Flow of a generalized Maxwell fluid induced by a constantly accelerating plate between two side walls

The unsteady flow of a viscoelastic fluid with the fractional Maxwell model, induced by a constantly accelerating plate between two side walls perpendicular to the plate, is investigated by means of the integral transforms. Exact solutions for the velocity field are presented under integral and series forms in terms of the derivatives of generalized Mittag–Leffler functions. The corresponding solutions for Maxwell fluids are obtained as limiting cases for β → 1. In the absence of the side walls, all solutions that have been determined reduce to those corresponding to the motion over an infinite plate.      

On a stopping rule for iterative orthogonalization of symmetric matrices

In this paper we consider three versions of Kovarik's iterative orthogonalization algorithms, for approximating the minimal norm solution of symmetric least squares problems. Although the convergence of these algorithms is linear, in practical applications we observed that a too big number of iterations can dramatically deteriorate the already obtained approximation. In this respect we analyse the above mentioned Kovarik–like methods according to the modifications they make on the “machine zero” eigenvalues of the problem (symmetric) matrix. We establish a theoretical almost optimal formula for the number of iterations necessary to obtain an enough accurate approximation, as well as to avoid the above mentioned troubles. Experiments on collocation discretization of a Fredholm first kind integral equation ilustrate the efficiency of our considerations. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Nonlinear Multigrid Methods for Numerical Solution of the Variably Saturated Flow Equation in Two Space Dimensions

The need of accurate and efficient numerical schemes to solve Richards’ equation is well recognized. This study is carried out to examine the numerical performances of the nonlinear multigrid method for numerical solving of the two-dimensional Richards’ equation modeling water flow in variably saturated porous media. The numerical approach is based on an implicit, second-order accurate time discretization combined with a vertex centered finite volume method for spatial discretization. The test problems simulate infiltration of water in 2D saturated–unsaturated soils with hydraulic properties described by van Genuchten–Mualem models. The numerical results obtained are compared with those provided by the modified Picard–preconditioned conjugated gradient (Krylov subspace) approach.     

铝电解中SnO2+Sb2O3+CuO惰性阳极的电流效率、腐蚀性及结构变化

系统研究了霍尔赫鲁特铝电解池中SnO₂基惰性阳极 (96%SnO₂+2%Sb₂O₃+2%CuO)的电流效率,腐蚀性以及结构变化. 评价了各种操作参数(温度、电流密度、阴阳两级的距离、冰晶石量比、Al₂O₃ 浓度和电解质组成)对电流效率和腐蚀性的影响.     

Facile formation of five-membered N-heterocyclic zirconacycloallenoids

The reaction of η(2)-iminozirconocene chloride complexes with trimethylsilylethynyl lithium leads to rapid C-C coupling at room temperature to yield the corresponding five-membered aza-zirconacycloallenoids. Such compounds were also obtained by trapping of in situ generated zirconocene with alkynyl imines.     

Reactivity of a Frustrated Lewis Pair and Small‐Molecule Activation by an Isolable Arduengo Carbene?B{3,5‐(CF3)2C6H3}3 Complex

Tris[3,5‐bis(trifluoromethyl)phenyl]borane reacts with the sterically demanding Arduengo carbenes 1,3‐di‐tert‐butylimidazolin‐2‐ylidene and 1,3‐bis(2,6‐diisopropylphenyl)imidazolin‐2‐ylidene to form isolable normal adducts. In the case of 1,3‐di‐tert‐butylimidazolin‐2‐ylidene, the adduct exhibits dynamic behaviour in solution and frustrated‐Lewis‐pair (FLP) reactivity. Fast cleavage of dihydrogen and THF, the C? H activation of phenylacetylene, and carbon dioxide fixation were achieved by using solutions of this adduct in benzene. This adduct is stable at room temperature in the absence of suitable substrates; however, thermal rearrangement into an abnormal carbene–borane adduct can be observed. In contrast, the 1,3‐bis(2,6‐diisopropylphenyl)imidazolin‐2‐ylidene adduct exhibits no evidence of FLP reactivity or of dissociation in solution. DFT calculations confirmed the experimental behaviour and stability of these carbene–borane adducts.     

A Brief Account on Lagrange’s Algebraic Identity

In Indiscrete Thoughts [18], G.-C. Rota remarked, ??The mystery, as well as the glory of mathematics, lies not so much in the fact that abstract theories do turn out to be useful in solving problems, but, wonder of wonders, in the fact that a theory meant for one type of problem is often the only way of solving problems of entirely different kinds, problems for which the theory was not intended. These coincidences occur so frequently, that they must belong to the essence of mathematics.?? Indeed, it happens often that abstract mathematics leads to concrete applications, and real-life problems constitute a source of inspiration for sophisticated theories. The strong synergy between pure mathematics and its applications advocates for teaching methods that intertwine physical intuition with mathematical abstraction, and recognize the universality of mathematical laws throughout the sciences.     

Carotenoid and fatty acid profiles of bilberries and cultivated blueberries from Romania

The worldwide consumption of blueberries has increased due to their potential health effects. They contain micronutrients, various phytochemicals and anti-oxidant pigments, represented especially by anthocyanins. In addition to these, carotenoids and fatty acids are also present. The aim of this study was the identification and quantification of carotenoids (by HPLC) and fatty acids (by GC with flame ionisation detection) in two bilberry genotypes (Wild 1 and 2) and three cultivars (BlueCrop, Elliot, and Duke). The main carotenoids identified were lutein, ??-cryptoxanthin, and ??-carotene, with the average total carotenoid content of 266 ??g per 100 g of fruit. The ratio of saturated fatty acids (SFAs) to polyunsaturated fatty acids (PUFAs) was 0.098 for Wild 1 and 0.11 for Wild 2 genotypes and ranged from 0.14 to 0.28 for cultivars. The main fatty acids identified were linoleic (18:2) and linolenic (18:3) acids in all the samples analysed. In Vaccinium myrtillus the amount of carotenoids and fatty acids was higher than in Vaccinium corymbosum species.     

Tapered plasmonic waveguides with efficient and broadband field transmission

In this paper we suggest, numerically simulate and discuss a tapered plasmonic nanostructure which allows efficient transmission of the wave beam energy into a weakly subwavelength (λ/4 … λ/2) spatial region within a broad frequency range. The frequency stable location of this region becomes possible due to unusual plasmonic modes we have theoretically revealed and used. Our structure is promising for prospective transducers between conventional optical waveguides and subwavelength nanoguides or nanocircuits.     

The structure of 2D semi-simple field theories

I classify the cohomological 2D field theories based on a semi-simple complex Frobenius algebra A. They are controlled by a linear combination of κ-classes and by an extension datum to the Deligne–Mumford boundary. Their effect on the Gromov–Witten potential is described by Givental’s Fock space formulae. This leads to the reconstruction of Gromov–Witten (ancestor) invariants from the quantum cup-product at a single semi-simple point and the first Chern class of the manifold, confirming Givental’s higher-genus reconstruction conjecture. This in turn implies the Virasoro conjecture for manifolds with semi-simple quantum cohomology. The classification uses the Mumford conjecture, proved by Madsen and Weiss (European Congress of Mathematics, pp. 283–303, 2005).