Generalized qd algorithm for block band matrices

The generalized qd algorithm for block band matrices is an extension of the block qd algorithm applied to a block tridiagonal matrix. This algorithm is applied to a positive definite symmetric block band matrix. The result concerning the behavior of the eigenvalues of the first and the last diagonal block of the matrix containing the entries q ^(k) which was obtained in the tridiagonal case is still valid for positive definite symmetric block band matrices. The eigenvalues of the first block constitute strictly increasing sequences and those of the last block constitute strictly decreasing sequences. The theorem of convergence, given in Draux and Sadik (Appl Numer Math 60:1300?C1308, 2010), also remains valid in this more general case.     

Catalytic adsorptive stripping voltammetric measurements of trace vanadium at bismuth film electrodes

Bismuth-coated glassy carbon electrodes have been successfully applied for catalytic adsorptive stripping voltammetric measurements of low levels of vanadium(V) in the presence of chloranilic acid (CAA) and bromate ion. The new protocol is based on the accumulation of the vanadium-chloranilic acid complex from an acetate buffer (pH 5.5) solution at a preplated bismuth film electrode held at −0.35 V (versus Ag/AgCl), followed by a square-wave voltammetric scan. Factors influencing the adsorptive stripping performance, including the CAA and bromate concentrations, solution pH, and accumulation potential or time have been optimized. The response compares favorably with that observed at mercury film electrodes. A linear response is observed over the 5-25 μg/L concentration range (2 min accumulation), along with a detection limit of 0.20 μg/L vanadium (10 min accumulation). High stability is indicated from the reproducible response of a 50 μg/L vanadium solution (n = 25; R.S.D. = 3.1%). Applicability to a groundwater sample is illustrated.     

The Synthesis and Reactivity of Trimethylsilyl Amide of Dichlorophosphoric(V) Acid,Me3 SiNHP(S)Cl2

Abstract

Trimethylsilylamid Me₃SiNHP(S)Cl₂ (I) was first obtained ¹⁾ by reaction P₂S₂OCl₄ with hexamethyldisilazane (HMDS) as a crystalline very reactive compound (m.p.=42°C, δ³¹ P=51,3ppm).     

Study on synthesis of superparamagnetic spinel cobalt ferrite nanoparticles as layered double hydroxides by co-precipitation method

Cobalt ferrite layered double hydroxide (LDH) nanoparticles with cubic structure were synthesized by the co-precipitation method: addition of NaOH solution to a solution of Co²⁺ and Fe³⁺. Formation of nanoparticles was confirmed by XRD, SEM, TEM, PSA, FT-IR, TGA, DSC, and magnetic characteristics were measured using VSM. Crystals produced by calcination at 900°C possessed high coercivity and pronounced physical and chemical stability. Nanoparticles of CoFe₂O₄ formed outer layers with poor crystallization on the surface of cobalt ferrite nanocrystals.     

An optimal algorithm for a class of equality constrained quadratic programming problems with bounded spectrum

The implementation of the recently proposed semi-monotonic augmented Lagrangian algorithm for the solution of large convex equality constrained quadratic programming problems is considered. It is proved that if the auxiliary problems are approximately solved by the conjugate gradient method, then the algorithm finds an approximate solution of the class of problems with uniformly bounded spectrum of the Hessian matrix at O(1) matrix–vector multiplications. If applied to the class of problems with the Hessian matrices that are in addition either sufficiently sparse or can be expressed as a product of such sparse matrices, then the cost of the solution is proportional to the dimension of the problems. Theoretical results are illustrated by numerical experiments. This research is supported by grants of the Ministry of Education No. S3086102, ET400300415 and MSM 6198910027.     

Numerical modeling of crystal growth under strong magnetic fields: An application to the travelling heater method

The article presents a 3-D numerical simulation study for the growth of single crystal semiconductors under strong magnetic fields. In such high fields, the magnetic body force components, which also depend on the flow velocity components present numerical challenges particularly in terms of convergence of iterations. To remedy such difficulties, a novel numerical approach was introduced in an in-house 3-D finite volume-based computer code. As an application, the Travelling Heater Method (THM) was selected for the growth of CdTe crystals under a static vertical magnetic field.     

Separable Spherical Constraints and the Decrease of a Quadratic Function in the Gradient Projection Step

We examine the decrease of a strictly convex quadratic function along the projected-gradient path and show that our earlier estimates obtained for the bound constraints are valid for more general feasible sets including those defined by separable spherical constraints. The result is useful for the development of in a sense optimal algorithms for the solution of some QPQC problems with separable constraints and is an important ingredient in the development of scalable algorithms for contact problems with friction.     

Synthesis and cytostatic activity of Pt(II) complexes of intramolecularly coordinated phosphine and stibine ligands

The intramolecularly coordinated phosphine and stibine ligands L¹PPh₂ ( 1 ), L²PPh₂ ( 2 ) and L²SbPh₂ ( 3 ) containing Y,C,Y‐chelating ligands, L¹ = 2,6‐(^tBuOCH₂)₂C₆H₄^? and L² = 2,6‐(Me₂NCH₂)₂C₆H₄^?, were prepared and characterized. The treatment of these ligands 1 , 2 , 3 with PtCl₂ yielded complexes trans‐{[2,6‐(^tBuOCH₂)₂C₆H₃]PPh₂}₂PtCl₂ (4), cis‐{[2,6‐(Me₂NCH₂)₂C₆H₃]PPh₂}PtCl₂ (5), and cis‐{[2,6‐(Me₂NCH₂)₂C₆H₃]SbPh₂}PtCl₂ (6) as the result of different ability of the starting compounds 1 , 2 , 3 to complex platinum centre. Compounds 1 , 2 , 3 , 4 , 5 , 6 were characterized by ¹H, ¹³C and ³¹P NMR spectroscopy and electrospray ionization mass spectrometry, and molecular structures of 3 , 4 , 5 , 6 were determined by X‐ray diffraction analysis. The substitution reactions of complexes 4 , 5 , 6 were also studied. The reaction of 5 and 6 with NaI yielded complexes {[2,6‐(Me₂NCH₂)₂C₆H₃]PPh₂}PtI₂ ( 7 ) and {[2,6‐(Me₂NCH₂)₂C₆H₃]SbPh₂}PtI₂ ( 8 ), while the same reaction of 4 with NaI did not proceed. As the compounds 7 and 8 structurally resemble cisplatin, complex {{[2‐(Me₂NCH₂)‐6‐(Me₂NHCH₂)C₆H₃]PPh₂}PtCl₂}⁺Cl^? ( 9 ) was prepared as water‐soluble platinum complex. The cytotoxic effect of complex 9 was evaluated on human T‐lymphocytic leukemia cells MOLT‐4 (IC₅₀ = 27.6 ± 1.8 µmol l^?1) and human promyelocytic leukemia HL‐60 (IC₅₀ = 55.9 ± 4.9 µmol l^?1). Copyright © 2012 John Wiley & Sons, Ltd.     

Total FETI for contact problems with additional nonlinearities

The paper is concerned with application of a new variant of the Finite Element Tearing and Interconnecting (FETI) method, referred to as the Total FETI (TFETI), to the solution to contact problems with additional nonlinearities. While the standard FETI methods assume that the prescribed Dirichlet conditions are inherited by subdomains, TFETI enforces both the compatibility between subdomains and the prescribed displacements by the Lagrange multipliers. If applied to the contact problems, this approach not only transforms the general nonpenetration constraints to the bound constraints, but it also generates an enriched natural coarse grid defined by the a priori known kernels of the stiffness matrices of the subdomains exhibiting rigid body modes. We combine our in a sense optimal algorithms for the solution to bound and equality constrained problems with geometric and material nonlinearities. The section on numerical experiments presents results of solution to bolt and nut contact problem with additional geometric and material nonlinear effects. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)