This paper deals with control of partially observable discrete-time stochastic systems. It introduces and studies Markov Decision Processes Incomplete Information semiuniform Feller transition probabilities. The important feature these models is that their classic reduction to Completely Observable belief states preserves continuity Under mild assumptions on cost functions, optimal policies exi...

We study the connection between the Goodwillie tower of the identity and the lower central series of the loop group on connected spaces. We define the simplicial theory of homotopy n-nilpotent groups. This notion interpolates between infinite loop spaces and loop spaces. We prove, that the set-valued algebraic theory obtained by applying π0 is the theory of ordinary n-nilpotent groups and that ...

A Hausdorff topological space X is van der Waerden if for every sequence (xn)n∈ω in X there is a converging subsequence (xn)n∈A where A ⊆ ω contains arithmetic progressions of all finite lengths. A Hausdorff topological space X is Hindman if for every sequence (xn)n∈ω in X there is an IP-converging subsequence (xn)n∈FS(B) for some infinite B ⊆ ω. We show that the continuum hypothesis implies th...

We consider a homotopy theory obtained from that of pointed spaces by inverting the maps inducing isomorphisms in $v_n$-periodic groups. The case $n=0$ corresponds to rational theory. In analogy with Quillen's results case, we prove this is equivalent Lie algebras $T(n)$-local spectra. also compare it commutative coalgebras spectra, where turns out there only an equivalence up certain convergen...

We study the connection between the Goodwillie tower of the identity and the lower central series of the loop group on connected spaces. We define the simplicial theory of homotopy n-nilpotent groups. This notion interpolates between infinite loop spaces and loop spaces. We prove that the set-valued algebraic theory obtained by applying π0 is the theory of ordinary n-nilpotent groups and that t...

We study the interaction between the EHP sequence and the Goodwillie tower of the identity evaluated at spheres at the prime 2. Both give rise to spectral sequences (the EHP spectral sequence and the Goodwillie spectral sequence, respectively) which compute the unstable homotopy groups of spheres. We relate the Goodwillie filtration to the P map, and the Goodwillie differentials to the H map. F...

In the present paper, we introduce some sequence spaces using ideal convergence and Musielak-Orlicz function ℳ = (M(k)). We also examine some topological properties of the resulting sequence spaces.

The purpose of this paper is to propose a compositeiterative scheme for approximating a common solution for a finitefamily of m-accretive operators in a strictly convex Banach spacehaving a uniformly Gateaux differentiable norm. As a consequence,the strong convergence of the scheme for a common fixed point ofa finite family of pseudocontractive mappings is also obtained.

The aim of this paper is to extend the truth value table oflattice-valued convergence spaces to a more general case andthen to use it to introduce and study the quantale-valued fuzzy Scotttopology in fuzzy domain theory. Let $(L,*,varepsilon)$ be acommutative unital quantale and let $otimes$ be a binary operationon $L$ which is distributive over nonempty subsets. The quadruple$(L,*,otimes,varep...