Analysis of Extended Fisher-Kolmogorov Equation in 2D Utilizing the Generalized Finite Difference Method with Supplementary Nodes

In this study,we propose an efficient numerical framework to attain the solution of the extended Fisher-Kolmogorov(EFK)problem.The temporal derivative in the EFK equation is approximated by utilizing the Crank-Nicolson scheme.Following temporal discretization,the generalized finite difference method(GFDM)with supplementary nodes is utilized to address the nonlinear boundary value problems at each time node.These supplementary nodes are distributed along the boundary to match the number of boundary nodes.By incorporating supplementary nodes,the resulting nonlinear algebraic equations can effectively satisfy the governing equation and boundary conditions of the EFK equation.To demonstrate the efficacy of our approach,we present three numerical examples showcasing its performance in solving this nonlinear problem.

An Effective Meshless Approach for Inverse Cauchy Problems in 2D and 3D Electroelastic Piezoelectric Structures

In the past decade,notable progress has been achieved in the development of the generalized finite difference method(GFDM).The underlying principle of GFDM involves dividing the domain into multiple sub-domains.Within each sub-domain,explicit formulas for the necessary partial derivatives of the partial differential equations(PDEs)can be obtained through the application of Taylor series expansion and moving-least square approximation methods.Consequently,the method generates a sparse coefficient matrix,exhibiting a banded structure,making it highly advantageous for large-scale engineering computations.In this study,we present the application of the GFDM to numerically solve inverse Cauchy problems in two-and three-dimensional piezoelectric structures.Through our preliminary numerical experiments,we demonstrate that the proposed GFDMapproach shows great promise for accurately simulating coupled electroelastic equations in inverse problems,even with 3%errors added to the input data.

LEIBNIZ′FORMULA OF GENERALIZED DIFFERENCE WITH RESPECT TO A CLASS OF DIFFERENTIAL OPERATORS AND RECURRENCE FORMULA OF THEIR GREEN′S FUNCTION

In this paper, Leibniz' formula of generalized divided difference with respect to a class of differential operators whose basic sets of solutions have power form, is considered. The recurrence formula of Green function about the operators is also given.

On Some Class of n-Normed Generalized Difference Sequences Related to l_p-Space

In this paper, we introduce the class of n-normed generalized difference sequences related to lp-space. Some properties of this sequence space like solidness, symmetricity, convergence-free etc. are studied. We obtain some inclusion relations involving this sequence space.

The Application of the Generalized Finite Difference Method (GFDM) for Modelling Geophysical Test

The possibility of using a nodal method allowing irregular distribution of nodes in a natural way is one of the main advantages of the generalized finite difference method (GFDM) with regard to the classical finite difference method. Moreover, this feature has made it one of the most-promising meshless methods because it also allows us to reduce the time-consuming task of mesh generation and the numerical solution of integrals. This characteristic allows us to shape geological features easily whilst maintaining accuracy in the results, which can be a source of great interest when dealing with this kind of problems. Two widespread geophysical investigation methods in civil engineering are the cross-hole method and the seismic refraction method. This paper shows the use of the GFDM to model the aforementioned geophysical investigation tests showing precision in the obtained results when comparing them with experimental data.

Does New Media Substitute Old Media? A Cohort Analysis of Media Use in China

This study examines generational differences in media use based on pooled-data analysis of CGSS(Chinese General Social Survey)2010-2015.In order to show a full picture of the substitutability between new and old media,the study brings age heterogeneity of respondents and time effect into consideration.This study distinguishes four generations based on the year of birth,with the“newspaper generation”(people who born before 1969),“broadcast generation”(1970-1979),“TV generation”(1980-1989),and“Internet generation”(born after 1990)and aims to explore whether generations differ in their frequency of media use.The research analyses five-year pooled data CGSS 2010-2015(CGSS 2014 data is missing)to examine the influence of Internet on old media among different birth cohorts and how this effect changes over time.New media refers to the Internet;old media includes newspaper,broadcast,and television.The results are summarized as follows:First,for the“newspaper generation”,“broadcast generation”,and“TV generation”,Internet heavy users are usually more willing to use newspaper and broadcast as well.Internet heavy users are information seekers.They have a strong need of information and usually are involved in multi-tasking media activities.Nevertheless,only the Internet heavy users in“TV generation”will regard TV as another channel to get more information,which indicates that generations may adopt specific patterns of media use when they are young and remain faithful to those throughout their lifespans.“TV generation”have a stronger attachment to television than their previous and later generation.Second,in terms of the time effect,the empirical data proved that the broadcast shows a stronger vitality in digital age compared with newspaper and television.The frequency of broadcast use does not drop significantly until 2015.However,the frequency of newspaper and television use has shown a significant downward trend since 2011.Third,for the“Internet generation”,the use of the Internet has no effect on the use of other media.Even Internet heavy user,the one who has strong need of information,would not choose other media to search more information.This suggests that these digital natives would rather confine themselves to the Internet cocoon than collect new information through old channels.This study provides new insight to understand the current media ecology.The relationship between the new and the old media is a changeable and dynamic process and cannot be simply understood as“more-more”or“more-less”relationship.

A Family of Asymmetrical Orthogonal Arrays with Run Sizes 4p^2

Nowadays orthogonal arrays play important roles in statistics, computer science, coding theory and cryptography. The usual difference matrices are essential for the construction of many mixed orthogonal arrays. But there are also many orthogonal arrays, especially mixed-level or asymmetrical which can not be obtained by the usual difference matrices. In order to construct these asymmetrical orthogonal arrays, a class of special matrices, so-called generalized difference matrices, were discovered by Zhang（1989, 1990, 1993） by the orthogonal decompositions of projective matrices. In this article, an interesting equivalent relationship between the orthogonal arrays and the generalized difference matrices is presented. As an application, a family of orthogonal arrays of run sizes 4p2, such as L36（6^13^42^10）, are constructed.

GEKF,GUKF and GGPF based prediction of chaotic time-series with additive and multiplicative noises

On the assumption that random interruptions in the observation process are modelled by a sequence of independent Bernoulli random variables, this paper generalize the extended Kalman filtering （EKF）, the unscented Kalman filtering （UKF） and the Gaussian particle filtering （GPF） to the case in which there is a positive probability that the observation in each time consists of noise alone and does not contain the chaotic signal （These generalized novel algorithms are referred to as GEKF, GUKF and GGPF correspondingly in this paper）. Using weights and network output of neural networks to constitute state equation and observation equation for chaotic time-series prediction to obtain the linear system state transition equation with continuous update scheme in an online fashion, and the prediction results of chaotic time series represented by the predicted observation value, these proposed novel algorithms are applied to the prediction of Mackey-Glass time-series with additive and multiplicative noises. Simulation results prove that the GGPF provides a relatively better prediction performance in comparison with GEKF and GUKF.

GENERALIZED DIFFERENCE METHODS ON ARBITRARYQUADRILATERAL NETWORKS

This paper considers the generalized difference methods on arbitrary networks for Poisson equations. Convergence order estimates are proved based on some a priori estimates. A supporting numerical example is provided.

Orthogonal arrays obtained by generalized difference matrices with g levels

Nowadays orthogonal arrays play important roles in statistics, computer science, coding theory and cryptography. The usual difference matrices are essential for the construction for many mixed orthogonal arrays. But there are also orthogonal arrays which cannot be obtained by the usual difference matrices, such as mixed orthogonal arrays of run size 60. In order to construct these mixed orthogonal arrays, a class of special so-called generalized difference matrices were discovered by Zhang (1989,1990,1993,2006) from the orthogonal decompositions of projection matrices. In this article, an interesting equivalent relationship between orthogonal arrays and the generalized difference matrices is presented and proved. As an application, a lot of new orthogonal arrays of run size 60 have been constructed.

Numerical study of detonation shock dynamics using generalized finite difference method

The generalized finite difference method (GFDM) used for irregular grids is first introduced into the numerical study of thelevel set equation, which is coupled with the theory of detonation shock dynamics (DSD) describing the propagation of thedetonation shock front. The numerical results of a rate-stick problem, a converging channel problem and an arc channel prob-lem for specified boundaries show that GFDM is effective on solving the level set equation in the irregular geometrical domain.The arrival time and the normal velocity distribution of the detonation shock front of these problems can then be obtainedconveniently with this method. The numerical results also confirm that when there is a curvature effect, the theory of DSDmust be considered for the propagation of detonation shock surface, while classic Huygens construction is not suitable anymore.

Integrating Krylov Deferred Correction and Generalized Finite Difference Methods for Dynamic Simulations of Wave Propagation Phenomena in Long-Time Intervals

In this paper,a high-accuracy numerical scheme is developed for long-time dynamic simulations of 2D and 3D wave propagation phenomena.In the derivation of the present approach,the second order time derivative of the physical quantity in the wave equation is treated as a substitution variable.Based on the temporal discretization with the Krylov deferred correction(KDC)technique,the original wave problem is then converted into the modified Helmholtz equation.The transformed boundary value problem(BVP)in space is efficiently simulated by using the meshless generalized finite difference method(GFDM)with Taylor series after truncating the second and fourth order approximations.The developed scheme is finally verified by four numerical experiments including cases with complicated domains or the temporally piecewise defined source function.Numerical results match with the analytical solutions and results by the COMSOL software,which demonstrates that the developed KDC-GFDM can allow large time-step sizes for wave propagation problems in longtime intervals.

SOME RESULTS ON GENERALIZED DIFFERENCE SETS

Sequences with ideal correlation functions have important applications in communications such as CDMA, FDMA, etc. It has been shown that difference sets can be used to construct such sequences. The author extends Pott and Bradley＇s method to a much broader case by proposing the concept of generalized difference sets. Some necessary conditions for the existence of generalized difference sets are established by means of some Diophantine equations. The author also provides an algorithm to determine the existence of generalized difference sets in the cyclic group Zv. Some examples are presented to illustrate that our method works.

A tunable optical parametric generator by using a quasi-phase-matched crystal with different wedge angles

We report a tunable quasi-phase-matched optical parametric generator （OPG） with different wedge angles, pumped by a commercially available Q-switched diode-pumped Nd：YVO4 laser with a repetition of 50 kHz. The nonlinear crystal is a periodically poled MgO-doped LiNbO3 （PPMgOLN） with a period of 30 μm. A congruent bulk LiNbO3 （LN） with three different wedge angles of 0°, 4°, and 9° is placed in front of PPMgOLN. Rapid tuning has been achieved by simply moving the LN crystal along its lateral direction and over 60-mW average signal output power was obtained in the whole wavelength tuning range of 1539-1570 nm.

Generalized Latin Matrix and Construction of Orthogonal Arrays

In this paper, generalized Latin matrix and orthogonal generalized Latin matrices are proposed. By using the property of orthogonal array, some methods for checking orthogonal generalized Latin matrices are presented. We study the relation between orthogonal array and orthogonal generalized Latin matrices and obtain some useful theorems for their construction. An example is given to illustrate applications of main theorems and a new class of mixed orthogonal arrays are obtained.

A new iterative algorithm for geolocating a known altitude target using TDOA and FDOA measurements in the presence of satellite location uncertainty

This paper considers the problem of geolocating a target on the Earth surface whose altitude is known previously using the target signal time difference of arrival （TDOA） and frequency difference of arrival （FDOA） measurements obtained at satellites. The number of satellites available for the geolocation task is more than sufficient and their locations are subject to random errors. This paper derives the constrained Cramor-Rao lower bound （CCRLB） of the target position, and on the basis of the CCRLB analysis, an approximately efficient constrained maximum likelihood estimator （CMLE） for geolocating the target is established. A new iterative algorithm for solving the CMLE is then proposed, where the updated target position estimate is shown to be the globally optimal solution to a generalized trust region sub-problem （GTRS） which can be found via a simple bisection search. First-order mean square error （MSE） analysis is conducted to quantify the performance degradation when the known target altitude is assumed to be precise but indeed has an unknown but deterministic error. Computer simulations are used to compare the performance of the proposed iterative geolocation technique with those of two benchmark algorithms. They verify the approximate efficiency of the proposed algorithm and the validity of the MSE analysis.