Existence Results for Periodic Solutions of Nonautonomous Second-Order Differential Systems with $(q,p)$-Laplacian

In this paper, we consider the existence for periodic solutions of nonautonomous second-order differential systems with $(q, p)$-Laplacian by using the least action principle and the minimax methods.     

A numerical approach for a crack problem by Gauss–Chebyshev quadrature

In this paper, a problem of a crack in an orthotropic strip is studied under plane strain conditions. It is assumed that normal displacements and shear stresses do not act on neither of the boundaries of the strip. Cauchy-type singular integral equation for the crack problem is derived by using the theory of plane elasticity and the Fourier transformation technique. A quadrature collocation approach is adopted for the numerical solutions of the singular integral equation. The effect of relative thickness and mechanical properties of strip on Mode I stress intensity factors (SIFs) are examined under different loading conditions. Some sample results are given for SIFs; also, material orthotropy and geometrical effects are discussed in detail.     

Boundedness of Sublinear Operators and Commutators on Generalized Morrey Spaces

In this paper the authors study the boundedness for a large class of sublinear operators \({T_{\alpha}, \alpha \in [0,n)}\) generated by Calderón–Zygmund operators (α = 0) and generated by Riesz potential operator (α > 0) on generalized Morrey spaces \({M_{p,\varphi}}\) . As an application of the above result, the boundeness of the commutator of sublinear operators \({T_{b,\alpha}, \alpha \in [0,n)}\) on generalized Morrey spaces is also obtained. In the case \({b \in BMO}\) and T _b,α is a sublinear operator, we find the sufficient conditions on the pair \({(\varphi_1,\varphi_2)}\) which ensures the boundedness of the operators \({T_{b,\alpha}, \alpha \in [0,n)}\) from one generalized Morrey space \({M_{p,\varphi_1}}\) to another \({M_{q,\varphi_2}}\) with 1/p ? 1/q = α/n. In all the cases the conditions for the boundedness are given in terms of Zygmund-type integral inequalities on \({(\varphi_1,\varphi_2)}\) , which do not assume any assumption on monotonicity of \({\varphi_1, \, \varphi_2}\) in r. Conditions of these theorems are satisfied by many important operators in analysis, in particular, Littlewood–Paley operator, Marcinkiewicz operator and Bochner–Riesz operator.     

Ultrasound-assisted rapid synthesis of <Emphasis Type=Italic>β</Emphasis>-aminoketones with direct-type catalytic Mannich reaction using bismuth(III) triflate in aqueous media at room temperature

An innovative, powerful, efficient and relatively rapid method was developed to synthesise various β-aminoketone derivatives from cyclohexanone, substituted aromatic amines and aromatic or hetero-aromatic aldehydes via ultrasound-assisted direct-type catalytic Mannich reaction using bismuth(III) triflate in water. Good yields of the desired β-aminoketones were obtained at room temperature by ultrasound-assisted reaction within 1–2 h. The major advantages of the proposed method are undemanding conditions, easy operation, low toxicity, shorter reaction time, anti selectivity and higher yields in comparison with conventional methods.     

The spectrum of eigenparameter-dependent discrete Sturm-Liouville equations

Let us consider the boundary value problem (BVP) for the discrete Sturm-Liouville equation

     

Background defining during the imine formation reaction in FT-IR liquid cell

Imine formation is a very important chemical reaction because of its relevance to biological process. Therefore, it is crucial to follow whole reaction process in detail. The current work performed to monitor the whole imination reaction in real time in liquid cell by FT-IR spectroscopy. The complex spectral futures due to solvent, unreacted reagents, acid catalysis and other additives are eliminated by defining a background at the beginning or at any time during the reaction. This procedure also makes it possible to monitor the changes in the concentration of each component in the liquid cell. The consumption of the functional groups of the reagents results in absorbance due to the direct difference spectra while the appearance of functional groups is monitored as percentage transmittance. The concentration changes in the cell arising from the reaction gives the product spectra without having to isolate it from the mixture. It is also possible to see the intermediates appearing and disappearing during the reaction. This report also illustrates a brief application of the technique by time dependence of the peak highs in absorption (ABS) mode.     

Magnetic trajectories in three-dimensional Lie groups

We study magnetic trajectories in Lie groups equipped with bi-invariant Riemannian metric. We define the Lorentz force of a magnetic field in a Lie group G, and then, we give the Lorentz force equation for the associated magnetic trajectories that are curves in G. When the manifold is a Lie group G equipped with bi-invariant Riemannian metric, we derive differential equation system that characterizes magnetic flow associated with the Killing magnetic curves with regard to the Lie reduction of the curve γ in G.     

Analysis of enzymopathies in the human red blood cells by constraint-based stoichiometric modeling approaches

The human red blood cell (RBC) metabolism is investigated by calculating steady state fluxes using constraint-based stoichiometric modeling approaches. For the normal RBC metabolism, flux balance analysis (FBA) is performed via optimization of various alternative objective functions, and the maximization of production of ATP and NADPH is found to be the primary objective of the RBC metabolism. FBA and two novel approaches, minimization of metabolic adjustment (MOMA) and regulatory on-off minimization (ROOM), which can describe the behavior of the metabolic networks in case of enzymopathies, are applied to observe the relative changes in the flux distribution of the deficient network. The deficiencies in several enzymes in RBC metabolism are investigated and the flux distributions are compared with the non-deficient FBA distribution to elucidate the metabolic changes in response to enzymopathies. It is found that the metabolism is mostly affected by the glucose-6-phosphate dehydrogenase (G6PDH) and phosphoglycerate kinase (PGK) enzymopathies, whereas the effects of the deficiency in DPGM on the metabolism are negligible. These stoichiometric modeling results are found to be in accordance with the experimental findings in the literature related to metabolic behavior of the human red blood cells, showing that human RBC metabolism can be modeled stoichiometrically.     

Tritium activity levels in drinking water of Adana,Turkey

Tritium activity in potable drinking water samples from Adana city were measured using liquid scintillation counting after distillation procedure. The results exposed that the activity concentrations of the tritium measured in one-third of these samples were lower than minimum detectable activity which has a value of 2 Bq/L for counting time of 1,500 min. However, the maximum and mean value of the tritium activity was found to be 9.1 Bq/L (77.3 TU) and 7.0 Bq/l (59.4 TU), respectively. These values were substantially below the 100 Bq/L which is normative limit in Turkey for waters intended for human consumption. The highest values of annual effective dose received by infants, children and adults due to measured tritium activity were estimated as 0.041, 0.057 and 0.120 μSv/y, respectively.