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Journal articles on the topic 'Multiplicators'

Author: Grafiati
Published: 4 June 2025
Last updated: 15 July 2025

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1

Vanity, Mugob Nshukwi. "A Performance Appraisal of the Pedagogic in Service Training Programme ISTP Multiplicators in C.B.C. Secondary Schools of the North West Region Teachers' Perspective." International Journal of Trend in Scientific Research and Development 3, no. 6 (2019): 914–28. https://doi.org/10.5281/zenodo.3589066.

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This paper sought to investigate the level of utilization of the prerequisites to supervision of instruction by the ISTP Multiplicators in CBC secondary schools of the NWR teachers perspective. The study progressed as guided by a specific research question To what extent do the ISTP Multiplicators use interpersonal skills in supervision of instruction This research question was transformed into a research hypothesis. The case study research design was used with proportionate and random sampling techniques respectively to ensure that respondents from all the schools were represented equally. Questionnaire for teachers was the instrument used for data collection. Data were analysed using statistical packages for social sciences SPSS version 21.0 for windows. Results were reported using descriptive statistics. Chi square and student t tests were used to determine relationships between respondents demographic characteristics and their view on some attributes of the ISTP Multiplicators. The decision rule was to reject the null hypothesis where the computed mean was statistically significantly greater than the expected value and accept the alternative hypothesis. Following this rule all the alternative hypotheses were rejected and the null hypotheses accepted. Recommendations were made to the Education secretary of the CBC, the ISTP Coordinator, the Principals and teachers of the schools concerned, the ISTP Multiplicators in order to improve performance levels of the ISTP Multiplicators. Suggestions for further research were given. Vanity Mugob Nshukwi "A Performance Appraisal of the Pedagogic in-Service Training Programme (ISTP) Multiplicators in C.B.C. Secondary Schools of the North-West Region: Teachers' Perspective" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-6 , October 2019, URL: https://www.ijtsrd.com/papers/ijtsrd29265.pdf
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2

EICK, BETTINA, and DÖRTE FEICHTENSCHLAGER. "COMPUTATION OF LOW-DIMENSIONAL (CO)HOMOLOGY GROUPS FOR INFINITE SEQUENCES OF p-GROUPS WITH FIXED COCLASS." International Journal of Algebra and Computation 21, no. 04 (2011): 635–49. http://dx.doi.org/10.1142/s021819671100639x.

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Eick and Leedham-Green introduced infinite sequences of p-groups of fixed coclass. Here we describe an algorithm to compute the Schur multiplicators of all groups in an infinite sequence simultaneously. Based on this, we prove that these Schur multiplicators can be described by a single parametrised presentation; this confirms a conjecture by Eick. Similar results are obtained for certain low-dimensional cohomology groups; these results support a conjecture by Carlson.
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3

Messemaker, Anne, Arthur Schall, Julia Haberstroh, and Johannes Pantel. "MultiTANDEM." GeroPsych 30, no. 4 (2017): 165–75. http://dx.doi.org/10.1024/1662-9647/a000178.

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Abstract. The MultiTANDEM system trains management staff at outpatient nursing facilities to be TANDEM trainers (i.e., multiplicators for social-skills training) of professional and family caregivers for people with dementia. We used a pre-post-1-post-2 follow-up design to evaluate intervention and implementation success. Results showed a significant increase in the communication skills of caregivers and a significant reduction in family caregiver burden. Analyses of the implementation showed high acceptability among multiplicators and a high penetration of TANDEM trainings among their fellow staff members. An evaluation of the sustainability yielded heterogeneous results. Evaluation of impeding factors showed a reluctance among family caregivers to participate. Further studies with larger sample sizes and including all implementation outcomes are recommended.
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4

Ladyzhenskaya, O. "On multiplicators in Hölder spaces with nonhomogeneous metric." Methods and Applications of Analysis 7, no. 3 (2000): 465–72. http://dx.doi.org/10.4310/maa.2000.v7.n3.a3.

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5

Volchkov, V. V. "On multiplicators of power series in Hardy spaces." Ukrainian Mathematical Journal 50, no. 4 (1998): 662–65. http://dx.doi.org/10.1007/bf02487396.

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6

Eick, Bettina. "Schur multiplicators of finite p-groups with fixed coclass." Israel Journal of Mathematics 166, no. 1 (2008): 157–66. http://dx.doi.org/10.1007/s11856-008-1025-y.

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7

Eick, Bettina. "Schur multiplicators of infinite pro-p-groups with finite coclass." Israel Journal of Mathematics 166, no. 1 (2008): 147–56. http://dx.doi.org/10.1007/s11856-008-1024-z.

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8

Rychkov, V. S. "Pointwise multiplicators in weighted Sobolev spaces on a half-line." Mathematical Notes 56, no. 1 (1994): 704–10. http://dx.doi.org/10.1007/bf02110561.

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9

Kokilashvili, V., and A. Meskhi. "Weighted inequalities for Hilbert transforms and multiplicators of Fourier transforms." Journal of Inequalities and Applications 1997, no. 3 (1997): 562605. http://dx.doi.org/10.1155/s1025583497000167.

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10

Nursultanov, E. D. "Concerning the multiplicators of Fourier series in the trigonometric system." Mathematical Notes 63, no. 2 (1998): 205–14. http://dx.doi.org/10.1007/bf02308760.

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11

Neiman-zade, M. I., and A. A. Shkalikov. "Schrödinger operators with singular potentials from the space of multiplicators." Mathematical Notes 66, no. 5 (1999): 599–607. http://dx.doi.org/10.1007/bf02674201.

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12

Nursultanov, E. D. "Concerning the multiplicators of fourier series in the trigonometric system." Mathematical Notes 65, no. 6 (1999): 801. http://dx.doi.org/10.1007/bf02675600.

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13

Koronovskii, Aleksei. "The multiplicators of periodical solutions for the generator with the piece-wise linear element." Izvestiya VUZ. Applied Nonlinear Dynamics 5, no. 2 (1997): 24–34. http://dx.doi.org/10.18500/0869-6632-1997-5-2-24-34.

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This article deals with systems with с phase space consisting of three linear subspaces. These systems аге described by n ordinary linear differential equations with plece~wise linear functions in their right side. The equations allowing to find the periodical solutions of these systems and its multiplicators depending upon the values of control parameters have been obtained. It allows to trace the regimes maps in the space of control parameters.
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14

Vil’danova, V. F., and F. Kh Mukminov. "Perturbations of Nonlinear Elliptic Operators by Potentials in the Space of Multiplicators." Journal of Mathematical Sciences 257, no. 5 (2021): 569–78. http://dx.doi.org/10.1007/s10958-021-05504-1.

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15

Cai, Guang Hui, Shu Wen Zheng, Ping Li, and Chuan Liang. "Design and Implementation of RS Encoder and Decoder in OFDM System Based on FPGA." Applied Mechanics and Materials 602-605 (August 2014): 2619–22. http://dx.doi.org/10.4028/www.scientific.net/amm.602-605.2619.

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This paper introduces the basic principle of RS codes in OFDM system and the design method of 16 shift registers, finite field multiplicators and adders, on and timing circuit are validated by using of EDA tools Quartus II. Finally, the simulation results is given and demonstrates that a good channel encoding and decoding can be achieved by using FPGA in OFDM system, which can save the cost, shorten the designing cycle , and is convenient to speed up the listing of products, occupy less hardware resources, and comply with the development trend of modern communication.
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16

Kuznetsova, A. Yu, and E. V. Patrin. "One class of C*-algebras generated by a family of partial isometries and multiplicators." Russian Mathematics 56, no. 6 (2012): 37–47. http://dx.doi.org/10.3103/s1066369x12060059.

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17

Agafonova, N. Yu. "Λ-Summability and Multiplicators of Holder Classes of Fourierseries with Respect ¨ to Character Systems". Izvestiya of Saratov University. New Series. Series: Mathematics. Mechanics. Informatics 11, № 2 (2011): 3–8. http://dx.doi.org/10.18500/1816-9791-2011-11-2-3-8.

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18

Kassym, A. S., and L. K. Kusainova. "On the Separation Property of the Sturm–Liouville Operator in Weighted Spaces of Multiplicators." Journal of Mathematical Sciences 241, no. 5 (2019): 596–604. http://dx.doi.org/10.1007/s10958-019-04448-x.

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19

Tvrdoň, J. "Economic aspects of rural areas sustainable development." Agricultural Economics (Zemědělská ekonomika) 51, No. 1 (2012): 12–19. http://dx.doi.org/10.17221/5070-agricecon.

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The articles deals with problems of different development of rural areas and their factors. In usual analysis of rural development, the position of agriculture is interpreted in broad range of opinions from the neglectable role to its non-substitutability in rural economics. The article follows strong sides of these concepts at simultaneous reduction of their weaknesses and is focused on problems of investigation of the mutual influence of endogenous as well as exogenous industries on rural regions. Applied approach leads to setting up model of economic base and deriving of multiplicators of rural development. It is obvious from the analysis that nonagricultural subsidy programs supporting development of the others industries in region have indirect influence upon its agriculture too. In different regions, this influence varies due to the factors investigated in the paper. 
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20

Choubey, Abhishek, Kola Shivapriya, and Shruti Bhargava Choubey. "Design of ALU based on Majority Logic for Low Power Applications." International Journal of Emerging Technology and Advanced Engineering 11, no. 6 (2021): 40–47. http://dx.doi.org/10.46338/ijetae0621_05.

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Approximate calculations are a new nanotechnology paradigm for improving efficiency and reducing energy use. Most of the logic extends to many contemporary nanotechnological developments and is used for the design of digital circuits in its basic portion (3 input plurality, MV). This paper suggests implementations of additional compressors and ML multiplicators. An additional bit discovery circuit is used for the proposed compressors. The size of the multiplier is calculated by a control factor for the importance of different extra bits. The designs proposed are tested with hardware (for example, time frame and port complexity) as well as with error calculation. These designs have superior performance in terms of area and delay. The validity of the proposed designs is also shown by case tests of the error resistance implementation.
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21

Tatarkin, D. A., E. N. Sidorova, and A. V. Trynov. "Development of the Investment Passport of the Region on the Basis of Multiplicators of the Matrix of Financial Flows." Bulletin of Ural Federal University. Series Economics and Management 16, no. 6 (2017): 909–27. http://dx.doi.org/10.15826/vestnik.2017.16.6.043.

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22

Savilov, A. V. "Electron Bunching at the Doubled Frequency of the Input Wave and the Use of This Effect in Klystron-Type Frequency Multiplicators." IEEE Transactions on Plasma Science 32, no. 3 (2004): 1147–51. http://dx.doi.org/10.1109/tps.2004.828792.

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23

Warneke, Konstantin, Andreas Konrad, and Jan Wilke. "The knowledge of movement experts about stretching effects: Does the science reach practice?" PLOS ONE 19, no. 1 (2024): e0295571. http://dx.doi.org/10.1371/journal.pone.0295571.

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Objective Stretching is performed with numerous purposes in multiple settings such as prevention, rehabilitation, fitness training and sports. Its patterns of use substantially depend on the education and beliefs of health care and exercise professionals as they represent the multiplicators recommending and prescribing interventions to clients, patients and athletes. This study investigated movement experts’ knowledge about the scientific evidence on stretching effects. Design Survey study. Participants A total of 117 exercise and health professionals (physiotherapists, sports scientists, coaches) attending a training convention in Austria (male: n = 44, female: n = 73, 36±11 years) completed a digital survey. With its 22 items, the questionnaire addressed the movement experts’ awareness of the evidence on stretching effects regarding a variety of related topics selected based on the findings of topical systematic reviews. Results The majority of the individuals (57–88%) assumed positive effects of stretching on recovery, prevention of muscle injury, range of motion, muscular imbalance and artery elasticity. No or adverse effects were mostly claimed on bone injury prevention, maximal/explosive strength, and delayed-onset muscle soreness. In only 10 of 22 items, participants’ classifications were in accord with the scientific evidence. Conclusions The awareness of research findings on stretching effects among exercise and health professionals is alarmingly low. Future studies may hence be geared to improve implementation and science communication.
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24

Rožukalne, Anda. "Internet news about Ukraine and the “audience agenda”: topics, sources and the audience aggressiveness." Žurnalistikos Tyrimai 8 (December 7, 2015): 17–37. http://dx.doi.org/10.15388/zt/jr.2015.8.8841.

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Euromaidan in Kiev, the annexation of Crimea and the war in Eastern Ukraine had become the most important international events that impacted media content in 2013 and 2014. This paper provides research that intends to analyse the interrelation between news content of the three largest news sites in Latvia (Delfi.lv, Apollo.lv, Tvnet.lv) and the Latvian and Russian-speaking audience reaction to the news about the events in Ukraine in 2014. By using a unique tool for audience behaviour analysis “The Index of Internet Aggressiveness” in this research, the level of audience aggressive­ness that appears within audience comments has been analysed with the aim to find out how and if the professional approach of the news producers influ­ences the aggressiveness of the news site’s audience.The three different groups of data from the Index of Internet Aggressive­ness are used to measure audience behaviour: the quantity of aggressive key­words used in the comments by audience members that create a significant rise in the Index of Internet Aggressiveness next to the news on Ukraine; content analysis of the most aggressively commented news articles about the events in Ukraine; the semi-structured qualitative interviews with editors of news sites that explain professional routines.The most significant conclusions of the research show the domination of the official Russian media outlets among the news sources about Ukraine. By republishing ready-made and easily accessible news stories, independent news sites of Latvia have become distributors and multiplicators of messages favourable to the Russian version of the events in Ukraine.
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25

Indrayani, Candra Yudha Satriya, Agus Triyono, Nadia Itona Siregar, and Anita Amaliyah. "INFLUENCERS AS DIGITAL LABOR IN LOCAL TOURISM DEVELOPMENT." Jurnal Netnografi Komunikasi 4, no. 1 (2025): 1–20. https://doi.org/10.59408/jnk.v4i1.74.

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The tourism sector is a priority driving the regional economy. One effort to build tourism is through the popularity of influencers who can be an alternative used indirectly to re-promote regional tourist destinations. Influencers actively utilize digital media as well-known as digital workers. This research explores the phenomenon of social media influencers in relation to digital workers regarding freedom as content creators and content commodification. Therefore, this research aims to describe the phenomenon of Influencers as Digital Workers in Indonesian Tourism Development in terms of content creation, content production and freedom in selecting tourism content. The method in this research is a qualitative research method with a phenomenological approach based on the concepts of digital labor, social media influencers and tourism development. Primary data from interviews with six local influencers who are members and ambassadors of the Generasi Pesona Indonesia (GenPI) community. Secondary data was obtained through journals, e-books, books, blogs and informant’s social media. To code the interview manuscript and create the co-manuscript networks, we used atlas.ti . The research results show that the communication process by influencers begins with input including content production competencies, content distribution competencies, interaction competencies, public persona, relationship quality and ability to influence. Then in terms of the role of local influencers as content creators, multiplicators, moderators and protagonists. Meanwhile, the output produced by local influencers is in the form of content, reach, interaction, personalization, peer effect, authenticity and credibility. In addition, the outcome is content distribution on various digital media platforms. Finally, in terms of impact, it includes networking and interaction.
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26

W. Kluszczyńsk, Ryszard. "Living between reality and virtuality – on the work of Monika Fleischmann and Wolfgang Strauss." AM Journal of Art and Media Studies, no. 2 (December 15, 2012): 40–46. http://dx.doi.org/10.25038/am.v0i2.20.

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It becomes clear that new media begin to function as multiplicators of new worlds, creating numerous virtual environments. This diversified, compound reality in many ways takes a shape of a network. New media art in this field of events has various functions. From one hand, it is one of the most refined instruments in the process of networkisation. From the other hand, it is also the tool of verification for these processes, critically but without prejudice evaluating its development, attentively observing what shapes do they took, as well as their real or possible results. In each case, new media art is an active participant of these processes, making full use of possibilities provided by the network system. Frequently while performing its activities it is intersected or linked with the processes which are a part of the world of science, creating together with them new cultural paradigm. Monika Fleischmann and Wolfgang Strauss undertook their joint, creative actions in combined fields of art and science in late 1980s. It was a special moment of a breakthrough for the formation of the character of modern civilization. Events taking place back then, as being a part of a sphere of phenomena generated by communication and information sciences, had enormous influence on the process of shaping a new cultural formation – cyber culture, and because of this, at the same time, had enormous influence on our ways of reality perception. From the beginning of their cooperation, Fleischmann and Strauss have found the tools appropriate for the realization of their works in the environemt of the internet. Their’s art has developed in parallel to the development of computer and internet environment, depicting dynamics of this network and inscribing, with the undertaken issues, in the circle of problems generated through out a development and transformations of accompanied cyber-cultural concepts.
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27

Muraz, Gilbert. "Multiplicateurs compacts." Bulletin of the Belgian Mathematical Society - Simon Stevin 4, no. 5 (1997): 601–12. http://dx.doi.org/10.36045/bbms/1105737763.

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28

Mandell, Michael A. "Cochain multiplications." American Journal of Mathematics 124, no. 3 (2002): 547–66. http://dx.doi.org/10.1353/ajm.2002.0017.

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29

Jabbar, Adil Kadir. "Presentation Ideals in Locally Multiplications Modules." Journal of Zankoy Sulaimani - Part A 16, no. 2 (2014): 47–51. http://dx.doi.org/10.17656/jzs.10292.

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30

Baaj, Saad, and Georges Skandalis. "Unitaires multiplicatifs commutatifs." Comptes Rendus Mathematique 336, no. 4 (2003): 299–304. http://dx.doi.org/10.1016/s1631-073x(03)00034-7.

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31

Hwang, Vincent, YoungBeom Kim, and Seog Chung Seo. "Multiplying Polynomials without Powerful Multiplication Instructions." IACR Transactions on Cryptographic Hardware and Embedded Systems 2025, no. 1 (2024): 160–202. https://doi.org/10.46586/tches.v2025.i1.160-202.

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We improve the performance of lattice-based cryptosystems Dilithium on Cortex-M3 with expensive multiplications. Our contribution is two-fold: (i) We generalize Barrett multiplication and show that the resulting shape-independent modular multiplication performs comparably to long multiplication on some platforms without special hardware when precomputation is free. We call a modular multiplication “shape-independent” if its correctness and efficiency depend only on the magnitude of moduli and not the shapes of the moduli. This was unknown in the literature even though modular multiplication has been studied for more than 40 years. In the literature, shape-independent modular multiplications often perform several times slower than long multiplications even if we ignore the cost of the precomputation. (ii) We show that polynomial multiplications based on Nussbaumer fast Fourier transform and Toom–Cook over Z2k perform the best when modular multiplications are expensive and k is not very close to the arithmetic precision.For practical evaluation, we implement assembly programs for the polynomial arithmetic used in the digital signature Dilithium on Cortex-M3. For the modular multiplications in Dilithium, our generalized Barrett multiplications are 1.92 times faster than the state-of-the-art assembly-optimized Montgomery multiplications, leading to 1.38−1.51 times faster Dilithium NTT/iNTT. Along with the improvement in accumulating products, the core polynomial arithmetic matrix-vector multiplications are 1.71−1.77 times faster. We further apply the FFT-based polynomial multiplications over Z2k to the challenge polynomial multiplication ct0, leading to 1.31 times faster computation for ct0.We additionally apply the ideas to Saber on Cortex-M3 and demonstrate their improvement to Dilithium and Saber on our 8-bit AVR environment. For Saber on Cortex-M3, we show that matrix-vector multiplications with FFT-based polynomial multiplications over Z2k are 1.42−1.46 faster than the ones with NTT-based polynomial multiplications over NTT-friendly coefficient rings. When moving to a platform with smaller arithmetic precision, such as 8-bit AVR, we improve the matrix-vector multiplication of Dilithium with our Barrett-based NTT/iNTT by a factor of 1.87−1.89. As for Saber on our 8-bit AVR environment, we show that matrixvector multiplications with NTT-based polynomial multiplications over NTT-friendly coefficient rings are faster than polynomial multiplications over Z2k due to the large k in Saber.
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32

Javier González Vieli, Francisco. "Construction de p-multiplicateurs." Studia Mathematica 105, no. 2 (1993): 135–42. http://dx.doi.org/10.4064/sm-105-2-135-142.

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33

D'Alberto, Paolo, and Alexandru Nicolau. "Adaptive Winograd's matrix multiplications." ACM Transactions on Mathematical Software 36, no. 1 (2009): 1–23. http://dx.doi.org/10.1145/1486525.1486528.

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34

Beidar, K., Y. Fong, W. F. Ke, and S. Y. Liang. "Nearring multiplications on groups." Communications in Algebra 23, no. 3 (1995): 999–1015. http://dx.doi.org/10.1080/00927879508825264.

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35

Hadwin, Don, and Jeanne Wald Kerr. "Local multiplications on algebras." Journal of Pure and Applied Algebra 115, no. 3 (1997): 231–39. http://dx.doi.org/10.1016/s0022-4049(96)00013-8.

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36

Hou, Xiang-dong, Ferruh Özbudak, and Yue Zhou. "Switchings of semifield multiplications." Designs, Codes and Cryptography 80, no. 2 (2015): 217–39. http://dx.doi.org/10.1007/s10623-015-0081-7.

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37

Turnšek, Aleksej. "Circular two-sided multiplications." Linear and Multilinear Algebra 64, no. 11 (2016): 2169–76. http://dx.doi.org/10.1080/03081087.2016.1143911.

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38

Woodcock, Chris. "Almost equal group multiplications." Journal of Pure and Applied Algebra 214, no. 8 (2010): 1497–500. http://dx.doi.org/10.1016/j.jpaa.2009.12.002.

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MIKHAILOV, ROMAN, and INDER BIR S. PASSI. "A TRANSFINITE FILTRATION OF SCHUR MULTIPLICATOR." International Journal of Algebra and Computation 15, no. 05n06 (2005): 1061–73. http://dx.doi.org/10.1142/s0218196705002785.

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We study certain subgroups of the Schur multiplicator of a group G. These subgroups are related to the identification of subgroups of G determind by ideals in its integral group ring ℤ[G]. Suitably defined transfinite powers of the augmentation ideal of ℤ[G] provide an increasing transfinite filtration of the Schur multiplicator of G. We investigate the relationship of this filtration with the transfinite lower central series of groups which are HZ-local in the sense of Bousfield.
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40

Wiegold, James. "On some groups with trivial multiplicator." Bulletin of the Australian Mathematical Society 40, no. 2 (1989): 331–32. http://dx.doi.org/10.1017/s000497270000441x.

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I discussed the sort of thing Bernhard had in mind concerning the BFC-problem in [3], an article written for his sixieth birthday. This vigesennial contribution deals with one of the “and others”, namely the zero deficiency problem. in his article [1] bearing the same title as this one, Bernhard gave 2-generator 2-relator presentations of some metacyclic groups; if one distils and formalises the process used there, one gets the following result, to be used later in constructing some zero-deficiency finite p-groups.
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41

Passi, I. B. S., and Sucheta. "Dimension subgroups and Schur multiplicator—II." Topology and its Applications 25, no. 2 (1987): 121–24. http://dx.doi.org/10.1016/0166-8641(87)90003-4.

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42

PASSI, I. B. S., SUCHETA, and Ken-Ichi TAHARA. "Dimension subgroups and Schur multiplicator-III." Japanese journal of mathematics. New series 13, no. 2 (1987): 371–79. http://dx.doi.org/10.4099/math1924.13.371.

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43

Astashkin, Serguei V., and Guillermo P. Curbera. "Symmetric kernel of Rademacher multiplicator spaces." Journal of Functional Analysis 226, no. 1 (2005): 173–92. http://dx.doi.org/10.1016/j.jfa.2005.01.014.

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44

Astashkin, Serguei V., and Guillermo P. Curbera. "Rearrangement invariance of Rademacher multiplicator spaces." Journal of Functional Analysis 256, no. 12 (2009): 4071–94. http://dx.doi.org/10.1016/j.jfa.2008.12.021.

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45

Newman, M. F. "On coclass and trivial Schur multiplicator." Journal of Algebra 322, no. 3 (2009): 910–13. http://dx.doi.org/10.1016/j.jalgebra.2009.04.033.

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46

Gustafson, John, and Srinivas Aluru. "Massively Parallel Searching for Better Algorithms or How to Do a Cross Product with Five Multiplications." Scientific Programming 5, no. 3 (1996): 203–17. http://dx.doi.org/10.1155/1996/284218.

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A number of "tricks" are known that trade multiplications for additions. The term "tricks" reflects the way these methods seem not to proceed from any general theory, but instead jump into existence as recipes that work. The Strassen method for 2 × 2 matrix product with seven multiplications is a well-known example, as is the method for finding a complex number product in three multiplications. We have created a practical computer program for finding such tricks automatically, where massive parallelism makes the combinatorially explosive search tolerable for small problems. One result of this program is a method for cross products of three-vectors that requires only five multiplications.
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47

Hubbuck, J. R., and Z. Mahmud. "The Two Multiplications on BU." Proceedings of the American Mathematical Society 93, no. 1 (1985): 151. http://dx.doi.org/10.2307/2044572.

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48

Anker, Jean-Philippe, and Noel Lohoue. "Multiplicateurs Sur Certains Espaces Symetriques." American Journal of Mathematics 108, no. 6 (1986): 1303. http://dx.doi.org/10.2307/2374528.

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49

Newman, D. J. "Computing when multiplications cost nothing." Mathematics of Computation 46, no. 173 (1986): 255. http://dx.doi.org/10.1090/s0025-5718-1986-0815847-8.

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50

Grone, Robert. "Markov chains and tensor multiplications." Journal of Algebra 109, no. 1 (1987): 14–24. http://dx.doi.org/10.1016/0021-8693(87)90160-8.

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