Energy level splitting of a 2D hydrogen atom with Rashba coupling in non-commutative space

We explore the non-commutative (NC) effects on the energy spectrum of a two-dimensional hydrogen atom. We consider a confined particle in a central potential and study the modified energy states of the hydrogen atom in both coordinates and momenta of non-commutativity spaces. By considering the Rashba interaction, we observe that the degeneracy of states can also be removed due to the spin of the particle in the presence of NC space. We obtain the upper bounds for both coordinates and momenta versions of NC parameters by the splitting of the energy levels in the hydrogen atom with Rashba coupling. Finally, we find a connection between the NC parameters and Lorentz violation parameters with the Rashba interaction.     

Electron energy spectrum in the field-ionized plasma

In this article, the effect of ionization on the energy spectrum of electrons within the interaction of a laser pulse with hydrogen atoms is investigated using particle-in-cell simulation codes. The results show that the behaviour of electrons' energy distribution function in the field-ionized plasma, which occurred due to the field ionization, compared with that in the pre-plasma strongly depends on the pulse shape. For short rise-time pulses (here 30 fs), due to the rapid enhancement of laser electric field, ionization occurs quickly, and as a result, there is not much difference in the electron energy in both the media. However, for pulses with rise time of 40 fs, in the pre-plasma state, the electron population reaches higher energies compared with the field-ionized plasma state. The main reason for this difference is the nonlinear wave breaking that happens earlier due to density inhomogeneity in the field-ionized plasma. On the other hand, at longer rise-time pulses (here 60 and 70 fs), electrons achieve higher energies in the field-ionized plasma than those in the case of pre-plasma. In this case, because of density fluctuations in the field-ionized plasma, the Raman backscattered radiations are seeded by a strong initial noise at the earlier times and the Mendonca condition for chaos threshold is met sooner. Therefore, the electrons gain more energy through the stochastic mechanism that is in agreement with chaotic nature of the motion.     

Approximate solutions in set-valued optimization problems with applications to maximal monotone operators

Positivity - This paper is devoted to the study of efficient elements for set-valued maps. We propose two new notions of relative weak $$\epsilon $$ -efficient element and strict relative weak...     

Green synthesis and chemical characterization of silver nanoparticles obtained using Allium saralicum aqueous extract and survey of in vitro antioxidant,cytotoxic, antibacterial and antifungal properties

Allium saralicum R.M. Fritsch has been used in Iranian traditional medicine as a remedial supplement for microbial diseases. This paper reports the green synthesis, chemical characterization and antioxidant, cytotoxic, antibacterial and antifungal properties of silver nanoparticles obtained using aqueous extract of A. saralicum leaves. In this synthesis, no surfactants or stabilizers were used. For characterization, UV–visible spectroscopy, transmission electron microscopy, X‐ray diffraction, energy‐dispersive X‐ray spectroscopy and field emission scanning electron microscopy were used. 2,2‐Diphenyl‐1‐picrylhydrazyl was used in experiments to assess the antioxidant potential of the silver nanoparticles, which revealed an impressive prevention in comparison with butylated hydroxytoluene. The synthesized silver nanoparticles at low doses (1–250 μg dl^?1) did not show marked cytotoxic activity (against cervical cancer cells (Hela), breast cancer cells (MCF‐7) and human embryonic kidney cells (HEK‐293)). Agar diffusion tests were applied to determine the antibacterial and antifungal characteristics. Compared with all standard antimicrobials, the silver nanoparticles showed higher antibacterial and antifungal activities (p ≤ 0.01). Also, the silver nanoparticles inhibited the growth of all bacteria and fungi at concentrations of 31–250 μg ml^?1, and destroyed them at concentrations of 31–500 μg ml^?1 (p ≤ 0.01). Because the silver nanoparticles obtained using aqueous extract of A. saralicum leaves have antioxidant, non‐cytotoxic, antifungal and antibacterial potentials, they can be used as a medical supplement or drug.     

Easy conversion of nitrogen‐rich silk cocoon biomass to magnetic nitrogen‐doped carbon nanomaterial for supporting of Palladium and its application

In this study, magnetic nitrogen‐doped carbon (MNC) was fabricated through facile carbonization and activation of natural silk cocoons containing nitrogen and then combined with Fe₃O₄ nanoparticles to create a good support material for palladium. Palladium immobilization on the support resulted in the formation of magnetic nitrogen‐doped carbon‐Pd (MNC‐Pd). The prepared heterogeneous catalyst was well characterized using FT‐IR, TGA, EDX, FE‐SEM, XRD, VSM, and ICP‐OES techniques. Thereafter, the synthesis of biaryl compounds was conducted to investigate the catalyst performance via the reaction of aryl halides and phenylboronic acid. Further, the catalyst could be used and recycled for six consecutive runs without any significant loss in its activity.     

Synthesis and photocatalytic activity assessing of the TiO<Subscript>2</Subscript> nanocomposites modified by some lanthanide ions and tin-derivative sandwich-type polyoxometalates

New nanocomposites containing sandwich-type polyoxometalate of [(PW₉O₃₄)₂(HOSn^IVOH)₃]^12? (P₂W₁₈Sn₃) loaded onto Ln-doped TiO₂ (Nd, Sm, Dy, Tb) nanoparticles were synthesized and their catalytic activities were assessed. The Ln–TiO₂ nanoparticles and Ln–TiO₂/P₂W₁₈Sn₃ nanocomposites were characterized by Fourier transform infrared spectroscopy (FT-IR), X-ray diffraction, field emission scanning electron microscope, energy dispersive analysis of X-rays spectra and diffuse reflectance spectra. The photocatalytic efficiency of the Ln–TiO₂ and Ln–TiO₂/P₂W₁₈Sn₃ were examined in the photodegradation of methyl orange and methylene blue solutions. It was revealed through different characterization techniques that the P₂W₁₈Sn₃ was successfully loaded on the lanthanide-doped anatase phase TiO₂ nanoparticles and the particles diameter were relatively 20–30 nanometers. It was revealed that doping by the lanthanide ions followed by loading of polyoxometalates improves the photocatalytic performance of TiO₂ effectively. The effects of operational parameters and the kinetics of photocatalytic degradation under UV light were discussed. The prepared nanocomposites were stable and could be easily separated from the reaction system.     

Guanidine Hydrochloride: A Highly Efficient Organocatalyst for the Synthesis of 12‐Aryl‐8,9,10,12‐tetrahydrobenzo[a]xanthene‐11‐ones Under Solvent‐Free Conditions

A new green protocol has been developed for the synthesis of 12‐aryl‐8,9,10,12‐tetrahydrobenzo[a]xanthen‐11‐ones using guanidine hydrochloride as an organocatalyst under solvent‐free conditions. Operational simplicity, mild reaction conditions, enhanced rates, high isolated yields of the pure products, and purification of products by nonchromatographic methods are significant advantages of the protocol presented here.