Abstract: A ring R is called left morphic if R/Ra ≅ l(a) for each a ∈ R, equivalently if there exists b ∈ R such that Ra = l(b) and l(a) = Rb. In this paper, we ask only that b and c exist such that Ra = l(b) and l(a) = Rc, and call R left quasi-morphic if this happens for every element a of R. This class of rings contains the regular rings and the left morphic rings, and it is shown that finite intersections of principal left ideals in such a ring are again principal. It is further proved that if R is quasi-morphic (left and right), then R is a Bezout ring and has the ACC on principal left ideals if and only if it is an artinian principal ideal ring.

Abstract: Let m>=2 and k>=2 be integers and let R be a commutative ring with a unit element denoted by 1. A k-th power diophantine m-tuple in R is an m-tuple (a_1, a_2, ..., a_m) of non-zero elements of R such that a_ia_j+1 is a k-th power of an element of R for 1 =3 and R=K[X], the ring of polynomials with coefficients in a field K of characteristic zero. We prove the following upper bounds on m, the size of diophantine m-tuple: m =5 ; m =8.

Abstract: It is known that although the Baer Criterion for injectivity holds for modules over rings with unit, it is not true for acts over an arbitrary monoid. Seeking a characterization for the Baer Criterion to hold for acts over a monoid, in this article, using the notion of completeness introduced by Giuli, we find some classes of monoids such that for acts over them the Baer Criterion holds.

Abstract: We prove a weak factorization result for the predual of the space Qp on the unit disc, that is, we show that functions in this space can be written as sums of products of functions in given weighted Dirichlet and Bergman spaces with the usual control on the norms.

Abstract: We Classify the rational quadratic extensions K and the finite groups G for which the group ring R[G] of G over the ring R of integers of K has the property that the group of units of augmentation 1 of R[G] is hyperbolic. We also construct units in a non-split quaternion algebra over R.

Abstract: Let G be an Abelian group whose p-component G p is summable and let F be a field of characteristic p. Let S(FG) be the normalized unit p-group of the group algebra FG. The main results of the present article are that G p is a direct factor of S(FG) with totally projective complement, provided G p is of countable length and F is perfect; and, in particular, under these circumstances S(FG) is summable if and only if G p is summable. Moreover, if FG≅ FH as F-algebras for some group H and if G p is summable, then H p is summablale. These achievements improve results due to Hill and Ullery (1997) and also their generalizations given by Danchev (2000a b 2001 2004).

Abstract: Click to increase image sizeClick to decrease image size Additional informationNotes on contributorsLuis E. VilaLuis E. Vila is Head of the Economics of Education Research Unit in the Department of Applied Economics at the University of Valencia, Spain. He is also a former visiting scholar at the Center for Educational Research at Stanford University (CERAS). Adela García-Aracil is Researcher at the Institute for Management of Innovation and Knowledge (INGENIO), Higher Council for Scientific Research (CSIC) and Technical University of Valencia (UPV), Spain. José-Ginés Mora is Director of the Valencian Agency for Evaluation and Accreditation in Education and Director of the Centre for Higher Education Management (CEGES) at the Technical University of Valencia (UPV), Spain.Adela Garcia-AracilLuis E. Vila is Head of the Economics of Education Research Unit in the Department of Applied Economics at the University of Valencia, Spain. He is also a former visiting scholar at the Center for Educational Research at Stanford University (CERAS). Adela García-Aracil is Researcher at the Institute for Management of Innovation and Knowledge (INGENIO), Higher Council for Scientific Research (CSIC) and Technical University of Valencia (UPV), Spain. José-Ginés Mora is Director of the Valencian Agency for Evaluation and Accreditation in Education and Director of the Centre for Higher Education Management (CEGES) at the Technical University of Valencia (UPV), Spain.Jose-Gines MoraLuis E. Vila is Head of the Economics of Education Research Unit in the Department of Applied Economics at the University of Valencia, Spain. He is also a former visiting scholar at the Center for Educational Research at Stanford University (CERAS). Adela García-Aracil is Researcher at the Institute for Management of Innovation and Knowledge (INGENIO), Higher Council for Scientific Research (CSIC) and Technical University of Valencia (UPV), Spain. José-Ginés Mora is Director of the Valencian Agency for Evaluation and Accreditation in Education and Director of the Centre for Higher Education Management (CEGES) at the Technical University of Valencia (UPV), Spain.

Abstract: PROBLEM TO BE SOLVED: To provide a projection type display device including a light source unit for projection which can be attached to/detached from a main body, and capable of detecting a case where the light source unit for projection other than normal standardized ones is used and a case where the light source unit for projection is exchanged, and to provide the light source unit for projection SOLUTION: In the projection type display device 1 including the attachable/detachable light source unit for projection 58, the light source unit for projection 58 includes a non-volatile storage part 55 readable from a main body, and the main body includes a light source information discrimination part 64 reading out light source information stored in the non-volatile storage part 55 of the light source unit for projection 58, and discriminating at least either of whether or not the light source unit for projection is the predetermined standardized one and whether or not the light source unit for projection is exchanged based on the light source information COPYRIGHT: (C)2008,JPO&INPIT

Abstract: Let G be a group acting via ring automorphisms on a commutative unital ring R. If G is finite, then the embedding RG ® R is universally going-down, with generalizations to certain classes of locally finite actions by infinite groups. If R is an integrally closed integral domain with a minimal overring and G is finite such that the order of G is a unit of R, then RG has a minimal overring which is the G-fixed ring of the Kaplansky transform of some radical ideal of R.

Abstract: The fastening element (10) has an inner ring arrangement (26) mounted on a head of a retaining part The ring arrangement has a set of individual segments (30), where an elastic ring (42) is arranged in an outer periphery side of the ring arrangement An outer ring arrangement (28) is arranged in an outer periphery side of the ring The outer ring arrangement is provided with nuts (38), which detachably fasten the fastening element to a frame of an engine cover The ring arrangements have a retaining unit for positioning the ring

Abstract: The present invention provides a combination unit capable of simply-forming simulative skiing blanket. Said combination unit includes a base seat and at least one row of comb-shaped components which can be placed on the base seat and can be formed from several parallelly-arranged supporting columns, and the top portion of every supporting column has a curved contact surface which can be contacted with skis. The invented combination unit can be extended towards four sides and arranged so as to form an artificial blanket-type skiing resort.

Abstract: A thin fan structure is composed of a driving unit and a rotating unit. The driving unit has a base, a coil circuit board and a shaft, in which the coil circuit board is disposed at the base. The rotating unit has a bearing, a fan blade, an iron-containing metal sheet and a magnet, in which the bearing has an outer ring and an inner ring. The fan blade, the iron-containing metal sheet and the magnet are fixed at the outer ring of the bearing, the inner ring of the bearing is fixed at the shaft of the driving unit and the coil circuit board of the driving unit is able to drive the rotating unit turning around.

Abstract: The sharp ring lemma states that if n ≥ 3 cyclically tangent discs with pairwise disjoint interiors are externally tangent to and surround the unit disc, then no disc has a radius below cn = (F2n-1 + F2n-2 - 1)-1 – where Fk denotes the kth Fibonacci number – and that the lower bound is attained in essentially unique Apollonian configurations. Here we give a proof by transforming the problem to a class of strip configurations, after which we closely follow a method of proof due to Aharonov and Stephenson. Generalizations to three dimensions are discussed, a version of the ring lemma in three dimensions is proved, and a natural generalization of the extremal two-dimensional configuration – thought to be extremal in three dimensions – is given. The sharp three-dimensional ring lemma constant of order n is shown to be bounded from below by the two-dimensional constant of order n-1.

Abstract: Let R be a ring and g(x) a polynomial in C[x], where C=C(R) denotes the center of R. Camillo and Simon called the ring g(x)-clean if every element of R can be written as the sum of a unit and a root of g(x). In this paper, we prove that for a, b ∈ C, the ring R is clean and b-a is invertible in R if and only if R is g1(x)-clean, where g1(x)=(x-a)(x-b). This implies that in some sense the notion of g(x)-clean rings in the Nicholson–Zhou Theorem and in the Camillo–Simon Theorem is indeed equivalent to the notion of clean rings.

Abstract: $W$ is the category of archimedean $l$ -groups with distinguished weak order unit, with $l$ -group homomorphisms which preserve unit. This category includes all rings of continuous functions $C(X)$ and all rings of measurable functions modulo null functions, with ring homomorphisms. The authors, and others, have studied previously the epimorphisms (right-cancellable morphisms) in $W$ . There is a rich theory. In this paper, we describe a topological approach to the analysis of these epimorphisms. On each $W$ – object $B$ , we define a topology $\tau^{B}$ and a convergence $\mathop{\longrightarrow}\limits^{B}$ . These have the same closure operator, and this closure “captures epics” in the sense: a divisible subobject $A$ of $B$ is dense iff $A$ is epically embedded. The topology is $T_{1}$ , but only sometimes Hausdorff or an $l$ -group topology. The convergence is a Hausdorff $l$ -group convergence, but only sometimes topological. The associations of $B$ to $\tau^{B}$ , and to $\mathop{\longrightarrow}\limits^{B}$ , are functorial.

Abstract: Consider a generic data unit of random size L that needs to be transmitted over a channel of unit capacity. The channel availability dynamics is modeled as an i.i.d. sequence {A, A_i},i>0 that is independent of L. During each period of time that the channel becomes available, say A_i, we attempt to transmit the data unit. If Lx] and P[A>x] impacts the distributions of N and T. In particular, we discover several functional criticality points that separate classes of different functional behavior of the distribution of N. We also discuss the engineering implications of our results on communication networks since retransmission strategy is a fundamental component of the existing network protocols on all communication layers, from the physical to the application one.

Abstract: The purpose of this paper is to provide new and simplified statements of local Paley?Wiener theorems on the (n ? 1)-dimensional unit sphere realized as a subset of n = 2, 3 Euclidean space. More precisely, given a function , whose restriction to an n ? 1 sphere is analytic, we establish necessary and sufficient conditions determining whether f is the Fourier transform of a compactly supported, bounded function . The essence of this investigation is that, because of the local nature of the problem, the mapping f ? F is not in general invertible and so the problem cannot be studied via a Fourier integral. Our proofs are new.

Abstract: FIELD: computer engineering, possible use for building automatic devices, functional units of control systems, etc. ^ SUBSTANCE: device for selecting the lesser one of two binary numbers contains AND element, 4(n-1) implication units and 3(n-2)+1 AND elements. Implication units and AND elements are grouped in n groups. Group number J contains two implication units and AND element. Group number M additionally contains two implication units and two AND elements. In group number r the output of i implication unit is connected to i input of first AND element. In m group output of i implication unit, connected by inverting input to first input of (i+1) AND element, and output of (i+1) AND element, connected by second input to of (3-i) implication unit, are connected respectively to inverting and non-inverting inputs of (i+2) implication unit. In first group, inverting and non-inverting inputs of first implication unit are connected respectively to non-inverting and inverting inputs of second implication unit, first and second inputs of first AND element. Output of i implication unit of first group and output of (i+2) implication unit of m group are connected respectively to inverting input of i implication unit of second group to inverting input of i implication unit of (m+1) group. Inputs of first AND element of first group, non-inverting inputs of implication units of r group and output of first AND element of j group form respectively (n+1), r, (n+r) inputs and j output of device for selecting the lesser one of two binary numbers. ^ EFFECT: expanded functional capabilities due to ensured selection of the lesser one of two n-bit binary numbers set by binary signals. ^ 1 dwg, 1 tbl

Abstract: Proposition B. Let J be a C1-smooth almost complex structure defined in R2n. Let v be a continuous map from the unit disc D ⊂ C into (R2n, J ). Let u be either a constant map from D into R2n or a proper J -holomorphic and C 2-smooth map from D into an open subset of R2n. Assume that v is J -holomorphic near z if v(z) ∈ u(D). If u ≡ u(0) then v is J -holomorphic on D; if u ≡ u(0) and v(0) ∈ u(D), either v maps a neighborhood of 0 into u(D), or v is J -holomorphic near 0. If u ≡ u(0) the hypothesis is thereof that v is J -holomorphic at any point z such that v(z) = u(0). Proposition B generalizes the classical Rado Theorem. The more general statements in the text that contain Propositions A and B are Theorem A and Theorem C. Parts One and Two are independent. A unifying theme is the elimination of exceptional sets on which no a-priori assumption is to be made, in the style of Rado’s Theorem. In some of our statements this is the only novelty. Another common feature is the role played by differential inequality of the type |∂f | ≤ |f | or |∂f | ≤ |∂f |.

Abstract: The timepiece has a discrete striking mechanism placed in a case, where the mechanism has an actuating unit driven by an energy source. The mechanism has a mobile ring (26) arranged in a wall of the case, and cooperating with the actuating unit. The ring is evolved between a position in which the ring is partially at an upper level with respect to the case, and another position in which the ring is entirely at an equal or lower level with respect to the case.