We propose a new approach for minimizing alternating Büchi automata (ABA). The approach is based on the so called mediated equivalence on states of ABA, which is the maximal equivalence contained in the so called mediated preorder. Two states p and q can be related by the mediated preorder if there is a mediator (mediating state) which forward simulates p and backward simulates q. Under some fu...

It is proved that the forcing apparatus can be built and set to work in ZFCA (=ZFC minus foundation plus the antifoundation axiom AFA). The key tools for this construction are greatest fixed points of continuous operators (a method sometimes referred to as “corecursion”). As an application it is shown that the generic extensions of standard models of ZFCA are models of ZFCA again.

in order to study the effects of intercropping on yield of black cumin in intercropping with chickpea and bean, an experiment was conducted in a complete randomized block design with four replications. crops were planted as pure stands and intercrops in three arrangements: a) alternating rows of a field crop and a medicinal plant, b) two rows of field crops and one row of medicinal plant, c) al...

We introduce a pure type system (PTS) λZ with four sorts and show that this PTS captures the proof-theoretic strength of Zermelo’s set theory. For that, we show that the embedding of the language of set theory into λZ via the ‘sets as pointed graphs’ translation makes λZ a conservative extension of IZ + AFA + TC (intuitionistic Zermelo’s set theory plus Aczel’s antifoundation axiom plus the axi...

Let T be an arbitrary n × n matrix with real entries. We consider the set of all matrices with a given complex number as an eigenvalue, as well as being given the corresponding left and right eigenvectors. We find the closest matrix A, in Frobenius norm, in this set to the matrix T . The normal cone to a matrix in this set is also obtained. We then investigate the problem of determining the clo...

let $gamma(s_n)$ be the minimum number of proper subgroups‎ ‎$h_i, i=1‎, ‎dots‎, ‎l $ of the symmetric group $s_n$ such that each element in $s_n$‎ ‎lies in some conjugate of one of the $h_i.$ in this paper we‎ ‎conjecture that $$gamma(s_n)=frac{n}{2}left(1-frac{1}{p_1}right)‎ ‎left(1-frac{1}{p_2}right)+2,$$ where $p_1,p_2$ are the two smallest primes‎ ‎in the factorization of $ninmathbb{n}$ an...

In this paper we consider an application of the theory of non–wellfounded sets to the modelling of epistemic updates triggered by assertions in dialogue. We concentrate mainly on what we might call defective dialogue, i.e. dialogue in epistemic contexts where the speaker has either erroneous beliefs or is not sincere in his language use. We develop our theory within a special possible worlds fr...

This paper develops an approach for solving convex feasibility problems where the constraints are given by the intersection of two convex cones in a Hilbert space. An extension to the feasibility problem for the intersection of two convex sets is presented as well. It is shown that one can solve such problems in a finite number of steps and an explicit upper bound for the required number of ste...

This paper considers the relaxed Peaceman-Rachford (PR) splitting method for finding an approximate solution of a monotone inclusion whose underlying operator consists of the sum of two maximal strongly monotone operators. Using general results obtained in the setting of a non-Euclidean hybrid proximal extragradient framework, convergence of the iterates, as well as pointwise and ergodic conver...