Let M be a manifold and V a Euclidean space. We use calculus of functors to study the rational homology and homotopy of the space Emb(M, V ), which is defined to be the homotopy fiber of the map Emb(M, V ) → Imm(M, V ). If M is one-dimensional, we get, essentially, the space of knots in R. One general point that we want to make is that quite a bit of what had been done for knots can be done for...

In this paper, we present a new semantics for the well-known normal system of modal logic K based on the notion of convergence spaces. The purpose is to use convergence spaces to model and reason about systems with both discrete and continuous states, so-called hybrid state spaces. K is sound and complete with respect to the class of convergence space models, and we show that Kripke frames and ...

In this paper, a new class of over-relaxed proximal point algorithms for solving nonlinear operator equations with (A,η,m)-monotonicity framework in Hilbert spaces is introduced and studied. Further, by using the generalized resolvent operator technique associated with the (A,η,m)-monotone operators, the approximation solvability of the operator equation problems and the convergence of iterativ...

The purpose of this paper is to study the convergence and the almost sure T-stability of the modied SP-type random iterative algorithm in a separable Banach spaces. The Bochner in-tegrability of andom xed points of this kind of random operators, the convergence and the almost sure T-stability for this kind of generalized asymptotically quasi-nonexpansive random mappings are obtained. Our result...

Effect of Tower rapeseed oil (RO) containing lower (0.4%) erucic acid on the piglet liver was studied by electron microscopy. The animals were placed in two groups of four and were fed the diets for eight weeks. Animals in the treated group were given a basal diet comprising corn-soybean plus Tower RO at a 10% concentration; animals that were given the basal diet with no added oil served as the...

Scannell and Sinha considered a spectral sequence to calculate the rational homotopy groups of spaces of long knots in Rn, for n ≥ 4. At the end of the paper they conjecture that when n is odd, the terms on the antidiagonal at the E2 stage precisely give the space of primitive Feynman diagrams related to the theory of Vassiliev invariants. In this paper we prove that conjecture. This has the ap...

In this paper, we introduce a new m-step iterative process for a finite family of multivalued mappings satisfying the condition (E). We then prove some strong and ∆-convergence theorems in CAT(0) spaces. In this way, we extend results of [8].

Dedicated to Professor Ivo Marek on the occasion of his sixtieth birthday. Equivalence is shown between different conditions for convergence of iterative methods for consistent singular systems of linear equations on Banach spaces. These systems appear in many applications, such as Markov chains and Markov processes. The conditions considered relate the range and null spaces of different operat...