Integral elements of K-theory and products of modular curves II

Yet Another Application of the Theory of ODE in the Theory of Vector Fields

In this paper we are supposed to define the θ−vector field on the n−surface S and then investigate about the existence and uniqueness of its integral curves by the Theory of Ordinary Differential Equations. Then thesubject is followed through some examples.

Integral elements in K-theory and products of modular curves

This paper has two aims. The primary one is to clarify the relation between results of Beilinson [1] and Flach [7]. We begin by briefly recalling the relevant parts of their papers. Suppose S is a connected smooth projective surface over Q. Beilinson’s conjectures relate the motivic cohomology groups H i M(S,Q(n)) = K (n) 2n−i(S) of S and the L-function of the motive h(S) at s = n. In what foll...

Common Fixed Point Theorems of Integral Type in Modular Spaces

$C$-class functions on common fixed point theorems for weak‎ ‎contraction mapping of integral type in modular spaces

‎In this paper‎, ‎we use the concept of $C$-class functions introduced‎ ‎by Ansari [4] to prove the existence and uniqueness of‎ ‎common fixed point for self-mappings in modular spaces of integral‎ ‎inequality‎. ‎Our results extended and generalized previous known‎ ‎results in this direction‎.

Fixed point theorem for non-self mappings and its applications in the modular ‎space

‎In this paper, based on [A. Razani, V. Rako$check{c}$evi$acute{c}$ and Z. Goodarzi, Nonself mappings in modular spaces and common fixed point theorems, Cent. Eur. J. Math. 2 (2010) 357-366.] a fixed point theorem for non-self contraction mapping $T$ in the modular space $X_rho$ is presented. Moreover, we study a new version of Krasnoseleskii's fixed point theorem for $S+T$, where $T$ is a cont...