the fitness function without changing the position of the extreme point of the fitness function,making the extreme point of the fitness function more prominent and improving the algorithm’s search ability while reducing the algorithm’s computational burden.Secondly,on the basis of themulti-loop fuzzy control systembased onmultiplemembership functions,it is merged with the filled function to improve the algorithm’s capacity to skip out of the local optimal solution.This approach can be used to identify the parameters of permanent magnet synchronous motors by sampling only the stator current,voltage,and speed data.The simulation results show that the method can effectively identify the electrical parameters of a permanent magnet synchronous motor,and it has superior global convergence performance and robustness.

The Similarity Transformation of Regularizing Functionals and Simularity Property of Their Fourier Transformations

Let and denote respectively the functionswhere λ≥1, The author discusses the similarity transformation of the regularizing functionals of these functions and the similar property of their Fourier transformation.

ANALYSIS OF REMOTE SENSING ARCHAEOLOGY ON TRAFFIC FUNCTION TRANSFORMATION OF TONGJI GRAND CANAL IN SUI AND TANG DYNASTIES

In China, most directions of river flowing are from west to east. During historic period, since the water traffic played an important role, it was very important to form a cross-horizontal net of water carriage route. Canals should be dug so as to make up the lack of north-south river. Tongji Grand Canal, dug in the first year of Daye (605 A.D.) in the Sui Dynasty, was the important component of north-south system of Grand Canals in China. It promoted economic and social development of the Sui, Tang and Song dynasties (605 A.D.-1279 A.D.). As Tongji Canal (i.e. Tongji Grand Canal) flowed across the Huaibei Plain, which is aggraded by abundant mud and sand deposit resulted from the Huanghe (Yellow) River flooding, many traces (such as old channel) and human culture heritages were buried under mud-sand. Tongji Canal was silted up, and disappeared in the Jin Dynasty (1115 A.D.-1234 A.D.). From then on, there were many different stories about the flowing route of the canal in historical literature. Based on space-bone and air-bone remote sensing imagery, we attempt to search the old channel of Tongji Canal, and supplement historical record. The paper discusses transformation process of Tongji Canal’s traffic function, and resumptively summarizes the reasons of the transformation, which results from synthetic function of physical geographical, political, economic, and social conditions.

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.

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.

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 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.

Selection of a Minimal Complexity of a Transformation Functions of Pressure Sensors with a Maintained Given Measurement Accuracy

For series manufacture of pressure sensors, stage of technological tests is performed, related to a definition of the manufacturing accuracy of the sensors. Technological test plan of pressure sensors involves testing the sensors on certain fixed temperature and pressure points available in the table. According to a test results, we determine transformation function mathematical model coefficients of sensors and accordance by the claimed accuracy class, of the manufactured sensors. The cost of pressure sensors mostly depends on the cost of this step and determined by the complexity of the used transformation function model. The analysis of a contemporary works associated with the choice of transformation functions for smart pressure sensors. A new proposed indicator of model complexity of a sensor transformation function. In details shown features of the complexity indicator use and given an example. In the article was set and resolved the task to reduce the cost of the tests for commercially available sensors, by reducing the number of temperature points, without compromising the accuracy of the sensor measurement ability.

Research on the Positioning of Government Functions in China under the Background of Smart City Construction

In the process of smart city construction, Beijing, Shanghai, Shenzhen and some other cities are facing many problems, among which the most essential one is the government＇ s leading role cannot give a better play due to the constraints of the traditional government functions. Therefore, it is necessary to carry out a reasonable position for the government functions in the construction of smart city. This paper issues that the government should reflect functions in the construction of smart city, such as the planning function of top-level design and unified planning; the organizational function of providing funds and talent protection; the coordinating function of promoting multiple-subject cooperation; the controlling function of establishing technical standards and legal norms.

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.

Logical-Structure Modeling for Conceptual Design

Based on the definition of a logic structure feature to relate logically functional requirements to geometric representation independent upon detailed geometric representation, this paper presents an idea of logical structure modeling for computer aided conceptual design and makes attempt to establish a representation formalism of logic structure modeling. The definition and representation of logical structure feature are given and an assembly module definition for supporting top down conceptual design is also proposed. The proposed scheme contributes to several aspects of conceptual design research, especially to provide elementarily a formal methodology for computer aided conceptual design system development and operation.

Determination of kinetic parameters from calorimetric study of solid state reactions in 7150 Al-Zn-Mg alloy

Differential scanning calorimetric （DSC） study was carried out at different heating rates to examine the solid state reactions in a 7150 A1-Zn-Mg alloy in water-quenched （WQ） state, naturally and artificially aged tempers. The exothermic and endothermic peaks of the thermograms indicating the solid state reaction sequence were identified. The shift of peak temperatures to higher temperatures with increasing heating rates suggests that the solid state reactions are thermally activated and kinetically controlled. The artificial aging behaviour of the alloy was assessed by measuring the variations of hardness with aging time. The fraction of transformation （Y）, the rate of transformation （dY/dt）, the transformation functionflY）, and the kinetic parameters such as activation energy （Q） and frequency factor （k0） of all the solid state reactions in the alloy were determined by analyzing the DSC data, i.e. heat flow involved with the corresponding DSC peaks. It was found that the kinetic parameters of the solid state reactions are in good agreement with the published data.

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.

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.

Exact Solutions to a Combined sinh-cosh-Gordon Equation

Based on a transformed Painlev~ property and the variable separated ODE method, a function transfor- mation method is proposed to search for exact solutions of some partial differential equations （PDEs） with hyperbolic or exponential functions. This approach provides a more systematical and convenient handling of the solution process of this kind of nonlinear equations. Its key point is to eradicate the hyperbolic or exponential terms by a transformed Painleve property and reduce the given PDEs to a variable-coefficient the resulting equations by some methods. As an application, are formally derived. ordinary differential equations, then we seek for solutions to exact solutions for the combined sinh-cosh-Gordon equation

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.

New Exact Solutions for a Class of Nonlinear Coupled Differential Equations

More new exact solutions for a class of nonlinear coupled differential equations are obtained by using a direct and efficient hyperbola function transform method based on the idea of the extended homogeneous balance method.