Characteristic Functional Structure of Infinitesimal Symmetry Transformations for Nonholonomic System

It was proved that velocity-dependent infinitesima l symmetry transformations of nonholonomic systems have a characteristic functio nal structure, which could be formulated by means of an auxiliary symmetry tra nsformation function and is manifestly dependent upon constants of motion of th e system. An example was given to illustrate the applicability of the results.

Relations Between Characteristic Function,Positive P-Representation and Coherent Thermal State

We employ the coherent thermal states(a kind of entangled states)in thermal field dynamics to establisha complete entangled state formalism expressing pseudo-classical representations of density operator for light field.Especially,the relationship between the coherent thermal state and the characteristic function and the positive Prepresentation in quantum optics theory are obtained.

CHARACTERISTIC FUNCTIONS OF BILINEAR TIME SERIES MODEL

Bilinear time series models are of importance to nonlinear time seriesanalysis.In this paper,the autocovariance function and the relation between linearand general bilinear time series models are derived.With the help of Volterra seriesexpansion,the impulse response function and frequency characteristic function of thegeneral bilinear time series model are also derived.

An Identity for Expectations and Characteristic Function of Matrix Variate Skew-normal Distribution with Applications to Associated Stochastic Orderings

We establish an identity for E f(Y)-E f(X),when X and Y both have matrix variate skew-normal distributions and the function f satisfies some weak conditions.The characteristic function of matrix variate skew normal distribution is then derived.We then make use of it to derive some necessary and sufficient conditions for the comparison of matrix variate skew-normal distributions under six different orders,such as usual stochastic order,convex order,increasing convex order,upper orthant order,directionally convex order and supermodular order.

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.

Finite dimensional of Brownian rough characteristic functions path

The Brownian rough path is the canonical lifting of Brownian motion to the free nilpotent Lie group of order 2. Equivalently, it is a process taking values in the algebra of Lie polynomials of degree 2, which is described explicitly by the Brownian motion coupled with its area process. The aim of this article is to compute the finite dimensional characteristic functions of the Brownian rough path in IRd and obtain an explicit formula for the case when d = 2.

Multilevel Characteristic Basis Function Method with ACA for Accelerated Solution of Electrically Large Scattering Problems

The multilevel characteristic basis function method(MLCBFM)with the adaptive cross approximation(ACA)algorithm for accelerated solution of electrically large scattering problems is studied in this paper.In the conventional MLCBFM based on Foldy-Lax multiple scattering equations,the improvement is only made in the generation of characteristic basis functions(CBFs).However,it does not provide a change in impedance matrix filling and reducing matrix calculation procedure,which is time-consuming.In reality,all the impedance and reduced matrix of each level of the MLCBFM have low-rank property and can be calculated efficiently.Therefore,ACA is used for the efficient generation of two-level CBFs and the fast calculation of reduced matrix in this study.Numerical results are given to demonstrate the accuracy and efficiency of the method.

Genetic-algorithm-based balanced distribution of functional characteristics for machines

In order to make reconfigurable manufacturing system （RMS） adapt to the fluctuations of production demand with the minimum number of reconflgurations in its full life cycle, we presented a method to design RMS based on the balanced distribution of functional characteristics for ma- chines. With this method, functional characteristics were classified based on machining functions of cutting-tools and machining accuracy of machines. Then the optimization objective was set as the to- tal shortest mobile distance that all the workpieces are moved from one machine to another, and an improved genetic algorithm （GA） was proposed to optimize the configuration. The elitist strategy was used to enhance the global optimization ability of GA, and excellent gene pool was designed to maintain the diversity of population. Software Matlab was used to realize the algorithm, and a case study of simulation was used to evaluate the method.

Construction of Transgenic Crop Germplasm Effective Function and Characteristic Analysis

Germplasm effect reflects the quantitative relation between production ability of germplasm elements and yield （quality） of a certain crop, which can be shown by mathematic function, namely, germplasm effect function. Germplasm effect of a crop variety is an aggregation of many effective factors, and is restrained by different effective factors; constant increase of any one effect of germplasm elements would lead to law of effect decline, therefore, possible modes of transgenic crops effect function were deduced according to the law of effect decline. The possible modes of single transgenic germplasm effect function and multi-transgenic germplasm effect regression equation were discussed, and the characteristics of germplasm effect regression equation were analyzed in this paper.

REFERENCE FUNCTIONAL AND CHARACTERISTIC SPACE FOR LAGRANGE AND BERNSTEIN OPERATORS

This paper deals with the description and the representation of polynomials defined over n-simplices, The polynomials are computed by using two recurrent schemes: the Neville-Aitken one for the Lagrange interpolating operator and the De Casteljau one for the Bernstein-Bezier approximating operator. Both schemes fall intothe framework of transformations of the form where the F iare given numbers (forexample, at the initial step they coincide with the values of the function on a given lattice), and the coefficients (x) are linear polynomials valued in x and x is fixed. A general theory for such sequence of transformations can be found in [2] where it is also proved that these tranformations are completely characterized in term of a linear functional, reference functional. This functional is associated with a linear space., characteristic space.The concepts of reference functionals and characteristic spaces will be used and we shall prove the existence of a characteristic space for the reference functional: associated with these operators.

ALGEBROIDAL FUNCTION AND ITS DERIVED FUNCTION IN UNIT CIRCULAR DISC

In this article,the authors define the derived function of an algeboidal function in the unit disc,prove it is an algabriodal function,and study the order of algebroidal function and that of its derived function in unit circular disc.

ON THE C.CHANG TYPE INEQUALITY OF ALGEBROID FUNCTIONS

In this paper,we investigate the growth relations between algebroid functions and their derivatives,and extend famous C.Chang inequality（see[1,4]）of meromorphic functions to algebroid functions.

AN INEQUALITY ON THE ZEROS AND POLES OF VECTOR VALUED MEROMORPHIC FUNCTIONS

The author proves that if f ： C → C^n is a transcendental vector valued mero-morphic function of finite order and assume, This result extends the related results for meromorphic function by Singh and Kulkarni.

Effects of ultra-high-pressure treatment on the structural and functional properties of buckwheat 13S globulin

Components with strong adsorption capacity for cholates from buckwheat proteins were screened, separated and purified by several methods, and the effects of ultra-high-pressure(UHP) on the structure and function of buckwheat 13S globulin(BW13SG) were studied. Samples were treated by UHP at different p H(3.0 and 7.0) value(s) and at 100–500 MPa for 10–30 min. The results showed that the tertiary structure of BW13SG was partially denatured and aggregated. The decrease in the unordered structure indicated that UHP resulted in a looser secondary structure of BW13SG. UHP treatment also increased solubility, emulsion activity and stability, foaming capacity and stability. The samples treated at 500 MPa, p H 3.0 for 30 min had the most enhanced functionality. Moreover, under this condition, the sodium cholate and sodium deoxycholate adsorption capacities of BW13SG were both higher than 98% and the adsorption capacity of sodium taurocholate, which can be difficult to adsorb, was higher than 60%.

Characteristics of Implicit Customer Needs in Product Design and Methods for Their Identification

The identification of customer needs is one of the important first⁃step works for product design.Contrary to explicit ones,the implicit customer needs are less obvious,thus relying on the designers to discover.Up till now,there still lacks a rational or systematic method on the identification of implicit customer needs.Designers have to rely on their own intuition and personal experience to do the work,hindering the product design and development further on.Therefore,it is necessary to study the implicit customer needs and their identification methods.To this end,this paper first studies the characteristics of implicit needs,and clarifies the relationship between implicit needs and explicit needs.Based on this,the concept of customer needs life cycle is put forward.After that,two methods for the identification of implicit needs are proposed,including an active approach and a passive approach.For the active approach,it is suggested to exploit the functional characteristics of the product and the products in the same series or categories,for which a direct acquisition method and an evaluation data mining method are proposed,and a treadmill design case is studied.For the passive approach,it is suggested to exploit the scenario elements of product usage,for which a scenario elements questionnaire method and a scenario adaptation problem method are proposed,and a spinning bike design case is studied.The two design cases have demonstrated the process of customer needs identification and also verified the applicability of the proposed methods.

Role-Based Network Embedding via Quantum Walk with Weighted Features Fusion

Role-based network embedding aims to embed role-similar nodes into a similar embedding space,which is widely used in graph mining tasks such as role classification and detection.Roles are sets of nodes in graph networks with similar structural patterns and functions.However,the rolesimilar nodes may be far away or even disconnected from each other.Meanwhile,the neighborhood node features and noise also affect the result of the role-based network embedding,which are also challenges of current network embedding work.In this paper,we propose a Role-based network Embedding via Quantum walk with weighted Features fusion(REQF),which simultaneously considers the influence of global and local role information,node features,and noise.Firstly,we capture the global role information of nodes via quantum walk based on its superposition property which emphasizes the local role information via biased quantum walk.Secondly,we utilize the quantum walkweighted characteristic function to extract and fuse features of nodes and their neighborhood by different distributions which contain role information implicitly.Finally,we leverage the Variational Auto-Encoder(VAE)to reduce the effect of noise.We conduct extensive experiments on seven real-world datasets,and the results show that REQF is more effective at capturing role information in the network,which outperforms the best baseline by up to 14.6% in role classification,and 23% in role detection on average.

Acceptance Sampling Plans with Truncated Life Tests for the Length-Biased Weighted Lomax Distribution

In this paper,we considered the Length-biased weighted Lomax distribution and constructed new acceptance sampling plans(ASPs)where the life test is assumed to be truncated at a pre-assigned time.For the new suggested ASPs,the tables of the minimum samples sizes needed to assert a specific mean life of the test units are obtained.In addition,the values of the corresponding operating characteristic function and the associated producer’s risks are calculated.Analyses of two real data sets are presented to investigate the applicability of the proposed acceptance sampling plans;one data set contains the first failure of 20 small electric carts,and the other data set contains the failure times of the air conditioning system of an airplane.Comparisons are made between the proposed acceptance sampling plans and some existing acceptance sampling plans considered in this study based on the minimum sample sizes.It is observed that the samples sizes based on the proposed acceptance sampling plans are less than their competitors considered in this study.The suggested acceptance sampling plans are recommended for practitioners in the field.

A closed-form pricing formula for European options in an illiquid asset market

This article addresses the problem of pricing European options when the underlying asset is not perfectly liquid.A liquidity discounting factor as a function of market-wide liquidity governed by a mean-reverting stochastic process and the sensitivity of the underlying price to market-wide liquidity is firstly introduced,so that the impact of liquidity on the underlying asset can be captured by the option pricing model.The characteristic function is analytically worked out using the Feynman–Kac theorem and a closed-form pricing formula for European options is successfully derived thereafter.Through numerical experiments,the accuracy of the newly derived formula is verified,and the significance of incorporating liquidity risk into option pricing is demonstrated.

WEAK UNCORRELATEDNESS OF RANDOM VARIABLES

New measures of independence for n random variables, based on their moments, are studied. A scale of degrees of independence for random variables which starts With uncorrelatedness （for n = 2） and finishes at independence is constructed. The scale provides a countable linearly ordered set of measures of independence.

Quantum pseudodots under the influence of external vector and scalar fields

We study the spherical quantum pseudodots in the Schr6dinger equation by using the pseudo-harmonic plus harmonic oscillator potentials considering the effect of the external electric and magnetic fields. The finite energy levels and the wave functions are calculated. Furthermore, the behavior of the essential thermodynamic quantities such as, the free energy, the mean energy, the entropy, the specific heat, the magnetization, the magnetic susceptibility, and the persistent currents are also studied by using the characteristic function. Our analytical results are found to be in good agreement with the other works. The numerical results on the energy levels as well as the thermodynamic quantities have also been given.