The Koch snowflake is one of the first fractals that were mathematically described. It is interesting because it has an infinite perimeter in the limit but its limit area is finite. In this paper, a recently proposed computational methodology allowing one to execute numerical computations with infinities and infinitesimals is applied to study the Koch snowflake at infinity. Numerical computatio...

Corresponding Author: Joseph Gladwin Sekar Department of ECE, SSN College of Engineering, Kalavakkam, India Email: [email protected] Abstract: This paper, deals with H-infinity channel estimation technique for Orthogonal Frequency Division Multiplexing (OFDM) systems, in fading channel. Channel estimation is important for wireless applications because, in practical transmission scenario, chann...

In this paper the Hochschild-cochain-complex of an A∞-algebra A with values in an A∞-bimodule M over A and maps between them is defined. Then, an∞-inner-product on A is defined to be an A∞-bimodule-map between A and its dual A∗. There is a graph-complex associated to A∞-algebras with ∞-inner-product.

This paper describes the use of a genetic search method in the design of a command augmentation system for a high-performance aircraft. A genetic algorithm is used to design H-infinity controllers for the longitudinal and lateral-directional channels. The integral of absolute value of error between actual response and that of an ideal model is used as the fitness criterion. Starting from an ini...

An actual infinity of colliding balls can be in a configuration in which the laws of mechanics lead to logical inconsistency. It is argued that one should therefore limit the domain of these laws to a finite, or only a potentially infinite number of elements. With this restriction indeterminism, energy nonconservation and creatio ex nihilo no longer occur. A numerical analysis of finite systems...

This article discusses Georg Cantor’s philosophical defence of the existence of actual infinities in mathematics. The metaphysical background to Cantor’s argument is documented, emphasizing the philosophical references in Cantor’s main work, Grundlagen (1883). Cantor’s engagement with the history of philosophy, particularly the writings of Spinoza and Leibniz on infinity, is also documented. Fi...

We calculate the mean fitness for evolution models, when the fitness is a function of the Hamming distance from a reference sequence, and there is a probability that this fitness is nullified (Eigen model case) or tends to the negative infinity (Crow-Kimura model case). We calculate the mean fitness of these models. The mean fitness is calculated also for the random fitnesses with logarithmic-n...