The Related Properties of Generalized Orthogonal Group in Specific Normed Linear Spaces

Firstly, in the general normed linear space, the concepts of generalized isosceles orthogonal group, generalized Birkhoff orthogonal group, generalized Roberts orthogonal group, strong Birkhoff orthogonal group and generalized orthogonal basis are introduced. Secondly, the conclusion that any two nonzero generalized orthogonal groups must be linearly independent group is proven. And the existence of nonzero generalized orthogonal group and its linear correlation are discussed preliminarily, as well as some related properties of nonempty generalized orthogonal group in specific normed linear space namely the lp space.

CHEBYSHEV CENTERS PROXIMINALITY AND FARTHEST POINTS IN STRONG NORMED ALMOST LINEAR SPACES

Some results from the theory of best (or best simultaneous) approximation in a narmed linear space have been extended to a normed almost linear space [strong normed almost linear space].

《Metric Linear Spaces》的两点注记

指出StefanRolewicz先生的名著《MetricLinearSpaces》中的三个定理的证明错误 。

Computational Analysis for Solving the Linear Space-Fractional Telegraph Equation

Over the last few years, there has been a significant increase in attention paid to fractional differential equations, given their wide array of applications in the fields of physics and engineering. The recent development of using fractional telegraph equations as models in some fields (e.g., the thermal diffusion in fractal media) has heightened the importance of examining the method of solutions for such equations (both approximate and analytic). The present work is designed to serve as a valuable contribution to work in this field. The key objective of this work is to propose a general framework that can be used to guide quadratic spline functions in order to create a numerical method for obtaining an approximation solution using the linear space-fractional telegraph equation. Additionally, the Von Neumann method was employed to measure the stability of the analytical scheme, which showed that the proposed method is conditionally stable. What’s more, the proposal contains a numerical example that illustrates how the proposed method can be implemented practically, whilst the error estimates and numerical stability results are discussed in depth. The findings indicate that the proposed model is highly effective, convenient and accurate for solving the relevant problems and is suitable for use with approximate solutions acquired through the two-dimensional differential transform method that has been developed for linear partial differential equations with space- and time-fractional derivatives.

Angles of Norm ed Linear Spaces and Characterizations of Inner Product Spaces

In [1],a family of angles are defined in normed linear spaces. In this paper,it is shown that if anyone of the angles satisfies certain euclidean triangle congruence properties,the space must be an inner product space.

CHARACTERIZATION OF BEST APPROXIMATIONS IN METRIC LINEAR SPACES

Let (X,d) be a real metric linear space, with translation-invariant metric d and G a linear subspace of X. In this paper we use functionals in the Lipschitz dual of X to characterize those elements of G which are best approximations to elements of X. We also give simultaneous characterization of elements of best approximation and also consider elements of e-approximation.

k-MAJOR ORDER IN REAL INFINITE-DIMENSIONAL LINEAR SPACE AND ITS APPLICATION

In this paper,the k major cone and strict k major cone in real infinite dimensional linear space are introduced,through which the k major order is defined,and their properties are also discussed.Therefore,with the help of them any two elements in real infinite dimensional linear space can be compared.

Space Topologies and Their Dual Space Topologies for Conventional Functional Space Topologies

In this paper, we have studied the topology of some classical functional spaces. Among these spaces, there are standard spaces, spaces that can be metrizable and others that cannot be metrizable. But they are all topological vector spaces and it is in this context that we have chosen to present this work. We are interested in the topology of its spaces and in the topologies of their dual spaces. The first part, we presented the fundamental topological properties of topological vector spaces. The second part, we studied Frechet spaces and particularly the space S(Rn) of functions of class C∞ on Rn which are as well as all their rapidly decreasing partial derivatives. We have also studied its dual S'(Rn) the space of tempered distributions. The last part aims to define a topological structure on an increasing union of Frechet spaces called inductive limit of Frechet spaces. We study in particular the space D(Ω) of functions of class C∞ with compact supports on Ω as well as its dual D' (Ω) the space distributions over the open set Ω.

从Place连接Space助推“机械原理”一流课程建设

基于教学实践,从教学内容、教学组织和双向评价这三个关键维度出发,分别在先进理论和现代设计方法、大规模在线教育和工程实践及教师评价“学”的过程和学生评价“教”的过程等重要方向建立连接,使课程体系从有限容量的线性place占位扩展到大容量现代化教学的多方向space占位。建设结果表明,多方向的space课程体系既能解决学生学习过程中的主动性、积极性问题,又能助推课程自身迭代,促使“机械原理”始终处于一流课程的领先地位。

Almost simple groups with socle ^3D_4(q)act on finite linear spaces

After the classification of flag-transitive linear spaces,attention has now turned to line-transitive linear spaces.Such spaces are first divided into the point-imprimitive and the point-primitive,the first class is usually easy by the theorem of Delandtsheer and Doyen.The primitive ones are now subdivided,according to the O'Nan-Scotte theorem and some further work by Camina,into the socles which are an elementary abelian or non-abelian simple.In this paper,we consider the latter.Namely,T ≤ G ≤ Aut(T) and G acts line-transitively on finite linear spaces,where T is a non-abelian simple.We obtain some useful lemmas.In particular,we prove that when T is isomorphic to 3D4(q),then T is line-transitive,where q is a power of the prime p.

Solvable line-transitive automorphism groups of finite linear spaces

Let S be a finite linear space, and let G be a group of automorphisms of S. If G is soluble and line-transitive, then for a given k but a finite number of pairs of ( S, G), S has v= pn points and G≤AΓ L(1,pn).

Smoothing methods based on coordinate transformation in a linear space and application in airfoil aerodynamic design optimization

In detailed aerodynamic design optimization,a large number of design variables in geometry parameterization are required to provide sufficient flexibility and obtain the potential optimum shape.However,with the increasing number of design variables,it becomes difficult to maintain the smoothness on the surface which consequently makes the optimization process progressively complex.In this paper,smoothing methods based on B-spline functions are studied to improve the smoothness and design efficiency.The wavelet smoothing method and the least square smoothing method are developed through coordinate transformation in a linear space constructed by B-spline basis functions.In these two methods,smoothing is achieved by a mapping from the linear space to itself such that the design space remains unchanged.A design example is presented where aerodynamic optimization of a supercritical airfoil is conducted with smoothing methods included in the optimization loop.Affirmative results from the design example confirm that these two smoothing methods can greatly improve quality and efficiency compared with the existing conventional non-smoothing method.

Line-primitive Linear Spaces with Fang-Li Parameter gcd（k,r） at Most 12

让 G 是重要有限线性空间 S 的自守组的亚群。如果 G 是有 Fang-Li 参数 gcd 的线原语，在这份报纸，我们证明那(k， r )= 11 和 12，那么， G 也是点原语。这扩大毒牙的结果，联合了的李(1993 )(2001 ) 和李和刘为 gcd 给结果(k， r ) 10。

Finite Line-transitive Linear Spaces:Theory and Search Strategies

纸总结存在理论和分类有限线及物的线性空格，进一步开发理论，并且以启用它的有效应用程序的一个方法组织它。起点是 Camina 和识别线性空格的三种线及物的自守组的第五个作者的一条定理。在二个这些盒子中，组可以是点上的 imprimitive，也就是说，这个组让点集合的一个重要分区不变。在第一个这些盒子，这个组与点及物的简单座石几乎简单，并且可以是点原语，当在第二个盒子中这个组有重要点不及物的正常亚群并且因此毫无疑问是 point-imprimitive 时。这里介绍的理论集中于 point-imprimitive 组。作为一个分类 point-imprimitive，线及物的组，和相应线性空格被给的一个重要应用程序，为它最大的普通除数 gcd (k， v − 1 )≤ 8 在 v 是的地方，点的数字，和 k 是线尺寸。这个分类的动机在 1993 来自 Weidong 毒牙和李惠玲的结果，仅仅有有限地许多重要 point-imprimitive，为 gcd 的给定的价值的线及物的线性空格(k， v −1 ) 。分类在强壮得多的限制 k ≤ 下面由 Camina 和 Mischke 加强分类8：没有另外的例子产生。纸为未来提供脊梁 point-imprimitive 的基于计算机的分类，有小参数的线及物的线性空格。为进一步的调查的几个建议被做。

JOINT SPACE-FREQUENCY MULTIUSER SYMBOL DETECTOR FOR MC-CDMA SYSTEM WITH UNIFORM LINEAR ARRAY

The MultiCarrier Code Division Multiple Access (MC-CDMA) scheme is promising for relieving capacity limit problems of Direct Sequence (DS-) CDMA systems due to serious InterChip Interference (ICI) and MultiUser Interference (MUI) in high-data-rate wireless communication systems. In this paper, the Uniform Linear Array (ULA) is applied to the base station of macrocellular MC-CDMA systems in a frequency-selective fading channel environment. A joint space-frequency multiuser symbol sequence detector is developed for all active users within one macrocell without space-frequency channel estimation. Simultaneously, Directions-Of-Arrivals (DOAs) of all active users can also be estimated. By dividing the ULA into two identical overlapping subarrays, a specific auxiliary matrix is constructed, which includes both symbol sequence and DOA information of all active users. Then, based on the subspace method, performing the eigen decomposition on such auxiliary matrix, the closed-form solution of symbol sequences and DOAs for all active users can be obtained. In comparison with schemes based on channel estimation, our algorithm need not explicitly estimate the space-frequency channel for each active user,so it has lower computation complexity. Extensive computer simulations demonstrate the overall performance of this novel scheme.

t-Singular Linear Spaces

作为单个线性空格的归纳，我们介绍 t 单个的线性空格的概念，使某 anzahl 成为 subspaces 的公式，并且决定 t 单个的线性组的 suborbits。

Line-transitive point-imprimitive linear spaces with Fang-Li parameter gcd（k, r） at most ten

这份报纸是对 linetransitive 的分类的进一步的贡献有限线性空格。如果，我们证明那是一个重要有限线性空格以便 Fang-Li 参数 gcd (k， r ) 是 9 或 10，并且组 G Aut() 是线及物的并且 point-imprimitive，那么是 Desarguesian 射影的飞机 PG (2， 9 ) 。

A NEW PERTURBATION THEOREM FOR MOORE-PENROSE METRIC GENERALIZED INVERSE OF BOUNDED LINEAR OPERATORS IN BANACH SPACES

In this paper,we investigate a new perturbation theorem for the Moore-Penrose metric generalized inverses of a bounded linear operator in Banach space. The main tool in this paper is "the generalized Neumann lemma" which is quite different from the method in [12] where "the generalized Banach lemma" was used. By the method of the perturbation analysis of bounded linear operators,we obtain an explicit perturbation theorem and three inequalities about error estimates for the Moore-Penrose metric generalized inverse of bounded linear operator under the generalized Neumann lemma and the concept of stable perturbations in Banach spaces.

ON PROBABILISTIC NORM OF A LINEAR OPERATORS AND SPACE OF OPERATORS

Since the PN space （E, F ） which satisfies condition （PN5） is just a Menger PNspace （E,F,min）, the results with regard to probabilistic norms of linear operators on PNspaces obtained by Xiao Jianzhong have bigger limitations. In this paper, problems respecting probabilistic norms of linear operators and spaces of operators are studied on more general Menger PNspaces. The results presented improve and generalize the corresponding results by Xiao.

More Properties of Semi-Linear Uniform Spaces

In this paper we shall generalize the definition given in [1] for Lipschitz condition and contractions for functions on a non-metrizable space, besides we shall give more properties of semi-linear uniform spaces.