Oxidation of Some Furanoselenium Compounds

The organoselenium fragmentation under oxidative conditions to form a carbon-carbon double bond under very mild condition is well established.¹ So [2, 3] -sigmatropic rearrangements of allylic selenium species are well-known.     

Linear fractional transformations of Stieltjes functions

Linear fractional transformations of Stieltjes (and inverse Stieljes) functions, which appear naturally in the extension theory of nonnegative symmetric operators with defect one in Hilbert spaces, are investigated. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Existence and multiplicity for quasilinear elliptic inclusions with nonmonotone discontinuous multifunction

We develop a flexible tool in terms of appropriately defined sub- and supersolutions that allows for obtaining existence, bounds, and multiplicity of solutions for quasilinear elliptic inclusions with a discontinuous multi-function that need neither be upper nor lower semicontinuous. The problem under consideration may be used to describe certain free boundary problems in mechanical models involving multi-valued constitutive laws. Our approach is based on a combined use of abstract fixed point results for monotone mappings on partially ordered sets, and on the existence and comparison results for multi-valued quasilinear elliptic problems with Clarke’s generalized gradient.     

Boundary Relations, Unitary Colligations, and Functional Models

Recently a new notion, the so-called boundary relation, has been introduced involving an analytic object, the so-called Weyl family. Weyl families and boundary relations establish a link between the class of Nevanlinna families and unitary relations acting from one Kreĭn space, a basic (state) space, to another Kreĭn space, a parameter space where the Nevanlinna family or Weyl family is acting. Nevanlinna families are a natural generalization of the class of operator-valued Nevanlinna functions and they are closely connected with the class of operator-valued Schur functions. This paper establishes the connection between boundary relations and their Weyl families on the one hand, and unitary colligations and their transfer functions on the other hand. From this connection there are various advances which will benefit the investigations on both sides, including operator theoretic as well as analytic aspects. As one of the main consequences a functional model for Nevanlinna families is obtained from a variant of the functional model of L. de Branges and J. Rovnyak for Schur functions. Here the model space is a reproducing kernel Hilbert space in which multiplication by the independent variable defines a closed simple symmetric operator. This operator gives rise to a boundary relation such that the given Nevanlinna family is realized as the corresponding Weyl family. Received: January 21, 2008., Revised: March 31, 2008.     

Mass Spectroscopy of the Antileukemic Drug MGBG and Related Bis(Amidinohydrazones) [‘Bis(Guanylhydrazones)’]

The first study on the mass spectroscopy of various bis(amidinohydrazones) is reported. The compounds studied included the investigational antileukemic drugs methylglyoxal bis(amidino-hydrazone) [‘methylglyoxal bis(guanylhydrazone)’, MGBG] and glyoxal bis(amidinohydrazone), as well as seven mono- and dialkylglyoxal analogs thereof. The results indicate that the free bases of these high-melting compounds are volatilized well enough to allow a facile detection of the molecular ions and to make mass spectroscopy of the underivatized compounds a suitable method for the verification of the identity of the substances. This result is of importance considering the development of novel analogs and derivatives. A compilation of electron-impact mass spectra is reported and possible fragmentation routes are outlined. The fragmentation of the various congeners appears to occur essentially similarly, the main paths involving breakage of the carbon-carbon single bond in the glyoxal moiety or breakage of either one of the nitrogen-nitrogen single bonds.     

Sturm-Liouville operators and their spectral functions

Assume that the differential operator −DpD+q in L²(0,∞) has 0 as a regular point and that the limit-point case prevails at ∞. If p≡1 and q satisfies some smoothness conditions, it was proved by Gelfand and Levitan that the spectral functions σ(t) for the Sturm-Liouville operator corresponding to the boundary conditions (pu′)(0)=τu(0), , satisfy the integrability condition . The boundary condition u(0)=0 is exceptional, since the corresponding spectral function does not satisfy such an integrability condition. In fact, this situation gives an example of a differential operator for which one can construct an analog of the Friedrichs extension, even though the underlying minimal operator is not semibounded. In the present paper it is shown with simple arguments and under mild conditions on the coefficients p and q, including the case p≡1, that there exists an analog of the Friedrichs extension for nonsemibounded second order differential operators of the form −DpD+q by establishing the above mentioned integrability conditions for the underlying spectral functions.     

A reproducing kernel space model for -functions

A new model for generalized Nevanlinna functions will be presented. It involves Bezoutians and companion operators associated with certain polynomials determined by the generalized zeros and poles of . The model is obtained by coupling two operator models and expressed by means of abstract boundary mappings and the corresponding Weyl functions.

     

Influence of massive projectile size and energy on secondary ion yields from organic surfaces

We investigated the influence of the projectile size and energy using Au_n^q+ clusters (5 < n < 400, 1 < q < 4) impacting on a glycine target with a 19q-34q keV energy range. We show that both CN⁻ fragment and Gly⁻ molecular ion yields are equivalent for projectiles with n > 9 and increase with the energy per projectile atoms. A maximum yield of 0.5 (50%) for both CN⁻ and Gly⁻ was obtained with the Au₄₀₀⁴⁺ projectile at 136 keV total energy. For Gly⁻, the yield enhancement is linear for Au_n when n > 5. Trends for the CN⁻ fragment are different. A nonlinear yield enhancement proportional to n³ is observed for Au_n when n < 9.