Monotone numerical schemes for a Dirichlet problem for elliptic operators in divergence form

We consider a second‐order differential operator A( x )=?∑?_ia_ij( x )?_j+ ∑?_j(b_j( x )·)+c( x ) on ?^d, on a bounded domain D with Dirichlet boundary conditions on ?D, under mild assumptions on the coefficients of the diffusion tensor a_ij. The object is to construct monotone numerical schemes to approximate the solution of the problem A( x )u( x )=µ( x ), x ∈D, where µ is a positive Radon measure. We start by briefly mentioning questions of existence and uniqueness introducing function spaces needed to prove convergence results. Then, we define non‐standard stencils on grid‐knots that lead to extended discretization schemes by matrices possessing compartmental structure. We proceed to discretization of elliptic operators, starting with constant diffusion tensor and ending with operators in divergence form. Finally, we discuss W‐convergence in detail, and mention convergence in C and L₁ spaces. We conclude by a numerical example illustrating the schemes and convergence results. Copyright © 2008 John Wiley & Sons, Ltd.     

Topography and surface free energy of DPPC layers deposited on a glass, mica, or PMMA support

An investigation of energetic properties of 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) layers deposited on glass, mica, and PMMA (poly(methyl methacrylate)) surfaces was carried out by means of contact angles measurements (advancing and receding) for three probe liquids (diiodomethane, water, and formamide). DPPC was deposited on the surfaces from water (on glass and mica) or methanol (on PMMA) solutions. The topography of the tested surfaces was determined with a help of scanning electron microscopy (SEM) and atomic force microscopy (AFM). Using the measured contact angles, the total apparent surface free energy and its components of the studied layers were determined from van Oss et al.'s (Lifshitz-van der Waals and acid-base components, LWAB) and contact angle hysteresis (CAH) approaches. It allowed us to learn about changes in the surface free energy of the layers (hydrophobicity/hydrophilicity) depending on their number and kind of support. It was found that the changes in the energy greatly depended on the surface properties of the substrate as well as the statistical number of monolayers of DPPC. However, principal changes took place for first three monolayers.     

Synthesis of [2‐aryl‐6‐oxo‐6H‐chromeno[6,7‐d]oxazol‐8‐yl]‐acetic acid ethyl esters

A number of coumarino[6,7‐d]oxazoles (nitrogen analogs of psoralens) have been synthesized from (7‐hydroxy‐2‐oxo‐2H‐chromen‐4‐yl) acetic acid ethyl ester 1 . The synthetic route began with the nitration of 1 with nitric acid in acetic acid to give (6‐nitro‐7‐hydroxy‐2‐oxo‐2H‐chromen‐4‐yl) acetic acid ethyl ester 2 ; (3,6‐dinitro‐7‐hydroxy‐2‐oxo‐2H‐chromen‐4‐yl) acetic acid ethyl ester 3 and (3,6,8‐trinitro‐7‐hydroxy‐2‐oxo‐2H‐chromen‐4‐yl) acetic acid ethyl ester 4 . The reduction of 2 was accomplished with tin(II) chloride, tin, and concentrated hydrochloric acid in ethanol giving (6‐amino‐7‐hydroxy‐2‐oxo‐2H‐chromen‐4‐yl) acetic acid ethyl ester 5 . After the condensation of aminocoumarin 5 with aromatic aldehyde in glacial acetic acid medium, followed the dehydrocyclization to coumarino[6,7‐d]oxazoles 7a‐k . The intermediate Schiff's bases 6a‐k have been obtained from 5 with aromatic aldehyde in ethanol. Antibacterial and antifungal activities of the compounds have been evaluated.     

Screening for acetylcholinesterase inhibition and antioxidant activity of selected plants from Croatia

The methanol, ethyl acetate and chloroform extracts of selected Croatian plants were tested for their acetylcholinesterase (AChE) inhibition and antioxidant activity. Assessment of AChE inhibition was carried out using microplate reader at 1?mg?mL?1. Antioxidant capacities were determined by 2,2-diphenyl-1-picrylhydrazyl (DPPH) radical scavenging test and ferric reducing/antioxidant power assay (FRAP). Total phenol content (TPC) of extracts were determined using Folin-Ciocalteu colorimetric method. Out of 48 extracts, only methanolic extract of the Salix alba L. cortex exerted modest activity towards AChE, reaching 50.80% inhibition at concentration of 1?mg?mL?1. All the other samples tested had activity below 20%. The same extract performed the best antioxidative activity using DPPH and FRAP method, too. In essence, among all extracts used in the screening, methanolic extracts showed the best antioxidative activity as well as highest TPC.     

Novel coumarin derivatives containing 1,2,4-triazole, 4,5-dicyanoimidazole and purine moieties: synthesis and evaluation of their cytostatic activity

We report here on the synthesis and in vitro anti-tumor effects of a series of novel 1,2,4-triazole (compounds 3-6), 4,5-dicyanoimidazole (compound 7), and purine (compounds 8-13) coumarin derivatives and their acyclic nucleoside analogues 14-18. Structures of novel compounds 3-18 were deduced from their ¹H- and ¹³C-NMR and corresponding mass spectra. Results of anti-proliferative assays performed on a panel of selected human tumor cell lines revealed that compound 6 had moderate cytostatic activity against the HeLa cell line (IC₅₀ = 35 μM), whereas compound 10 showed moderate activity against the HeLa (IC₅₀ = 33 μM), HepG2 (IC₅₀ = 25 μM) and SW620 (IC₅₀ = 35 μM) cell lines. These compounds showed no cytotoxic effects on normal (diploid) human fibroblasts.     

Antitumor efficacy of photodynamic therapy using novel nanoformulations of hypocrellin photosensitizer SL052

Recent preclinical and clinical testing of hypocrellin-based photosensitizer SL052 for use in photodynamic therapy (PDT) of cancer has shown encouraging results. Further optimization of its formulation for delivery could considerably extend the therapeutic efficiency of this drug. A nanoformulation encapsulating SL052 into biodegradable polymer poly(lactic-co-glycolic acid) (PLGA) was developed using a single-emulsion solvent evaporation technique and characterized in terms of particle size and loading of the photosensitizing agent. This nanoformulation, SL052-PLGA-nanoparticles (NPs), was compared with recently created nanoformulation based on polyvinylpyrrolidone (SL052-PVP-NPs) and standard liposomal SL052 preparation in terms of efficacy when used for PDT treatment of squamous cell carcinomas SCCVII growing subcutaneously in syngeneic mice. The therapeutic effect of PDT using these three different SL052 formulations was tested for both 1 and 4 h intervals between drug injection and tumor light exposure. The longer time interval produced higher tumor cure rates with all SL052 preparations. With both drug-light intervals, PDT based on SL052-PLGA-NPs produced superior therapeutic benefit compared with the other two SL052 formulations.     

Numerical simulations of water–gas flow in heterogeneous porous media with discontinuous capillary pressures by the concept of global pressure

We present an approach and numerical results for a new formulation modeling immiscible compressible two-phase flow in heterogeneous porous media with discontinuous capillary pressures. The main feature of this model is the introduction of a new global pressure, and it is fully equivalent to the original equations. The resulting equations are written in a fractional flow formulation and lead to a coupled degenerate system which consists of a nonlinear parabolic (the global pressure) equation and a nonlinear diffusion–convection one (the saturation equation) with nonlinear transmission conditions at the interfaces that separate different media. The resulting system is discretized using a vertex-centred finite volume method combined with pressure and flux interface conditions for the treatment of heterogeneities. An implicit Euler approach is used for time discretization. A Godunov-type method is used to treat the convection terms, and the diffusion terms are discretized by piecewise linear conforming finite elements. We present numerical simulations for three one-dimensional benchmark tests to demonstrate the ability of the method to approximate solutions of water–gas equations efficiently and accurately in nuclear underground waste disposal situations.     

Stability of binary model membranes--prediction of the liposome stability by the Langmuir monolayer study

In this paper, usefulness of the Langmuir monolayer study is demonstrated for predictions of the stability of liposomes composed of dipalmitoyl phosphatidylcholine (DPPC) and cholesterol (Chol). Thermodynamic analysis of the surface pressure (π)-area (A) isotherms of the DPPC/Chol systems was performed, which allowed for concluding on miscibility of the components, their molecular packing, and the interactions between molecules. It was found that the most stable system, in which the strongest interactions between molecules occured, was DPPC/Chol at x(Chol)=0.25. The stability of liposomes of the same composition as that in the Langmuir monolayers was analyzed by determining the size distribution of vesicles and the polydispersity as a function of time. The changes of these parameters confirmed that the system of the greatest stability is that with low Chol content.     

Dibenzo[b,f]oxepin‐10(11H)‐one and dibenzo[b,f]thiepin‐10(11H)‐one as useful synthons in the synthesis of various dibenzo[e,h]azulenes

The present review focuses on dibenzo[b,f]oxepin‐10(11H)‐one ( I , X = O) and dibenzo[b,f]thiepin‐10(11H)‐one ( I , X = S) as common synthons in the efficient synthesis of various dibenzoxepino[4,5‐ and dibenzothiepino[4,5]‐fused five‐membered heterocycles: [2,3] fused thiophene ( II ), [3,4] fused thiophene ( III ), furan ( IV ), pyrrole ( V ), imidazole ( VI ), pyrazole ( VII ), oxazole ( VIII ), and thiazole ( IX ). The potential of I to be converted into reactive intermediates that readily undergo heteroaromatic annulation reactions by cyclocondensation with proper binucleophiles allows formation of a range of enumerated functionalized dibenzo[e,h]azulene [4] structures ( II , III , IV , V , VI , VII , VIII , IX ). Dibenzo[e,h]azulenes as heterotetracyclic scaffold can be exploited in further modifications to obtain compounds with altered physicochemical and biological profile. J. Heterocyclic Chem., (2012).     

Non-uniform exponential tension splines

We describe explicitly each stage of a numerically stable algorithm for calculating with exponential tension B-splines with non-uniform choice of tension parameters. These splines are piecewisely in the kernel of D ²(D ²–p ²), where D stands for ordinary derivative, defined on arbitrary meshes, with a different choice of the tension parameter p on each interval. The algorithm provides values of the associated B-splines and their generalized and ordinary derivatives by performing positive linear combinations of positive quantities, described as lower-order exponential tension splines. We show that nothing else but the knot insertion algorithm and good approximation of a few elementary functions is needed to achieve machine accuracy. The underlying theory is that of splines based on Chebyshev canonical systems which are not smooth enough to be ECC-systems. First, by de Boor algorithm we construct exponential tension spline of class C ¹, and then we use quasi-Oslo type algorithms to evaluate classical non-uniform C ² tension exponential splines.