On equations for regular languages, finite automata, and sequential networks

We consider systems of equations of the form where A is the underlying alphabet, the Xi are variables, the Pi,a are boolean functions in the variables Xi, and each δi is either the empty word or the empty set. The symbols υ and denote concatenation and union of languages over A. We show that any such system has a unique solution which, moreover, is regular. These equations correspond to a type of automation, called boolean automation, which is a generalization of a nondeterministic automation. The equations are then used to determine the language accepted by a sequential network; they are obtainable directly from the network.

Regio-regular structure high molecular weight poly(propylene carbonate) by rare earth ternary catalyst and Lewis base cocatalyst

Lewis base modification strategy on rare earth ternary catalyst was disclosed to enhance nucleophilic ability of active center during copolymerization of carbon dioxide and propylene oxide (PO), poly(propylene carbonate) (PPC) with H-T linkages over 83%, and number-average molecular weight (M-n) up to 100 kg/mol was synthesized at room temperature using Y(CCl3OO)(3)-ZnEt2-glycerine catalyst and 1,10-phenanthroline (PHEN) cocatalyst. Coordination of PHEN with active Zinc center enhanced the nucleophilic ability of the metal carbonate, which became more regio-specific in attacking carbon in PO, leading to PPC with improved H-T linkages.

A novel way to synthesize high regular and periodic organic mesoporous silicas

Organic mesoporous silicas (OMSs) were synthesized in the presence of urea via one-pot synthesis method, in which tetraethyl orthosilicate (TEOS) and 3-aminopropyltriethoxysilica (APTES) were used as the silica resources, non-ionic surfactant was used as the template. XRD results showed that the average periodic mesopore sizes of OMSs in the presence of urea were larger than those in the absence of urea. It was also found that the pore sizes of the products in the presence of urea distributed more narrowly than those in the absence of urea, and the contents of organosiloxane incorporated into OMSs, the pore wall thicknesses, the pore volumes and the surface areas of the products all increased with the use of urea. This shows a novel way to synthesize high regular and periodic organic mesoporous silicas.

How to form regular polymer microstructures by surface-pattern-directed dewetting

The substrates with regular patterns of self-assembly monolayers (SAMs) produced by microcontact printing with octadecyltrichlorosilane (OTS) was employed to direct thin polystyrene dewetting to fabricate ordered micrometer scale pattern. The pattern sizes and pattern fashion can be manipulated by controlling the experimental parameters. The pattern formation mechanisms have been discussed. The dewetting pattern can be transferred to form PDMS stamp for future microfabrication process.

Formation of regular hole pattern in polymer films

Ordered macroporous materials recently have attracted much attention. A method that utilizes the condensation of monodisperse water droplets on a polymer solution is proposed for the preparation of honeycomb microporous films. Our results show that it is a general method that can be used for patterning a wide range of polymers. The presence of water vapor and polymer is necessary for the formation of regular holes in films. The formation of hexagonal packing instead of other kinds of packing takes place because the hexagonal packing has the lowest free energy. The formation mechanisms of regular hole pattern and imperfections in the hexagonal packing are proposed.

Biological rationale for regular physical exercise as an effective intervention for the prevention and treatment of depressive disorders

Depression is a major medical and social problem. Here we review current body of knowledge on the benefits of exercise as an effective strategy for both the prevention and treatment of this condition. We also analyze the biological pathways involved in such potential benefits, which include changes in neurotrophic factors, oxidative stress and inflammation, telomere length, brain volume and microvessels, neurotransmitters or hormones. We also identify major caveats in this field of research: further studies are needed to identify which are the most appropriate types of exercise interventions (intensity, duration, or frequency) to treat and prevent depression.

Experimental investigation of thermal structures in regular three-dimensional falling films

Interfacial waves on the surface of a falling liquid film are known to modify heat and mass transfer. Under non-isothermal conditions, the wave topology is strongly influenced by the presence of thermocapillary (Marangoni) forces at the interface which leads to a destabilization of the film flow and potentially to critical film thinning. In this context, the present study investigates the evolution of the surface topology and the evolution of the surface temperature for the case of regularly excited solitary-type waves on a falling liquid film under the influence of a wall-side heat flux. Combining film thickness (chromatic confocal imaging) and surface temperature information (infrared thermography), interactions between hydrodynamics and thermocapillary forces are revealed. These include the formation of rivulets, film thinning and wave number doubling in spanwise direction. Distinct thermal structures on the films’ surface can be associated to characteristics of the surface topology.

El tronco de dipirámide regular octagonal afín recta

A partir de tres vectores linealmente independientes en R3 , y bajo otras condiciones, se construye una norma ' sobre R3 cuyas esferas de centro G y radio r > 0, son troncos de dipirámide regular octagonal afín recta de centro G. También, dado un poliedro F de este tipo, se establece que F, es también un cuerpo normado, respecto a esa norma ' construida a partir de F. La representación unificada de ' permite el estudio riguroso y versátil de la estructura geométrica de F, asistida por la noción de homotecia.

Relations, residuals, regular interiors, and relative regular equivalence

Given a relation α (a binary sociogram) and an a priori equivalence relation π, both on the same set of individuals, it is interesting to look for the largest equivalence πo that is contained in and is regular with respect to α. The equivalence relation πo is called the regular interior of π with respect to α. The computation of πo involves the left and right residuals, a concept that generalized group inverses to the algebra of relations. A polynomial-time procedure is presented (Theorem 11) and illustrated with examples. In particular, the regular interior gives meet in the lattice of regular equivalences: the regular meet of regular equivalences is the regular interior of their intersection. Finally, the concept of relative regular equivalence is defined and compared with regular equivalence.

Computing regular equivalence: practical and theoretical issues

Social network analysts have tried to capture the idea of social role explicitly by proposing a framework that precisely gives conditions under which group actors are playing equivalent roles. They term these methods positional analysis techniques. The most general definition is regular equivalence which captures the idea that equivalent actors are related in a similar way to equivalent alters. Regular equivalence gives rise to a whole class of partitions on a network. Given a network we have two different computational problems. The first is how to find a particular regular equivalence. An algorithm exists to find the largest regular partition but there are not efficient algorithms to test whether there is a regular k-partition. That is a partition in k groups that is regular. In addition, when dealing with real data, it is unlikely that any regular partitions exist. To overcome this problem relaxations of regular equivalence have been proposed along with optimisation techniques to find nearly regular partitions. In this paper we review the algorithms that have developed to find particular regular equivalences and look at some of the recent theoretical results which give an insight into the complexity of finding regular partitions.