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Relevant bibliographies by topics / Perfect numbers

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Academic literature on the topic 'Perfect numbers'

Author: Grafiati

Published: 4 June 2021

Last updated: 29 July 2024

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Journal articles on the topic "Perfect numbers"

1

Hassler, Uwe. "Perfect Numbers." Euleriana 3, no. 2 (August 22, 2023): 176–85. http://dx.doi.org/10.56031/2693-9908.1052.

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Ausubel, Ramona. "Perfect Numbers." Ploughshares 50, no. 2 (June 2024): 32–46. http://dx.doi.org/10.1353/plo.2024.a932313.

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Abstract: The Summer 2024 Issue. Ploughshares is an award-winning journal of new writing. Since 1971, Ploughshares has discovered and cultivated the freshest voices in contemporary American literature, and now provides readers with thoughtful and entertaining literature in a variety of formats. Find out why the New York Times named Ploughshares “the Triton among minnows.” The Summer 2024 Issue, guest-edited by Rebecca Makkai, features prose by Dur e Aziz Amna, Ramona Ausubel, Peter Mountford, Khaddafina Mbabazi, DK Nnuro, and more.

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Holdener, Judy, and Emily Rachfal. "Perfect and Deficient Perfect Numbers." American Mathematical Monthly 126, no. 6 (May 29, 2019): 541–46. http://dx.doi.org/10.1080/00029890.2019.1584515.

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Fu, Ruiqin, Hai Yang, and Jing Wu. "The Perfect Numbers of Pell Number." Journal of Physics: Conference Series 1237 (June 2019): 022041. http://dx.doi.org/10.1088/1742-6596/1237/2/022041.

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Pollack, Paul, and Vladimir Shevelev. "On perfect and near-perfect numbers." Journal of Number Theory 132, no. 12 (December 2012): 3037–46. http://dx.doi.org/10.1016/j.jnt.2012.06.008.

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Heath-Brown, D. R. "Odd perfect numbers." Mathematical Proceedings of the Cambridge Philosophical Society 115, no. 2 (March 1994): 191–96. http://dx.doi.org/10.1017/s0305004100072030.

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It is not known whether or not odd perfect numbers can exist. However it is known that there is no such number below 10300 (see Brent[1]). Moreover it has been proved by Hagis[4]and Chein[2] independently that an odd perfect number must have at least 8 prime factors. In fact results of this latter type can in priniciple be obtained solely by calculation, in view of the result of Pomerance[6] who showed that if N is an odd perfect number with at most k prime factors, thenPomerance's work was preceded by a theorem of Dickson[3]showing that there can be only a finite number of such N. Clearly however the above bound is vastly too large to be of any practical use. The principal object of the present paper is to sharpen the estimate (1). Indeed we shall handle odd ‘multiply perfect’ numbers in general, as did Kanold[5], who extended Dickson's work, and Pomerance. Our result is the following.

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Klurman, Oleksiy. "Radical of perfect numbers and perfect numbers among polynomial values." International Journal of Number Theory 12, no. 03 (March 23, 2016): 585–91. http://dx.doi.org/10.1142/s1793042116500378.

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It is conjectured that [Formula: see text] for any perfect number [Formula: see text]. We prove that [Formula: see text] improving the previous bound of Luca and Pomerance as well as Acquaah and Konyagin. As a consequence, we prove that assuming the [Formula: see text]-conjecture, any integer polynomial of degree [Formula: see text] without repeated factors can take only finitely many perfect values. We also show that the latter holds unconditionally for even perfect numbers.

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Tang, Min, Xiao-Zhi Ren, and Meng Li. "On near-perfect and deficient-perfect numbers." Colloquium Mathematicum 133, no. 2 (2013): 221–26. http://dx.doi.org/10.4064/cm133-2-8.

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J. J., Segura, and Ortega S. "All KnownPerfect Numbers other than 6 Satisfy N=4+6n." international journal of mathematics and computer research 12, no. 03 (March 23, 2024): 4103–6. http://dx.doi.org/10.47191/ijmcr/v12i3.04.

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For all 51 known perfect numbers ranging from (p=2 to p= 82589933) and with the only exception of N=6, all perfect numbers belong to the group of natural numbers formed by N=4+6n. If this observation can be proven valid for all existing even perfect numbers, that would automatically exclude 2/3 of all even numbers out of the possibility of being perfect. If this can be proven a necessary condition for all perfect numbers, then it would rule out the possibility of having any odd perfect numbers.

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Jiang, Xing-Wang. "On even perfect numbers." Colloquium Mathematicum 154, no. 1 (2018): 131–36. http://dx.doi.org/10.4064/cm7374-11-2017.

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Dissertations / Theses on the topic "Perfect numbers"

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Yamada, Tomohiro. "Unitary super perfect numbers." 京都大学 (Kyoto University), 2009. http://hdl.handle.net/2433/124385.

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Abu-Arish, Hiba Ibrahim. "Perfect Numbers and Perfect Polynomials: Motivating Concepts From Kindergarten to College." The Ohio State University, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=osu1461154144.

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Kolenick, Joseph F. "On exponentially perfect numbers relatively prime to 15 /." Connect to resource online, 2007. http://rave.ohiolink.edu/etdc/view?acc_num=ysu1196698780.

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Kolenick, Joseph F. Jr. "On Exponentially Perfect Numbers Relatively Prime to 15." Youngstown State University / OhioLINK, 2007. http://rave.ohiolink.edu/etdc/view?acc_num=ysu1196698780.

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Sutharzan, Sreeskandarajan. "A GENOME-WIDE ANALYSIS OF PERFECT INVERTED REPEATS IN ARABIDOPSIS THALIANA." Miami University / OhioLINK, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=miami1386848607.

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Janse, Sarah A. "INFERENCE USING BHATTACHARYYA DISTANCE TO MODEL INTERACTION EFFECTS WHEN THE NUMBER OF PREDICTORS FAR EXCEEDS THE SAMPLE SIZE." UKnowledge, 2017. https://uknowledge.uky.edu/statistics_etds/30.

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In recent years, statistical analyses, algorithms, and modeling of big data have been constrained due to computational complexity. Further, the added complexity of relationships among response and explanatory variables, such as higher-order interaction effects, make identifying predictors using standard statistical techniques difficult. These difficulties are only exacerbated in the case of small sample sizes in some studies. Recent analyses have targeted the identification of interaction effects in big data, but the development of methods to identify higher-order interaction effects has been limited by computational concerns. One recently studied method is the Feasible Solutions Algorithm (FSA), a fast, flexible method that aims to find a set of statistically optimal models via a stochastic search algorithm. Although FSA has shown promise, its current limits include that the user must choose the number of times to run the algorithm. Here, statistical guidance is provided for this number iterations by deriving a lower bound on the probability of obtaining the statistically optimal model in a number of iterations of FSA. Moreover, logistic regression is severely limited when two predictors can perfectly separate the two outcomes. In the case of small sample sizes, this occurs quite often by chance, especially in the case of a large number of predictors. Bhattacharyya distance is proposed as an alternative method to address this limitation. However, little is known about the theoretical properties or distribution of B-distance. Thus, properties and the distribution of this distance measure are derived here. A hypothesis test and confidence interval are developed and tested on both simulated and real data.

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Benchetrit, Yohann. "Propriétés géométriques du nombre chromatique : polyèdres, structures et algorithmes." Thesis, Université Grenoble Alpes (ComUE), 2015. http://www.theses.fr/2015GREAM049/document.

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Le calcul du nombre chromatique et la détermination d'une colo- ration optimale des sommets d'un graphe sont des problèmes NP- difficiles en général. Ils peuvent cependant être résolus en temps po- lynomial dans les graphes parfaits. Par ailleurs, la perfection d'un graphe peut être décidée efficacement. Les graphes parfaits sont caractérisés par la structure de leur poly- tope des stables : les facettes non-triviales sont définies exclusivement par des inégalités de cliques. Réciproquement, une structure similaire des facettes du polytope des stables détermine-t-elle des propriétés combinatoires et algorithmiques intéressantes? Un graphe est h-parfait si les facettes non-triviales de son polytope des stables sont définies par des inégalités de cliques et de circuits impairs. On ne connaît que peu de résultats analogues au cas des graphes parfaits pour la h-perfection, et on ne sait pas si les problèmes sont NP-difficiles. Par exemple, les complexités algorithmiques de la re- connaissance des graphes h-parfaits et du calcul de leur nombre chro- matique sont toujours ouvertes. Par ailleurs, on ne dispose pas de borne sur la différence entre le nombre chromatique et la taille maxi- mum d'une clique d'un graphe h-parfait. Dans cette thèse, nous montrons tout d'abord que les opérations de t-mineurs conservent la h-perfection (ce qui fournit une extension non triviale d'un résultat de Gerards et Shepherd pour la t-perfection). De plus, nous prouvons qu'elles préservent la propriété de décompo- sition entière du polytope des stables. Nous utilisons ce résultat pour répondre négativement à une question de Shepherd sur les graphes h-parfaits 3-colorables. L'étude des graphes minimalement h-imparfaits (relativement aux t-mineurs) est liée à la recherche d'une caractérisation co-NP com- binatoire de la h-perfection. Nous faisons l'inventaire des exemples connus de tels graphes, donnons une description de leur polytope des stables et énonçons plusieurs conjectures à leur propos. D'autre part, nous montrons que le nombre chromatique (pondéré) de certains graphes h-parfaits peut être obtenu efficacement en ar- rondissant sa relaxation fractionnaire à l'entier supérieur. Ce résultat implique notamment un nouveau cas d'une conjecture de Goldberg et Seymour sur la coloration d'arêtes. Enfin, nous présentons un nouveau paramètre de graphe associé aux facettes du polytope des couplages et l'utilisons pour donner un algorithme simple et efficace de reconnaissance des graphes h- parfaits dans la classe des graphes adjoints
Computing the chromatic number and finding an optimal coloring of a perfect graph can be done efficiently, whereas it is an NP-hard problem in general. Furthermore, testing perfection can be carried- out in polynomial-time. Perfect graphs are characterized by a minimal structure of their sta- ble set polytope: the non-trivial facets are defined by clique-inequalities only. Conversely, does a similar facet-structure for the stable set polytope imply nice combinatorial and algorithmic properties of the graph ? A graph is h-perfect if its stable set polytope is completely de- scribed by non-negativity, clique and odd-circuit inequalities. Statements analogous to the results on perfection are far from being understood for h-perfection, and negative results are missing. For ex- ample, testing h-perfection and determining the chromatic number of an h-perfect graph are unsolved. Besides, no upper bound is known on the gap between the chromatic and clique numbers of an h-perfect graph. Our first main result states that the operations of t-minors keep h- perfection (this is a non-trivial extension of a result of Gerards and Shepherd on t-perfect graphs). We show that it also keeps the Integer Decomposition Property of the stable set polytope, and use this to answer a question of Shepherd on 3-colorable h-perfect graphs in the negative. The study of minimally h-imperfect graphs with respect to t-minors may yield a combinatorial co-NP characterization of h-perfection. We review the currently known examples of such graphs, study their stable set polytope and state several conjectures on their structure. On the other hand, we show that the (weighted) chromatic number of certain h-perfect graphs can be obtained efficiently by rounding-up its fractional relaxation. This is related to conjectures of Goldberg and Seymour on edge-colorings. Finally, we introduce a new parameter on the complexity of the matching polytope and use it to give an efficient and elementary al- gorithm for testing h-perfection in line-graphs

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Spa, Carvajal Carlos. "Time-domain numerical methods in room acoustics simulations." Doctoral thesis, Universitat Pompeu Fabra, 2009. http://hdl.handle.net/10803/7565.

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L'acústica de sales s'encarrega de l'estudi del comportament de les ones sonores en espais tancats.La informació acústica de qualsevol entorn, coneguda com la resposta impulsional, pot ser expressada en termes del camp acústic com una funció de l'espai i el temps. En general, és impossible obtenir solucions analítiques de funcions resposta en habitacions reals. Per tant, en aquests últims anys, l'ús d'ordinadors per resoldre aquest tipus de problemes ha emergit com una solució adecuada per calcular respostes impulsionals.
En aquesta Tesi hem centrat el nostre anàlisis en els mètodes basats en el comportament ondulatori dins del domini temporal. Més concretament, estudiem en detall les formulacions més importants del mètode de Diferències Finites, el qual s'utilitza en moltes aplicacions d'acústica de sales, i el recentment proposat mètode PseudoEspectral de Fourier. Ambdós mètodes es basen en la formulació discreta de les equacions analítiques que descriuen els fenòmens acústics en espais tancats.
Aquesta obra contribueix en els aspectes més importants en el càlcul numèric de respostes impulsionals: la propagació del so, la generació de fonts i les condicions de contorn de reactància local.
Room acoustics is the science concerned to study the behavior of sound waves in enclosed rooms. The acoustic information of any room, the so called impulse response, is expressed in terms of the acoustic field as a function of space and time. In general terms, it is nearly impossible to find analytical impulse responses of real rooms. Therefore, in the recent years, the use of computers for solving this type of problems has emerged as a proper alternative to calculate the impulse responses.
In this Thesis we focus on the analysis of the wavebased methods in the timedomain. More concretely, we study in detail the main formulations of FiniteDifference methods, which have been used in many room acoustics applications, and the recently proposed Fourier PseudoSpectral methods. Both methods are based on the discrete formulations of the analytical equations that describe the sound phenomena in enclosed rooms.
This work contributes to the main aspects in the computation of impulse responses: the wave propagation, the source generation and the locallyreacting boundary conditions.

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"Algorithms in the study of multiperfect and odd perfect numbers." Thesis, University of Technology, Sydney. Department of Mathematical Sciences, 2003. http://hdl.handle.net/10453/20034.

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University of Technology, Sydney. Department of Mathematical Sciences.
A long standing unanswered question in number theory concerns the existence (or not) of odd perfect numbers. Over time many properties of an odd perfect number have been established and refined. The initial goal of this research was to improve the lower bound on the number of distinct prime factors of an odd perfect number, if one exists, to at least 9. Previous approaches to this problem involved the analysis of a carefully chosen set of special cases with each then being eliminated by a contradiction. This thesis applies an algorithmic, factor chain approach to the problem. The implementation of such an approach as a computer program allows the speed, accuracy and flexibility of modern computer technology to not only assist but even direct the discovery process. In addition to considering odd perfect numbers, several related problems were investigated, concerned with (i) harmonic, (ii) even multiperfect and (iii) odd triperfect numbers. The aim in these cases was to demonstrate the correctness and versatility of the computer code and to fine tune its efficiency while seeking improved properties of these types of numbers. As a result of this work, significant improvements have been made to the understanding of harmonic numbers. The introduction of harmonic seeds, coupled with a straightforward procedure for generating most harmonic numbers below a chosen bound, expands the opportunities for further investigations of harmonic numbers and in particular allowed the determination of all harmonic numbers below 10 to the power 12 and a proof that there are no odd harmonic numbers below 10 to the power 15. When considering even multiperfect numbers, a search procedure was implemented to find the first 10-perfect number as well as several other new ones. As a fresh alternative to the factor chain search, a 0-1 linear programming model was constructed and used to show that all multiperfect numbers divisible by 2 to the power of a, for a being less than or equal to 65, subject to a modest constraint, are known in the literature. Odd triperfect numbers (if they exist) have properties which are similar to, but simpler than, those for odd perfect numbers. An extended test on the possible prime factors of such a number was developed that, with minor differences, applies to both odd triperfect and odd perfect numbers. When applicable, this test allows an earlier determination of a contradiction within a factor chain and so reduces the effort required. It was also shown that an odd triperfect number must be greater than 10 to the power 128. While the goal of proving that an odd perfect number must have at least 9 distinct prime factors was not achieved, due to mainly practical limitations, the algorithmic approach was able to show that for an odd perfect number with 8 distinct prime factors, (i) if it is exactly divisible by 3 to the power of 2a then a = 1, 2, 3, 5, 6 or a is greater than or equal to 31 (ii) if the special component is pi to the power of alpha, pi less than 10 to the 6 and pi to the (alpha+1) less than 10 to the 40, then alpha = 1.

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"Algorithms in the Study of Multiperfect and Odd Perfect Numbers." University of Technology, Sydney. Department of Mathematical Sciences, 2003. http://hdl.handle.net/2100/275.

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A long standing unanswered question in number theory concerns the existence (or not) of odd perfect numbers. Over time many properties of an odd perfect number have been established and refined. The initial goal of this research was to improve the lower bound on the number of distinct prime factors of an odd perfect number, if one exists, to at least 9. Previous approaches to this problem involved the analysis of a carefully chosen set of special cases with each then being eliminated by a contradiction. This thesis applies an algorithmic, factor chain approach to the problem. The implementation of such an approach as a computer program allows the speed, accuracy and flexibility of modern computer technology to not only assist but even direct the discovery process. In addition to considering odd perfect numbers, several related problems were investigated, concerned with (i) harmonic, (ii) even multiperfect and (iii) odd triperfect numbers. The aim in these cases was to demonstrate the correctness and versatility of the computer code and to fine tune its efficiency while seeking improved properties of these types of numbers. As a result of this work, significant improvements have been made to the understanding of harmonic numbers. The introduction of harmonic seeds, coupled with a straightforward procedure for generating most harmonic numbers below a chosen bound, expands the opportunities for further investigations of harmonic numbers and in particular allowed the determination of all harmonic numbers below 10 to the power 12 and a proof that there are no odd harmonic numbers below 10 to the power 15. When considering even multiperfect numbers, a search procedure was implemented to find the first 10-perfect number as well as several other new ones. As a fresh alternative to the factor chain search, a 0-1 linear programming model was constructed and used to show that all multiperfect numbers divisible by 2 to the power of a, for a being less than or equal to 65, subject to a modest constraint, are known in the literature. Odd triperfect numbers (if they exist) have properties which are similar to, but simpler than, those for odd perfect numbers. An extended test on the possible prime factors of such a number was developed that, with minor differences, applies to both odd triperfect and odd perfect numbers. When applicable, this test allows an earlier determination of a contradiction within a factor chain and so reduces the effort required. It was also shown that an odd triperfect number must be greater than 10 to the power 128. While the goal of proving that an odd perfect number must have at least 9 distinct prime factors was not achieved, due to mainly practical limitations, the algorithmic approach was able to show that for an odd perfect number with 8 distinct prime factors, (i) if it is exactly divisible by 3 to the power of 2a then a = 1, 2, 3, 5, 6 or a is greater than or equal to 31 (ii) if the special component is pi to the power of alpha, pi less than 10 to the 6 and pi to the (alpha+1) less than 10 to the 40, then alpha = 1.

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Books on the topic "Perfect numbers"

1

R, Jorge Emilio Molina. La tetraléctica de los números perfectos. La Paz, Bolivia: Producciones CIMA, 1999.

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Rivero, Jorge Emilio Molina. La tetraléctica de los números perfectos. La Paz, Bolivia: Producciones CIMA, 1999.

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Julia, Line, ed. The book of love numbers: Use your love number to discover your perfect partner. Wellingborough, Northamptonshire: Aquarian Press, 1986.

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Coppa, Max. Does your love life add up?: How to use numbers to find your perfect relationship. New York: Jeremy P. Tarcher/Penguin, 2009.

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Moraes, Augusto C. M. Compressible laminar boundary layers for perfect and real gases in equilibrium at Mach numbers to 30. Washington, D. C: American Institute of Aeronautics and Astronautics, 1992.

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Perfect, Amicable and Sociable Numbers: A Computational Approach. World Scientific Publishing Co Pte Ltd, 1996.

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Perfect, amicable, and sociable numbers: A computational approach. Singapore: World Scientific, 1996.

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Perfect, Amicable and Sociable Numbers: A Computational Approach. World Scientific Publishing Co Pte Ltd, 1996.

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Deza, Elena. Perfect and Amicable Numbers. World Scientific Publishing Co Pte Ltd, 2022.

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Cai, Tianxin. Perfect Numbers and Fibonacci Sequences. World Scientific Publishing Co Pte Ltd, 2022.

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Book chapters on the topic "Perfect numbers"

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Anglin, W. S., and J. Lambek. "Perfect Numbers." In The Heritage of Thales, 37–40. New York, NY: Springer New York, 1995. http://dx.doi.org/10.1007/978-1-4612-0803-7_9.

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Hunacek, Mark. "Perfect Numbers." In Introduction to Number Theory, 65–70. Boca Raton: Chapman and Hall/CRC, 2023. http://dx.doi.org/10.1201/9781003318712-5.

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Rassias, Michael Th. "Perfect numbers, Fermat numbers." In Problem-Solving and Selected Topics in Number Theory, 29–35. New York, NY: Springer New York, 2010. http://dx.doi.org/10.1007/978-1-4419-0495-9_3.

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Bressoud, David M. "Primes and Perfect Numbers." In Factorization and Primality Testing, 17–29. New York, NY: Springer New York, 1989. http://dx.doi.org/10.1007/978-1-4612-4544-5_2.

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Solov’eva, Faina I. "Switchings and Perfect Codes." In Numbers, Information and Complexity, 311–24. Boston, MA: Springer US, 2000. http://dx.doi.org/10.1007/978-1-4757-6048-4_25.

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Cook, R. "Bounds for odd perfect numbers." In CRM Proceedings and Lecture Notes, 67–71. Providence, Rhode Island: American Mathematical Society, 1999. http://dx.doi.org/10.1090/crmp/019/07.

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Allen, G. Donald. "Primes, Perfect Numbers and Magic Numbers (Just for Fun)." In Pedagogy and Content in Middle and High School Mathematics, 25–28. Rotterdam: SensePublishers, 2017. http://dx.doi.org/10.1007/978-94-6351-137-7_7.

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Sándor, J., and B. Crstici. "Perfect numbers: Old and new issues; perspectives." In Handbook of Number Theory II, 15–96. Dordrecht: Springer Netherlands, 2004. http://dx.doi.org/10.1007/1-4020-2547-5_1.

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Ford, Kevin, D. R. Heath-Brown, and Sergei Konyagin. "Large Gaps Between Consecutive Prime Numbers Containing Perfect Powers." In Analytic Number Theory, 83–92. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-22240-0_5.

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Belmonte, Rémy, Pinar Heggernes, Pim van ’t Hof, and Reza Saei. "Ramsey Numbers for Line Graphs and Perfect Graphs." In Lecture Notes in Computer Science, 204–15. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-32241-9_18.

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Conference papers on the topic "Perfect numbers"

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Irmak, Nurettin, and Abdullah Açikel. "On perfect numbers close to Tribonacci numbers." In 1ST INTERNATIONAL CONFERENCE ON MATHEMATICAL AND RELATED SCIENCES (ICMRS 2018). Author(s), 2018. http://dx.doi.org/10.1063/1.5047878.

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Savarimuthu, Sabeenian Royappan, Kalaiselvi Cinnu Muthuraji, and Paramasivam Muthan Eswaran. "Square root for perfect square numbers using Vedic mathematics." In 24TH TOPICAL CONFERENCE ON RADIO-FREQUENCY POWER IN PLASMAS. AIP Publishing, 2023. http://dx.doi.org/10.1063/5.0164287.

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Rathore, Tejmal. "Arranging Integer Numbers on a Loop Such That the Sum of any Two Adjacent Numbers Is a Perfect Square." In 2022 IEEE Region 10 Symposium (TENSYMP). IEEE, 2022. http://dx.doi.org/10.1109/tensymp54529.2022.9864484.

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Lohmann, A., W. Stork, and G. Stucke. "Optical Implementation of the Perfect Shuffle." In Optical Computing. Washington, D.C.: Optica Publishing Group, 1985. http://dx.doi.org/10.1364/optcomp.1985.wa3.

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The "perfect shuffle" (PS) is a well-known concept for global interconnection networks in parallel computers. It performs a certain permutation of N = 2k elements. Fig. 1 shows two different graphical representations of the PS-operation. In Fig. 1a the actual pathways of the N elements in one PS-step are drawn. If the addresses (positions) of the elements are represented by binary numbers, ranging from 0 to N-1, it is apparent that the PS can be described as a cyclical rotation (to the left) of the address bits (Fig. 1b).

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aus der Wiesche, Stefan, Felix Reinker, Robert Wagner, Leander Hake, and Max Passmann. "Critical and Choking Mach Numbers for Organic Vapor Flows Through Turbine Cascades." In ASME Turbo Expo 2021: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2021. http://dx.doi.org/10.1115/gt2021-59013.

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Abstract Results are presented of a theoretical and experimental study dealing with critical and choking Mach numbers of organic vapor flows through turbine cascades. A correlation was derived for predicting choking Mach numbers for organic vapor flows using an asymptotic series expansion valid for isentropic exponents close to unity. The theoretical prediction was tested employing a linear turbine cascade and a circular cylinder in a closed-loop organic vapor wind tunnel. The cascade was based on a classical transonic turbine airfoil for which perfect gas literature data were available. The cascade was manufactured by Selective Laser Melting (SLM), and a comparable low surface roughness level was established by subsequent surface finishing. Because the return of the closed-loop wind tunnel was equipped with an independent mass flow sensor and the test facility enabled stable long-term operation behavior, it was possible to obtain the choking Mach number with high accuracy. It was observed that non-perfect gas dynamics affect the critical Mach number locally, but the observed choking behavior of the turbine cascade was in good agreement with the asymptotic result for the considered dilute gas flow regime.

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Wan, Lingxiao, Huihui Zhu, Bo Wang, Hui Zhang, Leong Chuan Kwek, and Ai Qun Liu. "A Boson Sampling Chip for Graph Perfect Matching." In CLEO: QELS_Fundamental Science. Washington, D.C.: Optica Publishing Group, 2022. http://dx.doi.org/10.1364/cleo_qels.2022.ff2i.6.

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We map the perfect matching problem in graph theory to a reconfigurable GBS model with the connection of the Hafnian of a matrix. We configure the linear optical circuit and squeeze parameter of the GBS model according to the decomposed unitary matrix and diagonal matrix of the graph’s adjacency matrix. The perfect matching numbers can be directly acquired from the 4-photon coincidence counts with a distribution similarity of 0.9304.

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MORAES, AUGUSTO, JOSEPH FLAHERTY, and HENRY NAGAMATSU. "Compressible laminar boundary layers for perfect and real gases in equilibrium at Mach numbers to 30." In 30th Aerospace Sciences Meeting and Exhibit. Reston, Virigina: American Institute of Aeronautics and Astronautics, 1992. http://dx.doi.org/10.2514/6.1992-757.

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Shade, Gary F., and Bhanu Sood. "The “Perfect Storm” Now Appearing in FA Labs Everywhere." In ISTFA 2011. ASM International, 2011. http://dx.doi.org/10.31399/asm.cp.istfa2011p0446.

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Abstract The International Symposium for Testing and Failure Analysis (ISTFA) 2010 event added a focus topic on Counterfeiting in Electronics. This topic was chosen because of the emergence of this concern and the critical role that Failure Analysis plays in this challenge. Failure Analysts will be involved deeply as companies worldwide are attempting to reduce the impact of increasing numbers of counterfeit products in the supply line and in fielded products. This paper will attempt to provide an overview of the topic and support the contributors to ISTFA 2010 while providing additional resources for information.

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Wettstein, Hans E. "Quality Key Numbers of Gas Turbine Combined Cycles." In ASME Turbo Expo 2020: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/gt2020-14508.

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Abstract The most relevant quality key numbers for the largest and most efficient Gas Turbine Combined Cycles (GTCC) are not (only) the data published by the original engine manufacturers OEM’s. Additional numbers are here evaluated with educated guesses based on published data of the latest announcements of the “big four OEM’s” [8]. Such data are of interest for potential customers but also for nailing down the current state-of-the-art for all kind of further cycle studies using turbomachinery components and also as a contemporary history record. Making educated guesses means thermodynamic 1D simulation based on additional assumptions for pressure losses and other cycle data, which have a limited influence on the (unpublished) target quality numbers, such as: • Mixed turbine inlet temperature Tmix. This is a key value describing the technology level. It can be derived independently of the (unpublished) TCLA value. It is a quality number for the general cooling design and for the secondary air systems. • Polytropic efficiency of the compressor blading. This number describes the aerodynamic quality of the compressor blading. • Polytropic efficiency of the turbine blading. It describes the quality level of both the blading aerodynamics and of the open air cooling design. • Distribution of the exergy losses within the GT and in the bottoming cycle. The exergy losses describe the remaining opportunities for further improvements in the thermodynamic cycle design. But they also indicate its limits. However already the determination of the Tmix is tricky. It depends on the analysis method and on the fluid data applied. The polytropic efficiency of the turbine blading and the exergy losses will depend both on the used methods and on the Tmix found. Achieving a trustable result therefore requires a transparent and reproducible method. In case of application of the found results for performance prediction of similar cycles the same method has to be applied in order to avoid mistakes. In this paper real gas data with consideration of dissociation in equilibrium are used, while the polytropic efficiencies are determined with an incremental method based directly on the classic definitions of Stodola [3] and Dzung [4]. Therefore the still most used method using semi-perfect gas properties and corresponding formulas is bypassed. In order to keep it as simple as possible the evaluation is limited to base load at ISO ambient condition (15°C, 60% relative humidity, sea level). The fuel is limited to pure methane according to the practice in current catalogue data. The main focus is on the gas turbine with its components. The steam bottoming cycle is captured with its effect on the overall exergy and energy balance of the GTCC, which identifies exhaust and condensation losses.

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Ignatenko, Yaroslav, Oleg Bocharov, and Roland May. "Movement of a Sphere on a Flat Wall in Non-Newtonian Shear Flow." In ASME 2017 36th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/omae2017-61131.

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For a particle on a wall or cuttings bed in a multiphase flow in confined geometries a condition for onset and lift-off is very important. In this case, a fundamental problem of hydrodynamic forces and torque acting on a particle moving near and on the wall in a viscous fluid needs to be solved. In this paper, systematical simulation of a flow was performed around a perfect rolling or sliding spherical particle near the wall. A shear flow of Newtonian and Herschel-Bulkley fluids was investigated. The simulation was conducted for Reynolds numbers up to 200 and the dimensionless positive particle velocity Vp < 1.4. The relative particle velocity was made dimensionless by dividing it by the incoming flow velocity in front of the particle. The simulation was performed using the open-source CFD package OpenFOAM. The simulation results for Newtonian fluid agree with data presented in the literature. For the particle’s low translational velocity the drag force coefficient in the non-Newtonian fluid is lower than in Newtonian fluid, but for increasing translational velocity the drag force coefficient increases. The lift force coefficient behavior is non-monotonic versus rheology parameters. Lift and drag force show a sudden drop for very small translational velocities. Our simulation shows that in the case of large Bingham numbers the particle’s lift force can be negative for steady perfect particle rolling. Thus, friction between particle and surface prevents particle’s take-off in some cases. Knowing the dependence of the lift force on Reynolds number and rheological parameters allows one to determine incipient motion and take-off conditions for a spherical particle.

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Reports on the topic "Perfect numbers"

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Gates, Allison, Michelle Gates, Shannon Sim, Sarah A. Elliott, Jennifer Pillay, and Lisa Hartling. Creating Efficiencies in the Extraction of Data From Randomized Trials: A Prospective Evaluation of a Machine Learning and Text Mining Tool. Agency for Healthcare Research and Quality (AHRQ), August 2021. http://dx.doi.org/10.23970/ahrqepcmethodscreatingefficiencies.

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Background. Machine learning tools that semi-automate data extraction may create efficiencies in systematic review production. We prospectively evaluated an online machine learning and text mining tool’s ability to (a) automatically extract data elements from randomized trials, and (b) save time compared with manual extraction and verification. Methods. For 75 randomized trials published in 2017, we manually extracted and verified data for 21 unique data elements. We uploaded the randomized trials to ExaCT, an online machine learning and text mining tool, and quantified performance by evaluating the tool’s ability to identify the reporting of data elements (reported or not reported), and the relevance of the extracted sentences, fragments, and overall solutions. For each randomized trial, we measured the time to complete manual extraction and verification, and to review and amend the data extracted by ExaCT (simulating semi-automated data extraction). We summarized the relevance of the extractions for each data element using counts and proportions, and calculated the median and interquartile range (IQR) across data elements. We calculated the median (IQR) time for manual and semiautomated data extraction, and overall time savings. Results. The tool identified the reporting (reported or not reported) of data elements with median (IQR) 91 percent (75% to 99%) accuracy. Performance was perfect for four data elements: eligibility criteria, enrolment end date, control arm, and primary outcome(s). Among the top five sentences for each data element at least one sentence was relevant in a median (IQR) 88 percent (83% to 99%) of cases. Performance was perfect for four data elements: funding number, registration number, enrolment start date, and route of administration. Among a median (IQR) 90 percent (86% to 96%) of relevant sentences, pertinent fragments had been highlighted by the system; exact matches were unreliable (median (IQR) 52 percent [32% to 73%]). A median 48 percent of solutions were fully correct, but performance varied greatly across data elements (IQR 21% to 71%). Using ExaCT to assist the first reviewer resulted in a modest time savings compared with manual extraction by a single reviewer (17.9 vs. 21.6 hours total extraction time across 75 randomized trials). Conclusions. Using ExaCT to assist with data extraction resulted in modest gains in efficiency compared with manual extraction. The tool was reliable for identifying the reporting of most data elements. The tool’s ability to identify at least one relevant sentence and highlight pertinent fragments was generally good, but changes to sentence selection and/or highlighting were often required.

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Cheng, Peng, James V. Krogmeier, Mark R. Bell, Joshua Li, and Guangwei Yang. Detection and Classification of Concrete Patches by Integrating GPR and Surface Imaging. Purdue University, 2021. http://dx.doi.org/10.5703/1288284317320.

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This research considers the detection, location, and classification of patches in concrete and asphalt-on-concrete pavements using data taken from ground penetrating radar (GPR) and the WayLink 3D Imaging System. In particular, the project seeks to develop a patching table for “inverted-T” patches. A number of deep neural net methods were investigated for patch detection from 3D elevation and image observation, but the success was inconclusive, partly because of a dearth of training data. Later, a method based on thresholding IRI values computed on a 12-foot window was used to localize pavement distress, particularly as seen by patch settling. This method was far more promising. In addition, algorithms were developed for segmentation of the GPR data and for classification of the ambient pavement and the locations and types of patches found in it. The results so far are promising but far from perfect, with a relatively high rate of false alarms. The two project parts were combined to produce a fused patching table. Several hundred miles of data was captured with the Waylink System to compare with a much more limited GPR dataset. The primary dataset was captured on I-74. A software application for MATLAB has been written to aid in automation of patch table creation.

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Cheng, Peng, James V. Krogmeier, Mark R. Bell, Joshua Li, and Guangwei Yang. Detection and Classification of Concrete Patches by Integrating GPR and Surface Imaging. Purdue University, 2021. http://dx.doi.org/10.5703/1288284317320.

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This research considers the detection, location, and classification of patches in concrete and asphalt-on-concrete pavements using data taken from ground penetrating radar (GPR) and the WayLink 3D Imaging System. In particular, the project seeks to develop a patching table for “inverted-T” patches. A number of deep neural net methods were investigated for patch detection from 3D elevation and image observation, but the success was inconclusive, partly because of a dearth of training data. Later, a method based on thresholding IRI values computed on a 12-foot window was used to localize pavement distress, particularly as seen by patch settling. This method was far more promising. In addition, algorithms were developed for segmentation of the GPR data and for classification of the ambient pavement and the locations and types of patches found in it. The results so far are promising but far from perfect, with a relatively high rate of false alarms. The two project parts were combined to produce a fused patching table. Several hundred miles of data was captured with the Waylink System to compare with a much more limited GPR dataset. The primary dataset was captured on I-74. A software application for MATLAB has been written to aid in automation of patch table creation.

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Tang, Jiqin, Gong Zhang, Jinxiao Xing, Ying Yu, and Tao Han. Network Meta-analysis of Heat-clearing and Detoxifying Oral Liquid of Chinese Medicines in Treatment of Children’s Hand-foot-mouth Disease：a protocol for systematic review. INPLASY - International Platform of Registered Systematic Review and Meta-analysis Protocols, January 2022. http://dx.doi.org/10.37766/inplasy2022.1.0032.

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Review question / Objective: The type of study was clinical randomized controlled trial (RCT). The object of study is the patients with HFMD. There is no limit to gender and race. In the case of clear diagnosis standard, curative effect judgment standard and consistent baseline treatment, the experimental group was treated with pure oral liquid of traditional Chinese medicine(A: Fuganlin oral liquid, B: huangzhihua oral liquid, C: Lanqin oral liquid, D: antiviral oral liquid, E: Huangqin oral liquid, F: Pudilan oral liquid, G: Shuanghuanglian oral liquid.)and the control group was treated with ribavirin or any oral liquid of traditional Chinese medicine. The data were extracted by two researchers independently, cross checked and reviewed according to the pre-determined tables. The data extraction content is (1) Basic information (including the first author, published journal and year, research topic). (2) Relevant information (including number of cases, total number of cases, gender, age, intervention measures, course of treatment of the experimental group and the control group in the literature). (3) Design type and quality evaluation information of the included literature. (4) Outcome measures (effective rate, healing time of oral ulcer, regression time of hand and foot rash, regression time of fever, adverse reactions.). The seven traditional Chinese medicine oral liquids are comparable in clinical practice, but their actual clinical efficacy is lack of evidence-based basis. Therefore, the purpose of this study is to use the network meta-analysis method to integrate the clinical relevant evidence of direct and indirect comparative relationship, to make quantitative comprehensive statistical analysis and sequencing of different oral liquid of traditional Chinese medicine with the same evidence body for the treatment of the disease, and then to explore the advantages and disadvantages of the efficacy and safety of different oral liquid of traditional Chinese medicine to get the best treatment plan, so as to provide reference value and evidence-based medicine evidence for clinical optimization of drug selection. Condition being studied: Hand foot mouth disease (HFMD) is a common infectious disease in pediatrics caused by a variety of enteroviruses. Its clinical manifestations are mainly characterized by persistent fever, hand foot rash, oral herpes, ulcers, etc. Because it is often found in preschool children, its immune system development is not perfect, so it is very vulnerable to infection by pathogens and epidemic diseases, resulting in rapid progress of the disease. A few patients will also have neurogenic pulmonary edema Meningitis, myocarditis and other serious complications even lead to death, so effectively improve the cure rate, shorten the course of disease, prevent the deterioration of the disease as the focus of the study. In recent years, traditional Chinese medicine has played an important role in the research of antiviral treatment. Many clinical practices have confirmed that oral liquid of traditional Chinese medicine can effectively play the role of antiviral and improve the body's immunity.

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Israel, Alvaro, and John Merrill. Production of Seed Stocks for Sustainable Tank Cultivation of the Red Edible Seaweed Porphyra. United States Department of Agriculture, 2006. http://dx.doi.org/10.32747/2006.7696527.bard.

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Porphyra species (commonly known as ‘nori’ or ‘purple laver’) are edible red seaweeds rich in proteins, vitamins and other highly valued biogenic compounds. For years Porphyra has been cultured using seeded nets extended in the open sea, and its biomass consumed primarily in the Far East. While demands for international markets have increased steadily at an average of 20% per year, supplies are on the verge and not expected to meet future demands. Alternatively, land-based cultivation of seaweed has become attractive in the mariculture industry since (1) important growth parameters can be controlled, (2) is environmentally friendly and (3) perfectly matches with integrated aquaculture leading to sustainable, high quality products. During the last few years a tank cultivation technology for Porphyra has been developed at the Israeli institution. This technology is based on indoor production of asexual spores and their subsequent growth to 1-2 mm seedlings. The seedlings are then transferred to outdoor tanks and ponds when seawater temperatures drop to 20 °C, or below, and days become shorter during winter time. However, the current technology efficiently serves only about 100 m2 of ponds during one growth season. In order to produce seedlings in sufficient amounts, it is critical to address both technical and biological aspects of seedling production, securing optimal up-scale to commercial-size cultivation farms. We hypothesize that massive production of spores is related to thalli origin, thalli age and sporulation triggers, and that seedling survival and their subsequent growth potential is determined by the seawater quality and overall indoor growth conditions imposed. A series of bio-reactors were constructed and tested in which spore release and spore growth were separately studied. The main assessment criteria for optimal viability of the seedlings will be by determining their electron transport rate using PAM fluorometry and by subsequent growth and biomass yields in outdoor ponds. Altogether the project showed (1), controlled sporulation is possible in big outdoor/growth chamber settings provided initial stock material (small frozen seedlings) is at hand, (2), contamination problems can be almost completely avoided if stock material is properly handled (clean as possible and partially dehydrated prior to freezing), (3), spore release can significantly be enhance using high nutrient levels during thawing for P. yezoensis and P. haitanensis, but not for P. rosengurttii, (4), PAM fluorometry is an efficient tool to estimate growth capacity in both seedlings and juvenile thalli. The BARD funding also served to explore other aspects of Porphyra biology and cultivation. For example, the taxonomical status of Porphyra strains used in this study was defined (see appendix), and the potential use of this seaweed in bioremediation was well substantiated. In addition, BARD funding supported a number of opportunities and activities in the Israeli lab, direct or indirectly related to the initial objectives of the project such as: additional molecular work in other seaweeds, description of at least 2 new species for the Israeli Mediterranean, and continuous support for the writing of a book on Global Change and applied aspects of seaweeds. The technology for Porphyra cultivation in land-based ponds is readily available. This study corroborated previous know-how of Porphyra growth in tanks and ponds, and yet offers important improvements regarding seedling production and their handling for successful cultivation. This study supported various other activities opening additional important issues in the biology/cultivation/use of Porphyra and other seaweeds.

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