Global Rigidity: The Effect of Coning

Recent results have confirmed that the global rigidity of bar-and-joint frameworks on a graph G is a generic property in Euclidean spaces of all dimensions. Although it is not known if there is a deterministic algorithm that runs in polynomial time and space, to decide if a graph is generically globally rigid, there is an algorithm (Gortler et al. in Characterizing generic global rigidity, arXiv:, 2007) running in polynomial time and space that will decide with no false positives and only has false negatives with low probability. When there is a framework that is infinitesimally rigid with a stress matrix of maximal rank, we describe it as a certificate which guarantees that the graph is generically globally rigid, although this framework, itself, may not be globally rigid. We present a set of examples which clarify a number of aspects of global rigidity.     

Quantum superarrivals and information transfer through a time-varying boundary

The time-dependent Schrödinger equation is solved numerically for the case of a Gaussian wave packet incident on a time-varying potential barrier. The time evolving reflection and transmission probabilities of the wave packet are computed for several different time-dependent boundary conditions obtained by reducing or increasing the height of the potential barrier. We show that in the case when the barrier height is reduced to zero, a time interval is found during which the reflection probability is larger (superarrivals) compared to the unperturbed case. We further show that the transmission probability exhibits superarrivals when the barrier is raised from zero to a finite value of its height. Superarrivals could be understood by ascribing the features of a real physical field to the Schrödinger wave function which acts as a carrier through which a disturbance, resulting from the boundary condition being perturbed, prpagates from the barrier to the detectors measuring reflected and transmitted probabilities. The speed of propagation of this effect depends upon the rate of reducing or raising the barrier height, thus suggesting an application for secure information transfer using superarrivals.     

Sauerstoffbestimmung in Eisen und Stahl

Ohne Zusammenfassung     

Logic and invariant theory IV. Invariants and syzygies in combinatorial geometry

Previous work has recast the invariant theory of projective geometry in terms of first order logic. This approach is applied to two categories connected with combinatorial projective geometry and coordinatized combinatorial pregeometries to characterize those invariant formulas (capable of expressing geometric properties) in terms of the language of brackets or determinants. The axioms for the theory of coordinatized pregeometries in this language are presented and conclusions drawn about the significance of identities or syzygies in the study of combinatorial geometry.     

The Crystal Structure of (1, 1′-ferrocenediyl)diphenylsilane

The crystal structure of (1,1′-ferrocenediyl)diphenylsilane has been determined from analysis of photographic X-ray data. The crystal system is orthorhombic, a = 14.18(2), b = 12.54(2), c = 9.28(1) Å, space group Pnma with four formula units. The molecule has crystallographic m (C_s) symmetry with atoms Fe and Si lying in the mirror plane, which bisects the two phenyl groups. The planar cyclopentadienyl rings are bridged by a single silicon atom, and are tilted 19.2° with respect to one another. The Fe—C(Cp) distances vary from 2.01(1) to 2.11(1) Å. The bridging angle C(1)—Si—C(1′) is 99.1°, while the Si—C(sp²) bond lengths range from 1.86 to 1.88 Å. The exocyclic C(1)—Si bond makes an angle of 40° with respect to the plane of the cyclopentadienyl ring.     

Constant Cwall ultrafiltration process control

Ultrafiltration processes normally operate with constant transmembrane pressure. The tradition of such control derives from its inherent simplicity. Both fundamental and practical considerations suggest, however, that ultrafiltration processes should be controlled by maintaining a constant wall concentration (C_w) of fully retained solutes. Since protein sieving, solubility, and adsorption losses as well as time and area optimization are dependent on C_w, we investigated a control strategy using constant C_w instead of constant transmembrane pressure. We explored three different strategies for such control and evaluated the theoretical and industrial implications for single solute systems. The effects of solute wall concentration on process time and product yield were also evaluated. Implementation of this technology required the development of a novel methodology for determination of mass transfer coefficients. The use of C_w technology also led to the development of new optimization schemes for both concentration and diafiltration. Industrial scale processes using constant C_w control have been successfully implemented on several recombinant DNA derived human protein pharmaceuticals. Constant C_w control has eliminated variability in process time, enhanced product yields, and provided insurance of tight protein product quality specifications. Optimum process design based on fundamental filtration theory has replaced empirical development procedures.     

Need for better rheological understanding and control

Summary A plea for greater attention to rheological characteristics of paints, especially by the smaller producers with limited resources, and for rheologists to devise simpler and cheaper methods of instrumentation (perhaps impossible), or at least of presentation of results.Presented at the Joint Meeting of the British Society of Rheology and Research Association of British Paint, Colour and Varnish Manufacturers at Teddington, April 29, 1964.     

Rigidity and polarity

Consider a weaving — a set of rods in the plane, woven over and under at their crossing points. The theory of when such weavings are stable, or rigid, in the plane is developed as the projective polar of the theory of static equilibrium and static rigidity for plane tensegrity frameworks with cables and struts. Work supported, in part, by grants from NSERC (Canada) and FCAR (Québec).