交换L*-环

我们证明一个交换整环或交换局部环是一个L*-环当且仅当它是一个O*-环.文中还证明了一些一般性的条件使之一个交换环不是L*.     

Division closed partially ordered rings

Fuchs called a partially-ordered integral domain, say D, division closed if it has the property that whenever a > 0 and ab > 0, then b > 0. He showed that if D is a lattice-ordered division closed field, then D is totally ordered. In fact, it is known that for a lattice-ordered division ring, the following three conditions are equivalent: a) squares are positive, b) the order is total, and c) the ring is division closed. In the present article, our aim is to study \({\ell}\)-rings that possibly possess zerodivisors and focus on a natural generalization of the property of being division closed, what we call regular division closed. Our investigations lead us to the concept of a positive separating element in an \({\ell}\)-ring, which is related to the well-known concept of a positive d-element.     

Directed partial orders on the field of generalized complex numbers with $$1\not >0$$ 1 ≯ 0

Positivity - Let F be a non-archimedean o-field and $$C=F(i)$$ be the field of generalized complex numbers over F. In Ma et al. (Order 35:461–466, 2018), all directed partial orders on C with...     

Some applications of cross-section measures in Minkowski spaces

Summary The purpose of this paper is to establish extremal values for inner and outer radii of the unit ball of a Minkowski space for the Holmes--Thompson and Busemann measures. Furthermore, we confirm a conjecture of C. A. Rogers and G. C. Shephard on ellipsoids.     

New 3D metal–organic framework isomer containing trinuclear oxo-centered mixed valence iron

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Directed partial orders on real quaternions

It is shown that a division ring of real quaternions can be made into a partially ordered ring with a directed partial order.     

Regular Unital Finite-Dimensional Lattice-Ordered Algebras

The main result in this article is to show that a regular unital finite-dimensional lattice-ordered algebra over ? with zero ?-radical is isomorphic to a finite direct sum of lattice-ordered matrix algebras of lattice-ordered group algebras of finite groups over ?.     

Commutative L*-rings II

It is shown that for several important classes of commutative rings, L? and O? are equivalent. In particular, a commutative artinian ring is L? if and only if it is O?. More examples of O?-fields are provided.     

The first enantioselective synthesis of (S)-5-bromo-3-(1-methyl-2-pyrrolidinyl)pyridine: a key intermediate for the preparation of SIB-1508Y

The first enantioselective synthesis of (S)-5-bromo-3-(1-methyl-2-pyrrolidinyl)pyridine is described via intramolecular hydroboration–cycloalkylation of an azido-olefin intermediate. The chiral homoallylic alcohol was efficiently synthesized by enantioselective reduction of the corresponding ketone using (+)-diisopinocamphenylchloroborane as the key reaction. The total synthesis of (S)-SIB-1508Y was achieved with an enantiomeric excess (e.e.) of 94% in ten steps and in 18% overall yield from the commercially available 5-bromo-3-pyridinecarboxylic acid.     

The numerical simulation of friction constrained motions (II): Multiple degrees of freedom models

In a previous article (Ref. [R. Glowinski, L.J. Shiau, Y.M. Kuo, G. Nasser, The numerical simulation of friction constrained motions (I): One degree of freedom models, Applied Mathematics Letters 17 (2004) 801–807]) the authors discussed the application of operator-splitting methods to the time-discretization of those mathematical relations describing the behavior of elasto-dynamical systems with friction, focusing on one-degree of freedom models. The main goal of the present article is to generalize the methodology discussed in Ref. [R. Glowinski, L.J. Shiau, Y.M. Kuo, G. Nasser, The numerical simulation of friction constrained motions (I): One degree of freedom models, Applied Mathematics Letters 17 (2004) 801–807]; there are no conceptual difficulties in doing so, the main issue being the computation of a vector-valued multiplier modeling the friction forces (or part of them). An iterative method allowing the computation of this multiplier will be discussed and the results of numerical experiments will be presented.