New Finite Difference Mapped WENO Schemes with Increasingly High Order of Accuracy

In this paper,a new type of finite difference mapped weighted essentially non-oscillatory(MWENO)schemes with unequal-sized stencils,such as the seventh-order and ninthorder versions,is constructed for solving hyperbolic conservation laws.For the purpose of designing increasingly high-order finite difference WENO schemes,the equal-sized stencils are becoming more and more wider.The more we use wider candidate stencils,the bigger the probability of discontinuities lies in all stencils.Therefore,one innovation of these new WENO schemes is to introduce a new splitting stencil methodology to divide some fourpoint or five-point stencils into several smaller three-point stencils.By the usage of this new methodology in high-order spatial reconstruction procedure,we get different degree polynomials defined on these unequal-sized stencils,and calculate the linear weights,smoothness indicators,and nonlinear weights as specified in Jiang and Shu(J.Comput.Phys.126:202228,1996).Since the difference between the nonlinear weights and the linear weights is too big to keep the optimal order of accuracy in smooth regions,another crucial innovation is to present the new mapping functions which are used to obtain the mapped nonlinear weights and decrease the difference quantity between the mapped nonlinear weights and the linear weights,so as to keep the optimal order of accuracy in smooth regions.These new MWENO schemes can also be applied to compute some extreme examples,such as the double rarefaction wave problem,the Sedov blast wave problem,and the Leblanc problem with a normal CFL number.Extensive numerical results are provided to illustrate the good performance of the new finite difference MWENO schemes.

Common Fixed Point Theorems for Sequences of φ-type Contraction Set-valued Mappings

In complete metric spaces, the common fixed point theorems for sequences of φ-type contraction set-valued mappings are established, and the corresponding random com- mon fixed point theorems for set-valued mappings are also obtained.

CONVERGENCE OF IMPLICIT ITERATIVE PROCESS WITH ERRORS FOR A FINITE FAMILY OF ASYMPTOTICALLY NONEXPANSIVE MAPPINGS

The purpose of this article is to study the weak and strong convergence of implicit iteration process with errors to a common fixed point for a finite family of asymptotically nonexpansive mappings and nonexpansive mappings in Banach spaces. The results presented in this article extend and improve the corresponding results of [1, 2, 4-9, 11-15].

The closed finite-to-one mappings and their applications

In this paper,we discuss the closed finite-to-one mapping theorems on generalized metric spaces and their applications.It is proved that point-G_δ properties,■-snf-countability and csf-countability are invariants and inverse invariants under closed finite-to-one mappings.By the relationships between the weak first-countabilities,we obtain the closed finite-to-one mapping theorems of weak quasi-first-countability,quasi-first-countability,snf-countability,gfcountability and sof-countability.Furthermore,these results are applied to the study of symmetric products of topological spaces.

Natural Mappings on Set-valued Mapping Spaces

In this paper,we discuss the continuities of some natural mappings on pointcompact continuous set-valued mapping spaces with compact-open topology and obtain the properties of set-valued injective mappings,set-valued diagonal mappings,induced mappings,set-valued evaluation mappings,set-valued topological sum mappings and set-valued topological product mappings.

Proximal point algorithm for a new class of fuzzy set-valued variational inclusions with (H,η)-monotone mappings

We introduced a new class of fuzzy set-valued variational inclusions with (H,η)-monotone mappings. Using the resolvent operator method in Hilbert spaces, we suggested a new proximal point algorithm for finding approximate solutions, which strongly converge to the exact solution of a fuzzy set-valued variational inclusion with (H,η)-monotone. The results improved and generalized the general quasi-variational inclusions with fuzzy set-valued mappings proposed by Jin and Tian Jin MM, Perturbed proximal point algorithm for general quasi-variational inclusions with fuzzy set-valued mappings, OR Transactions, 2005, 9(3): 31-38, (In Chinese); Tian YX, Generalized nonlinear implicit quasi-variational inclusions with fuzzy mappings, Computers & Mathematics with Applications, 2001, 42: 101-108.

Set-Valued Stochastic Integrals with Respect to Finite Variation Processes

In a Euclidean space Rd, the Lebesgue-Stieltjes integral of set-valued stochastic processes with respect to real valued finite variation process is defined directly by employing all integrably bounded selections instead of taking the decomposable closure appearing in some existed references. We shall show that this kind of integral is measurable, continuous in t under the Hausdorff metric and L2-bounded.

A survey of ergodicity on the set-valued mappings

In this paper, we give a survey on the PhD thesis of the first author. There theexistence and ergodicity on invariant measures of set-valued mappings are discused.

Almost Injective Mappings of Totally Bounded Metric Spaces into Finite Dimensional Euclidean Spaces

Let χ= be a metric space and let ε be a positive real number. Then a function f: X→Y is defined to be an ε-map if and only if for all y∈Y, the diameter of f-1(y)?is at most ε. In Theorem 10 we will give a new proof for the following well known fact: if χ is totally bounded, then for all ε there exists a finite number n and a continuous ε-map fε: X→Rn (here Rn is the usual n-dimensional Euclidean space endowed with the Euclidean metric). If ε is “small”, then fε is “almost injective”;and still exists even if χ has infinite covering dimension (in this case, n depends on ε, of course). Contrary to the known proofs, our proof technique is effective in the sense, that it allows establishing estimations for n in terms of ε and structural properties of χ.

ON THE GENERALIZED FRITZ JOHN OPTIMALITY CONDITIONS OF VECTOR OPTIMIZATION WITH SET-VALUED MAPS UNDER BENSON PROPER EFFICIENCY

A kind of tangent derivative and the concepts of strong and weak * pseudoconvexity for a set-valued map are introduced. By the standard separation theorems of the convex sets and cones the optimality Fritz John condition of set-valued optimization under Benson proper efficiency is established, its sufficience is discussed. The form of the optimality conditions obtained here completely tally with the classical results when the set-valued map is specialized to be a single-valued map.

Benson proper efficiency for vector optimization of generalized subconvexlike set-valued maps in ordered linear spaces

Several equivalent statements of generalized subconvexlike set-valued map are established in ordered linear spaces. Using vector closure, we introduce Benson proper efficient solution of vector optimization problem. Under the assumption of generalized subconvexlikeness, scalarization, multiplier and saddle point theorems are obtained in the sense of Benson proper efficiency.

ε-super Effcient Solutions of Optimization Problems with Set-valued Maps in Locally Convex Space

In this paper,the ε-super effcient solution for set-valued map vector optimization in locally convex space is introduced.And under the assumption of the nearly generalized cone-subconvexlikeness for set-valued maps,used new methods,the scalarization theorem and Lagrange multiplier theorem for ε-super effcient solution are established.

Measuring the Qatar-Kazeron Fault Dip Using Random Finite Fault Simulation of September 27, 2010 Kazeron Earthquake and Analytical Signal Map of Satellite Magnetic Data

In this research the fault parameters causing the September 27, 2010 Kazeron Earthquake with a magnitude of MW = 5.8 (BHRC) were determined using the random finite fault method. The parameters were recorded by 27 accelerometer stations. Simulation of strong ground motion is very useful for areas about which little information and data are available. Considering the distribution of earthquake records and the existing relationships, for the fault plane causing the September 27, 2010 Kazeron Earthquake the length of the fault along the strike direction and the width of the fault along the dip direction were determined to be 10 km and 7 km, respectively. Moreover, 10 elements were assumed along the length and 7 were assumed along the width of the plane. Research results indicated that the epicenter of the earthquake had a geographic coordination of 29.88N - 51.77E, which complied with the results reported by the Institute of Geophysics Tehran University (IGTU). In addition, the strike and dip measured for the fault causing the Kazeron Earthquake were 27 and 50 degrees, respectively. Therefore, the causing fault was almost parallel to and coincident with the fault. There are magnetic discontinuities on the analytical signal map with a north-south strike followed by a northwest-southeast strike. The discontinuities are consistent with the trend of Kazeron fault but are several kilometers away from it. Therefore, they show the fault depth at a distance of 12 km from the fault surface.

Mapping-Based 3D Hexahedral Finite Element Mesh Generation Method

Mapping mesh generation is widely applied in pre-processes of Finite Element Method （FEM）. In this study, the basic 3D mapping equations by Lagrange interpolating function are founded. Based these equations, a mapping pattern library, which maps essential configurations e.g. line, circle, rotary body, sphere etc. to hexahedral FEM mesh, has been built. Then available FEM mesh will be generated by clipping and assembling the mapped essential objects. Study case illustrates that the proposed method is simple and efficient to generate valid FEM mesh for complex 3D engineering structure.

Formal Concept Analysis Based on Set-valued Mapping

Formal concept analysis （FCA） is a discipline that studied the hierarchical structures induced by a binary relation between a pair of sets, and applies in data analysis, information retrieval, knowledge discovery, etc. In this paper, it is shown that a formal context T is equivalent to a set-valued mapping S ： G → P（М）, and formal concepts could be defined in the set-valued mapping S. It is known that the topology and set-valued mapping are linked. Hence, the advantage of this paper is that the conclusion make us to construct formal concept lattice based on the topology.

Iterative Processes with Errors for Generalized Set-Valued φ-Hemi-contractive Mapping in Banach Spaces

A new conception of generalized set-valued Ф-hemi-contractive mapping in Banach spaces is presented. Some strong convergence theorems of Ishikawa and Mann iterative approximation with errors is proved. The results in this paper improve and extend the earlier results.

Mapping relationship analysis of welding assembly properties for thin-walled parts with finite element and machine learning algorithm

The finite element(FE)-based simulation of welding characteristics was carried out to explore the relationship among welding assembly properties for the parallel T-shaped thin-walled parts of an antenna structure.The effects of welding direction,clamping,fixture release time,fixed constraints,and welding sequences on these properties were analyzed,and the mapping relationship among welding characteristics was thoroughly examined.Different machine learning algorithms,including the generalized regression neural network(GRNN),wavelet neural network(WNN),and fuzzy neural network(FNN),are used to predict the multiple welding properties of thin-walled parts to mirror their variation trend and verify the correctness of the mapping relationship.Compared with those from GRNN and WNN,the maximum mean relative errors for the predicted values of deformation,temperature,and residual stress with FNN were less than 4.8%,1.4%,and 4.4%,respectively.These results indicate that FNN generated the best predicted welding characteristics.Analysis under various welding conditions also shows a mapping relationship among welding deformation,temperature,and residual stress over a period of time.This finding further provides a paramount basis for the control of welding assembly errors of an antenna structure in the future.

Iterative Approximation with Errors for Generalized Set-Valued Strongly Accretive Mapping in Banach Spaces

A new concept of generalized set-valued strongly accretive mappings in Banach spaces was given and some strong convergence theorems of Ishikawa and Mann iterative process with errors approximation methods by Huang et al. was proved. The results presented in this paper improve and extend the earlier results obtained by Huang et al.

Linear Commuting Maps on Parabolic Subalgebras of Finite-dimensional Simple Lie Algebras

A map φ on a Lie algebra g is called to be commuting if [φ(x), x] = 0 for all x ∈ g. Let L be a finite-dimensional simple Lie algebra over an algebraically closed field F of characteristic 0, P a parabolic subalgebra of L. In this paper, we prove that a linear mapφon P is commuting if and only if φ is a scalar multiplication map on P.

Topological Stability and Entropy for Certain Set-valued Maps

In this paper,the dynamics(including shadowing property,expansiveness,topological stability and entropy)of several types of upper semi-continuous set-valued maps are mainly considered from differentiable dynamical systems points of view.It is shown that(1)if f is a hyperbolic endomorphism then for eachε>0 there exists a C^(1)-neighborhood U of f such that the induced set-valued map F_(f,U)has theε-shadowing property,and moreover,if f is an expanding endomorphism then there exists a C^(1)-neighborhood U of f such that the induced set-valued map F_(f,U)has the Lipschitz shadowing property;(2)when a set-valued map F is generated by finite expanding endomorphisms,it has the shadowing property,and moreover,if the collection of the generators has no coincidence point then F is expansive and hence is topologically stable;(3)if f is an expanding endomorphism then for eachε>0 there exists a C^(1)-neighborhood U of f such that h(F_(f,U,ε))=h(f);(4)when F is generated by finite expanding endomorphisms with no coincidence point,the entropy formula of F is given.Furthermore,the dynamics of the set-valued maps based on discontinuous maps on the interval are also considered.