Nonstandard methods for the convective‐dispersive transport equation with nonlinear reactions

A new nonstandard Eulerian‐Lagrangian method is constructed for the one‐dimensional, transient convective‐dispersive transport equation with nonlinear reaction terms. An “exact” difference scheme is applied to the convection‐reaction part of the equation to produce a semi‐discrete approximation with zero local truncation errors with respect to time. The spatial derivatives involved in the remaining dispersion term are then approximated using standard numerical methods. This approach leads to significant, qualitative improvements in the behavior of the numerical solution. It suppresses the numerical instabilities that arise from the incorrect modeling of derivatives and nonlinear reaction terms. Numerical experiments demonstrate the scheme's ability to model convection‐dominated, reactive transport problems. © 1999 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 15: 617–624, 1999     

Planar Crossing Numbers of Graphs of Bounded Genus

Pach and Tóth proved that any n-vertex graph of genus g and maximum degree d has a planar crossing number at most c ^g dn, for a constant c>1. We improve on this result by decreasing the bound to O(dgn), and also prove that our result is tight within a constant factor. Our proof is constructive and yields an algorithm with time complexity O(dgn). As a consequence of our main result, we show a relation between the planar crossing number and the surface crossing number.     

Extreme self‐adjoint extensions of a semibounded ‐difference operator

For a certain q‐difference operator introduced and studied in a series of articles by the same authors, we investigate its extreme self‐adjoint extensions, i.e., the so‐called Friedrichs and Kre?n extensions. We show that for the interval of parameters under consideration, the Friedrichs extension and the Kre?n extension are distinct and give values of the parameter in the von Neumann formulas that correspond to those extensions and describe their resolvent operators. A crucial rôle in our investigation plays the fact that both the Friedrichs and the Kre?n extensions are scale invariant.     

Nonsmooth Analysis of Singular Values. Part II: Applications

In this work we continue the nonsmooth analysis of absolutely symmetric functions of the singular values of a real rectangular matrix. Absolutely symmetric functions are invariant under permutations and sign changes of its arguments. We extend previous work on subgradients to analogous formulae for the proximal subdifferential and Clarke subdifferential when the function is either locally Lipschitz or just lower semicontinuous. We illustrate the results by calculating the various subdifferentials of individual singular values. Another application gives a nonsmooth proof of Lidskii’s theorem for weak majorization. Mathematics Subject Classifications (2000) Primary 90C31, 15A18; secondary 49K40, 26B05.Research supported by NSERC.     

Nonsmooth Analysis of Singular Values. Part I: Theory

The singular values of a rectangular matrix are nonsmooth functions of its entries. In this work we study the nonsmooth analysis of functions of singular values. In particular we give simple formulae for the regular subdifferential, the limiting subdifferential, and the horizon subdifferential, of such functions. Along the way to the main result we give several applications and in particular derive von Neumann’s trace inequality for singular values. Mathematics Subject Classifications (2000) Primary 90C31, 15A18; secondary 49K40, 26B05.Research supported by NSERC.     

Clarke Generalized Jacobian of the Projection onto the Cone of Positive Semidefinite Matrices

This paper studies the differentiability properties of the projection onto the cone of positive semidefinite matrices. In particular, the expression of the Clarke generalized Jacobian of the projection at any symmetric matrix is given.*Research supported by NSERC.     

DFT study of the structure and spectral behavior of new pt(II) complexes with 5‐methyl‐5(4‐pyridyl)hydantoin

Platinum complexes are a great interest of study, because of the antitumor activity and the clinical use of some of them in the recent anticancer chemotherapy. In many cases, computational studies can be very useful for predicting the structure and some physicochemical properties of metal complexes. Theoretical calculations can also be used for the rational design of new complexes with optimal ratio: antitumor activity/toxicity. The geometry of three new Pt(II) complexes with general formula cis‐[PtL₂X₂] (where L is 5‐methyl‐5(4‐pyridyl)hydantoin and X = Cl^?, Br^?, I^?) and of the free organic ligand were optimized using the hybrid DFT method B3LYP with LAN2DZ basis sets. The results were in very good correlation with the data of similar compounds from the literature. The same DFT method was used for the study of their spectral behavior, by reproducing their IR and Raman spectra and comparing them with experimental data. In addition, the distribution of charges by ESP analysis was calculated. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

Electrospun Hybrid Nanofibers Based on Chitosan or N‐Carboxyethylchitosan and Silver Nanoparticles

Hybrid nanofibers from chitosan or N‐carboxyethylchitosan (CECh) and silver nanoparticles (AgNPs) were prepared by electrospinning using HCOOH as a solvent. AgNPs were synthesized in situ in the spinning solution. HCOOH slowed down the cross‐linking of the polysaccharides with GA enabling the reactive electrospinning in the presence of poly(ethylene oxide) (PEO). EDX analyses showed that AgNPs are uniformly dispersed in the nanofibers. Since AgNPs hampered the cross‐linking of chitosan and CECh with GA in the hybrid fibers, the imparting of water insolubility to the fibers was achieved at a second stage using GA vapors. The surface of chitosan/PEO/AgNPs nanofibers was enriched in chitosan and 15 wt.‐% of the incorporated AgNPs were on the fiber surface as evidenced by XPS.

     

X-ray photoelectron spectroscopy study of neodymium niobate and tantalate precursors and thin films

Neodymium niobate NdNbO₄ (NNO) and tantalate NdTaO₄ (NTO) thin films (~100 nm) were prepared by sol-gel/spin-coating process on Al₂O₃ substrate with LaNbO₄/PbZrO₃ interlayer and annealing at 1000°C. Surface chemistry was investigated by X-ray photoelectron spectroscopy (XPS). The core-level XPS studies of sol-gel NNO and NTO were performed for the first time. The binding energy differences Δ(O―Nb) and Δ(O―Ta) were used to characterize average energies of Nb―O bonding in NNO (322.9 eV) and Ta―O bonding in NTO (504.2 eV). The XPS demonstrated single valence state of Nd (Nd³⁺) in precursors. Nd concentration (at. %) decreases from 22% in precursors to 7% in films considering the substrate contains C, Al, Si, Pb, and Zr elements (37%) at Nb or Ta (5%) and O (51%). The X-ray diffraction analyses verified formation of the monoclinic (M-NdNbO₄ or M′-NdTaO₄), orthorhombic (O-NdNbO₄) and tetragonal (T-NdTaO₄) phases in precursors and films. Single valence state of Nd³⁺ was confirmed in these films designed for the application in environmental electrolytic thin film devices.     

On the irreducibility of the Hilbert scheme of space curves

Denote by the Hilbert scheme parametrizing smooth irreducible complex curves of degree and genus embedded in . In 1921 Severi claimed that is irreducible if . As it has turned out in recent years, the conjecture is true for and , while for it is incorrect. We prove that , and are irreducible, provided that , and , correspondingly. This augments the results obtained previously by Ein (1986), (1987) and by Keem and Kim (1992).