Solvability of a nonlinear fifth‐order difference equation

Some formulas for well‐defined solutions to four very special cases of a nonlinear fifth‐order difference equation have been presented recently in this journal, where some of them were proved by the method of induction, some are only quoted, and no any theory behind the formulas was given. Here, we show in an elegant constructive way how the general solution to the difference equation can be obtained, from which the special cases very easily follow, which is also demonstrated here. We also give some comments on the local stability results on the special cases of the nonlinear fifth‐order difference equation previously publish in this journal.     

Effects of composition grading at heterointefaces and layer thickness variations on Bragg mirror quality

GaAs/AlAs Bragg mirrors on GaAs with varied number of layer pairs were grown, by molecular beam epitaxy (MBE), to be applied for semiconductor saturable absorber mirrors (SESAMs) and intensity modulators. Due to the random variation of the growth rate, substrate surface roughness, and interdiffusion at the interfaces, precise control of the growth conditions of deposited layers poses a serious problem. Usually, thickness variations and composition grading at the heterointefaces result in variations of the mirror reflectivity. In this paper, the high resolution X-ray diffraction (HRXRD), optical reflectance, Rutherford backscattering/channelling (RBS), supported by numerical evaluation methods were employed to determine both the exact thickness of each layer and the composition grading at the interface between succeeding layers of GaAs/AlAs-based mirrors. To reduce ambiguity and to speed up the analysis, the rocking curves and RBS spectra were simulated concurrently, using results of one simulation to verify the others. This process was carried out until the best fit between experimental and calculated curves was achieved. The complementary use of both methods results in improved sensitivity and makes the whole process of evaluation of the thickness variation of each layer and the size of the composition grading at the interfaces less time consuming.     

Evaluation of a Gelatin-Modified Poly(ε-Caprolactone) Film as a Scaffold for Lung Disease

Lung transplantation is a necessary step for the patients with the end stage of chronic obstructive pulmonary disease. The use of artificial lungs is a promising alternative to natural lung transplantation which is complicated and is restricted by low organ donations. For successful lung engineering, it is important to choose the correct combination of specific biological cells and a synthetic carrier polymer. The focus of this study was to investigate the interactions of human lung epithelial cell line NCl-H292 that is involved in lung tissue development with the biodegradable poly(ε-caprolactone) before and after its chemical modification to evaluate potential for use in artificial lung formation. Also, the effect of polymer chemical modification on its mechanical and surface properties has been investigated. The poly(ε-caprolactone) surface was modified using aminolysis followed by immobilization of gelatin. The unmodified and modified polymer surfaces were characterized for roughness, tensile strength, and NCl-H292 metabolic cell activity. The results showed for the first time the possibility for NCI-H292 cells to adhere on this polymeric material. The resazurin assay showed that the metabolic activity at 24?h postseeding of 80% in the presence of the unmodified and greater than 100% in the presence of the modified polymer was observed. The roughness of the poly(ε-caprolactone) increased from 4 to 26?nm and the film strength increased from 0.01 to 0.045 kN when the material was chemically modified. The results obtained to date show potential for using modified poly(ε-caprolactone) as a scaffold for lung tissue engineering.     

Optimization of Preparation Techniques for Poly(Lactic Acid-Co-Glycolic Acid) Nanoparticles

Microparticles and nanoparticles of poly(lactic acid-co-glycolic acid) (PLAGA) are excellent candidates for the controlled release of many pharmaceutical compounds because of their biodegradable nature. The preparation of submicron PLAGA particles poses serious challenges that are not necessarily present when preparing microparticles. We have evaluated several combinations of organic solvents and surfactants used in the formulation of PLAGA nanoparticles. Critical factors such as the ability to separate the nanoparticles from the surfactant, the ability to re-suspend the nanoparticles after freeze-drying, formulation yield and nanoparticle size were studied. The smallest particles were obtained using the surfactant/solvent combination of sodium dodecyl sulfate and ethyl acetate (65 nm) and the largest particles were obtained using poly(vinyl alcohol) and dichloromethane (466 nm). However, the optimal nanoparticles were produced using either acetone or ethyl acetate as the organic solvent and poly(vinyl alcohol) or human serum albumin as the surfactant. This is because the most critical measure of performance of these nanoparticles proved to be their ability to re-suspend after freeze-drying.     

More on oscillation ofnth-order equations

In this paper we prove that a higher-order differential equation with one middle term has every bounded solution oscillatory. Moreover, the behavior of unbounded solutions is given. Two other results dealing with positive solutions are also given.     

More on a hyperbolic‐cotangent class of difference equations

We present a natural method for solving the difference equation where , parameter a, and initial values x_?j, , , are real or complex numbers. As a concrete example, the case k = 1, l = 2 is studied in detail, and several interesting formulas for solutions and objects used in the analysis of the equation are given. A useful remark on solvability of difference equations on complex domains is presented and used here.     

The Aerial Parts of Agrimonia procera Wallr. and Agrimonia eupatoria L. as a Source of Polyphenols,and Especially Agrimoniin and Flavonoids

Plants of the genus Agrimonia L. perfectly fit the current trends in nutrition and food technology, namely, the need for raw materials with a high content of bioactive natural compounds, including polyphenols, which could be added to food. The composition of polyphenolics, including agrimoniin and flavonoids, in the aerial parts of Agrimonia procera Wallr. (A. procera) and Agrimonia eupatoria L. (A. eupatoria) (Rosaceae) was determined using HPLC-DAD-MS. The polyphenolic content of A. procera was found to be 3.9%, 3.2%, 2.9%, 1.8% and 1.1%, and that of A. eupatoria was determined to be 1.3%, 0.3%, 0.9%, 0.6% and 0.5% in the dry matter of leaves, stems, fruits, seeds and hypanthia, respectively. Except for A. procera hypanthia, agrimoniin was the main polyphenolic compound in the aerial parts of the studied Agrimonia species. Both plants are also a valuable source of flavonoid glycosides, especially apigenin, luteolin and quercetin. The obtained data indicate that both A. procera and A. eupatoria are potentially good sources of polyphenols (albeit significantly different in terms of their qualitative and quantitative composition), and may not only be a medicinal raw material, but also a valuable material for food use such as nutraceuticals or functional food ingredients.