1.2 The theorem 1.1 contrasts the rank one case, where the secondary class of the flat bundle, associated to a representation ρ : π1(X) → GL1(C) = C ∗ is essentially the representation itself, so it may be completely arbitrary. But this freedom becomes limited when one looks at the line bundles over curves, corresponding via the Deligne-Ramakrishnan construction to elements of K2(X). The map r ...

We describe a construction of an object associated to the fundamental group of P−{0, 1,∞} in the Bloch-Kriz category of mixed Tate motives. This description involves Massey products of Steinberg symbols in the motivic cohomology of the ground field.

Recommended by Radu Precup The boundedness and compactness of the weighted composition operators from logarithmic Bloch-type spaces to Bloch-type spaces are studied here.

Nitrate is a noxious and persistent oxyanion in drinking waters. It themed as one of the most common water quality violations worldwide. electrocatalytic reduction appears to be viable solution. However, use platinum group elements (PGEs) electrocatalysts must avoided due their high cost limited availability. In this study, earth-abundant nano-Fe3O4 electrodes were synthesized surpass those imp...

By using the concept of the weak subordination, we examine the stability a class of analytic functions in the unit disk is said to be stable if it is closed under weak subordination for a class of admissible functions in complex Banach spaces. The stability of analytic functions in the following classes is discussed: Bloch class, little Bloch class, hyperbolic little Bloch class, extend Bloch c...

Let φ(z) = (φ 1 (z),. .. , φ n (z)) be a holomorphic self-map of U n and ψ(z) a holomorphic function on U n , where U n is the unit polydisk of C n. Let p ≥ 0, q ≥ 0, this paper gives some necessary and sufficient conditions for the weighted composition operator W ψ,φ induced by ψ and φ to be bounded and compact between p-Bloch space B p (U n) and q-Bloch space B q (U n).

Let φ be a holomorphic self-map of the open unit polydisk U in C and p, q > 0. In this paper, the generally weighted Bloch spaces B log(U ) are introduced, and the boundedness and compactness of composition operator Cφ from B p log(U ) to B log(U ) are investigated.

In this short note we provide computational evidence for the main result found in On the Bloch-Kato conjecture for elliptic modular forms of square-free level.