General relativity and quantum mechanics: towards a generalization of the Lambert W function A Generalization of the Lambert W Function

We present a canonical form for a natural and necessary generalization of the Lambert W function, natural in that it requires minimal mathematical definitions for this generalization, and necessary in that it provides a means of expressing solutions to a number of physical problems of fundamental nature. This generalization expresses the exact solutions for general-relativistic self-gravitating N-body systems in one spatial and one time dimension, and a previously unknown mathematical link between the (1+1) gravity problem and the Schrödinger wave equation.     

Scene Graph and Frame Update Algorithms for Smooth and Scalable 3D Visualization of Simulated Construction Operations

One of the prime reasons inhibiting the widespread use of discrete-event simulation in construction planning is the absence of appropriate visual communication tools. Visualizing modeled operations in 3D is arguably the best form of communicating the logic and the inner working of simulation models and can be of immense help in establishing the credibility of analyses. New software development technologies emerge at incredible rates that allow engineers and scientists to create novel, domain-specific applications. The authors capitalized on a computer graphics technology based on the concept of the scene graph to design and implement a general-purpose 3D visualization system that is simulation and CAD-software independent. This system, the Dynamic Construction Visualizer, enables realistic visualization of modeled construction operations and the resulting products and can be used in conjunction with a wide variety of simulation tools. This paper describes the scene graph architecture and the frame updating algorithms used in designing the Dynamic Construction Visualizer.     

Ridge hypoplasia and ridge dissociation: minor physical anomalies in autistic children

Ten term newborns underwent CT of the brain 12-24 h following vacuum extractor delivery. Haemorrhage in the area of the tentorium was demonstrated in all of them, with similar findings in all cases. CT 1 week later demonstrated reabsorption of the blood without demonstrating any other brain pathology. Clinical and CT examination a year after delivery did not reveal any abnormality. The haemorrhage appears to be a benign condition.     

On Synchronous Robotic Networks—Part II: Time Complexity of Rendezvous and Deployment Algorithms

This paper analyzes a number of basic coordination algorithms running on synchronous robotic networks. We provide upper and lower bounds on the time complexity of the move-toward-average and circumcenter laws, both achieving rendezvous, and of the centroid law, achieving deployment over a region of interest. The results are derived via novel analysis methods, including a set of results on the convergence rates of linear dynamical systems defined by tridiagonal Toeplitz and circulant matrices.     

Drying of persimmons (Diospyros kaki L.) and the following changes in the studied bioactive compounds and the total radical scavenging activities

Fresh persimmons were subjected to two different processes: sun-drying during 1 month and dehydration at 60 °C during 12 h. To assess the effect of this process on nutritional and health-related properties of persimmons dietary fibers, minerals, trace elements, polyphenols and the total radical scavenging activities (TRSAs) were determined before and after processing. It was found that the contents of dietary fibers, minerals and trace elements in fresh and dried persimmons fruits were comparable. Total polyphenols in fresh persimmons was higher than in dried fruits (1.3 vs. 0.9 and 0.8 mg/100 g FW, respectively) and percentage of inhibition was higher than in dried fruits (70% vs. 59% and 55% and 58% vs. 53% and 46% for 1,1-diphenyl-2-picrylhydrazyl (DPPH) and 2,2′-azino-bis (3-ethylbenzthiazoline-6-sulfonic acid) [ABTS] radicals, respectively (P>0.05 in all cases). In conclusion: (1) the differences in the contents of dietary fibers, minerals and trace elements in fresh and dried persimmons are not significant; (2) the contents of polyphenols and the level of the TRSA are higher in fresh persimmons than in dried fruits; however, both variables are also high in dried persimmons; (3) when fresh fruits are not available, proper dried persimmons could be used as a valuable substitute.     

Kaolinite-mullite reaction series: a TEM study

The kaolinite-mullite reaction series in single crystal kaolinite has been characterized by transmission electron microscopy. The exotherm observed at 980° C is attributed to the formation of a spinel phase. Mullite crystallites have also been observed with the spinel phase and both phases have a composition near that of 32 mullite. Subsequent heat treatment leads to the growth of mullite crystallites on the original kaolinite plates with the c-axis perpendicular to the plate.     

Conductive PE-carbon composites by elongation flow injection moulding

In Part 1 and Part 2 of this paper the preparation of linear polyethylene (PE)-carbon black processed composites with conducting electrical properties was examined by means of elongation flow injection moulding. Mould geometry was optimized in the form of oriented double-armed bars so as to give enhanced mechanical properties combined with a high degree of electrical homogeneity. The present paper deals with composites using a high molecular weight PE matrix. It is shown that the injection-moulded composite material exhibits not only a lower percolation threshold, _c, than the conventionally pressure-moulded isotropic sample, but also conductivities two to three orders of magnitude larger than the latter. The radial and axial conductivity profiles, for concentrations well above _c, are discussed in the light of the molecular orientation variations across the bars as determined by birefringence. A segregation of primary filler particles, during flow-induced orientation, into axial channels has been shown to explain the enhancement of conductivity detected in the injected mouldings. In addition, for filler concentrations near 7%, -profile analysis indicates the development of a uniform conductive-stiff inner cylinder, several millimetres wide, homogeneously extending along the full length of the injected material.