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A new approach for fuzzy gyronorms on gyrogroups and its fuzzy topologies

Yu Shen, Conghua Yan (2024)

Kybernetika

In this paper, a new approach for fuzzy gyronorms on gyrogroups is presented. The relations between fuzzy metrics(in the sense of Morsi), fuzzy gyronorms, gyronorms on gyrogroups are studied. Also, some sufficient conditions, which can make a fuzzy normed gyrogroup to be a topological gyrogroup and a fuzzy topological gyrogroup, are found. Meanwhile, the relations between topological gyrogroups, fuzzy topological gyrogroups and stratified fuzzy topological gyrogroups are studied. Finally, the properties...

A new approach to generalized chaos synchronization based on the stability of the error system

Zhi Liang Zhu, Shuping Li, Hai Yu (2008)

Kybernetika

With a chaotic system being divided into linear and nonlinear parts, a new approach is presented to realize generalized chaos synchronization by using feedback control and parameter commutation. Based on a linear transformation, the problem of generalized synchronization (GS) is transformed into the stability problem of the synchronous error system, and an existence condition for GS is derived. Furthermore, the performance of GS can be improved according to the configuration of the GS velocity....

A new class of almost complex structures on tangent bundle of a Riemannian manifold

Amir Baghban, Esmaeil Abedi (2018)

Communications in Mathematics

In this paper, the standard almost complex structure on the tangent bunle of a Riemannian manifold will be generalized. We will generalize the standard one to the new ones such that the induced ( 0 , 2 ) -tensor on the tangent bundle using these structures and Liouville 1 -form will be a Riemannian metric. Moreover, under the integrability condition, the curvature operator of the base manifold will be classified.

A new infinite order formulation of variational sequences

Raffaele Vitolo (1998)

Archivum Mathematicum

The theory of variational bicomplexes is a natural geometrical setting for the calculus of variations on a fibred manifold. It is a well–established theory although not spread out very much among theoretical and mathematical physicists. Here, we present a new approach to infinite order variational bicomplexes based upon the finite order approach due to Krupka. In this approach the information related to the order of jets is lost, but we have a considerable simplification both in the exposition...

A new Lagrangian dynamic reduction in field theory

François Gay-Balmaz, Tudor S. Ratiu (2010)

Annales de l’institut Fourier

For symmetric classical field theories on principal bundles there are two methods of symmetry reduction: covariant and dynamic. Assume that the classical field theory is given by a symmetric covariant Lagrangian density defined on the first jet bundle of a principal bundle. It is shown that covariant and dynamic reduction lead to equivalent equations of motion. This is achieved by constructing a new Lagrangian defined on an infinite dimensional space which turns out to be gauge group invariant.

A new numerical model for propagation of tsunami waves

Karel Švadlenka (2007)

Kybernetika

A new model for propagation of long waves including the coastal area is introduced. This model considers only the motion of the surface of the sea under the condition of preservation of mass and the sea floor is inserted into the model as an obstacle to the motion. Thus we obtain a constrained hyperbolic free-boundary problem which is then solved numerically by a minimizing method called the discrete Morse semi-flow. The results of the computation in 1D show the adequacy of the proposed model.

A new proof of Fréchet differentiability of Lipschitz functions

Joram Lindenstrauss, David Preiss (2000)

Journal of the European Mathematical Society

We give a relatively simple (self-contained) proof that every real-valued Lipschitz function on ℓ 2 (or more generally on an Asplund space) has points of Fréchet differentiability. Somewhat more generally, we show that a real-valued Lipschitz function on a separable Banach space has points of Fréchet differentiability provided that the w * closure of the set of its points of Gâteaux differentiability is norm separable.

A new Taylor type formula and C ∞ extensions for asymptotically developable functions

M. Zurro (1997)

Studia Mathematica

The paper studies the relation between asymptotically developable functions in several complex variables and their extensions as functions of real variables. A new Taylor type formula with integral remainder in several variables is an essential tool. We prove that strongly asymptotically developable functions defined on polysectors have C ∞ extensions from any subpolysector; the Gevrey case is included.

A nilpotent Lie algebra and eigenvalue estimates

Jacek Dziubański, Andrzej Hulanicki, Joe Jenkins (1995)

Colloquium Mathematicae

The aim of this paper is to demonstrate how a fairly simple nilpotent Lie algebra can be used as a tool to study differential operators on ℝ n with polynomial coefficients, especially when the property studied depends only on the degree of the polynomials involved and/or the number of variables.

A noncommutative 2-sphere generated by the quantum complex plane

Ismael Cohen, Elmar Wagner (2012)

Banach Center Publications

S. L. Woronowicz's theory of C*-algebras generated by unbounded elements is applied to q-normal operators satisfying the defining relation of the quantum complex plane. The unique non-degenerate C*-algebra of bounded operators generated by a q-normal operator is computed and an abstract description is given by using crossed product algebras. If the spectrum of the modulus of the q-normal operator is the positive half line, this C*-algebra will be considered as the algebra of continuous functions...

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