இணை இயக்கி (Tamil Wikipedia)

Analysis of information sources in references of the Wikipedia article "இணை இயக்கி" in Tamil language version.

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archive.org

Kersey (the elder), John (1673). "Chapter I: Concerning the Scope of this fourth Book and the Signification of Characters, Abbreviations and Citations used therein". The Elements of that Mathematical Art, commonly called Algebra. Vol. Book IV - The Elements of the Algebraical Arts. London: Thomas Passinger, Three-Bibles, London-Bridge. pp. 177–178. Archived from the original on 2020-08-05. Retrieved 2019-08-09.
Cajori, Florian (1993) [September 1928]. "§ 184, § 359, § 368". A History of Mathematical Notations – Notations in Elementary Mathematics. Vol. 1 (two volumes in one unaltered reprint ed.). Chicago, US: Open court publishing company. pp. 193, 402–403, 411–412. ISBN 0-486-67766-4. LCCN 93-29211. Retrieved 2019-07-22. pp. 402–403, 411–412: §359. […] ∥ for parallel occurs in Oughtred's Opuscula mathematica hactenus inedita (1677) [p. 197], a posthumous work (§ 184) […] §368. Signs for parallel lines. […] when Recorde's sign of equality won its way upon the Continent, vertical lines came to be used for parallelism. We find ∥ for "parallel" in Kersey,^[A] Caswell, Jones,^[B] Wilson,^[C] Emerson,^[D] Kambly,^[E] and the writers of the last fifty years who have been already quoted in connection with other pictographs. Before about 1875 it does not occur as often […] Hall and Stevens^[F] use "par^[F] or ∥" for parallel […] [A] John Kersey, Algebra (London, 1673), Book IV, p. 177. [B] W. Jones, Synopsis palmarioum matheseos (London, 1706). [C] John Wilson, Trigonometry (Edinburgh, 1714), characters explained. [D] W. Emerson, Elements of Geometry (London, 1763), p. 4. [E] L. Kambly|Deutsch (de) , Die Elementar-Mathematik, Part 2: Planimetrie, 43. edition (Breslau, 1876), p. 8. […] [F] H. S. Hall and F. H. Stevens, Euclid's Elements, Parts I and II (London, 1889), p. 10. […] [3]

berkeley.edu

inst.eecs.berkeley.edu

Ranade, Gireeja; Stojanovic, Vladimir, eds. (Fall 2018). "Chapter 15.7.2 Parallel Resistors" (PDF). EECS 16A Designing Information Devices and Systems I (PDF) (lecture notes). கலிபோர்னியா பல்கலைக்கழகம் (பெர்க்லி). p. 12. Note 15. Archived (PDF) from the original on 2018-12-27. Retrieved 2018-12-28. p. 12: […] This mathematical relationship comes up often enough that it actually has a name: the "parallel operator", denoted ∥. When we say x∥y, it means ${\frac {xy}{x+y}}$ . Note that this is a mathematical operator and does not say anything about the actual configuration. In the case of resistors the parallel operator is used for parallel resistors, but for other components (like capacitors) this is not the case. […] (16 pages)

books.google.com

Duffin, Richard James (1971) [1970, 1969]. "Network Models". Written at Durham, North Carolina, USA. In Wilf, Herbert Saul; Hararay, Frank (eds.). Mathematical Aspects of Electrical Network Analysis. Proceedings of a Symposium in Applied Mathematics of the American Mathematical Society and the Society for Industrial and Applied Mathematics held in New York City, 1969-04-02/03. Vol. III of SIAM-AMS Proceedings (illustrated ed.). Providence, Rhode Island: American Mathematical Society (AMS) / Society for Industrial and Applied Mathematics (SIAM). pp. 65–92 [68]. ISBN 0-8218-1322-6. ISSN 0080-5084. LCCN 79-167683. பன்னாட்டுத் தரப்புத்தக எண் 978-0-8218-1322-5. Report 69-21. Retrieved 2019-08-05. pp. 68–69: […] To have a convenient short notation for the joint resistance of resistors connected in parallel let […] A:B = AB/(A+B) […] A:B may be regarded as a new operation termed parallel addition […] Parallel addition is defined for any nonnegative numbers. The network model shows that parallel addition is commutative, associative. Moreover, multiplication is distributive over this operation. Consider now an algebraic expression in the operations (+) and (:) operating on positive numbers A, B, C, etc. […] To give a network interpretation of such a polynomial read A + B as "A series B" and A : B as "A parallel B" then it is clear that the expression […] is the joint resistance of the network […] [1] [2] (206 pages)
Bober, William; Stevens, Andrew (2016). "Chapter 7.6. Laplace Transforms Applied to Circuits". Numerical and Analytical Methods with MATLAB for Electrical Engineers. Applied and Computational Mechanics (1 ed.). CRC Press. p. 224. ISBN 978-1-46657607-0. பன்னாட்டுத் தரப்புத்தக எண் 1-46657607-3. (388 pages)
Ellerman, David Patterson (1995-03-21). "Chapter 12: Parallel Addition, Series-Parallel Duality, and Financial Mathematics". Intellectual Trespassing as a Way of Life: Essays in Philosophy, Economics, and Mathematics (PDF). G – Reference, Information and Interdisciplinary Subjects Series (illustrated ed.). Rowman & Littlefield Publishers, Inc. pp. 237–268. ISBN 0-8476-7932-2. Archived (PDF) from the original on 2016-03-05. Retrieved 2019-08-09. p. 237: […] When resistors with resistance a and b are placed in series, their compound resistance is the usual sum (hereafter the கூட்டல்) of the resistances a + b. If the resistances are placed in parallel, their compound resistance is the parallel sum of the resistances, which is denoted by the முக்கால்புள்ளி […] {{cite book}}: |work= ignored (help) [4] (271 pages)

cmu.edu

kilthub.cmu.edu

Duffin, Richard James (1971) [1970, 1969]. "Network Models". Written at Durham, North Carolina, USA. In Wilf, Herbert Saul; Hararay, Frank (eds.). Mathematical Aspects of Electrical Network Analysis. Proceedings of a Symposium in Applied Mathematics of the American Mathematical Society and the Society for Industrial and Applied Mathematics held in New York City, 1969-04-02/03. Vol. III of SIAM-AMS Proceedings (illustrated ed.). Providence, Rhode Island: American Mathematical Society (AMS) / Society for Industrial and Applied Mathematics (SIAM). pp. 65–92 [68]. ISBN 0-8218-1322-6. ISSN 0080-5084. LCCN 79-167683. பன்னாட்டுத் தரப்புத்தக எண் 978-0-8218-1322-5. Report 69-21. Retrieved 2019-08-05. pp. 68–69: […] To have a convenient short notation for the joint resistance of resistors connected in parallel let […] A:B = AB/(A+B) […] A:B may be regarded as a new operation termed parallel addition […] Parallel addition is defined for any nonnegative numbers. The network model shows that parallel addition is commutative, associative. Moreover, multiplication is distributive over this operation. Consider now an algebraic expression in the operations (+) and (:) operating on positive numbers A, B, C, etc. […] To give a network interpretation of such a polynomial read A + B as "A series B" and A : B as "A parallel B" then it is clear that the expression […] is the joint resistance of the network […] [1] [2] (206 pages)

ellerman.org

Ellerman, David Patterson (1995-03-21). "Chapter 12: Parallel Addition, Series-Parallel Duality, and Financial Mathematics". Intellectual Trespassing as a Way of Life: Essays in Philosophy, Economics, and Mathematics (PDF). G – Reference, Information and Interdisciplinary Subjects Series (illustrated ed.). Rowman & Littlefield Publishers, Inc. pp. 237–268. ISBN 0-8476-7932-2. Archived (PDF) from the original on 2016-03-05. Retrieved 2019-08-09. p. 237: […] When resistors with resistance a and b are placed in series, their compound resistance is the usual sum (hereafter the கூட்டல்) of the resistances a + b. If the resistances are placed in parallel, their compound resistance is the parallel sum of the resistances, which is denoted by the முக்கால்புள்ளி […] {{cite book}}: |work= ignored (help) [4] (271 pages)
Ellerman, David Patterson (May 2004) [1995-03-21]. "Introduction to Series-Parallel Duality" (PDF). University of California at Riverside. CiteSeerX 10.1.1.90.3666. Archived from the original on 2019-08-10. Retrieved 2019-08-09. The parallel sum of two positive real numbers x:y = [(1/x) + (1/y)]⁻¹ arises in electrical circuit theory as the resistance resulting from hooking two resistances x and y in parallel. There is a duality between the usual (series) sum and the parallel sum. […] [5] (24 pages)

loc.gov

lccn.loc.gov

Duffin, Richard James (1971) [1970, 1969]. "Network Models". Written at Durham, North Carolina, USA. In Wilf, Herbert Saul; Hararay, Frank (eds.). Mathematical Aspects of Electrical Network Analysis. Proceedings of a Symposium in Applied Mathematics of the American Mathematical Society and the Society for Industrial and Applied Mathematics held in New York City, 1969-04-02/03. Vol. III of SIAM-AMS Proceedings (illustrated ed.). Providence, Rhode Island: American Mathematical Society (AMS) / Society for Industrial and Applied Mathematics (SIAM). pp. 65–92 [68]. ISBN 0-8218-1322-6. ISSN 0080-5084. LCCN 79-167683. பன்னாட்டுத் தரப்புத்தக எண் 978-0-8218-1322-5. Report 69-21. Retrieved 2019-08-05. pp. 68–69: […] To have a convenient short notation for the joint resistance of resistors connected in parallel let […] A:B = AB/(A+B) […] A:B may be regarded as a new operation termed parallel addition […] Parallel addition is defined for any nonnegative numbers. The network model shows that parallel addition is commutative, associative. Moreover, multiplication is distributive over this operation. Consider now an algebraic expression in the operations (+) and (:) operating on positive numbers A, B, C, etc. […] To give a network interpretation of such a polynomial read A + B as "A series B" and A : B as "A parallel B" then it is clear that the expression […] is the joint resistance of the network […] [1] [2] (206 pages)
Cajori, Florian (1993) [September 1928]. "§ 184, § 359, § 368". A History of Mathematical Notations – Notations in Elementary Mathematics. Vol. 1 (two volumes in one unaltered reprint ed.). Chicago, US: Open court publishing company. pp. 193, 402–403, 411–412. ISBN 0-486-67766-4. LCCN 93-29211. Retrieved 2019-07-22. pp. 402–403, 411–412: §359. […] ∥ for parallel occurs in Oughtred's Opuscula mathematica hactenus inedita (1677) [p. 197], a posthumous work (§ 184) […] §368. Signs for parallel lines. […] when Recorde's sign of equality won its way upon the Continent, vertical lines came to be used for parallelism. We find ∥ for "parallel" in Kersey,^[A] Caswell, Jones,^[B] Wilson,^[C] Emerson,^[D] Kambly,^[E] and the writers of the last fifty years who have been already quoted in connection with other pictographs. Before about 1875 it does not occur as often […] Hall and Stevens^[F] use "par^[F] or ∥" for parallel […] [A] John Kersey, Algebra (London, 1673), Book IV, p. 177. [B] W. Jones, Synopsis palmarioum matheseos (London, 1706). [C] John Wilson, Trigonometry (Edinburgh, 1714), characters explained. [D] W. Emerson, Elements of Geometry (London, 1763), p. 4. [E] L. Kambly|Deutsch (de) , Die Elementar-Mathematik, Part 2: Planimetrie, 43. edition (Breslau, 1876), p. 8. […] [F] H. S. Hall and F. H. Stevens, Euclid's Elements, Parts I and II (London, 1889), p. 10. […] [3]

monoskop.org

Cajori, Florian (1993) [September 1928]. "§ 184, § 359, § 368". A History of Mathematical Notations – Notations in Elementary Mathematics. Vol. 1 (two volumes in one unaltered reprint ed.). Chicago, US: Open court publishing company. pp. 193, 402–403, 411–412. ISBN 0-486-67766-4. LCCN 93-29211. Retrieved 2019-07-22. pp. 402–403, 411–412: §359. […] ∥ for parallel occurs in Oughtred's Opuscula mathematica hactenus inedita (1677) [p. 197], a posthumous work (§ 184) […] §368. Signs for parallel lines. […] when Recorde's sign of equality won its way upon the Continent, vertical lines came to be used for parallelism. We find ∥ for "parallel" in Kersey,^[A] Caswell, Jones,^[B] Wilson,^[C] Emerson,^[D] Kambly,^[E] and the writers of the last fifty years who have been already quoted in connection with other pictographs. Before about 1875 it does not occur as often […] Hall and Stevens^[F] use "par^[F] or ∥" for parallel […] [A] John Kersey, Algebra (London, 1673), Book IV, p. 177. [B] W. Jones, Synopsis palmarioum matheseos (London, 1706). [C] John Wilson, Trigonometry (Edinburgh, 1714), characters explained. [D] W. Emerson, Elements of Geometry (London, 1763), p. 4. [E] L. Kambly|Deutsch (de) , Die Elementar-Mathematik, Part 2: Planimetrie, 43. edition (Breslau, 1876), p. 8. […] [F] H. S. Hall and F. H. Stevens, Euclid's Elements, Parts I and II (London, 1889), p. 10. […] [3]

psu.edu

citeseerx.ist.psu.edu

Ellerman, David Patterson (May 2004) [1995-03-21]. "Introduction to Series-Parallel Duality" (PDF). University of California at Riverside. CiteSeerX 10.1.1.90.3666. Archived from the original on 2019-08-10. Retrieved 2019-08-09. The parallel sum of two positive real numbers x:y = [(1/x) + (1/y)]⁻¹ arises in electrical circuit theory as the resistance resulting from hooking two resistances x and y in parallel. There is a duality between the usual (series) sum and the parallel sum. […] [5] (24 pages)

ti.com

"INA 326/INA 327 – Precision, Rail-to-Rail I/O Instrumentation Amplifier" (PDF). Burr-Brown / Texas Instruments. 2018 [November 2004, November 2001]. pp. 3, 9, 13. SBOS222D. Archived (PDF) from the original on 2019-07-13. Retrieved 2019-07-13.

web.archive.org

Kersey (the elder), John (1673). "Chapter I: Concerning the Scope of this fourth Book and the Signification of Characters, Abbreviations and Citations used therein". The Elements of that Mathematical Art, commonly called Algebra. Vol. Book IV - The Elements of the Algebraical Arts. London: Thomas Passinger, Three-Bibles, London-Bridge. pp. 177–178. Archived from the original on 2020-08-05. Retrieved 2019-08-09.
"INA 326/INA 327 – Precision, Rail-to-Rail I/O Instrumentation Amplifier" (PDF). Burr-Brown / Texas Instruments. 2018 [November 2004, November 2001]. pp. 3, 9, 13. SBOS222D. Archived (PDF) from the original on 2019-07-13. Retrieved 2019-07-13.
Ranade, Gireeja; Stojanovic, Vladimir, eds. (Fall 2018). "Chapter 15.7.2 Parallel Resistors" (PDF). EECS 16A Designing Information Devices and Systems I (PDF) (lecture notes). கலிபோர்னியா பல்கலைக்கழகம் (பெர்க்லி). p. 12. Note 15. Archived (PDF) from the original on 2018-12-27. Retrieved 2018-12-28. p. 12: […] This mathematical relationship comes up often enough that it actually has a name: the "parallel operator", denoted ∥. When we say x∥y, it means ${\frac {xy}{x+y}}$ . Note that this is a mathematical operator and does not say anything about the actual configuration. In the case of resistors the parallel operator is used for parallel resistors, but for other components (like capacitors) this is not the case. […] (16 pages)
Ellerman, David Patterson (1995-03-21). "Chapter 12: Parallel Addition, Series-Parallel Duality, and Financial Mathematics". Intellectual Trespassing as a Way of Life: Essays in Philosophy, Economics, and Mathematics (PDF). G – Reference, Information and Interdisciplinary Subjects Series (illustrated ed.). Rowman & Littlefield Publishers, Inc. pp. 237–268. ISBN 0-8476-7932-2. Archived (PDF) from the original on 2016-03-05. Retrieved 2019-08-09. p. 237: […] When resistors with resistance a and b are placed in series, their compound resistance is the usual sum (hereafter the கூட்டல்) of the resistances a + b. If the resistances are placed in parallel, their compound resistance is the parallel sum of the resistances, which is denoted by the முக்கால்புள்ளி […] {{cite book}}: |work= ignored (help) [4] (271 pages)
Ellerman, David Patterson (May 2004) [1995-03-21]. "Introduction to Series-Parallel Duality" (PDF). University of California at Riverside. CiteSeerX 10.1.1.90.3666. Archived from the original on 2019-08-10. Retrieved 2019-08-09. The parallel sum of two positive real numbers x:y = [(1/x) + (1/y)]⁻¹ arises in electrical circuit theory as the resistance resulting from hooking two resistances x and y in parallel. There is a duality between the usual (series) sum and the parallel sum. […] [5] (24 pages)

worldcat.org

search.worldcat.org

Duffin, Richard James (1971) [1970, 1969]. "Network Models". Written at Durham, North Carolina, USA. In Wilf, Herbert Saul; Hararay, Frank (eds.). Mathematical Aspects of Electrical Network Analysis. Proceedings of a Symposium in Applied Mathematics of the American Mathematical Society and the Society for Industrial and Applied Mathematics held in New York City, 1969-04-02/03. Vol. III of SIAM-AMS Proceedings (illustrated ed.). Providence, Rhode Island: American Mathematical Society (AMS) / Society for Industrial and Applied Mathematics (SIAM). pp. 65–92 [68]. ISBN 0-8218-1322-6. ISSN 0080-5084. LCCN 79-167683. பன்னாட்டுத் தரப்புத்தக எண் 978-0-8218-1322-5. Report 69-21. Retrieved 2019-08-05. pp. 68–69: […] To have a convenient short notation for the joint resistance of resistors connected in parallel let […] A:B = AB/(A+B) […] A:B may be regarded as a new operation termed parallel addition […] Parallel addition is defined for any nonnegative numbers. The network model shows that parallel addition is commutative, associative. Moreover, multiplication is distributive over this operation. Consider now an algebraic expression in the operations (+) and (:) operating on positive numbers A, B, C, etc. […] To give a network interpretation of such a polynomial read A + B as "A series B" and A : B as "A parallel B" then it is clear that the expression […] is the joint resistance of the network […] [1] [2] (206 pages)