On physical analysis of entropy measures for sodium oxide via statistical models

This study delves into a comprehensive physical analysis of entropy measures applied to sodium oxide ${\text{Na}}_2\text{O}$. A key idea in information theory and thermodynamics, entropy is essential to comprehending the stability of a system. The study clarifies the intricate relationships and physical properties of ${\text{Na}}_2\text{O}$ by combining theoretical analysis with statistical methods, providing important knowledge for material design and industrial operations. In a chemical graph, atoms are shown by vertices while their bonding are illustrated by edges. Sodium oxide is a major contributor to manufacture glass, it also has potential applications in ${\text{CO}}_2$ sequestration, transparent materials, biomedical devices and nano grating glass. A topological index is a relationship between the molecular graph and its topology. We have computed various graph entropies based on different topological indices of chemical graph of sodium oxide. Further we have integrated these graph entropies with distinct thermodynamical measures of sodium oxide by developing mathematical models between both quantities. We have developed these mathematical frameworks in MATLAB. All the models are selected relying on the least mean squared error or sum of squared error.     

Design of a Simple Integrated Coupler for SPP Excitation in a Dielectric Coated Ag Thin Film

A simple integrated coupler is proposed for the efficient excitation of surface plasmon polariton （SPP） mode in a thin metal film. The SPP mode is generated in a single Ag-dielectric interface by the incident field and coupled with an Ag thin film. The coupling efficiency at different wavelengths using two different dielectrics, gallium lanthanum sulfide （GLS） and aluminum gallium arsenide （AIGaAs） is calculated by analyzing the SPP propagation dynamics with the finite difference time domain method. A maximum coupling efficiency of 70~ is obtained at a wavelength of 46Ohm when GLS is used, whereas the corresponding value obtained for A1GaAs is 60~o at 56Onto. The proposed structure can be used to excite SPPs in a nano-thin film from an external bulky source and is easier to fabricate since a single interface metal-dielectric configuration is used to excite the metal-thin film.     

Measurement of ablative laser propulsion parameters for aluminum, Co–Ni ferrite and polyurethane polymer

Laser ablation propulsion is a form of beam-powered propulsion in which a pulsed laser ablates a target material thus producing thrust. We report in this work the measurements of various parameters related to laser-induced micropropulsion in toluene diisocyanate-based polyurethane polymer, aluminum and Co–Ni ferrite. The targets were irradiated by a Q-switched pulsed Nd–YAG laser at 1064 nm (pulse duration 5 ns) under atmospheric conditions. A contact-free optical triangulation method was used to measure the laser ablation induced thrust in the samples. The measurements and calculations depict that Co–Ni ferrite is better in terms of critical propulsion parameters C _m and I _sp. It has been observed that the propulsion parameters depend on the energy per pulse of the incident laser beam.     

Modified Spectrophotometric Method for the Determination of Some Important Antibiotics Through Charge - Transfere Complexation Reaction with Chloranil

Abstract

A new modified Spectrophotometric procedures are presented for the determination of three pharmaceutical antibiotic compounds through charge-transfere complexation reaction with chloranil. The complex shows an absorption mAxima at 550 nm, having a molar absorptivity coefficient of 5.55×10³,7.81×10³ and 1.38×10⁴ 1. mol^?1cm^?1 for ampicillin, amoxycillin and neomycin, respectively. Optimization of the reaction conditions has been investigated Obediance to Beer's law (40μg/ml) permitted the assay of thes drugs in its dosage forms A variety of pharmaceutical dosage forms containing ampicillin, amoxycillin and neomycin are successfully analysed by the proposed procedure.     

Stability analysis and observational measurement in 5-D Brans–Dicke cosmology

This Letter is a study of the effects of higher dimensional gravity and Brans–Dicke (BD) scalar field on cosmic acceleration in 5-D BD cosmological model. We assume a flat cosmological model in which the matter content of the universe is either cold dark matter or radiation. In a framework to study attractor solutions in the phase space we simultaneously constrain the model parameters with the observational data for distance modulus. The phase space analysis illustrates that the universe begins from an unstable state in the past and eventually reaches an asymptotically stable state (attractor). We examine the model by performing Hubble parameter test in addition to statefinder diagnosis. We also reconstruct the equation of state parameter, the scale factor in 3-D space and along extra dimension. The results show that due to the presence of extra dimension and Brans–Dicke scalar field in the model, the universe undergoes a period of acceleration.     

Modules with a“nice”endomorphism ring and a new characterization of semisimple modules and rings

In this work we introduce some classes of modules whose endomorphism rings have some of the properties of the endomorphism rings of vector spaces. Then we apply these notions to obtain new characterizations of semisimple rings and modules.     

On the h-triangles of sequentially (S r ) simplicial complexes via algebraic shifting

Recently, Haghighi, Terai, Yassemi, and Zaare-Nahandi introduced the notion of a sequentially (S _r ) simplicial complex. This notion gives a generalization of two properties for simplicial complexes: being sequentially Cohen–Macaulay and satisfying Serre’s condition (S _r ). Let Δ be a (d?1)-dimensional simplicial complex with Γ(Δ) as its algebraic shifting. Also let (h _i,j (Δ))_{0≤j≤i≤d} be the h-triangle of Δ and (h _i,j (Γ(Δ)))_{0≤j≤i≤d} be the h-triangle of Γ(Δ). In this paper, it is shown that for a Δ being sequentially (S _r ) and for every i and j with 0≤j≤i≤r?1, the equality h _i,j (Δ)=h _i,j (Γ(Δ)) holds true.     

The ADMB-KdV equation in a time-weighted space

This paper studies the ADM-BKdV equation. The associated initial value problem will be proved to be locally well-posed in anisotropic Sobolev spaces $H^{s_1,s_2}\left( \mathbb R ^2\right) $ for $s_1>-3/2,\,s_2>-1/2$ and $2s_1+4s_2>-1$ .     

A capacitive biosensor for detection of staphylococcal enterotoxin B

A sensitive method for the detection of staphylococcal enterotoxin B (SEB) using a flow-injection capacitive biosensor is presented. SEB was purified from a crude culture filtrate of Staphylococcus aureus through three chromatographic steps. The first two steps were based on ion-exchange chromatography, and the last step was carried out on a gel filtration column. The SEB recovery values after the purification stages were 88%, 74%, and 12%, respectively. A horseradish peroxidase labeled antistaphylococcal enterotoxin B was prepared by the periodate method and was further employed in a sandwich-enzyme-linked immunosorbent assay (ELISA) for the determination of SEB concentrations in different samples obtained during the processing of the crude filtrate. The capacitive biosensor could detect SEB concentrations as low as 0.3 pg ml⁻¹ with a linearity ranging from 2.8 pg ml⁻¹ to 2.8 ng ml⁻¹ under optimized conditions. The response time was about 10 min. A good agreement was achieved between the developed capacitive biosensor system and ELISA as a reference method for detection of SEB levels in different purification samples. The newly developed sensor has the benefits of simplicity, high sensitivity, and multiple use capability.     

BPS invariants for resolutions of polyhedral singularities

We study the BPS invariants of the preferred Calabi–Yau resolution of ADE polyhedral singularities ${\mathbb{C}^3/G}$ given by Nakamura’s G-Hilbert schemes. Genus 0 BPS invariants are defined by means of the moduli space of torsion sheaves as proposed by Katz (J Differ Geom 79(2):185–195, 2008). We show that these invariants are equal to half the number of certain positive roots of an ADE root system associated to G. This is in agreement with the prediction given in Bryan and Gholampour (Invent Math, in press) via Gromov–Witten theory.