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Опубліковано: 30 травня 2022
Оновлено: 31 травня 2022

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Статті в журналах з теми "An elementary divisor ring"

1

Chen, Huanyin, and Marjan Sheibani Abdolyousefi. "Elementary matrix reduction over Bézout domains." Journal of Algebra and Its Applications 18, no. 08 (July 5, 2019): 1950141. http://dx.doi.org/10.1142/s021949881950141x.

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Анотація:
A ring [Formula: see text] is an elementary divisor ring if every matrix over [Formula: see text] admits a diagonal reduction. If [Formula: see text] is an elementary divisor domain, we prove that [Formula: see text] is a Bézout duo-domain if and only if for any [Formula: see text], [Formula: see text] such that [Formula: see text]. We explore certain stable-like conditions on a Bézout domain under which it is an elementary divisor ring. Many known results are thereby generalized to much wider class of rings.
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2

Zabavsky, B. V., O. Romaniv, B. Kuznitska, and T. Hlova. "Comaximal factorization in a commutative Bezout ring." Algebra and Discrete Mathematics 30, no. 1 (2020): 150–60. http://dx.doi.org/10.12958/adm1203.

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3

KABBOUR, MOHAMMED, and NAJIB MAHDOU. "AMALGAMATION OF RINGS DEFINED BY BÉZOUT-LIKE CONDITIONS." Journal of Algebra and Its Applications 10, no. 06 (December 2011): 1343–50. http://dx.doi.org/10.1142/s0219498811005683.

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Let f : A → B be a ring homomorphism and let J be an ideal of B. In this paper, we investigate the transfer of notions elementary divisor ring, Hermite ring and Bézout ring to the amalgamation A ⋈f J. We provide necessary and sufficient conditions for A ⋈f J to be an elementary divisor ring where A and B are integral domains. In this case it is shown that A ⋈f J is an Hermite ring if and only if it is a Bézout ring. In particular, we study the transfer of the previous notions to the amalgamated duplication of a ring A along an A-submodule E of Q(A) such that E2 ⊆ E.
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4

Gatalevich, A. I., and B. V. Zabavs'kii. "Noncommutative elementary divisor rings." Journal of Mathematical Sciences 96, no. 2 (August 1999): 3013–16. http://dx.doi.org/10.1007/bf02169697.

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5

Zabavskii, B. V. "Noncommutative elementary divisor rings." Ukrainian Mathematical Journal 39, no. 4 (1988): 349–53. http://dx.doi.org/10.1007/bf01060766.

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6

Zabavs’kyi, B. V. "A Sharp Bézout Domain is an Elementary Divisor Ring." Ukrainian Mathematical Journal 66, no. 2 (July 2014): 317–21. http://dx.doi.org/10.1007/s11253-014-0932-9.

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7

Zabavsky, B. V., and O. M. Romaniv. "Commutative Bezout domains in which any nonzero prime ideal is contained in a finite set of maximal ideals." Carpathian Mathematical Publications 10, no. 2 (December 31, 2018): 402–7. http://dx.doi.org/10.15330/cmp.10.2.402-407.

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Анотація:
We investigate commutative Bezout domains in which any nonzero prime ideal is contained in a finite set of maximal ideals. In particular, we have described the class of such rings, which are elementary divisor rings. A ring $R$ is called an elementary divisor ring if every matrix over $R$ has a canonical diagonal reduction (we say that a matrix $A$ over $R$ has a canonical diagonal reduction if for the matrix $A$ there exist invertible matrices $P$ and $Q$ of appropriate sizes and a diagonal matrix $D=\mathrm{diag}(\varepsilon_1,\varepsilon_2,\dots,\varepsilon_r,0,\dots,0)$ such that $PAQ=D$ and $R\varepsilon_i\subseteq R\varepsilon_{i+1}$ for every $1\le i\le r-1$). We proved that a commutative Bezout domain $R$ in which any nonze\-ro prime ideal is contained in a finite set of maximal ideals and for any nonzero element $a\in R$ the ideal $aR$ a decomposed into a product $aR = Q_1\ldots Q_n$, where $Q_i$ ($i=1,\ldots, n$) are pairwise comaximal ideals and $\mathrm{rad}\,Q_i\in\mathrm{spec}\, R$, is an elementary divisor ring.
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8

Zabavsky, Bohdan. "Rings of dyadic range 1." Journal of Algebra and Its Applications 18, no. 11 (August 19, 2019): 1950206. http://dx.doi.org/10.1142/s0219498819502062.

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Анотація:
In this paper, we introduced the concept of a ring of a right (left) dyadic range 1. We proved that a Bezout ring of right (left) dyadic range 1 is a ring of stable range 2. And we proved that a commutative Bezout ring is an elementary divisor ring if and only if it is a ring of dyadic range 1.
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9

Zabavs’kyi, B. V., and B. M. Kuznits’ka. "A Stable Range of Class Full Matrices over Elementary Divisor Ring." Ukrainian Mathematical Journal 66, no. 5 (October 2014): 792–95. http://dx.doi.org/10.1007/s11253-014-0973-0.

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10

Zabavsky, B. V., O. V. Domsha, and O. M. Romaniv. "Clear rings and clear elements." Matematychni Studii 55, no. 1 (March 3, 2021): 3–9. http://dx.doi.org/10.30970/ms.55.1.3-9.

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Анотація:
An element of a ring $R$ is called clear if it is a sum of a unit-regular element and a unit. An associative ring is clear if each of its elements is clear.In this paper we defined clear rings and extended many results to a wider class. Finally, we proved that a commutative Bezout domain is an elementary divisor ring if and only if every full $2\times 2$ matrix over it is nontrivially clear.
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Більше джерел

Дисертації з теми "An elementary divisor ring"

1

Wilding, David. "Linear algebra over semirings." Thesis, University of Manchester, 2015. https://www.research.manchester.ac.uk/portal/en/theses/linear-algebra-over-semirings(1dfe7143-9341-4dd1-a0d1-ab976628442d).html.

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Motivated by results of linear algebra over fields, rings and tropical semirings, we present a systematic way to understand the behaviour of matrices with entries in an arbitrary semiring. We focus on three closely related problems concerning the row and column spaces of matrices. This allows us to isolate and extract common properties that hold for different reasons over different semirings, yet also lets us identify which features of linear algebra are specific to particular types of semiring. For instance, the row and column spaces of a matrix over a field are isomorphic to each others' duals, as well as to each other, but over a tropical semiring only the first of these properties holds in general (this in itself is a surprising fact). Instead of being isomorphic, the row space and column space of a tropical matrix are anti-isomorphic in a certain order-theoretic and algebraic sense. The first problem is to describe the kernels of the row and column spaces of a given matrix. These equivalence relations generalise the orthogonal complement of a set of vectors, and the nature of their equivalence classes is entirely dependent upon the kind of semiring in question. The second, Hahn-Banach type, problem is to decide which linear functionals on row and column spaces of matrices have a linear extension. If they all do, the underlying semiring is called exact, and in this case the row and column spaces of any matrix are isomorphic to each others' duals. The final problem is to explain the connection between the row space and column space of each matrix. Our notion of a conjugation on a semiring accounts for the different possibilities in a unified manner, as it guarantees the existence of bijections between row and column spaces and lets us focus on the peculiarities of those bijections. Our main original contribution is the systematic approach described above, but along the way we establish several new results about exactness of semirings. We give sufficient conditions for a subsemiring of an exact semiring to inherit exactness, and we apply these conditions to show that exactness transfers to finite group semirings. We also show that every Boolean ring is exact. This result is interesting because it allows us to construct a ring which is exact (also known as FP-injective) but not self-injective. Finally, we consider exactness for residuated lattices, showing that every involutive residuated lattice is exact. We end by showing that the residuated lattice of subsets of a finite monoid is exact if and only if the monoid is a group.
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2

Kahn, Eric B. "THE GENERALIZED BURNSIDE AND REPRESENTATION RINGS." UKnowledge, 2009. http://uknowledge.uky.edu/gradschool_diss/707.

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Making use of linear and homological algebra techniques we study the linearization map between the generalized Burnside and rational representation rings of a group G. For groups G and H, the generalized Burnside ring is the Grothendieck construction of the semiring of G × H-sets with a free H-action. The generalized representation ring is the Grothendieck construction of the semiring of rational G×H-modules that are free as rational H-modules. The canonical map between these two rings mapping the isomorphism class of a G-set X to the class of its permutation module is known as the linearization map. For p a prime number and H the unique group of order p, we describe the generators of the kernel of this map in the cases where G is an elementary abelian p-group or a cyclic p-group. In addition we introduce the methods needed to study the Bredon homology theory of a G-CW-complex with coefficients coming from the classical Burnside ring.
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3

Brook, Nicholas H. "The flavour dependence of charged hadron production at large transverse momenta using high energy photon and hadron beams at the OMEGA spectrometer : equipped with a ring imaging Cherenkov detector." Thesis, University of Manchester, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.328282.

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4

Souza, Leticia Vasconcellos de. "Congruência modular nas séries finais do ensino fundamental." Universidade Federal de Juiz de Fora, 2015. https://repositorio.ufjf.br/jspui/handle/ufjf/1441.

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Анотація:
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Este trabalho é voltado para professores que atuam nas séries finais do Ensino Fundamental. Tem como objetivo mostrar que é possível introduzir o estudo de Congruência Modular nesse segmento de ensino, buscando facilitar a resolução de diversas situações-problema. A motivação para escolha desse tema é que há a possibilidade de tornar mais simples a resolução de muitos exercícios trabalhados nessa etapa de ensino e que são inclusive cobrados em provas de admissão à escolas militares e em olimpíadas de Matemática para esse nível de escolaridade. Inicialmente é feita uma breve síntese do conjunto dos Números Inteiros, com suas operações básicas, relembrando também o conceito de números primos, onde é apresentado o crivo de Eratóstenes; o mmc (mínimo múltiplo comum) e o mdc (máximo divisor comum), juntamente com o Algoritmo de Euclides. Apresenta-se alguns exemplos de situações-problema e exercícios resolvidos envolvendo restos deixados por uma divisão para então, em seguida, ser dada a definição de congruência modular. Finalmente, são apresentadas sugestões de exercícios para serem trabalhados em sala de aula, com uma breve resolução.
The aims of this work is teachers working in the final grades of elementary school. It aspires to show that it is possible to introduce the study of Modular congruence this educational segment, seeking to facilitate the resolution of numerous problem situations. The motivation for choosing this theme is that there is the possibility to make it simpler to solve many problems worked at this stage of education and are even requested for admittance exams to military schools and mathematical Olympiads for that level of education. We begin with a brief summary about integer numbers, their basic operations, also recalling the concept of prime numbers, where the sieve of Eratosthenes is presented; the lcm (least common multiple) and the gcd (greatest common divisor), along with the Euclidean algorithm. We present some examples of problem situations and solved exercises involving debris left by a division and then, we give the definition of modular congruence . Finally , we present suggestions for exercises to be worked in the classroom, with a short resolution.
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5

Lin, Che-Ming, and 林哲民. "The Study of Elementary Students’ Learning Progression for Divisor and Multiple." Thesis, 2013. http://ndltd.ncl.edu.tw/handle/61633072543950382329.

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Анотація:
碩士
國立臺灣師範大學
科學教育研究所
101
The purpose of my dissertation is to look for the elementary school students’ learning progressions on the divisor and multiple and to develop initially the assessments about the learning progressions on the divisor and multiple. On the base of my research purposes, I have two research questions as follows. 1.What are the contents of the elementary school students’ learning progressions on the divisor and multiple? 2.How well are my initial assessments concerning the learning progressions on the divisor and multiple? When it comes to my research procedures, I discussed the relative paper, native or foreign, at first so as to clarify the meaning, the character, and the research mode of the learning progressions. Then I based on the discussed research modes to develop my learning progression instrument for elementary school students on the divisor and multiple, and I tested my instrument by testing some elementary school students. My research methods are survey research and documentary analysis. Based on the relative research paper about divisor and multiple and based on the past research results and based on the nowadays students’ performance, I asked fourteen students, including six 6-grade, two 2- grade, two 3- grade, two 4-grade, two 5-grade students in Kaohsiung, so that I may understand those different grades students’ performance on the concept of divisor and multiple, and that would help me develop my learning progression instrument. After my initial instrument, I built my assessment to test the attributive level of the students. In this stage, there were 619 students, ranging from 3-grade to 6-grade of five elementary schools in Kaohsiung, participating my assessment and finally I tested their scores and their performance to see whether they agreed with. There are three learning progressions in my research, including the learning progression of concept of being divided with no remainder, the learning progression of concept of divisor, and the learning progression of concept of multiple. Based on my result, I found that (1) on the learning progression of concept of being divided with no remainder, the students had to clear the concept first, then they would differ the sentence “A is divisible by B” from the sentence “A divides B”; (2) on the learning progression of concept of divisor, students have to understand the relation among every element from multiplication and division first, then they will know the concept of divisor; after they master the concept of divisor, they look out that a number may, at the same time, be a divisor of two different numbers, and they will develop the concept of common divisor; at last, they extract the meaning of great common divisor from understanding the concept of common divisor; (3) on the learning progression of concept of multiple, students have to understand the relation among every element from multiplication and division first, then they will know the concept of multiple; after they master the concept of multiple, they look out that a number may, at the same time, be a multiple of two different numbers, and they will develop the concept of common multiple; at last, they extract the meaning of least common multiple from understanding the concept of common multiple; (4) when they first understood the meaning of divisor and multiple, they knew the inverse relation of divisor and multiple; also, with their extent about those concepts, they may apply the concept of inverse relation of divisor and multiple; (5) students could solve the highest level routine examinations, yet could not solve lower level non-routine examinations. Based on the assessment, I distributed 498 students (80.4%, accounting for all 619 students) to my learning progression of concept of being divided with no remainder, 348 students (76.7%, accounting for 454 students) to my learning progression of concept of divisor, and 453 students (73.2%, accounting for 619 students) to my learning progression of concept of multiple. I thought that my assessment did work for some extent, and after some adjusting and revising, it may explain much more about students’ levels of learning progressions. From the above result, I suggest that the future researcher use my learning progression instrument to track students’ learning circumstance so that they may do some more conferring. As for the assessment, I suggest that the future researcher give consideration on routine tests and non-routine tests, as well as use more quantity of tests and multi-principles to judge which level the students have.
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6

Wen, Whei-Ru, and 温惠如. "The Analysis of Teaching Guide Content for Elementary School Mathematics：Take Divisor and Multiple for Example." Thesis, 2015. http://ndltd.ncl.edu.tw/handle/g685ek.

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Анотація:
碩士
國立臺北教育大學
數學暨資訊教育學系(含數學教育碩士班)
103
Abstract The method of this research is content analysis, which is to analyze the content and the structures in four versions (represented as A,B,C and D in this essay) of math teacher’s guides of the academic year 2014, Taiwanese year 103, and to review and compare the emphasis about the chapters “Divisors and Multiples” in the math teachers’ guide books. The results are listed as following: 1. For the content and structures; (1) All the four versions of math teacher’s guides are consistent with the basic ideas of mathematic curriculum guidelines from grade 1 through grade 9 in Taiwan. (2) For the composition of teaching materials, all the four versions of math teacher’s guides contain instructional status, competence Indicators of Grade 1-9 curriculum, instructional studies, instructional recommendations, instructional activities, pre-test papers for supplementary instruction , post-test papers, supplementary exercises, and references, etc. (3) Versions B,C and D give examples of teaching materials in order to make teachers dominate and organize the curriculum for around three years. The 9th volume of guidelines of version A focus exclusively on the content of the 9th volume of math book. (4) All the versions of math teacher’s guides list references to assist the teachers with instruction. 2. For the instructional study of the chapter “Divisors and Multiples”; (1) All four versions of math teacher’s guides for instructional status are consistent with the organization of curriculum. (2) Version A indicates that the internal and external links of mathematics by structural connections. Version B, C and D are correspondent with links by guidelines. (3) Version A and version C of math teacher’s guides contain the instructional review of mathematics. (4) Version D of math teacher’s guides illustrates in the section ”Discovery of teaching materials” why we should teach common multiples first before common divisors. (5) Version A and C of math teacher’s guide contain the instructional goals, including principles and specifications. 3. For the instructional emphasis of the chapter “Divisors and Multiples”, (1) Each page of instructional goals in four versions of math teacher’s guide emphasize more on the dimension of cognitive process in memorizing, comprehending, applying and analyzing , predominantly in comprehending. (2) As for instructional recommendations; version B and D emphasize more on explaining problem solving strategies , version A explains more about curriculum and guidelines; version C emphasizes more on explaining the conception of mathematics. (3) Version A, B and C explain step by step problem solving tips, although they still emphasize more on guiding students the ways of thinking; version D only contains the instructional recommendations without problem solving tips. Nevertheless it still provides in instructional recommendations lots of explanations on problem solving strategies.
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7

Shih, Mei-To, and 施美多. "The study on item analysis-a research on elementary school sixth grades students’ conceptualization of divisor." Thesis, 2007. http://ndltd.ncl.edu.tw/handle/05186483666454456075.

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Анотація:
碩士
國立臺中教育大學
數學教育學系在職進修教學碩士學位班
95
This study explores the differences between the knowledge construct of school-aged children and experts in learning the concept of divisor. It also discusses commonly-made mistakes and fallacious concepts of school-aged children in learning the concept of divisor. The research subjects are a class of sixth graders in Chang Hua County. elementary school Self-constructed tests of the concept of divisor are used as the research tool. SPSS/PC statistic software and the IRS computer program of the Theory of Item Relation Structure are used in the analysis. The following is a summary of the research results. 1. The knowledge construct of school-aged children in the concept of divisor is as follows: 1.1 The “concept of relatively prime” is a sub-concept of the “concept of prime.” 1.2 The “concept of composite” is a sub-concept of the “concept of prime.” 1.3 The “concept of common divisor” is a sub-concept of the “concept of decomposition of prime factor.” 2. The commonly-made mistakes and fallacious concepts of the concept of divisor of school-aged children are as follows: 2.1 It is more difficult for school-aged children to consider the characteristic of a number (i.e. prime number) than to consider the relationship between two numbers (i.e. relatively prime). 2.2 Many school-aged children have misconceptions as to whether one is relatively prime. 2.3 It is easier for school-aged children to accept the concept of divisor when introducing with the Division Algorithm than with the Multiplication Algorithm. 2.4 Almost 30% of the school-aged children are not equipped with thoroughly considered process concept. Without the concept of tacit knowledge, they are not able to ponder on the meaning of tacit knowledge in the process of problem solving. 2.5 Almost 20 % of the school-aged children are often oblivious of the basic member of divisor—one, when considering divisor. Based on the results of the study, several suggestions are offered as reference for educators and future research.
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8

Cassady, Allison Hanna. "Managing the three-ring circus : a study of student teachers’ understanding and learning of classroom management decision making." 2011. http://hdl.handle.net/2152/11885.

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Анотація:
Learning to manage a classroom of twenty-two elementary students is often likened to conducting a three-ring circus, particularly in the eyes of student teachers. As they enter the field, student teachers are given their first opportunities to observe and experience the delicate art of managing a classroom. They are faced with the challenges of handling the various aspects of teaching. Concurrently, they are enrolled in various methods courses as assigned by their university teacher preparation program, instructing them in various theories and best practices of their craft. In addition to enduring these challenges, student teachers must learn to think and make decisions as teachers. They are instructed to teach using explicit steps and procedures, yet the decision-making processes necessary for becoming a successful educator and manager are not addressed. Through qualitative case study, five student teachers share their observations and experiences as they met the challenges of learning to manage a classroom, focusing upon the need for sound decision making skills. Data for this investigation was taken from observations, interviews, reflections, and archived documents. Cross-case analyses revealed that participants felt anxious and unprepared when managing a classroom and lacked the decision-making skills necessary for successful management. The themes and findings derived from the data suggest that a great deal of management learning and decision-making skills come from time in the elementary classroom in conjunction with explicit teaching and conversations concerning these skills. Likewise, the relationship between the cooperating teacher and the student teacher, the authority the student teacher possesses in the classroom, as well as the teaching philosophies held by both greatly affect the successful acquisition of management decision-making skills. This study holds implications for the preparation student teachers receive, with regard to classroom management decision making, in their field-placement classrooms and university teacher preparation programs.
text
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9

Kao, Shu-chuan, and 高淑娟. "The Correlation between Mathematics-Word-Problem Solving Performance and Reading Comprehension of the 5th-Grade Elementary School Students :Taking Divisor and Multiple as an Example." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/69919937111436615382.

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Анотація:
碩士
國立臺南大學
數學教育學系碩士班
98
The purpose of this study is to explore the correlation between mathematics-word-problem solving performance and reading comprehension of the 5th-grade elementary school students。 The method of this study is questionnaire survey .The subjects of this study include 122 5th-graders from four classes at one elementary school in Tainan County. There are two study instruments in this study：「Mathematics-Word-Problem Solving Performance Test」and「Reading Comprehension Test」。 All the collected data carries on the descriptive statistics first by the spss statistics software and then applies methodology of statistics such us “Pearson correlation analysis” and “Independent T-test”. The results of this study are stated as follows: 1.About the overall components performance of mathematical-word-problem solving of the 5th-grade elementary school students , among them,the performance of“problem integration” brings about the best achievement. Others are “problem translation”,“solution planning ＆ monitoring”, and “solution execution” in descending score order. 2. There is significant correlation among whole performance of mathematical-word-problem solving and reading comprehension of the 5th-grade elementary school students. 3. There is significant correlation among overall components performance of mathematical-word-problem solving and reading comprehension of the 5th-grade elementary school students. 4. There are significant differences in whole performance of mathematical-word-problem solving of the 5th-grade elementary school students between different reading comprehension degrees. 5. There are significant differences in overall components performance of mathematical-word-problem solving of the 5th-grade elementary school students between different reading comprehension degrees. 6. There aren’t significant differences in mathematical- word-problem solving performance of the 5th-grade elementary school students between different genders. 7. There aren’t significant differences in reading comprehension performance of the 5th-grade elementary school students between different genders.
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10

Nasehpour, Peyman. "Content Algebras and Zero-Divisors." Doctoral thesis, 2011. https://repositorium.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-201102107989.

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This thesis concerns two topics. The first topic, that is related to the Dedekind-Mertens Lemma, the notion of the so-called content algebra, is discussed in chapter 2. Let $R$ be a commutative ring with identity and $M$ be a unitary $R$-module and $c$ the function from $M$ to the ideals of $R$ defined by $c(x) = \cap \lbrace I \colon I \text{~is an ideal of~} R \text{~and~} x \in IM \rbrace $. $M$ is said to be a \textit{content} $R$-module if $x \in c(x)M $, for all $x \in M$. The $R$-algebra $B$ is called a \textit{content} $R$-algebra, if it is a faithfully flat and content $R$-module and it satisfies the Dedekind-Mertens content formula. In chapter 2, it is proved that in content extensions, minimal primes extend to minimal primes, and zero-divisors of a content algebra over a ring which has Property (A) or whose set of zero-divisors is a finite union of prime ideals are discussed. The preservation of diameter of zero-divisor graph under content extensions is also examined. Gaussian and Armendariz algebras and localization of content algebras at the multiplicatively closed set $S^ \prime = \lbrace f \in B \colon c(f) = R \rbrace$ are considered as well. In chapter 3, the second topic of the thesis, that is about the grade of the zero-divisor modules, is discussed. Let $R$ be a commutative ring, $I$ a finitely generated ideal of $R$, and $M$ a zero-divisor $R$-module. It is shown that the $M$-grade of $I$ defined by the Koszul complex is consistent with the definition of $M$-grade of $I$ defined by the length of maximal $M$-sequences in I$. Chapter 1 is a preliminarily chapter and dedicated to the introduction of content modules and also locally Nakayama modules.
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Книги з теми "An elementary divisor ring"

1

Muhammed Ali - King of the Ring: Level 2 - Elementary (Nelson Readers). Nelson ELT, 1991.

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2

Marseken, Susan F., Miriam T. Timpledon, and Lambert M. Surhone, eds. Ring of Symmetric Functions: Algebra, Algebraic Combinatorics, Symmetric Polynomial, Representation Theory of the Symmetric Group, Polynomial Ring, Elementary Symmetric Polynomial, Newton's Identities. Betascript Publishers, 2010.

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Частини книг з теми "An elementary divisor ring"

1

Fuchs, László. "Elementary Divisor Domains as Endomorphism Rings." In Algebraic Techniques and Their Use in Describing and Processing Uncertainty, 33–40. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-38565-1_3.

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2

LaGrange, John D. "Divisor Graphs of a Commutative Ring." In Trends in Mathematics, 217–44. Singapore: Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-13-7028-1_11.

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3

Erdős, P., J. L. Nicolas, and A. Sárközy. "On Large Values of the Divisor Function." In Analytic and Elementary Number Theory, 225–45. Boston, MA: Springer US, 1998. http://dx.doi.org/10.1007/978-1-4757-4507-8_14.

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Fridman, Alexei M., and Nikolai N. Gorkavyi. "Elementary Particle Dynamics II Ring Cosmogony." In Astronomy and Astrophysics Library, 95–114. Berlin, Heidelberg: Springer Berlin Heidelberg, 1999. http://dx.doi.org/10.1007/978-3-662-03918-2_5.

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5

Albu, Toma. "Applications of Cogalois Theory to Elementary Field Arithmetic." In Advances in Ring Theory, 1–17. Basel: Birkhäuser Basel, 2010. http://dx.doi.org/10.1007/978-3-0346-0286-0_1.

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6

Münzenberg, G. "Storage-Ring Experiments with Exotic Nuclei: From Mass Measurements to the Future." In Structure and Dynamics of Elementary Matter, 507–14. Dordrecht: Springer Netherlands, 2004. http://dx.doi.org/10.1007/978-1-4020-2705-5_40.

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7

Robert, Wisbauer. "Elementary properties of rings." In Foundations of Module and Ring Theory, 1–35. Routledge, 2018. http://dx.doi.org/10.1201/9780203755532-1.

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8

Anderson, David F., Andrea Frazier, Aaron Lauve, and Philip S. Livingston. "The Zero‐Divisor Graph of a Commutative Ring, II." In Ideal Theoretic Methods in Commutative Algebra, 61–72. CRC Press, 2019. http://dx.doi.org/10.1201/9780429187902-5.

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9

Gabdrakipov, A. V., L. D. Volkova, N. A. Zakarina, and V. Z. Gabdrakipov. "15-P-14-Nonempirical (ab-initio) and semiempirical calculations of the elementary fragments of zeolites. Permeability of ring zeolite fragments." In Studies in Surface Science and Catalysis, 258. Elsevier, 2001. http://dx.doi.org/10.1016/s0167-2991(01)81553-6.

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10

Turing, Alan. "The Chemical Basis of Morphogenesis (1952)." In The Essential Turing. Oxford University Press, 2004. http://dx.doi.org/10.1093/oso/9780198250791.003.0022.

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It is suggested that a system of chemical substances, called morphogens, reacting together and diffusing through a tissue, is adequate to account for the main phenomena of morphogenesis. Such a system, although it may originally be quite homogenous, may later develop a pattern or structure due to an instability of the homogeneous equilibrium, which is triggered off by random disturbances. Such reaction-diffusion systems are considered in some detail in the case of an isolated ring of cells, a mathematically convenient, though biologically unusual system. The investigation is chiefly concerned with the onset of instability. It is found that there are six essentially different forms which this may take. In the most interesting form stationary waves appear on the ring. It is suggested that this might account, for instance, for the tentacle patterns on Hydra and for whorled leaves. A system of reactions and diffusion on a sphere is also considered. Such a system appears to account for gastrulation. Another reaction system in two dimensions gives rise to patterns reminiscent of dappling. It is also suggested that stationary waves in two dimensions could account for the phenomena of phyllotaxis. The purpose of this paper is to discuss a possible mechanism by which the genes of a zygote may determine the anatomical structure of the resulting organism. The theory does not make any new hypotheses; it merely suggests that certain well-known physical laws are sufficient to account for many of the facts. The full understanding of the paper requires a good knowledge of mathematics, some biology, and some elementary chemistry. Since readers cannot be expected to be experts in all of these subjects, a number of elementary facts are explained, which can be found in text-books, but whose omission would make the paper difficult reading. In this section a mathematical model of the growing embryo will be described. This model will be a simplification and an idealization, and consequently a falsification. It is to be hoped that the features retained for discussion are those of greatest importance in the present state of knowledge. The model takes two slightly different forms. In one of them the cell theory is recognized but the cells are idealized into geometrical points.
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Тези доповідей конференцій з теми "An elementary divisor ring"

1

Rilwan, N. Mohamed, and R. Radha. "Decycling on zero divisor graphs of commutative ring." In PROCEEDINGS OF INTERNATIONAL CONFERENCE ON ADVANCES IN MATERIALS RESEARCH (ICAMR - 2019). AIP Publishing, 2020. http://dx.doi.org/10.1063/5.0016962.

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2

Tang, Gaohua, Huadong Su, and Yangjiang Wei. "Commutative rings and zero-divisor semigroups of regular polyhedrons." In 5th China–Japan–Korea International Ring Theory Conference. WORLD SCIENTIFIC, 2008. http://dx.doi.org/10.1142/9789812818331_0017.

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3

Chao, Alexander W. "Elementary design and scaling considerations of storage ring colliders." In PHYSICS OF PARTICLE ACCELERATORS: SLAC Summer School, 1985 and Fermilab Summer School 1984. AIP, 1987. http://dx.doi.org/10.1063/1.36363.

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4

Schwiening, Jochen. "DIRC, the internally reflecting ring imaging Čerenkov detector for BABAR: Properties of the quartz radiators." In Instrumentation in elementary particle physics. AIP, 1998. http://dx.doi.org/10.1063/1.55065.

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5

Perrin, Hélène. "Quantum gas flowing in a ring: the elementary atomtronic circuit." In Cold Atoms for Quantum Technologies, edited by Sonja Franke-Arnold. SPIE, 2020. http://dx.doi.org/10.1117/12.2584831.

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6

Maresca, L., M. De Laurentis, M. Riccio, A. Irace, and G. Breglio. "Floating field ring technique applied to enhance fill factor of silicon photomultiplier elementary cell." In SPIE Optics + Optoelectronics, edited by Ivan Prochazka and Jaromír Fiurásek. SPIE, 2011. http://dx.doi.org/10.1117/12.886803.

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7

Hittinger, Christoph, Johannes Wagner, and Ingo Hahn. "Influence of elementary model parameter variations on simulated ferromagnetic hysteresis using a ring-shaped 3D dipole collective." In 2017 20th International Conference on Electrical Machines and Systems (ICEMS). IEEE, 2017. http://dx.doi.org/10.1109/icems.2017.8055949.

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8

Saada, A., and P. Velex. "An Extended Model for the Analysis of the Dynamic Behavior of Planetary Trains." In ASME 1992 Design Technical Conferences. American Society of Mechanical Engineers, 1992. http://dx.doi.org/10.1115/detc1992-0066.

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Abstract An extended model for determining dynamic tooth loads on spur and helical gear planetary trains is proposed. Torsional, flexural and axial generalized displacements of all the components are considered and a finite element procedure is used for generality. In order to avoid modulations between meshing pulsations and the carrier angular velocity, equations are written relative to rotating frames fixed to satellite centers. Depending on their architectures, complex drives are broken down in basic 12 degree of freedom elements, namely: - external gear element (sun-satellite element) - internal gear element (ring-satellite element) - pin-carrier element - classical elements for shafts, bearings, couplings, ... Details are given for elementary stiffness matrices. Due to contact conditions between mating teeth, these matrices are full and torsional, bending and traction effects are coupled. State equations point to parametrically excited differential systems with gyroscopic contributions. A first application of the model is conducted on a 3 satellite epicyclic drive whose gyroscopic terms are neglected. Potentially dangerous frequencies for sun-satellite and satellite-ring contacts are determined and contributions of the environment of the planetary train are discussed. Numerical results underline the influence of satellite-carrier links on critical frequencies for tooth loading.
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9

Courtin, Stephan, and Philippe Gilles. "Detailed Simulation of an Overlay Repair on a 14” Dissimilar Material Weld." In ASME 2006 Pressure Vessels and Piping/ICPVT-11 Conference. ASMEDC, 2006. http://dx.doi.org/10.1115/pvp2006-icpvt-11-93823.

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In nuclear reactors, ferritic low alloy steel heavy section components are connected with austenitic stainless steel piping systems. Despite a special manufacturing procedure to ensure a good resistance of the joint, several experiences from the field confirm sensitivity to fatigue and corrosion in this type of junction. Overlay welding is a process widely used to mitigate dissimilar material weld (DMW) stress corrosion cracking by replacing inside tensile stresses by compressive stresses. Taking into account the costs generated by mock-up manufacturing, predictive Finite Element (FE) residual stress calculations are of great interest to prove the effectiveness of the overlay welding and to adjust the parameters of the process and particularly the overlay thickness. This paper presents residual stress computations performed by Framatome-ANP on a 14” pipe geometry, resembling many mid size DMW in the US. Considering 2D axisymmetric hypotheses, the analysis simulates each elementary step of the mock-up manufacturing procedure. In particular, the pass-by-pass welding simulation reproduces the deposit of each bead by thermo-metallurgical and mechanical calculations. Thanks to residual stress measurements carried out on 2 mock-ups (with/without overlay), the numerical approach has been validated and highlights the beneficial overlay effect. However, some discrepancies raise various problems: the backing ring modelling, the machining heating effect, the experimental scatter and the weld material hardening. The simulation being able to analyze the influence of an overlay layer going up to 1 time the original pipe thickness, further work on the stabilization of the residual stress fields obtained here after the deposit of 4 or 5 layers, may lead to a better adjustment of the overlay thickness and to a cut in the operation costs too.
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