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Confusion in the Church-Turing Thesis [article]

Barry Jay, Jose Vergara
<span title="2014-11-06">2014</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
However, a modern combinatory calculus, the SF-calculus, can define equality of its closed normal forms, and so yields a model of computability that is equivalent to the Turing model.  ...  The Church-Turing Thesis confuses numerical computations with symbolic computations.  ...  Acknowledgments We thank Jacques Carette, Robin Cockett, John Crossley, Nachum Dershowitz, Thomas Given-Wilson, Neil Jones, Jens Palsberg, Reuben Rowe, Peter Selinger, and Eric Torreborre for comments on drafts of  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1410.7103v2">arXiv:1410.7103v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ybkzeatss5bdrpvhsj5c5p5bii">fatcat:ybkzeatss5bdrpvhsj5c5p5bii</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200915055450/https://arxiv.org/pdf/1410.7103v2.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/3d/49/3d49f7d60b3ddd91232d53a3d5f93ad9482b40e8.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1410.7103v2" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Lambda Obfuscation [chapter]

Pengwei Lan, Pei Wang, Shuai Wang, Dinghao Wu
<span title="">2018</span> <i title="Springer International Publishing"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/jajl7qtqc5cy7oavratsldrv2y" style="color: black;">Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering</a> </i> &nbsp;
Our obfuscator replaces the conditional instructions with lambda calculus function calls that simulate the same behavior with a more complicated execution model.  ...  Branch conditions contain important control flow logic of a program.  ...  This research was supported in part by the National Science Foundation (NSF) under grant CNS-1652790, and the Office of Naval Research (ONR) under grants N00014-13-1-0175, N00014-16-1-2265, and N00014-  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-319-78813-5_11">doi:10.1007/978-3-319-78813-5_11</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/rejp26s6unejblib54ck7tad2u">fatcat:rejp26s6unejblib54ck7tad2u</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190225152524/http://pdfs.semanticscholar.org/6134/5a445ea8dea4e575660ea59ad55176d50f91.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/61/34/61345a445ea8dea4e575660ea59ad55176d50f91.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-319-78813-5_11"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Programming Complex Systems [article]

Philip Maymin
<span title="1997-10-15">1997</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Classical programming languages cannot model essential elements of complex systems such as true random number generation.  ...  Since satisfiability is believed to be beyond the capabilities of quantum computers, the lambda-q calculus may be strictly stronger.  ...  Introduction The purpose of this paper is to introduce a formalism for expressing models of complex systems.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/quant-ph/9710035v1">arXiv:quant-ph/9710035v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/k6rvzrv3ezfurl655w4gdb4nlu">fatcat:k6rvzrv3ezfurl655w4gdb4nlu</a> </span>
<a target="_blank" rel="noopener" href="https://archive.org/download/arxiv-quant-ph9710035/quant-ph9710035.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> File Archive [PDF] </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/quant-ph/9710035v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Numerical simulation for SI model with variable-order fractional

Hanaa Abdel Hameed Asfour, Mohamed Gamal M. Ibrahim
<span title="2016-04-10">2016</span> <i title="New Trends in Mathematical Science"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/dvkaxdf7lfhkrit2hmduxzen2a" style="color: black;">New Trends in Mathematical Sciences</a> </i> &nbsp;
Numerical test examples are presented to demonstrate utility of the method. Chaotic behaviors are observed in variable-order one dimensional delayed systems.  ...  In this paper numerical studies for the variable-order fractional delay differential equations are presented.  ...  By using the Adams-Bash forth-Moulton method, we obtain the numerical solution of the variable-order fractional SI Model We present a convergent of SI Model in section 4, also we prove that the Existence  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.20852/ntmsci.2016217004">doi:10.20852/ntmsci.2016217004</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/rbawm4wsxrgl3mbukxil3dykzm">fatcat:rbawm4wsxrgl3mbukxil3dykzm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20171202093042/http://www.ntmsci.com/ajaxtool/GetArticleByPublishedArticleId?PublishedArticleId=7131" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/06/d3/06d3fa8b6b401a7e257a8525175c9ec675d19891.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.20852/ntmsci.2016217004"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

Noncommutative Geometry and Stochastic Calculus: Applications in Mathematical Finance

Eric A. Forgy
<span title="">2002</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/tol7woxlqjeg5bmzadeg6qrg3e" style="color: black;">Social Science Research Network</a> </i> &nbsp;
The abstract construction allows for the straightforward generalization to lattice theories for the direct implementation of numerical models.  ...  As an elementary demonstration of the formalism, the standard Black-Scholes model for option pricing is reformulated.  ...  This promises to provide for a robust mathematical framework for constructing numerical models of stochastic differential equations in any number of dimensions.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2139/ssrn.1420239">doi:10.2139/ssrn.1420239</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/3d5lloymczhnfgsvtwwy5mrpxu">fatcat:3d5lloymczhnfgsvtwwy5mrpxu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20060823001854/http://www.fastalgorithms.com:80/eric/papers/blackscholes.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/ec/b9/ecb94de60bc824280219ea25082406f8cbf72da1.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2139/ssrn.1420239"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ssrn.com </button> </a>

OPUS: a Calculus for Modelling Object-Oriented Concepts [chapter]

Tom Mens, Kim Mens, Patrick Steyaert
<span title="">1995</span> <i title="Springer London"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/zp6vvyc7jffedmaq2rppbj56ny" style="color: black;">OOIS&#39;94</a> </i> &nbsp;
State and encapsulated inheritance are modelled by means of an incremental modification operator.  ...  We propose a very concise calculus for modelling object-oriented concepts such as objects, message sending, encapsulation and incremental modification.  ...  Our calculus is based on the model of substitutable objects.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-1-4471-3016-1_12">doi:10.1007/978-1-4471-3016-1_12</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/oois/MensMS94.html">dblp:conf/oois/MensMS94</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/avfeqybz45dn5f46tdkauzvucq">fatcat:avfeqybz45dn5f46tdkauzvucq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170922002722/http://soft.vub.ac.be/Publications/1994/vub-tinf-tr-94-04.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/5a/10/5a103569c1028479481337a000c2f6411cfdc6d8.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-1-4471-3016-1_12"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

What is a model for a semantically linear -calculus?

M. Gaboardi, M. Piccolo
<span title="2012-06-12">2012</span> <i title="Oxford University Press (OUP)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/crzmi3qeiramtlvcrfycib3qg4" style="color: black;">Journal of Logic and Computation</a> </i> &nbsp;
In this work, we introduce the notion of S λ-category, which is able to describe a large class of sound models of S λ-calculus.  ...  This paper is about a categorical approach to model a simple term calculus, named S λcalculus.  ...  -model We introduce here the second notion of categorical model for the S λ-calculus. Definition 26 (Categorical S λ ! -model). A categorical S λ !  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1093/logcom/exs023">doi:10.1093/logcom/exs023</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/4rtxyn5bkncbfpa6vnndhbu2za">fatcat:4rtxyn5bkncbfpa6vnndhbu2za</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190225172551/http://pdfs.semanticscholar.org/6608/6d6fd28e76b536b52784d793eef9769ff082.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/66/08/66086d6fd28e76b536b52784d793eef9769ff082.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1093/logcom/exs023"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> oup.com </button> </a>

The fractional and nonlinear magneto-flexible rod

S A David, J M Balthazar, B H S Julio, C Oliveira
<span title="2012-08-22">2012</span> <i title="IOP Publishing"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/wxgp7pobnrfetfizidmpebi4qy" style="color: black;">Journal of Physics, Conference Series</a> </i> &nbsp;
This fact motivated us to analyze such a mechanical system based on modeling and numerical simulation involving both, integer order calculus (IOC) and fractional order calculus (FOC) approaches.  ...  a flexible rod subjected to magnetic forces that can bend it while simultaneously subjected to external excitations produces complex and nonlinear dynamic behavior, which may present different types of  ...  In this article we investigate, by means of numerical simulations, the modified magneto-flexible rod dynamic equations (12) , i.e., t F x x x x ω δ λ λ cos 3 1 = + − + + (12) We presented the time responses  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1088/1742-6596/382/1/012056">doi:10.1088/1742-6596/382/1/012056</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/6uzpa7ivs5e6vh6327fo2q53py">fatcat:6uzpa7ivs5e6vh6327fo2q53py</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180719061556/http://iopscience.iop.org/article/10.1088/1742-6596/382/1/012056/pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/ac/91/ac91c86e124e1cdd62415148f2554c9d25e60d68.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1088/1742-6596/382/1/012056"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> iop.org </button> </a>

The lambda-q calculus can efficiently simulate quantum computers [article]

Philip Maymin
<span title="1997-02-26">1997</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We show that the lambda-q calculus can efficiently simulate quantum Turing machines by showing how the lambda-q calculus can efficiently simulate a class of quantum cellular automaton that are equivalent  ...  We conclude by noting that the lambda-q calculus may be strictly stronger than quantum computers because NP-complete problems such as satisfiability are efficiently solvable in the lambda-q calculus but  ...  T k times to the representation of c in the λ q -calculus.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/quant-ph/9702057v1">arXiv:quant-ph/9702057v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/as4m3zhnjfai7cvz7f3n7ka354">fatcat:as4m3zhnjfai7cvz7f3n7ka354</a> </span>
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Evolving the Incremental λ Calculus into a Model of Forward Automatic Differentiation (AD) [article]

Robert Kelly and Barak A. Pearlmutter and Jeffrey Mark Siskind
<span title="2016-11-10">2016</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
A newcomer to this list is the incremental λ-calculus, or ILC, a "theory of changes" that deploys a formal apparatus allowing the automatic generation of efficient update functions which perform incremental  ...  These steps can also be applied to the proofs, resulting in machine-checked proofs of the correctness of this model of forward AD.  ...  Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the sponsors.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1611.03429v1">arXiv:1611.03429v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/3wwvylycuffrzf6a4phoj5maay">fatcat:3wwvylycuffrzf6a4phoj5maay</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200909151005/https://arxiv.org/pdf/1611.03429v1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/3d/41/3d41a624019a4430f38e69799a5e06b896d57c69.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1611.03429v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

On Constructor Rewrite Systems and the Lambda-Calculus [chapter]

Ugo Dal Lago, Simone Martini
<span title="">2009</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
weak c-b-v λ-calculus are both reasonable machines, under their natural cost models: number of rewriting steps, and number of beta-reductions.  ...  and weak c-b-v λ-calculus are both reasonable machines, under their natural cost models: number of rewriting steps, and number of beta-reductions.  ...  Conclusions Constructor rewriting and weak c-b-v λ-calculus are both reasonable machines, under their natural cost models: number of rewriting steps, and number of beta-reductions.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-02930-1_14">doi:10.1007/978-3-642-02930-1_14</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/7npxlgdiavgrnluo2gaiiq52nq">fatcat:7npxlgdiavgrnluo2gaiiq52nq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170809070426/http://www.cs.unibo.it/martini/TALKS/icalp2009.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/da/5b/da5b21c0b1f0809fba2e772705b79edeac9ac015.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-02930-1_14"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Application of numerical inverse Laplace transform algorithms in fractional calculus

Hu Sheng, Yan Li, YangQuan Chen
<span title="">2011</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/k45e5zmenjbd3ewfbaacyemdq4" style="color: black;">Journal of the Franklin Institute</a> </i> &nbsp;
calculus.  ...  Motivated by finding an easy way to numerically solve the fractional-order differential equations, we investigated the validity of applying numerical inverse Laplace transform algorithms in fractional  ...  ACKNOWLEDGEMENTS This work is partially supported by the Projects of National 863 Program (Grant No. 2009AA04Z220 and 2006AA040206) and the Shandong University Research Startup Fund to Yan Li.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.jfranklin.2010.11.009">doi:10.1016/j.jfranklin.2010.11.009</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/zopvtv5xdfbv3kiaebqz6jbo7m">fatcat:zopvtv5xdfbv3kiaebqz6jbo7m</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20110912160008/http://mechatronics.ece.usu.edu/yqchen/paper/10/Application%20of%20Numerical%20Inverse%20Laplace%20transform%20algorithms%20in%20fractional%20calculus.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/70/84/708433a7f27f7e5dbf8ff296a9e84d28952c2918.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.jfranklin.2010.11.009"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Higher-Dimensional Fractional Order Modelling for Plasma Particles with Partial Slip Boundaries: A Numerical Study

Tamour Zubair, Muhammad Imran Asjad, Muhammad Usman, Jan Awrejcewicz
<span title="2021-10-28">2021</span> <i title="MDPI AG"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/jdgqfwsfhzegdhmzc3cgj3t7jy" style="color: black;">Nanomaterials</a> </i> &nbsp;
A detailed analysis of the proposed model with plotted figures is also included in the paper.  ...  We integrate fractional calculus and plasma modelling concepts with specific geometry in this article, and further formulate a higher dimensional time-fractional Vlasov Maxwell system.  ...  The main idea of this paper is that we formulated an extended version of VMS using the concepts of fractional calculus and further numerical simulations of the problem, which is influenced by the concepts  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3390/nano11112884">doi:10.3390/nano11112884</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/34835647">pmid:34835647</a> <a target="_blank" rel="external noopener" href="https://pubmed.ncbi.nlm.nih.gov/PMC8620451/">pmcid:PMC8620451</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/lbb7tfjdo5a23hgozvx6w6njcm">fatcat:lbb7tfjdo5a23hgozvx6w6njcm</a> </span>
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Replication is Recursion; or, Lambda: the Biological Imperative [article]

Scott Federhen
<span title="2015-05-01">2015</span> <i title="Cold Spring Harbor Laboratory"> bioRxiv </i> &nbsp; <span class="release-stage" >pre-print</span>
The following discussion will present enough of the mathematics to allow biologists to make sense of the symmetries in the logo.  ...  Living organisms are information processors – the genome encodes instructions for the process of life much as computer programs encode instructions for a computer.  ...  (When applied to two numbers, the Church numeral 1 actually computes (x↑y) -'unity is power' in the λ-calculus!)  ... 
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<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190430223017/https://www.biorxiv.org/content/biorxiv/early/2015/05/01/018804.full.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/0d/42/0d4239e31a76cbd2ab66b6a2e64067238a76ba36.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1101/018804"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> biorxiv.org </button> </a>

Mathematical Modeling and Algebraic Technique for Resolving a Single-Producer Multi-Retailer Integrated Inventory System with Scrap

Yuan-Shyi Peter Chiu, Chien-Hua Lee, Nong Pan, Singa Wang Chiu
<span title="2013-02-01">2013</span> <i title="Maxwell Scientific Publication Corp."> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/itifugluyrhulokjxf64yqrfey" style="color: black;">Research Journal of Applied Sciences Engineering and Technology</a> </i> &nbsp;
that enables practitioners who may not have sufficient knowledge of calculus to understand and manage more effectively the real-life systems.  ...  Conventional method is by the use of differential calculus on system cost function to derive the optimal policy (Chiu et al., 2012c) , whereas the proposed algebraic approach is a straightforward method  ...  ACKNOWLEDGMENT The authors appreciate National Science Council of Taiwan for supporting this research under grant number: NSC 99-2221-E-324-017.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.19026/rjaset.5.4881">doi:10.19026/rjaset.5.4881</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/bcca7vxuq5hfxhd4gxhitb7qny">fatcat:bcca7vxuq5hfxhd4gxhitb7qny</a> </span>
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