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Articles 1 - 8 of 8
Full-Text Articles in Other Mathematics
Research On Fractal Mathematics And Some Application In Mechanics, Yang Xiaojun
Research On Fractal Mathematics And Some Application In Mechanics, Yang Xiaojun
Xiao-Jun Yang
Since Mandelbrot proposed the concept of fractal in 1970s’, fractal has been applied in various areas such as science, economics, cultures and arts because of the universality of fractal phenomena. It provides a new analytical tool to reveal the complexity of the real world. Nowadays the calculus in a fractal space becomes a hot topic in the world. Based on the established definitions of fractal derivative and fractal integral, the fundamental theorems of fractal derivatives and fractal integrals are investigated in detail. The fractal double integral and fractal triple integral are discussed and the variational principle in fractal space has …
The Logic Of Bailout Strategies, Rudolf Kaehr
The Logic Of Bailout Strategies, Rudolf Kaehr
Rudolf Kaehr
Some thoughts about/of the logic, blend, chiasm and diamond of bailout strategies. Eliciting aspects of the maxim: “Without insurrection, no resurrection".
Diamond Semiotic Short Studies, Rudolf Kaehr
Diamond Semiotic Short Studies, Rudolf Kaehr
Rudolf Kaehr
A collection of papers on semiotics, polycontexturality and diamond theory
The Fundamentals Of Local Fractional Derivative Of The One-Variable Non-Differentiable Functions, Yang Xiaojun
The Fundamentals Of Local Fractional Derivative Of The One-Variable Non-Differentiable Functions, Yang Xiaojun
Xiao-Jun Yang
Based on the theory of Jumarie’s fractional calculus, local fractional derivative is modified in detail and its fundamentals of local fractional derivative are proposed in this paper. The uniqueness of local fractional derivative is obtained and the Rolle’s theorem, the mean value theorem, the Cauchy’s generalized mean value theorem and the L’Hospital’s rules are proved.
Local Fractional Newton’S Method Derived From Modified Local Fractional Calculus, Yang Xiao-Jun
Local Fractional Newton’S Method Derived From Modified Local Fractional Calculus, Yang Xiao-Jun
Xiao-Jun Yang
A local fractional Newton’s method, which is derived from the modified local fractional calculus , is proposed in the present paper. Its iterative function is obtained and the convergence of the iterative function is discussed. The comparison between the classical Newton iteration and the local fractional Newton iteration has been carried out. It is shown that the iterative value of the local fractional Newton method better approximates the real-value than that of the classical one.
Equational Coalgebraic Logic, Alexander Kurz, Raul Leal
Equational Coalgebraic Logic, Alexander Kurz, Raul Leal
Engineering Faculty Articles and Research
Coalgebra develops a general theory of transition systems, parametric in a functor T; the functor T specifies the possible one-step behaviours of the system. A fundamental question in this area is how to obtain, for an arbitrary functor T, a logic for T-coalgebras. We compare two existing proposals, Moss’s coalgebraic logic and the logic of all predicate liftings, by providing one-step translations between them, extending the results in [21] by making systematic use of Stone duality. Our main contribution then is a novel coalgebraic logic, which can be seen as an equational axiomatization of Moss’s logic. The three logics are …
Problems Of Local Fractional Definite Integral Of The One-Variable Non-Differentiable Function, Yang Xiao-Jun
Problems Of Local Fractional Definite Integral Of The One-Variable Non-Differentiable Function, Yang Xiao-Jun
Xiao-Jun Yang
It is proposed that local fractional calculas introduced by Kolwankar and Gangal is extended by the concept of Jumarie’s fractional calculus and local fractional definite integral is redefined. The properties and the theorems of local fractional calculus are discussed in this paper.
Diamond Theory Collections. A Collection Of Papers And Fragments Towards Diamond Theory 2007-2009, Rudolf Kaehr
Diamond Theory Collections. A Collection Of Papers And Fragments Towards Diamond Theory 2007-2009, Rudolf Kaehr
Rudolf Kaehr
No abstract provided.