Three-dimensional semi-symmetric homogeneous Lorentzian manifolds

Because of the different possible forms (Segre types) of the Ricci operator, semi-symmetry assumption for the curvature of a Lorentzian manifold turns out to have very different consequences with respect to the Riemannian case. In fact, a semi-symmetric homogeneous Riemannian manifold is necessarily symmetric, while we find some three-dimensional homogeneous Lorentzian manifolds which are semi-symmetric but not symmetric. The complete classification of three-dimensional semi-symmetric homogeneous Lorentzian manifolds is obtained.     

ON SEMI-SYMMETRIC RECURRENT-METRIC S-CONCIRCULAR CONNECTIONS

In this paper, the semi-symmetric recurrent-metric S-concircular connec-tion on a Riernannian manifold are defined. Some properties of semi-symmetric recurrent-metric S-concircular connections have been obtained.     

Symmetries of Null Geometry in Indefinite Kenmotsu Manifolds

Null hypersurfaces have metrics with vanishing determinants and this degeneracy of these metrics leads to several difficulties. In this paper, null hypersurfaces of indefinite Kenmotsu space forms, tangent to the structure vector field, are studied with specific attention to locally symmetric, semi-symmetric and Ricci semi-symmetric null hypersurfaces. We show that locally symmetric and semi-symmetric null hypersurfaces are totally geodesic and parallel. These also hold for Ricci semi-symmetric null hypersurfaces, under a certain condition. We prove that, in null Einstein hypersurfaces of an indefinite Kenmotsu space form, tangent to the structure vector field, the local symmetry, semisymmetry and Ricci semi-symmetry notions are equivalent. For totally contact umbilical null hypersurfaces, we show that there are η-“Weyl” connections adapted to the induced structure on the null hypersurface.     

Semi-symmetric Lorentzian Three-manifolds Admitting a Parallel Degenerate Line Field

We characterize semi-symmetric Lorentzian three-manifolds (M,g _f ) admitting a parallel degenerate line field, through a condition on the defining function f. The admissible Segre types of the Ricci operator of (M,g _f ) are also completely described, and semi-symmetric curvature homogeneous examples are presented in the possible different cases.     

The existence of weakly symmetric and weakly Ricci-symmetric Sasakian manifolds admitting a quarter-symmetric metric connection

The object of the present work is to obtain a necessary condition for the existence of weakly symmetric and weakly Ricci-symmetric Sasakian manifolds admitting a quarter-symmetric metric connection.     

Affine hypersurfaces with the Ricci semi-symmetry

The purpose of the present paper is to prove that either a proper affine hypersphere or an affine cylindrical (See Introduction) is the only nondegenerate affine hypersurface of affine space with torsion free affine connection which satisfies the Ricci semi-symmetry and to study the equivalence of semi-symmetric and Ricci semi-symmetric in the case of affine hypersurfaces     

On a Kaehler hypersurface with the cyclic Ricci semi-symmetric tensor

The purpose of the present paper is to prove that a Kaehler hypersurface with the cyclic Ricci semi-symmetric tensor is locally symmetric.     

ISOTROPIC WEYL MANIFOLD WITH A SEMI-SYMMETRIC CONNECTION

In this work,it is proved that every isotropic Weyl manifold with a semi- symmetric connection is locally conformal to an Einstein manifold with a semi-symmetric connection.     

On almost complex structures which are not compatible with symplectic forms

In this Note we prove that the underlying almost complex structure to a non-Kähler almost Hermitian structure admitting a compatible connection with skew-symmetric torsion cannot be calibrated by a symplectic form even locally.     

Some Remarks on Complex Crowns of Riemannian Symmetric Spaces

We discuss several results and problems in which complex geometric constructions appear in the geometry of real pseudo Riemannian symmetric spaces in connection with analysis on such spaces.     

Some Invariant Properties of Semi-symmetric Metric Recurrent Connections and Curvature Tensor Expressions

The projective transformation of the special semi-symmetric metric recurrent connection is studied in this paper. First of all, an invariant under this transformation is granted; Secondly, by inducing of the invariant and making use of the properties that the corresponding covariant derivative keeps being fixed under the distinctness connection, the curvature tensor expression of the Riemannian manifold is posed at the same time.     

Changing market conditions and advertising strategies: theory and evidence

Using a modified continuous Lanchester model of advertising competition and following a game theoretic approach, this paper investigates analytically the sensitivity of optimal advertising to changes in model parameters in the cases of symmetric and semi-symmetric competition. The theoretical results show that non-dominant firms in both market structures behave similarly whereas the dominant firm in the latter structure behaves considerably differently.We estimate a modified Lanchester model using ready-to-eat cereal data. Based on the obtained estimated parameters, we conduct an empirical analysis to assess the robustness of the theoretical estimated results. In the reported application, we demonstrate that when the model parameters change, non-dominant competitors as well as the dominant rival behave in a manner consistent with the theoretical results related to the semi-symmetric competitive structure.     

具有半对称度量联络的复空间型中全实子流形的Chen型不等式

In this paper, we obtain Chen＇s inequalities for totally real submanifolds in complex space forms with a semi-symmetric metric connection. Also, some results of A. Mihai and C. Ozgiir＇s paper have been modified.     

Proper conformal Killing vectors in static plane symmetric space–times

Conformal Killing vectors (CKVs) in static plane symmetric space–times were recently studied by Saifullah and Yazdan, who concluded by remarking that static plane symmetric space–times do not admit any proper CKV except in the case where these space–times are conformally flat. We present some non-conformally flat static plane symmetric space–time metrics admitting proper CKVs. For these space–times, we also investigate a special type of CKVs, known as inheriting CKVs.     

容有半对称度量联络的广义复空间中子流形上的Chen-Ricci不等式

本文研究了容有半对称度量联络的广义复空间中的子流形上的Chen-Ricci不等式.利用代数技巧,建立了子流形上的Chen-Ricci不等式.这些不等式给出了子流形的外在几何量-关于半对称联络的平均曲率与内在几何量-Ricci曲率及k-Ricci曲率之间的关系,推广了Mihai和Özgür的一些结果.     

Double exponential map on symmetric spaces

We establish an asymptotic formula for the double exponential map operator on affine symmetric spaces. This operator plays an important role in the geometric calculus of symbols of (pseudo)differential operators on manifolds with connection, whose foundations were laid by Sharafutdinov. To obtain this result, we essentially use the structural theory of symmetric spaces and techniques of the Lie group theory. One of the key moments is an application of the Campbell-Hausdorff series in Dynkin form.     

Complex Wavelets and Framelets from Pseudo Splines

In this paper, we introduce complex pseudo splines that are derived from pseudo splines of type I. First, we show that the shifts of every complex pseudo spline are linearly independent. Therefore we can construct a biorthogonal wavelet system. Next, we investigate the Riesz basis property of the corresponding wavelet system generated by complex pseudo splines. The regularity of the complex pseudo splines will be analyzed. Furthermore, by using complex pseudo splines, we will construct symmetric or antisymmetric complex tight framelets with desired approximation order.     

A class of highly symmetric graphs,symmetric cylindrical constructions and their spectra

In this article, we introduce the algebra of block-symmetric cylinders and we show that symmetric cylindrical constructions on base-graphs admitting commutative decompositions behave as generalized tensor products. We compute the characteristic polynomial of such symmetric cylindrical constructions in terms of the spectra of the base-graph and the cylinders in a general setting. This gives rise to a simultaneous generalization of some well-known results on the spectra of a variety of graph amalgams, as various graph products, graph subdivisions and generalized Petersen graph constructions. While our main result introduces a connection between spectral graph theory and commutative decompositions of graphs, we focus on commutative cyclic decompositions of complete graphs and tree-cylinders along with a subtle group labeling of trees to introduce a class of highly symmetric graphs containing the Petersen and the Coxeter graphs. Also, using techniques based on recursive polynomials we compute the characteristic polynomials of these highly symmetric graphs as an application of our main result.     

ON SUFFICIENCY AND DUALITY OF SOLUTIONS FOR QUASI Bs-INVEX SEMI-INFINITE PROGRAMMING

1　IntroductionRecently,various kinds of generalized convex functions were introduced.Bector andSingh[1 ] introduced a class of functions which called B-vex function.Bector,Suneja,andLalitha[2 ] introduced quasi B-vex function,pseudo B-vex function,B-invex function,quasi B-invex function,and pseudo B-invex function.We[3] extended invex function[4] ,gave thedefinitions of the symmetricη-function,symmetricη-pseudoconvex function,symmetricη-quasiconvex function for symmetric differentiable…     

Coefficient characterization of linear differential equations with maximal symmetries

A characterization of the general linear equation in standard form admitting a maximal symmetry algebra is obtained in terms of a simple set of conditions relating the coefficients of the equation. As a consequence, it is shown that in its general form such an equation can be expressed in terms of only two arbitrary functions, and its connection with the Laguerre–Forsyth form is clarified. The characterizing conditions are also used to derive an infinite family of semi-invariants, each corresponding to an arbitrary order of the linear equation. Finally a simplifying ansatz is established, which allows an easier determination of the infinitesimal generators of the induced pseudo group of equivalence transformations, for all the three most common canonical forms of the equation.