Shared Hyperplanes and Normal Families of Holomorphic Curves

In theorem LP [1], Liu proves the theorem when N = 2, but it can’t be ex-tended to the general case in his proof. So we consider the condition that the families of holomorphic curves share eleven hyperplanes, and we get the theorem 1.1.

Reducibility of hyperplane arrangements

Certain problems on reducibility of central hyperplane arrangements are settled. Firstly, a necessary and sufficient condition on reducibility is obtained. More precisely, it is proved that the number of irreducible components of a central hyperplane arrangement equals the dimension of the space consisting of the logarithmic derivations of the arrangement with degree zero or one. Secondly, it is proved that the decomposition of an arrangement into a direct sum of its irreducible components is unique up to an isomorphism of the ambient space. Thirdly, an effective algorithm for determining the number of irreducible components and decomposing an arrangement into a direct sum of its irreducible components is offered. This algorithm can decide whether an arrangement is reducible, and if it is the case, what the defining equations of irreducible components are.

Results on Uniqueness Problem for Meromorphic Mappings Sharing Moving Hyperplanes in General Position Under More General and Weak Conditions

The aim of the paper is to deal with the algebraic dependence and uniqueness problem for meromorphic mappings by using the new second main theorem with different weights involved the truncated counting functions,and some interesting uniqueness results are obtained under more general and weak conditions where the moving hyperplanes in general position are partly shared by mappings from Cn into PN(C),which can be seen as the improvements of previous well-known results.

A Cutting Hyperplane Projection Method for Solving Generalized Quasi-Variational Inequalities

The generalized quasi-variational inequality is a generalization of the generalized variational inequality and the quasi-variational inequality.The study for the generalized quasi-variational inequality is mainly concerned with the solution existence theory.In this paper,we present a cutting hyperplane projection method for solving generalized quasi-variational inequalities.Our method is neweven if it reduces to solve the generalized variational inequalities.The global convergence is proved under certain assumptions.Numerical experiments have shown that our method has less total number of iterative steps than the most recent projection-like methods of Zhang et al.(Comput Optim Appl 45:89–109,2010)for solving quasi-variational inequality problems and outperforms the method of Li and He(J Comput Appl Math 228:212–218,2009)for solving generalized variational inequality problems.

Theory and Method of Power System Integrated Security Region Irrelevant to Operation States:An Introduction

How to comprehensively consider the power flow constraints and various stability constraints in a series of power system optimization problems without affecting the calculation speed is always a problem.The computational burden of probabilistic security assessment is even more unimaginable.In order to solve such problems,a security region(SR)methodology is proposed,which is a brand-new methodology developed on the basis of the classical point-wise method.Tianjin University has been studying the SR methodology since the 1980s,and has achieved a series of original breakthroughs that are described in this paper.The integrated SR introduced in this paper is mainly defined in the power injection space,and includes SRs to ensure steady-state security,transient stability,static voltage stability,and smalldisturbance stability.These SRs are uniquely determined for a given network topology(as well as location and clearing process for transient faults)and given system component parameters,and are irrelevant to operation states.This paper presents 11 facts and related remarks to introduce the basic concepts,composition,dynamics nature,and topological and geometric characteristics of SRs.It also provides a practical mathematical description of SR boundaries and fast calculation methods to determine them in a concise and systematic way.Thus,this article provides support for the systematic understanding,future research,and applications of SRs.The most critical finding on the topological and geometric characteristics of SRs is that,within the scope of engineering concern,the practical boundaries of SRs in the power injection space can be approximated by one or a few hyperplanes.Based on this finding,the calculation time for power system probabilistic security assessment(i.e.,risk analysis)and power system optimization with security constraints can be decreased by orders of magnitude.

mproving the Input of Classified Neural Networks Through Feature Construction

A general classification algorithm of neural networks is unable to obtain satisfied results because of the uncertain problems existing among the features in moot classification programs, such as interaction. With new features constructed by optimizing decision trees of examples, the input of neural networks is improved and an optimized classification algorithm based on neural networks is presented. A concept of dispersion of a classification program is also introduced too in this paper. At the end of the paper, an analysis is made with an example.

CONTINUOUS SELECTIONS OF THE SET-VALUED METRIC GENERALIZED INVERSE IN 2-STRICTLY CONVEX BANACH SPACES

In this paper,we prove that if X is an almost convex and 2-strictly convex space,linear operator T:X→Y is bounded,N(T)is an approximative compact Chebyshev subspace of X and R(T)is a 3-Chebyshev hyperplane,then there exists a homogeneous selection T^(σ)of T^(■)such that continuous points of T^(σ)and T^(■)are dense on Y.

NORMAL CRITERIA FOR A FAMILY OF HOLOMORPHIC CURVES

In this paper,we extend the concept of holomorphic curves sharing hyperplanes and introduce definitions of restricted hyperplanes and partial shared hypersurfaces.Then,we prove several normal criteria of the family of holomorphic curves and holomorphic mappings that concern restricted hyperplanes and partial shared hypersurfaces.These results generalize the Montel-type normal criterion of holomorphic curves.

Dynamic Spatial Discrimination Maps of Discriminative Activation between Different Tasks Based on Support Vector Machines

As a set of supervised pattern recognition methods, support vector machines (SVMs) have been successfully applied to functional magnetic resonance imaging (fMRI) field, but few studies have focused on visualizing discriminative regions of whole brain between different cognitive tasks dynamically. This paper presents a SVM-based method for visualizing dynamically discriminative activation of whole-brain voxels between two kinds of tasks without any contrast. Our method provides a series of dynamic spatial discrimination maps (DSDMs), representing the temporal evolution of discriminative brain activation during a duty cycle and describing how the discriminating information changes over the duty cycle. The proposed method was applied to investigate discriminative brain functional activations of whole brain voxels dynamically based on a hand-motor task experiment. A set of DSDMs between left hand movement and right hand movement were reached. Our results demonstrated not only where but also when the discriminative activations of whole brain voxels occurred between left hand movement and right hand movement during one duty cycle.

Best Simultaneous Approximation of Finite Set in Inner Product Space

In this paper, we find a way to give best simultaneous approximation of n arbitrary points in convex sets. First, we introduce a special hyperplane which is based on those n points. Then by using this hyperplane, we define best approximation of each point and achieve our purpose.

Isometries in hyperbolic spaces

Suppose that f:Hn → Hn (n≥2) maps any r-dimensional hyperplane (1≤r<n) into an r-dimensional hyperplane. In this paper, we prove that f is an isometry if and only if f is a surjective map. This result gives an affirmative answer to a recent conjecture due to Li and Yao.

Kinematic generation of ruled surface based on rational motion of point-line

This paper studies representation of rigid combination of a directed line and a reference point on it(here referred to as a "point-line") using dual quaternions.The geometric problem of rational ruled surface design is viewed as the kinematic prob-lem of rational point-line motion design.By using the screw theory in kinematics,mappings from the spaces of lines and point-lines in Euclidean three-dimensional space into the hyperplanes in dual quaternion space are constructed,respectively.The problem of rational point-line motion design is then converted to that of projective Bézier or B-spline image curve design in hyperplane of dual quaternions.This kinematic method can unify the geometric design of ruled surfaces and tool path gen-eration for five-axis numerical control(NC) machining.

The diffeomorphic types of the complements of arrangements in CP^3Ⅱ

For any arrangement of hyperplanes in CP^3,we introduce the soul of this arrangement. The soul,which is a pseudo-complex,is determined by the combinatorics of the arrangement of hyper- planes.In this paper,we give a sufficient combinatoric condition for two arrangements of hyperplanes to be diffeomorphic to each other.In particular we have found sufficient conditions on combinatorics for the arrangement of hyperplanes whose moduli space is connected.This generalizes our previous result on hyperplane point arrangements in CP^3.

THE LARGE-SAMPLE LOWER BOUNDS FOR THE TAILS OF THE DISTRIBUTIONS OF PP KOLMOGOROV-SMIRNOV STATISTICS

Let X1, X2, … be i. i. d. random vectors defined on a probability space （Ω, τ, P ） and take values in Pp （p≥1 ） with common law P. We can construct PP Kolmogorov-Smimov statistics as follows by the projection pursuit （abbreviated to PP ）method:

Diffeomorphic types of complements of nice point arrangements in CP^l

We use a new method to study arrangement in CPl,define a class of nice point arrangements and show that if two nice point arrangements have the same combinatorics,then their complements are diffeomorphic to each other.In particular,the moduli space of nice point arrangements with same combinatorics in CPl is connected.It generalizes the result on point arrangements in CP3 to point arrangements in CPl for any l.

A Uniqueness Theorem of Meromorphic Maps and a Generalization of the Borel’s Lemma

This paper gives a generalization of the classical Borel’s Lemma. Then as an application of this generalized Borel’s Lemma, a uniqueness theorem for two linearly non-degenerate meromorphic maps of Cm into P^n(C)(n ≥ 2) sharing 2n + 2 hyperplanes in general position is proved.

Extensions of Farkas-Minkowski's Lemma and Stiemke's Lemma in the Space l^1

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A Generalization of Lappan's Theorem to Higher Dimensional Complex Projective Space

In this paper,the authors discuss a generalization of Lappan’s theorem to higher dimensional complex projective space and get the following result:Let f be a holomorphic mapping of△into P^(n)(C),and let H_(1),…,H_(q)be hyperplanes in general position in P^(n)(C).Assume that sup{(1-|z|^(2))f^(#)(z):z∈q∪j=1f^(-1)(H_(j))}<∞,if q≥2n^(2)+3,then f is normal.

Nonparallel Support Vector Machine Based on One Optimization Problem for Pattern Recognition

In this paper,we present a novel nonparallel support vector machine based on one optimization problem(NSVMOOP)for binary classification.Our NSVMOOP is formulated aiming to separate classes from the largest possible angle between the normal vectors and the decision hyperplanes in the feature space,at the same time implementing the structural risk minimization principle.Different from other nonparallel classifiers,such as the representative twin support vector machine,it constructs two nonparallel hyperplanes simultaneously by solving a single quadratic programming problem,on which a modified sequential minimization optimization algorithm is explored.The NSVMOOP is analyzed theoretically and implemented experimentally.Experimental results on both artificial and publicly available benchmark datasets show its feasibility and effectiveness.