We study resolution of tame cyclic quotient singularities on arithmetic surfaces, and use it to prove that for any subgroup H ⊆ (Z/pZ)×/{±1} the map XH(p) = X1(p)/H → X0(p) induces an injection Φ(JH(p)) → Φ(J0(p)) on mod p component groups, with image equal to that of H in Φ(J0(p)) when the latter is viewed as a quotient of the cyclic group (Z/pZ)×/{±1}. In particular, Φ(JH(p)) is always Eisens...

We study resolution of tame cyclic quotient singularities on arithmetic surfaces, and use it to prove that for any subgroup H ⊆ (Z/pZ)×/{±1} the map XH(p) = X1(p)/H → X0(p) induces an injection Φ(JH(p)) → Φ(J0(p)) on mod p component groups, with image equal to that of H in Φ(J0(p)) when the latter is viewed as a quotient of the cyclic group (Z/pZ)×/{±1}. In particular, Φ(JH(p)) is always Eisens...

in this paper direct proofs of some common fixed point results for two and three mappings under weak contractive conditions are given. some of these results are improved by using different arguments of control functions. examples are presented showing that some generalizations cannot be obtained and also that our results are distinct from the existing ones.

Let φ be an analytic self-map of D and g∈H(D) . The boundedness and compactness of generalized composition operators

Cognitive Vision has to represent, reason and learn about objects in its environment it has to manipulate and react to. There are deformable objects like humans which cannot be described easily in simple geometric terms. In many cases they are composed of several pieces forming a “structured subset” of R or Z. We introduce the potential topological representations for structured objects: plane ...

We prove by elementary methods the following generalization of a theorem due to Gleason, Kahane, and Żelazko. Let A be a real algebra with unit 1 such that the spectrum of every element in A is bounded and let φ : A→ C be a linear map such that φ(1) = 1 and (φ(a))2 + (φ(b))2 = 0 for all a, b in A satisfying ab = ba and a2 + b2 is invertible. Then φ(ab) = φ(a)φ(b) for all a, b in A. Similar resu...

in this paper, we establish and prove the existence of best proximity points for multivalued cyclic $f$- contraction mappings in complete metric spaces. our results improve and extend various results in literature.