This paper is the first of a two part series. In this paper, we first prove that the variety of dually quasi-De Morgan Stone semi-Heyting algebras of level 1 satisfies the strongly blended $lor$-De Morgan law introduced in cite{Sa12}. Then, using this result and the results of cite{Sa12}, we prove our main result which gives an explicit description of simple algebras(=subdirectly irreducibles) ...

The aim of this paper is to introduce the notion of commutative pseudo BE-algebras and investigate their properties.We generalize some results proved by A. Walendziak for the case of commutative BE-algebras.We prove that the class of commutative pseudo BE-algebras is equivalent to the class of commutative pseudo BCK-algebras. Based on this result, all results holding for commutative pseudo BCK-...

The chapter represents a comparison of ultrapower fields (loosely surreals, hyper-reals, long line) and number fields generated by infinite primes having a physical interpretation in Topological Geometrodynamics. Ultrapower fields are discussed in very physicist friendly manner in the articles of Elemer Rosinger and these articles are taken as a convenient starting point. The physical interpret...

The paper mostly concerns the study of generalized differential properties of the so-called minimal time functions associated, in particular, with constant dynamics and arbitrary closed target sets in control theory. Functions of this type play a significant role in many aspects of optimization, control theory: and Hamilton-Jacobi partial differential equations. We pay the main attention to com...

We propose a method for learning skills by learning kinesthetic skills via trajectory optimization. We recreate demonstrations by optimizing the trajectory to be near the demonstration. We use the trajectory optimizer, TrajOpt to turn distance metrics, the Frechet and Hausdorff distances, into cost functions that penalize a trajectory from deviating from the demonstration. Using a few technique...

"In this paper we investigate the existence of solutions initial value problems (IVP for short), partial hyperbolic functional and neutral differential inclusions fractional order involving Caputo derivative with finite delay by using nonlinear alternative Frigon type multivalued admissible contraction in Frechet spaces."

This paper presents Stieltjes-type integration for operator-valued functions with respect to spectral families. The relation between RiemannStieltjes integrals associated with some classes of spectral families including, in particular, those that arise in the context of the Stone representation theorem for Banach spaces is established. The developed approach is applied to the structural analysi...

In this note we provide a topological description of the MacNeille completion of a Heyting algebra similar to the description of the MacNeille completion of a Boolean algebra in terms of regular open sets of its Stone space. We also show that the only varieties of Heyting algebras that are closed under MacNeille completions are the trivial variety, the variety of all Boolean algebras, and the v...

We give an example of a countable theory T such that for every cardinal λ ≥ א2 there is a fully indiscernible set A of power λ such that the principal types are dense over A, yet there is no atomic model of T over A. In particular, T (A) is a theory of size λ where the principal types are dense, yet T (A) has no atomic model. If a complete theory T has an atomic model then the principal types a...

A study is made of Boolean product representations of bounded lattices over the Stone space of their centres. Special emphasis is placed on relating topological properties such as clopen or regular open equalizers to their equivalent lattice theoretic counterparts. Results are also presented connecting various properties of a lattice with properties of its individual stalks. Mathematics Subject...