Biological Activity of Triazolopyrimidine Copper(II) Complexes Modulated by an Auxiliary N-N-Chelating Heterocycle Ligands

Novel complexes of type [Cu(N-N)(dmtp)₂(OH₂)](ClO₄)₂·dmtp ((1) N-N: 2,2′-bipyridine; (2) L: 1,10-phenantroline and dmtp: 5,7-dimethyl-1,2,4-triazolo[1,5-a]pyrimidine) were designed in order to obtain biologically active compounds. Complexes were characterized as mononuclear species that crystallized in the space group P-1 of the triclinic system with a square pyramidal geometry around the copper (II). In addition to the antiproliferative effect on murine melanoma B16 cells, complex (1) exhibited low toxicity on normal BJ cells and did not affect membrane integrity. Complex (2) proved to be a more potent antimicrobial in comparison with (1), but both compounds were more active in comparison with dmtp—both against planktonic cells and biofilms. A stronger antimicrobial and antibiofilm effect was noticed against the Gram-positive strains, including methicillin-resistant Staphylococcus aureus (MRSA). Both electron paramagnetic resonance (EPR) and Saccharomyces cerevisiae studies indicated that the complexes were scavengers rather than reactive oxygen species promoters. Their DNA intercalating capacity was evidenced by modifications in both absorption and fluorescence spectra. Furthermore, both complexes exhibited nuclease-like activity, which increased in the presence of hydrogen peroxide.     

Linear analysis of quandrature domains. II

The natural correspondence between bounded planar quadrature domains, in the terminology of Aharonov-Shapiro, and certain square matrices with a distinguished cyclic vector is further exploited. Two different cubature formulas on quadrature domains, that is the computation of the integral of a real polynomial, are presented. The minimal defining polynomial of a quadrature domain is decomposed uniquely into a linear combination of moduli squares of complex polynomials. The geometry of a canonical rational embedding of a quadrature domain into the projective complemnt of a real affine ball is also investigated. Explicit computations on order-two quadrature domains illustrate the main results. Paper partially supported by the National Science Foundation Grant DMS-95000954.     

On the equivalence of two variational problems

We consider the following problems where is a convex function, is an open bounded subset of is a closed convex subset of such that and and are suitable obstacles. We give conditions on the function {\it g} under which the two problems are equivalent. Received March 24, 1999/ Accepted January 14, 2000 / Published online June 28, 2000     

Sur l'effectivité numérique des images inverses de fibrés en droites

Sans résumé

---

Re?u le 7 Octobre 1996     

Eigenvalue problems for anisotropic quasilinear elliptic equations with variable exponent

In this paper we are concerned with a new class of anisotropic quasilinear elliptic equations with a power-like variable reaction term. One of the main features of our work is that the differential operator involves partial derivatives with different variable exponents, so that the functional-analytic framework relies upon anisotropic Sobolev and Lebesgue spaces. Existence and nonexistence results are deeply influenced by the competition between the growth rates of the anisotropic coefficients. Our main results point out some striking phenomena related to the existence of a continuous spectrum in several distinct situations.     

The power of programmed grammars with graphs from various classes

Programmed grammars, one of the most important and well investigated classes of grammars with context-free rules and a mechanism controlling the application of the rules, can be described by graphs. We investigate whether or not the restriction to special classes of graphs restricts the generative power of programmed grammars with erasing rules and without appearance checking, too. We obtain that Eulerian, Hamiltonian, planar and bipartite graphs and regular graphs of degree at least three are pr-universal in that sense that any language which can be generated by programmed grammars (with erasing rules and without appearance checking) can be obtained by programmed grammars where the underlying graph belongs to the given special class of graphs, whereas complete graphs, regular graphs of degree 2 and backbone graphs lead to proper subfamilies of the family of programmed languages.     

Complex symmetric operators and applications

We study a few classes of Hilbert space operators whose matrix representations are complex symmetric with respect to a preferred orthonormal basis. The existence of this additional symmetry has notable implications and, in particular, it explains from a unifying point of view some classical results. We explore applications of this symmetry to Jordan canonical models, self-adjoint extensions of symmetric operators, rank-one unitary perturbations of the compressed shift, Darlington synthesis and matrix-valued inner functions, and free bounded analytic interpolation in the disk.

     

Temperature field modeling during multi-modes CO2 laser irradiation of human enamel

We examine the temperature fields of human enamel [Yu D, Fox JL, Hsu J, Lynn Powell G, Higuchi WI. Computer simulation of surface temperature profiles during CO₂ laser irradiation of human enamel. Opt Eng 1993; 32(2)] during multi-modes CO₂ laser irradiation. For this we use the integral transform method as well as direct and inverse Laplace transform [Oane M, Sporea D. Temperature profiles modeling in IR optical components during high power laser irradiation. Infrared Phys Technol 2001; 42(1): 31–40; Oane M, Sporea D. Study of heat transfer in IR optical components during CO₂ laser irradiation. Proc SPIE 2001; 4430: 898–904; Oane M. Mathematical modeling of the thermal field distributions in solids under multiple laser irradiations. Proc SPIE 2003; 5227: 329–34; Oane M, Apostol I, Timcu A. Temperature field modeling in laser heated metals for laser cleaning of surfaces. Proc SPIE 2003; 5227: 323–8]. The enamel block is modeled as homogeneous cylinder in three dimensions. Results indicate that (i) the thermal field depends on multi-modes structure; (ii) heat transfer coefficient plays an important role in temperature distribution.