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.

The Supersolvable Order of Hyperplanes of an Arrangement

This paper mainly gives a sufficient and necessary condition for an order of hyperplanes of a graphic arrangement being supersolvable. In addition, we give the relations between the set of supersolvable orders of hyperplanes and the set of quadratic orders of hyperplanes for a supersolvable arrangement.

Radon transforms of the Wigner operator on hyperplanes

The generalization of tomographic maps to byperplanes is considered. We find that the Radon transform of the Wigner operator in multi-dimensional phase space leads to a normally ordered operator in binomial distribution-a mixed-state density operator. Reconstruction of the Wigner operator is also feasible. The normally ordered form and the Weyl ordered form of the Wigner operator are used in our derivation. The operator quantum tomography theory is expressed in terms of some operator identities, with the merit of revealing the essence of the theory in a simple and concise way.

Properties of fuzzy hyperplanes

Some properties of closed fuzzy matroid and those of its hyperplanes are investigated. A fuzzy hyperplane property, which extends the analog of a crisp matroid from crisp set systems to fuzzy set systems, is proved.

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.

The Static Stability Region of an Integrated Electricity-Gas System Considering Voltage and Gas Pressure

In an integrated electricity-gas system(IEGS),load fluctuations affect not only the voltage in the power system but also the gas pressure in the natural gas system.The static voltage stability region(SVSR)method is a tool for analyzing the overall static voltage stability in a power system.However,in an IEGS,the SVSR boundary may be overly optimistic because the gas pressure may collapse before the voltage collapses.Thus,the SVSR method cannot be directly applied to an IEGS.In this paper,the concept of the SVSR is extended to the IEGS-static stability region(SSR)while considering voltage and gas pressure.First,criteria for static gas pressure stability in a natural gas system are proposed,based on the static voltage stability criteria in a power system.Then,the IEGS-SSR is defined as a set of active power injections that satisfies multi-energy flow(MEF)equations and static voltage and gas pressure stability constraints in the active power injection space of natural gas-fired generator units(NGUs).To determine the IEGSSSR,a continuation MEF(CMEF)method is employed to trace the boundary point in one specific NGU scheduling direction.A multidimensional hyperplane sampling method is also proposed to sample the NGU scheduling directions evenly.The obtained boundary points are further used to form the IEGSSSR in three-dimensional(3D)space via a Delaunay triangulation hypersurface fitting method.Finally,the numerical results of typical case studies are presented to demonstrate that the proposed method can effectively form the IEGS-SSR,providing a tool for IEGS online monitoring and dispatching.

MKEAH:Multimodal knowledge extraction and accumulation based on hyperplane embedding for knowledge-based visual question answering

Background External knowledge representations play an essential role in knowledge-based visual question and answering to better understand complex scenarios in the open world.Recent entity-relationship embedding approaches are deficient in representing some complex relations,resulting in a lack of topic-related knowledge and redundancy in topic-irrelevant information.Methods To this end,we propose MKEAH:Multimodal Knowledge Extraction and Accumulation on Hyperplanes.To ensure that the lengths of the feature vectors projected onto the hyperplane compare equally and to filter out sufficient topic-irrelevant information,two losses are proposed to learn the triplet representations from the complementary views:range loss and orthogonal loss.To interpret the capability of extracting topic-related knowledge,we present the Topic Similarity(TS)between topic and entity-relations.Results Experimental results demonstrate the effectiveness of hyperplane embedding for knowledge representation in knowledge-based visual question answering.Our model outperformed state-of-the-art methods by 2.12%and 3.24%on two challenging knowledge-request datasets:OK-VQA and KRVQA,respectively.Conclusions The obvious advantages of our model in TS show that using hyperplane embedding to represent multimodal knowledge can improve its ability to extract topic-related knowledge.

Two Results on Binary Matroids

Aim To research new characterization and circuit property of binary matroid. Methods Constract the modular pairs of hyperplanes of a a matroid. Results and Conclusion It is proved that a matroid M on finite set S is binary if and only if for any two distinct hyper-planes H1 and H2, if H1H2S ,and H1 and H2 are modular pair, then S-(H1H2) is a hyperplande .And a necessary and sufficient condition for a binary matroid to have a k-circuit is obtained.

LEARNING ALGORITHM OF FEEDFORWARD NEURAL NETWORK WITH HARD LIMITER USED FOR CLASSIFICATION

A learning algorithm based on a hard limiter for feedforward neural networks (NN) is presented,and is applied in solving classification problems on separable convex sets and disjoint sets.It has been proved that the algorithm has stronger classification ability than that of the back propagation (BP) algorithm for the feedforward NN using sigmoid function by simulation.What is more,the models can be implemented with lower cost hardware than that of the BP NN.LEARNIN

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.

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.

A new heuristic algorithm for general integer linear programming problems

A new heuristic algorithm is proposed for solving general integer linear programming problems. In the algorithm, the objective function hyperplane is used as a cutting plane, and then by introducing a special set of assistant sets, an efficient heuristic search for the solution to the integer linear program is carried out in the sets on the objective function hyperplane. A simple numerical example shows that the algorithm is efficient for some problems, and therefore, of practical interest.

Improving 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.

An Algorithm for Reducibility of 3-arrangements

We consider a central hyperplane arrangement in a three-dimensional vector space. The definition of characteristic form to a hyperplane arrangement is given and we could make use of characteristic form to judge the reducibility of this arrangement. In addition, the relationship between the reducibility and freeness of a hyperplane arrangement is given

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.

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.

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.

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.