DOCSLIB.ORG

Number-System of Algebra

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Number-System of Algebra Tim th eo reti c al part o f this little book i s an elementary o f b e xposition of the nature the num er concept, of the posi o f a o f b tive integer, and the four artifici l fo rms num er w v th e “ b hich, with the positi e integer, constitute num er ” th f b v i z . e system o alge ra, the negative , fraction, the irra h e o f i nal . T t o , and the imaginary discussion the artificial a numbers follows, in gener l, the same lines as my pam i phlet : On the Fo rms of N umber ari si ng i n Co mmo n Al ebra but x g , it is much more e haustive and thorough n Th e v o ne b goi g . point of iew is the first suggested y P b eacock and Gregory, and accepted ymathematicians gen erally since the discovery of quaterni ons and th e Ausdeh nun sleh re G a b a fi g of rassmann, that lge r is completely de ned formally by the laws o f combinati o n to which its funda b mental Operations are su j ect ; that, speaking generally, ' these laws alo ne define th e Operations and the operations b t bo the various artificial num ers , as heir formal or sym lic . T v for results his doctrine was fully de eloped the negative, b H Co m lexe the fraction, and the imaginary y ankel, in his p ’ a hlens stemen 1 867 and e m b C Z y , in , mad co plete y antor s b o f 1 871 but eautiful theory the irrational in , it has not as yet received adequate tre atment in English . Any large degree o f originality in work o f this kind is f I naturally out o the question . have borrowed from a i v PR E FA CE . Pe G n g reat many sources , especially from acock, rassman , C and T Theo ri e d er' Hankel, Weierstrass , antor, homae ( einer co m lemen era nd erli hen I ana lyti schen Functi o nen p V c ) . o r may mention, however, as more less distinctive features um b i 1 Of my discussion , the treatment of n er, count ng a 4 th e and the equ tion , and the prominence given n f b t laws o f the d etermi nate e ss o su trac ion and division . Much care and labor have been expended o n the hi s T o ut to ri cal chapters o f th e book . hese were meant at the set to contain only a brief account o f the origin and history a But I l d no t b o f the artifici l numbers . cou ring myself to ignore primitive counting and the dev elopment of numeral I notation, and soon found that a clear and connected accoun t o f the origin o f the negative and im aginary is possible only when embodied in a sketch of the early his I tory o f the equation . have thus been led to write a r’ é sumé of th e history of th e most important parts of ele mentary arithmetic and algebra ’ Moritz Cantor s Vo rlesung en uber di e Geschi chte derMa the mati k . b fo r , Vol I, has een my principal authority the h n 1 2 A D . Fo r t e v i . 0 e t e 0 . tire period which it co ers, to I sa o n th e 1 200 1 600 I e little have to y period to , hav fl b m b o n depended chie y, though y no eans a solutely, H ankel : Z ur Geschichte der Mathematik i n Altertum und Th f m M ittela lter . e remainder o y sketch is for the most o n th e part based original sources . HE NRY B FINE . A 1 89 1 . PRINCETON , pril , In n f this second editio 3. number o important corrections n hav e b een made . But there h as bee no attempt at a f complete revision o the book . Y FINE . HENR B . I S 1 902 . PR NCETON , eptember, C ON T E N TS . THEOR E TIC A L I . I I V IN TH E S . I . PO T E TEGER Th e number co ncept Additi o n and its laws A ND NE GATIv E I II . SUBTRACTION THE NTEGER . o Numerical subtracti n . Determinateness o f numerical subtractio n Limitatio ns o f numerical subtractio n o f a o i a o Principle perm nence . S ymb l c subtr cti n Zero Recapitulatio n o f th e arg ument o f the chapter “ III . DIVI SION AND THE FRACTION . Determinateness o f numerical di visio n Fo a o f d vi rm l rules i si o n . Limitatio ns o f numerical di vi sio n Symbo li c di visio n . Th e fractio n Negative fractio ns General test o f th e equality o r inequality o f fractio ns Indeterminateness o f di visio n by zero vi CON TE N TS . Determi nateness o f symbo li c di visio n Th e vanishing o f a pro duct The system o f ratio nal numbers V TH E I I . RRATIONAL . Inadequateness o f the system o f ratio nal numbers ” ul a i a o a Numbers defined by reg r sequences . The rr ti n l d d n o o f z o o a Generaliz e efi iti ns er , p sitive , neg tive Of the fo ur fund amental Operatio ns Of equality and g reater and lesser in equality Th e number defined by a reg ular sequence its limiting value Divisio n by z ero The number- system defined by reg ular sequences o f ratio nals a c lo sed and c o ntinuo us system V . TH E IM MP X N M . AGINARY . CO LE U BERS Co mplex numbers The fundamental Operatio ns o n complex numbers . Numerical compariso n o f co mplex numbers Adequateness o f the system o f c omplex numbers F f undamental ch aracteristics o f the algebra o number . V I P I R P I N M . THE V . I . GRA H CAL E RESENTAT ON OF U BER S AR ABLE Co rrespo ndence between the real number - system and the po ints o f a line Th e co ntinuo us vari able C o rrespo ndence between the co mplex number- System and the p o ints o f a plane Defin itio ns o f mo dulus and argument o f a c omplex number and o f o and a a r o f an a 45 48 Sine , c sine , circul r me su e ngle , D o a o a a £6 c o s 0 i 0 ei 9 45 48 em nstr ti n th t p ( sin ) p , o o o f th e o n th e sum d ff C nstructi n p i ts which represent , i erence , o d c and o o f two o 46 47 pr u t, qu tient c mplex numbers , VII . TH E M OF A FUNDAMENTAL THEORE LGEBRA . Definitio ns o f the algebraic equati o n and its ro o ts Demo nstratio n that an algebraic equati o n o f th e nth degree h as CON TEN TS . vii I N M D I D I N . VII . U BERS EF NE BY NFI ITE SERIES PAGE R S I S . I . EAL ER E D n o o f sum o and di efi iti ns , c nvergence, vergence . General test o f A so and o d o a o b lute c n iti n l c nvergence . S a s o f o . peci l te ts c nvergence 0 0 0 0 0 0 0 0 C O O - 1 0 0 0 0 0 0 0 0 0 Limits o f co nvergence Th e fu da a o a o o n i n ment l per ti ns infin te series . Q O O O Q O O O O O O O O O II . M P X I S CO LE SER E . test Of o n r a c ve enc e o o 0 - 0 Gener l g o o c 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 A o and o d o a o bs lute c n iti n l c nvergence . Th e regio n o f co nvergence A theo rem respecting c omplex series The fun d amental o peratio ns o n complex series IX THE ExP ONE NTI A L A N D L M I F . OGARITH C UNCTIONS. M D I I S . IN V I A ND V TH E UNDETER INE COEFF C ENT OLUT ON E OLUTION . I M I M B NO AL THEORE . f n o Definitio n o f u cti n . Functio nal equatio n o f th e expo nential functio n d d o ffi Un etermine c e cients .
Load more

Recommended publications
  • The Number-System of Algebra : Treated Theoretically and Historically
    - ; THE NUMBER-SYSTEM OF ALGEBRA TKEATED THEORETICALLY AND HISTORICALLY BY HENRY B. FINE, PH.D. PROFESSOR OF MATHEMATICS IN PRINCETON UNIVERSITY SECOND EDITION, WITH CORRECTIONS BOSTON, U.S.A. D. C. HEATH & CO., PUBLISHERS 1907 COPYRIGHT, 1890, BY HENRY B. FINE. 66 f 6 T PREFACE. THE theoretical part of this little book is an elementary of exposition the nature of the number concept, of the posi- tive integer, and of the four artificial forms of number which, with the positive integer, constitute the "number- " system of algebra, viz. the negative, the fraction, the irra- tional, and the imaginary. The discussion of the artificial numbers follows, in general, the same lines as my pam- phlet : On the Forms of Number arising in Common Algebra, but it is much more exhaustive and thorough- going. The point of view is the one first suggested by Peacock and Gregory, and accepted by mathematicians gen- erally since the discovery of quaternions and the Ausdeh- nungslehre of Grassmann, that algebra is completely defined formally by the laws of combination to which its funda- mental operations are subject; that, speaking generally, these laws alone define the operations, and the operations the various artificial numbers, as their formal or symbolic results. This doctrine was fully developed for the neg the fraction, and the imaginary by Hankel, in his Complexe Zahlensystemen, in 1867, and made complete by Cantor's beautiful theory of the irrational in 1871, but it has not as yet received adequate treatment in English. this kind is Any large degree of originality in work of from a naturally out of the question.
    [Show full text]
  • A Review on Handwritten Devnagari Numerals Recognition Using Support Vector Machine
    Proceedings of VESCOMM-2016 4th NATIONAL CONFERENCE ON “RECENT TRENDES IN VLSI, EMBEDED SYSTEM, SIGNAL PROCESSING AND COMMUNICATION In Association with “The Institution of Engineers (India)” and IJRPET February 12th, 2016 Paper ID: VESCOMM03 A REVIEW ON HANDWRITTEN DEVNAGARI NUMERALS RECOGNITION USING SUPPORT VECTOR MACHINE Rupali Vitthalrao Suryawanshi Department of Electronics Engineering, Bharatratna Indira Gandhi College, Solapur, India, 413006 [email protected] Abstract— Handwriting has continued to persist as a mean of SVM stands for Support Vector Machine and this method of communication and recording information in day-to-day life even recognition is gaining immense popularity now-a-days. SVM with the invention of new technologies. Natural handwriting is classifier gives better results as compared to the other one of the easiest ways of information exchange between a human classifiers for the handwritten numeral recognition of Kannada and a computer. Handwriting recognition has attracted many script in [3]. In [6], SVM approach is used to recognize researchers across the world since many years. Recognition of strokes in Telugu script. The set of strokes are segmented into online handwritten Devanagari numerals is a goal of many subsets based on the relative position of the stroke in a research efforts in the pattern recognition field The main goal of character. An SVM based classifier is built for recognition of the work is the recognition of online hand written Devanagari strokes in each subset. A rule based approach is used to numerals using support vector machine. In the data collection recognize a character from the sequence of stroke classes phase, co-ordinate points of the input handwritten numeral are given by the stroke classifier.
    [Show full text]
  • Elements of South-Indian Palaeography, from the Fourth To
    This is a reproduction of a library book that was digitized by Google as part of an ongoing effort to preserve the information in books and make it universally accessible. https://books.google.com ELEMENTS SOUTH-INDIAN PALfi3&BAPBY FROM THE FOURTH TO THE SEVENTEENTH CENTURY A. D. BEIN1 AN INTRODUCTION TO ?TIK STUDY OF SOUTH-INDIAN INSCRIPTIONS AND MSS. BY A. C. BURNELL HON'. PH. O. OF TUE UNIVERSITY M. K. A, ri'VORE PIS I. A SOClfcTE MANGALORE \ BASEL MISSION BOOK & TRACT DEPOSITORY ft !<3 1874 19 Vi? TRUBNER & Co. 57 & 69 LUDOATE HILL' . ' \jj *£=ggs3|fg r DISTRIBUTION of S INDIAN alphabets up to 1550 a d. ELEMENTS OF SOUTH-INDIAN PALEOGRAPHY FROM THE FOURTH TO THE SEVENTEENTH CENTURY A. D. BEING AN INTRODUCTION TO THE STUDY OF SOUTH-INDIAN INSCRIPTIONS AND MSS. BY A. p. j^URNELL HON. PH. D. OF THE UNIVERSITY OF STRASSBUB.G; M. R. A. S.; MEMBKE DE LA S0CIETE ASIATIQUE, ETC. ETC. MANGALORE PRINTED BY STOLZ & HIRNER, BASEL MISSION PRESS 1874 LONDON TRtlBNER & Co. 57 & 59 LUDGATE HILL 3« w i d m « t als ^'ctdjcn kr §anltekcit fiir Mc i|jm bdic<jcnc JJoctorMvk ttcsc fetlings^kit auf rincm fejjcr mtfrckntcn Jfclk bet 1®4 INTRODUCTION. I trust that this elementary Sketch of South-Indian Palaeography may supply a want long felt by those who are desirous of investigating the real history of the peninsula of India. Trom the beginning of this century (when Buchanan executed the only archaeological survey that has ever been done in even a part of the South of India) up to the present time, a number of well meaning persons have gone about with much simplicity and faith collecting a mass of rubbish which they term traditions and accept as history.
    [Show full text]
  • Numbering Systems Developed by the Ancient Mesopotamians
    Emergent Culture 2011 August http://emergent-culture.com/2011/08/ Home About Contact RSS-Email Alerts Current Events Emergent Featured Global Crisis Know Your Culture Legend of 2012 Synchronicity August, 2011 Legend of 2012 Wednesday, August 31, 2011 11:43 - 4 Comments Cosmic Time Meets Earth Time: The Numbers of Supreme Wholeness and Reconciliation Revealed In the process of writing about the precessional cycle I fell down a rabbit hole of sorts and in the process of finding my way around I made what I think are 4 significant discoveries about cycles of time and the numbers that underlie and unify cosmic and earthly time . Discovery number 1: A painting by Salvador Dali. It turns that clocks are not as bad as we think them to be. The units of time that segment the day into hours, minutes and seconds are in fact reconciled by the units of time that compose the Meso American Calendrical system or MAC for short. It was a surprise to me because one of the world’s foremost authorities in calendrical science the late Dr.Jose Arguelles had vilified the numbers of Western timekeeping as a most grievious error . So much so that he attributed much of the worlds problems to the use of the 12 month calendar and the 24 hour, 60 minute, 60 second day, also known by its handy acronym 12-60 time. I never bought into his argument that the use of those time factors was at fault for our largely miserable human-planetary condition. But I was content to dismiss mechanized time as nothing more than a convenient tool to facilitate the activities of complex societies.
    [Show full text]
  • A History of Elementary Mathematics, with Hints on Methods of Teaching
    ;-NRLF I 1 UNIVERSITY OF CALIFORNIA PEFARTMENT OF CIVIL ENGINEERING BERKELEY, CALIFORNIA Engineering Library A HISTORY OF ELEMENTARY MATHEMATICS THE MACMILLAN COMPANY NEW YORK BOSTON CHICAGO DALLAS ATLANTA SAN FRANCISCO MACMILLAN & CO., LIMITED LONDON BOMBAY CALCUTTA MELBOURNE THE MACMILLAN CO. OF CANADA, LTD. TORONTO A HISTORY OF ELEMENTARY MATHEMATICS WITH HINTS ON METHODS OF TEACHING BY FLORIAN CAJORI, PH.D. PROFESSOR OF MATHEMATICS IN COLORADO COLLEGE REVISED AND ENLARGED EDITION THE MACMILLAN COMPANY LONDON : MACMILLAN & CO., LTD. 1917 All rights reserved Engineering Library COPYRIGHT, 1896 AND 1917, BY THE MACMILLAN COMPANY. Set up and electrotyped September, 1896. Reprinted August, 1897; March, 1905; October, 1907; August, 1910; February, 1914. Revised and enlarged edition, February, 1917. o ^ PREFACE TO THE FIRST EDITION "THE education of the child must accord both in mode and arrangement with the education of mankind as consid- ered in other the of historically ; or, words, genesis knowledge in the individual must follow the same course as the genesis of knowledge in the race. To M. Comte we believe society owes the enunciation of this doctrine a doctrine which we may accept without committing ourselves to his theory of 1 the genesis of knowledge, either in its causes or its order." If this principle, held also by Pestalozzi and Froebel, be correct, then it would seem as if the knowledge of the history of a science must be an effectual aid in teaching that science. Be this doctrine true or false, certainly the experience of many instructors establishes the importance 2 of mathematical history in teaching. With the hope of being of some assistance to my fellow-teachers, I have pre- pared this book and have interlined my narrative with occasional remarks and suggestions on methods of teaching.
    [Show full text]
  • The Project Gutenberg Ebook #31061: a History of Mathematics
    The Project Gutenberg EBook of A History of Mathematics, by Florian Cajori This eBook is for the use of anyone anywhere at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this eBook or online at www.gutenberg.org Title: A History of Mathematics Author: Florian Cajori Release Date: January 24, 2010 [EBook #31061] Language: English Character set encoding: ISO-8859-1 *** START OF THIS PROJECT GUTENBERG EBOOK A HISTORY OF MATHEMATICS *** Produced by Andrew D. Hwang, Peter Vachuska, Carl Hudkins and the Online Distributed Proofreading Team at http://www.pgdp.net transcriber's note Figures may have been moved with respect to the surrounding text. Minor typographical corrections and presentational changes have been made without comment. This PDF file is formatted for screen viewing, but may be easily formatted for printing. Please consult the preamble of the LATEX source file for instructions. A HISTORY OF MATHEMATICS A HISTORY OF MATHEMATICS BY FLORIAN CAJORI, Ph.D. Formerly Professor of Applied Mathematics in the Tulane University of Louisiana; now Professor of Physics in Colorado College \I am sure that no subject loses more than mathematics by any attempt to dissociate it from its history."|J. W. L. Glaisher New York THE MACMILLAN COMPANY LONDON: MACMILLAN & CO., Ltd. 1909 All rights reserved Copyright, 1893, By MACMILLAN AND CO. Set up and electrotyped January, 1894. Reprinted March, 1895; October, 1897; November, 1901; January, 1906; July, 1909. Norwood Pre&: J. S. Cushing & Co.|Berwick & Smith.
    [Show full text]
  • Support Vector Machine for Handwritten Devanagari Numeral Recognition Shailedra Kumar Shrivastava Sanjay S
    International Journal of Computer Applications (0975 – 8887) Volume 7– No.11, October 2010 Support Vector Machine for Handwritten Devanagari Numeral Recognition Shailedra Kumar Shrivastava Sanjay S. Gharde HOD, Information Technology Department Research Scholar, Information Technology Department Samrat Ashok Technological Institute Samrat Ashok Technological Institute Vidisha, (M. P.) INDIA Vidisha, (M. P.) INDIA ABSTRACT characters by applying different techniques, but very less work Support Vector Machines (SVM) is used for classification in has been performed on Handwritten Devanagari numerals. So, pattern recognition widely. This paper applies this technique for this research work has been conducted on Handwritten recognizing handwritten numerals of Devanagari Script. Since Devanagari numeral. benchmark database does not exist globally, this system is constructed database by implementing Automated Numeral Recognition of Handwritten Devanagari Numerals or Extraction and Segmentation Program (ANESP). Preprocessing is Characters [1, 2] is a complicated task due to the unconstrained manifested in the same program which reduces most of the shape variations, different writing style and different kinds of efforts. 2000 samples are collected from 20 different people noise. Also, handwriting depends much on the writer and because having variation in writing style. Moment Invariant and Affine we do not always write the same digit in exactly the same way, Moment Invariant techniques are used as feature extractor. These building a general recognition system that would recognize any techniques extract 18 features from each image which is used in digit with good reliability in every application is not possible. In Support Vector Machine for recognition purpose. Binary recent time, specialists have made use of different techniques classification techniques of Support Vector Machine is such as Modified Discrimination Function (MQDF) [10], implemented and linear kernel function is used in SVM.
    [Show full text]
  • Preliminary Proposal to Encode Devanagari Letter Numerals L2/17
    Preliminary proposal to encode Devanagari letter numerals Srinidhi A and Sridatta A Tumakuru, India [email protected], [email protected] January 17, 2017 1 Introduction This is preliminary proposal to encode letter numerals found in Devanagari script. The objective is to bring them to the attention of the Unicode Technical Committee and to seek advice regarding the encoding of the numerals. 2 Background The modern Devanagari has a set of digits with the use of zero. In addition to digits, a distinct numerical notation system is attested early and medieval manuscripts. These numerals are referred as ‘letter numerals’ in the scholarly literature to distinguish from regular digits. The letter numerals were largely used for marking page numbers in manuscripts. These numbers are derived from Brahmi numbers (U+11052…U+11065). These Devanagari numerals are paleographically analogous to letter numerals found in closely related North Indic scripts like Bhaikṣukī, Tocharian, Khotanese, Ranjana, Newa and Sharada. Often the numbers were used alongside with digits. Letter numerals are written in the margin to the left, whereas digits are written in the margin to the right. North Indian letters numerals are distinct from alphasyllabic numeration used in of other parts of India such as Aksharapalli and Katapayadi systems. In these notations existing letters are reused, whereas the North Indian numerals are evolved from Brahmi numbers. The term ‘letter-numerals’ here does not symbolize that these numerals are evolved or conceptually derived from letters. These numerals were used predominantly in states of Gujarat and Rajasthan of Western India. These numerals occur in both ‘Jainanagari’ and regular styles of Devanagari.
    [Show full text]
  • Neural Combination of ANN and HMM for Handwritten Devanagari Numeral Recognition U
    Neural Combination of ANN and HMM for Handwritten Devanagari Numeral Recognition U. Bhattacharya, S.K. Parui, B. Shaw, K. Bhattacharya To cite this version: U. Bhattacharya, S.K. Parui, B. Shaw, K. Bhattacharya. Neural Combination of ANN and HMM for Handwritten Devanagari Numeral Recognition. Tenth International Workshop on Frontiers in Handwriting Recognition, Université de Rennes 1, Oct 2006, La Baule (France). inria-00104481 HAL Id: inria-00104481 https://hal.inria.fr/inria-00104481 Submitted on 6 Oct 2006 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Neural Combination of ANN and HMM for Handwritten Devanagari Numeral Recognition U. Bhattacharya S. K. Parui B. Shaw K. Bhattacharya CVPR Unit CVPR Unit CVPR Unit B-Tech Final Year Indian Statistical Indian Statistical Indian Statistical Dept. of CS&E Institute, Kolkata Institute, Kolkata Institute, Kolkata University of Calcutta [email protected] [email protected] mrbikashshaw kuntal.bhattacharya @yahoo.co.in @gmail.com Abstract recognition of hand printed Devanagari characters is found in [3]. For recognition of handwritten Devanagari In this article, a two-stage classification system for numerals, Ramakrishnan et al. [4] used independent recognition of handwritten Devanagari numerals is component analysis technique for feature extraction presented.
    [Show full text]
  • Offline Handwritten Character Recognition Using Neural Networks
    International Journal of Computer Sciences and Engineering Open Access Research Paper Vol.-7, Issue-5, May 2019 E-ISSN: 2347-2693 Offline Handwritten Character Recognition using Neural Networks Hemant Yadav1*, Sapna Jain2 1 Department of Computer Science, MRK Institute of Engineering and Technology, Saharanwas, Rewari, India 2 Department of Computer Science, MRK Institute of Engineering and Technology, Saharanwas, Rewari, India *Corresponding Author: [email protected], Tel.: +91-98182-63577 DOI: https://doi.org/10.26438/ijcse/v7i5.838845 | Available online at: www.ijcseonline.org Accepted: 10/May/2019, Published: 31/May/2019 Abstract— Handwritten character recognition is currently a under research field. A lot research is getting done in this field in which the point of interest is to receive as higher accuracy as possible in a distorted writing. That is as we know the way of writing of different person is different, so to recognize every writing with a greater accuracy is the point of concern. In this paper we proposed a method for different languages handwritten character recognition. The main focus is to train the model with pre-set data and then using that trained model to test the handwritten character passed to it. In our proposed method we used MATLAB to design our code, in this the model can be trained on runtime also. Keywords— Handwritten Character, Character Recognition, Feature Extraction, Neural Networks, Image Recognition, Offline Character Recognition. I. INTRODUCTION Indian scripts' character recognition, most of the published works deal with pre-printed papers, but there are only rare Handwriting is an age-old and elegant way of research papers representing handwritten character communication and is a distinctive characteristic of an recognition.
    [Show full text]
  • Radial Basis Function for Handwritten Devanagari Numeral Recognition
    (IJACSA) International Journal of Advanced Computer Science and Applications, Vol. 2, No. 5, 2011 Radial Basis Function For Handwritten Devanagari Numeral Recognition Prerna Singh Nidhi Tyagi M.Tech Student Assistant Professor Shobhit University, ISCEIT. Shobhit University, Meerut, India Meerut, India Abstract—The task of recognizing handwritten numerals, using a different languages like English [2] ,Chinese[3] , Arabian classifier, has great importance. This paper applies the technique ,Persian , Bengali , Guajarati .Different classifiers have been of Radial Basis Function for handwritten numeral recognition of used for handwritten digit recognition using neural network. Devanagari Script. Lot of work has been done on Devanagari Recently, signifi- cant contribution towards the improvement of numeral recognition using different techniques for increasing the recognition rates have been made by means of different accuracy of recognition. Since the database is not globally combination strategies [4] and by the use of support vector created, firstly we created the database by implementing pre- machines [5] . processing on the set of training data. Then by the use of Principal Component Analysis we have extracted the features of Machine learning is a artificial system[6] capable of each image, some researchers have also used density feature autonomous acquisition & integration of knowle- dge.This extraction. Since different people have different writing style, so capacity to learn from experience, analy- tical observation other here we are trying to form a system where recognition of numeral means, results in system that can improve its own speed or becomes easy. Then at the hidden layer centers are determined performance and allows computer to “learn“. It can be and the weights between the hidden layer and the output layer of categorized into supervised learning, unsupervised learning, each neuron are determined to calculate the output, where output semi-supervised learning and reinforcement learning [7].
    [Show full text]
  • Comparison of Feature Extraction Techniques for Gujarati Isolated Numerals Dr
    International Journal of Modern Trends in Engineering and Research www.ijmter.com e-ISSN No.:2349-9745, Date: 28-30 April, 2016 Comparison of Feature Extraction Techniques for Gujarati Isolated Numerals Dr. Mamta Baheti Department of Computer Science, Hislop College, Nagpur [email protected] Abstract— This paper is for recognition of isolated Gujarati numerals. As per the reported work, Gujarati is widely spoken across world along with Indian states. In the proposed study, we have used noisy handwritten numerals in procedure of training and testing. After applying pre-processing to the scanned image, they are then treated with the proposed algorithm. In our proposed algorithm we have used affine invariant moments and invariant moments as feature extraction technique and Gaussian distribution function as classifier. We produced pleasing results for some numerals. We compared the results for both the extraction techniques and found that for our database Affine invariant moments gave better results but they could be improved by giving better quality images for training and testing. Keywords- Affine Invariant Moments; Invariant Moments; Gaussian Distribution Function I. INTRODUCTION In the present scenario, every day task is being computerized. Each user wants the computer to have user-friendly interactions. In recent years a good amount of reported work has been contributed for recognition of handwritten characters. Variation in writing styles and recognition accuracy has a milestone to achieve. It has been noted that there are approximately 22 regional official languages are used in India [1-4]. Every regional official language has the wide variety as well some peculiar similarities. Out of these, one language is Gujarati which is spoken in Gujarat and some parts of India and also in South Africa.
    [Show full text]