The Diffie–Hellman problem and generalization of Verheul’s theorem

Bilinear pairings on elliptic curves have been of much interest in cryptography recently. Most of the protocols involving pairings rely on the hardness of the bilinear Diffie–Hellman problem. In contrast to the discrete log (or Diffie–Hellman) problem in a finite field, the difficulty of this problem has not yet been much studied. In 2001, Verheul (Advances in Cryptology—EUROCRYPT 2001, LNCS 2045, pp. 195–210, 2001) proved that on a certain class of curves, the discrete log and Diffie–Hellman problems are unlikely to be provably equivalent to the same problems in a corresponding finite field unless both Diffie–Hellman problems are easy. In this paper we generalize Verheul’s theorem and discuss the implications on the security of pairing based systems.      

Consequences of Pure Point Diffraction Spectra for Multiset Substitution Systems

Abstract. There is a growing body of results in the theory of discrete point sets and tiling systems giving conditions under which such systems are pure point diffractive. Here we look at the opposite direction: what can we infer about a discrete point set or tiling, defined through a primitive substitution system, given that it is pure point diffractive? Our basic objects are Delone multisets and tilings, which are self-replicating under a primitive substitution system of affine mappings with a common expansive map Q . Our first result gives a partial answer to a question of Lagarias and Wang: we characterize repetitive substitution Delone multisets that can be represented by substitution tilings using a concept of ``legal cluster.' This allows us to move freely between both types of objects. Our main result is that for lattice substitution multiset systems (in arbitrary dimensions), being a regular model set is not only sufficient for having pure point spectrum—a known fact—but is also necessary. This completes a circle of equivalences relating pure point dynamical and diffraction spectra, modular coincidence, and model sets for lattice substitution systems begun by the first two authors of this paper.     

Multi-enzyme electrodes for the determination of starch by flow injection

A tri-enzyme electrode has been developed for determining starch in a flowing stream based on amperometric monitoring of hydrogen peroxide at a potential of +600 mV versus a silver--silver chloride reference electrode. The nylon-based starch-sensing membranes (over a platinum electrode) were prepared from an enzyme cocktail containing various ratios of amyloglucosidase (AMG), mutarotase (MUT) and glucose oxidase (GO). The best starch-sensing membrane (to give the type A electrode) was made from an enzyme cocktail of AMG--MUT--GO (2000 + 100 + 100 U; where 1 U = 16.67 nanokatals), i.e., containing a high level of AMG. In this system, starch samples were first incubated with soluble alpha-amylase (alpha-AMY) (1000 U) for 1 h at room temperature prior to analysis with the tri-enzyme electrode. Attempts were also made to immobilize alpha-AMY on to nylon net, either alone or as a component of a four-membrane starch-enzyme electrode but starch signals were weak compared with those generated by starch pre-treated with soluble alpha-AMY. This system, associated with the type A starch electrode, not only exhibited a calibration of wide linear range (1 x 10(-4)-0.1% m/v starch) but also showed promising operational properties. It has excellent thermal stability over the range 30-70 degrees C.     

Gaussian Cubature Arising from Hybrid Characters of Simple Lie Groups

Lie groups with two different root lengths allow two ‘mixed sign’ homomorphisms on their corresponding Weyl groups, which in turn give rise to two families of hybrid Weyl group orbit functions and characters. In this paper we extend the ideas leading to the Gaussian cubature formulas for families of polynomials arising from the characters of irreducible representations of any simple Lie group, to new cubature formulas based on the corresponding hybrid characters. These formulas are new forms of Gaussian cubature in the short root length case and new forms of Radau cubature in the long root case. The nodes for the cubature arise quite naturally from the (computationally efficient) elements of finite order of the Lie group.     

A study of singular spectrum analysis with global optimization techniques

Singular spectrum analysis has recently become an attractive tool in a broad range of applications. Its main mechanism of alternating between rank reduction and Hankel projection to produce an approximation to a particular component of the original time series, however, deserves further mathematical justification. One paramount question to ask is how good an approximation that such a straightforward apparatus can provide when comparing to the absolute optimal solution. This paper reexamines this issue by exploiting a natural parametrization of a general Hankel matrix via its Vandermonde factorization. Such a formulation makes it possible to recast the notion of singular spectrum analysis as a semi-linear least squares problem over a compact feasible set, whence global optimization techniques can be employed to find the absolute best approximation. This framework might not be immediately suitable for practical application because global optimization is expectedly more expensive, but it does provide a theoretical baseline for comparison. As such, our empirical results indicate that the simpler SSA algorithm usually is amazingly sufficient as a handy tool for constructing exploratory model. The more complicated global methods could be used as an alternative of rigorous affirmative procedure for verifying or assessing the quality of approximation.     

Dynamic kinetic resolution of 2-methyl-2-nitrocyclohexanol: Combining the intramolecular nitroaldol (Henry) reaction & lipase-catalysed resolution

Efforts to combine the intramolecular nitroaldol reaction with lipase-catalysed resolution of the resulting nitroaldol adduct in a one-pot dynamic kinetic resolution (DKR) are described. Significant challenges were encountered in the combination of the two systems. trans-2-Methyl-2-nitrocyclohexyl acetate (±)-3b was isolated in excellent enantiopurity (>98% ee) via a sequential DKR sequence where the lipase-mediated resolution and base-mediated interconversion of 2-methyl-2-nitrocyclohexanol 2 were effected alternately, demonstrating the feasibility of this approach initially. Further work showed, for the first time, evidence that a DKR-type system is possible for 2. Reaction engineering allowed the design of a sequential one-pot reaction system which furnished the products with excellent enantioselectivity, and good diastereoselectivity.     

Applied potential and radiotracer studies on poly(vinyl chloride) matrix ion-selective electrode membranes

This paper reports the effect of applied potentials on PVC matrix membranes containing (i) the barium ion-sensitive barium-Antarox C0880 complex and 2-nitrophenyl phenyl ether solvent mediator, and (ii) the calcium ion-sensitive Orion 92-20-02 phosphate-based calcium liquid ion-exchanger. Platinum electrodes were placed in solutions on each side of the membranes. The barium ion-sensitive membranes are unable to maintain stable current flows but the calcium ion-sensitive membranes are characterized by stable current flows over prolonged periods even after successive polarity reversals. Results are presented, from radiotracer experiments for permeation of ions through the membranes with and without an applied potential. No evidence was found for significant permeation of barium-133 ions through the barium ion-sensing membranes into an initially inactive solution, but it was found that barium-133 ions were incorporated into the membranes after removal of the applied potential. Permeation of sodium-22 ions through the calcium ion-sensing membranes occurred only to a limited extent in the presence of an applied potential and not at all in its absence, confirming electrode selectivity trends for calcium and sodium. Calcium-45 ions did not permeate the calcium ion-sensing membranes into an inactive counter-solution against the potential gradient, but on reversal of the polarity, permeation occurred to a far greater extent than in the absence of an applied potential. These differences in behaviour are compatible with the more complicated membrane pathways of the barium ion-sensing membranes, imposed by the complexing of barium ions by the ethyleneoxy units of Antarox C0880 in a tight helical conformation. The calcium ion-sensing membranes are much less constrained, thus permitting more facile replacement of the calcium ions in the membrane by ions from solution.     

Sets and indices in linear programming modelling and their integration with relational data models

LP models are usually constructed using index sets and data tables which are closely related to the attributes and relations of relational database (RDB) systems. We extend the syntax of MPL, an existing LP modelling language, in order to connect it to a given RDB system. This approach reuses existing modelling and database software, provides a rich modelling environment and achieves model and data independence. This integrated software enables Mathematical Programming to be widely used as a decision support tool by unlocking the data residing in corporate databases.     

Modal testing of an avlb bridge

Experimental Techniques -