a generalization of schauder basis associated with the concept of generalized analytic functions is introduced. corresponding concepts of density, completeness, biorthogonality and basicity are defined. also, corresponding concept of the space of coefficients is introduced. under certain conditions for the  corresponding operators, some properties of the space of coefficients and basicity crite...

A generalization of Schauder basis associated with the concept of generalized analytic functions is introduced. Corresponding concepts of density, completeness, biorthogonality and basicity are defined. Also, corresponding concept of the space of coefficients is introduced. Under certain conditions for the  corresponding operators, some properties of the space of coefficients and basicity crite...

Given a static Schwarzschild spacetime of ADM mass M , it is wellknown that no ingoing causal geodesic starting in the outer domain r > 2M will cross the event horizon r = 2M in finite Schwarzschild time. In the present paper we show that in gravitational collapse of Vlasov matter this behaviour can be very different. We construct initial data for which a black hole forms and all matter crosses...

In this paper, we give a kind of Cauchy 1-completeness in probabilistic quasi-uniform spaces by using 1-filters. Utilizingthe relationships among probabilistic quasi-uniformities, classical quasi-uniformities and Hutton [0, 1]-quasi-uniformities,we show the relationships between their completeness. In fuzzy quasi-metric spaces, we establish the relationshipsbetween the completeness of induced p...

Propositional dynamic logic (PDL) is complete but not compact. As a consequence, strong completeness (the property j= ' ) ` ') does not hold for the standard nitary axiomatisation. In this paper, we present an in nitary proof system of PDL and prove strong completeness. The result is extended to epistemic logic with common knowledge.

We introduce a new formal logic, called equality propositional logic. It has two basic connectives, $boldsymbol{wedge}$ (conjunction) and $equiv$ (equivalence). Moreover, the $Rightarrow$ (implication) connective can be derived as $ARightarrow B:=(Aboldsymbol{wedge}B)equiv A$. We formulate the equality propositional logic and demonstrate that the resulting logic has reasonable properties such a...

Today, great observatories around the world, devote a substantial amount of observing time to sky surveys. The resulted images are inputs of source finder modules. These modules search for the target objects and provide us with source catalogues. We sought to quantify the ability of detection tools in recovering faint galaxies regularly encountered in deep surveys. Our approach was based on com...

Complex classical Cayley-Klein categories A(j), B(j), C(j) and D(j) are constructed by the method of categorical extension of the complex classical Cayley-Klein groups SL(2n; j;C), SO(2n + 1; j;C), Sp(2n; j;C) and SO(2n; j;C), respectively. The explicit construction of the irreducible representations of the complex classical Cayley-Klein categories is received. Completeness of lists of the irre...

The main text for the course is: Computational Complexity. Christos H. Papadimitriou. Introduction to the Theory of Computation. Michael Sipser. Other useful references include: Computers and Intractability: A guide to the theory of NP-completeness. Michael R. Garey and David S. Johnson. Structural Complexity. Vols I and II. J.L. Balcázar, J. Dı́az and J. Gabarró. Computability and Complexity fr...