NONEMPTY INTERSECTION THEOREMS AND SYSTEM OF GENERALIZED VECTOR EQUILIBRIUM PROBLEMS IN PRODUCT G-CONVEX SPACES

By using an existence theorems of maximal elements for a family of set-valued mappings in G-convex spaces due to the author, some new nonempty intersection theorems for a family of set-valued mappings were established in noncompact product G-convex spaces. As applications, some equilibrium existence theorems for a system of generalized vector equilibrium problems were proved in noncompact product G-convex spaces. These theorems unify, improve and generalize some important known results in literature.

Research of the Unity Theory Between Three-level Space Vector and Carrier-based PWM Modulation Strategy

两电平空间矢量脉宽调制（space vector pulse widthmodulation,SVPWM）与正弦脉宽调制（sinusoidal pulse widthmodulation,SPWM）存有一定的本质关系,对于三电平,在常见的8段式SVPWM序列中可以证明,SVPWM与SPWM本质上也存在某种统一。实际的SVPWM调制中,由于要考虑中点电压平衡、减少谐波等其它性能问题,一般会利用开关冗余状态得到8段以上的开关调制序列。目前的文献中还未曾有对这些情况进行统一性地验证,因此三电平SVPWM与SPWM的统一理论存在一定的不足。研究发现,可通过严格地理论推导将传统意义上的调制波分解为2个子调制波,再进行SPWM调制,可以得到与SVPWM完全吻合的序列。该文在此方法基础上深入研究了8段以上（10、12、14段）的SVPWM调制序列与SPWM的统一。经过严格地理论推导,成功实现了含任意段数的SVPWM序列与SPWM的统一。仿真结果证明了该理论的正确性。

NONEMPTY INTERSECTION THEOREMS AND SYSTEM OF GENERALIZED VECTOR EQUILIBRIUM PROBLEMS IN PRODUCT G-CONVEX SPACES

By using an existence theorems of maximal elements for a family of set-valued mappings in G-convex spaces due to the author, some new nonempty intersection theorems for a family of set-valued mappings were established in noncompact product G-convex spaces. As applications, some equilibrium existence theorems for a system of generalized vector equilibrium problems were proved in noncompact product G-convex spaces. These theorems unify, improve and generalize some important known results in literature.

Evaluation of Modified Vector Space Representation Using ADFA-LD and ADFA-WD Datasets

Predicting anomalous behaviour of a running process using system call trace is a common practice among security community and it is still an active research area. It is a typical pattern recognition problem and can be dealt with machine learning algorithms. Standard system call datasets were employed to train these algorithms. However, advancements in operating systems made these datasets outdated and un-relevant. Australian Defence Force Academy Linux Dataset (ADFA-LD) and Australian Defence Force Academy Windows Dataset (ADFA-WD) are new generation system calls datasets that contain labelled system call traces for modern exploits and attacks on various applications. In this paper, we evaluate performance of Modified Vector Space Representation technique on ADFA-LD and ADFA-WD datasets using various classification algorithms. Our experimental results show that our method performs well and it helps accurately distinguishing process behaviour through system calls.

Composition Operators with Linear Fractional Symbols on Vector-Valued Bergman Spaces

Let φ and ψ be linear fractional self\|maps of the unit disk D and X a separable Hilbert space. In this paper we completely characterize the weak compactness of the product operators of a composition operation C φ with another one's adjoint C * ψ on the vector\|valued Bergman space B 1(X) for forms C φC * ψ and C * ψC φ.

Orbit Weighting Scheme in the Context of Vector Space Information Retrieval

This study introduces the Orbit Weighting Scheme(OWS),a novel approach aimed at enhancing the precision and efficiency of Vector Space information retrieval(IR)models,which have traditionally relied on weighting schemes like tf-idf and BM25.These conventional methods often struggle with accurately capturing document relevance,leading to inefficiencies in both retrieval performance and index size management.OWS proposes a dynamic weighting mechanism that evaluates the significance of terms based on their orbital position within the vector space,emphasizing term relationships and distribution patterns overlooked by existing models.Our research focuses on evaluating OWS’s impact on model accuracy using Information Retrieval metrics like Recall,Precision,InterpolatedAverage Precision(IAP),andMeanAverage Precision(MAP).Additionally,we assessOWS’s effectiveness in reducing the inverted index size,crucial for model efficiency.We compare OWS-based retrieval models against others using different schemes,including tf-idf variations and BM25Delta.Results reveal OWS’s superiority,achieving a 54%Recall and 81%MAP,and a notable 38%reduction in the inverted index size.This highlights OWS’s potential in optimizing retrieval processes and underscores the need for further research in this underrepresented area to fully leverage OWS’s capabilities in information retrieval methodologies.

SYSTEM OF GENERALIZED VECTOR QUASI-EQUILIBRIUM PROBLEMS ON PRODUCT FC-SPACES

By applying a maximal element theorem on product FC-space due to author, some new equilibrium existence theorems for generalized games with fuzzy constraint correspondences are proved in FC-spaces. By using these equilibrium existence theorems, some new existence theorems of solutions for the system of generalized vector quasi-equilibrium problems are established in noncompact product FC-spaces. These results improve and generalize some recent results in literature to product FC-spaces without any convexity structure.

Phase Space Prediction of Chaotic Time Series with Nu-Support Vector Machine Regression

A new class of support vector machine, nil-support vector machine, isdiscussed which can handle both classification and regression. We focus on nu-support vector machineregression and use it for phase space prediction of chaotic time series. The effectiveness of themethod is demonstrated by applying it to the Henon map. This study also compares nu-support vectormachine with back propagation (BP) networks in order to better evaluate the performance of theproposed methods. The experimental results show that the nu-support vector machine regressionobtains lower root mean squared error than the BP networks and provides an accurate chaotic timeseries prediction. These results can be attributable to the fact that nu-support vector machineimplements the structural risk minimization principle and this leads to better generalization thanthe BP networks.

Applying two channels to vector space secret sharing based multi-signature scheme

Secret sharing and digital signature is an important research area in information security and has wide applications in such fields as safeguarding and legal use of confidential information, secure multiparty computation and electronic commerce. But up to now, study of signature based on general vector space secret sharing is very weak. Aiming at this drawback, the authors did some research on vector space secret sharing against cheaters, and proposed an efficient but secure vector space secret sharing based multi-signature scheme, which is implemented in two channels. In this scheme, the group signature can be easily produced if an authorized subset of participants pool their secret shadows and it is impossible for them to generate a group signature if an unauthorized subset of participants pool their secret shadows. The validity of the group signature can be verified by means of verification equations. A group signature of authorized subset of participants cannot be impersonated by any other set of partici- pants. Moreover, the suspected forgery can be traced, and the malicious participants can be detected in the scheme. None of several possible attacks can successfully break this scheme.

EMBEDDING THEOREMS ON CAMPANATO-MORREY SPACES FOR VECTOR FIELDS OF HoRMANDER TYPE

This paper deals with embedding theorems on Campanato-Marrey spaces formed by degenerate vector fields, which include Honnander and Grushin type of vector fields. These embedding theorems are somewhat different from the known Poincare estimates. The main ingredients of the proofs rely on the fractional maximal functions. These results evidently have applications to the regularity of subelliptic PDE.

The Dual of the Two-Variable Exponent Amalgam Spaces (Lq(),lp())(Ω)

Wiener amalgam spaces are a class of function spaces where the function’s local and global behavior can be easily distinguished. These spaces are ex-tensively used in Harmonic analysis that originated in the work of Wiener. In this paper: we first introduce a two-variable exponent amalgam space (Lq(),lp())(Ω). Secondly, we investigate some basic properties of these spaces, and finally, we study their dual.

Modified Lorentz Transformations and Space-Time Splitting According to the Inverse Relativity Model

Analysis of a four-dimensional displacement vector on the fabric of space-time in the special or general case into two Four-dimensional vectors, according to specific conditions leads to the splitting of the total fabric of space-time into a positive subspace-time that represents the space of causality and a negative subspace-time which represents a space without causality, thus, in the special case, we have new transformations for the coordinates of space and time modified from Lorentz transformations specific to each subspace, where the contraction of length disappears and the speed of light is no longer a universal constant. In the general case, we have new types of matric tensor, one for positive subspace-time and the other for negative subspace-time. We also find that the speed of the photon decreases in positive subspace-time until it reaches zero and increases in negative subspace-time until it reaches the speed of light when the photon reaches the Schwarzschild radius.

Systems of generalized vector quasi-variational inclusions and systems of generalized vector quasi-optimization problems in locally FC-uniform spaces

In this paper, we introduce some new systems of generalized vector quasi-variational inclusion problems and system of generalized vector ideal （resp., proper, Pareto, weak） quasi-optimization problems in locally FC-uniform spaces without convexity structure. By using the KKM type theorem and Himmelberg type fixed point theorem proposed by the author, some new existence theorems of solutions for the systems of generalized vector quasi-variational inclusion problems are proved. As to its applications, we obtain some existence results of solutions for systems of generalized vector quasi-optimization problems.

Research on Parallel Interleaved Inverters with Discontinuous Space-Vector Modulation

Parallel converter can significantly increase the capacity of the converter and improve the power quality of AC side, but the circulation which can lead to high switching loss and even damage the devices will easily exist in the direct parallel converters. In this paper, the average model of parallel interleaved inverters system to analyze the circulation current is shown, and the cross current is relevant to DC-bus voltage and the overlap time of zero vectors in the switching period. Based on this observation, a discontinuous space vector modulation without using zero vectors (000) is eliminate and suppress the zero-sequence current to entire system. Finally, the effectiveness of modulation strategy is verified by the simulations in this paper.

GENERALIZED VECTOR QUASI-EQUILIBRIUM PROBLEMSIN LOCALLY G-CONVEX SPACES

Some classes of generalized vector quasi-equilibrium problems ( in short, GVQEP) are introduced and studied in locally G-convex spaces which includes most of generalized vector equilibrium problems; generalized vector variational inequality problems, quasi-equilibrium problems and quasi-variational inequality problems as special cases. First, an equilibrium existence theorem for one person games is proved in locally G-convex spaces.. As applications, some new existence theorems of solutions for the GVQEP are established in noncompact locally G-convex spaces. These results and argument methods are new and completely different from that in recent literature.

Near-Vector Spaces Constructed over Zp, for p a Prime

The purpose of this paper is to construct near-vector spaces using a result by Van der Walt, with Zp for p a prime, as the underlying near-field. There are two notions of near-vector spaces, we focus on those studied by André [1]. These near-vector spaces have recently proven to be very useful in finite linear games. We will discuss the construction and properties, give examples of these near-vector spaces and give its application in finite linear games.

A Space Vector PWM Scheme for Multilevel Inverters Based on Two-Level Space Vector PWM

Ⅰ. INTRODUCTION MULTILEVEL inverters are increasingly being used in high-power medium voltage applications due to their superior performance compared to two-level inverters, such as lower common-mode voltage, lower dv/dt, lower harmonics in output voltage and current, and reduced voltage on the power switches.

Application of the sun line-of-sight vector in the optimal attitude estimation of deep-space probe

This paper proposed an optimal algorithm using the sun line-of-sight vector to improve the probe attitude estimation accuracy in deep-space mission.Firstly,the elaborate analysis of the attitude estimation error from vector observations was done to demonstrate that the geometric relation between the reference vectors is an important factor which influences the accuracy of attitude estimation.Then,with introduction of the sun line-of-sight vector,the attitude quaternion obtained from the star-sensor was converted into a pair of mutually perpendicular reference vectors perpendicular to the sun vector.The normalized weights were calculated according to the accuracy of the sensors.Furthermore,the optimal attitude estimation in the least squares sense was achieved with the quaternion estimation method.Finally,the results of simulation demonstrated the validity of the proposed optimal algorithm based on the practical data of the Deep Impact mission.

Concircular π-Vector Fields and Special Finsler Spaces

The aim of the present paper is to investigate intrinsically the notion of a concircular π-vector field in Finsler geometry. This generalizes the concept of a concircular vector field in Riemannian geometry and the concept of concurrent vector field in Finsler geometry. Some properties of concircular π-vector fields are obtained. Different types of recurrence are discussed. The effect of the existence of a concircular π-vector field on some important special Finsler spaces is investigated. Almost all results obtained in this work are formulated in a coordinate-free form.