(PDF) Formulae | Kapil Kothandapani

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Abstract

Useful Formulae

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Mathematical Formulae in Wikimedia Projects 2020André Greiner-Petter

Proceedings of the ACM/IEEE Joint Conference on Digital Libraries in 2020, 2020

This poster summarizes our contributions to Wikimedia's processing pipeline for mathematical formulae. We describe how we have supported the transition from rendering formulae as course-grained PNG images in 2001 to providing modern semantically enriched language-independent MathML formulae in 2020. Additionally, we describe our plans to improve the accessibility and discoverability of mathematical knowledge in Wikimedia projects further.

downloadDownload free PDFView PDFchevron_rightSearching the ACL Anthology with Math Formulas and TextAyush Kumar Shah, Abhisek Dey, Matt Langsenkamp

Proceedings of the 46th International ACM SIGIR Conference on Research and Development in Information Retrieval

Mathematical notation is a key analytical resource for science and technology. Unfortunately, current math-aware search engines require L A T E X or template palettes to construct formulas, which can be challenging for non-experts. Also, their indexed collections are primarily web pages where formulas are represented explicitly in machine-readable formats (e.g., L A T E X, Presentation MathML). The new MathDeck system searches PDF documents in a portion of the ACL Anthology using both formulas and text, and shows matched words and formulas along with other extracted formulas in-context. In PDF, formulas are not demarcated: a new indexing module extracts formulas using PDF vector graphics information and computer vision techniques. For non-expert users and visual editing, a central design feature of MathDeck's interface is formula 'chips' usable in formula creation, search, reuse, and annotation with titles and descriptions in cards. For experts, L A T E X is supported in the text query box and the visual formula editor. MathDeck is open-source, and our demo is available online. CCS CONCEPTS • Information systems → Search interfaces; Search engine indexing; Content analysis and feature selection; Mathematics retrieval; Structured text search.

downloadDownload free PDFView PDFchevron_rightMethods of Writing Constitutional FormulasNenad Raos

2012

Chemical formulas, as well as any linguistic entity, have to fulfill two basic requirements – expressiveness and economy, i.e. they have to express the maximal meaning with minimal means. Besides, chemical formula, being a scientific notation, has not to convey vague and scientifically unapproved meanings. This article presents the development of various kinds of chemical formulas and discusses their meaning in the historical context. Special attention is paid to line notation, developed for computers (WLN, SMILES, InChI etc.). We also discuss Seymour B. Elk's “biparametric nomenclature”, based on the concept of 3-simplex, which was claimed to be universally applicable to all classes of compounds.

downloadDownload free PDFView PDFchevron_rightA Preface to FormulaMr Frog

In Formula: Units of Speech – ‘Words’ of Verbal Art: Working Papers of the Seminar-Workshop, 17th–19th May 2017, Helsinki, Finland. Ed. Frog. Folkloristiikan toimite 21. Helsinki: Folklore Studies, University of Helsinki. Pp. 9–19. , 2017

An introduction to the pre-print working papers of the seminar-workshop held in Helsinki in May 2017. Of wider interest may be its short discussion of formulaic language in the section "The Construct of the ‘Poetry’ versus ‘Not Poetry’ Dichotomy". This section may be relevant both to researchers of formulaic language in conversational or prose discourse interested in understanding how this relates to work done on formulaic language in poetry, and vice versa. It may also be of use to scholars interested in using Oral-Formulaic Theory but stumble over Parry's definition of formula as something that occurs "under the same metrical conditions" when studying prose or poetry without a periodic meter.

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arXiv (Cornell University), 1995

Simple derivations of the Heisenberg uncertainty principle and of related inequalities are presented. In addition, the formula is used in an instructive paradox which clarifies a fundamental notion in quantum mechanics.

downloadDownload free PDFView PDFchevron_rightThe Use of Mathematical Formulae in an E-Learning EnvironmentAntoni Pérez-navarro

InTech eBooks, 2012

The Use of Mathematical Formulae in an E-Learning Environment 109 child relationships according to the expression semantics, the mathematical meaning of the combination and information about the expression constants and variables. Translating: In the last step, a recognized expression is produced and translated into a script or a source code suitable for being used in third-party software like TeX or Mathematica. As we stated in Section 1, currently there is not much research into the particular context of a virtual learning environment, regarding the use of the mathematics language. The main communication method in this kind of environment is the use of e-mail, so students have to adapt their communications, including the mathematical notation within them, to this particular communication tool. Next, Section 3 shows how this is carried out by students and teachers and also explains the different available methods.

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Problem Books in Mathematics, 2013

This chapter contains a 56-page-long list of formulae from the calculus on manifolds, and tables concerning different topics: Lie groups, Lie algebras and symmetric spaces, a list of Poincaré polynomials of compact simple Lie groups, an overview of real forms of classical complex simple Lie algebras and their corresponding simple Lie groups, a table of irreducible Riemannian symmetric spaces of type I and III, a table of Riemannian symmetric spaces of classical type with noncompact isotropy group, etc. One can find the formulae for Christoffel symbols, the curvature tensor, Bianchi identities, Ricci tensor, the basic differential operators, the expression for conformal changes of Riemannian metrics, Cartan structure equations for pseudo-Riemannian manifolds, and many more. Several of these formulae are used throughout the book; others are not, but they have been included since such a collection might prove useful as an aide-mémoire, also to lecturers and researchers.

downloadDownload free PDFView PDFchevron_rightSOME USEFUL SHORTCUT FORMULAE IN GEOMETRYKalai Maran

In Geometric, Triangle is one of the two-dimensional plane having three sides and which is very important to solve problems related to Geometry and sometimes in other subject also. Some fundamental concept /theorems of triangles are required to solve such problems and such theorems are (i) Pythagoras 1st theorem[1] (ii) Pythagoras 2nd theorem (iii) Appollonius theorem (iv) Euclid’s 1st theorem[2] and (v) Euclid’s 2nd theorem (Altitude theorem) [3]. In addition to these, Author has attempted to develop a new formula related to triangle. By this theorem the value of ‘d’ in any scalene triangle can be easily evaluated. While doing calculation related to Geometry, sometimes it is required to additional formulae and it needs extra manpower time and complete basic knowledge about fundamental concept and theorems. The author has now derived some new formulas from the basic mathematical concepts and theorems are as follows: 1. Formulae for Scalene Triangle (4 Nos.) 2. Formulae for Right-angled Triangle (2 Nos.) 3. Formulae for Parallelogram (1 No.) These formulae are shown in the mathematical expressions also and these may be used to determine any one of the variables without using any trigonometric functions or formulae such as (i) Sine rule, (ii) Cosine rule, (iii) Pythagoras theorem, (iv) Projection rule and etc., These are in readymade form and these are very useful for those working or engaged with the related subject.

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Lecture Notes in Computer Science, 2014

The purpose of the NIST Digital Repository of Mathematical Formulae (DRMF) is to create a digital compendium of mathematical formulae for orthogonal polynomials and special functions (OPSF) and of associated mathematical data. The DRMF addresses needs of working mathematicians, physicists and engineers: providing a platform for publication and interaction with OPSF formulae on the web. Using MediaWiki extensions and other existing technology (such as software and macro collections developed for the NIST Digital Library of Mathematical Functions), the DRMF acts as an interactive web domain for OPSF formulae. Whereas Wikipedia and other web authoring tools manifest notions or descriptions as first class objects, the DRMF does that with mathematical formulae. See http://gw32.iu.xsede.org/index.php/Main_Page.

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This paper is a continuation of the first paper on drug formularies. It details the various types of formularies, and speculates on the future of formularies as an instrument for improving rational drug therapy.

downloadDownload free PDFView PDFchevron_rightSurvey of Mathematical Formulae RecognitionDaniel Prusa

2005

The goal of this survey is to give a classification of problems the recognition of mathematical formulae focuses on and a taxonomy of methods that are used to accomplish the recognition. Recognition of mathematical formulae can be basically divided into two groups: off-line recognition and on-line recognition. By off-line recognition we mean recognition of scanned formulae. In this case, the input is a picture -a two-dimensional array of pixels. Scanned pictures typically contain printed formulae, but handwritten expressions can be considered as well. This method is assumed to be applied to convert printed mathematical texts into an electronic form. On the other hand, on-line recognition is connected to pen-based computing technologies like electronic tablets. The input is a sequence of strokes. Elements of the sequence are sorted by the time of creation. Each stroke is a sequence of points written by one move of the pen. Since the pen is driven by hand, on-line recognition focuses on handwritten formulae.

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