We present an updated cosmic-ray mass composition analysis in the energy range $10^{16.8}$ to $10^{18.3}$ eV from 334 air showers measured with LOFAR radio telescope, and selected for minimal bias. In this range, origin of cosmic rays is expected shift galactic extragalactic sources. The based on improved method infer depth maximum $X_{\rm max}$ extensive measurements shower simulations. show r...

The polyadic algebras that arise from the algebraization of the first-order extensions of a SIC are characterized and a representation theorem is proved. Standard implicational calculi (SIC)’s were considered by H. Rasiowa [19] and include classical and intuitionistic logic and their various weakenings and fragments, the many-valued logics of Post and Lukasiewicz, modal logics that admit the ru...

The aim of this paper is to explore the class of intermediate logics between the truth-preserving Lukasiewicz logic L and its degree-preserving companion L≤. From a syntactical point of view, we introduce some families of inference rules (that generalize the explosion rule) that are admissible in L≤ and derivable in L and we characterize the corresponding intermediate logics. From a semantical ...

In this paper, we propose extensions of affine classical linear algebra(ACL-algebra) and many-valued algebra(MV-algebra), the emphasis is being on the latter. MV-algebras are algebraic models of à Lukasiewicz א0-valued logic(à Lא0) and that was established long back in 1958 by C.C. Chang. MV-algebra is recently studied from the angle of fuzzy set theory. Also it is investigated in connection wi...

Prolog is a programming language based on a restricted subset of classical rst order predicate logic. In order to overcome some problems of classical logic to handle imperfect human knowledge, we provide a formal framework for a Lukasiewicz logic based Prolog system. The use of Lukasiewicz logic with its connection to Ulam games enables us to deal with partial inconsistencies by interpreting th...

We study a family of polynomials in two variables, identifying them as the moments of a two-parameter family of orthogonal polynomials. The coefficient array of these orthogonal polynomials is shown to be an ordinary Riordan array. We express the generating function of the sequence of polynomials under study as a continued fraction, and determine the corresponding Hankel transform. An alternati...

Picture fuzzy relation is an important and powerful concept which suitable for describing correspondences between objects. It represents the strength of association elements picture sets. In this paper we have defined min-max composition relations some properties are explored based on definition. Also discussed max-min relations. Finally, application as illustration to show how applied in decis...

The paper presents an elementary approach for the calculation of the entropy of a class of languages. This approach is based on the consideration of roots of a real polynomial and is also suitable for calculating the Bernoulli measure. The class of languages we consider here is a generalisation of the Lukasiewicz language. Mathematics Subject Classification. 68Q30, 68Q45, 94A17.