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Page 4938 of Mathematical Reviews Vol. , Issue 2003g [page]

<span title="">2003</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
pair of clones and of any minimal partial projection clone distinct from J, U Q;.  ...  A set {M, M;} of minimal clones (minimal partial clones) on a k-element set k (k > 2) is called gigantic if the least clone (partial clone) containing M, U---UM, is @ (A), the set of all total (partial  ... 
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Completeness theory for the product of finite partial algebras

B.A. Romov
<span title="">2004</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/civgv5utqzhu7aj6voo6vc5vx4" style="color: black;">Discrete Mathematics</a> </i> &nbsp;
This is used to obtain the full description of all maximal partial n-clones via multiple-base invariant relations and, thus, to solve the general completeness problem in P(ki).  ...  ¿ 2) is considered and a Galois connection between the lattice of subclones of P(ki), called partial n-clones, and the lattice of subalgebras of multiple-base invariant relation algebra, with operations  ...  any maximal partial n-clone (n ¿ 2).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0012-365x(03)00091-8">doi:10.1016/s0012-365x(03)00091-8</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/cyvmiitecnf2jgjw7f5w5f5ooq">fatcat:cyvmiitecnf2jgjw7f5w5f5ooq</a> </span>
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Extendable local partial clones

B.A. Romov
<span title="">2008</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/civgv5utqzhu7aj6voo6vc5vx4" style="color: black;">Discrete Mathematics</a> </i> &nbsp;
Considering local completeness (interpolation property) the structure of a maximal local partial clone is described via its intersections with the full partial clones on every finite k-element (k 2) subset  ...  Finally, based on these criteria the description of all extendable maximal local partial clones defined on the countable set is provided.  ...  Peter Hammer considered the theory of extension of partial to everywhere defined operations which preserves the same properties to be very significant, having profound theoretical and applied interest.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.disc.2007.07.080">doi:10.1016/j.disc.2007.07.080</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/zw7hdaacibg35dsufwttdzxnbu">fatcat:zw7hdaacibg35dsufwttdzxnbu</a> </span>
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Uniqueness of minimal coverings of maximal partial clones

Karsten Schölzel
<span title="">2011</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/3g7sk2fqarhcrmieipwvp62bfe" style="color: black;">Algebra Universalis</a> </i> &nbsp;
Since this holds if and only if f belongs to no maximal partial clone on E k , a characterization of partial Sheffer functions reduces to finding families of minimal coverings of maximal partial clones  ...  We show that for each k ≥ 2 there exists a unique minimal covering.  ...  A maximal partial clone (a maximal clone) on E k is a co-atom of P k and P k , respectively.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s00012-011-0138-z">doi:10.1007/s00012-011-0138-z</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/4znt2nu7pre4veyqgbdzziv6qq">fatcat:4znt2nu7pre4veyqgbdzziv6qq</a> </span>
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Page 7718 of Mathematical Reviews Vol. , Issue 2001K [page]

<span title="">2001</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
(H-AOS; Budapest); Szendrei, Agnes (H-SZEG-B; Szeged) The join of two minimal clones and the meet of two maximal clones. (English summary) Conference on Lattices and Universal Algebra (Szeged, 1998).  ...  In this paper the authors construct two minimal clones on any finite set such that the join of the two clones contains all operations.  ... 
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Minimal partial clones

F. Börner, L. Haddad, R. Pöschel
<span title="">1991</span> <i title="Cambridge University Press (CUP)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/qea6koy5crhvfgkjwgnwojjkrm" style="color: black;">Bulletin of the Australian Mathematical Society</a> </i> &nbsp;
We show that the minimal partial clones on A are: (a) minimal clones of full operations or (b) generated by partial projections defined on a totally reflexive and totally symmetric domain.  ...  Recently maximal partial clones were completely described by combinatorial properties [4].  ...  Every minimal clone on A is either a total minimal clone (that is, an atom in both Lo, and L p A ) or is a proper partial projection clone.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1017/s0004972700029919">doi:10.1017/s0004972700029919</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/d3p44hrmavh3he7qh32eebu3q4">fatcat:d3p44hrmavh3he7qh32eebu3q4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170808044228/http://www.math.tu-dresden.de/~poeschel/poePUBLICATIONSpdf/1991BoernerHaddadPoe.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/a2/2b/a22b9dc226a4e18b4ae23b6b8d9a2bf7ef398e5f.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1017/s0004972700029919"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> cambridge.org </button> </a>

Page 5373 of Mathematical Reviews Vol. , Issue 92j [page]

<span title="">1992</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
It is proved that the lattice of partial clones on A is atomic, and the minimal partial clones are exactly the minimal clones of full operations and the proper partial clones generated by partial projections  ...  A set of partial operations on A is called a partial clone if it is closed under superposition of partial operations and contains the (full) projections.  ... 
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A Short Introduction to Clones

Sebastian Kerkhoff, Reinhard Pöschel, Friedrich Martin Schneider
<span title="">2014</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/uy5mv2ncw5eahkdx47hkrglxmm" style="color: black;">Electronical Notes in Theoretical Computer Science</a> </i> &nbsp;
We conclude the paper by explaining the connection between clones and the closely related category theoretic notion of Lawvere theory.  ...  We also discuss what is arguably the most important tool to study clones -the Galois connection between operations and relations built on the notion of preservation.  ...  This is not surprising since, unlike maximality, minimality of a clone is an abstract property, that is, a clone is minimal if and only if its abstract clone has no proper (abstract) subclones.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.entcs.2014.02.006">doi:10.1016/j.entcs.2014.02.006</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/q4y5bcqcrnehle5zvrbm3ajowa">fatcat:q4y5bcqcrnehle5zvrbm3ajowa</a> </span>
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Experimental demonstration of optimal universal asymmetric quantum cloning of polarization states of single photons by partial symmetrization

Antonín Černoch, Jan Soubusta, Lucie Čelechovská, Miloslav Dušek, Jaromír Fiurášek
<span title="2009-12-02">2009</span> <i title="American Physical Society (APS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/iedolmzeofgc3ezyedga7h4eba" style="color: black;">Physical Review A. Atomic, Molecular, and Optical Physics</a> </i> &nbsp;
Our linear optical machine performs asymmetric cloning by partially symmetrizing the input polarization state of signal photon and a blank copy idler photon prepared in a maximally mixed state.  ...  We report on experimental implementation of the optimal universal asymmetric 1->2 quantum cloning machine for qubits encoded into polarization states of single photons.  ...  One photon from this maximally entangled pair would replace the idler photon and be injected into the partial symmetrizer together with a signal photon whose polarization state should be cloned.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1103/physreva.80.062306">doi:10.1103/physreva.80.062306</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/wv5jtn6s3fbp7ns4wlo23yi6se">fatcat:wv5jtn6s3fbp7ns4wlo23yi6se</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190308035832/http://pdfs.semanticscholar.org/ec29/6bb42ffbd5f97b4e94a247b77959567b8d82.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/29/ec296bb42ffbd5f97b4e94a247b77959567b8d82.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1103/physreva.80.062306"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> aps.org </button> </a>

Page 29 of Mathematical Reviews Vol. , Issue 87a [page]

<span title="">1987</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
These papers are concerned with determining the maximal closed sets of partial functions of k-valued logic.  ...  Essentially minimal TC-clones on a three-element set. (Russian. English and Hungarian summaries) K6ézl.—MTA Szdémitdstech. Automat. Kuiaté Int. Budapest No. 31 (1984), 115-151.  ... 
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The broadcast quantum channel for classical information transmission [article]

A.E. Allahverdyan, D.B. Saakian
<span title="1998-05-22">1998</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Instead the clones are correlated, and this breaks their usefulness: The entanglement increases with non-orthogonality of the states.  ...  We consider the optimal copying transformation which is adapted to classical information transmission by two linearly independent quantum states, and show that there is no additional contribution to the  ...  If 0-channel is out (totally noised) then R 1 (R 2 ) is maximal (minimal), and if 0-channel is noise-free then the opposite case is realized: R 2 (R 1 ) is maximal (minimal).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/quant-ph/9805067v1">arXiv:quant-ph/9805067v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/y4c6gdfvnvdh7ewpenxxc4en3y">fatcat:y4c6gdfvnvdh7ewpenxxc4en3y</a> </span>
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Optimal reactive power flow incorporating static voltage stability based on multi-objective adaptive immune algorithm

Hugang Xiong, Haozhong Cheng, Haiyu Li
<span title="">2008</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/wahc3ygvi5gzpmxve2hi3pfm3y" style="color: black;">Energy Conversion and Management</a> </i> &nbsp;
The second part uses adaptive crossover, mutation and clone rates for antibodies to maintain the antibodies diversity.  ...  The first part defines both partial affinity and global affinity to evaluate the antibody affinity to the multi-objective functions.  ...  Acknowledgments The work reported in this paper has been supported by the National 863 Project of China (No. 2005AA505101-621) and Important Science and Technology Research Project of Shanghai (No. 041612012  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.enconman.2007.09.005">doi:10.1016/j.enconman.2007.09.005</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/3hi3wvtsrbb5xcplda6dv7645y">fatcat:3hi3wvtsrbb5xcplda6dv7645y</a> </span>
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Page 9 of Mathematical Reviews Vol. , Issue 2003A [page]

<span title="">2003</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
Rosenberg, On the intersection of maximal partial clones and the join of minimal partial clones (396-401); Yasunori Nagata, D.  ...  Fugére], Maximal chains of partial clones containing all idempotent partial functions (80 84); Lucien Haddad and Dietlinde Lau, Partial clones and their generating sets (85-90); Elena Dubrova, Evaluation  ... 
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On Finite Generability of Clones of Finite Posets

Ádám Kunos, Miklós Maróti, László Zádori
<span title="2019-04-04">2019</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/7mt242gntfeabftbttg3gwnsmq" style="color: black;">Order</a> </i> &nbsp;
We prove that the clones of bounded posets are generated by certain ascending idempotent monotone operations and the 0 and 1 constant operations.  ...  operation and the 0 and 1 constant operations.  ...  reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s11083-019-09486-3">doi:10.1007/s11083-019-09486-3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/i6mse56whbe45js4gephn37lfq">fatcat:i6mse56whbe45js4gephn37lfq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200310094414/https://link.springer.com/content/pdf/10.1007%2Fs11083-019-09486-3.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/37/85/37852cebbc9a3cf85f4335d2a33c1fe52f08d68e.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s11083-019-09486-3"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Maximal partial clones determined by the areflexive relations

Lucien Haddad, I.G. Rosenberg
<span title="">1989</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/lx7dev2le5anbg6oarljwh7lie" style="color: black;">Discrete Applied Mathematics</a> </i> &nbsp;
A universal completeness criterion reduces to finding the complete list of maximal partial clones.  ...  To each such clone C (with one exception, in fact a non-strong maximal clone) there is an h-ary relation on A so that C consists of all partial operations f admitting co as subalgebra of (A,f) h.  ...  Such a criterion may be based on the knowledge of all maximal partial clones (i.e. the dual atoms or tile co-atoms in the lattice of partial clones).  ... 
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