Solitary wave solutions for some nonlinear time-fractional partial differential equations

In this paper, we have studied the hybrid projective synchronisation for incommensurate, integer and commensurate fractional-order financial systems with unknown disturbance. To tackle the problem of unknown bounded disturbance, fractional-order disturbance observer is designed to approximate the unknown disturbance. Further, we have introduced simple sliding mode surface and designed adaptive sliding mode controllers incorporating with the designed fractional-order disturbance observer to achieve a bounded hybrid projective synchronisation between two identical fractional-order financial model with different initial conditions. It is shown that the slave system with disturbance can be synchronised with the projection of the master system generated through state transformation. Simulation results are presented to ensure the validity and effectiveness of the proposed sliding mode control scheme in the presence of external bounded unknown disturbance. Also, synchronisation error for commensurate, integer and incommensurate fractional-order financial systems is studied in numerical simulation.     

Two validated chromatographic determinations of an antifungal drug,its toxic impurities and degradation product: A comparative study

Tolnaftate, a thionoester anti‐fungal drug, was subjected to alkaline hydrolysis to produce methyl(m‐tolyl)carbamic acid and β ‐naphthol (tolnaftate impurity A). N‐Methyl‐m‐toluidine, tolnaftate impurity D, was synthesized and structurally elucidated along with tolnaftate alkaline degradation products using IR, H¹NMR and MS. Two stability‐indicating HPTLC and RP‐HPLC methods were developed and validated, for the first time, for determination of tolnaftate, its alkaline degradation products and toxic impurities in the presence of methyl paraben, as a preservative in Tinea Cure^® cream. The proposed HPTLC method depended on separation of the studied components on TLC silica gel F₂₅₄ plates using hexane–glacial acetic acid (8:2, v/v) as a developing system and scanning wavelength of 230 nm. The proposed RP‐HPLC method was based on separation of the five components on an Eclipse plus C₁₈ column. The mobile phase used was acetonitrile–water containing 1% ammonium formate (40:60, v/v), with a flow rate of 1 mL/min and detection wavelength of 230 nm. The proposed methods allowed the assay of tolnaftate toxic impurities, β ‐naphthol and N‐methyl‐m‐toluidine, down to 2%, allowing tracing of β ‐naphthol that could be absorbed by the skin causing systemic toxic effects, unlike tolnaftate, indicating the high significance of such determination. International Conference on Harmonization guidelines were followed for validation.     

Comprehensive Metabolite Profiling in Genetic Resources of Garlic (Allium sativum L.) Collected from Different Geographical Regions

Garlic (Allium sativum) is the second most important Allium crop that has been used as a vegetable and condiment from ancient times due to its characteristic flavor and taste. Although garlic is a sterile plant that reproduces vegetatively through cloves, garlic shows high biodiversity, as well as phenotypic plasticity and environmental adaptation capacity. To determine the possible mechanism underlying this phenomenon and to provide new genetic materials for the development of a novel garlic cultivar with useful agronomic traits, the metabolic profiles in the leaf tissue of 30 garlic accessions collected from different geographical regions, with a special focus on the Asian region, were investigated using LC/MS. In addition, the total saponin and fructan contents in the roots and cloves of the investigated garlic accessions were also evaluated. Total saponin and fructan contents did not separate the garlic accessions based on their geographical origin, implying that saponin and fructan contents were clone-specific and agroclimatic changes have affected the quantitative and qualitative levels of saponins in garlic over a long history of cultivation. Principal component analysis (PCA) and dendrogram clustering of the LC/MS-based metabolite profiling showed two major clusters. Specifically, many Japanese and Central Asia accessions were grouped in cluster I and showed high accumulations of flavonol glucosides, alliin, and methiin. On the other hand, garlic accessions grouped in cluster II exhibited a high accumulation of anthocyanin glucosides and amino acids. Although most of the accessions were not separated based on country of origin, the Central Asia accessions were clustered in one group, implying that these accessions exhibited distinct metabolic profiles. The present study provides useful information that can be used for germplasm selection and the development of new garlic varieties with beneficial biotic and abiotic stress-adaptive traits.     

A Comprehensive Review on Therapeutic Perspectives of Phytosterols in Insulin Resistance: A Mechanistic Approach

Natural products in the form of functional foods have become increasingly popular due to their protective effects against life-threatening diseases, low risk of adverse effects, affordability, and accessibility. Plant components such as phytosterol, in particular, have drawn a lot of press recently due to a link between their consumption and a modest incidence of global problems, such as Type 2 Diabetes mellitus (T2DM), cancer, and cardiovascular disease. In the management of diet-related metabolic diseases, such as T2DM and cardiovascular disorders, these plant-based functional foods and nutritional supplements have unquestionably led the market in terms of cost-effectiveness, therapeutic efficacy, and safety. Diabetes mellitus is a metabolic disorder categoriszed by high blood sugar and insulin resistance, which influence major metabolic organs, such as the liver, adipose tissue, and skeletal muscle. These chronic hyperglycemia fallouts result in decreased glucose consumption by body cells, increased fat mobilisation from fat storage cells, and protein depletion in human tissues, keeping the tissues in a state of crisis. In addition, functional foods such as phytosterols improve the body’s healing process from these crises by promoting a proper physiological metabolism and cellular activities. They are plant-derived steroid molecules having structure and function similar to cholesterol, which is found in vegetables, grains, nuts, olive oil, wood pulp, legumes, cereals, and leaves, and are abundant in nature, along with phytosterol derivatives. The most copious phytosterols seen in the human diet are sitosterol, stigmasterol, and campesterol, which can be found in free form, as fatty acid/cinnamic acid esters or as glycosides processed by pancreatic enzymes. Accumulating evidence reveals that phytosterols and diets enriched with them can control glucose and lipid metabolism, as well as insulin resistance. Despite this, few studies on the advantages of sterol control in diabetes care have been published. As a basis, the primary objective of this review is to convey extensive updated information on the possibility of managing diabetes and associated complications with sterol-rich foods in molecular aspects.     

Analyses of axisymmetric waves in layered piezoelectric rods and their composites

An exact treatment of the propagation of axisymmetric waves in coaxial anisotropic assembly of piezoelectric rod systems is presented. The rod system consists of an arbitrary number of coaxial layers, each possessing transversely isotropic symmetry properties. The treatment, which is based on the transfer matrix technique, is capable of deriving the dispersion relations for a variety of situations. These include the case of a single rod system that is either embedded in an infinitely extended solid or fluid host or kept free. The procedure is also adapted to derive approximate solutions for the cases of a periodic fiber distribution in a matrix material, which model unidirectional fiber-reinforced composites. The results are numerically illustrated for a widely used piezoelectric-polymer composite. It is seen that piezoelectric coupling can significantly change the morphology of the dispersive behavior of the composite.     

On the moduli space of deformations of bihamiltonian hierarchies of hydrodynamic type

We investigate the deformation theory of the simplest bihamiltonian structure of hydrodynamic type, that of the dispersionless KdV hierarchy. We prove that all of its deformations are quasi-trivial in the sense of B. Dubrovin and Y. Zhang, that is, trivial after allowing transformations where the first partial derivative ∂u of the field is inverted. We reformulate the question about deformations as a question about the cohomology of a certain double complex, and calculate the appropriate cohomology group.     

Simulation of ion beam extraction and focusing system

The characteristics of ion beam extraction and focused to a volume as small as possible were investigated with the aid of computer code SIMION 3D version 7. This has been used to evaluate the extraction characteristics (accel-decel system) to generate an ion beam with low beam emittance and high brightness. The simulation process can provide a good study for optimizing the extraction and focusing system of the ion beam without any losses and transported to the required target. Also, a study of a simulation model for the extraction system of the ion source was used to describe the possible plasma boundary curvatures during the ion extraction that may be affected by the change in an extraction potential with a constant plasma density meniscus.     

Synthesis of Some Novel Heterocyclic Xylidinyl Amines and Carboxamides

The xylidines 1a , 1b undergo condensation with ethyl cyanoacetate 2 and ethyl benzoyl acetate 15 to afford the cyano acetanilides 3a , 3b and the β‐diketones 16a , 16b , respectively. Compounds 3a , 3b react with hydrazine and phenyl hydrazine to afford the azine‐bis derivatives 5a , 5b and 7a , 7b , whereas 16a , 16b react with the same reagents to afford the pyrazolyl amine derivatives 17a , 17b and 18a , 18b , respectively. Compounds 3a , 3b react also with dimethylformamide dimethylacetal to afford the enaminonitriles 8a , 8b , whereas 16a , 16b react with the same reagent to afford only the enaminone 19b . The enaminonitriles 8a , 8b react with hydrazine and phenyl hydrazine to afford also the azine‐bis derivatives 11a , 11b and 14a , 14b , respectively.