In this paper we consider admissible domain representations of topological spaces. A domain representation D of a space X is λ-admissible if, in principle, all other λ-based domain representations E of X can be reduced to D via a continuous function from E to D. We present a characterisation theorem of when a topological space has a λ-admissible and κ-based domain representation. We also prove ...

Consider non-negative lattice paths ending at their maximum height, which will be called admissible paths. We show that the probability for a lattice path to be admissible is related to the Chebyshev polynomials of the first or second kind, depending on whether the lattice path is defined with a reflective barrier or not. Parameters like the number of admissible paths with given length or the e...

In this note further clue decisive observations on cobweb admissible sequences are shared with the audience. In particular an announced proof of the Theorem 1 (by Dziemia´nczuk) from [1] announced in India-Kolkata-December 2007 is delivered here. Namely here and there we claim that any cobweb admissible sequence F is at the point product of primary cobweb admissible sequences taking values one ...

Finding a pivot rule for the simplex method that is strongly polynomial is an open question. In fact, the shortest length of simplex pivots from any feasible basis to some optimal basis is not known to be polynomially bounded. An admissible pivot is a common generalization of simplex and dual simplex pivots, and there are various admissible pivot methods that are nite, including the least-index...

Let P d n be the the space of real algebraic polynomials of d variables and degree at most n, K ⊂ R a compact set, ||p||K := supx∈K |p(x)| the usual supremum norm on K, card(Y ) the cardinality of a finite set Y . A family of sets Y = {Yn ⊂ K, n ∈ N} is called an admissible mesh in K if there exists a constant c1 > 0 depending only on K such that ||p||K ≤ c1||p||Yn , p ∈ P d n , n ∈ N, where th...

This paper shows that the problem of control under linear symmetrical input constraints of linear stabilizable systems can always be solved by restricting the set of admissible initial states to a polyhedral domain of the state space. This result can be obtained by an appropriate closed-loop eigenstructure assignment. Two subsequent problems are then addressed: the maximal size of the domain of...

In this paper, we study the notion of admissibility for randomised strategies in concurrent games. Intuitively, an admissible strategy is one where the player plays ‘as well as possible’, because there is no other strategy that dominates it, i.e., that wins (almost surely) against a superset of adversarial strategies. We prove that admissible strategies always exist in concurrent games, and we ...

In the present study, natural convective heat transfer in a partitioned square cavity utilizing nanofluids is studied. The vertical left and right walls are considered as the hot and cold walls, respectively and the partitions assumed to be adiabatic. The nanofluid used in this study is Al2O3 with the volume fraction of 20%. It is assumed that nanofluid is a single phase f...