On the minimum degree,edge-connectivity and connectivity of power graphs of finite groups

In this paper, the minimum degree of power graphs of certain cyclic groups, abelian p-groups, dihedral groups and dicyclic groups are obtained. It is ascertained that the edge-connectivity and minimum degree of power graphs are equal, and consequently, the minimum disconnecting sets of power graphs of the aforementioned groups are determined. In order to investigate the equality of connectivity and minimum degree of power graphs, certain necessary conditions for finite groups and a necessary and su?cient condition for finite cyclic groups are obtained. Moreover, the equality is discussed for the power graphs of abelian p-groups, dihedral groups and dicyclic groups.     

A relativistic core-envelope model on pseudospheroidal space-time

A core-envelope model for superdense matter distribution with the feature- core consisting of anisotropic fluid distribution and envelope with isotropic fluid distribution is reported on the background of pseudospheroidal space-time. The physical plausibility of the model is examined analytically and numerically.     

The Cauchy Problem for Non-linear Higher Order Hartree Type Equation in Modulation Spaces

Journal of Fourier Analysis and Applications - We study the Cauchy problem for Hartree equation with cubic convolution nonlinearity $$F(u) = (K \star |u|^{2k})u$$ under a specified condition on...     

FTIR spectra of plasticized high molecular weight PVC–LiCF3SO3 electrolytes

Fourier transform infrared spectroscopy studies have been conducted to investigate the interaction among components in a system of high molecular weight polyvinylchloride (PVC)–lithium trifluoromethanesulfonate (LiCF₃SO₃) incorporated with different type of plasticizers, namely, ethylene carbonate (EC), propylene carbonate (PC), and dibutylphthalate (DBP). Interaction between PVC and LiCF₃SO₃ was confirmed by C–H rocking mode at 1,255 cm⁻¹ for PVC shift to 1,252 cm⁻¹ in PVC–LiCF₃SO₃. The plasticizers’ carbonyl (C=O) oxygen atom which carries lone pair electrons interact with Li⁺ of LiCF₃SO₃ and methine hydrogen of PVC in LiCF₃SO₃–plasticizer system and PVC–plasticizer system, respectively. Changes in peaks assigned to 1,264 cm⁻¹ (ν _as(SO₃)), 1,033 cm⁻¹ (ν _s(SO₃)), 1,181 cm⁻¹ (ν _as(CF₃)), 1,230 cm⁻¹ (ν _s(CF₃)), 765 cm⁻¹ (δ _s(CF₃)), 644 cm⁻¹ (δ _s(SO₃)), 578 cm⁻¹ (δ _as(CF₃)), and 519 cm⁻¹ (δ _as(SO₃)) indicate the occurrence of complexation in the PVC–LiCF₃SO₃ system, LiCF₃SO₃–plasticizer system, and PVC–LiCF₃SO₃–plasticizer system.     

Statistics and schools

This paper considers the place of statistics in school, putting forward the view that it should be seen as an interdisciplinary subject, relevant to all pupils, rather than solely as a separate specialism for a minority of children.     

Ionic liquid enhanced magnesium-based polymer electrolytes for electrical double-layer capacitors

This paper describes the preparation and characterization of poly(vinyl alcohol) (PVA)-added ionic liquid-based ion conductors. The polymer electrolyte is incorporated with magnesium triflate [Mg(CF₃SO₃)₂ or MgTf] as salt and 1-butyl-3-methylimidazolium bromide (BmImBr) as ionic liquid. Differential scanning calorimetry (DSC) is carried out to investigate the glass transition temperature which is used to study the plasticizing effect of the ionic liquid. The highest conducting ionic liquid-based polymer electrolyte is used to fabricate electrical double-layer capacitors (EDLC). The electrochemical potential window is evaluated using linear sweep voltammetry (LSV). The electrochemical capacitance of the EDLC is evaluated through cyclic voltammetry (CV) and galvanostatic charge–discharge (GCD). The electrochemical potential window of ionic liquid-added polymer electrolyte is extended from 1.35 to 2.6 V. Cyclic voltammetry (CV) proves the improvement in specific capacitance of the electrical double-layer capacitors (EDLCs) containing ionic liquid-added polymer electrolyte.     

Influence of γ-ray-induced effects on dielectric dispersion of CuO-doped calcium fluoroborophosphate glass system

γ-Ray-induced dielectric dispersion in CaF₂–B₂O₃–P₂O₅ glasses doped with different concentrations of CuO was investigated. The glass samples were exposed to γ-rays with dose varying within the range 0–10 kGy. The dielectric dispersion and spectroscopic properties were measured before and after γ-ray treatment. Additionally, thermoluminescence studies were performed on post-irradiated glass samples. The results of dielectric properties and dielectric breakdown strength indicated a substantial increase in the insulating strength of CuO containing glasses due to γ-ray irradiation. The analysis of these results together with UV-vis optical absorption, IR spectra, and thermoluminescence studies have indicated a gradual increase in the concentration of mono-valent copper ions due to γ-ray treatment of the glass network. The additional studies have confirmed that these Cu⁺ ions occupy network-forming positions, increase the polymerization of the borophosphate glass network, and facilitates for the increase of insulating strength of the titled glass.     

Synthesis and Structures of Arene Ruthenium (II)–NHC Complexes: Efficient Catalytic α‐alkylation of ketones via Hydrogen Auto Transfer Reaction

A panel of six new arene Ru (II)‐NHC complexes 2a‐f , (NHC = 1,3‐diethyl‐(5,6‐dimethyl)benzimidazolin‐2‐ylidene 1a , 1,3‐dicyclohexylmethyl‐(5,6‐dimethyl)benzimidazolin‐2‐ylidene 1b and 1,3‐dibenzyl‐(5,6‐dimethyl)benzimidazolin‐2‐ylidene 1c ) were synthesized from the transmetallation reaction of Ag‐NHC with [(η⁶‐arene)RuCl₂]₂ and characterized. The ruthenium (II)‐NHC complexes 2a‐f were developed as effective catalysts for α‐alkylation of ketones and synthesis of bioactive quinoline using primary/amino alcohols as coupling partners respectively. The reactions were performed with 0.5 mol% catalyst load in 8 h under aerobic condition and the maximum yield was up to 96%. Besides, the different alkyl wingtips on NHC and arene moieties were studied to differentiate the catalytic robustness of the complexes in the transformations.     

Palladium‐catalysed room‐temperature Suzuki–Miyaura coupling in water extract of pomegranate ash,a bio‐derived sustainable and renewable medium

An agro waste‐derived, ‘water extract of pomegranate ash’ (WEPA), has been utilized for the first time as a renewable medium for Pd(OAc)₂‐catalysed Suzuki–Miyaura cross‐coupling at room temperature. This method offers a simple and sustainable synthesis of biaryls from aryl halides and arylboronic acids under ligand‐ and external base‐free aerobic and ambient conditions. This method has been found effective for both activated and unactivated aryl halides in the production of biaryls with moderate to nearly quantitative yields. The protocol shows high chemoselectivity over identical/similar reactive sites in aryl halides (i.e. selectivity over identical halogens or different halogens of aryl halides). This method exhibits high regioselectivity, i.e. the selective reactivity of a halogen over other identical halogens at different positions on the aromatic nucleus. Therefore, we disclose here a clean, benign, substantial chemo‐ and regioselective and highly economic alternative method for the palladium‐assisted synthesis of biaryls using an agro waste‐derived medium.     

Enantioselective LC‐ESI‐MS/MS determination of dropropizine enantiomers in rat plasma and application to a pharmacokinetic study

We developed and validated a simple, sensitive, selective and reliable LC–ESI‐MS/MS method for direct quantitation of dropropizine enantiomers namely levodropropizine (LDP) and dextrodropropizine (DDP) in rat plasma without the need for derivatization as per regulatory guidelines. Dropropizine enantiomers and carbamazepine (internal standard) were extracted from 50 μL rat plasma using ethyl acetate. LDP and DDP resolved with good baseline separation (R_s = 4.45) on a Chiralpak IG‐3 column. The mobile phase consisted of methanol with 0.05% diethylamine pumped at a flow rate of 0.5 mL/min. Detection and quantitation were done in multiple reaction monitoring mode following the transitions m/z 237 → 160 and 237 → 194 for dropropizine enantiomers and the internal standard, respectively, in the positive ionization mode. The proposed method provided accurate and reproducible results over the linearity range of 3.23–2022 ng/mL for each enantiomer. The intra‐ and inter‐day precisions were in the ranges of 3.38–13.6 and 5.11–13.8 for LDP and 4.19–11.8 and 8.89–10.1 for DDP. Both LDP and DDP were found to be stable under different stability conditions. The method was successfully used in a stereoselective pharmacokinetic study of dropropizine enantiomers in rats following oral administration of racemate dropropizine at 100 mg/kg. The pharmacokinetic results indicate that the disposition of dropropizine enantiomers is not stereoselective and chiral inversion does not occur in rats.