Biorder Structure of the Bilinear Form Semigroup

If X and Y are two-finite dimensional vector spaces over a field K and B: X × Y K is a bilinear form, in [6], we have established that the set of adjoint pairs of linear maps forms a regular subsemigroup of L(X) × L(Y)^op. We call it the bilinear form semigroup. Here, we see that the maximal class in this semigroup is a Completely Simple Orthodox semigroup. Again, we note that given any idempotent. We can find a maximal covering chain containing it and ending at a maximal idempotent. We use this to obtain an estimate for the degeneracy of the bilinear form in terms of the rank of maximal idempotents.AMS Subject Classification (2000): 20M17, 15A04     

Solving nonlinear reaction–diffusion problem in electrostatic interaction with reaction-generated pH change on the kinetics of immobilized enzyme systems using Taylor series method

A mathematical model of electrostatic interaction with reaction-generated pH change on the kinetics of immobilized enzyme is discussed. The model involves the coupled system of non-linear reaction–diffusion equations of substrate and hydrogen ion. The non-linear term in this model is related to the Michaelis–Menten reaction of the substrate and non-Michaelis–Menten kinetics of hydrogen ion. The approximate analytical expression of concentration of substrate and hydrogen ion has been derived by solving the non-linear reactions using Taylor’s series method. Reaction rate and effectiveness factor are also reported. A comparison between the analytical approximation and numerical solution is also presented. The effects of external mass transfer coefficient and the electrostatic potential on the overall reaction rate were also discussed.

     

Investigations of gold nanoparticles-mediated carbon nanotube reinforced hydroxyapatite composite for bone regenerations

An excellent combination of biomaterials permits prompt features and high-throughput investigations in various fields, particularly in the biomedical applications. This article investigates the bone regeneration ability and compatibility of the Gold (Au) Nanoparticles (NPs) medicated carbon nanotube reinforced hydroxyapatite (HAP) composite. The morphologies of the synthesized Au NPs, HAP and HAP/CNT, and HAP/CNT-Au composites vary suggestively with modifying the components and the final composite showing as bone mimic extracellular matrix morphology. The structure, phase, and composition of the as-synthesized HAP were studied by FTIR, XRD, EDAX, and TEM techniques. The materials' biocompatibility was investigated in the Stimulated Body Fluid (SBF) solution, which resulted in the composite having good biocompatibility, bioactivity nature and hydroxyapatite layer formed on the composite surface. The composite shows good viability with Adipose Tissue-derived Stem Cells (ADSC) to cell growth and cell proliferation in the biological evaluation. It represented the composites having a good ability for cell formation development. Since the HAP/CNT-Au composite are useful in medicinal applications such as orthopedic and orthodontic repair/regenerations after the evaluations of animal and clinical investigations.     

Analytical expression of non-steady-state concentrations and current pertaining to compounds present in the enzyme membrane of biosensor

A mathematical model of trienzyme biosensor at an internal diffusion limitation for a non-steady-state condition has been developed. The model is based on diffusion equations containing a linear term related to Michaelis-Menten kinetics of the enzymatic reaction. Analytical expressions of concentrations and current of compounds in trienzyme membrane are derived. An excellent agreement with simulation data is noted. When time tends to infinity, the analytical expression of non-steady-state concentration and current approaches the steady-state value, thereby confirming the validity of the mathematical analysis. Furthermore, in this work we employ the complex inversion formula to solve the boundary value problem.     

Sol–gel synthesis and characterisation of nanoporous zirconium titanate coated on 316L SS for biomedical applications

In this study, the nanoporous zirconium titanate was prepared using sol–gel process and coated over 316L SS implants via dip-coating technique. XRD patterns of zirconium titanate are crystalline and orthorhombic in structure. FT-IR spectra showed a broad band between 3,500 and 3,300 cm⁻¹, which was assigned to fundamental stretching vibrations of hydroxyl groups. The set of overlapping peaks in the range of 810–520 cm⁻¹ are related to Zr–O and Zr–O–Ti groups. SEM-EDAX and TEM showed the surface morphology of coated zirconium titanate to be porous and uniform. Excellent adhesion of the coating to the substrate has been achieved. The contact angle value was found to be 12°. The coating acts as a barrier layer to the metallic implants and induces the formation of hydroxyapatite layer on the metal surfaces. These results revealed that the nano zirconium titanate coated 316L SS exhibit higher bioactivity compared to that of uncoated 316L SS.     

Two-dimensional DNA origami assemblies using a four-way connector

Two-dimensional self-assembly of DNA origami structures was carried out using a connector that has connection sites at all four edges. By utilizing this four-way connector, five and eight origami monomers were assembled to form a cruciate and a hollow square structure, respectively.     

An atomic gravitational wave interferometric sensor in low earth orbit (AGIS-LEO)

We propose an atom interferometer gravitational wave detector in low Earth orbit (AGIS-LEO). Gravitational waves can be observed by comparing a pair of atom interferometers separated by a 30 km baseline. In the proposed configuration, one or three of these interferometer pairs are simultaneously operated through the use of two or three satellites in formation flight. The three satellite configuration allows for the increased suppression of multiple noise sources and for the detection of stochastic gravitational wave signals. The mission will offer a strain sensitivity of ${<10^{-18}/\sqrt{{\rm Hz}}}$ in the 50mHz?C10Hz frequency range, providing access to a rich scientific region with substantial discovery potential. This band is not currently addressed with the LIGO, VIRGO, or LISA instruments. We analyze systematic backgrounds that are relevant to the mission and discuss how they can be mitigated at the required levels. Some of these effects do not appear to have been considered previously in the context of atom interferometry, and we therefore expect that our analysis will be broadly relevant to atom interferometric precision measurements. Finally, we present a brief conceptual overview of shorter-baseline $({\lesssim100\,{\rm m}})$ atom interferometer configurations that could be deployed as proof-of-principle instruments on the International Space Station (AGIS-ISS) or an independent satellite.     

Synthesis of functionalized diaryl alkanes from azines using Lewis acidic ionic liquids

Novel Lewis acidic ionic liquids containing thionyl cations and chlorozincate anions were obtained by one pot synthesis for the first time. This ionic liquid is used as catalyst for Friedel–Crafts alkylation of benzalazines and acetophenone azines for the synthesis of substituted diaryl alkanes. The products were characterized by elemental and spectral (FT-IR, 1H-NMR and 13C-NMR) analyses.