In 2010, Long and Zeng introduced a new generalization of the Bernstein polynomials that depends on a parameter  and called -Bernstein polynomials. After that, in 2018, Lain and Zhou studied the uniform convergence for these -polynomials and obtained a Voronovaskaja-type asymptotic formula in ordinary approximation. This paper studies the convergence theorem and gives two Voronovaskaja-type asymptotic formulas of the sequence of -Bernstein polynomials in both ordinary and simultaneous approximations. For this purpose, we discuss the possibility of finding the recurrence relations of the -th order moment for these polynomials and evaluate the values of -Bernstein for the functions ,  is a non-negative integer

      Some cases of common fixed point theory for classes of generalized nonexpansive maps are studied. Also, we show that the Picard-Mann scheme can be employed to approximate the unique solution of a mixed-type Volterra-Fredholm functional nonlinear integral equation.

Many approaches have been developed over time to counter the bioavailability limitations of poorly soluble drugs. With advances in nanotechnology in recent decades, this issue has been approached through the formulation of drugs as nanocrystals. Nanocrystals consist of pure drug(s) and a minimum of surface active agent(s) required for stabilization. They are carrier-free submicron colloidal drug delivery systems with a mean particle size typically in the range of 200 - 500 nm. By reducing particle size to nanoscale, the surface area available for dissolution is increased, and thus bioavailability is enhanced. Drug nanocrystals constitute a versatile formulation approach to enhance the pharmacokinetic and pharmacodynamic properties of poorly

Two samples of (Ag NPs-zeolite) nanocomposite thin films have been prepared by easy hydrothermal method for 4 hours and 8 hours inside the hydrothermal autoclave at temperatures of 100°C. The two samples were used in a photoelectrochemical cell as a photocatalyst inside a cell consisting of three electrodes: the working electrode photoanode (AgNPs-zeolite), platinum as a cathode electrode, and Ag/AgCl as a reference electrode, to study the performance of AgNPs-zeolite under dark current and 473 nm laser light for water splitting. The results show the high performance of an eight-hour sample with high crystallinity compared with a four-hour sample as a reliable photocatalyst to generate hydrogen for renewable energies.

Titanium alloy (Ti-6Al-4V) samples were nitrided in low pressure (1.3, 3 mbar) dc-glow discharge plasmas of nitrogen. The treating time was 5, 10 and 15 hour and the temperatures range of the samples during the nitriding process was close to 800oC. The obtained microstructures of the nitride layers were studied by x-ray diffraction and optical microscopy. The ε –Ti2N, ζ-Ti3N3-x and η-Ti3N2-x.phases were formed and addition to the solid solution of nitrogen in titanium, α (Ti,N). Micro hardness measurements exhibit an increment for the Ti-alloy specimens which nitrided at 800oC for 10 and 15h.Corrosion measurements were obtained for the Ti-6Al-4V alloy in Ringer solution after plasma nitriding. The clear improving in the corrosion r

Colloidal crystals (opals) made of close-packed polymethylmethacrylate (PMMA) were fabricated and grown by Template-Directed methods to obtain porous materials with well-ordered periodicity and interconnected pore systems to manufacture photonic crystals. Opals were made from aqueous suspensions of monodisperse PMMA spheres with diameters between 280 and 415 nm. SEM confirmed the PMMA spheres crystallized uniformly in a face-centered cubic (FCC) array. Optical properties of synthesized pores PMMA were characterized by UV–Visible spectroscopy. It shows that the colloidal crystals possess pseudo photonic band gaps in the visible region. A combination of Bragg’s law of diffraction and Snell’s law of refraction were used to calculate t

Polyaniline (PANI) and Ag/PANI nanocomposite thin films have prepared by microwave induced plasma. The Ag powder of average particle size of 50 nm, were used to prepare Ag/PANI nanocomposite thin films. The Ag/PANI nanocomposite thin films prepared by polymerization in plasma and characterized by UV-VIS, FTIR, AFM and SEM to study the effect of silver nanoparticles on the optical properties, morphology and structure of the thin films. The optical properties studies showed that the energy band gap of the Ag/PANI (5%wt silver) decreased from 3.6 to 3.2 eV, where the substrate location varied from 4.4 to 3.4 cm from the axis of the cylindrical plasma chamber. Also the optical energy gap decreased systematically from 3.3 to 3 eV with increas

Flexible joint robot (FJR) manipulators can offer many attractive features over rigid manipulators, including light weight, safe operation, and high power efficiency. However, the tracking control of the FJR is challenging due to its inherent problems, such as underactuation, coupling, nonlinearities, uncertainties, and unknown external disturbances. In this article, a terminal sliding mode control (TSMC) is proposed for the FJR system to guarantee the finite-time convergence of the systems output, and to achieve the total robustness against the lumped disturbance and estimation error. By using two coordinate transformations, the FJR dynamics is turned into a canonical form. A cascaded finite-time sliding mode observer (CFTSMO) is construct

This paper presents designing an adaptive state feedback controller (ASFC) for a magnetic levitation system (MLS), which is an unstable system and has high nonlinearity and represents a challenging control problem. First, a nonadaptive state feedback controller (SFC) is designed by linearization about a selected equilibrium point and designing a SFC by pole-placement method to achieve maximum overshoot of 1.5% and settling time of 1s (5% criterion). When the operating point changes, the designed controller can no longer achieve the design specifications, since it is designed based on a linearization about a different operating point. This gives rise to utilizing the adaptive control scheme to parameterize the state feedback controll

The preparation of the title compound, C₂₆H₂₅N, was achieved by the condensation of an ethanolic mixture of benzaldehyde, cyclohexanone and ammonium acetate in a 2:1:1 molar ratio. There are two crystallographically independent molecules in the asymmetric unit. The two cyclohexyl rings adopt ananti-envelope conformation with the benzyl moiety adopting acisconformation with respect to the nitrogen atom of the phenanthridine segment. In the crystal, molecules are linked through C—H...N interactions into hydrogen-bonded chains that are further arranged into distinct layers by weak offset π–π interactions.