Parallel (operator): Difference between revisions

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<ref name="McWane_1981">{{cite book |title=Introduction to Electronics and Instrumentation |author-first=John W. |author-last=McWane <!-- |contribution=Illustrations |contributor-first1=Barry I. |contributor-last1=Levine |contributor-first2=Julie |contributor-last2=Gecha --> |date=1981-05-01 |edition=illustrated |publisher=[[Breton Publishers]], [[Wadsworth, Inc.]] |___location=North Scituate, Massachusetts, USA |isbn=0-53400938-7 |id={{ISBN|978-0-53400938-0}} |pages=78, 96–98, 100, 104 |url=https://books.google.com/books?id=NKy1nQ8Y_V0C |access-date=2019-08-04 |quote-page=xiii, 96–98, 100 |quote=[…] Bruce D. Wedlock […] was the principle contributing author to Part I, {{citeref|Wedlock|1978|BASIC CIRCUIT NETWORKS|style=plain}} including the design of the companion examples. […] Most of the development of the IEI program was undertaken as part of the {{citeref|Wiesner|Johnson|Killian, Jr.|1978|Technical Curriculum Research and Development Project|style=plain}} of the [[MIT Center of Advanced Engineering Study]]. […] shorthand notation […] shorthand symbol ∥ […]}} (xiii+545 pages) (NB. In 1981, a 216-pages laboratory manual accompanying this book existed as well. The work grew out of an [[Massachusetts Institute of Technology|MIT]] course program "{{citeref|Wiesner|Johnson|Killian, Jr.|1978|The MIT Technical Curriculum Development Project - Introduction to Electronics and Instrumentation|style=plain}}" developed between 1974 and 1979. In 1986, a second edition of this book was published under the title "Introduction to Electronics Technology".)</ref>

<ref name="Eriksson-Bique-Leutwiler_1989">{{cite journal |author-last1=Eriksson-Bique |author-first1=Sirkka-Liisa Anneli |author-link1=:fi:Sirkka-Liisa Eriksson |author-last2=Leutwiler |author-first2=Heinz |title=A generalization of parallel addition |journal=[[Aequationes Mathematicae]] |publisher=[[Birkhäuser Verlag]] |date=February 1989 |orig-date=1989-01-10 |volume=38 |issue=1 |pages=99–110 |doi=10.1007/BF01839498 |url=https://link.springer.com/content/pdf/10.1007/BF01839498.pdf |access-date=2020-08-20 |url-status=live |archive-url=https://web.archive.org/web/20200820155352/https://link.springer.com/content/pdf/10.1007/BF01839498.pdf |archive-date=2020-08-20}}</ref>

<ref name="Ellerman_1995">{{cite book |title=Intellectual Trespassing as a Way of Life: Essays in Philosophy, Economics, and Mathematics |chapter=Chapter 12: Parallel Addition, Series-Parallel Duality, and Financial Mathematics |series=G – Reference, Information and Interdisciplinary Subjects Series |workseries=The worldly philosophy: studies in intersection of philosophy and economics |author-first=David Patterson |author-last=Ellerman |author-link=David Patterson Ellerman |edition=illustrated |publisher=[[Rowman & Littlefield Publishers, Inc.]] |date=1995-03-21 |isbn=0-8476-7932-2 |pages=237–268 |url=http://www.ellerman.org/wp-content/uploads/2012/12/IntellectualTrespassingBook.pdf |chapter-url=https://books.google.com/books?id=NgJqXXk7zAAC&pg=PA237 |access-date=2019-08-09 |url-status=live |archive-url=https://web.archive.org/web/20160305012729/http://www.ellerman.org/wp-content/uploads/2012/12/IntellectualTrespassingBook.pdf |archive-date=2016-03-05 |quote-page=237 |quote=[…] When resistors with resistance a and b are placed in series, their compound resistance is the usual sum (hereafter the ''[[series sum]]'') of the resistances a&nbsp;+ b. If the resistances are placed in parallel, their compound resistance is the ''parallel sum'' of the resistances, which is denoted by the [[full colon]] […]}} [https://web.archive.org/web/20150917191423/http://www.ellerman.org/Davids-Stuff/Maths/sp_math.doc] (271 pages)</ref>

<ref name="Georg_1999">{{cite book |title=Elektromagnetische Felder und Netzwerke: Anwendungen in Mathcad und PSpice |chapter=Chapter 2.11.4.3: Aufstellen der Differentialgleichung aus der komplexen Darstellung - MATHCAD Anwendung 2.11-6: Benutzerdefinierte Operatoren |chapter-url=https://books.google.com/books?id=wBAjBgAAQBAJ&pg=PA246 |language=de |author-first=Otfried |author-last=Georg |date=2013 |orig-date=1999 |edition=1 |series=Springer-Lehrbuch |publisher=[[Springer-Verlag]] |isbn=978-3-642-58420-6 |id={{ISBN|3-642-58420-9}} |doi=10.1007/978-3-642-58420-6 |pages=246–248 |url=https://books.google.com/books?id=wBAjBgAAQBAJ |access-date=2019-08-04}} (728 pages)</ref>

<ref name="Ellerman_2004">{{cite web |title=Introduction to Series-Parallel Duality |author-first=David Patterson |author-last=Ellerman |author-link=David Patterson Ellerman |publisher=[[University of California at Riverside]] |date=May 2004 |orig-date=1995-03-21 |citeseerx=10.1.1.90.3666 |url=http://www.ellerman.org/wp-content/uploads/2012/12/Series-Parallel-Duality.CV_.pdf |access-date=2019-08-09 |url-status=live |archive-url=https://web.archive.org/web/20190810011716/http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.90.3666&rep=rep1&type=pdf<!-- https://archive.today/20190810080659/http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.90.3666&rep=rep1&type=pdf --> |archive-date=2019-08-10 |quote=The parallel sum of two positive real numbers x:y&nbsp;= [(1/x)&nbsp;+ (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 (mathematics)|duality]] between the usual [[series sum|(series) sum]] and the parallel sum. […]}} [http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.90.3666&rep=rep1&type=pdf] (24 pages)</ref>