This paper presents a transformational approach for the derivation of asynchronous parallel programs. Transformation rules are based on a theory, called Pei. This theory includes the deenitions of problems , programs and transformation rules. It is founded on the simple mathematical concepts of multiset and of an equivalence between their representations as data elds. Program transformations ar...

A simple and deep standard mathematical theorem asserts the existence, for any oneparameter differentiable group, of an additive parameter, such as the angle for rotations and the rapidity parameter for Lorentz transformations. The importance of this theorem for the applications of group theory in physics is stressed, and an elementary proof is given. The theorem then is applied to the construc...

Due to the variety of shapes and sizes that present both living organisms and static objects, the necessity to look for automated systems of identification, both in industry and scientific research has arisen. During the 1960s, the scientific community in the field of optics has used the Fourier transform and other types of mathematical transformations for pattern recognition, taking advantage ...

Conservation laws, i.e. conserved quantities along Euler–Lagrange extremals, which are obtained on the basis of Noether’s theorem, play an prominent role in mathematical analysis and physical applications. In this paper we present a general and constructive method to obtain conserved quantities along the Pontryagin extremals of optimal control problems, which are invariant under a family of tra...

We study the notion of twisted bundles on noncommutative space. Due to the existence of projective operators in the algebra of functions on the noncommutative space, there are twisted bundles with non-constant dimension. The U(1) instanton solution of Nekrasov and Schwarz is such an example. As a mathematical motivation for not excluding such bundles, we find gauge transformations by which a bu...

An algorithm for identifying parameters in dynamical systems is developed in this work using homotopy transformations and the single-shooting method. The equations governing the dynamics of the mathematical model are augmented with observer-like homotopy terms that smooth the objective function. As a result, premature convergence to a local minimum is avoided and the obtained parameter estimate...

In this paper, nonlocal mathematical morphology operators are introduced as a natural extension of nonlocal-means in the max-plus algebra. Firstly, we show that nonlocal morphology is a particular case of adaptive morphology. Secondly, we present the necessary properties to have algebraic properties on the associated pair of transformations. Finally, we recommend a sparse version to introduce a...

The work is devoted to the investigation of the key concepts of mathematical theory of pattern recognition: image equivalence and invariance. Different ways to determine equivalence on the image set are considered and relations between image equivalence and invariance are analyzed. It is proved that the image recognition task in standard formulation can be reduced to the task that has a correct...

We give a review of infinite-dimensional Lie groups and algebras and show some applications and examples in mathematical physics. This includes diffeomorphism groups and their natural subgroups like volume-preserving and symplectic transformations, as well as gauge groups and loop groups. Applications include fluid dynamics, Maxwell’s equations, and plasma physics. We discuss applications in qu...

The body core temperatures of 31 patients suffering from severe cerebral lesions were measured. Evidence for the existence or nonexistence of circadian rhythms in these patients was found to be associated with diagnosis (acute versus chronic lesions), with the level of consciousness, and with neurological findings (such as best motor response and pupillary reaction), but not with heart rate, co...