Classification of trivectors of an eight-dimensional real vector space

Let U?V denote the tensor product of two finite dimensional vector spaces U and V over an infinite field. Let k be a positive integer such that kdim U and k dim V Let D_k denote the set of all non-zero elements of U?V of rank less than k. In this paper we study linear transformations T on U?V such that (TD_k )?D_k .     

Synergic liquid/liquid extraction of lithium and sodium with 4-acyl-5-pyrazolones with bulky substituents and tri-n-octylphosphine oxide

The synergic liquid/liquid extraction of lithium and sodium with 4-acyl-5-pyrazolones having bulky substituents and tri-n-octylphosphine oxide (TOPO) is described. The maximum percentage extraction and the separation of lithium and sodium were improved by introducing bulky substituents. Quantitative extraction (? 99% ) of lithium could be achieved by adduct formation with TOPO, which enhanced the extraction much more than did triphenylphosphine oxide. The extraction decreased in the solvent order cyclohexane ? benzene ? chloroform, which is the general trend in synergic extractions.     

Fredholm theory and transversality for noncompact pseudoholomorphic mapsin symplectizations

We study pseudoholomorphic maps from a punctured Riemann surface into the symplectization of a contact manifold. A Fredholm theory yields the virtual dimension of the moduli spaces of such maps in terms of the Euler characteristic of the Riemann surface and the asymptotics data given by the periodic solutions of the Reeb vector field associated to the contact form. The transversality results establish the existence of additional structure for these spaces. To be more precise, we prove that these spaces are generically smooth manifolds, and therefore their virtual dimension coincides with their actual dimension. © 2004 Wiley Periodicals, Inc.     

Helly-Type Theorems on Common Supporting Lines for Nonoverlapping Families of Convex Bodies in the Plane

Helly-type results are established relating to the existence of a line supporting a family of nonoverlapping convex bodies in the plane.     

Some Shift-Invariant Integral Operators, Univariate Case, Revisited

In recent articles the first author and H. Gonska [e.g., see G. Anastassiou, C. Cottin, and H. Gonska, Global smoothness of approximating functions, Analysis, 11, 43–57 (1991); G. Anastassiou and H. Gonska, On some shift-invariant integral operators, univariate case, Ann. Pol. Math. LXI.3, 225–243 (1995)] studied global smoothness preservation by some univariate and multivariate linear operators over compact domains and ⁿ , n 1. In particular, they studied a very general positive linear integral type operator [e.g., see G. Anastassiou and H. Gonska, On some shift-invariant integral operators, univariate case, Ann. Pol. Math. LXI.3, 225–243 (1995)] over ⁿ that was introduced through a convolution-like integration of another general positive linear operator with a scaling-type function. In this article the authors, among others, extend and generalize [G. Anastassiou and H. Gonska, On some shift-invariant integral operators, univariate case, Ann. Pol. Math. LXI.3, 225–243 (1995)]. Also certain new similar but more general integral operators are introduced and studied. These operators arise in a natural way, and for all these sufficient conditions are given for shift invariance, preservation of higher-order global smoothness and sharpness of the related inequalities, convergence to the unit using the first modulus of continuity, shape preservation, and preservation of continuous probabilistic distribution functions. Several examples of very general specialized operators, old and new, are given that satisfy all the above properties.     

Anodic stripping voltammetry at a nickel-based mercury film electrode

The electrochemical properties of the nickel-based mercury film electrode (Ni-MFE) were investigated with respect to application of the electrode in the anodic stripping voltammetry (a.s.v.) of heavy metal ions. The hydrogen overpotential at the Ni-MFE is higher than those at MFEs based on other metals, and high enough to get quantitative a.s.v. peaks of lead and cadmium. The mercury film of the Ni-MFE is stable both mechanically and chemically; a.s.v. peaks at a Ni-MFE which had been used fifty times within 300 h after its preparation were identical with those at the freshly prepared electrode. With the Ni-MFE, 5 × 10^?10–10^?7 M lead(II) and 2 × 10^?10–10^?7 M cadmium(II) in the solution can be determined with relative standard deviations of 11 and 12%, respectively. These results are comparable to those obtained by a.s.v. at an in situ mercury-plated g]assy carbon electrode.     

Synthesis and Stereochemistry of Some New 1,3-Dioxane Derivatives of 1,4-Diacetylbenzene

Summary.  The synthesis and stereochemistry of new 1,3-dioxane derivatives of 1,4-diacetylbenzene are reported. The anancomeric structure of these compounds, the axial orientation of the aryl group for both 1,3-dioxane rings, and the cis and trans isomerism of some of these compounds is discussed considering data of conformational analysis, NMR investigations, and single crystal X-ray diffractometry. Received September 12, 2001. Accepted (revised) November 5, 2001     

Monte Carlo-studium der ireversiblen terpolymerisation: Das modell und anwendungen

The Monte Carlo model of the ternary irreversible copolymerization is presented. The computer program MEMøRY-4, which implements the described model, is used to study the methyl methacrylate/methyl acrylate/maleic anhydride, butadiene/styrene/2-methyl-5-vinylpyridine, and styrene/methacrylonitrile/α-methyl styrene terpolymers. One discusses the problem of transferability of reactivity ratios determined for binary copolymerizations to the ternary ones. It can be concluded that the transferability is not assured, but using only composition data it is difficult to achieve a safe conclusion (Fisher statistics).