A rational approximate solution for generalized pantograph‐delay differential equations

In this paper, a new rational approximation based on a rational interpolation and collocation method is proposed for the solutions of generalized pantograph equations. A comprehensive error analysis is provided. The first part of the error analysis gives an upper bound for the absolute error. The second part is based on residual error procedure that estimates the absolute error. Some numerical examples are given to illustrate the method. The theoretical results support the numerical results. Copyright © 2015 John Wiley & Sons, Ltd.     

Spinor Frenet Equations in Three Dimensional Lie Groups

In this paper, we study spinor Frenet equations in three dimensional Lie groups with a bi-invariant metric. Also, we obtain spinor Frenet equations for some special cases of three dimensional Lie groups.     

Temperature-dependent optical properties of GaSe layered single crystals

Optical properties of GaSe single crystals have been investigated using temperature-dependent transmission and room temperature reflection measurements in the wavelength range of 380–1100 nm. The analysis of the absorption data at room temperature showed the existence of indirect transitions in the crystal with energy band gap of 1.98 eV. Temperature dependence of the transmission measurements revealed the shift of the absorption edge toward lower energy as temperature is increased from 10 to 280 K. The rate of change of the indirect band gap was found as γ = ?6.6 × 10^?4 eV/K from the analysis of experimental data under the light of theoretical relation giving the band gap energy as a function of temperature. The absolute zero value of the band gap energy and Debye temperature were calculated from the same analysis. The Wemple–DiDomenico single-effective-oscillator model applied to refractive index dispersion data was used to determine the oscillator energy, dispersion energy, oscillator strength and zero-frequency refractive index values.     

Simultaneous detection of L-glutamate and nitric oxide from adherently growing cells at known distance using disk shaped dual electrodes

An ex vivo system for simultaneous detection of nitric oxide (NO) and L-glutamate using integrated dual 250 microm platinum disk electrodes modified individually with suitable sensing chemistries has been developed. One of the sensors was coated with an electrocatalytic layer of Ni tetrasulfonate phthalocyanine tetrasodium salt (Ni-TSPc) covered by second layer of Nafion, which stabilises on the one hand the primary oxidation product NO(+) and prevents interferences from negatively charged compounds such as NO(2)(-). For glutamate determination, the second electrode was modified with a crosslinked redox hydrogel consisting of Os complex modified poly(vinylimidazol), glutamate oxidase and peroxidase. A manual x-y-z micromanipulator on top of an inverted optical microscope was used to position the dual electrode sensor at a defined distance of 5 microm from a cell population under visual control. C6 glioma cells were stimulated simultaneously with bradykinin or VEGF to release NO while KCl was used to invoke glutamate release. For evaluation of the glutamate sensors, in some experiments HN10 cells were used. To investigate the sensitivity and reliability of the system, several drugs were applied to the cells, e.g. Ca(2+)-channel inhibitors for testing Ca(2+)-dependence of the release of NO and glutamate, rotenone for inducing oxidative stress and glutamate antagonists for analysing glutamate release. With these drugs the NO and glutamate release was modulated in a similar way then expected from previously described systems or even in-vivo measurements. We therefore conclude that our system is suitable to analyse stress-induced mechanisms in cell lines.     

Regioselective synthesis of some novel pyrazoles,isoxazoles, pyrazolo[3,4‐d]pyridazines and isoxazolo[3,4‐d]pyridazines pendant to benzimidazole

2‐Acetyl‐1‐methyl‐1H‐benzimidazole reacts with dimethylformamide‐dimethyl‐acetal (DMF‐DMA) to afford the corresponding E‐1‐(1‐methyl‐1H‐benzimidazol‐2‐yl)‐3‐N,N‐dimethylaminoprop‐2‐enone. The latter compound reacts regioselectively with some nitrilimines and nitrile oxides to afford the corresponding pyrazole and isoxazole derivatives, respectively. These reaction products react with hydrazine hydrate to give the novel pyrazolo[3,4‐d]pyridazine and isoxazolo[3,4‐d]pyridazine derivatives, respectively.     

Application of artificial neural network to evaluation of dimensional accuracy of 3D-printed polylactic acid parts

Additive manufacturing (AM) has begun to replace traditional fabrication because of its advantages, such as easy manufacturing of parts with complex geometry, and mass production. The most important limitation of AM is that dimensional accuracy cannot be achieved in all parts. Dimensional accuracy is essential for high reliability, high performance, and useful final products. This study investigates the impact of printing parameters on the dimensional accuracy of samples fabricated through fused deposition modeling (FDM), an additive manufacturing (AM) method utilizing polylactic acid (PLA) material. The experimental design process was performed using Taguchi methodology. ANOVA was used to determine the most important parameter affecting accuracy. Based on experimental studies, the optimal printing parameters for parts are determined as follows: concentric infill pattern, 3 mm wall thickness, 70% infill density, and a layer thickness of 200 μm. Artificial neural network (ANN) was used in the evaluation and prediction of the results. The R-square (R²) performance evaluation criterion was above 95% from the ANN results. This value shows that the results are significant. The data acquired from this study may assist in identifying optimal parameters that contribute to the fabrication of samples with high dimensional accuracy using the FDM method.     

Influence of terminal substituent on non-linear S-shaped oligomers consisting of azobenzene moieties at the peripheral arm: Synthesis,characterisation and phase transition behaviour

A series of symmetrical S-shaped mesogens based on 4,4′-bis-(6-bromohexyloxy)biphenyl as a central unit containing two 2-{6-[4-(4-substitutedphenylazo)phenoxy]hexyloxy}phenol as side-chain groups has been successfully synthesised. The terminal substituent was varied from halogen (X = F, Cl, Br and I) to non-halogen (X = C₂H₅ and OC₂H₅). The oligomers with C₂H₅ and OC₂H₅ substituents exhibit predominantly the monotropic nematic (N) phase. The OC₂H₅-containing derivatives possess long-range stability of N phase than its C₂H₅-containing analogue in which it has small range of N phase stability. As for halogen-containing analogues, oligomer with F exhibits monotropic N phase whilst oligomers with Cl and Br exhibit monotropic N and smectic A (SmA) phases. In addition, homologue with Br shows additional phase which is smectic B (SmB) phase upon further cooling. However, the oligomers in which F, Cl and Br were substituted by I exhibits purely monotropic SmA and SmB phases. X-ray diffraction measurements reveal that the smectic phase is inclined to the monolayer structure.     

Molecular Docking and Dynamics Investigations for Identifying Potential Inhibitors of the 3-Chymotrypsin-like Protease of SARS-CoV-2: Repurposing of Approved Pyrimidonic Pharmaceuticals for COVID-19 Treatment

This study demonstrates the inhibitory effect of 42 pyrimidonic pharmaceuticals (PPs) on the 3-chymotrypsin-like protease of SARS-CoV-2 (3CL^pro) through molecular docking, molecular dynamics simulations, and free binding energies by means of molecular mechanics–Poisson Boltzmann surface area (MM-PBSA) and molecular mechanics–generalized Born surface area (MM-GBSA). Of these tested PPs, 11 drugs approved by the US Food and Drug Administration showed an excellent binding affinity to the catalytic residues of 3CL^pro of His41 and Cys145: uracil mustard, cytarabine, floxuridine, trifluridine, stavudine, lamivudine, zalcitabine, telbivudine, tipiracil, citicoline, and uridine triacetate. Their percentage of residues involved in binding at the active sites ranged from 56 to 100, and their binding affinities were in the range from −4.6 ± 0.14 to −7.0 ± 0.19 kcal/mol. The molecular dynamics as determined by a 200 ns simulation run of solvated docked complexes confirmed the stability of PP conformations that bound to the catalytic dyad and the active sites of 3CL^pro. The free energy of binding also demonstrates the stability of the PP–3CL^pro complexes. Citicoline and uridine triacetate showed free binding energies of −25.53 and −7.07 kcal/mol, respectively. Therefore, I recommend that they be repurposed for the fight against COVID-19, following proper experimental and clinical validation.     

New nonautonomous combined multi-wave solutions for ( $$\varvec{2+1}$$ 2 + 1 )-dimensional variable coefficients KdV equation

Nonlinear Dynamics - A variety of new types of nonautonomous combined multi-wave solutions of the ( $$2+1$$ )-dimensional variable coefficients KdV equation is derived by means of the generalized...     

Modelling of the blanking process of high-carbon steel using Lemaitre damage model

This paper presents a methodology to model a blanking process using a continuum mechanical damage model. A variant of the Lemaitre model, in which the quasi-unilateral conditions are taken into consideration to modify the damage behavior under compressive stress states, is selected as material model. S45C high-carbon steel is analyzed experimentally. To characterize the damage behavior of the material, notched round bar tensile tests with three different notch radii (6 mm, 10 mm, and 20 mm) using image analysis are performed. Using digital image processing, the strain at the deformation zone can be computed for the load–strain curves. Those curves are used as an objective function to determine the parameters of the Lemaitre damage model. The experimental results are compared with the results of the FE analysis of the tensile test. The identified model parameters are used in numerical investigations of axisymmetric blanking. The effect of the model's extension to quasi-unilateral damage evolution is discussed. The crack progress in high-carbon steel sheet during blanking and the final sheared part morphology are predicted and compared with the experimental results. Sheared surface and burr height obtained by the analysis coincide with the results of the blanking experiment.