Bounds for the Kirchhoff index via majorization techniques

Using a majorization technique that identifies the maximal and minimal vectors of a variety of subsets of ${\mathbb{R}^{n}}$ , we find upper and lower bounds for the Kirchhoff index K(G) of an arbitrary simple connected graph G that improve those existing in the literature. Specifically we show that $$K(G) \geq \frac{n}{d_{1}} \left[ \frac{1}{1+\frac{\sigma}{\sqrt{n-1}}} + \frac{(n-2)^{2}}{n-1-\frac{\sigma}{\sqrt{n-1}}}\right] ,$$ where d ₁ is the largest degree among all vertices in G, $$\sigma ^{2} = \frac{2}{n} \sum_{(i, j) \in E} \frac{1}{d_{i}d_{j}} = \left( \frac{2}{n}\right) R_{-1}(G),$$ and R _?1(G) is the general Randi? index of G for ${\alpha =-1}$ . Also we show that $$K(G) \leq \frac{n}{d_{n}}\left( \frac{n-k-2}{1-\lambda _{2}}+\frac{k}{2}+\frac{1}{\theta}\right) ,$$ where d _n is the smallest degree, ${\lambda _{2}}$ is the second eigenvalue of the transition probability of the random walk on G, $$k = \left \lfloor \frac{\lambda _{2} \left( n-1\right) +1}{\lambda _{2}+1}\right\rfloor {\rm and}\quad\theta = \lambda _{2} \left( n-k-2\right) -k+2.$$      

Mesomorphic behaviour and TSDC measurements of ortho-metallated palladium(II) and platinum(II) complexes with S,O-donor co-ligands

A series of ortho-metallated Pd and Pt complexes containing an imine ligand carrying three alkoxy chains and N-benzoylthiourea derivatives as co-ligands were prepared and their liquid crystalline properties investigated. Their structures were assigned based on elemental analysis, IR and ¹H NMR spectroscopy, whereas thermal properties were investigated by differential scanning calotimetry and polarising optical microscopy. All the compounds exhibit monotropic transitions involving nematic and smectic A phases, with the mesomorphic behaviour strongly related to the type of N-benzoylthiourea as well as the metal centre used. The thermally stimulated depolarisation current technique was employed to determine the conduction mechanism, phase transition temperature and the activation energies for one of the ortho-metallated Pd complexes.     

Determination of Required HLB of Capryol 90

The required hydrophilic-lipophilic balance (HLB) of an oily substance indicates the HLB of the surfactants required to prepare a stable emulsion using the oil. This study utilizes empirical method to calculate required HLB (RHLB) of Capryol 90 using surfactant blends (Span 20, Tween 20, vitamin E TPGS, Pluronic F68, Span 60, and Tween 80). The methods used were assessment of degree of creaming after centrifugation and after shelf storage for 28 days at room temperature, turbidimetric method, accelerated stability study, and droplet size analysis. The droplet size was found to be in the range of 15 to 2 µm and v/v% separation after centrifugation was found to be 0–82%. The RHLB for Capryol 90 was found to be 15. The effect of various surfactant blends was investigated. Results revealed that a blend of tocopherol polyethylene glycol succinate (TPGS) and Pluronic F68 gave the most stable emulsion for Capryol 90.     

An In Vitro Pilot Fermentation Study on the Impact of Chlorella pyrenoidosa on Gut Microbiome Composition and Metabolites in Healthy and Coeliac Subjects

The response of a coeliac and a healthy gut microbiota to the green algae Chlorella pyrenoidosa was evaluated using an in vitro continuous, pH controlled, gut model system, which simulated the human colon. The effect of C. pyrenoidosa on the microbial structure was determined by 16S rRNA gene sequencing and inferred metagenomics, whereas the metabolic activitywas determined by¹H-nuclear magnetic resonancespectroscopic analysis. The addition of C. pyrenoidosa significantly increased the abundance of the genera Prevotella, Ruminococcus and Faecalibacterium in the healthy donor, while an increase in Faecalibacterium, Bifidobacterium and Megasphaera and a decrease in Enterobacteriaceae were observed in the coeliac donor. C. pyrenoidosa also altered several microbial pathways including those involved in short-chain fatty acid (SCFA) production. At the metabolic level, a significant increase from baseline was seen in butyrate and propionate (p < 0.0001) in the healthy donor, especially in vessels 2 and 3. While acetate was significantly higher in the healthy donor at baseline in vessel 3 (p < 0.001) compared to the coeliac donor, this was markedly decreased after in vitro fermentation with C. pyrenoidosa. This is the first in vitro fermentation study of C. pyrenoidosa and human gut microbiota, however, further in vivo studies are needed to prove its efficacy.     

Intra- and Inter-molecular Sulf- hydryl Hydrogen Bonding: Facilitating Proton Transfer Events for Determination of pH in Sea Water

This work presents the electrochemical response of a 2-(methylthio)phenol glassy carbon based electrode for a promising voltammetric pH sensor in both buffered and low-buffered solutions. Electropolymerization of the redox species was performed with the resulting polymer presenting a Nernstian response in buffered media, with a sensitivity of 51 mV/pH unit. The effectiveness of the sulfhydryl bond to facilitate proton transfer from the bulk solution to the phenol molecules has been confirmed, providing an accurate pH measurement of 8.28 in sea water media, compared to that measured with a calibrated glass pH probe of 8.30.     

Inherently Chiral Macrocyclic Oligothiophenes: Easily Accessible Electrosensitive Cavities with Outstanding Enantioselection Performances

Linear conjugated oligothiophenes of variable length and different substitution pattern are ubiquitous in technologically advanced optoelectronic devices, though limitations in application derive from insolubility, scarce processability and chain‐end effects. This study describes an easy access to chiral cyclic oligothiophenes constituted by 12 and 18 fully conjugated thiophene units. Chemical oxidation of an “inherently chiral” sexithiophene monomer, synthesized in two steps from commercially available materials, induces the formation of an elliptical dimer and a triangular trimer endowed with electrosensitive cavities of different tunable sizes. Combination of chirality with electroactivity makes these molecules unique in the current oligothiophenes literature. These macrocycles, which are stable and soluble in most organic solvents, show outstanding chiroptical properties, high circularly polarized luminescence effects and an exceptional enantiorecognition ability.     

Columnar bis(pyridinium) ionic liquid crystals derived from 4-hydroxypyridine: synthesis,mesomorphism and emission properties

A series of flexibly linked bis(pyridinium) salts with various counterions (Br^?, PF₆^?, BF₄^? and OTf-) was designed and prepared starting from corresponding N-alkylated 4-pyridones precursors with mesogenic 3,4,5-tris(alkyloxy)benzyl moieties (alkyl = dodecyl or tetradecyl). These salts were investigated for their liquid crystalline properties by a combination of differential scanning calorimetry, polarising optical microscopy and temperature-dependent powder X-ray diffraction (XRD). Their thermal stability was checked by thermogravimetric analysis. All bis(pyridinium) salts, except the triflate salt with shorter terminal carbon chain, display an enantiotropic liquid crystalline behaviour with a hexagonal columnar (Col_h) phase assigned on the basis of its characteristic texture and XRD studies. It was found that these luminescent bis(pyridinium) salts show weak emission in dichloromethane solutions at room temperature and a pronounced red-shifted emission in solid state. The emission properties of these bis(pyridinium) salts do not depend significantly on the nature of counterion employed.     

α-Fe2O3-In2O3 mixed oxide nanoparticles synthesized under hydrothermal supercritical conditions

α-Fe₂O₃-In₂O₃ mixed oxide nanoparticles system has been synthesized by hydrothermal supercritical and postannealing route, starting with (1−x)Fe(NO₃)₃·9H₂O·xIn(NO₃)₃·5H₂O aqueous solution (x=0-1). X-ray diffraction and Mössbauer spectroscopy have been used to study the phase structure and substitutions in the nanosized samples. The concentration regions for the existence of the solid solutions in the α-Fe₂O₃-In₂O₃ nanoparticle system together with the solubility limits of In³⁺ ions in the hematite lattice and of Fe³⁺ ions in the cubic In₂O₃ structure have been evidenced. In general, the substitution level is considerably lower than the nominal concentration x. A justification of the processes leading to the formation of iron and indium phases in the investigated supercritical hydrothermal system has been given.