Fixed points of non-Newtonian contraction mappings on non-Newtonian metric spaces

The study of non-Newtonian calculi was started in 1972 by Grossman and Katz. These calculi provide an alternative to the classical calculus and they include the geometric, anageometric and bigeometric calculi, etc. Recently, Çakmak and Ba?ar (2002) have studied the concept of non-Newtonian metric. Also they have given the triangle and Minkowski’s inequalities in the sense of non-Newtonian calculus. In this paper, we introduce a fixed point theory by defining some topological structures of the relevant non-Newtonian metric space.     

Computing the integer programming gap

We determine the maximal gap between the optimal values of an integer program and its linear programming relaxation, where the matrix and cost function are fixed but the right hand side is unspecified. Our formula involves irreducible decomposition of monomial ideals. The gap can be computed in polynomial time when the dimension is fixed. Partially supported by the National Science Foundation (DMS-0200729).     

A new perspective to stress–strength models

The stress–strength models have been widely used for reliability design of systems. In these models the reliability is defined as the probability that the strength is larger than the stress. The analysis is then based on the binary reliability theory since there are two possible states for the system. In this paper, we study the stress–strength reliability in a different framework assigning more than two states to the system depending on the difference between strength and stress values. In other words, the stress–strength reliability is studied under multi-state system modeling. System state probabilities are evaluated and estimated under various assumptions on the system. The multicomponent form is also studied and some results are provided for large systems.     

Improvement of catalytic properties of Candida rugosa lipase by sol-gel encapsulation in the presence of magnetic calix[4]arene nanoparticles

Candida rugosa lipase (CRL) was encapsulated within a chemically inert sol-gel support prepared by polycondensation with tetraethoxysilane (TEOS) and octyltriethoxysilane (OTES) in the presence of N-methylglucamine based calix[4]arene magnetic nanoparticles. The results indicate that the magnetic calix[4]arene based encapsulated lipase particularly has shown high conversion and enantioselectivity. It has also been noticed that the magnetic calix[4]arene based encapsulated lipase has excellent enantioselectivity (E = 460) as compared to the free enzyme (E = 166) with an ee value of >98% for S-Naproxen.     

Catalytic effect of calix[n]arene based sol–gel encapsulated or covalent immobilized lipases on enantioselective hydrolysis of (R/S)-naproxen methyl ester

In this paper the catalytic performance of the immobilized lipases was investigated in the presence of calixarene based polymers using different immobilization techniques. For this reason, Candida rugosa lipase was encapsulated in sol–gel matrices using alkoxysilane precursors and calix[n]arene based silica polymers as additives. The hydrolytic activities of encapsulated lipases were evaluated and compared with the free lipase and covalently immobilized lipases (CnP-L). These encapsulated lipases were also used in the kinetic resolution of the R/S-Naproxen methyl ester. The results indicated that the C6P encapsulated lipase has significantly higher conversion and enantioselectivity as compared to the free lipase; other encapsulated lipases and CnP-L. The optimal pH and temperature region of the C6P encapsulated lipase in the kinetic resolution of the R/S-naproxen methyl ester were 7.0 and 55?°C. Nevertheless, the encapsulated lipases have good stability, adaptability and reusability in comparison with the free enzyme.     

Consistent empirical physical formula construction for recoil energy distribution in HPGe detectors by using artificial neural networks

The gamma-ray tracking technique is a highly efficient detection method in experimental nuclear structure physics. On the basis of this method, two gamma-ray tracking arrays, AGATA in Europe and GRETA in the USA, are currently being tested. The interactions of neutrons in these detectors lead to an unwanted background in the gamma-ray spectra. Thus, the interaction points of neutrons in these detectors have to be determined in the gamma-ray tracking process in order to improve photo-peak efficiencies and peak-to-total ratios of the gamma-ray peaks. In this paper, the recoil energy distributions of germanium nuclei due to inelastic scatterings of 1–5 MeV neutrons were first obtained by simulation experiments. Secondly, as a novel approach, for these highly nonlinear detector responses of recoiling germanium nuclei, consistent empirical physical formulas (EPFs) were constructed by appropriate feedforward neural networks (LFNNs). The LFNN-EPFs are of explicit mathematical functional form. Therefore, the LFNN-EPFs can be used to derive further physical functions which could be potentially relevant for the determination of neutron interactions in gamma-ray tracking process.     

LC-DAD-ESI-MS/MS-based phenolic profiling of St John’s Wort Teas and their antioxidant activity: Eliciting infusion induced changes

Infusion-induced changes in the phenolics, antioxidant and colour propeties of St John’s wort (genus, Hypericum; specie, Hypericum perforatum L.) teas were studied for the first time. SJW teas prepared as three different infusions and coded as three (3?min), six (6?min) and twelve minutes (12?min). Investigation of phenolic compounds were performed by LC-DAD-ESI-MS/MS. A total of 18 phenolics including six chlorogenic acids, three phenolic acids, seven flavonoids and two naphtodianthrones were detected. It is worth noting that the phenolic profiles of St John’s wort teas were similar. However, the quantities of phenolic compounds individually and totally changed significantly for different infusion times. The highest total concentration was detected in 12?min (60.03?mg/L), followed by 6?min (54.81?mg/L) and 3?min (33.07?mg/L). The main difference for different infusion times was the hyperoside found as the most abundant phenolic only in 3?min samples. However, for 6?min and 12?minin infusions, chlorogenic acid was the most dominant phenolic compound. Similar to phenolics, antioxidant capacity of tea infusions showed an increasing trend with the extension of infusion time.     

Coumarin Based Highly Selective “off-on-off” Type Novel Fluorescent Sensor for Cu<Superscript>2+</Superscript> and S<Superscript>2−</Superscript> in Aqueous Solution

Solvent free synthesis of 6,7-dihydroxy-3-(3-chlorophenyl) coumarin (CFHC) was designed and obtained by the interaction of 2-(2,4,5-trimethoxyphenyl)-1-(3-chlorophenyl)acrylonitrile with pyridinium hydrochloride in the presence of silica gel by using microwave irradiation. The characterization of CFHC was confirmed by FT-IR, ¹H, ¹³C, ¹³C–APT and 2D HETCOR spectroscopy methods. The optical behavior of CFHC towards metal ions was investigated by UV-visible and fluorescence spectroscopy. CFHC showed “on–off” type fluorescence response towards Cu²⁺ with high selectivity in aqueous solution (CH₃CN/H₂O, 9/1, v/v). Once binding with Cu²⁺, CFHC-Cu²⁺ complex also displayed high selectivity for sulfide, resulting in “off–on” type sensing of sulfide anion.

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Graphical abstract Visual fluorescence changes upon addition of various metal ions (5.0 eq.) to CFHC in CH₃CN/H₂O (90:10, v/v) under UV excitation (365 nm)

     

Linear stability analysis in compressible, flat-plate boundary-layers

The stability problem of two-dimensional compressible flat-plate boundary layers is handled using the linear stability theory. The stability equations obtained from three-dimensional compressible Navier–Stokes equations are solved simultaneously with two-dimensional mean flow equations, using an efficient shoot-search technique for adiabatic wall condition. In the analysis, a wide range of Mach numbers extending well into the hypersonic range are considered for the mean flow, whereas both two- and three-dimensional disturbances are taken into account for the perturbation flow. All fluid properties, including the Prandtl number, are taken as temperature-dependent. The results of the analysis ascertain the presence of the second mode of instability (Mack mode), in addition to the first mode related to the Tollmien–Schlichting mode present in incompressible flows. The effect of reference temperature on stability characteristics is also studied. The results of the analysis reveal that the stability characteristics remain almost unchanged for the most unstable wave direction for Mach numbers above 4.0. The obtained results are compared with existing numerical and experimental data in the literature, yielding encouraging agreement both qualitatively and quantitatively.