Journal•ISSN: 0971-8044

# Resonance

Springer Science+Business Media

About: Resonance is an academic journal published by Springer Science+Business Media. The journal publishes majorly in the area(s): Science education & Earthquake engineering. It has an ISSN identifier of 0971-8044. Over the lifetime, 2290 publications have been published receiving 27123 citations. The journal is also known as: Resonance.

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TL;DR: In this article, a language similar to logo is used to draw geometric pictures using this language and programs are developed to draw geometrical pictures using it, which is similar to the one we use in this paper.

Abstract: The primary purpose of a programming language is to assist the programmer in the practice of her art. Each language is either designed for a class of problems or supports a different style of programming. In other words, a programming language turns the computer into a ‘virtual machine’ whose features and capabilities are unlimited. In this article, we illustrate these aspects through a language similar tologo. Programs are developed to draw geometric pictures using this language.

5,749 citations

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TL;DR: A minimum-redundancy code is one constructed in such a way that the average number of coding digits per message is minimized.

Abstract: An optimum method of coding an ensemble of messages consisting of a finite number of members is developed. A minimum-redundancy code is one constructed in such a way that the average number of coding digits per message is minimized.

3,528 citations

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TL;DR: Narasimhan as discussed by the authors showed that the ground state energy of a very general and nontrivial system was the result of minimising an expression that only contained a function of three variables.

Abstract: Shobhana Narasimhan’s article ‘A Tryst With Density’ in this issue of Resonance describes a remarkable
theorem proved by Hohenberg and Kohn in 1964, and its aftermath. These authors considered a system of
electrons in an external potential. This is an excellent idealised model of an atom, molecule or solid because
the nuclei are so much heavier than the electrons and can be treated as an external potential. The difficulty
lies in accounting for the interaction between the electrons – what one electron is doing depends on what
all the others are doing. It therefore came as a shock when the ground state energy of this very general
and nontrivial system was shown by Hohenberg and Kohn to be the result of minimising an expression
which only contained a function of three variables. This function was just the number of electrons per unit
volume as a function of position, something which chemists and crystallographers had long dealt with as a
very meaningful and measurable quantity. The theorem showed that such an expression exists, but did not
provide the form, which could contain nonlinear terms, derivatives, and integrals of the electron density.
While approximate theories of this kind had been proposed before, it was unexpected that the idea of using
the electron density could be made exact. What a marvellous turn of events that an existence theorem,
proved by contradiction in a modestly written paper would revolutionise the modeling of materials half a
century later and win a Nobel Prize in Chemistry for one of the authors!

1,288 citations

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TL;DR: The theory of chemical processes is based on theoretical physics as mentioned in this paper, and physics supplies the foundation of chemistry, and the biological example of writing information on a small scale has inspired to think of something that should be possible.

Abstract: The theory of chemical processes is based on theoretical physics. In this sense, physics supplies the foundation of chemistry. The biological example of writing information on a small scale has inspired to think of something that should be possible. Suppose, to be conservative, that a bit of information is going to require a little cube of atoms 5 times 5 times 5 – that is 125 atoms. The magnetic properties on a very small scale are not the same as on a large scale; there is the "domain" problem involved. The electron microscope is not quite good enough, with the greatest care and effort, it can only resolve about 10 angstroms. The wave length of the electron in such a microscope is only 1/20 of an angstrom. Atoms on a small scale behave like nothing on a large scale, for they satisfy the laws of quantum mechanics.

925 citations