Let/. It :0 ---0 G be any two self maps of a compact connected oriented Lie group G. In this paper, for each positive integer k , we associate an integer with fk,hi . We relate this number with Lefschetz coincidence number. We deduce that for any two differentiable maps f, there exists a positive integer k such that k 5.2+1 , and there is a point x C G such that ft (x) = (x) , where A is the rank of G . Introduction Let G be an n-dimensional com -pact connected Lie group with multip-lication p ( .e 44:0 xG--+G such that p ( x , y) = x.y ) and unit e . Let [G, G] be the set of homotopy classes of maps G G . Given two maps f , f G ---• Jollowing [3], we write f. f 'to denote the map G-.Gdefined by 01.11® =A/WO= fiat® ,sea Given a point g

this paper give a proof of known conditions for the existence of peridic conincidence points of continuius maps using lindemann theotem on transcendental numbers

    In this paper, we prove some coincidence and common fixed point theorems for a pair of discontinuous weakly compatible self mappings satisfying generalized contractive condition in the setting of Cone-b- metric space under assumption that the Cone which is used is nonnormal. Our results are generalizations of some recent results.

The main purpose of this paper is to introduce and prove some fixed point theorems for two maps that

satisfy -contractive conditions with rational expression in partially ordered metric spaces, our results improve and unify a multitude of fixed point theorems and generalize some recent results in ordered partially metric space.

This paper aims to study the asymptotic stability of the equilibrium points of the index 2 and index 3 Hesenberg differential algebraic equations. The problem reformulated to an equivalent explicit differential algebraic equations system, so the asymptotic stability is easily investigated. The singular points such as impasse points and singularity induced bifurcation points are identified in this kind of differential algebraic equations by using conclusion of the explicit differential algebraic equations.

This paper aims to study the asymptotic stability of the equilibrium points of the index 2 and index 3 Hesenberg differential algebraic equations. The problem reformulated to an equivalent explicit differential algebraic equations system, so the asymptotic stability is easily investigated. The singular points such as impasse points and singularity induced bifurcation points are identified in this kind of differential algebraic equations by using conclusion of the explicit differential algebraic equations.

This paper aims to study the asymptotic stability of the equilibrium points of the index 2 and index 3 Hesenberg differential algebraic equations. The problem reformulated to an equivalent explicit differential algebraic equations system, so the asymptotic stability is easily investigated. The singular points such as impasse points and singularity induced bifurcation points are identified in this kind of differential algebraic equations by using conclusion of the explicit differential algebraic equations.

    This paper deals with finding an approximate solution to the index-2 time-varying linear differential algebraic control system based on the theory of variational formulation. The solution of index-2 time-varying differential algebraic equations (DAEs) is the critical point of the equivalent variational formulation. In addition, the variational problem is transformed from the indirect into direct method by using a generalized Ritz bases approach. The approximate solution is found by solving an explicit linear algebraic equation, which makes the proposed technique reliable and efficient for many physical problems. From the numerical results, it can be implied that very good efficiency, accuracy, and simplicity of the pre