Parabolic geometries may be considered as curved analogues of the homogeneous spaces G/P where G is a semisimple Lie group and P ⊂ G a parabolic subgroup. Conformal geometries and CR geometries are examples of such structures. We present a uniform description of a calculus, called tractor calculus, based on natural bundles with canonical linear connections for all parabolic geometries. It is sh...

The current paper recovers dispersive optical solitons in birefringent fibers that are modeled by the Schrödinger–Hirota equation with differential group delay and white noise. Itô Calculus conducts preliminary analysis. G′/G-expansion approach enhanced Kudryashov’s scheme gave way to a wide spectrum of soliton solutions noise component reflected phase soliton.

Propositional Gödel logic G extends intuitionistic logic with the non-constructive principle of linearity (A→ B) ∨ (B → A). We introduce a Curry–Howard correspondence for G and show that a simple natural deduction calculus can be used as a typing system. The resulting functional language extends the simply typed λ-calculus via a synchronous communication mechanism between parallel processes, wh...

Finite Fibonomial Operator Calculus (FFOC) is a special case of Extented Finite Operator Calculus (FOC). The ”Calculus of Sequences” was started by Ward in 1936 [1] and considered by many authors after him. The very foundations of FOC were given by O.V.Viskov, G. Markowsky and finally by the author of [8, 2, 3] . The idea of FFOC due to A.K.Kwaśniewski [2] (see Example 2.1) is now continued [4]...

We define a noncommutative differential calculus constructed from the inner derivation, then several relevant examples are showed. It is of interest to note that for certain C∗-algebra, this calculus is closely related to the classical one when the algebra associates a deformation parameter. Introduction Noncommutative geometry is developed by Alain Connes. In his work [8], the cyclic cohomolog...

although there are many excellent ways presenting the principle of the classical calculus, the novel presentations probably leads most naturally to the development of the non-newtonian calculus. the important point to note is that the non-newtonian calculus is a self-contained system independent of any other system of calculus. since this self-contained work is intended for a wide audience, inc...

Our broader goal is to automatically translate English sentences into formulas in appropriate knowledge representation languages as a step towards understanding and thus answering questions with respect to English text. Our focus in this paper is on the language of Answer Set Programming (ASP). Our approach to translate sentences to ASP rules is inspired by Montague’s use of lambda calculus for...

Our broader goal is to automatically translate English sentences into formulas in appropriate knowledge representation languages as a step towards understanding and thus answering questions with respect to English text. Our focus in this paper is on the language of Answer Set Programming (ASP). Our approach to translate sentences to ASP rules is inspired by Montague’s use of lambda calculus for...

The bicovariant differential calculi on quantum groups of Woronowicz have the drawback that their dimensions do not agree with that of the corresponding classical calculus. In this paper we discuss the first-order differential calculus which arises from a simple quantum Lie algebra lh(g). This calculus has the correct dimension and is shown to be bicovariant and complete. But it does not satisf...