Related papers: Boole's Method I. A Modern Version

We study the explicit formula of Euler numbers and polynomials of higher order

In this paper, we consider the q-extensions of Boole polynomials. From those polynomials, we derive some new and interesting properties and identities related to special polynomials.

In this paper we give two theorems from the Propositional Calculus of the Boolean Logic with their consequences and applications and we prove them axiomatically.

Following an idea due to Euler, we evaluate the alternating sums of powers of consrcutive integers.

In this paper, the author gives two methods to construct complete Lie algebras. Both methods show that the derivation algebras of some Lie algebras are complete.

We discuss the notion of reduction of a special type of explicit solutions which generalize the solutions appearing in the classical Laplace cascade method of integration of hyperbolic equations of the second order in the plane. We give…

This paper from 2000 is a presentation of a status qu{\ae}stionis at that tiime, to wit of the problem of the interpretability logic of {\em all}\/ reasonable arithmetical theories. We present both the arithmetical side and the modal side…

Methods of solving big Boolean equations can be broadly classified as algebraic, tabular, numerical and map methods. The most prominent among these classes are the algebraic and map methods. This paper surveys and compares these two types…

We show a model construction for a system of higher-order illative combinatory logic $\mathcal{I}_\omega$, thus establishing its strong consistency. We also use a variant of this construction to provide a complete embedding of first-order…

The aim of this work is to develop a study from the perspective of Abstract Algebraic Logic of some bilattice-based logical systems introduced in the nineties by Ofer Arieli and Arnon Avron. The motivation for such an investigation has two…

In this paper we consider a class of Burgers equation. We propose a new method of investigation for existence of classical solutions.

In the present paper we introduce a new methodology for the construction of numerical methods for the approximate solution of the one-dimensional Schr\"odinger equation. The new methodology is based on the requirement of vanishing the…

A class of generalized Schr\"{o}dinger problems in bounded domain is studied. A complete overview of the set of solutions is provided, depending on the values assumed by parameters involved in the problem. In order to obtain the results, we…

The probability axioms by R. T. Cox can be regarded as the modern foundations of Bayesian inference, the idea of assigning degrees of belief to logical propositions in a manner consistent with Boolean logic. In this work it is shown that…

We describe three methods to determine the structure of (sufficiently continuous) representations of the algebra B^a(E) of all adjointable operators on a Hilbert B-module E by operators on a Hilbert C-module. While the last and latest proof…

We introduce higher order polynomial deformations of $A_1$ Lie algebra. We construct their unitary representations and the corresponding single-variable differential operator realizations. We then use the results to obtain exact (Bethe…

Some of the conclusions of an improved JWKB method by Eleuch H., Rostovtsev Y. V. and Scully M. O., EPL, 89 (2010) 50004 are clarified. The degree of approximation to exact solutions is quantitatively assessed. The improved JWKB method is…

In this paper we considered the extension of the First-order Logic (FOL) by Bealer's intensional abstraction operator. Contemporary use of the term 'intension' derives from the traditional logical Frege-Russell's doctrine that an idea…

Logic has pride of place in mathematics and its 20th century offshoot, computer science. Modern symbolic logic was developed, in part, as a way to provide a formal framework for mathematics: Frege, Peano, Whitehead and Russell, as well as…

We propose a novel discretization procedure for the classical Euler equation based on the theory of Galois differential algebras and the finite operator calculus developed by G.C. Rota and collaborators. This procedure allows us to define…