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A Note on PIN Polynomials and PRIN Rational Functions

M.Z.Q. Chen
<span title="">2008</span> <i title="Institute of Electrical and Electronics Engineers (IEEE)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/c352rf3zizflhbzkvxrawww7mu" style="color: black;">IEEE Transactions on Circuits and Systems - II - Express Briefs</a> </i> &nbsp;
This brief presents a necessary and sufficient condition for testing positive, real, imaginary, and negative rational functions.  ...  A related term, the positive, imaginary, and negative polynomial, is defined and two necessary and sufficient conditions for testing it are given.  ...  Two necessary and sufficient conditions for testing such polynomials were presented. In turn, a necessary and sufficient condition for testing PRIN rational functions was given.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/tcsii.2007.912686">doi:10.1109/tcsii.2007.912686</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/3yihm6cx5fezjf4dm6ens3nnrq">fatcat:3yihm6cx5fezjf4dm6ens3nnrq</a> </span>
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Page 1221 of Mathematical Reviews Vol. 33, Issue 5 [page]

<span title="">1967</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;
Muroga, Saburo 7203 Functional forms of dual-comparable functions and a necessary and sufficient condition for realizability of a majority function. IEEE Trans.  ...  Necessary and sufficient conditions for the existence of a system of non-adjacent representatives are suggested.” Mirkin, B. G. 7209 On dual automata. (Russian.  ... 
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Observability and Controllability of MIMO Control Systems via Difference Equations

Elizabeth. S, Jothilakshmi. R
<span title="2013-01-18">2013</span> <i title="Foundation of Computer Science"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/b637noqf3vhmhjevdfk3h5pdsu" style="color: black;">International Journal of Computer Applications</a> </i> &nbsp;
The necessary and sufficient condition for irreducibility of the set of nonlinear multi input-multi output (MIMO) is presented in terms of the greatest common left divisor of two polynomial matrices describing  ...  the behavior of the system which is suitable for constructing an observable and accessible state space realization.  ...  and sufficient conditions for existence of their observable state space realizations.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.5120/10048-4634">doi:10.5120/10048-4634</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/lsbjfw76qvdklh6sbt4fxnv4ru">fatcat:lsbjfw76qvdklh6sbt4fxnv4ru</a> </span>
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Page 1107 of Mathematical Reviews Vol. 56, Issue 3 [page]

<span title="">1978</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;
At first several simple theorems are proved to give necessary and sufficient conditions for a given function / of n variables to have prime subfunctions.  ...  Authors’ summary: “‘The conditions of necessity and sufficiency for the effort and flow equations of junction structures have been examined.  ... 
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Page 957 of Automation and Remote Control Vol. 22, Issue 8 [page]

<span title="">1961</span> <i title="Springer Science &amp; Business Media"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_automation-and-remote-control" style="color: black;">Automation and Remote Control </a> </i> &nbsp;
Therefore, when it is necessary to realize a new optimum condition no information on the form of optimal @r almos® circuits is necessary.  ...  sed tis - sy pose fi- example is the algorithm for obtaining the minimal form of a Boolean function given in the disjunctive 4 > fo 4, % > normal form [1].  ... 
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Page 1247 of Mathematical Reviews Vol. 29, Issue 6 [page]

<span title="">1965</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;
The author obtains the necessary and sufficient conditions for a function F to be of the form F=A,,(x,, %2)+ Agq(%g,%4) + Age(%s, Xe) in F, =f (x1, 2g), Fo=9(%1,4a), F,= W(xs, 24), Py=x(%p, 2), fa=91,  ...  The author obtains the necessary and sufficient conditions for a function to be of-the form F=A,,(2,, %2)+ Asq(Xg, %4) + Ag(%s) + Ag(%e) in F, =f (x1, 22), Fo= (x1, Xa), F,= (Xp, %), Fe=x(%g, %), F5=0(  ... 
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Page 1466 of Automation and Remote Control Vol. 33, Issue 9 [page]

<span title="">1972</span> <i title="Springer Science &amp; Business Media"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_automation-and-remote-control" style="color: black;">Automation and Remote Control </a> </i> &nbsp;
of the quadratic forms and the choice of P is reduced to a nonlinear programming problem in the space of parameters Pij- The algorithm is realized on a digital computer.  ...  By means of majorization and taking into account the subsystem interaction, the problem of constructing LVF is reduced to finding a constant, positive Hurwitz matrix P which satisfies the conditions av  ... 
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Page 1483 of Mathematical Reviews Vol. 58, Issue 2 [page]

<span title="">1979</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;
Previ- ous works have given necessary and sufficient conditions for a system to be 4, fault diagnosable, i.e., a system for which one test is sufficient to identify all sets of permanently faulty units  ...  Necessary and sufficient condi- tions for a function to have bilineal separability are given, and test 58 #9870  ... 
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Table of contents

<span title="">1961</span> <i title="IEEE"> 2nd Annual Symposium on Switching Circuit Theory and Logical Design (SWCT 1961) </i> &nbsp;
Chow • If • • • .34 Functional Forms of Majority Functions and a Necessary and Sufficient ••••• 39 Condition for their Realizability by S.  ...  . ••• 87 One Method for Designing Speed Independent Logic for a Control ••••••••• 94 by R. E. Swartwout Problems in the Physical Realization of Speed Ind.pendent Circuit' by J. E.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/focs.1961.32">doi:10.1109/focs.1961.32</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/7h5e6lakpfdjjiyyzt2o2aaaxq">fatcat:7h5e6lakpfdjjiyyzt2o2aaaxq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170830080249/https://www.computer.org/csdl/proceedings/focs/1961/5428/00/5397268.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/07/86/07865515e20bd4a312a50ed001c9684635541bab.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/focs.1961.32"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>

Page 1349 of Mathematical Reviews Vol. , Issue 86c [page]

<span title="">1986</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;
A new necessary condition is derived which the invariant polynomials must satisfy. The sufficiency condition of Rosenbrock and Hayton is proved in an alternative way.  ...  It is based on the block observable lower Hessenberg form of (A, C), and all its initial and major computation involves only the orthogonal operations.”  ... 
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Transfer Matrix Approach to the Triangular Decoupling of General Neutral Multi-Delay Systems

F.N. Koumboulis, G.E. Panagiotakis
<span title="">2008</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/p3wtlm3j2fedxitkuu4bs3scau" style="color: black;">IFAC Proceedings Volumes</a> </i> &nbsp;
: The necessary and sufficient conditions for the problem to have a realizable solution and the general analytical expressions of the proportional realizable TD controller matrices.  ...  The conditions and the solution of the controller matrices are computed using a finite step pure algebraic approach.  ...  Acknowledgement: The present work has been funded by the Greek General Secretariat for Research and Technology, Joint Research and Technology Programmes, Greece-Spain, Project: E-Science for Control Engineering  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3182/20080706-5-kr-1001.00220">doi:10.3182/20080706-5-kr-1001.00220</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/gckyz7dq7bhzvoud6vgnozmxje">fatcat:gckyz7dq7bhzvoud6vgnozmxje</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170815161215/http://folk.ntnu.no/skoge/prost/proceedings/ifac2008/data/papers/3824.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/3f/88/3f88e0b2ed3f647dfbc11a8994375f67b5e04428.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3182/20080706-5-kr-1001.00220"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Page 2347 of Mathematical Reviews Vol. 56, Issue 6 [page]

<span title="">1978</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;
Moreover, necessary and sufficient conditions for particular values of t and n are stated.” {For the entire collection see MR 54 #14419.} Desoer, C.  ...  normal forms assume values i for x #0 and 0 for x=0.  ... 
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A Simple Solution to a Major Problem: Proof of the Riemann Hypothesis [article]

Fayang Qiu
<span title="2018-01-29">2018</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Starting from the symmetrical reflection functional equation of the zeta function, we have found that the sigma values satisfying zeta(s) = 0 must also satisfy both |zeta(s)| = |zeta(1 - s)| and |gamma  ...  if (8) is true: 2 1 2 ib ib           (8) In this case, (6) and (8) are mutually sufficient and necessary conditions to each other.  ...  [3] Therefore,  = ½ is a necessary condition for the Riemann zeta function to have nontrivial zeros, which is equivalent to the statement that all nontrivial zeros of the zeta function have real part  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/0801.4072v6">arXiv:0801.4072v6</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/6gfwpnorabcoph5xh76lvlm2rm">fatcat:6gfwpnorabcoph5xh76lvlm2rm</a> </span>
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Contextual Emergence and Its Applications in Philosophy of Mind and Cognitive Science

Robert Poczobut
<span title="">2018</span> <i title="Towarzystwo Naukowe KUL"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/v7ic63axnjcfli2zf3qwvzxghe" style="color: black;">Roczniki Filozoficzne</a> </i> &nbsp;
However, they are not able to explain all of the details connected with their realization -they determine the necessary conditions, but are insufficient for the existence and the functioning of the mind  ...  organizational level delivers necessary and sufficient conditions for introducing a descrip-tion of properties at a higher organizational level.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.18290/rf.2018.66.3-6">doi:10.18290/rf.2018.66.3-6</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/tbofaun5sjdijmjpzeyuxxypxu">fatcat:tbofaun5sjdijmjpzeyuxxypxu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200320065036/http://czasopisma.tnkul.pl/index.php/RF/article/download/10053/10069" 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/c8/7c/c87c990adc0978bf131e601530bb30291efb7e1d.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.18290/rf.2018.66.3-6"> <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>

Dynamical structure function identifiability conditions enabling signal structure reconstruction

J. Adebayo, T. Southwick, V. Chetty, E. Yeung, Y. Yuan, J. Goncalves, J. Grose, J. Prince, G.B. Stan, S. Warnick
<span title="">2012</span> <i title="IEEE"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/wjd7b2sxyfahnaei4xvi46vwsu" style="color: black;">2012 IEEE 51st IEEE Conference on Decision and Control (CDC)</a> </i> &nbsp;
This work extends these results to demonstrate precisely the a priori structural information that is both necessary and sufficient to reconstruct the network from input-output data.  ...  Consequently, one method previously suggested for obtaining the necessary a priori structural information is to leverage knowledge about target specificity of the controlled inputs.  ...  The main result then follows, with necessary and sufficient identifiability conditions for reconstructing a system's DSF.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/cdc.2012.6426183">doi:10.1109/cdc.2012.6426183</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/cdc/AdebayoSCYYGGPSW12.html">dblp:conf/cdc/AdebayoSCYYGGPSW12</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/kyodaapvhjguvbkvrodvzv4mce">fatcat:kyodaapvhjguvbkvrodvzv4mce</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20161110091547/http://www.bg.ic.ac.uk/research/g.stan/CDC_2012c.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/8a/cf/8acfae0e8c33719bc2b3c2ade291afe9bce47d09.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/cdc.2012.6426183"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>
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