Common fixed points of nonlinear hybrid mappings under strict contractions in semi-metric spaces

In this paper, we extend the notion of common property (E.A) to pairs of hybrid mappings defined on an arbitrary set with values in a semi-metric space and use it to prove some coincidence and common fixed point theorems in semi-metric (potent semi-metric) spaces under strict contractions. Our results generalize several previously known fixed point theorems of the existing literature.     

Stability of Bragg grating solitons in a semilinear dual-core system with cubic–quintic nonlinearity

The existence and stability of quiescent Bragg grating solitons in a dual-core fiber, where one core contains a Bragg grating with cubic–quintic nonlinearity, and the other is a linear are studied. The model admits two disjoint bandgaps when the relative group velocity in the linear core, c, is zero: one in the upper half and the other in the lower half of the system’s linear spectrum. In the general case (i.e., \(c\ne 0\)), a central gap (which is a genuine gap) is formed, while the lower and upper gaps overlap with one branch of continuous spectrum, and therefore, they are not genuine bandgaps. For quiescent solitons, exact analytical solutions are found in implicit form for \(c=0\). For nonzero c, soliton solutions are obtained numerically. The system supports two disjoint families (referred to as Type 1 and Type 2) of zero-velocity soliton solutions, separated by a border. Both Type 1 and Type 2 soliton solutions exist throughout the upper and lower gaps but not in the central gap. The stability of both soliton families is investigated by means of systematic numerical simulations. It is found that Type 2 solitons are always unstable and are destroyed upon propagation. On the other hand, unstable Type 1 solitons may either decay into radiation or radiate some energy and evolve into a moving Type 1 soliton. Also, in the case of Type 1 solitons, we have identified stable regions in the plane of quintic nonlinearity and frequency. The influence of coupling coefficient and the relative group velocity in the linear core on the stability of solitons are analyzed.     

Charge and size selective molecular transport by amphiphilic organic nanotubes

Amphiphilic constructs with accessible, nanometer-size cavities can enable selective encapsulation, separation, and purification of nanomaterials and biomacromolecules on a similar length scale. We have developed a new method for the fabrication of amphiphilic organic nanotubes from multicomponent bottlebrush copolymers with triblock terpolymer side chains. The obtained nanotubes were demonstrated to be very effective and highly selective carriers for positively charged molecules and nanometer-size macromolecules by means of liquid-liquid extractions. Unprecedented discrimination between dendrimers with about 2 nm size differential was achieved.     

Enhancing the Photo and Thermal Stability of Nicotine through Crystal Engineering with Gentisic Acid

The use of crystal engineering to convert liquids into crystalline solids remains a powerful method for inhibiting undesired degradation pathways. When nicotine, a liquid sensitive to both light and air, is combined with the GRAS-listed compound, gentisic acid, the resulting crystalline solid, exhibits enhanced photo and thermal stability. Despite a modest ΔT_m of 42.7 °C, the melting point of 155.9 °C for the nicotinium gentisate salt is the highest reported for nicotine-containing crystalline solids. An analysis of the crystal packing and thermodynamic properties provides context for the observed properties.     

On some imbedding relations between certain sequence spaces

We introduce a space of sequences l_p^l \ell_p^\lambda of nonabsolute type, which is a p-normed space and a BK-space in the cases of 0 < p < 1 and 1 ≤ p < ∞; respectively. Further, we deduce some imbedding relations and construct a basis for the space l_p^l \ell_p^\lambda , where 1 ≤ p < ∞.     

Investigating semiconductor layered systems of photonics

The structure of a heterostructures-based semiconductor laser is experimentally investigated by complex means involving systems of scanning electron microscopy, scanning probe microscopy, and Raman spectroscopy. The possibilities of high-resolution microscopy for diagnostics of layered microelectronic systems are demonstrated.     

Risk assessment,development and validation of a GC-ECD-based method for the quantification of cypermethrin from green pea

The present work describes the persistence, dissipation behaviour, half-life, risk assessment and novel gas chromatography method for the residue estimation of cypermethrin in green pea by spraying cypermethrin 10EC at 50 g a.i. ha⁻¹ at fruiting stage followed by another application at a 10 day interval. The sample extraction and cleanup was followed bya modified quick, easy, cheap, effective, rugged, and safe method, and the residues of cypermethrin were determined using a validated gas chromatography method. The initial deposits were found to be 1.21 mg kg⁻¹ following the application of insecticide at 50 g a.i. ha⁻¹. Cypermethrin residues declined to below the detection limit of 0.05 mg kg⁻¹ after 15 days at the recommended dosage. The half-life of cypermethrin was 2.66 days at 50 g a.i. ha⁻¹. For risk assessment studies, the waiting period of 15 days is recommended as safe for consumption for the insecticide. The GC-ECD method was validated according to the SANTE guidelines by various analytical parameters including linearity, accuracy, detection and quantification limits. The developed method is simple, selective and repeatable, and can be used for the standardization of pesticides on fruits and vegetables.     

Response Surface Methodology (RSM)-Based Optimization of Ultrasound-Assisted Extraction of Sennoside A,Sennoside B,Aloe-Emodin,Emodin, and Chrysophanol from Senna alexandrina (Aerial Parts): HPLC-UV and Antioxidant Analysis

In this study, ultrasound-assisted extraction conditions were optimized to maximize the yields of sennoside A, sennoside B, aloe-emodin, emodin, and chrysophanol from S. alexandrina (aerial parts). The three UAE factors, extraction temperature (S₁), extraction time (S₂), and liquid to solid ratio (S₃), were optimized using response surface methodology (RSM). A Box–Behnken design was used for experimental design and phytoconstituent analysis was performed using high-performance liquid chromatography-UV. The optimal extraction conditions were found to be a 64.2 °C extraction temperature, 52.1 min extraction time, and 25.2 mL/g liquid to solid ratio. The experimental values of sennoside A, sennoside B, aloe-emodin, emodin, and chrysophanol (2.237, 12.792, 2.457, 0.261, and 1.529%, respectively) agreed with those predicted (2.152, 12.031, 2.331, 0.214, and 1.411%, respectively) by RSM models, thus demonstrating the appropriateness of the model used and the accomplishment of RSM in optimizing the extraction conditions. Excellent antioxidant properties were exhibited by S. alexandrina methanol extract obtained using the optimized extraction conditions with a DPPH assay (IC50 = 59.7 ± 1.93, µg/mL) and ABTS method (47.2 ± 1.40, µg/mL) compared to standard ascorbic acid.     

Acid Gas Converting to Organosulfur and Hydrogen in Methanol Thiolation Using Alkali Promoted Catalysts: Case Study

Catalysis Surveys from Asia - An acid gas stream was utilized instead of pure H2S as feedstock in the methanol thiolation reaction with Alkali/W/γ-Al2O3 catalysts. The catalysts were...