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OALib Journal期刊

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Strong Convergence Results for Hierarchical Circularly Iterative Method about Hierarchical Circularly Optimization  [PDF]
Hongbo Liu
Advances in Pure Mathematics (APM) , 2013, DOI: 10.4236/apm.2013.37079
Abstract:

An hierarchical circularly iterative method is introduced for solving a system of variational circularly inequalities with set of fixed points of strongly quasi-nonexpansive mapping problems in this paper. Under some suitable conditions, strong convergence results for the hierarchical circularly iterative sequence are proved in the setting of Hilbert spaces. Our scheme can be regarded as a more general variant of the algorithm proposed by Maingé.

Experiments with Two New Boosting Algorithms  [PDF]
Xiaowei Sun, Hongbo Zhou
Intelligent Information Management (IIM) , 2010, DOI: 10.4236/iim.2010.26047
Abstract: Boosting is an effective classifier combination method, which can improve classification performance of an unstable learning algorithm. But it dose not make much more improvement of a stable learning algorithm. In this paper, multiple TAN classifiers are combined by a combination method called Boosting-MultiTAN that is compared with the Boosting-BAN classifier which is boosting based on BAN combination. We describe experiments that carried out to assess how well the two algorithms perform on real learning problems. Fi- nally, experimental results show that the Boosting-BAN has higher classification accuracy on most data sets, but Boosting-MultiTAN has good effect on others. These results argue that boosting algorithm deserve more attention in machine learning and data mining communities.
The Ordinary College Undergraduate Course Teaching Mode Research  [PDF]
Jianling Wang, Hongbo Lai
Creative Education (CE) , 2012, DOI: 10.4236/ce.2012.37B034
Abstract: The teaching mode is reformed for the university talents training target, namely the cultivation of innovative talents. The teaching model is introduced into the classroom, compared with the traditional teaching model, the teaching mode gains achieved good results.
Convergence Theorems for k-Strictly Pseudononspreading Multivalued in Hilbert Spaces  [PDF]
Hongbo Liu, Yi Li
Advances in Pure Mathematics (APM) , 2014, DOI: 10.4236/apm.2014.47042
Abstract:

We introduce a k-strictly pseudononspreading multivalued in Hilbert spaces more general than the class of nonspreading multivalued. We establish some weak convergence theorems of the sequences generated by our iterative process. Some new iterative sequences for finding a common element of the set of solutions for equilibrium problem was introduced. The results improve and extend the corresponding results of Osilike Isiogugu [1] (Nonlinear Anal.74 (2011)) and others.

Convergence Theorem of Hybrid Iterative Algorithm for Equilibrium Problems and Fixed Point Problems of Finite Families of Uniformly Asymptotically Nonexpansive Semigroups  [PDF]
Hongbo Liu, Yi Li
Advances in Pure Mathematics (APM) , 2014, DOI: 10.4236/apm.2014.46033
Abstract:

Throughout this paper, we introduce a new hybrid iterative algorithm for finding a common element of the set of common fixed points of a finite family of uniformly asymptotically nonexpansive semigroups and the set of solutions of an equilibrium problem in the framework of Hilbert spaces. We then prove the strong convergence theorem with respect to the proposed iterative algorithm. Our results in this paper extend and improve some recent known results.

Hyperbolic geometry with geometric algebra
Hongbo Li
Chinese Science Bulletin , 1997, DOI: 10.1007/BF02882454
Abstract:
On Risks and Control of Social Security Fund Entering Security Market in China
Hongbo Duan
International Business Research , 2010, DOI: 10.5539/ibr.v3n4p91
Abstract: On the basis of broad literature and data, this paper elaborates the connotation of the risks of social security fund entering security market. We analyze risks facing social security fund entering security market in China from two perspectives: external environment of China’s capital market and internal operation of social security fund. And then we propose corresponding policy countermeasures to risks prevention appropriately.
Remarks on a Class of Nonlinear Schr?dinger Equations with Potential Vanishing at Infinity
Hongbo Zhu
Discrete Dynamics in Nature and Society , 2013, DOI: 10.1155/2013/786736
Abstract: We study the following nonlinear Schr?dinger equation , where the potential vanishes at infinity. Working in weighted Sobolev space, we obtain the ground states of problem under a Nahari type condition. Furthermore, if are radically symmetric with respect to , it is shown that problem has a positive solution with some more general growth conditions of the nonlinearity. Particularly, if , then the growth restriction in Ambrosetti et al. (2005) can be relaxed to , where if . 1. Introduction The motivation of the paper is concerned with the existence of standing waves of the following nonlinear Schr?dinger equation: where is the imaginary unit, is a real function on , , and is supposed to satisfy that for all . Problem (1) arises in many applications. For example, in some problems arising in nonlinear optics, in plasma physics, and in condensed matter physics, the presence of many particles leads one to consider nonlinear terms which simulates the interaction effect among them. For problem (1), we are interested in looking for a stationary solution; that is, with in and (the frequency); then it is not difficult to see that must satisfy Here and below, . Variational approach to (2) was initiated by Rabinowtiz [1], and since then several authors have studied (2) under different assumptions on and the nonlinearity. If is positive and bounded away from zero, then, by the well-known concentration compactness principle [2, 3], it is shown that there is bound states for problem (2); we mention here the work by Jeanjean and Tanaka [4, 5], Liu and Wang [6], Li et al. [7], Zhu [8], and the references therein. If the potential decays to zero at infinity, the methods used in the proceeding papers cannot be employed because the variational theory in cannot be used here. The earlier work on (2) we know of where decays at infinity, is that by Ambrosetti et al. [9]; the authors proved that problem (2) has bounded states for with where Following [9], by requiring some further assumptions on , in [10], the authors showed that there exist bound states of equation , , , for all satisfying , provided that is sufficiently small. Motivated by the works [9, 10], in paper [11], the authors extended the results to potentials that can both vanish and decay to zero at infinity. And since then, there are many papers on problem (2) with potential vanishing at infinity; see, for example, [12–16]. In this paper, more precisely we will focus on the following model equation: To our best knowledge, it seems that there are few results on problem (5), where does not satisfy condition; that
Status of the EAS studies of cosmic rays with energy below 10**16 eV
Hongbo Hu
Physics , 2009,
Abstract: This paper briefly summarizes the status of the cosmic ray observations by EAS (Extended Air Shower) experiments with energy below 10**16eV and the related studies of the hadronic interaction models. Based on the observed sharp knee structure and the irregularities of the cosmic ray spectrum around knee energy, plus the newly discovered electron and positron excess, the origin of the galactic cosmic rays and the single source model interpretation are discussed, but convincing evidence is not yet available. High precision measurements of the mass composition of primary cosmic rays at knee energy will be very useful to disentangle the problem. To reach this goal, a better understanding of the hadronic interaction models is crucial. It is good to see that more dedicated accelerator and cosmic ray experiments will be conducted soon. As one EAS component, the muon distribution and muon charge ratio are important for testing the hadronic interaction models. In addition muons are an important background to neutrino experiments and all underground ultra-low background experiments. They are also a very useful tool for the meteorological studies.
A Recipe for Symbolic Geometric Computing: Long Geometric Product, BREEFS and Clifford Factorization
Hongbo Li
Mathematics , 2007,
Abstract: In symbolic computing, a major bottleneck is middle expression swell. Symbolic geometric computing based on invariant algebras can alleviate this difficulty. For example, the size of projective geometric computing based on bracket algebra can often be restrained to two terms, using final polynomials, area method, Cayley expansion, etc. This is the "binomial" feature of projective geometric computing in the language of bracket algebra. In this paper we report a stunning discovery in Euclidean geometric computing: the term preservation phenomenon. Input an expression in the language of Null Bracket Algebra (NBA), by the recipe we are to propose in this paper, the computing procedure can often be controlled to within the same number of terms as the input, through to the end. In particular, the conclusions of most Euclidean geometric theorems can be expressed by monomials in NBA, and the expression size in the proving procedure can often be controlled to within one term! Euclidean geometric computing can now be announced as having a "monomial" feature in the language of NBA. The recipe is composed of three parts: use long geometric product to represent and compute multiplicatively, use "BREEFS" to control the expression size locally, and use Clifford factorization for term reduction and transition from algebra to geometry. By the time this paper is being written, the recipe has been tested by 70+ examples from \cite{chou}, among which 30+ have monomial proofs. Among those outside the scope, the famous Miquel's five-circle theorem \cite{chou2}, whose analytic proof is straightforward but very difficult symbolic computing, is discovered to have a 3-termed elegant proof with the recipe.
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