INTERSECTIONS AND POLAR FUNCTIONS OF FRACTIONAL BROWNIAN SHEETS

Let B^H={B^H（t）,t∈R^N＋}be a real-valued（N,d）fractional Brownian sheet with Hurst index H=（H1,…,HN）.The characteristics of the polar functions for B^H are discussed.The relationship between the class of continuous functions satisfying Lipschitz condition and the class of polar-functions of B^H is obtained.The Hausdorff dimension about the fixed points and the inequality about the Kolmogorov’s entropy index for B^H are presented.Furthermore,it is proved that any two independent fractional Brownian sheets are nonintersecting in some conditions.A problem proposed by LeGall about the existence of no-polar continuous functions satisfying the Holder condition is also solved.

Conservation Laws and Symmetries of the Levi Equation

The conservation laws of the Levi equation are presented.Two types of symmetry of the Levi equationhierarchy are deduced.Further it is proved that these symmetries construct an infinite-dimensional Lie algebra.

FRACTAL PROPERTIES OF POLAR SETS OF RANDOM STRING PROCESSES

This paper studies fractal properties of polar sets for random string processes. We give upper and lower bounds of the hitting probabilities on compact sets and prove some sufficient conditions and necessary conditions for compact sets to be polar for the random string process. Moreover, we also determine the smallest Hausdorff dimensions of non-polar sets by constructing a Cantor-type set to connect its Hausdorff dimension and capacity.

Algebraic Method for Constructing Exact Discrete Soliton Solutions of Toda and mKdV Lattices

In this paper, with the aid of symbolic computation, we present a new method for constructing soliton solutions to nonlinear differentiM-difference equations. And we successfully solve Toda and mKdV lattice.

A Limit Symmetry of Modified KdV Equation and Its Applications

In this letter we consider a limit symmetry of the modified KdV equation and its application. The similarity reduction leads to limit solutions of the modified KdV equation. Besides, a modified KdV equation with new self-consistent sources is obtained and its solutions are derived.

POLAR SETS OF MULTIPARAMETER BIFRACTIONAL BROWNIAN SHEETS

Let B^H＇K={B^H＇K（t）, t∈R＋^N} be an （N,d）-bifractional Brownian sheet with Hurst indices H = （H1,…,HN） C∈0,1）^N and K = （K1,…,KN） ∈ （0,1]^N. The properties of the polar sets of B^H＇K are discussed. The sufficient conditions and necessary conditions for a compact set to be polar for B^H＇K are proved. The infimum of Hausdorff dimensions of its non-polar sets are obtained by means of constructing a Cantor-type set to connect its Hausdorff dimension and capacity.

Insights into financial technology (FinTech):a bibliometric and visual study

This paper conducted a comprehensive analysis based on bibliometrics and science mapping analysis.First,848 publications were obtained from Web of Science.Their fundamental characteristics were analyzed,including the types,annual publications,hot research directions,and foci(by theme analysis,co-occurrence analysis,and timeline analysis of author keywords).Next,the prolific objects(at the level of countries/regions,institutions,journals,and authors)and corresponding pivotal cooperative relationship networks were used to highlight who pays attention to FinTech.Furthermore,the citation structures of authors and journals were investigated,including citation and co-citation.Additionally,this paper presents the burst detection analysis of cited authors,journals,and references.Finally,combining the analysis results with the current financial environment,the challenges and future development opportunities are discussed further.Accordingly,a comprehensive study of the FinTech documents not only reviews the current research characteristics and trajectories but also helps scholars find the appropriate research entry point and conduct in-depth research.

Application of Exp-Function Method to Discrete Nonlinear Schrdinger Lattice Equation with Symbolic Computation

In this paper, we present an extended Exp-function method to differential-difference equation（s）. With the help of symbolic computation, we solve discrete nonlinear Schrodinger lattice as an example, and obtain a series of general solutions in forms of Exp-function.

ON INTERSECTIONS OF INDEPENDENT NONDEGENERATE DIFFUSION PROCESSES

Let X（1） = {X（1）（s）, s ∈ R＋} and X（2） = {X（2）（t）, t ∈ R＋} be two inde-pendent nondegenerate diffusion processes with values in Rd. The existence and fractal dimension of intersections of the sample paths of X （1） and X （2） are studied. More gener-ally, let E1, E2？（0,∞） and F ？Rd be Borel sets. A necessary condition and a suffcient condition for P{X（1）（E1）∩X（2）（E2）∩F 6=？}〉0 are proved in terms of the Bessel-Riesz type capacity and Hausdorff measure of E1 × E2 × F in the metric space （R＋× R＋× Rd,ρb）, whereρb is an unsymmetric metric defined in R＋× R＋× Rd. Under reasonable conditions, results resembling those of Browian motion are obtained.

TESTING THE ADEQUACY OF GARCH-TYPE MODELS IN TIME SERIES

In this article a new approach for checking the adequacy of GARCH-type models in time series was proposed. The resulted tests involve weight functions, which provide them with the flexibility in choosing scores to enhance power performance. The choice of weight functions and the power properties of the tests are studied. For a large number of alternatives, asymptotically distribution-free maximin test is constructed. The tests are asymptotically chi-squared under the null hypothesis and easy to implement. Simulation results indicate that the tests perform well.

Exact Solutions of Two Nonlinear Partial Differential Equations by the First Integral Method

In recent years, many methods have been used to find the exact solutions of nonlinear partial differential equations. One of them is called the first integral method, which is based on the ring theory of commutative algebra. In this paper, exact travelling wave solutions of the Non-Boussinesq wavepacket model and the (2 + 1)-dimensional Zoomeron equation are studied by using the first integral method. From the solving process and results, the first integral method has the characteristics of simplicity, directness and effectiveness about solving the exact travelling wave solutions of nonlinear partial differential equations. In other words, tedious calculations can be avoided by Maple software;the solutions of more accurate and richer travelling wave solutions are obtained. Therefore, this method is an effective method for solving exact solutions of nonlinear partial differential equations.

MULTI-VALUED TOTALLY QUASI-φ-ASYMPTOTICALLY NONEXPANSIVE SEMI-GROUPS AND STRONG CONVERGENCE THEOREMS IN BANACH SPACES

The purpose of this article is first to introduce the concept of multi-valued to- tally Quasi-φ-asymptotically nonexpansive semi-groups, which contains many kinds of semi- groups as its special cases, and then to modify the Halpern-Mann-type iteration algorithm for multi-valued totally Quasi-cS-asymptotically nonexpansive semi-groups to have the strong convergence under a limit condition only in the framework of Banach spaces. The results presented in this article improve and extend the corresponding results announced by many authors recently.

GENERALIZED BROWNIAN SHEET IMAGES AND BESSEL-RIESZ CAPACITY

Let W^~ be a two-parameter, R^d-valued generalized Brownian sheet. The author obtains an explicit Bessel-Riesz capacity estimate for the images of a two-dimensional set under W^~. He also presents the connections between the Lebesgue measure of the image of W^~ and Bessel-Riesz capacity. His conclusions also solve a problem proposed by J.- P.Kahane.

The least squares problem of the matrix equation A_1X_1B_1~T+A_2X_2B_2~T=T

The matrix least squares （LS） problem minx ｜｜AXB^T--T｜｜F is trivial and its solution can be simply formulated in terms of the generalized inverse of A and B. Its generalized problem minx1,x2 ｜｜A1X1B1^T ＋ A2X2B2^T - T｜｜F can also be regarded as the constrained LS problem minx=diag（x1,x2） ｜｜AXB^T -T｜｜F with A = [A1, A2] and B = [B1, B2]. The authors transform T to T such that min x1,x2 ｜｜A1X1B1^T＋A2X2B2^T -T｜｜F is equivalent to min x=diag（x1 ,x2） ｜｜AXB^T - T｜｜F whose solutions are included in the solution set of unconstrained problem minx ｜｜AXB^T - T｜｜F. So the general solutions of min x1,x2 ｜｜A1X1B^T ＋ A2X2B2^T -T｜｜F are reconstructed by selecting the parameter matrix in that of minx ｜｜AXB^T - T｜｜F.

New Integrable Decomposition of Super AKNS Equation

In this paper, a new 7×7 matrix spectral problem, which is associated with the super AKNS equation isconstructed.With the use of the binary nonlinearization method, a new integrable decomposition of the super AKNSequation is presented.

Novel Complex T-Spherical Dual Hesitant Uncertain Linguistic Muirhead Mean Operators and Their Application in Decision-Making

In this manuscript,the theory of complex T-spherical dual hesitant uncertain linguistic set is discovered,which is the mixture of three different ideas like the complex T-spherical fuzzy set,dual hesitant fuzzy set,and uncertain linguistic set.The complex T-spherical dual hesitant uncertain linguistic set composes the uncertain linguistic set,truth grade,abstinence grade,and falsity grade.Whose real and imaginary parts are the subset of a unit interval,and some of their operational laws are also presented.The theory of complex T-spherical dual hesitant uncertain linguistic Muirhead mean operator,complex T-spherical dual hesitant uncertain linguistic weighted Muirhead mean operator,complex T-spherical dual hesitant uncertain linguistic dual Muirhead mean operator and complex T-spherical dual hesitant uncertain linguistic weighted dual Muirhead mean operator are discovered.Some exceptional cases of the proposed operators are also examined.A multi-attribute decision making technique is further utilized based on explored operators.Moreover,an enterprise informatization level evaluation issue is resolved by using the presented operators to verify the proficiency and capability of the discovered approaches.Finally,some comparative analysis and advantages of the explored works are further developed to express that it is more flexible and effective than the existing methods.

Analysis of Outlets Retail Market Based on Chinese Tourists

Outlets are a new challenge to the retail industry after the continuous development of the market economy.However,academic research on outlets is very scarce.The purpose of this research is to study the relationship between outlets'marketing methods and customer perception.This research cooperates with Shanghai International Fashion Education Center(SIFEC),and conducts convenience sampling on the research objects as the samples.By using quantitative research methods and questionnaire survey tools,the researchers studied the relationships among experience marketing,perceived value,customer satisfaction and loyalty of customers to outlets.The research found that outlets'experience marketing will influence customer perceived value effectively and affect consumer satisfaction and loyalty indirectly.

Exact Travelling Wave Solutions of Two Nonlinear Schrödinger Equations by Using Two Methods

The special kind of (G’/G)-expansion method and the new mapping method are easy and significant mathematical methods. In this paper, exact travelling wave solutions of the higher order dispersive Cubic-quintic nonlinear Schrödinger equation and the generalized nonlinear Schrödinger equation are studied by using the two methods. Finally, the solitary wave solutions, singular soliton solutions, bright and dark soliton solutions and periodic solutions of the two nonlinear Schrödinger equations are obtained. The results show that this method is effective for solving exact solutions of nonlinear partial differential equations.

Quantitative Analysis of Influence Force of Shanghai Expo on GGDP

Quantitative study of the impact of Shanghai World Expo on green GDP （GGDP） is significant for deploying sustainable development policy in China. The formula of GGDP is： GGDP = GDP--the loss of natural resources environment relegation cost ＋ comprehensive utilized value of waste. Based on this, the study employed vector autoregressive （VAR） model to predict the value of GGDP and other economic variables on condition that there was no Shanghai World Expo. Then Influence of Expo is defined as the rate of increase of GGDP. The result demonstrated that Shanghai World Expo had accelerated the growth rate of GGDP vastly with the elimination of effect of Beijing Olympics. Additionally, the quantitative analysis between GGDP and other economic variables suggested GGDP would replace GDP to evaluate the development of economy. Finally, the paper proposed that incidents like World Expo can enhance the level of influence for a country and that post-impact of Shanghai Expo should continue to be used to promote GGDP and that GGDP should serve as one of the indicators in assessment of political achievement.