On some generalizations of certain retarded nonlinear integral inequalities with iterated integrals and an application in retarded differential equation

AbstractIn this paper, we investigate some new nonlinear retarded integral inequalities of Gronwall–Bellman–Pachpatte type. These inequalities generalize some former famous inequalities and can be used as handy tools to study the qualitative as well as the quantitative properties of solutions of some nonlinear retarded differential and integral equations. An application is also presented to illustrate the usefulness of some of our results in estimation of solution of certain retarded nonlinear differential equations with the initial conditions

Therapeutic Effect of Curcumin, Ginger and Tamarind on Oral and Paraoral Tissues: (Histological Overview)

Background: Biocompatible substances from plant origin have been more in focus in contemporary dentistry. Aim: This review, aimed to highpoint the influence of curcumin, ginger and tamarind on different oral and paraoral tissues from histological point of view. Material and methods: A narrative review was carried out based on publications in PubMed, google and Scopus database. The documents published up to 2021 were included. The research was based on inclusion criteria of 89 studies.Results: Curcumin inhibits alveolar bone resorption, reduces inflammatory cell infiltration, aids in epithelial regeneration and improves salivary glands architecture. Ginger was found to be beneficial in re-organization of periodontal ligaments, reducing inflammatory cells and osteoclasts differentiation, as well as restoring mucosal and salivary glands configuration. On the other hand, tamarind is a potent anti-inflammatory agent in periodontitis, enhances collagen synthesis and fibroblasts proliferation, acts as a matrix for hydroxyapatite crystals growth and aids in regaining of tongue papillae. However, it may be an underlying cause for oral submucous fibrosis.Conclusions: Dental applications of curcumin, ginger and tamarind are based on their anti-inflammatory and anti-oxidant effects. Curcumin is valuable in treatment of periodontitis and wound healing. Though, ginger has regenerative ability on various tissues. Limited studies are available concerning the effect of tamarind on oral tissues

Evaluation of Biological Control Potential for Different Trichoderma Strains Against Root-Knot Nematode Meloidogyne Javanica

Twenty strains of four Trichoderma species (Trichoderma harzianum, Trichoderma viride, Trichoderma koningii and Trichoderma asperellum) were evaluated for its potential to control the root-knot nematode Meloidogyne javanica. Culture filtrates from Trichoderma strains were tested in 24-well tissue culture plates for effects on Meloidogyne javanica. Chitwood egg hatch and mobility of hatched second-stage juveniles (J2) were evaluated, all the twenty Trichoderma strains showed the ability to colonize M. javanica separated eggs and second-stage juveniles (J2) in sterile in vitro assays. T. asperellum possess the strongest egg-parasitic ability and very effective against 2nd stage larvae of M. javanica. In this investigation, randomly amplified polymorphic DNA (RAPD) markers was used to estimate the genetic variations between four strains of Trichoderma asperellum (KC898190, KC898191, KC898192 and KC898193) which were previously isolated from the rhizospheres of different plants growing in Fayoum Governorate, Egypt as a new strain of T. asperellum in Egypt. RAPD assay using 6 random primers identified T. asperellum strains with 5 specific unique markers

Finite-Volume Spectra of the Lee-Yang Model

We consider the non-unitary Lee-Yang minimal model ${\cal M}(2,5)$ in three different finite geometries: (i) on the interval with integrable boundary conditions labelled by the Kac labels $(r,s)=(1,1),(1,2)$, (ii) on the circle with periodic boundary conditions and (iii) on the periodic circle including an integrable purely transmitting defect. We apply $\varphi_{1,3}$ integrable perturbations on the boundary and on the defect and describe the flow of the spectrum. Adding a $\Phi_{1,3}$ integrable perturbation to move off-criticality in the bulk, we determine the finite size spectrum of the massive scattering theory in the three geometries via Thermodynamic Bethe Ansatz (TBA) equations. We derive these integral equations for all excitations by solving, in the continuum scaling limit, the TBA functional equations satisfied by the transfer matrices of the associated $A_{4}$ RSOS lattice model of Forrester and Baxter in Regime III. The excitations are classified in terms of $(m,n)$ systems. The excited state TBA equations agree with the previously conjectured equations in the boundary and periodic cases. In the defect case, new TBA equations confirm previously conjectured transmission factors.Comment: LateX, 42 pages with 22 eps figure

Thermophoresis for characterizing biomolecular interaction

The study of biomolecular interactions is crucial to get more insight into the biological system. The interactions of protein-protein, protein-nucleic acids, protein-sugars, nucleic acid-nucleic acids and proteinsmall molecules are supporting therapeutics and technological developments. Recently, the development in a large number of analytical techniques for characterizing biomolecular interactions reflect the promising research investments in this field. In this review, microscale thermophoresis technology (MST) is presented as an analytical technique for characterizing biomolecular interactions. Recent years have seen much progress and several applications established. MST is a powerful technique in quantitation of binding events based on the movement of molecules in microscopic temperature gradient. Simplicity, free solutions analysis, low sample volume, short analysis time, and immobilization free are the MST advantages over other competitive techniques. A wide range of studies in biomolecular interactions have been successfully carried out using MST, which tend to the versatility of the technique to use in screening binding events in order to save time, cost and obtained high data qualit

2-[(2-Meth­oxy­eth­yl)sulfan­yl]-4-(2-methyl­prop­yl)-6-oxo-1,6-dihydro­pyrimidine-5-carbonitrile

In the title compound, C12H17N3O2S, the 4-methyl-2-methyl­sulfanyl-6-oxo-1,6-dihydro­pyrimidine-5-carbonitrile part of the mol­ecule is almost planar (r.m.s deviation = 0.062 Å). In the crystal, mol­ecules form centrosymmetric dimers via pairs of N—H⋯O hydrogen bonds

1-[(Cyclo­propyl­meth­oxy)meth­yl]-5-ethyl-6-(4-methyl­benzyl)-1,2,3,4-tetra­hydro­pyrimidine-2,4-dione

The pyrimidine ring in the title compound, C19H24N2O3, is nearly planar (r.m.s. deviation = 0.008 Å); the C atom at the 5-position deviates by 0.054 (3) Å from the mean plane and the C atom at the 6-position by 0.006 (3) Å in the opposite direction. The benzene ring is approximately perpendicular to the pyrimidine ring [dihedral angle = 83.90 (10)°]. The amino group is hydrogen-bond donor to the exocyclic O atom at the 2-position of an adjacent mol­ecule, the hydrogen bond generating an inversion dimer. The cyclo­propyl ring is disordered over two sets of sites with the major component having 71.5 (4)% occupancy

Dynamic Hardy type inequalities via alpha-conformable derivatives on time scales

We prove new Hardy-type $\alpha$-conformable dynamic inequalities on time scales. Our results are proved by using Keller's chain rule, the integration by parts formula, and the dynamic H\"{o}lder inequality on time scales. When $\alpha=1$, then we obtain some well-known time-scale inequalities due to Hardy. As special cases, we obtain new continuous, discrete, and quantum inequalities.Comment: 27 page

Comparing monolithic and fused core HPLC columns for fast chromatographic analysis of fat soluble vitamins

HPLC stationary phases of monolithic and fused core type can be used to achieve fast chromatographic separation as an alternative to UPLC. In this study, monolithic and fused core stationary phases are compared for fast separation of four fat-soluble vitamins. Three new methods on the first and second generation monolithic silica RP-18e columns and a fused core pentafluoro-phenyl propyl column were developed. Application of three fused core columns offered comparable separations of retinyl palmitate, DL-α-tocopheryl acetate, cholecalciferol and menadione in terms of elution speed and separation efficiency. Separation was achieved in approx. 5 min with good resolution (Rs >5) and precision (RSD ≤ 0.6 %). Monolithic columns showed, however, a higher number of theoretical plates, better precision and lower column backpressure than the fused core column. The three developed methods were successfully applied to separate and quantitate fat-soluble vitamins in commercial products

6-(3,5-Dimethyl­benz­yl)-5-ethyl-1-[(3-phenyl­prop­oxy)meth­yl]-1,2,3,4-tetra­hydro­pyrimidine-2,4-dione

The pyrimidine ring of the title compound, C25H30N2O3, is approximately planar (r.m.s. deviation = 0.003 Å); the C atom at the 5-position deviates by 0.012 (3) Å from the mean plane and the C atom at the 6-position by 0.038 (3) Å. In the mol­ecule, the pyrimidine ring is oriented at 86.72 (9) and 59.75 (9)° with respect to the two benzene rings, and the two benzene rings are inclined to each other at 58.35 (9)°. In the crystal, the amino group is hydrogen-bond donor to the exocyclic O atom at the 4-position of an adjacent mol­ecule, the hydrogen bond generating an inversion dimer