Coloring update methods

For linear update methods (such as SOR), a coloring method is introduced for which the multicolor iteration matrix has the same spectrum as the original iteration matrix. It applies to general linear systems, not necessarily arising from PDEs. When the iteration matrices are nonsingular, it is shown that they are similar to each other.     

Stereochemistry of the sn2′ displacement of chiral 1, 3-disubstituted bromoallenes to form chiral acetylenes

Optically active 1,3-disubstituted bromoallenes react with a variety of cuprate reagents preferentially in an S_N2′ fashion with very high $\text{anti}$ selectivity.     

An inclusive study of π-, K0 and a production from pn reactions at 11.6 GeV/c

Cross sections, multiplicities and particle inclusive spectra are presented for π^-, K⁰ and Λ produced in pn reactions at 11.6 GeV/c beam momentum. The results are compared with the data from pp interactions in the same energy range. Correlations between two π^- are also discussed. The main results are: the π^-, K⁰ and Λ all behave similarly as a function of transverse momentum squared; π^- in the forward c.m. hemisphere have spectra in x and y consistent with that of pp interactions, whereas the spectra of π^- in the backward hemisphere fall off more slowly with ∥x∥ and ∥y∥ than those in the forward hemisphere, suggesting n-fragmentation effects. The K⁰ and Λ have x and y distribution roughly similar to those in pp interactions. The K⁰ and Λ are consistent with a modified form of KNO scaling.     

The physics of categorization

In the context of cognition, categorization is the process through which several elements (i.e., words) are grouped into a single set which by naming becomes an abstraction of its elements. For example, tiger, kitty, and max can be categorized as Cats. In this article, we aim to show how the physical, biological and cognitive dimensions are related in the process of categorization or abstraction through the physics of computation. Drawing on Landauer's principle, we show that the price paid in terms of entropy is higher when grouping elements of low ranking (high probability) than when grouping elements of high ranking (low probability). Therefore, the logic of the cognitive process of abstraction is explained through constraints imposed by memory on the computation of categories. © 2015 Wiley Periodicals, Inc. Complexity 21: 269–274, 2016     

A short proof of Gowers’ lower bound for the regularity lemma

A celebrated result of Gowers states that for every ?>0 there is a graph G such that every ?-regular partition of G (in the sense of Szemerédi’s regularity lemma) has order given by a tower of exponents of height polynomial in 1/?. In this note we give a new proof of this result that uses a construction and proof of correctness that are significantly simpler and shorter.     

Graphene enterprise: mapping innovation and business development in a strategic emerging technology

This paper explores enterprise development and commercialization in the field of graphene. Firm characteristics and relationships, value chain positioning, and factors associated with product entry are examined for a set of 65 graphene-oriented small and medium-sized enterprises located in 16 different countries. As well as secondary sources and bibliometric methods to profile developments in graphene, we use computerized data mining and analytical techniques, including cluster and regression modeling, to identify patterns from publicly available online information on enterprise web sites. We identify groups of graphene small and medium-sized enterprises differentiated by how they are involved with graphene, the materials they target, whether they make equipment, and their orientation toward science and intellectual property. In general, access to finance and the firms’ location are significant factors that are associated with graphene product introductions. We also find that patents and scientific publications are not statistically significant predictors of product development in our sample of graphene enterprises. We further identify a cohort of graphene-oriented firms that are signaling plans to develop intermediate graphene products that should have higher value in the marketplace. Our findings suggest that policy needs to ensure attention to the introduction and scale-up of downstream intermediate and final graphene products and associated financial, intermediary, and market identification support. The paper demonstrates novel data methods that can be combined with existing information for real-time intelligence to understand and map enterprise development and commercialization in a rapidly emerging and growing new technology.     

Measure theoretical entropy of covers

In this paper we introduce three notions of measure theoretical entropy of a measurable cover in a measure theoretical dynamical system. Two of them were already introduced in [R] and the new one is defined only in the ergodic case. We then prove that these three notions coincide, thus answering a question posed in [R], and recover a variational inequality (proved in [GW]) and a proof of the classical variational principle based on a comparison between the entropies of covers and partitions.     

Preconditioning spectral element schemes for definite and indefinite problems

Spectral element schemes for the solution of elliptic boundary value problems are considered. Preconditioning methods based on finite difference and finite element schemes are implemented. Numerical experiments show that inverting the preconditioner by a single multigrid iteration is most efficient and that the finite difference preconditioner is superior to the finite element one for both definite and indefinite problems. A multigrid preconditioner is also derived from the finite difference preconditioner and is found suitable for the CGS acceleration method. It is pointed out that, for the finite difference and finite element preconditioners, CGS does not always converge to the accurate algebraic solution. © 1999 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 15: 535–543, 1999