Abstract: We present a simple extension of the classical Hilton-Eckmann argument which proves that the endomorphism monoid of the unit object in a monoidal category is commutative. It allows us to recover in a uniform way well-known results on the graded-commutativity of cup products defined on the cohomology theories attached to various algebraic structures, as well as some more recent results.

Abstract: A ring is called strongly clean if every element is the sum of an idempotent and a unit which commute In 1999 Nicholson asked whether every semiperfect ring is strongly clean and whether the matrix ring of a strongly clean ring is strongly clean In this paper, we prove that if R = {m/n ∈ ℚ: n is odd}, then M2(R) is a semiperfect ring but not strongly clean Thus, we give negative answers to both questions It is also proved that every upper triangular matrix ring over the ring R is strongly clean

Abstract: Developmental Medicine & Child NeurologyVolume 46, Issue 11 p. 789-789 Free Access ‘A child with severe night terrors and sleep-walking responds to melatonin therapy’ JE Jan MD FRCP(C), Corresponding Author JE Jan MD FRCP(C) Melatonin Research Group, Mental Health Research Unit, Children and Women's Health Centre of British Columbia, Vancouver, Canada*Correspondence to: jjan@cw.bc.caSearch for more papers by this authorRD Freeman MD FRCP(C), RD Freeman MD FRCP(C) Melatonin Research Group, Mental Health Research Unit, Children and Women's Health Centre of British Columbia, Vancouver, CanadaSearch for more papers by this authorMB Wasdell MA, MB Wasdell MA Melatonin Research Group, Mental Health Research Unit, Children and Women's Health Centre of British Columbia, Vancouver, CanadaSearch for more papers by this authorMM Bomben MSc, MM Bomben MSc Melatonin Research Group, Mental Health Research Unit, Children and Women's Health Centre of British Columbia, Vancouver, CanadaSearch for more papers by this author JE Jan MD FRCP(C), Corresponding Author JE Jan MD FRCP(C) Melatonin Research Group, Mental Health Research Unit, Children and Women's Health Centre of British Columbia, Vancouver, Canada*Correspondence to: jjan@cw.bc.caSearch for more papers by this authorRD Freeman MD FRCP(C), RD Freeman MD FRCP(C) Melatonin Research Group, Mental Health Research Unit, Children and Women's Health Centre of British Columbia, Vancouver, CanadaSearch for more papers by this authorMB Wasdell MA, MB Wasdell MA Melatonin Research Group, Mental Health Research Unit, Children and Women's Health Centre of British Columbia, Vancouver, CanadaSearch for more papers by this authorMM Bomben MSc, MM Bomben MSc Melatonin Research Group, Mental Health Research Unit, Children and Women's Health Centre of British Columbia, Vancouver, CanadaSearch for more papers by this author First published: 13 February 2007 https://doi.org/10.1111/j.1469-8749.2004.tb01003.xCitations: 28AboutPDF 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 onFacebookTwitterLinked InRedditWechat No abstract is available for this article.Citing Literature Volume46, Issue11November 2004Pages 789-789 ReferencesRelatedInformation

Abstract: We give a new proof of the Jung-Abhyankar theorem: Let $ F \in k [[X_{1},\ldots, X_{n}]][Z], k $ an algebraically closed field of characteristic 0, be a Weierstras polynomial with discriminant $ X_1^{\mu_1}\cdots X_n^{\mu_n}U, $ where U is a unit; then its roots are fractionary power series.

Abstract: Let G be a finite group and let p be a prime. We show that the unit group of the integral group ring $$ \mathbb{Z}[G] $$ contains the free product Z p * Z if and only if G has a noncentral element of order p. Moreover, when this occurs, then the Z p -part of the free product can be taken to be a suitable noncentral subgroup of G of order p.

Abstract: This paper presents a time-delayed impulsive feedback approach to the problem of stabilization of periodic orbits in chaotic hybrid systems The rigorous stability analysis of the proposed method is given Using the time-delayed impulsive feedback method, we analyze the problem of detecting various periodic orbits in a special class of hybrid system, a switched arrival system, which is a prototype model of many manufacturing systems and computer systems where a large amount of work is processed in a unit time We also consider the problem of stabilization of periodic orbits of chaotic piecewise affine systems, especially Chua's circuit, which is another important special class of hybrid systems

Abstract: Let f and g be two commuting holomorphic self-maps of the open unit disc D in the complex plane with a common Wolff point tau epsilon partial derivativeD: if these two maps agree at tau up to the third order, then f equivalent to g.

Abstract: It is shown that a non-unital regular ring R has stable range one if and only if for all regular unitizations of R, every element x ∈ R is a sum of an idempotent and a unit such that x = e + u and .

Abstract: Let R be a commutative ring with identity. An algebraic element α over R is called an “integral algebraic element” over R if there exists a minimal polynomial of α over R which is monic. Let R be a direct product of m indecomposable rings R i , m ∊ ℕ. Denote by RG the group ring of G over R and by R∗ the multiplicative group of R. Let G be a finite Abelian group of exponent n and n ∊ R. In this paper we give a decomposition of RG, up to isomorphism, into a direct sum of extensions of the ring R, taking into account the number of the repetitions of these extensions. If the ring R is a field, then this result is proved in Perlis and Walker (1950). Let G be a splitting Abelian group with a torsion subgroup G 0. Denote by G p the p -component of G. We give a description of the unit group U(RG) of RG in the following cases: when R i is a ring of prime characteristic p i , G 0/G p i is finite and the exponent of G 0/G p i belongs to R i ∗; when R i is of characteristic zero, R i has no nilpotents, G 0 is finite...

Abstract: An associative ring R with unit element is called semilocal if R modulo its Jacobson radical is an artinian ring. It is proved that the multiplicative group R* of a semilocal ring R generated by R* satisfies an n-Engel condition for some positive integer n if and only if R is m-Engel as a Lie ring for some positive integer m depending only on n.

Abstract: In this paper, we investigate one-sided unit-regular ideals of regular rings. Let $I$ be a purely infinite, simple and essential ideal of a regular ring $R$. It is shown that $R$ is one-sided unit-regular if and only if so is $R/I$. Also we prove that every square matrix over one-sided unit-regular ideals of regular rings admits a diagonal matrix with idempotent entries.

Abstract: In this paper, we investigate necessary and sufficient conditions under which a ring R satisfies unit ideal–stable range conditions. We prove that if I is a bounded regular ideal of a ring R, then unit (I)-stable range condition, unit ⟨I⟩-stable range condition and unit [I]-stable range condition coincide with each other.

Abstract: The objective of this paper is to present and test a simple triangular finite shell element that uses five degrees of freedom at each node. The element is characterized by three position vectors and three unit directors. It depicts the plane stress state version of the element presented (Comput. Struct. 1989; 32(2):379). The element is of the ANS-type (assumed natural strain (J. Appl. Mech. 1981; 48:587). All strains inside the element contain dot products of the six actual element nodal vectors. The construction of the element also allows non-linear material behaviour. Since an enhancement of the membrane strains by the EAS (enhanced assumed strain method) is not possible inside a three node triangle element, the membrane strains perform poor. But via the DKT (discrete Kirchhoff theory) the three directors reveal an excellent bending behaviour for thin shells. The main concern of this paper is to test, if superimposing the CST (constant srain) with the classic DKT leads to good results in standard benchmark tests. Copyright © 2004 John Wiley & Sons, Ltd.

Abstract: A polymer complex compound comprising a repeating unit of the following formula (1) and a metal complex structure showing light emission from triplet excited state, having visible light emission in the solid state, and having a polystyrene reduced number-average molecular weight of 10 3 to 10 8 : (wherein, Ring P and Ring Q each independently represent an aromatic ring, but Ring P may be either existent or non-existent. When Ring P is existent, two connecting bonds respectively are on Ring P and/or Ring Q, and when Ring P is non-existent, two connecting bonds respectively are on 5 membered ring containing Y, and/or Ring Q. Y represents —O—, —S— and the like).

Abstract: PROBLEM TO BE SOLVED: To attain completely restorable invertible transform in mutually direct- and inverse-transforming data between unit systems different in resolution levels, particularly, different in color spaces. SOLUTION: This data format inverse transforming method is for mutually direct- and inverse-transforming data between unit systems different in resolution levels. Using the first unit system having a lower resolution level for a common unit system in the direct and inverse transforms, invertible data transform is conducted by the integer calculation of data of the first unit system having the lower resolution level, and data of the second unit system having a higher resolution level than that of the first unit system. COPYRIGHT: (C)2004,JPO&NCIPI

Abstract: MV-algebras can be viewed either as the Lindenbaum algebras of Lukasiewicz infinite-valued logic, or as unit intervals [0,u] of lattice-ordered abelian groups in which a strong order unit u>0 has been fixed. They form an equational class, and the free n-generated free MV-algebra is representable as an algebra of piecewise-linear continuous functions with integer coefficients over the unit n-dimensional cube. In this paper we show that the automorphism group of such a free algebra contains elements having strongly chaotic behaviour, is the sense that their duals are measure-theoretically isomorphic to a Bernoulli shift. This fact is noteworthy from the viewpoint of algebraic logic, since it gives a distinguished status to Lebesgue measure as an averaging measure on the space of valuations. As an ergodic theory fact, it provides explicit examples of volume-preserving homeomorphisms of the unit cube which are piecewise-linear with integer coefficients, preserve the denominators of rational points, and enjoy the Bernoulli property.

Abstract: Let R be an associative ring with unit and let N(R) denote the set of nilpotent elements of R. R is said to be stronglyπ-regular if for each x∈R, there exist a positive integer n and an element y∈R such that xn=xn+1y and xy=yx. R is said to be periodic if for each x∈R there are integers m,n≥ 1 such that m≠n and xm=xn. Assume that the idempotents in R are central. It is shown in this paper that R is a strongly π-regular ring if and only if N(R) coincides with the Jacobson radical of R and R/N(R) is regular. Some similar conditions for periodic rings are also obtained.

Abstract: Bearing arrangement (1) has inner ring (5) and outer ring (6) connected as single element and contains hollow cylindrical basic outline. Extension of outer ring is double the extension of inner ring in radial direction (R). Construction unit which is to be stored in outer ring is drum shaped and has lesser strength than outer ring of bearing (4). Extension of inner ring lies between 15mm and 30mm in radial direction and its inner diameter (DI) ranges between 1.000mm and 2.000mm. The bearing is formed as roller bearing. Rolling elements (8) are arranged between inner ring and outer ring. The inner ring, outer ring and rolling elements are so tolerated that preloading exists in bearing.

Abstract: We investigate necessary and sufficient conditions under which a ring satisfies unit 1-stable range for an ideal. As an application, we prove that R satisfies unit 1-stable range for I if and only if QM2(R) satisfies unit 1-stable range for QM2(I).

Abstract: PROBLEM TO BE SOLVED: To provide a ring, replaceably using functional units of light emission, sound generation, vibration and part movement depending on arbitrary conditions. SOLUTION: This unit type finger ring is composed of: a ring body; a unit storing part provided on the ring body; and a unit body including a watch and arbitrary functions such as a light emitting means and a sound generating means in arbitrary setting. COPYRIGHT: (C)2004,JPO

Abstract: PROBLEM TO BE SOLVED: To secure superior visibility and operability even with a small size, a low cost, and a simple constitution of an illumination-type switch. SOLUTION: A push button unit UB is constituted so that a diffusion sheet 20 and a button body 10 are mounted on a housing of a lamp 30. Holes 60a, 60b for terminals, and a hole 60c for a guide are formed in the substrate 60, and a switch unit US and an LED 40 are adjacently arranged. A guide pin 30d of the housing of the lamp 30 is inserted through the hole 60c for the guide, and a head 52a of a driven part 52 of the unit US is fitted to and retained in a fitting hole 30ca of a fitting part 30c. If a press-down operation part 10b is pushed down, the pushbutton unit UB is operated together with the driven part 52. In reciprocal operations, the guide pin 30d slides in the hole 60c for the guide, and the action of the pushbutton unit UB is guided because a slide-contact face 30ea of a guide rib 30e slidably contacts with a vertical plane 51a. COPYRIGHT: (C)2004,JPO

Abstract: We prove that if a one-to-one mapping f:ℝn→ℝn(n≥2) preserves the unit circles, then f is a linear isometry up to translation.

Abstract: In the title compound, C2Cl3N3OS, there are four independent mol­ecules in the asymmetric unit; their geometries are the same within experimental error. The six atoms of the thia­triazine ring and the 3,5-chloro atoms are all essentially coplanar.

Abstract: In this paper, we introduce the concept of quasi dimension of weakly regular algebras and study its some properties. Moreover, we provide characterizations between regular and weakly regular algebras. 1. Introduction and Preliminaries All algebras in this paper are associative with unit ,and all modules are unital. An algebra A is called regular,if for each a ∈ A, there exists b ∈ A such that a = aba. An algebra A is weakly regular,if for each a ∈ A, there exist b, c ∈ A such that a = abac .I t is clear that every regular algebra is weakly regular. We know that an algebra A is regular if and only if for every right A-module is flat and an algebra A is regular if and only if weakly dimension w.dimA of A, w.dimA = 0. In ((6)),Y.F.Xiao introduce the concept of semiflat module and obtain that an algebra A is weakly regular if and only if for every right A-module is semiflat.In this paper, we introduce the concept of quasi dimension of weakly regular algebras and study its some properties. Moreover, we provide characterizations between regular and regular algebras. In this paper,we use w.dim, q.dim and f.dim to denote the weakly dimension, quasi dimension and flat dimension respectively.

Abstract: Journal of Pediatric Gastroenterology and NutritionVolume 39, Issue S1 p. S40-S40 ABSTRACTS: Oral Presentation Abstracts O0085 IMPROVEMENTS IN OUTCOME OF CHRONIC INTESTINAL FAILURE IN THE UK 1989–2002 G. L. Gupte, G. L. Gupte Liver Unit, Birmingham Children’s Hospital, Birmingham, United KingdomSearch for more papers by this authorS. Protheroe, S. Protheroe Gastroenterology Unit, Birmingham Children’s Hospital, Birmingham, United KingdomSearch for more papers by this authorP. McKiernan, P. McKiernan Liver Unit, Birmingham Children’s Hospital, Birmingham, United KingdomSearch for more papers by this authorS. Murphy, S. Murphy Gastroenterology Unit, Birmingham Children’s Hospital, Birmingham, United KingdomSearch for more papers by this authorI. Booth, I. Booth Gastroenterology Unit, Birmingham Children’s Hospital, Birmingham, United KingdomSearch for more papers by this authorD. Kelly, D. Kelly Liver Unit, Birmingham Children’s Hospital, Birmingham, United KingdomSearch for more papers by this authorS. Beath, S. Beath Liver Unit, Birmingham Children’s Hospital, Birmingham, United KingdomSearch for more papers by this author G. L. Gupte, G. L. Gupte Liver Unit, Birmingham Children’s Hospital, Birmingham, United KingdomSearch for more papers by this authorS. Protheroe, S. Protheroe Gastroenterology Unit, Birmingham Children’s Hospital, Birmingham, United KingdomSearch for more papers by this authorP. McKiernan, P. McKiernan Liver Unit, Birmingham Children’s Hospital, Birmingham, United KingdomSearch for more papers by this authorS. Murphy, S. Murphy Gastroenterology Unit, Birmingham Children’s Hospital, Birmingham, United KingdomSearch for more papers by this authorI. Booth, I. Booth Gastroenterology Unit, Birmingham Children’s Hospital, Birmingham, United KingdomSearch for more papers by this authorD. Kelly, D. Kelly Liver Unit, Birmingham Children’s Hospital, Birmingham, United KingdomSearch for more papers by this authorS. Beath, S. Beath Liver Unit, Birmingham Children’s Hospital, Birmingham, United KingdomSearch for more papers by this author First published: 01 June 2004 https://doi.org/10.1002/j.1536-4801.2004.tb12393.x Submitted by: [email protected] Read 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. Volume39, IssueS1June 2004Pages S40-S40 RelatedInformation