FIXED POINTS OF A PAIR OF ASYMPTOTICALLY REGULAR MAPPINGS

In this paper some theorems on fixed points of pair of asymptotically regularmappings in p-uniformly convex Banach space are proved For these mappings somefixed point theorems in a Hilbert space.in Lp spaces in Hardy spaces Hp and in Sobolev spaces Hpk for 1<P<+∞ and K>0 are also established.Thus resultsof Gornicki Kruppel and others are extended.

Convergence Analysis of General Version of Gauss-Type Proximal Point Method for Metrically Regular Mappings

We introduce and study in the present paper the general version of Gauss-type proximal point algorithm (in short GG-PPA) for solving the inclusion , where T is a set-valued mapping which is not necessarily monotone acting from a Banach space X to a subset of a Banach space Y with locally closed graph. The convergence of the GG-PPA is present here by choosing a sequence of functions with , which is Lipschitz continuous in a neighbourhood O of the origin and when T is metrically regular. More precisely, semi-local and local convergence of GG-PPA are analyzed. Moreover, we present a numerical example to validate the convergence result of GG-PPA.

Metrically regular mappings and its application to convergence analysis of a confined Newton-type method for nonsmooth generalized equations

Notion of metrically regular property and certain types of point-based approximations are used for solving the nonsmooth generalized equation f(x)+F(x)?0,where X and Y are Banach spaces,and U is an open subset of X,f:U→Y is a nonsmooth function and F:X■Y is a set-valued mapping with closed graph.We introduce a confined Newton-type method for solving the above nonsmooth generalized equation and analyze the semilocal and local convergence of this method.Specifically,under the point-based approximation of f on U and metrically regular property of f+F,we present quadratic rate of convergence of this method.Furthermore,superlinear rate of convergence of this method is provided under the conditions that f admits p-point-based approximation on U and f+F is metrically regular.An example of nonsmooth functions that have p-point-based approximation is given.Moreover,a numerical experiment is given which illustrates the theoretical result.

A New Inequality for Weakly (K_1,K_2)-Quasiregular Mappings

We obtain a new inequality for weakly （K1,K2）-quasiregular mappings by using the McShane extension method. This inequality can be used to derive the self-improving regularity of （K1, K2）-Quasiregular Mappings.

Counting Rooted Nearly 2-regular Planar Maps

The number of rooted nearly 2-regular maps with the valency of root-vertex, the number of non-rooted vertices and the valency of root-face as three parameters is obtained. Furthermore, the explicit expressions of the special cases including loopless nearly 2-regular maps and simple nearly 2-regular maps in terms of the above three parameters are derived.

Regular Maps of Graphs of Order 4p

A 2-cell embedding f ： X → S of a graph X into a closed orientable surface S can be described combinatorially by a pair M = （X; p） called a map, where p is a product of disjoint cycle permutations each of which is the permutation of the arc set of X initiated at the same vertex following the orientation of S. It is well known that the automorphism group of M acts semi-regularly on the arc set of X and if the action is regular, then the map M and the embedding f are called regular. Let p and q be primes. Duet al. [J. Algebraic Combin., 19, 123 141 （2004）] classified the regular maps of graphs of order pq. In this paper all pairwise non-isomorphic regular maps of graphs of order 4p are constructed explicitly and the genera of such regular maps are computed. As a result, there are twelve sporadic and six infinite families of regular maps of graphs of order 4p; two of the infinite families are regular maps with the complete bipartite graphs K2p,2p as underlying graphs and the other four infinite families are regular balanced Cayley maps on the groups Z4p, Z22 × Zp and D4p.

METRICALLY REGULAR MAPPING AND ITS UTILIZATION TO CONVERGENCE ANALYSIS OF A RESTRICTED INEXACT NEWTON-TYPE METHOD

In the present paper,we study the restricted inexact Newton-type method for solving the generalized equation 0∈f(x)+F(x),where X and Y are Banach spaces,f:X→Y is a Frechet differentiable function and F:X■Y is a set-valued mapping with closed graph.We establish the convergence criteria of the restricted inexact Newton-type method,which guarantees the existence of any sequence generated by this method and show this generated sequence is convergent linearly and quadratically according to the particular assumptions on the Frechet derivative of f.Indeed,we obtain semilocal and local convergence results of restricted inexact Newton-type method for solving the above generalized equation when the Frechet derivative of f is continuous and Lipschitz continuous as well as f+F is metrically regular.An application of this method to variational inequality is given.In addition,a numerical experiment is given which illustrates the theoretical result.

M?bius Regular Maps of Order pq

M?bius regular maps are surface embeddings of graphs with doubled edges such that(i)the automorphism group of the embedding acts regularly on flags and(ii) each doubled edge is a center of a M?bius band on the surface. In this paper, we classify M?bius regular maps of order pq for any two primes p and q, where p≠q.

COUNTING ROOTED NEAR-4-REGULAR EULERIAN MAPSON SOME SURFACES

In this article the rooted planar near-4-regular Eulerian trails are enum erated and an explicit form ula for such m aps is presented. Further, the rooted near-4-regular Eulerian m aps on the torus are counted in an exact w ay.

《南岭成矿带成矿规律图》研编创新点及其找矿意义

由中国地质科学院矿产资源所编制出版的《南岭成矿带成矿规律图(1∶80万)》,是迄今为止矿种最全、资料最新、信息量最大的全面反映我国南岭勘查成果与成矿规律的区带级别(Ⅲ级成矿单元)成矿规律图。该图件研编实现了4大创新点:①涵盖了南岭已发现的2903处独立矿产地,包括能源、金属、非金属和水气矿产等4大类的76个矿种,实现了南岭成矿带矿种与矿产地的全覆盖;②归并了地质底图的地层并淡化显示,突出华南岩体、隐伏岩体的特色,使得不同构造—建造层地质单元的分布格局一目了然;③实现了矿产地、规模、类型、时代、成矿系列五位一体的综合图例设计,矿产地表达更简洁、直观;④综合成矿系列图、表、成矿体系图、剖面图等,以区域规律图编制的新思路和新方法,更集中反映和彰显南岭成矿带最新科研成果。该图件的研编有助于直观展示南岭成矿带矿产的时空分布格局,深入总结成矿规律,科学圈定重要找矿远景区,对于全面指导南岭的地质找矿工作具有重要的意义。

Lb-coequalizers and Lb-regular Epimorphisms in the Category of L-sets and Bi-induced Maps

In this paper,it gives the definition of the category of ■-sets and bi-induced maps whose true value set is a Locale,a complete Heyting algebra.In this category it defines the L_b-monomorphisms and the L_b-epimorphisms.Especially,it gives the definition,the judgmental theorem of L_b-coequalizers.Furthermore,it defines L_b-regular epimorphisms and proves the judgmental theorem.At the end it concludes a result:the category of ■-sets and bi-induced maps is finitely cocomplete.

一种自适应正则MAP超分辨率重建方法

提出了一种简单、通用的基于自适应正则化技术的MAP超分辨率重建新方法,该方法可以自适应地选择正则化参数,并充分利用中间重建结果的信息,不断对其进行更新,通过迭代过程得到最终的重建影像。利用模拟序列影像和真实序列影像分别对本文方法进行了验证,结果表明,本文方法可以根据不同影像序列的特点,自适应确定相应的正则化参数,并能找到最优解,适用性较强。

基于双HSIC和稀疏正则化的多标签特征选择

为了合理地利用多标签数据中的样本信息和标签信息,提高模型的分类性能,提出了基于双希尔伯特-施密特独立性准则(Hilbert-Schmidt independence criterion,HSIC)和稀疏正则化的多标签特征选择(DHSR)。该方法在线性映射的基础上引入双HSIC作为正则项,增强伪标签空间和特征空间之间的依赖关系,增强伪标签空间和真实标签空间之间的依赖关系。并使用L2,1范数作为稀疏正则项,以提高模型的泛化能力和减少模型的计算复杂度。最后,在多个经典多标签数据集上的对比实验结果验证了DHSR的有效性和优越性。

MDS-MAP算法在不同传播模型中定位误差的比较

主要介绍了MDS-MAP算法在通过4种不同传播模型时定位误差的不同,通过仿真可以看到MDS-MAP算法在各个传播模型中的定位误差图。从仿真结果可以得出,在环境好的情况下,规则模型与不规则模型的定位误差相差不大,当环境变化时,不规则传播模型比规则传播模型更能适应恶劣的环境。介绍了两种情况,随着环境的改变,传播模型相关参数也会有所改变进而影响定位误差的变化。

REGULARITIES AND SINGULARITIES OF THE ENERGY MINIMIZERS OF THE HEISENBERG GROUP TARGETS

In this paper, the properties of the maps for the Heisenberg group targets are studied. For u e∈W1,α(Ω, Hm), some Poincare type inequalities are proved. For the energy minimizers, the ∈-regularity theorems and the singularity theorems are obtained.

LAVRENTIEV'S REGULARIZATION METHOD FOR NONLINEAR ILL-POSED EQUATIONS IN BANACH SPACES

In this paper, we deal with nonlinear ill-posed problems involving m-accretive mappings in Banach spaces. We consider a derivative and inverse free method for the imple- mentation of Lavrentiev regularization method. Using general HSlder type source condition we obtain an optimal order error estimate. Also we consider the adaptive parameter choice strategy proposed by Pereverzev and Schock （2005） for choosing the regularization parameter.

APPROXIMATION CAPABILITIES OF MULTILAYER FEEDFORWARD REGULAR FUZZY NEURAL NETWORKS

Four layer feedforward regular fuzzy neural networks are constructed. Universal approximations to some continuous fuzzy functions defined on F 0 (R) n by the four layer fuzzy neural networks are shown. At first,multivariate Bernstein polynomials associated with fuzzy valued functions are empolyed to approximate continuous fuzzy valued functions defined on each compact set of R n . Secondly,by introducing cut preserving fuzzy mapping,the equivalent conditions for continuous fuzzy functions that can be arbitrarily closely approximated by regular fuzzy neural networks are shown. Finally a few of sufficient and necessary conditions for characterizing approximation capabilities of regular fuzzy neural networks are obtained. And some concrete fuzzy functions demonstrate our conclusions.

Solitary Wave Solution of the Two-Dimensional Regularized Long-Wave and Davey-Stewartson Equations in Fluids and Plasmas

This paper investigates the solitary wave solutions of the (2+1)-dimensional regularized long-wave (2DRLG) equation which is arising in the investigation of the Rossby waves in rotating flows and the drift waves in plasmas and (2+1) dimensional Davey-Stewartson (DS) equation which is governing the dynamics of weakly nonlinear modulation of a lattice wave packet in a multidimensional lattice. By using extended mapping method technique, we have shown that the 2DRLG-2DDS equations can be reduced to the elliptic-like equation. Then, the extended mapping method is used to obtain a series of solutions including the single and the combined non degenerative Jacobi elliptic function solutions and their degenerative solutions to the above mentioned class of nonlinear partial differential equations (NLPDEs).

ON THE EXISTENCE OF COMMON FIXED POINTS FOR A PAIR OF LIPSCHITZIAN MAPPINGS IN BANACH SPACES

The existence of common fixed points for a pair of Lipschitzian mappings in Banach spaces is proved. By using this result, some common fixed point theorems are also established for these mappings in Hilbert spaces, in L p spaces, in Hardy spaces H p, and in Sobolev spaces H r,p , for 1<p<+∞ and r≥0.

Modification of the Convergence of GG-PPA for Solving Generalized Equations

A modified Gauss-type Proximal Point Algorithm (modified GG-PPA) is presented in this paper for solving the generalized equations like 0 &#8712;T(x), where T is a set-valued mapping acts between two different Banach spaces X and Y. By considering some necessary assumptions, we show the existence of any sequence generated by the modified GG-PPA and prove the semi-local and local convergence results by using metrically regular mapping. In addition, we give a numerical example to justify the result of semi-local convergence.