Numerically stable algorithm for cycloidal splines

We propose a knot insertion algorithm for splines that are piecewisely in L{1, x, sin x, cos x}. Since an ECC-system on [0, 2π] in this case does not exist, we construct a CCC-system by choosing the appropriate measures in the canonical representation. In this way, a B-basis can be constructed in much the same way as for weighted and tension splines. Thus we develop a corner cutting algorithm for lower order cycloidal curves , though a straightforward generalization to higher order curves, where ECC-systems exist, is more complex. The important feature of the algorithm is high numerical stability and simple implementation. This research was supported by Grant 037-1193086-2771, by the Ministry of science, higher education and sports of the Republic of Croatia.     

Antimony(III) chloride-catalysed Biginelli reaction: a versatile method for the synthesis of dihydropyrimidinones through a different reaction mechanism

Antimony(III) chloride (20 mol %) in refluxing acetonitrile efficiently catalyses the synthesis of dihydropyrimidinones (50-90% yields) by the Biginelli reaction of aromatic aldehydes, acetoacetate esters and urea. This reaction proceeds through 3-ureido-crotonates followed by cyclisation with an aromatic aldehyde to the dihydropyrimidinone.     

The associated variety of an induced representation

This paper studies the behavior of the associated variety under induction from real parabolic subgroups. We derive a formula for the associated variety of an induced module which is analogous to the formula for the wave front set of a derived functor module obtained by Barbasch and Vogan.

     

Ferric chloride/tetraethyl orthosilicate as an efficient system for synthesis of dihydropyrimidinones by Biginelli reaction

An efficient method for the Biginelli reaction of aldehydes, acetoacetate esters and urea employing tetraethyl orthosilicate in the presence of ferric chloride is described. These improved reaction conditions allow the preparation of a wide variety of substituted dihydropyrimidinones (including sterically encumbered ones) in high yields and purity under mild reaction conditions.     

Calcium trifluoromethanesulfonate-catalysed aminolysis of epoxides

Aminolysis of epoxides catalysed by calcium trifluoromethanesulfonate under mild reaction conditions is described. The novel method is very efficient in the synthesis of wide variety of β-amino alcohols with high regio- and stereoselectivity.     

Realistic Interaction-Free Detection of Objects in a Resonator

We propose a realistic device for detecting objects almost without transferring a single quantum of energy to them. The device can work with an efficiency close to 100% and relies on two detectors counting both presence and absence of the objects. Its possible usage in performing fundamental experiments as well as possible applications are discussed.     

Optimizing the separation of gaseous enantiomers by simulated moving bed and pressure swing adsorption

The resolution of racemic gas mixtures by simulated moving bed (SMB) and pressure swing adsorption (PSA) is investigated by dynamic simulation and optimization. Enantiomer separation of inhalation anesthetics is important because there is evidence that the purified enantiomers may have different pharmacological properties than the racemate. The model parameters reported in an experimental investigation performed elsewhere are used to study the feasibility of this separation using SMB and PSA configurations. Both processes were modeled in gPROMS^® as systems of differential algebraic equations. Operating conditions are optimized such that the feed throughput and product recovery for each process were maximized subject to equal constraints on the pressures and superficial gas velocities. SMB was found to be capable of resolving racemic feed mixtures with purity and recovery exceeding 99%. On the other hand, PSA was also able to provide a single purified enantiomer with low recovery of about 30% which may limit its application to enantiomer separation. Nevertheless, PSA consumes less desorbent, and achieves higher throughput at the sacrifice of lower recovery.     

Small time two-sided LIL behavior for Lévy processes at zero

We wish to characterize when a Lévy process X _t crosses boundaries b(t), in a two-sided sense, for small times t, where b(t) satisfies very mild conditions. An integral test is furnished for computing the value of sup _t→0|X _t |/b(t) = c. In some cases, we also specify a function b(t) in terms of the Lévy triplet, such that sup _t→0 |X _t |/b(t) = 1.     

Modeling and Numerical Simulations of Immiscible Compressible Two-Phase Flow in Porous Media by the Concept of Global Pressure

A new formulation is presented for the modeling of immiscible compressible two-phase flow in porous media taking into account gravity, capillary effects, and heterogeneity. The formulation is intended for the numerical simulation of multidimensional flows and is fully equivalent to the original equations, contrary to the one introduced in Chavent and Jaffré (Mathematical Models and Finite Elements for Reservoir Simulation, 1986). The main feature of this formulation is the introduction of a global pressure. The resulting equations are written in a fractional flow formulation and lead to a coupled system which consists of a nonlinear parabolic (the global pressure equation) and a nonlinear diffusion–convection one (the saturation equation) which can be efficiently solved numerically. A finite volume method is used to solve the global pressure equation and the saturation equation for the water and gas phase in the context of gas migration through engineered and geological barriers for a deep repository for radioactive waste. Numerical results for the one-dimensional problem are presented. The accuracy of the fully equivalent fractional flow model is demonstrated through comparison with the simplified model already developed in Chavent and Jaffré (Mathematical Models and Finite Elements for Reservoir Simulation, 1986).