On the analysis of vibration equation involving a fractional derivative with Mittag-Leffler law

The present article deals with a fractional extension of the vibration equation for very large membranes with distinct special cases. The fractional derivative is considered in Atangana-Baleanu sense. A numerical algorithm based on homotopic technique is employed to examine the fractional vibration equation. The stability analysis is conducted for the suggested scheme. The maple software package is utilized for numerical simulation. In order to illustrate the effects of space, time, and order of Atangana-Baleanu derivative on the displacement, the outcomes of this study are demonstrated graphically. The results revel that the Atangana-Baleanu fractional derivative is very efficient in describing vibrations in large membranes.     

Regularized gap functions and error bounds for split mixed vector quasivariational inequality problems

In this paper, we consider a class of split mixed vector quasivariational inequality problems in real Hilbert spaces and establish new gap functions by using the method of the nonlinear scalarization function. Further, we obtain some error bounds for the underlying split mixed vector quasivariational inequality problems in terms of regularized gap functions. Finally, we give some examples to illustrate our results. The results obtained in this paper are new.     

Solitons in PT–symmetric optical lattices with spatially periodic modulation of nonlinearity

We study the existence and stability of solitons forming in PT–symmetric optical lattices with spatially periodic modulation of the local strength of the nonlinear media. We found that the spatial modulation of the nonlinearity significantly affects the stability of solitons in PT–symmetric optical lattices. With the decrease of the strength of nonlinear refractive index modulation, the soliton's stability domain increases, whereas with the increase of the period of nonlinear refractive index modulation, the corresponding soliton's stability range narrows. In addition, we also investigate the influence of variation of the amplitude of the linear PT–symmetric lattice potential on soliton dynamics, in the presence of spatially periodic modulation of nonlinearity.     

Arresting wave collapse by wave self-rectification

We put forward a mechanism for tailoring, and even arresting, the collapse of wave packets in nonlinear media, whose dynamics is governed by nonlocal two-dimensional nonlinear Schr?dinger-like equations. The key ingredient of the scheme is the self-generation of nonlocal nonlinearities mediated by wave rectification.     

A Fractional Schrödinger Equation and Its Solution

This paper presents a fractional Schrödinger equation and its solution. The fractional Schrödinger equation may be obtained using a fractional variational principle and a fractional Klein-Gordon equation; both methods are considered here. We extend the variational formulations for fractional discrete systems to fractional field systems defined in terms of Caputo derivatives to obtain the fractional Euler-Lagrange equations of motion. We present the Lagrangian for the fractional Schrödinger equation of order α. We also use a fractional Klein-Gordon equation to obtain the fractional Schrödinger equation which is the same as that obtained using the fractional variational principle. As an example, we consider the eigensolutions of a particle in an infinite potential well. The solutions are obtained in terms of the sines of the Mittag-Leffler function.     

Polyphenols from Dichrostachys cinerea Fruits Anti-Inflammatory,Analgesic, and Antioxidant Capacity in Freund’s Adjuvant-Induced Arthritic Rat Model

Dichrostachys cinerea (L.) Wigth & Arn. (DC) is widely used in traditional medicine against several inflammatory diseases, especially rheumatoid arthritis, because of its antioxidant and anti-inflammatory effects. This study aimed to characterize the polyphenol-rich DC fruit extracts and investigate the analgesic, anti-inflammatory, and antioxidant effects in a rat inflammation model induced by complete Freund’s adjuvant (CFA). Water and ethanolic extracts were characterized using liquid chromatography coupled with mass spectrometry (LC-MS), Fourier-transform infrared (FTIR) spectroscopy, and gas chromatography coupled with mass spectrometry (GC-MS). The polyphenol-rich extracts were administered in three different concentrations for 30 days. Pain threshold, thermal hyperalgesia, edema, and serum biomarkers specific to inflammatory processes or oxidative stress were evaluated. Both extracts were rich in polyphenolic compounds, mainly flavan-3-ols, proanthocyanidins, and flavone glycosides, which had important in vitro antioxidant capacity. DC fruit extracts administration had the maximum antinociceptive and anti-inflammatory effects after one day since the CFA injection and showed promising results for long-term use as well. The measurement of pro-inflammatory cytokines, cortisol, and oxidative stress parameters showed that DC extracts significantly reduced these parameters, being dose and extract-type dependent. These results showed potential anti-inflammatory, analgesic, and antioxidative properties and revealed the necessity of using a standardized polyphenolic DC extract to avoid result variability.     

Qualitative and quantitative analysis of gallic acid in Alchemilla vulgaris, Allium ursinum, Acorus calamus and Solidago virga-aurea by chip-electrospray ionization mass spectrometry and high performance liquid chromatography

This study presents the results obtained from qualitative and quantitative analysis of gallic acid from hydro-alcoholic extracts (methanol, ethanol) of plants from Plantae regnum. Plant qualitative analysis was performed using a novel mass spectrometric (MS) method based on fully automated chip-nanoelectrospray ionization (nanoESI) high capacity ion trap (HCT) while quantitative analysis was carried out by high performance liquid chromatography (HPLC). These methods were applied to Alchemilla vulgaris — common lady’s-mantle (aerial part), Allium ursinum — bear’s garlic (leaves), Acorus calamus — common sweet flag (roots), Solidago virga-aurea — goldenrod (aerial part). Obtained results indicated that methanol extracts (96%, 80%) have a gallic acid content ranging between 0.0011–0.0576 mg mL⁻¹ extract while the ethanol extracts (96%, 60%) exhibit a gallic acid concentration that varies between 0.0010–0.0182 mg mL⁻¹ extract.      

Homogenization heat treatment and segregation analysis of equiaxed CMSX-4 superalloy for gas turbine components

Journal of Thermal Analysis and Calorimetry - Two new zinc(II) coordination compounds have been synthesized by the reaction of diazine-ring containing Schiff bases di(2-pyridyl) ketone...     

Physical properties (thermal,thermomechanical, magnetic,and adhesive) of some smart orthodontic wires

Thermal, thermomechanical, and caloric properties of commercial orthodontic wires (produced by Natural Orthodontics Corp., USA) with cylindrical and rectangular geometry were studied. Depending on the applied forces, there were identified the range of elasticity, the elasticity–viscoelasticity coexistence domain and the domain in which a maximum force of 18 N is applied, for the orthodontic wires. When increasing the thickness of orthodontic wires, deformation decreases. The Controlled Force Module, in the tension mode, was used for the determination of the orthodontic wires elongation at application of the stretching forces from 0 to 13 N, at 35 °C, maintaining each static force value for 3 min. The increase in the cross-sectional area of the orthodontic wires disfavors the process of elongation of the sample, at the same applied static force. Using the Multi-Frequency–Strain–Stress modulus, in the tension mode, DMA cyclic heating–cooling measurements were performed. The measured physical quantities for orthodontic wires were Storage Modulus, Loss Modulus, Tanδ and Stiffness, at heating and cooling. Thus, the characteristic temperatures of the phase transitions (A_s, A_f, M_s, M_f), of all the studied orthodontic wires were identified. Also, the values of the elasticity modulus (Young’s Modulus) of the orthodontic wires were calculated at 35 °C. With the DSC Q200 device, using temperature-modulated differential scanning calorimetry method, a multi-step temperature variation program, was applied to a rectangular wire, in three stages (cooling–heating–cooling). Through the interpretation of heat fluxes (reversible, irreversible and total), the phase transitions in the formation of martensite, austenite, but also of the rombohedral phase (R-phase), were identified. Formations of austenite and martensite were also evidenced by the classical DSC method, but the classical DSC method also enabled the R-phase identification. The adherence of some food dyes on the orthodontic wires, as well as the modification of the surface roughness of the orthodontic wire after the deposition of the food dye, was also studied. By magnetic measurements, it was established that the orthodontic wires had paramagnetic properties at room temperature, and nitinol was a mixture of 49.2% austenite and 50.8% martensite.

     

Compatibility study of the acetylsalicylic acid with different solid dosage forms excipients

This study is part of a research project aimed to find and optimize methods by which drug-excipient compatibility can be reliably and quickly assessed. The objective of the present study was to evaluate the compatibility of the acetylsalicylic acid (ASA), an non-steroidal anti-inflammatory drug, with pharmaceutical excipients of common use including diluents, binders, disintegrants, lubricants and solubilising agents. In order to investigate the possible interactions between ASA and eleven excipients differential scanning calorimetry (DSC) and thermogravimetry/derivative thermogravimetry analysis completed by Fourier transform infrared spectroscopy (FT-IR) and X-ray powder diffraction were used for compatibility study. The DSC has proven to be, among the selected analytical techniques, the most sensitive and specific in assessing the compatibility. The samples, as physical mixtures, were prepared by mixing the analyte and excipients in a proportion of 1:1 (w:w). On the basis of thermal results (especially DSC), confirmed by FT-IR and X-ray analysis, a possible chemical interaction was found between the ASA with polyvinylpyrrolidone K30 (PVP) and magnesium stearate, respectively a possible physical interaction with colloidal silicon dioxide and stearic acid (Ac. St.).