Linearity of Space-Time Transformations¶Without the One-to-One, Line-onto-Line, or Constancy-of-Speed-of-Light Assumptions

Using a version of the fundamental theorem of geometry without the 1-to-1 assumption, recently obtained by the authors, the following is proved: Let n≥ 2 and T be a mapping ofℝ ⁿ onto itself which maps every timelike lineℓ into an arbitrary line so that the image of every future ray ofℓcontains at least two distinct points or the same holds for every past ray ofℓ. Then T is affine. A version of the Pappus theorem under minimal assumptions is also given, which is then used as a tool in this paper. Related results have been obtained by Borchers and Hegerfeldt. Received: 3 May 1999 / Accepted: 7 July 2000     

Carbon Nanostructures Derived through Hypergolic Reaction of Conductive Polymers with Fuming Nitric Acid at Ambient Conditions

Hypergolic systems rely on organic fuel and a powerful oxidizer that spontaneously ignites upon contact without any external ignition source. Although their main utilization pertains to rocket fuels and propellants, it is only recently that hypergolics has been established from our group as a new general method for the synthesis of different morphologies of carbon nanostructures depending on the hypergolic pair (organic fuel-oxidizer). In search of new pairs, the hypergolic mixture described here contains polyaniline as the organic source of carbon and fuming nitric acid as strong oxidizer. Specifically, the two reagents react rapidly and spontaneously upon contact at ambient conditions to afford carbon nanosheets. Further liquid-phase exfoliation of the nanosheets in dimethylformamide results in dispersed single layers exhibiting strong Tyndall effect. The method can be extended to other conductive polymers, such as polythiophene and polypyrrole, leading to the formation of different type carbon nanostructures (e.g., photolumincent carbon dots). Apart from being a new synthesis pathway towards carbon nanomaterials and a new type of reaction for conductive polymers, the present hypergolic pairs also provide a novel set of rocket bipropellants based on conductive polymers.     

Exact inequalities for sums of asymmetric random variables, with applications

Let be independent identically distributed random variables each having the standardized Bernoulli distribution with parameter . Let if and . Let . Let f be such a function that f and f′′ are nondecreasing and convex. Then it is proved that for all nonnegative numbers one has the inequality where . The lower bound on m is exact for each . Moreover, is Schur-concave in . A number of corollaries are obtained, including upper bounds on generalized moments and tail probabilities of (super)martingales with differences of bounded asymmetry, and also upper bounds on the maximal function of such (super)martingales. Applications to generalized self-normalized sums and t-statistics are given.      

Heat invariants of Riemannian manifolds

We calculate heat invariants of arbitrary Riemannian manifolds without boundary. Every heat invariant is expressed in terms of powers of the Laplacian and the distance function. Our approach is based on a multidimensional generalization of the Agmon-Kannai method. An application to computation of the Korteweg-de Vries hierarchy is also presented.     

Regularized Traces and Taylor Expansions for the Heat Semigroup

The coefficients in asymptotics of regularized traces and associatedtrace (spectral) distributions for Schrödinger operatorswith short and long range potentials are computed. A kernelexpansion for the Schrödinger semigroup is derived, anda connection with non-commutative Taylor formulas is established.     

Sand consolidation with calcium phosphate-polyelectrolyte composites

A new method for the consolidation of loose sand formations has been developed. The method involves in situ precipitation of a composite calcium phosphate-polyelectrolyte salt that binds together with loose sand grains, thus resulting to their consolidation. Three different polyelectrolytes (PE) were tested, i.e., polyacrylic acid (PAA), polyallylamine hydrochloride (PAH), and polyethylenimine (PEI). The effect of PE tested on the thermodynamics and the kinetics of precipitation of calcium phosphate salts was investigated. Three types of experiments were done. Investigation of the adsorption of PE on either hydroxyapatite (Ca(5)(PO(4))(3)OH, HAP) crystals or on sand grains. Measurement of the kinetics of heterogeneous nucleation of HAP on the solid substrates and the mechanical properties of the obtained crystals in batch experiments of low and high supersaturation solutions, respectively. Evaluation of the consolidation in sand packs in order to investigate the effectiveness of the method. The crystallization rates, R(p), on HAP crystals in the presence of the PE tested were found in the order R(p)(PAA)>R(p)(PEI)>R(p)(PAH), while nucleation and crystal growth on silicate sand took place only in the absence of adsorbed PE. PAH favored strongly the consolidation process, whereas PEI and PAA resulted in the formation of poorly consolidated grain agglomerates.