Low-frequency scattering of acoustic waves by a bounded rough surface in a half-plane

The problem of the scattering of harmonic plane waves by a rough half-plane is studied here. The surface roughness is finite. The slope of the irregularity is taken as arbitrary. Two boundary conditions are considered, those of Dirichlet and Neumann. An asymptotic solution is obtained, when the wavelength lambda of the incident wave is much larger than the characteristic length of the roughness iota, by means of the method of matched asymptotic expansions in terms of the small parameter epsilon= 2piiota/lambda. For the Dirichlet problem, the solution of the near and far fields is obtained up to O(epsilon2). The far field solution is given in terms of a coefficient that have a simple explicit expression, which also appears in the corresponding solution to the Neumann problem, already solved. Also the scattering cross section is given by simple formulas to O(epsilon3). It is noted that, for the Dirichlet problem, the leading term is of order epsilon3 which, by contrast, is different from that of the circular cylinder in full space, that is, of order epsilon(-1) (log epsilon)(-2). Some examples display the simplicity of the general results based on conformal mapping, which involve arcs of circle, polygonal lines, surface cracks and the like.     

Health-Promoting Capacities of In Vitro and Cultivated Goji (Lycium chinense Mill.) Fruit and Leaves; Polyphenols,Antimicrobial Activity,Macro- and Microelements and Heavy Metals

There is a growing interest among the public in fruit with a positive impact on human health. Two goji berry cultivars (‘No. 1’ and ‘New Big’) were propagated in vitro, grown in an orchard and then evaluated for macro- and microelements and harmful heavy metals (i.e., Pb, Ni, and Cd). The leaves and fruit were also assessed for nutritional value, polyphenols and the antimicrobial activity of the leaves. ‘New Big’ was characterized by a higher content of macro elements in the leaves (in vitro and orchard) and a higher content of microelements in the fruit. The harmful substances content was below the minimum value. Furthermore, neither the fruit nor the leaves contained cadmium. This study also indicated that leaves had a higher content of polyphenols compared to the fruit. The fruits were characterized by their health-promoting capacities, while the leaves were characterized by their antibacterial activity. Among the Gram-positive bacteria, the most sensitive strain was Bacillus subtilis, and among the Gram-negative bacteria, it was Proteus vulgaris. Taking into consideration the Recommended Daily Allowance (RDA) for minerals, goji berries can be declared to be a source of Cu, Fe, Mn, Zn and P.     

Phenolic compounds and bioactive properties of Verbascum glabratum subsp. bosnense (K. Malý) Murb., an endemic plant species

Abstract

Detailed analysis of phenolic composition and antioxidant and antimicrobial activities of Verbascum glabratum subsp. bosnense (K. Malý) Murb., an endemic species of southeastern Dinaric Alps was performed for the first time. The phenolic composition measured via UHPLC-MS/MS of four extract with different polarity suggested this plant species is very rich in both phenolic acids and flavonoids. Ethanol extract was chemically the most versatile containing 12 compounds with quercitrin and rosmarinic acid as the majors, while water extracts were rich in 4-hydroxybenzoic acid, salicylic acid, morin, and apigenin. All extracts showed high antioxidant potential measured spectrophotometrically with IC₅₀ values ranging 0.139 - 0.021?mg/mL. Antimicrobial testing using agar diffusion test showed that ethanol extract was the most potent against all tested organisms. Also, these activities are correlated with the content of phenolic compounds, which suggest they are active ingredients of the extracts.     

Multiplicity of solutions to a nonlinear elliptic problem with nonlinear boundary conditions

We study the problem $$\left\{\begin{array}{ll}\Delta_p u = |u|^{q-2}u, & \quad x \in \Omega ,\\ |\nabla u|^{p-2} \frac{\partial u}{\partial \nu}= \lambda |u|^{p-2}u, &\quad x \in \partial \Omega, \end{array}\right.$$ where \({\Omega \subset \mathbb{R}^N}\) is a bounded smooth domain, \({\nu}\) is the outward unit normal at \({\partial \Omega}\) and \({\lambda > 0}\) is regarded as a bifurcation parameter. When p = 2 and in the superlinear regime q > 2, we show existence of n nontrivial solutions for all \({\lambda > \lambda_n}\) , \({\lambda_n}\) being the n-th Steklov eigenvalue. It is proved in addition that bifurcation from the trivial solution takes place at all \({\lambda_n}\) ’s. Similar results are obtained in the sublinear case 1 < q < 2. In this case, bifurcation from infinity takes place in those \({\lambda_n}\) with odd multiplicity. Partial extensions of these features are shown in the nonlinear diffusion case \({p \neq 2}\) and related problems under spatially heterogeneous reactions are also addressed.     

An application of the maximum principle to describe the layer behavior of large solutions and related problems

This work is devoted to the analysis of the asymptotic behavior of positive solutions to some problems of variable exponent reaction-diffusion equations, when the boundary condition goes to infinity (large solutions). Specifically, we deal with the equations ??u = u ^p(x), ??u = ?m(x)u?+?a(x)u ^p(x) where a(x)??? a ₀ >?0, p(x)??? 1 in ??, and ??u = e ^p(x) where p(x)??? 0 in ??. In the first two cases p is allowed to take the value 1 in a whole subdomain ${\Omega_c\subset \Omega}$ , while in the last case p can vanish in a whole subdomain ${\Omega_c\subset \Omega}$ . Special emphasis is put in the layer behavior of solutions on the interphase ?? _i :?= ??? _c ???. A similar study of the development of singularities in the solutions of several logistic equations is also performed. For example, we consider ???u = ?? m(x)u?a(x) u ^p(x) in ??, u = 0 on ???, being a(x) and p(x) as in the first problem. Positive solutions are shown to exist only when the parameter ?? lies in certain intervals: bifurcation from zero and from infinity arises when ?? approaches the boundary of those intervals. Such bifurcations together with the associated limit profiles are analyzed in detail. For the study of the layer behavior of solutions the introduction of a suitable variant of the well-known maximum principle is crucial.     

Antibacterial,Antioxidant and Binding Studies of Some Novel Diaryl Sulphide Derivatives

Abstract

A series of novel acyclic and cyclic diaryl sulphides was synthesized from 2,2′-dithiobenzoic acid. The various diaryl sulphides were characterized by use of spectral (IR, ¹H and ¹³C NMR, ESI/MS) and elemental analyses. The antimicrobial activities of the compounds were evaluated in terms of their minimum inhibition concentration (MIC) against a panel of clinical isolates bacteria and were found to possess only moderate antimicrobial activities. N,N′-Bis(2-hydroxyphenyl)-2,2′-thiodibenzamide (13), exhibiting a hydroxy group at the phenyl ring, was the most active antimicrobial agent within the series, with MIC values of 0.05 mg mL^–1 and 10 mg mL^–1 against Staphylococcus aureus and Bacillus cereus, respectively. The antioxidant efficiency of the diaryl sulphides was determined by 2,2-diphenyl-1-picrylhydrazyl (DPPH) scavenging activity with 13 being the most active compound. The interaction of 2,2′-thiodibenzanilide, N,N′-bis(2-methylphenyl)-2,2′-thiodibenzamide, and N,N′-bis(2-hydroxyphenyl)-2,2′-thiobenzamide with guanine, glutamic acid, and urea were studied quantitatively with binding constants ranging from 1 × 10³ M^?1 to 2.7 × 10⁴ M^?1.     

A modified electrode for the electrochemical detection of biogenic amines and their amino acid precursors separated by microchip capillary electrophoresis

The use of a mixed-valent ruthenium oxide/hexacyanoruthenate polymeric film electrochemically deposited onto glassy carbon electrodes is proposed here for the detection of biogenic amines and their amino acid precursors, following their separation by microchip capillary electrophoresis. The ability of this ruthenium coating to electrocatalyze the oxidation of aliphatic and heterocyclic amines, as well as their amino acid precursors, was checked by using ethanolamine, tryptamine and tryptophane as prototype compounds and adopting a 25 mM sulphuric acid as the electrolyte in the detection cell, where a constant potential of 1.05 V versus Ag/AgCl, 3 M KCl was applied to the modified working electrode. Optimization of parameters affecting both detection and separation steps led to satisfactory separations when performed by using a 20 mM phosphate running buffer (pH 2.5) and applying a high voltage of 2.5 kV both in the separation and in the electrokinetic injection (duration 4 s). The recorded peaks were characterized by good repeatability (RSD ≤ 3.6%), high sensitivity and a wide linear range. Detection limits of 23 μM (1.4 mg/L), 27 μM (4.3 mg/L) and 34 μM (6.8 mg/L) were inferred for ethanolamine, tryptamine and tryptophane, respectively. The approach proposed here was also applied for the analysis of some double malt dark beers spiked with a controlled amount of the analytes considered.     

Experimental determination and prediction of bilitranslocase transport activity

The transport activity of a membrane protein, bilitranslocase (T.C. # 2.A.65.1.1), which acts as a transporter of bilirubin from blood to liver cells, was experimentally determined for a large set of various endogenous compounds, drugs, purine and pyrimidine derivatives. On these grounds, the structure-activity models were developed following the OECD principles of QSAR models and their predictive ability for new chemicals was evaluated. The applicability domain of the models was estimated by Euclidean distances criteria according to the applied modeling method. The selection of the most influential structural variables was an important stage in the adopted modeling methodology. The interpretation of selected variables was performed in order to get an insight into the mechanism of transport through the cell membrane via bilitranslocase. Validation of the optimized models was performed by a previously determined validation set. The classification model was build to separate active from inactive compounds. The resulting accuracy, sensitivity, and specificity were 0.73, 0.89, and 0.64, respectively. Only active compounds were used to develop a predictive model for bilitranslocase inhibition constants. The model showed good predictive ability; Root Mean Squared error of the validation set, RMS(V)=0.29 log units.