Synthesis and Structural Study of Amidrazone Derived Pyrrole-2,5-Dione Derivatives: Potential Anti-Inflammatory Agents

1H-pyrrole-2,5-dione derivatives are known for their wide range of pharmacological properties, including anti-inflammatory and antimicrobial activities. This study aimed to synthesize new 3,4-dimethyl-1H-pyrrole-2,5-dione derivatives 2a–2f in the reaction of N³-substituted amidrazones with 2,3-dimethylmaleic anhydride and evaluate their structural and biological properties. Compounds 2a–2f were studied by the ¹H-¹³C NMR two-dimensional techniques (HMQC, HMBC) and single-crystal X-ray diffraction (derivatives 2a and 2d). The anti-inflammatory activity of compounds 2a–2f was examined by both an anti-proliferative study and a production study on the inhibition of pro-inflammatory cytokines (IL-6 and TNF-α) in anti-CD3 antibody- or lipopolysaccharide-stimulated human peripheral blood mononuclear cell (PBMC) cultures. The antibacterial activity of compounds 2a–2f against Staphylococcus aureus, Enterococcus faecalis, Micrococcus luteus, Esherichia coli, Pseudomonas aeruginosa, Yersinia enterocolitica, Mycobacterium smegmatis and Nocardia corralina strains was determined using the broth microdilution method. Structural studies of 2a–2f revealed the presence of distinct Z and E stereoisomers in the solid state and the solution. All compounds significantly inhibited the proliferation of PBMCs in anti-CD3-stimulated cultures. The strongest effect was observed for derivatives 2a–2d. The strongest inhibition of pro-inflammatory cytokine production was observed for the most promising anti-inflammatory compound 2a.     

Analysis of a coupled finite-infinite element method for exterior Helmholtz problems

Summary. This analysis of convergence of a coupled FEM-IEM is based on our previous work on the FEM and the IEM for exterior Helmholtz problems. The key idea is to represent both the exact and the numerical solution by the Dirichlet-to-Neumann operators that they induce on the coupling hypersurface in the exterior of an obstacle. The investigation of convergence can then be related to a spectral analysis of these DtN operators. We give a general outline of our method and then proceed to a detailed investigation of the case that the coupling surface is a sphere. Our main goal is to explore the convergence mechanism. In this context, we show well-posedness of both the continuous and the discrete models. We further show that the discrete inf-sup constants have a positive lower bound that does not depend on the number of DOF of the IEM. The proofs are based on lemmas on the spectra of the continuous and the discrete DtN operators, where the spectral characterization of the discrete DtN operator is given as a conjecture from numerical experiments. In our convergence analysis, we show algebraic (in terms of N) convergence of arbitrary order and generalize this result to exponential convergence. Received April 10, 1999 / Revised version received November 10, 1999 / Published online October 16, 2000     

On Fefferman and Burkholder–Davis–Gundy inequalities for ℰ-martingales

In a previous paper we introduced a new concept, the notion of ℰ-martingales and we extended the well-known Doob inequality (for 1 < p < + ∞) and the Burkholder–Davis–Gundy inequalities (for p = 2) to ℰ-martingales. After showing new Fefferman-type inequalities that involve sharp brackets as well as the space bmo _q , we extend the Burkholder–Davis–Gundy inequalities (for 1 < p < + ∞) to ℰ-martingales. By means of these inequalities we give sufficient conditions for the closedness in L ^p of a space of stochastic integrals with respect to a fixed ℝ^d-valued semimartingale, a question which arises naturally in the applications to financial mathematics. Finally we investigate the relation between uniform convergence in probability and semimartingale topology. Received: 22 July 1997 / Revised version: 3 July 1998     

Interactions of porphyrinyl-nucleosides with DNA using the example of porphyrinyl-thymidine

meso-Tri(N-memyl-4-pyridinium)porphyrinyl-p-phenylene-5′-O-thymidine, interacting with plasmid ds DNA showed an 8 nm red-shift of the Soret band. The observed Soret band shift was 4 run less than the shift of the respective meso-tetra(N-methyl-4-pyridinium)porphyrin, which is usually assumed to indicate intercalation. Experimental spectra and the MMX- and AM-1 calculations of a series of model structures further suggest that the investigated porphyrinyl-thymidine also interacts with adenine due to its nucleobase. The possibility of intercalation was also viewed based on interaction of immobilized porphyrin with ds DNA. Theoretical considerations suggested that there are no steric limitations to the formation of a system in which the porphyrinyl-thymidine in question interacts with a molecule of porphyrinyl-adenosine, via A-T base pairing, to join two ds DNA molecules.     

The numerical analysis of an orthotropic cylindrical shell

This paper is devoted to an orthotropic cylindricall simply supported shell subjected to external pressure. This analysis is focused on determining geometrical shape of shell. Main subject of investigation is to maximize the stability of the shell. Mathematical model of double layer shell was implemented. Numerical solution was obtained for particular class of shells by using the finite element code ABAQUS. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Existence Theorems for Periodic Differential Inclusions in IR^N

We study the periodic problem for differential inclusions in R~N.First we look for extremal periodicsolutions.Using techniques from multivalued analysis and a fixed point argument we establish an existencetheorem under some general hypotheses.We also consider the“nonconvex periodic problem”under lowersemicontinuity hypotheses,and the“convex periodic problem”under general upper semicontinuity hypotheseson the multivalued vector field.For both problems,we prove existence theorems under very general hypotheses.Our approach extends existing results in the literature and appear to be the most general results on the nonconvexperiodic problem.     

Experimental and quantum-chemical studies of 1H, 13C and 15N NMR coordination shifts in Pd(II) and Pt(II) chloride complexes with quinoline, isoquinoline, and 2,2'-biquinoline

1H, 13C, and 15N NMR studies of platinide(II) (M=Pd, Pt) chloride complexes with quinolines (L=quinoline-quin, or isoquinoline-isoquin; LL=2,2'-biquinoline-bquin), having the general formulae trans-/cis-[ML2Cl2] and [M(LL)Cl2], were performed and the respective chemical shifts (delta1H, delta13C, delta15N) reported. 1H coordination shifts of various signs and magnitudes (Delta1Hcoord=delta1Hcomplex-delta1Hligand) are discussed in relation to the changes of diamagnetic contribution to the relevant 1H shielding constants. The comparison to the literature data for similar complexes containing auxiliary ligands other than chlorides exhibited a large dependence of delta1H parameters on electron density variations and ring-current effects (inductive and anisotropic phenomena). The influence of deviations from planarity, concerning either MN2Cl2 chromophores or azine ring systems, revealed by the known X-ray structures of [Pd(bquin)Cl2] and [Pt(bquin)Cl2], is discussed in respect to 1H NMR spectra. 15N coordination shifts (Delta15Ncoord=delta15Ncomplex-delta15Nligand) of ca. 78-100 ppm (to lower frequency) are attributed mainly to the decrease of the absolute value of paramagnetic contribution in the relevant 15N shielding constants, this phenomenon being noticeably dependent on the type of a platinide metal and coordination sphere geometry. The absolute magnitude of Delta15Ncoord parameter increased by ca 15 ppm upon Pd(II)-->Pt(II) replacement but decreased by ca. 15 ppm following trans-->cis transition. Experimental 1H, 13C, 15N NMR chemical shifts are compared to those quantum-chemically calculated by B3LYP/LanL2DZ+6-31G**//B3LYP/LanL2DZ+6-31G*, both in vacuo and in CHCl3 or DMF solution.     

Photoacoustic investigations of the optical absorption spectra of porous silicon layers on a silicon backing

This paper presents a series of experimental photoacoustic spectra of porous silicon layers on crystalline silicon and their numerical analysis performed in the proposed two-layer model. The goal of the analysis was to calculate the optical absorption spectra of porous silicon from the photoacoustic spectra of porous silicon layers on a silicon background. The experimental character of the observed absorption band associated with the porous silicon was revealed. This is the first attempt at a theoretical interpretation of the photoacoustic spectra of porous silicon on a silicon backing.