THE MAPPING RELATION AMONG SOLUTION OF SOME NONLINEAR EQUATIONS

Among the solutions of three kinds of nonlinear equations in one dimensional systems, cubic nonlinear Klein-Gordon (including Φ~4), Sine-Gordon and double Sine-Gordon, some mapping relations exist. When a solution of any one equation is known, so are the other two.

Iterative convergence theorems for maximal monotone operators and relatively nonexpansive mappings

In this paper, some iterative schemes for approximating the common element of the set of zero points of maximal monotone operators and the set of fixed points of relatively nonexpansive mappings in a real uniformly smooth and uniformly convex Banach space are proposed. Some strong convergence theorems are obtained, to extend the previous work.

Strong convergence theorem for relatively nonexpansive mapping and inverse-strongly-monotone mapping in a Banach space

In this paper, we introduce an iterative sequence for finding a common element of the set of fixed points of a relatively nonexpansive mapping and the set of solutions of the variational inequality for an inverse-strongly-monotone mapping in a Banach space. Then, we show that the sequence converges strongly to a common element of the two sets. Our results improve and extend the corresponding results reported by many others.

Design of Lattice Structures Using Local Relative Density Mapping Method

In order to solve the problem of substantial computational resources of lattice structure during optimization, a local relative density mapping(LRDM) method is proposed. The proposed method uses solid isotropic microstructures with penalization to optimize a model at the macroscopic scale. The local relative density information is obtained from the topology optimization result. The contour lines of an optimized model are extracted using a density contour approach, and the triangular mesh is generated using a mesh generator. A local mapping relationship between the elements’ relative density and the struts’ relative cross?sectional area is established to automatically determine the diameter of each individual strut in the lattice structures. The proposed LRDM method can be applied to local finite element meshes and local density elements, but it is also suitable for global ones. In addition, some cases are con?sidered in order to test the e ectiveness of the LRDM method. The results show that the solution time of the LRDM is lower than the RDM method by approximately 50%. The proposed method provides instructions for the design of more complex lattice structures.

CONVERGENCE ANALYSIS FOR SYSTEM OF EQUILIBRIUM PROBLEMS AND LEFT BREGMAN STRONGLY RELATIVELY NONEXPANSIVE MAPPING

In this paper, we prove strong convergence theorems for approximation of a fixed point of a left Bregman strongly relatively nonexpansive mapping which is also a solution to a finite system of equilibrium problems in the framework of reflexive real Banach spaces. We also discuss the approximation of a common fixed point of a family of left Bregman strongly nonexpansive mappings which is also solution to a finite system of equilibrium problems in reflexive real Banach spaces. Our results complement many known recent results in the literature.

New iterative schemes for strongly relatively nonexpansive mappings and maximal monotone operators

In this paper, some new iterative schemes for approximating the common element of the set of fixed points of strongly relatively nonexpansive mappings and the set of zero points of maximal monotone operators in a real uniformly smooth and uniformly convex Banach space are proposed. Some weak convergence theorems are obtained, which extend and complement some previous work.

Application of Ultra-High Resolution STXM-NEXAFS and Nano-SIMS on the Mapping of Carbon Related Samples

Nano-Scale mapping of minerals and organic compounds give unprecedented high resolution information on the origin and nature of substances,and provide new insight on their correlative distribution and interaction,thus present a powerful tool to study the progressive changes of geological samples,and may even be applied to study extraterrestrial samples in search of life.One example we present here explore the use of elemental microprobe,X-Ray Photon Spectroscopy(XPS),and synchrotron-based Scanning Transmission X-ray Microscopy(STXM) coupled with Near Edge X-ray Absorption Fine Structure(NEXAFS) Spectroscopy to investigate the surface properties and stability of micron-size organic carbonaceous particles from Central Amazon,Brazil,specifically focusing on black carbon in Kaolinitic Oxisol originated from anthropogenic processes,and their interaction with cations.

Fixed Point Theorems in Intuitionistics Fuzzy Metric Spaces Using Implicit Relations

In this paper, we proved some fixed point theorems in intuitionistic fuzzy metric spaces applying the properties of weakly compatible mapping and satisfying the concept of implicit relations for t norms and t connorms.

强代数格的关系表示(英文)

In this paper,we introduce and investigate the strongly regular relation.Then we give the relational representations and an intrinsic characterization of strongly algebraic lattices via mapping relation and strongly regular relation.

WEAK CONVERGENCE THEOREMS FOR GENERAL EQUILIBRIUM PROBLEMS AND VARIATIONAL INEQUALITY PROBLEMS AND FIXED POINT PROBLEMS IN BANACH SPACES

In this paper, we introduce two new iterative algorithms for finding a common element of the set of solutions of a general equilibrium problem and the set of solutions of the variational inequality for an inverse-strongly monotone operator and the set of common fixed points of two infinite families of relatively nonexpansive mappings or the set of common fixed points of an infinite family of relatively quasi-nonexpansive mappings in Banach spaces. Then we study the weak convergence of the two iterative sequences. Our results improve and extend the results announced by many others.

1:2500 000 Map of Precambrian Dyke Swarms and Related Units in North China

A 1:2500 000 map of major Precambrian mafic dyke swarms and related units in the North China Craton will be presented,and the features and geological implications of;0 swarms will be discussed and summarized:

Hybrid projection method for generalized mixed equilibrium problems,variational inequality problems,and fixed point problems in Banach spaces

A new hybrid projection iterative scheme is introduced to approximate a common element of the solution set of a generalized mixed equilibrium problem, the solution set of a variational inequality problem, and the set of fixed points of a relatively weak nonexpansive mapping in the Banach spaces. The obtained results generalize and improve the recent results announced by many other authors.

The Mathematical Origin of Gravitational Singularities

In this note we give a geometrical presentation to the 4D Riemannian curvature as it relates to the Newtonian gravity in the 4D Lorentz manifold. The compacting of the proper time as is necessary for the unification with the Maxwell electrodynamics, as given by Einstein and Kaluza-Klein, should the universe be only of 4D space-time, led to the concept of gravitational field singularity sinks known as black holes, that would not be acceptable under a 5D homogeneous manifold through which the 4D Lorentz manifold evolved by application of the Perelman-Ricci Flow entropy mapping, which is consistent with both Maxwell suggested magnetic monopole, the quantum Higgs vacuum theory and the Gell-Mann standard model for hadrons.

Map of Mafic Dyke Swarms and Related Units of Russia and Adjacent Regions

Work is currently underway to produce a map in Arc GISTM 10 of the mafic dyke swarms and related units(volcanics,sills and layered intrusions)of Russia and adjacent regions at a scale of 1:5,000,000.Over the past

Weak Convergence of a Projection Algorithm for Variational Inequalities and Relatively Nonexpansive Mappings in a Banach Space

In this paper, we introduce an iterative sequence for finding a common element of the set of fixed points of a relatively nonexpansive mapping and the set of solutions of the variational inequality for an inverse-strongly-monotone mapping in a Banach space. Then we show that the sequence converges weakly to a common element of two sets.

Effects of Surface Roughness on Interface Bonding Performance for 316H Stainless Steel in Hot-Compression Bonding

The metallurgical bonding quality of bonding joints is affected by the substrate surface state in hot-compression bonding(HCB),and the surface roughness is a core indicator of the surface state.However,the effects of surface roughness on interface bonding performance(IBP)in the HCB process are unclear for substrates with refractory oxide scales.This study presents the effects of surface roughness on IBP for 316H stainless steel joints fabricated by HCB.A set of HCB parameters for interface bonding critical state of 316H stainless steel joints was determined.The HCB experiments were carried out under parameters of interface bonding critical state to amplify the effect of surface roughness.The interface morphologies,element distribution,and tensile properties were used to characterize the IBP.As a result,the formation mechanisms of the interface pits were revealed and the variation trend of pit number with the roughness was summarized.Finally,the mapping relation between surface roughness and IBP was established.The results show that the degree of rotational dynamic recrystallization becomes weaker with the decrease in the surface roughness and the interface bonding mechanism is completely transformed into discontinuous dynamic recrystallization when the roughness is lower than 0.020μm Sa.The number of interfacial pits decreases as the roughness decreases owing to the weakening of oxide scale aggregation and abrasive inclusion mechanism.The elongation of the tensile specimen cannot increase significantly while the roughness is lower than 0.698μm Sa.

Modified Block Iterative Method for Solving Convex Feasibility Problem, Equilibrium Problems and Variational Inequality Problems

The purpose of this paper is by using the modified block iterative method to propose an algorithm for finding a common element in the intersection of the set of common fixed points of an infinite family of quasi-C-asymptotically nonexpansive and the set of solutions to an equilibrium problem and the set of solutions to a variational inequality. Under suitable conditions some strong convergence theorems are established in 2-uniformly convex and uniformly smooth Banach spaces. As applications we utilize the results presented in the paper to solving the convex feasibility problem （CFP） and zero point problem of maximal monotone mappings in Banach spaces. The results presented in the paper improve and extend the corresponding results announced by many authors.

弱相对非扩张映像不动点单调CQ算法与应用(英文)

Matsushita, Takahashi[4] proved a strong convergence theorem for relatively nonex- pansive mappings in a Banach space by using the hybrid method (CQ method) in mathematical programming. The purpose of this paper is to modify the hybrid method of Matsushita, Taka- hashi by monotone CQ method, and to prove strong convergence theorems for weak relatively nonexpansive mappings and maximal monotone operators in Banach spaces. The convergence rate of monotone CQ method is faster than the hybrid method of Matsushita, Takahashi. In addition, the Cauchy sequence method is used in this paper without using the Kadec-Klee prop- erty. The results of this paper modify and improve the results of Matsushita, Takahashi and some others.

A Weak Convergence Theorem for Equilibrium Problems,Variational Inequalities and Fixed Point Problems in 2-Uniformly Convex Banach Spaces

In this paper,we introduce a new iterative scheme for finding the common element of the set of solutions of an equilibrium problem,the set of solutions of variational inequalities for an α-inversely strongly monotone operator and the set of fixed points of relatively nonexpansive mappings in a real uniformly smooth and 2-uniformly convex Banach space.Some weak convergence theorems are obtained,to extend the previous work.