New implementation of radial basis functions for solving Burgers‐Fisher equation

In this article, we consider the problem of solving Burgers‐Fisher equation. The approximate solution is found using the radial basis functions collocation method. Also for solving of the resulted nonlinear system of equations, we proposed a predictor corrector method based on the fixed point iterations. The numerical tests show that this method is accurate and efficient for finding a closed form approximation of the solution of nonlinear partial differential equations. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 28: 248–262, 2012     

Flexural sensitivity and resonance of cantilever micro-sensors based on nonlocal elasticity theory

Sensors based on microcantilevers, especially ones with uniform structure, have ultrahigh sensitivities. The normalized natural frequencies and the sensitivity of lateral vibration of an elastic microcantilever sensor in contact with a surface are derived analytically based on the Euler–Bernoulli beam theory by taking into account the small scale effect. The interaction of the sensor with the surface is modeled by linear springs, which restricts the results to experiments involving low-amplitude excitations. The results show that the normalized natural frequencies of nonlocal microcantilever are smaller than those for its local counterpart, especially for higher values of small scale parameters. Also, each mode has a different sensitivity to variations in surface stiffness. Moreover, the most sensitivity is observed at the first mode of vibration. When the nonlocal effect is not taken into account, the natural frequencies and the sensitivity of the microcantilever in contact with the surface are compared with those obtained in previous study without considering the nonlocal effect.     

BTZ black holes in massive gravity

We analyze certain aspects of BTZ black holes in massive theory of gravity. The black hole solution is obtained by using the Vainshtein and dRGT mechanism, which is asymptotically AdS with an electric charge. We study the Hawking radiation using the tunneling formalism as well as analyze the black hole chemistry for such system. Subsequently, we use the thermodynamic pressure-volume diagram to explore the efficiency of the Carnot heat engine for this system. Some of the important features arising from our solution include the non-existence of quantum effects, critical Van der Walls behaviour, thermal fluctuations and instabilities. Moreover, our solution violates the Reverse Isoperimetric Inequality and, thus, the black hole is super-entropic, perhaps which turns out to be the most interesting characteristics of the BTZ black hole in massive gravity.     

SPACES OF ANALYTIC FUNCTIONS REPRESENTED BY DIRICHLET SERIES OF TWO COMPLEX VARIABLES

We consider the space X of all analytic functions f(s1,s2)=∑∞m，n=1 amnexp(s1λm s2μn) of two complex variables s1 and s2,equipping it with the natural locally convex topology and using the growth parameter,the order of f as defined recently by the authors.Under this topology X becomes a Frechet space.Apart from finding the characterization of continuous linear functionals,linear transformation on X,we have obtained the necessary and sufficient conditions for a double sequence in X to be a proper bases.     

Design,synthesis, biological evaluation,and docking study of new acridine-9-carboxamide linked to 1,2,3-triazole derivatives as antidiabetic agents targeting α-glucosidase

A new series of acridine-9-carboxamide-1,2,3-triazole derivatives 7a-m were designed, synthesized, and evaluated as novel α-glucosidase inhibitors. Acridine-9-carboxamide-1,2,3-triazole scaffold has been designed by combination of effective moieties from potent α-glucosidase inhibitors. Most of the synthesized compounds were more potent than standard inhibitor acarbose. Among the title compounds, the most potent compounds were compounds 7j , 7k , and 7a with IC₅₀ values of 120.2 ± 1.0, 151.1 ± 1.4, and 157.6 ± 1.6 μM, respectively (IC₅₀ value of acarbose = 750.0 ± 10.0 μM). Docking study of the most potent compounds demonstrated that these compounds formed stable complexes with α-glucosidase active site. Anti-α-amylase assay of compounds 7j , 7k , and 7a was performed and no activity was observed. in vitro cytotoxicity assay of the latter compounds revealed that these compounds were not cytotoxic toward human normal (HDF) and cancer (MCF-7) cell lines. ADME and toxicity prediction of compounds 7j , 7k , and 7a were also performed.     

Reconfigurable T-junction DNA Origami

DNA self-assembly allows the construction of nanometre-scale structures and devices. Structures with thousands of unique components are routinely assembled in good yield. Experimental progress has been rapid, based largely on empirical design rules. Herein, we demonstrate a DNA origami technique designed as a model system with which to explore the mechanism of assembly. The origami fold is controlled through single-stranded loops embedded in a double-stranded DNA template and is programmed by a set of double-stranded linkers that specify pairwise interactions between loop sequences. Assembly is via T-junctions formed by hybridization of single-stranded overhangs on the linkers with the loops. The sequence of loops on the template and the set of interaction rules embodied in the linkers can be reconfigured with ease. We show that a set of just two interaction rules can be used to assemble simple T-junction origami motifs and that assembly can be performed at room temperature.     

Nano‐structured gemini‐based supramolecular solvent for the microextraction of cyhalothrin and fenvalerate

A novel supramolecular solvent‐based microextraction followed by high‐performance liquid chromatography with ultraviolet detection method has been developed for the extraction and determination of two pyrethroid analytes, cyhalothrin and fenvalerate, in water and soil samples. The liquid–liquid‐phase separation of surfactants has been used in analytical extraction. The surfactant‐rich phase is a nano‐structured liquid, recently named as a supramolecular solvent, generated from the amphiphiles. The alkyl carboxylic acid based supramolecular solvents were introduced before. Coacervates made up of gemini surfactant, consisting of two amphiphilic moieties, were first used as solvent. The effective parameters on extraction (i.e., type of organic solvent, the amount of surfactant and volume of tetrahydrofuran, sample solution pH, salt addition, ultrasonic and centrifugation time) were investigated and optimized. Under the optimum conditions, preconcentration factors of 110 and 145 were obtained for the analytes. The linearity was 0.5–200.0 μg/L with the correlation of determination of (R²) ≥ 0.9984. The limit of detection of the method was (S/N = 3) 0.2 μg/L, and precisions in the range of 6.3–10.3% (RSDs, n = 5) were obtained. This method has been successfully applied to analyze real samples, and good recoveries in the range of 101.2–108.8% were obtained.