Relevant bibliographies by topics / Quotient operation

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Quotient operation'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Quotient operation"

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BRZOZOWSKI, JANUSZ, and BO LIU. "QUOTIENT COMPLEXITY OF STAR-FREE LANGUAGES." International Journal of Foundations of Computer Science 23, no. 06 (September 2012): 1261–76. http://dx.doi.org/10.1142/s0129054112400515.

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The quotient complexity, also known as state complexity, of a regular language is the number of distinct left quotients of the language. The quotient complexity of an operation is the maximal quotient complexity of the language resulting from the operation, as a function of the quotient complexities of the operands. The class of star-free languages is the smallest class containing the finite languages and closed under boolean operations and concatenation. We prove that the tight bounds on the quotient complexities of union, intersection, difference, symmetric difference, concatenation and star for star-free languages are the same as those for regular languages, with some small exceptions, whereas 2n-1 is a lower bound for reversal.
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Bae, Yongju, and Seongjeong Kim. "On quotient structure of Takasaki quandles II." Journal of Knot Theory and Its Ramifications 23, no. 07 (June 2014): 1460012. http://dx.doi.org/10.1142/s0218216514600128.

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A Takasaki quandle (T(G), *) is a quandle under the binary operation * defined by a*b = 2b-a for an abelian group (G, +). In this paper, we will show that if a subquandle X of a Takasaki quandle G is a image of subgroup of G under a quandle automorphism of T(G), then the set {X * g | g ∈ G} is a quandle under the binary operation *′ defined by (X * g) *′ (X * h) = X * (g * h). On the other hand, the quotient structure studied in [On quotients of quandles, J. Knot Theory Ramifications 19(9) (2010) 1145–1156] can be applied to the Takasaki quandles. In this paper, we will review the quotient structure studied in [On quotients of quandles, J. Knot Theory Ramifications 19(9) (2010) 1145–1156], and show that the quotient quandle coincides with the quotient quandle defined by Bunch, Lofgren, Rapp and Yetter in [On quotients of quandles, J. Knot Theory Ramifications 19(9) (2010) 1145–1156] for connected Takasaki quandles.
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Okhotin, Alexander, and Kai Salomaa. "State Complexity of the Quotient Operation on Input-Driven Pushdown Automata." International Journal of Foundations of Computer Science 30, no. 06n07 (September 2019): 1217–35. http://dx.doi.org/10.1142/s0129054119400367.

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The quotient of a formal language [Formula: see text] by another language [Formula: see text] is the set of all strings obtained by taking a string from [Formula: see text] that ends with a suffix of a string from [Formula: see text], and removing that suffix. The quotient of a regular language by any language is always regular, whereas the context-free languages and many of their subfamilies, such as the linear and the deterministic languages, are not closed under the quotient operation. This paper establishes the closure of the family of languages recognized by input-driven pushdown automata (IDPDA), also known as visibly pushdown automata, under the quotient operation. A construction of automata representing the result of the operation is given, and its state complexity with respect to nondeterministic IDPDA is shown to be exactly [Formula: see text], where [Formula: see text] and [Formula: see text] are the numbers of states in the automata recognizing [Formula: see text] and [Formula: see text], respectively.
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Tarmizi, Mahfuz, and Saman Abdurrahman. "GRUP FAKTOR YANG DIBANGUN DARI SUBGRUP NORMAL FUZZY." JURNAL MATEMATIKA MURNI DAN TERAPAN EPSILON 13, no. 1 (September 26, 2019): 1. http://dx.doi.org/10.20527/epsilon.v13i1.1240.

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A Quotient group is a set which contains coset members and satisfies group definition. These cosets are formed by group and its normal subgroup. A set which contains fuzzy coset members is also called a quotient group. These fuzzy cosets are formed by a group and its fuzzy normal subgroup. The purpose of this research is to explain quotient groups induced by fuzzy normal subgroups and isomorphic between them. This research construct sets which contain fuzzy coset members, define an operation between fuzzy cosets and prove these sets under an operation between fuzzy coset satisfy group definition, and prove theorems relating to qoutient groups and homomorphism. The results of this research are is a qoutient group induced by a fuzzy normal subgroup, where is a fuzzy normal subgroup of a group , is a fuzzy coset, and the binary operation is “” where for every . An epimorphism from a group to a group and a fuzzy normal subgroup of which is constant on cause quotient goup and are isomorphic.
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KAWACHI, Shoji, Takao YAMANOUE, Osafumi YUGE, and Michio MORIO. "The effects of glucose administration on resoiratory quotient during operation." JOURNAL OF JAPAN SOCIETY FOR CLINICAL ANESTHESIA 7, no. 2 (1987): 213–19. http://dx.doi.org/10.2199/jjsca.7.213.

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BAE, YONGJU, and SEONGJEONG KIM. "ON QUOTIENT STRUCTURE OF TAKASAKI QUANDLES." Journal of Knot Theory and Its Ramifications 22, no. 12 (October 2013): 1341001. http://dx.doi.org/10.1142/s0218216513410010.

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A Takasaki quandle is defined by the binary operation a * b = 2b - a on an abelian group G. A Takasaki quandle depends on the algebraic properties of the underlying abelian group. In this paper, we will study the quotient structure of a Takasaki quandle in terms of its subquandle. If a subquandle X of a quandle Q is a subgroup of the underlying group Q, then we can define the quandle structure on the set {X * g | g ∈ Q}, which is called the quotient quandle of Q. Also we will study conditions for a subquandle X to be a subgroup of the underlying group when it contains the identity element.
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Zafrullah, Muhaamad. "The v-operation and intersections of quotient rings of integral domains." Communications in Algebra 13, no. 8 (January 1985): 1699–712. http://dx.doi.org/10.1080/00927878508823247.

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Yoon, Seonah, and Hyunjung Yang. "The Study on the Development and Validation of Brain Operation Quotient Test." Journal of Humanities and Social sciences 21 10, no. 6 (December 31, 2019): 1679–94. http://dx.doi.org/10.22143/hss21.10.6.123.

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Dassow, Jürgen. "Further Remarks on the Operational Nonterminal Complexity." International Journal of Foundations of Computer Science 32, no. 05 (January 30, 2021): 439–53. http://dx.doi.org/10.1142/s0129054121410021.

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For a regular language [Formula: see text], let [Formula: see text] be the minimal number of nonterminals necessary to generate [Formula: see text] by right linear grammars. Moreover, for natural numbers [Formula: see text] and an [Formula: see text]-ary regularity preserving operation [Formula: see text], let the range [Formula: see text] be the set of all numbers [Formula: see text] such that there are regular languages [Formula: see text] with [Formula: see text] for [Formula: see text] and [Formula: see text]. We show that, for the circular shift operation [Formula: see text], [Formula: see text] is infinite for all [Formula: see text], and we completely determine the set [Formula: see text]. Moreover, we give a precise range for the left right quotient and a partial result for the left quotient. Furthermore, we add some values to the range for the operation intersection which improves the result of [ 2 ].
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El Baghdadi, Said, Marco Fontana, and Muhammad Zafrullah. "Intersections of quotient rings and Prüfer v-multiplication domains." Journal of Algebra and Its Applications 15, no. 08 (July 24, 2016): 1650149. http://dx.doi.org/10.1142/s0219498816501498.

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Let [Formula: see text] be an integral domain with quotient field [Formula: see text]. Call an overring [Formula: see text] of [Formula: see text] a subring of [Formula: see text] containing [Formula: see text] as a subring. A family [Formula: see text] of overrings of [Formula: see text] is called a defining family of [Formula: see text], if [Formula: see text]. Call an overring [Formula: see text] a sublocalization of [Formula: see text], if [Formula: see text] has a defining family consisting of rings of fractions of [Formula: see text]. Sublocalizations and their intersections exhibit interesting examples of semistar or star operations [D. D. Anderson, Star operations induced by overrings, Comm. Algebra 16 (1988) 2535–2553]. We show as a consequence of our work that domains that are locally finite intersections of Prüfer [Formula: see text]-multiplication (respectively, Mori) sublocalizations turn out to be Prüfer [Formula: see text]-multiplication domains (PvMDs) (respectively, Mori); in particular, for the Mori domain case, we reobtain a special case of Théorème 1 of [J. Querré, Intersections d’anneaux intègers, J. Algebra 43 (1976) 55–60] and Proposition 3.2 of [N. Dessagnes, Intersections d’anneaux de Mori — exemples, Port. Math. 44 (1987) 379–392]. We also show that, more than the finite character of the defining family, it is the finite character of the star operation induced by the defining family that causes the interesting results. As a particular case of this theory, we provide a purely algebraic approach for characterizing P vMDs as a subclass of the class of essential domains (see also Theorem 2.4 of [C. A. Finocchiaro and F. Tartarone, On a topological characterization of Prüfer [Formula: see text]-multiplication domains among essential domains, preprint (2014), arXiv:1410.4037]).
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Dissertations / Theses on the topic "Quotient operation"

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Björkner, Eva. "Why so different? - Aspects of voice characteristics in operatic and musical theatre singing : Aspects of voice characteristics in operatic and musical theatre singing." Doctoral thesis, KTH, Tal, musik och hörsel, TMH, 2006. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-4198.

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This thesis addresses aspects of voice characteristics in operatic and musical theatre singing. The common aim of the studies was to identify respiratory, phonatory and resonatory characteristics accounting for salient voice timbre differences between singing styles. The velopharyngeal opening (VPO) was analyzed in professional operatic singers, using nasofiberscopy. Differing shapes of VPOs suggested that singers may use a VPO to fine-tune the vocal tract resonance characteristics and hence voice timbre. A listening test revealed no correlation between rated nasal quality and the presence of a VPO. The voice quality referred to as “throaty”, a term sometimes used for characterizing speech and “non-classical” vocalists, was examined with respect to subglottal pressure (Psub) and formant frequencies. Vocal tract shapes were determined by magnetic resonance imaging. The throaty versions of four vowels showed a typical narrowing of the pharynx. Throatiness was characterized by increased first formant frequency and lowering of higher formants. Also, voice source parameter analyses suggested a hyper-functional voice production. Female musical theatre singers typically use two vocal registers (chest and head). Voice source parameters, including closed-quotient, peak-to-peak pulse amplitude, maximum flow declination rate, and normalized amplitude quotient (NAQ), were analyzed at ten equally spaced subglottal pressures representing a wide range of vocal loudness. Chest register showed higher values in all glottal parameters except for NAQ. Operatic baritone singer voices were analyzed in order to explore the informative power of the amplitude quotient (AQ), and its normalized version NAQ, suggested to reflect glottal adduction. Differences in NAQ were found between fundamental frequency values while AQ was basically unaffected. Voice timbre differs between musical theatre and operatic singers. Measurements of voice source parameters as functions of subglottal pressure, covering a wide range of vocal loudness, showed that both groups varied Psub systematically. The musical theatre singers used somewhat higher pressures, produced higher sound pressure levels, and did not show the opera singers’ characteristic clustering of higher formants. Musical theatre and operatic singers show highly controlled and consistent behaviors, characteristic for each style. A common feature is the precise control of subglottal pressure, while laryngeal and vocal tract conditions differ between singing styles. In addition, opera singers tend to sing with a stronger voice source fundamental than musical theatre singers.

QC 20100812

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Malheiro, Diana Mazo. "Sugestões complementares para o ensino de números fracionários tendo por base a organização proposta pelo Estado de São Paulo após a nova proposta curricular." Pontifícia Universidade Católica de São Paulo, 2011. https://tede2.pucsp.br/handle/handle/10868.

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Made available in DSpace on 2016-04-27T16:57:06Z (GMT). No. of bitstreams: 1 Diana Mazo Malheiro.pdf: 6282691 bytes, checksum: a46fef7e4a9774bb3feb0dedf10ab1f7 (MD5) Previous issue date: 2011-05-19
Secretaria da Educação do Estado de São Paulo
This study aimed to draw up a supplementary material for teachers in state schools of São Paulo, making suggestions for the teaching of fractional numbers. To prepare this material analyzed the organization of the notebook of teacher and student, developed and proposed by the Ministry of Education of São Paulo, for the teaching of fractional numbers in the 5th and 6th grade (6 and 7 years) Elementary School Second Cycle, in use since 2008. This analysis relied on studies and research in mathematics education and has a theoretical semiotic representation of the records of Raymond Duval (2003) and the meanings of fractional numbers: part-whole, measure, quotient, ratio and operator
Este estudo teve por objetivo analisar o material sugerido para professores da rede estadual de ensino do Estado de São Paulo, apresentando de possíveis sugestões para o ensino de números fracionários. Para elaboração deste material analisamos a organização do caderno do professor e do aluno, desenvolvido e proposto pela Secretaria da Educação de São Paulo, para o ensino dos números fracionários, na 5ª e 6º série (6º e 7º ano) do Ensino Fundamental ciclo II, em uso desde 2008. Esta análise contou com estudos e pesquisas em Educação Matemática e teve como referencial teórico os registros de representação semiótica de Raymond Duval (2003) e os significados dos números fracionários: parte-todo, medida, quociente, razão e operador
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PIAO, XIAOXUE. "State Complexity of Tree Automata." Thesis, 2012. http://hdl.handle.net/1974/6937.

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Modern applications of XML use automata operating on unranked trees. A common definition of tree automata operating on unranked trees uses a set of vertical states that define the bottom-up computation, and the transitions on vertical states are determined by so called horizontal languages recognized by finite automata on strings. The bottom-up computation of an unranked tree automaton may be either deterministic or nondeterministic, and further variants arise depending on whether the horizontal string languages defining the transitions are represented by DFAs or NFAs. There is also an alternative syntactic definition of determinism introduced by Cristau et al. It is known that a deterministic tree automaton with the smallest total number of states does not need to be unique nor have the smallest possible number of vertical states. We consider the question by how much we can reduce the total number of states by introducing additional vertical states. We give an upper bound for the state trade-off for deterministic tree automata where the horizontal languages are defined by DFAs, and a lower bound construction that, for variable sized alphabets, is close to the upper bound. We establish upper and lower bounds for the state complexity of conversions between different types of deterministic and nondeterministic unranked tree automata. The bounds are, usually, tight for the numbers of vertical states. Because a minimal deterministic unranked tree automaton need not be unique, establishing lower bounds for the number of horizontal states, that is, the combined size of DFAs used to define the horizontal languages, is challenging. Based on existing lower bound results for unambiguous finite automata we develop a lower bound criterion for the number of horizontal states. We consider the state complexity of operations on regular unranked tree languages. The concatenation of trees can be defined either as a sequential or a parallel operation. Furthermore, there are two essentially different ways to iterate sequential concatenation. We establish tight state complexity bounds for concatenation-like operations. In particular, for sequential concatenation and bottom-up iterated concatenation the bounds differ by an order of magnitude from the corresponding state complexity bounds for regular string languages.
Thesis (Ph.D, Computing) -- Queen's University, 2012-01-04 14:48:02.916
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Tseng, Fa-Hao, and 曾發鎬. "A paper to discuss the corporate characteristics and operating performance for Companies that changed their independent directors and supervisors. – Quoting electronic industry as an example." Thesis, 2007. http://ndltd.ncl.edu.tw/handle/47475459310556860103.

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碩士
國立臺北大學
會計學系
95
This study looks at typical corporate characteristics of companies that have voluntary changes in independent directors and supervisors. How Company performance changes before and after movement of independent directors and supervisors. Further, is there any distinctive difference in corporate characteristics and performance between companies that can find replacement for independent directors and supervisors and companies that cannot find replacement? This study aims to identify factors that influence changes in independent directors and supervisors and how Companies may be affected by their ability to find replacements to fill up vacant positions. Based on statistical analysis and empirical investigation, the following conclusion can be drawn: 1. Companies that recorded changes in their independent directors and supervisors often have poor corporate performance and financial structure comparing to other Companies. 2. Company performance is generally better before occurrence of any changes in independent directors and supervisors. 3. For Companies that can fill up vacancies for their independent directors and supervisors, they generally display better performance comparing to companies that cannot do so. Keywords: Corporate Governance, Independent Director, Independent Supervisor, Operating Performance.
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Books on the topic "Quotient operation"

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Caramello, Olivia. Some Applications. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198758914.003.0012.

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This chapter describes some applications of the theory developed in the previous chapters in a variety of different mathematical contexts. The main methodology used to generate such applications is the ‘bridge technique’ presented in Chapter 2. The discussed topics include restrictions of Morita equivalences to quotients of the two theories involved, give a solution to a prozblem of Lawvere concerning the boundary operator on subtoposes, establish syntax-semantics ‘bridges’ for quotients of theories of presheaf type, present topos-theoretic interpretations and generalizations of Fraïssé’s theorem in model theory on countably categorical theories and of topological Galois theory, develop a notion of maximal spectrum of a commutative ring with unit and investigate compactness conditions for geometric theories allowing one to identify theories lying in smaller fragments of geometric logic.
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Book chapters on the topic "Quotient operation"

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Okhotin, Alexander, and Kai Salomaa. "The Quotient Operation on Input-Driven Pushdown Automata." In Descriptional Complexity of Formal Systems, 299–310. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-60252-3_24.

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Douglas, Ronald G., and Gadadhar Misra. "On quotient modules." In Recent Advances in Operator Theory and Related Topics, 203–9. Basel: Birkhäuser Basel, 2001. http://dx.doi.org/10.1007/978-3-0348-8374-0_11.

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Vasilescu, Florian-Horia. "Spectral Capacities in Quotient Fréchet Spaces." In Topics in Operator Theory, 243–63. Basel: Birkhäuser Basel, 1988. http://dx.doi.org/10.1007/978-3-0348-5475-7_13.

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Bell, Jason, Janusz Brzozowski, Nelma Moreira, and Rogério Reis. "Symmetric Groups and Quotient Complexity of Boolean Operations." In Automata, Languages, and Programming, 1–12. Berlin, Heidelberg: Springer Berlin Heidelberg, 2014. http://dx.doi.org/10.1007/978-3-662-43951-7_1.

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Waelbroeck, Lucien. "The Category of Quotient Bornological Spaces." In Operator Extensions, Interpolation of Functions and Related Topics, 201–12. Basel: Birkhäuser Basel, 1993. http://dx.doi.org/10.1007/978-3-0348-8575-1_12.

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Davidson, Kenneth R., Timothy G. Feeman, and Allen L. Shields. "Extreme Points in Quotients of Operator Algebras." In Topics in Operator Theory, 67–91. Basel: Birkhäuser Basel, 1988. http://dx.doi.org/10.1007/978-3-0348-5475-7_7.

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Shalit, Orr. "Operator Theory and Function Theory in Drury–Arveson Space and Its Quotients." In Operator Theory, 1125–80. Basel: Springer Basel, 2015. http://dx.doi.org/10.1007/978-3-0348-0667-1_60.

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Shalit, Orr, and Orr Shalit. "Operator Theory and Function Theory in Drury–Arveson Space and Its Quotients." In Operator Theory, 1–50. Basel: Springer Basel, 2014. http://dx.doi.org/10.1007/978-3-0348-0692-3_60-1.

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Kono, Akira, and Kiminao Ishitoya. "Squaring operations in mod 2 cohomology of quotients of compact lie groups by maximal tori." In Algebraic Topology Barcelona 1986, 192–206. Berlin, Heidelberg: Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/bfb0083010.

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Zhao, Liquan, and Ling Zhang. "Advances in the Quotient Space Theory and its Applications." In Transdisciplinary Advancements in Cognitive Mechanisms and Human Information Processing, 250–61. IGI Global, 2011. http://dx.doi.org/10.4018/978-1-60960-553-7.ch015.

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Quotient space theory (QST), a new granule computing tool dealing with imprecise, incomplete and uncertain knowledge, uses a triplet, including the universe, its structure and attributes, to describe a problem space or simply a space. As one of important theories of granular computing (GrC), QST is very helpful to the study of cognitive informatics (CI). This article summarizes the quotient space’s model and its main principle. Then some basic operations on quotient space are introduced, and the significant properties of the fuzzy quotient space family are elaborated. Finally the main applications of quotient space theory are discussed.
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Conference papers on the topic "Quotient operation"

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Amaricai, Alexandru, and Oana Boncalo. "Improving the Performance of the Divide-Add Fused Operation Using Variable Latency Quotient Generation." In 2009 12th Euromicro Conference on Digital System Design, Architectures, Methods and Tools (DSD). IEEE, 2009. http://dx.doi.org/10.1109/dsd.2009.188.

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Zhong, Yan, and Qi Zhang. "Strengthening Marketing Operation and Enlarging the Quotient of Freight Express Transportation Market for Railway." In Second International Conference on Transportation and Traffic Studies (ICTTS ). Reston, VA: American Society of Civil Engineers, 2000. http://dx.doi.org/10.1061/40503(277)52.

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Wang, Yu-Xin, Yu-Tong Li, and Jian-Wei Wang. "Behavior-Form Double Directions Creative Conceptual Design Model and Its Quotient Space Implementation." In ASME 2008 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2008. http://dx.doi.org/10.1115/detc2008-49315.

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This paper presents a novel indirect matching approach between the function layer and the form layer to enhance the capability for the FBS method to obtain the creative conceptual design results. Firstly, the basic operation actions set, which is composed of the basic operation actions obtained by decomposing each function in the lowest level of the function decomposition tree in the FBS model into the sub-functions, in the function layer is regrouped dynamically. This behavior regroup process has introduced the new design variables into the conceptual design process and leads the behavior creativity to produce. On the other hand, considering the multi-functions for each basic structure to have and representing these functions with the basic operation actions, then the basic operation actions set in the form layer is set up. Dynamic regrouping this set in the form layer, the new design variables has been introduced into the conceptual design process, and leads the form creativity to produce. Through the above behavior-form double directions creative process, the solution scope of the conceptual design is enlarged obviously. Therefore, the method present in this paper has enough capability to obtain the creative conceptual results. Furthermore, the model presented in this paper is represented with the quotient space mathematically. The case study has shown that in the function layer, through adjusting the attribute function, which determines the partition grain of the basic operation actions set in the function layer or in the form layer, the new behaviors can be generated.
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Shahidi, Parham, Steve C. Southward, and Mehdi Ahmadian. "Estimating Crew Alertness From Speech." In 2010 Joint Rail Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/jrc2010-36261.

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With the latest initiative of the government to develop a high speed passenger rail system in the United States the first and most important strategic transportation goal is to “Ensure safe and efficient transportation choices. A key element of safe railroad operation is to address the issue of fatigue among railroad operating employees and how to fight it. In this paper, we are presenting a novel approach to estimating fatigue levels of train conductors by analyzing the speech signal in the communication between the conductor and dispatch. We extract vocal indicators of fatigue from the speech signal and use Fuzzy Logic to generate an estimate of the mental state of the train conductor. Previous research has shown that sleeping disorders, reduced hours of rest and disrupted circadian rhythms lead to significantly increased fatigue levels which manifest themselves in alterations of speech patterns as compared to alert states of mind. To make a decision about the level of fatigue, we are proposing a Fuzzy Logic algorithm which combines inputs such as word production rate and speech intensity to generate a Fatigue Quotient at any moment in time when speech is present. The computation of the Fatigue Quotient relies on a rule base which draws from existing knowledge about fatigue indicators and their relation to the level of fatigue of the subject. For this project, the rule base and the membership functions associated with it were derived from real time testing and the subsequent tuning of parameters to refine the detection of changes in patterns. It was successfully shown that Fuzzy Logic can be implemented to estimate alertness levels from speech metrics in real-time and that the membership functions for this purpose can be found empirically through iterative testing. Furthermore, this study has proven that the framework to run such an analysis continuously as a monitoring function in locomotive cabins is feasible and can be realized with relatively inexpensive hardware.
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Zeng, Lingfu, Lennart G. Jansson, and Alexander Börjesson. "Piping Vibration and Vibration Damage Prevention Through Screening of Dynamic Susceptibility." In 2017 25th International Conference on Nuclear Engineering. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/icone25-66658.

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This paper continues our recent discussion on piping vibration and practical measures for preventing vibration-related damage in nuclear power industries. Our emphasis is on an empirical approach, which attempts to estimate a so-called “dynamic susceptibility” at various locations in a piping system. This approach uses a dynamic susceptibility factor (DS), which is a quotient of the modal stress to the modal velocity, as an indicator of the risk levels of vibration to measure the vibration sensitivity for excitation sources in a given frequency interval of particular interest. In the present paper, Benchmark examples tested by the general purpose finite element program ANSYS, and commercial piping programs CAEPIPE and PIPESTRESS, are presented and the potential of using DS parameters as a screening tool for determining “potentially-large” alternating stresses is illustrated. It is demonstrated that, combined with knowledge of typical vibration sources, this is a practical and cost effective way for forming a base for the vibration control prior to installation and for the planning of post-installation vibration monitoring of a piping system under operation.
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Hanschke, Benjamin, Thomas Klauke, and Arnold Kühhorn. "The Effect of Foreign Object Damage on Compressor Blade High Cycle Fatigue Strength." In ASME Turbo Expo 2017: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/gt2017-63599.

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For a considerable amount of time blade integrated disks (blisks) are established as a standard component of high pressure compressors (HPCs) in aero engines. Due to the steady requirement to increase the efficiency of modern HPCs, blade profiles get thinned out and aerodynamic stage loading increases. Ever since, aerofoil design has to balance structural and aerodynamic requirements. One particularity of aero engines is the possibility to ingest different kinds of debris during operation and some of those particles are hard enough to seriously damage the aerofoil. Lately, a growing number of blisk-equipped aero engines entered service and the question of foreign object damage (FOD) sensitivity relating to compressor blade high cycle fatigue (HCF) has emerged. Correct prediction of fatigue strength drop due to a FOD provides a huge chance for cost cutting in the service sector as on-wing repairs (e.g. borescope blending) are much more convenient than the replacement of whole blisks and corresponding engine strips. The aim of this paper is to identify critical FOD-areas of a modern HPC stage and to analyze the effects of stress concentrations — caused by FOD — on the fatigue strength. A process chain has been developed, that automatically creates damaged geometries, meshes the parts and analyses the fatigue strength. Amplitude frequency strength (af-strength) has been chosen as fatigue strength indicator owing to the fact, that amplitudes and frequencies of blade vibrations are commonly measured either by blade tip timing or strain gauges. Furthermore, static and dynamic stress concentrations in damaged geometries compared to the reference design were computed. A random variation of input parameters was performed, such as the radial damage position at blade leading edge and damage diameter. Based on results of the different samples, correlations of input parameters and the fatigue strength drop have been investigated. Evaluation shows a significant mode dependence of critical blade areas with a large scatter between drops in fatigue strength visible for mode to mode comparison. Keeping in mind the necessity of fast response times in the in-service sector, FOD sensitivity computations could be performed for all blade rows of the HPC — including the analysis of possible borescope blending geometries — in the design stage. Finally, the actual amplitude frequency levels (af-levels) of the modes excited during operation have to be appropriately taken into consideration. For example, a pronounced af-strength drop due to a FOD may not be critical for safe engine operations because the observed mode is excited by small af-levels during operation. Hence, the endurance ratio — a quotient of af-level and af-strength — is used as assessment criterion.
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7

Şahan, Tunçar, and Osman Mucuk. "Normality and quotient of crossed modules within group with operations." In CURRENT TRENDS IN RENEWABLE AND ALTERNATE ENERGY. Author(s), 2019. http://dx.doi.org/10.1063/1.5095117.

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8

Koch, R., S. Wittig, H. J. Feld, and H. J. Mohr. "In-Situ Soot Measurements in an Operating Engine Gas Turbine Combustor." In ASME 1991 International Gas Turbine and Aeroengine Congress and Exposition. American Society of Mechanical Engineers, 1991. http://dx.doi.org/10.1115/91-gt-177.

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The dispersion quotient method, an optical measuring technique for particles, has been applied to in situ measurements of the soot particle size and density in the secondary zone of a KHD GT-216 gas turbine combustor under operating engine conditions. The optical technique, which has been developed at the Institut of Thermische Strömungsmaschinen, is based on the light extinction at different wavelength by a particle cloud due to absorption and scattering. It is of particular advantage in applications, where particles of small size (d ≤ 1.0μ) and high density are to be investigated. In the present investigation, two idling running conditions of the turbine have been studied: 30.000 rpm and 47.000 rpm. The results show, that the dispersion quotient method is well suited for soot measurements in pressurized flames. In particular, it was found, that the soot particle diameter is not effected by the rotating speed of the turbine. The size of the soot particles was always in the range from 0.1 to 0.3 mircon. The soot volume fraction, however, was found to be strongly influenced by different rotating speeds, with higher rotating speed causing higher volume fraction of soot.
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9

Dillon, Heather E., and Whitney G. Colella. "Independent Evaluation of Measured Performance Data for Cutting-Edge Combined Heat and Power Fuel Cell Systems Installed in Buildings." In ASME 2012 6th International Conference on Energy Sustainability collocated with the ASME 2012 10th International Conference on Fuel Cell Science, Engineering and Technology. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/es2012-91471.

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Pacific Northwest National Laboratory (PNNL) is working with industry to independently monitor up to fifteen distinct 5 kilowatt-electric (kWe) combined heat and power (CHP) high temperature (HT) proton exchange membrane (PEM) fuel cell systems (FCSs) installed in light commercial buildings. This research paper discusses an evaluation of the first six months of measured performance data acquired at a one-second sampling rate from real-time monitoring equipment attached to the FCSs at building sites. Engineering performance parameters are independently evaluated. Based on an analysis of the first few months of measured operating data, FCS performance is consistent with manufacturer-stated performance. Initial data indicate that the FCSs have relatively stable performance and a long term average production of about 4.57 kWe of power. This value is consistent with, but slightly below, the manufacturer’s stated rated electric power output of 5 kWe. The measured system net electric efficiency has averaged 33.7%, based on the higher heating value (HHV) of natural gas fuel. This value, also, is consistent with, but slightly below, the manufacturer’s stated rated electric efficiency of 36%. The FCSs provide low-grade hot water to the building at a measured average temperature of about 48.4°C, lower than the manufacturer’s stated maximum hot water delivery temperature of 65°C. The uptime of the systems is also evaluated. System availability can be defined as the quotient of total operating time compared to time since commissioning. The average values for system availability vary between 96.1 and 97.3%, depending on the FCS evaluated in the field. Performance at Rated Value for electrical efficiency (PRVeff) can be defined as the quotient of the system time operating at or above the rated electric efficiency and the time since commissioning. The PRVeff varies between 5.6% and 31.6%, depending on the FCS field unit evaluated. Performance at Rated Value for electrical power (PRVp) can be defined as the quotient of the system time operating at or above the rated electric power and the time since commissioning. PRVp varies between 6.5% and 16.2%. Performance at Rated Value for electrical efficiency and power (PRVt) can be defined as the quotient of the system time operating at or above both the rated electric efficiency and the electric power output compared to the time since commissioning. PRVt varies between 0.2% and 1.4%. Optimization to determine the manufacturer rating required to achieve PRVt greater than 80% has been performed based on the collected data. For example, for FCS unit 130 to achieve a PRVt of 95%, it would have to be down-rated to an electrical power output of 3.2 kWe and an electrical efficiency of 29%.The use of PRV as an assessment metric for FCSs has been developed and reported for the first time in this paper. For FCS Unit 130, a 20% decline in electric power output was observed from approximately 5 kWe to 4 kWe over a 1,500 hour period between Dec. 14th 2011 and Feb. 14th 2012.
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10

Dillon, Heather E., and Whitney G. Colella. "Real-Time Measured Performance of Micro Combined Heat and Power Fuel Cell Systems Independently Evaluated in the Field." In ASME 2012 10th International Conference on Fuel Cell Science, Engineering and Technology collocated with the ASME 2012 6th International Conference on Energy Sustainability. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/fuelcell2012-91470.

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Abstract:
Pacific Northwest National Laboratory (PNNL) is working with industry to independently monitor up to fifteen distinct 5 kilowatt-electric (kWe) combined heat and power (CHP) high temperature (HT) proton exchange membrane (PEM) fuel cell systems (FCSs) installed in light commercial buildings. This research paper discusses an evaluation of the first six months of measured performance data acquired at a one-second sampling rate from real-time monitoring equipment attached to the FCSs at building sites. Engineering performance parameters are independently evaluated. Based on an analysis of the first few months of measured operating data, FCS performance is consistent with manufacturer-stated performance. Initial data indicate that the FCSs have relatively stable performance and a long term average production of about 4.57 kWe of power. This value is consistent with, but slightly below, the manufacturer’s stated rated electric power output of 5 kWe. The measured system net electric efficiency has averaged 33.7%, based on the higher heating value (HHV) of natural gas fuel. This value, also, is consistent with, but slightly below, the manufacturer’s stated rated electric efficiency of 36%. The FCSs provide low-grade hot water to the building at a measured average temperature of about 48.4°C, lower than the manufacturer’s stated maximum hot water delivery temperature of 65°C. The uptime of the systems is also evaluated. System availability can be defined as the quotient of total operating time compared to time since commissioning. The average values for system availability vary between 96.1 and 97.3%, depending on the FCS evaluated in the field. Performance at Rated Value for electrical efficiency (PRVeff) can be defined as the quotient of the system time operating at or above the rated electric efficiency and the time since commissioning. The PRVeff varies between 5.6% and 31.6%, depending on the FCS field unit evaluated. Performance at Rated Value for electrical power (PRVp) can be defined as the quotient of the system time operating at or above the rated electric power and the time since commissioning. PRVp varies between 6.5% and 16.2%. Performance at Rated Value for electrical efficiency and power (PRVt) can be defined as the quotient of the system time operating at or above both the rated electric efficiency and the electric power output compared to the time since commissioning. PRVt varies between 0.2% and 1.4%. Optimization to determine the manufacturer rating required to achieve PRVt greater than 80% has been performed based on the collected data. For example, for FCS unit 130 to achieve a PRVt of 95%, it would have to be down-rated to an electrical power output of 3.2 kWe and an electrical efficiency of 29%.The use of PRV as an assessment metric for FCSs has been developed and reported for the first time in this paper. For FCS Unit 130, a 20% decline in electric power output was observed from approximately 5 kWe to 4 kWe over a 1,500 hour period between Dec. 14th 2011 and Feb. 14th 2012.
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