Showing papers on "Unit (ring theory) published in 2003"
Patent•
[...]
12 Aug 2003
Abstract: PROBLEM TO BE SOLVED: To provide a superior inkjet printer head which is made compact so that a space to be occupied by the inkjet head, a paper feed mechanism and the like in a printer can be made as small as possible SOLUTION: The inkjet printer head 1 has a plurality of piezoelectric element units 18 arranged in a longitudinal direction at a head body 8 with a piezoelectric element arrangement face 8a formed long The piezoelectric element unit 18 has a plurality of piezoelectric element unit structures 18a arranged thereat Each piezoelectric element unit 18 has a trapezoidal shape The piezoelectric element units 18 are set so that respective bases 19a of the trapezoidal shapes are alternately opposed towards a longitudinal center line LO of the arrangement face 8a Each piezoelectric element unit 18 has the upper base 19a, a lower base 19b, a first hypotenuse 19c connecting one end of the upper base 19a and one end of the lower base 19b each other, and a second hypotenuse 19d connecting the other end of the upper base 19a and the other end of the lower base 19b each other in the trapezoidal shape COPYRIGHT: (C)2003,JPO
46 citations
TL;DR: Estimation of demand systems with theoretically compatible Engel curves and unit value specifications. This paper develops a method for estimating price reactions using unit value data, exploiting the implicit links between quantity and unit value choices.
Abstract: We develop a method for estimation of price reactions using unit value data which exploits the implicit links between quantity and unit value choices. This allows us to combine appealing Engel curve specifications with a model of unit value determination in a way which is consistent with demand theory, unlike methods hitherto prominent in the literature. The method is applied to Czech data.
45 citations
Patent•
16 May 2003
TL;DR: In this paper, a polymeric compound is characterized by comprising a repeating unit represented by formula (1) wherein X denotes an atom or divalent group which forms a five-membered ring or six-mbered ring together with two atoms on A ring and two atoms in B ring, the atom or the divalent groups contains at least one atom selected from the group consisting of oxygen atom, sulfur atom, selenium atom and silicon atom.
Abstract: PROBLEM TO BE SOLVED: To provide a novel polymeric compound which is usable as a material of a light emitting layer, a hole injection layer, a hole transporting layer and the like, and to provide a polymeric light emitting element using the same. SOLUTION: The polymeric compound is characterized by comprising a repeating unit represented by formula (1) wherein X denotes an atom or divalent group which forms a five-membered ring or six-membered ring together with two atoms on A ring and two atoms on B ring, the atom or the divalent group contains at least one atom selected from the group consisting of oxygen atom, sulfur atom, selenium atom and silicon atom, A ring and B ring denote an aromatic hydrocarbon ring or heterocyclic ring, Ar1 denotes a divalent organic group having a divalent aromatic hydrocarbon group or heterocyclic ring skeleton, Ar2 and Ar3 denote a monovalent organic group having a monovalent aromatic hydrocarbon group or heterocyclic ring skeleton, R * denotes a linkage group and h denotes 0 or 1. COPYRIGHT: (C)2007,JPO&INPIT
36 citations
Posted Content•
TL;DR: In this article, the Farrell-Jones Isomorphism Conjecture about the algebraic K-theory of a group ring was proved for the case where the group G is the fundamental group of a closed Riemannian manifold with strictly negative sectional curvature.
Abstract: We prove the Farrell-Jones Isomorphism Conjecture about the algebraic K-theory of a group ring RG in the case where the group G is the fundamental group of a closed Riemannian manifold with strictly negative sectional curvature. The coefficient ring R is an arbitrary associative ring with unit and the result applies to all dimensions.
26 citations
TL;DR: In this paper, the orthogonal group 7(R) was used to classify all 8-dimensional real absolute-valued algebras with left unit and solved the isomorphism problem.
Abstract: We classify, by means of the orthogonal group 7(R), all eight-dimensional real absolute-valued algebras with left unit, and we solve the isomorphism problem. We give an example of those algebras which contain no four-dimensional subalgebras and characterise with the use of the automorphism group those algebras which contain one.
21 citations
Posted Content•
TL;DR: In this paper, it was shown that a paratopological group G is saturated if and only if G admits a continuous bijective homomorphism to a (totally bounded) [abelian] group G such that for each neighborhood U ½ H of the unit e there is a closed subset of G with e 2 h−1(F) ½ U.
Abstract: A paratopological group G is saturated if the in-
verse U−1 of each non-empty set U ½ G has non-empty interior. It
is shown that a [first-countable] paratopological group H is a closed
subgroup of a saturated (totally bounded) [abelian] paratopological
group if and only if H admits a continuous bijective homomorphism
onto a (totally bounded) [abelian] topological group G [such that
for each neighborhood U ½ H of the unit e there is a closed subset
F ½ G with e 2 h−1(F) ½ U]. As an application we construct a
paratopological group whose character exceeds its ¼-weight as well
as the character of its group reflexion. Also we present several ex-
amples of (para)topological groups which are subgroups of totally
bounded paratopological groups but fail to be subgroups of regular
totally bounded paratopological groups.
18 citations
TL;DR: In this article, Bergman et al. showed that surjective homomorphisms which are local, i.e., map non-units to non-unit, do not diminish the monoid of projectives.
Abstract: The homological classification of rings is based on the length of projective resolutions of modules, but it tells us nothing about the projective modules themselves. For information on them we have to turn to the monoid of projectives; thus for any ring R we have P(R), the monoid of (isomorphism classes of) finitely generated projective R-modules, with the operation [P ] + [Q] = [P ⊕ Q]. The simplest form that this monoid can take is P(R) ∼= N, the natural numbers, with [R] corresponding to 1. It means that every finitely generated projective R-module is free, of unique rank. Such a ring is said to be projective-free; in particular, since the rank of any free module is unique, such a ring has invariant basis number (IBN). Our aim in this note is to derive some results on projective-free rings. We shall show in Section 2 that surjective homomorphisms which are local, i.e. map non-units to non-units, do not diminish the monoid of projectives. In particular, we shall obtain conditions ensuring that a ring homomorphism reflects projective-freeness. A slightly weaker conclusion is reached in Section 3 by assuming the regularity of full matrices. I am indebted to G. M. Bergman whose comments on an earlier version greatly improved the presentation; in particular, Lemma 1 and suggestions leading to Theorem 2 are due to him. Throughout all rings are associative, with a unit element 1 which is preserved by homomorphisms and inherited by subrings.
17 citations
1 Jan 2003
TL;DR: In this paper, the authors considered F-linear tensor categories with simple objects and showed that Z(C) is modular and weakly monoidally Morita equivalent to C ⊗F C op.
Abstract: For every tensor category C there is a braided tensor category Z(C), the ‘center’ of C I t is well known to be related to Drinfel’d’s notion of the quantumdouble of a 7nite dim ensional Hopf algebra H by an equivalence Z(H -mod) ⊗ � br D(H )-mod of braided tensor categories In the Hopf algebra situation, whenever D(H )-mod is semisimple (which is the case i: D(H )i s semisimple i: H is semisimple and cosemisimple i: S 2 = id and char FA dim H ) it is modular in the sense of Turaev, ie its S-matrix is invertible (This was proven by Etingof and Gelaki in characteristic zero We give a fairly general proof in the appendix) The present paper is concerned with a generalization of this and other results to the quantumdouble (center) of m ore general tensor categories We consider F-linear tensor categories C with simple unit and 7nitely many isomorphism classes of simple objects We assume that C is either a ∗-category (ie F = C and there is a positive ∗-operation on the morphisms) or semisimple and spherical over an algebraically closed 7eld F In the latter case we assume dimC ≡ � i d(Xi) 2 � 0, where the summation runs over the isomorphism classes of simple objects We prove that Z(C) (i) is a semisimple spherical (or ∗-) category and (ii) is weakly monoidally Morita equivalent (in the sense of M, uger (J Pure Appl Algebra 180 (2003) 81–157)) to C ⊗F C op This implies dimZ(C) = (dimC) 2 (iii) We analyze the simple objects of Z(C) in terms of certain 7nite dimensional algebras, of which Ocneanu’s tube algebra is the smallest We prove the conjecture of Gelfand and Kazhdan according to which the number of simple objects of Z(C) coincides with the dimension of the state space HS1×S1 of the torus in the triangulation TQFT built from C (iv) We prove that Z(C) is modular and
16 citations
TL;DR: Adolescent admissions to a tertiary paediatric hospital in Victoria, Australia, are high, with nearly one in three admissions being of adolescents aged 10 years and above.
Abstract: Introduction: Adolescent inpatient facilities emerged in Australia in the 1980s to cater for an increasing number of young people with chronic illness and disability. Yet, there is minimal published data on the number of young people admitted to hospital within these units, their unit of admission, length of stay or reason for admission. A 12-year audit of adolescents admitted to a tertiary hospital with a dedicated adolescent unit and adolescent medicine programme in Victoria, Australia, was conducted to review the pattern of hospitalisation in young people in order to provide data to assist healthcare policy and planning agendas. Materials and Methods: Admissions to the Royal Children’s Hospital in Victoria, Australia, of adolescents aged 10 years and above were reviewed over a 12-year period from 1990 to 2001. We identified the annual number of adolescents admitted, the proportion of adolescents admitted to the Adolescent Inpatient Unit (ward) and annual admissions under the Adolescent Medicine Unit (department). Results: Adolescents now constitute nearly 30% of all admissions at this children’s hospital. Over this period, admissions to the Adolescent Inpatient Unit have nearly doubled and annual admissions under the Adolescent Medicine Unit rose from 38 to 288. The majority of adolescents were admitted under specialty medical and surgical units. Conclusions: The knowledge that nearly one in three admissions to this tertiary children’s hospital is over 10 years old should help promote the development of planning and policy agendas that better balance both health and developmental priorities in this age group.
13 citations
TL;DR: The complex (p-methoxyphenyl oxazoline)Cr(CO)3 is converted in two steps into a cis-fused [6,8] ring system containing a cycohexadiene ring unit, a cyclooctenone ring and a quaternary carbon at the ring junction.
Abstract: The complex (p-methoxyphenyl oxazoline)Cr(CO)3 is converted in two steps into a cis-fused [6,8] ring system containing a cycohexadiene ring unit, a cyclooctenone ring and a quaternary carbon at the ring junction. The key steps involve a diastereoselective addition of three C-substituents across an arene double bond, followed by an allylation and ring closing metathesis step. cis-Fused [6,7], [6,6], and [6,5] ring systems are also accessible via this methodology.
12 citations
TL;DR: A strongly π-regular ring is defined in this article as a group ring with unit elements that is both left (right) and right (left) π -regular.
Abstract: Let R be an associative ring with unit. An element x ∈ R is said to be left (right) π-regular if there exist y ∈ R and a positive integer n such that $$x^{n}=yx^{n+1}(x^{n}=x^{n+1}y)$$
. If x is both left and right π-regular, then it is said to be strongly π-regular. R is said to be a strongly π-regular ring if all its elements are strongly π-regular. In this paper we determine some conditions which are necessary or sufficient for a group ring to be strongly π-regular.
[...]
TL;DR: Ethnographic research in police organisations presents dilemmas and opportunities, requiring reflexivity and vulnerability.
Abstract: Abstract This paper explores the dilemmas and opportunities that confront ethnographers of police organisations. It recounts my experience of doing ethnographic research in the Durban Public Order Police unit, previously known as the Riot Unit or the Internal Stability Division. I argue that being reflexive about your own personal characteristics and standpoint is crucial to the outcome of ethnographic research. Ethnographic research in organisations such as the police may also lead to moral compromises and vulnerability to potential danger, dilemmas that individual ethnographers have to negotiate in ways that are most ‘comfortable’ to them.
TL;DR: In this article, the title compound, C17H9N3O, cyrstallizes with two independent mol-ecules in the asymmetric unit, and the angles between the planes of the quinoline group and the phenyl ring of the phthalo-nitrile group in the two molmecules are 84.36 and 83.69
Abstract: The title compound, C17H9N3O, cyrstallizes with two molecules in the asymmetric unit. Both independent molecules have essentially the same geometry. The angles between the planes of the quinoline group and the phenyl ring of the phthalonitrile group in the two molecules are 84.36 (4) and 83.69 (4)°.
TL;DR: In this article, it was shown that R ad is locally nilpotent if and only if R is a locally Lie-nilpotent ring, where the set of all elements of an associative ring R, not necessarily with a unit element, forms a semigroup R ad under the circle operation r ∘ s = r+s+rs+rs for all r, s in R.
Abstract: The set of all elements of an associative ring R, not necessarily with a unit element, forms a semigroup R ad under the circle operation r ∘ s = r + s + rs for all r, s in R. This semigroup is locally nilpotent if every finitely generated subsemigroup of R ad is nilpotent (in sense of A. I. Mal'cev or B. H. Neumann and T. Taylor). The ring R is locally Lie-nilpotent if every finitely generated subring of R is Lie-nilpotent. It is proved that R ad is a locally nilpotent semigroup if and only if R is a locally Lie-nilpotent ring.
TL;DR: Crop-soil simulation models are used to predict crop yields and soil properties in developing countries.
Abstract: Journal of Environmental QualityVolume 32, Issue 6 p. 2445-2446 Article Crop–Soil Simulation Models Applications in Developing Countries S.A. Saseendran, Corresponding Author S.A. Saseendran [email protected] USDA Agricultural Research Service, Great Plains Systems Research Unit, Fort Collins, CO, 80522[email protected]Search for more papers by this authorL.R. Ahuja, L.R. Ahuja USDA Agricultural Research Service, Great Plains Systems Research Unit, Fort Collins, CO, 80522Search for more papers by this authorL. MA, L. MA USDA Agricultural Research Service, Great Plains Systems Research Unit, Fort Collins, CO, 80522Search for more papers by this author S.A. Saseendran, Corresponding Author S.A. Saseendran [email protected] USDA Agricultural Research Service, Great Plains Systems Research Unit, Fort Collins, CO, 80522[email protected]Search for more papers by this authorL.R. Ahuja, L.R. Ahuja USDA Agricultural Research Service, Great Plains Systems Research Unit, Fort Collins, CO, 80522Search for more papers by this authorL. MA, L. MA USDA Agricultural Research Service, Great Plains Systems Research Unit, Fort Collins, CO, 80522Search for more papers by this author First published: 01 November 2003 https://doi.org/10.2134/jeq2003.2445dupRead the full textAboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onEmailFacebookTwitterLinkedInRedditWechat No abstract is available for this article. Volume32, Issue6November 2003Pages 2445-2446 RelatedInformation
Dissertation•
14 May 2003
TL;DR: In this paper, the authors compare the modes of construction of the parenthood in two societal versions in France and Germany and compare the effects of the participation of the parents in the labour market, as well as of the family policies and the social protection on the other hand.
Abstract: The contemporary evolutions of the family and their dynamics are the starting point of our research Our object is to show how these changes have placed the relations between the child and his two parents in the center of attention and social normalisation We call this process "Parentalism", studying it in two of his societal versions in France and Germany To this end, we compare the modes of construction of the parenthood in both countries, as the result of the family practices, the effects on these practices of the participation of the parents in the labour market, on the one hand, and of the family policies and the social protection on the other handIn the first chapter, we look at the forms of parenthood through the socio-demographic evolutions of the family configurations and parental practices This highlights the way in which the parenthood is becoming a new "theoretical" unit, and enables us to define more precisely the current forms of parenthood: according to the existence of a parental couple for the child ("bilateral" or "unilateral parenthood") and regarding the biological or social origin of the relation ("first" and "mixed parenthood") Then, we compare the occupation of the fathers and the mothers and their effects on the nature and the form of the relations between the child and both of his parents Lastly, we study the evolutions of the social and family policies in the way of how they determine the parental roles and their division between the genders, but also between the parents and the state Two new models are proposed, the "exclusive parenthood" (the exercise of the parental functions only) and the "reconciled parenthood" (as a concurrent exercise of an occupation and the parental functions)In the second chapter, we look at the construction of the norms of parenthood through the social treatment of the family risks generated by the marital ruptures Under consideration of the evolutions of the legal treatment, we look at the way in which the current norm is built in united and separated families While the place of the child is the same in the both countries, the roles of the fathers and mothers are different in their personal relations with the child as well as in the couple The gender construction and the nature of the relationship between the state and the family explain these divergences The chapter concludes on the model of "co-parenthood" for the French case (which defines a norm of parental cooperation) and of "bi-parenthood" for the German case (which indicates a gender differentiation, an individualisation of the relationship to the child, and an non-interference of the state into the marital relations)The third chapter analyses the practices of parenthood and the division of "family work" by taking account of the possibilities of delegation to institutions, the effect of the occupation of each parent and the role of the informal network of the household Our concept of "family work" indicates towards the process of negotiation of all the activities (professional, parental and domestic) carried out by the mothers and the fathers Our objective is to show how varied the family practices of division of "family work" are, according to the various levels of integration in the labour market The distribution of parental work is not only carried out according to the distinctions of gender, but also according to the exercise of parenthood (which is directed more and more towards a norm of equality in spite of some persistent inequalities)In conclusion, we identify that the relationship between the child and his two parents currently regulates the family relations, the family risk and the division of family work: a process, which we define as "Parentalism" We recall the evolution of the modes of public regulation of the family: "parentalism" continues in France what began with the "familialism" of the post-war period, then with the "feminism" in the 1970s and 1980s In Germany, "parentalism" succeeded in the 1990s the "conjugalism" of the post-war period So, the two countries converge towards this new mode of social regulation, notwithstanding their societal differences due to the specific effects between the family, state and labour market
1 Jan 2003
TL;DR: For m;n 2 and 1 < p < 2, this article proved that a map u2 W 1;p loc ( ;S n 1 ) from an open domain R m into the unit (n 1)-sphere, which solves a generalized version of the harmonic map equation, is smooth, provided that 2 p and [u]BMO() are both suciently small.
Abstract: For m;n 2 and 1 < p < 2, we prove that a map u2 W 1;p loc ( ;S n 1 ) from an open domain R m into the unit (n 1)-sphere, which solves a generalized version of the harmonic map equation, is smooth, provided that 2 p and [u]BMO() are both suciently small. This extends a
Patent•
[...]
10 Feb 2003
TL;DR: In this paper, the same song being played a plurality of times during random playback of a playlist was eliminated by a playback processing unit, where only audio files of a single artist were registered, and random playback was specified.
Abstract: An object of the present invention is to eliminate the same song being played a plurality of times during random playback of a playlist [Structure] A playback processing unit 2022 is a case where a playlist 212 specified by a user is a playlist 212 in which only audio files 213 of songs of a single artist are registered, and random playback is specified In some cases, a plurality of audio files 213 containing music pieces having the same title included in the play list 212 are excluded from reproduction targets except for one Then, each playlist-registered audio file except for the audio file 213 excluded from the reproduction target is reproduced in random order [Selection diagram] FIG
TL;DR: In this article, the authors show that the construction of mathematical structures from open physical, chemical, and biological problems leads to new intriguing mathematics of increasing complexity called iso-, geno-, and hyper-mathematics for the treatment of matter in reversible, irreversible, and multi-valued conditions, respectively, plus anti-isomorphic images called isodual mathematics, which are based on the lifting of the multiplicative unit of ordinary fields from its traditional value +1 into: (1) invertible, Hermitean, and single-valued units for isomathemat
Abstract: Pre-existing mathematical formulations are generally used for the treatment of new scientific problems. In this note we show that the construction of mathematical structures from open physical, chemical, and biological problems leads to new intriguing mathematics of increasing complexity called iso-, geno-, and hyper-mathematics for the treatment of matter in reversible, irreversible, and multi-valued conditions, respectively, plus anti-isomorphic images called isodual mathematics for the treatment of antimatter. These novel mathematics are based on the lifting of the multiplicative unit of ordinary fields (with characteristic zero) from its traditional value +1 into: (1) invertible, Hermitean, and single-valued units for isomathematics; (2) invertible, non-Hermitean, and single-valued units for genomathematics; and (3) invertible, non-Hermitean, and multi-valued units for hypermathematics; with corresponding liftings of the conventional associative product and consequential lifting of all branches of mathematics admitting a (left and right) multiplicative unit. An anti-Hermitean conjugation applied to the totality of quantities and their operation of the preceding mathematics characterizes the isodual mathematics. Intriguingly, the emerging formulations preserve the abstract axioms of conventional mathematics (that based on the unit +1). As such, the new formulations result to be new realizations of existing abstract mathematical axioms. We then show that the above mathematical advances permit corresponding liftings of conventional classical and quantum theories with a resolution of basic open problems in physics, chemistry, and biology, numerous experimental verifications, as well as new industrial applications.
Patent•
19 Dec 2003
TL;DR: An encoder-equipped seal mounted on a wheel bearing unit on an automotive vehicle as discussed by the authors includes an elastic element and a reinforcing ring for sealing said wheel bearing units and for detecting the number of revolutions of the wheel.
Abstract: An encoder-equipped seal mounted on a wheel bearing unit on an automotive vehicle, and includes an elastic element and a reinforcing ring for sealing said wheel bearing unit and for detecting the number of revolutions of the wheel. In according with the present invention, the encoder-equipped seal further includes a first ring element and a second ring element, wherein the the first ring element includes a first reinforcing ring having a first cylindrical portion extending in the axial direction of the wheel bearing unit and a first flanged portion extending from the first cylindrical portion in the radial direction, and a magnetic ring attached to the first flanged portion of the first reinforcing ring, and the second ring element includes a second reinforcing ring having a second flanged portion extending in the radial direction, and a seal lip arranged radially on the circumferential edge of the second flanged portion of the second reinforcing ring, and wherein the first ring element and the second ring element are united into one unit by allowing one to engage the other, in such a manner that the first ring element is located axially outwardly of the wheel bearing unit and the second ring element is located axially inwardly of the wheel bearing unit.
Patent•
10 Oct 2003
TL;DR: In this paper, the inverse element calculation unit consists of: the divisor unit which acquires M and t which satisfies N=M×2 t (M is the odd number).
Abstract: PROBLEM TO BE SOLVED: To provide an inverse element calculation unit in which the division of many precisions is not used, of which memory capacity is reduced, and which determines an inverse element on a residue class ring in which the value of a divisor is even. SOLUTION: The inverse element calculation unit consists of: the divisor unit which acquires M and t which satisfies N=M×2 t (M is the odd number), and a first inverse element calculation unit which calculates the inverse element on the residue class ring which makes the divisor as the acquired value M, for the value of the divisor whose number is even; and a second inverse element calculation unit which calculates the inverse element on the residue class ring which makes 2 t as the divisor, and a synthetic calculation unit which calculates the inverse element on the residue class ring which makes N as the divisor from a value acquired with each inverse element calculation unit, for the acquired t. Thus, the inverse element calculation is calculated by controlling every calculation units. COPYRIGHT: (C)2004,JPO
1 Jan 2003
TL;DR: In this article, the notion of unit-regular ideals for unital rings was introduced, which is a natural generalization of unit regular rings, and it is shown that every square matrix over unit regular ideals admits a diagonal reduction, if and only if pseudo-similarity via the ideal is similarity.
Abstract: In this paper we introduce the notion of unit-regular ideals for unital rings, which is a natural generalization of unit-regular rings. It is shown that every square matrix over unit-regular ideals admits a diagonal reduction. We also prove that a regular ideal of a unital ring is unit-regular if and only if pseudo-similarity via the ideal is similarity. Let I be an ideal of a unital ring R. We say that I is regular in case for every x ∈ I there exists y ∈ I such that x = xyx. Following Goodearl (7), a unital ring R is unit-regular provided that for every x ∈ R there exists u ∈ U (R) such that x = xux. Unit-regular rings play an important role in the structure theory of regular rings. In this paper we introduce the notion of unit-regular ideals for unital rings, which is a natural generalization of unit-regular rings. We say that an ideal I of a unital ring R is unit-regular in case for every x ∈ I, there exists u ∈ U (R)
TL;DR: In this article, the concept of generalized cu-rings was introduced, and the related power comparability of modules was studied for any regular unit π-regular ring with a positive integer n and an idempotent e.
Abstract: In this paper, we introduce the concept of generalized cu-rings, study the related power comparability of modules. Let R be an exchange ring, we show that the following are equivalent: (1) For any R-modules A and B, R R ⊕ A ≅ R R ⊕ B implies that there exist a positive integer n and an idempotent e ∈ B(R) such that (2) Given any R-module decompositions M = A 1 ⊕ B 1 = A 2 ⊕ B 2 with A 1 ≅ R R ≅ A 2, there exist n ≥ 1 and C, D, E ≤ M n such that where D is a direct summad of , E is a direct summand of and De = 0, E(1 − e) = 0 for some e ∈ B(R). (3) For any idempotents e, f ∈ R with e = 1 + ab and f = 1 + ba for some a, b ∈ R, there exist u ∈ B(R) and n ≥ 1 such that (4) For any regular element a ∈ R, there exists some n ≥ 1 such that aI n is related unit regular in M n (R). Also, we show that every regular related unit π-regular ring is a generalized cu-ring. These generalize the corresponding results in (1), (2), (3) and (4).
1 Jan 2003
TL;DR: Continuous Archimedean t-norms are generated by automorphisms of the unit interval with its usual order structure as mentioned in this paper, where the group operation being composition of functions plays an important role in the theory.
Abstract: Continuous Archimedean t-norms are generated by automorphisms of the unit interval with its usual order structure Certain subgroups of the group A of automorphisms of the unit interval—the group operation being composition of functions—play an important role in the theory, for example the multiplicative group of positive real numbers, which is embedded in A by r(x) = x r Several standard families of t-norms are in natural one-to-one correspondence with subgroups of A We examine this phenomenon, and various other group theoretic aspects of t-norm theory
Patent•
16 Sep 2003
TL;DR: In this article, the problem of obtaining a new cyclic acetylene compound applicable to a material for a display device, an optical film, and the like, to provide a method for producing the compound, and to obtain the material for the display device or the optical film each using the compound.
Abstract: PROBLEM TO BE SOLVED: To obtain a new cyclic acetylene compound applicable to a material for a display device, an optical film, and the like, to provide a method for producing the compound, and to obtain the material for the display device or the optical film each using the compound. SOLUTION: The cyclic acetylene compound is represented by formula (1), the method for producing the compound is provided, and the display device and the optical film each using the compound are provided. In formula (1), the ring C and the ring A are each a benzene ring; the ring D and the ring B are each a pyridine ring; the bracketed unit containing two rings C or rings A and the bracketed unit containing two rings D or rings B may be in any order; (s), (t), (n) and (p) are each an integer of 1-10; s+t=1 to 10; n+p=1 to 10; and X is represented by formula (2). COPYRIGHT: (C)2003,JPO
TL;DR: In this article, the notion of coendofinite complex is introduced and a t-structure in a right coherent associative ring with unit is associated to such a complex.
Abstract: Let A be a right coherent associative ring with unit. We introduce the notion of coendofinite complex and we associate to such a complex a t-structure in D b (mod A). We give conditions for the heart of that t-structure to be a module category. We also give some applications in connection with derived equivalent rings and tilting theory. In particular for a tilting module over a finite dimensional k-algebra, we get a reformulation of Brenner-Butler's theorem in terms of t-structures.
Patent•
23 Apr 2003
TL;DR: In this paper, the magnetic ring unit is constituted of a magnetic ring 1 of an eccentric ring shape whose central point of the inner diameter is eccentric relative to the central points of the outer diameter.
Abstract: PROBLEM TO BE SOLVED: To control the revolution direction of magnetic flux freely and with high reproducibility, with simple construction without heat process such as pinning, concerning a magnetic ring unit and a magnetic memory apparatus. SOLUTION: The magnetic ring unit is constituted of a magnetic ring 1 of an eccentric ring shape whose central point of the inner diameter is eccentric relative to the central point of the outer diameter. COPYRIGHT: (C)2005,JPO&NCIPI