Optimal control problems for the variational inequality of static elastoplasticity with linear kinematic hardening are considered. The controlto-state map is shown to be weakly directionally differentiable, and local optimal controls are proved to verify an optimality system of B-stationary type. For a modified problem, local minimizers are shown to even satisfy an optimality system of strongly...

The following theorem is surprising because it says that if A is a suspension, then for any map A→ X, the homotopy fiber of the cofiber Fib(X → X/A) and A have unstably quite a lot in common (see corollary 8.9): Theorem. Let A→ X → X/A be a cofibration sequence of pointed and connected spaces and Y be a pointed space. If A is weakly equivalent to a suspension of a connected space, then the foll...

Motivated by the computational complexity of determining whether a graph is hamiltonian, we study under algorithmic aspects a class of polyhedra called k-pyramids, introduced in [Zamfirescu and Zamfirescu, Math. Nachr. 284 (2011) 1739–1747], and discuss related applications. We prove that determining whether a given graph is the 1-skeleton of a k-pyramid, and if so whether it is belted or not, ...

We consider weakly coupled analytic expanding circle maps on the lattice Z d (for d 1), with small coupling strength and coupling between two sites decaying exponentially with the distance. We study the spectrum of the associated (Perron-Frobenius) transfer operators. We give a Fr echet space on which the operator associated to the full system has a simple eigenvalue at 1 (corresponding to the ...

We prove the existence and uniqueness of fixed points of T-stability for an iteration on partial cone metric space of Zamfirescu contraction. As an application, we prove a theorem for integral equation. We also give illustrative examples to verify our results.

In this article, we present the concept of supra paracompact spaces and study its basic properties. We elucidate its relationship with supra compact spaces and prove that the property of being a supra paracompact space is weakly hereditary and topological properties. Also, we provide some examples to show some results concerning paracompactness on topology are invalid on supra topology. Finally...

There is only one finite, 2-connected, linearly convex graph in the Archimedean triangular tiling that does not have a Hamiltonian cycle. The vertices and polygonal edges of the planar Archimedean tilings 44 and 36 of the plane, partially shown in Figs. 1 and 2, respectively, are called the square tiling graph (STG) and the triangular tiling graph (TTG). (See [1].) A subgraph G of TTG is linear...

Given a number L ≥ 1, a weakly L-quasiregular map on a domainΩ in spaceRn is amapu in a Sobolev spaceW 1,p loc (Ω;R n) that satisfies |Du(x)|n ≤ LdetDu(x) almost everywhere in Ω. In this paper, we study the problem concerning linear boundary values of weakly L-quasiregular mappings in spaceRn with dimension n ≥ 3. It turns out this problem depends on the power p of the underlyingSobolev space. ...