In the present investigation, the authors prove several inclusion relations associated with the (n, δ)-neighborhoods of certain subclasses of p-valently analytic functions of complex order, which are introduced here by means of the Hadamard’s Convolution. Special cases of some of these inclusion relations are shown to yield many known results. 2000 Mathematics Subject Classification: Primary 30...

An operator family of densely defined closed linear operators and the multiplication operator associated with it are considered. The spectrum of this multiplication operator is expressed in terms of the spectra of the operators in the given family. Mathematics Subject Classification (2000). Primary 47A10; Secondary 47A56, 47B40, 47E05, 76B99.

We give a necessary and sufficient condition for k-step nilmanifolds associated with graphs (k ≥ 3) to admit Anosov automorphisms. We also prove nonexistence of Anosov automorphisms on certain classes of 2-step and 3-step nilmanifolds. 2000 Mathematics Subject Classification. Primary 37D20; Secondary 22E25

We study some new isoperimetric inequalities on graphs. We etablish a relation between the volume entropy (or asymptotic volume), the systole and the first Betti number of weighted graphs. We also find bounds for the volume, associated to some special measure, of the unit ball for the stable norm of graphs. Mathematics Subject Classification (2000) : 05C35, 37B10 .

We describe a generalisation of the FontaineWintenberger theory of the “field of norms” functor to local fields with imperfect residue field, generalising work of Abrashkin for higher dimensional local fields. We also compute the cohomology of associated p-adic Galois representations using (φ,Γ)-modules. 2000 Mathematics Subject Classification: 11S15, 11S23, 11S25, 12G05

A triangular grid graph is a finite induced subgraph of the infinite graph associated with the two-dimensional triangular grid. We show that the problem Hamiltonian Cycle is NP-complete for triangular grid graphs, while a hamiltonian cycle in connected, locally connected triangular grid graph can be found in polynomial time. 2000 Mathematics Subject Classification: 05C38 (05C45, 68Q25).

In this note, we give characterizations for certain HNN extensions of polycyclic-by-finite groups with central associated subgroups to be subgroup separable and conjugacy separable. We shall do this by showing the equivalence of subgroup separability and conjugacy separability in this type of HNN extensions. 2000 Mathematics Subject Classification: Primary 20E06, 20E26; Secondary 20F10, 20F19

Some properties on stem extensions and stem covers of Leibniz algebras are studied by means of exact sequences associated to a central extension of Leibniz algebras. We obtain particular results in case of perfect Leibniz algebras. 2000 Mathematics Subject Classification: 17A32.

We introduce complex differential geometry twisted by a real line bundle. This provides a new approach to understand the various real objects that are associated with an antiholomorphic involution. We also generalize a result of Greenleaf about real analytic sheaves from dimension 2 to higher dimensions. 2000 Mathematics subject classification: 58A05, 53C07, 14J60, 53C56.

Nonrational nonsimple convex polytopes can be considered in quasilattices. We prove that the corresponding complex quasitori can be compactified by suitably adding smaller dimensional orbits. The final objects, constructed as complex quotients, are spaces stratified by complex quasifolds that perfectly mimic the features of toric varieties associated to rational convex polytopes. 2000 Mathemati...