Mexican hat wavelet transform of distributions

Theory of Weierstrass transform is exploited to derive many interesting new properties of the Mexican hat wavelet transform. A real inversion formula in the differential operator form for the Mexican hat wavelet transform is established. Mexican hat wavelet transform of distributions is defined and its properties are studied. An approximation property of the distributional wavelet transform is investigated which is supported by a nice example.     

K-Carrageenan Stimulates Pre-Osteoblast Proliferation and Osteogenic Differentiation: A Potential Factor for the Promotion of Bone Regeneration?

Current cell-based bone tissue regeneration strategies cannot cover large bone defects. K-carrageenan is a highly hydrophilic and biocompatible seaweed-derived sulfated polysaccharide, that has been proposed as a promising candidate for tissue engineering applications. Whether κ-carrageenan can be used to enhance bone regeneration is still unclear. In this study, we aimed to investigate whether κ-carrageenan has osteogenic potential by testing its effect on pre-osteoblast proliferation and osteogenic differentiation in vitro. Treatment with κ-carrageenan (0.5 and 2 mg/mL) increased both MC3T3-E1 pre-osteoblast adhesion and spreading at 1 h. K-carrageenan (0.125–2 mg/mL) dose-dependently increased pre-osteoblast proliferation and metabolic activity, with a maximum effect at 2 mg/mL at day three. K-carrageenan (0.5 and 2 mg/mL) increased osteogenic differentiation, as shown by enhanced alkaline phosphatase activity (1.8-fold increase at 2 mg/mL) at day four, and matrix mineralization (6.2-fold increase at 2 mg/mL) at day 21. K-carrageenan enhanced osteogenic gene expression (Opn, Dmp1, and Mepe) at day 14 and 21. In conclusion, κ-carrageenan promoted MC3T3-E1 pre-osteoblast adhesion and spreading, metabolic activity, proliferation, and osteogenic differentiation, suggesting that κ-carrageenan is a potential osteogenic inductive factor for clinical application to enhance bone regeneration.     

Gastroprotective Effects of Biological Macromolecule: Polysaccharides

The large molecular weight of the macromolecules sets them apart from all other components. This may range from 10 000 to over a million. While the molecular weight of other plant metabolites is seldom beyond 1000. Chemically, macromolecules are made up of long chains and little “building pieces,” which are joined covalently in a variety of ways. Biological macromolecules are large, naturally occurring cellular building blocks that play a range of crucial roles in the development and existence of living organisms. Biomacromolecules are essential in the biomedical field and other related professions. They feature a variety of beneficial properties, including excellent biodegradability, suitable mechanical strength, enhanced bioavailability, etc. They also have significant biocompatibility. They display a variety of biological characteristics, such as antimalignant, antidiabetic, antibacterial, antioxidant, and immunomodulatory. The use of essential carbohydrates including alginate, chitosan, pectin, starches, carrageenan, fucoidan, etc. is common in commercial applications. Natural substance-based pharmacotherapy is now considered to be a highly promising future alternative to conventional medicine. Along with proteins and polynucleotides, polysaccharide is a vital biomacromolecule that has a crucial function in the growth and expansion of living things. A crucial element of higher plants, cell membranes of animal, and cell walls of microbes is polysaccharide. It is intimately tied to physiological processes as well. The importance of polysaccharides as a significant class of bioactive natural compounds has received more attention recently. Numerous studies have shown that natural polysaccharides contain bioactivities, which have led to the use of polysaccharides in the treatment of illness. The many parts of the research findings on the bioactivities of polysaccharides in gastro-protection are included in this paper.     

Degeneracy in one dimension: Role of singular potentials

That the bound energy eigenstates of one-dimensional quantum systems can be degenerate in the presence of specific singular or supersingular potentials is demonstrated by choosing a family of bistable and other oscillators. Relevance of our study to spectroscopic observations is noted. Quasi-degeneracy is found even in the absence of any singularity in the potential and the importance of tunneling is highlighted in this context to analyze the general nature of such potentials leading to double degeneracy. Additionally, the case of spiked oscillators is discussed with particular reference to the “Klauder phenomenon,” revealing clearly that the mere presence of singularity in the potential is not a sufficient criterion for the occurrence of degeneracy. © 1996 John Wiley & Sons, Inc.     

Characteristics of alpha projectile fragments emission in interaction of nuclei with emulsion

The properties of the relativistic alpha fragments produced in interactions of ⁸⁴Kr at around 1 A GeV in nuclear emulsion are investigated. The experimental results are compared with the similar results obtained from various projectiles with emulsion interactions at different energies. The total, partial nuclear cross-sections and production rates of alpha fragmentation channels in relativistic nucleus-nucleus collisions and their dependence on the mass number and initial energy of the incident projectile nucleus are investigated. The yields of multiple alpha fragments emitted from the interactions of projectile nuclei with the nuclei of light, medium and heavy target groups of emulsion-detector are discussed and they indicate that the projectile-breakup mechanism seems to be free from the target mass number. It is found that the multiplicity distributions of alpha fragments are well described by the Koba-Nielsen-Olesen (KNO) scaling presentation. The mean multiplicities of the freshly produced or newly created charged secondary particles, normally known as shower and secondary particles associated with target in the events where the emission of alpha fragments were accompanied by heavy projectile fragments having Z ≥ 3 seem to be constant as the alpha fragments multiplicity increases, and exhibit a behavior independent of the alpha fragments multiplicity.     

NHC-catalysed diastereoselective synthesis of multifunctionalised piperidines via cascade reaction of enals with azalactones

NHC-catalysed azalactone ring-opening and piperidine ring-closing cascade with α,β-unsaturated aldehydes (enals) in a one-pot operation is reported. The present reaction cascade offers a convenient method for a highly diastereoselective synthesis of multifunctionalised piperidines in excellent yields under mild conditions.     

Magnetic, magnetocaloric, and magnetotransport properties of RCo1.8Mn0.2 (R=Er, Ho, Dy, and Tb) compounds

The magnetic, magnetocaloric, and magnetotransport properties of RCo_1.8Mn_0.2 (R=Er, Ho, Dy, and Tb) were studied by room temperature X-ray diffraction, magnetization, and resistivity measurements at a temperature interval of 5-400 K and magnetic fields up to 5 T. The Curie temperature of RCo₂ was found to increase significantly when 10% Mn was substituted for Co. The effective paramagnetic moments were found to be in reasonable agreement with their theoretical values. A large magnetoresistance (MR) of Δρ/ρ_o≈−13.5% for R=Ho at T≈153 K for ΔH=5 T has been observed. The maximum relative cooling capacities vary from 467 J/kg at low temperature for R=Er to 202 J/kg at the near room temperature for R=Tb.     

Direct synthesis of Poly(Ԑ-Caprolactone)-block-poly (glycidyl methacrylate) copolymer and its usage as a potential nano micelles carrier for hydrophobic drugs

Ring-opening (ROP) and enzymatic copolymerization (ECP) are among the most widely used approaches for synthesizing copolymers of polycaprolactone (PCL). It involves multiple-step reactions and the utilization of enzymes that make the process a lot more complicated, time consuming, and expensive. Atom transfer radical polymerization (ATRP) has been adopted to synthesize a novel amphiphilic copolymer in our study. The study presents a method to eliminate the ROP/ECP multiple steps in monomer polymerization thus making the process simpler and smoother. The synthesis of cationic polymer micelles copolymer of PCL-PGMA (polycaprolactone grafted poly glycidyl methacrylate) was carried out using direct functionalization of hydroxy group in crude PCL to achieve a higher degree of functionalization, i.e., 12.8% for macroinitiator. FTIR and ¹H-NMR confirmed the successful synthesis of the copolymer with better control over the molecular weight with a PDI (1.84). DSC and XRD results showed the reduction of crystallinity by 86.81%, making copolymer more compatible for drug delivery application. The synthesized copolymer was further converted to nano-micelles drug carrier having an average size of 96.08 ± 21.22 nm. The drug encapsulation efficiency achieved was 60.0 ± 1.7%, and nano-micelles rendered a slow and controlled release of naproxen with long-term storage stability.     

Esterification of butyric acid with n-butanol: Kinetic study using experimental data and modeling

Present study involves the investigation of the esterification kinetics between butyric acid and n-butanol. This reaction was conducted in a batch reactor, utilizing homogeneous methanesulfonic acid (MSA) catalyst. Response surface methodology (RSM) was conducted prior to the kinetic study using “Design Expert; version-11.0” for finding the causal factors influencing the conversion of butyric acid. Most important factors identified with their limits against conversions (during optimization of the process using RSM) were taken up to critically analyze the effect of them on butyric acid conversion. Concentration and activity-based model of the process were proposed assuming second order reversible reaction scheme using homogeneous MSA catalyst. During the study of non-ideal behavior of the system, UNIFAC model was adapted for assessing the activity coefficients of species present in equilibrated liquid phase. Experimental data were used to evaluate kinetic and thermodynamic parameters such as rate constants, activation energy, enthalpy, and entropy of the system. The endothermic nature of esterification was confirmed by positive value of enthalpy obtained. The effect of various levels of causal variables like temperature (60–90°C), catalyst concentration (0.5–1.5 wt.%), and molar ratio of n-butanol to butyric acid (1–3) on conversion kinetics of butyric acid was investigated during transient and equilibrium phase of the reaction. It has been observed that molar ratio of butanol to butyric acid has the highest influence on the conversion. The rate equation derived offered a kinetic and thermodynamic framework to the generated data. It also exhibits a notable degree of conformity of predicted data to the experimental ones and effectively characterizes the system across different reaction temperatures, reactant molar ratio, and catalyst concentration.