Kantorovich variant of a new kind of q‐Bernstein–Schurer operators

Ren and Zeng (2013) introduced a new kind of q‐Bernstein–Schurer operators and studied some approximation properties. Acu et al. (2016) defined the Durrmeyer modification of these operators and studied the rate of convergence and statistical approximation. The purpose of this paper is to introduce a Kantorovich modification of these operators by using q‐Riemann integral and investigate the rate of convergence by means of the Lipschitz class and the Peetre's K‐functional. Next, we introduce the bivariate case of q‐Bernstein–Schurer–Kantorovich operators and study the degree of approximation with the aid of the partial modulus continuity, Lipschitz space, and the Peetre's K‐functional. Finally, we define the generalized Boolean sum operators of the q‐Bernstein–Schurer–Kantorovich type and investigate the approximation of the Bögel continuous and Bögel differentiable functions by using the mixed modulus of smoothness. Furthermore, we illustrate the convergence of the operators considered in the paper for the univariate case and the associated generalized Boolean sum operators to certain functions by means of graphics using Maple algorithms. Copyright © 2017 John Wiley & Sons, Ltd.     

Photosynthetic,Biochemical and Secondary Metabolite Changes in a Medicinal Plant Chlorophytum borivillianum (Safed musli) against Low and High Doses of UV-B Radiation

Plants are inevitably grown in presence of sunlight, therefore bound to be exposed to natural UV-B radiation. Several studies have already been conducted with UV-B and medicinal plants and only few studies showed dose dependent variation. The present study aims to find out the variations and adaptation in Chlorophytum borivillianum under two different doses of UV-B radiation; ambient + low (3.2 kJm⁻² d⁻¹) and high (7.2 kJm⁻² d⁻¹) UV-B dose, denoted as LD and HD, respectively. Reduction in photosynthetic rate was higher at HD, while plants receiving LD displayed nonsignificant variation. During vegetative and reproductive stage, significant reduction (P ≤ 0.001) in stomatal conductance was obtained when exposed to HD-eUV-B. F_v/F_m showed more reductions in HD-eUV-B (12.6%) followed by LD-eUV-B (7.9%). Low and high doses of UV-B enhanced the anthocyanin content but the increase was significant in HD, indicates epidermal protection strategy by the plants. Under LD-eUV-B, the content of saponin, a major phytochemical constituent was enhanced by 26%. Phytochemical analysis of roots revealed reduction mostly in fatty acid components whereas the steroidal components (stigmasterol and sarsasapogenin) showed enhancement in response to LD. The study suggests the importance of LD-eUV-B in the stimulation of medicinal compounds in C. borivillianum.     

Dynamic responses of orthotropic plates under moving masses

Summary The problem considered is that of heavy masses moving on lightweight rectangular plates of orthotropic materials, slated for use in space structures. The dynamic equation of motion for orthotropic plates which contains singularities in both space and time variables is first presented. The response is expressed as a summation of double series of eigenfunctions. The equation of motion is transformed into an integro-differential equation for modal amplitudes using the Green's function. The Green's function is chosen to satisfy the initial conditions, the boundary conditions, and the transient conditions due to the moving masses. The solution series exhibits a good convergence. The effect of orthotropicity on natural frequencies and dynamic responses is demonstrated.

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Dynamische Antwort orthotroper Platten auf bewegte Massenpunkte

übersicht Behandelt wird die Bewegung von Massenpunkten auf rechteckigen Leichtbau-Platten aus orthotropem Werkstoff, die für Raumfahrtkonstruktionen vorgesehen sind. ZunÄchst wird die Bewegungsgleichung orthotroper Platten mit singulÄren Ausdrücken in den Raum- und Zeitkoordinaten angegeben. Die Antwort wird als Doppelsumme einer zweifachen Reihenentwicklung dargestellt und die Bewegungsgleichung mit Hilfe der Greenschen Funktion in eine Integro-Differentialgleichung für die Modalamplituden transformiert. Die Greensche Funktion ist so gewÄhlt, da\ sie die Anfangs- und Randbedingungen sowie die übergangsbedingungen unter der bewegten Masse erfüllt. Die Lösung durch Reihenentwicklung zeigt gute Konvergenz. Der Einflu\ der Orthotropie auf die Eigenfrequenzen und die dynamischen Antworten wird veranschaulicht.

     

Application of rainbow schlieren deflectometry for concentration measurements in an axisymmetric helium jet

 The rainbow schlieren deflectometry technique was used to measure oxygen concentrations in a laminar, isothermal helium jet discharged vertically into ambient air. The concentration distributions were inferred from the color schlieren image by taking into consideration the sampling interval and noise in measurements, especially near the jet center. Excellent quantitative agreement was reached between measurements from schlieren and a continuous sampling probe. This work demonstrates the capability of the schlieren technique for providing accurate, spatially-resolved, nonintrusive, full-field of view measurements of species concentration in an isothermal binary system. Because the basic quantity measured is the refractive index, the present schlieren technique can be extended for quantitative measurements of other scalar flow properties related to the refractive index. Received: 21 April 1997 / Accepted: 14 November 1997     

Integral equation formulation for buoyancy-driven convection problems

An integral equation formulation for buoyancy-driven convection problems is developed and illustrated. Buoyancy-driven convection in a bounded cylindrical geometry with a free surface is studied for a range of aspect ratios and Nusselt numbers. The critical Rayleigh number, the nature of the cellular motion, and the heat transfer enhancement are computed using linear theory. Green's functions are used to convert the linear problem into linear Fredholm integral equations. Theorems are proved which establish the properties of the eigenvalues and eigenfunctions of the linear integral operator which appears in these equations.     

Properties of vortices in the self-similar turbulent jet

Instantaneous, two-dimensional velocity measurements were conducted in the axial plane of a self-similar turbulent axisymmetric jet. The velocity fields were high-pass filtered to expose the vortical structures. An automated method was used to identify the radial and axial coordinates of the vortex centers and rotational sense, and to measure their size, circulation, vorticity, and energy. New insights into turbulent jets are obtained by plotting statistical distributions for vortex properties as functions of Reynolds number and radial position. While the probability of finding a vortex is uniform up to the edge of the jet, the strongest eddies in the high-pass filtered field occur near the jet axis. The average circulation is directly proportional to the vortex size. The Reynolds number strongly affects the average vorticity, circulation, and energy of the eddies. However, the normalized curves show a good collapse implying that the jet is indeed self-similar. Results for the left and right half-planes of the jet are also presented. Interestingly, we find that contrary to customary drawings of jet flows, a substantial number of both clockwise and counter-clockwise rotating eddies exist on both sides of the jet axis, with almost equal numbers of oppositely rotating vortices close to the jet axis. Further, the disparity in the number of oppositely rotating eddies in each half-plane increases with the eddy size. Nevertheless, these results are consistent with the well-known radial vorticity distribution of axisymmetric jets.     

In situ synthesis of Ag-SiO2 Janus particles with epoxy functionality for textile applications

A facile method for the synthesis of silver-silica（Ag-SiO₂） Janus particles with functionalities suitable for textile applications is reported.Silica nanoparticles prepared by the Stober method were functionalized with epoxy,amine,and thiol groups,which were confirmed by Fourier transform infrared analysis.The functionalized silica nanoparticles were used to produce Pickering emulsions,and the exposed surface was used for the attachment of silver nanoparticles（AgNPs） via the low-temperature chemical reduction method.The morphology and structure of the Ag-SiO₂ Janus particles were characterized by scanning electron microscopy,scanning transmission electron microscopy,high-resolution transmission electron microscopy,energy-dispersive X-ray analysis,and UV-vis spectroscopy.Because of their specific functionalities,these Ag-SiO₂ Janus particles are proposed for applications on textile substrates,as they can overcome several drawbacks of direct application of AgNPs on textiles,such as leaching,agglomeration,and instability during storage.     

Abnormal Nucleophilic Substitution on Methoxytropone Derivatives: Steric Strategy to Synthesize 5-Substituted Azulenes

Azulene is a non-alternant non-benzenoid aromatic system, and in turn, it possesses unusual photophysical properties. Azulene-based conjugated systems have received increasing interest in recent years as optoelectronic materials. Despite the routes available for the preparation of substituted azulene derivatives, there remain few methods that allow regioselective substitution on the seven-membered ring of azulenes due to the subtle reactivity difference among the various positions. This report explores the reactivity of substituted tropolones as the azulene precursors and also provides a new method to create 5-substituted azulenes. The reaction of cyanoacetate enolate with unsubstituted 2-methoxytropone affords azulene through the attack of the nucleophile on the C-2 center (normal pathway). We have observed that 3-substituted 2-methoxytropones undergo steric-guided nucleophilic addition at the C-7 center (abnormal pathway) to afford 5-substituted azulene derivatives. Based on this observation and DFT calculation, a new synthetic strategy is devised for the regioselective synthesis of 5-substituted multifunctional azulenes, which cannot be accessed by any other method.     

Induced twisted-grain-boundary phases in the binary mixtures of a cholesteric and a nematic compound

Thermodynamical, optical-texture and dielectric studies have been performed to study the phase diagram of the binary system of 5-cholesten-3β-ol-octanoate and 4-n-nonyloxybenzoic acid. It is observed that low concentrations of 5-cholesten-3β-ol-octanoate (2–30?mol?%) in 4-n-nonyloxybenzoic acid induce a mean-field phase diagram derived by Renn within the framework of the chiral Chen–Lubenski model. Various optical textures of the twisted-grain-boundary (TGB) phases under different conditions of molecular anchoring have been observed. Weak transitions related to the TGB phases have been detected by temperature dependent dielectric spectroscopy.     

Oxidative Esterification of Benzaldehyde and Deactivated Aromatic Aldehydes with N-Bromosuccinimide-pyridine

Whereas the oxidative esterification of benzaldehyde to methyl benzoate with N-bromosuccinimide (NBS)-pyridine requires dark conditions and 5 equivalents each of NBS and K₂CO₃ and gave only moderate yield (52%) of the product (McDonald et al. J. Org. Chem. 1989, 54, 1213), simple change of base to pyridine gave the desired product in 83% gas chromatographic yield with only 1 equivalent each of NBS and pyridine. Moreover, the reaction could be conducted without exclusion of light. Aromatic aldehydes bearing electron-withdrawing substituents at meta/para position yielded the corresponding methyl esters in still better yields.

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