On spectra of Hermitian Randic matrix of second kind

We propose the Hermitian Randi\'c matrix $R^\omega(X)=(R^\omega_{ij})$, where $\omega=\frac{1+i \sqrt{3}}{2}$ and $R^\omega_{ij}={1}/{\sqrt{d_id_j}}$ if $v_iv_j$ is an unoriented edge, ${\omega}/{\sqrt{d_id_j}}$ if $v_i\rightarrow v_j$, ${\overline{\omega}}/{\sqrt{d_id_j}}$ if $v_i\leftarrow v_j$, and 0 otherwise. This appears to be more natural because of $\omega+\overline{\omega}=1$ and $|\omega|=1$. In this paper, we investigate some features of this novel Hermitian matrix and study a few properties like positiveness, bipartiteness, edge-interlacing etc. We also compute the characteristic polynomial for this new matrix and obtain some upper and lower bounds for the eigenvalues and the energy of this matrix

ynthesis, characterisation and thermal studies of ruthenium(II) carbonyl complexes of functionalised tripodal phosphine chalcogen donor ligands, [CH3C(CH2P(X)Ph2)3], where X = Se, S, O

diphenylphosphinomethyl) ethane trichalcogenide ligands, [CH3C(CH2P(X)Ph2)3], where X= Se(a), S(b) and O(c) in 1:1 (metal:ligand) molar ratio to afford hexa-coordinated complexes of the type �2-(X,X)- [Ru(CO)2Cl2P3X3] (1a–c). The complexes 1a–c exhibit two equally intense �(CO) bands in the range 1979–2060cm−1 indicating cis-disposition of the two terminal carbonyl groups. The values of �(CO) frequencies containing different ligands, in general, follow the order: P3O3 >P3S3 >P3Se3 which may be explained in terms of ‘Soft–Hard’ (Ru(II)–O) and ‘Soft–Soft’ (Ru(II)–S/Se) interactions. The complexes have been characterized by elemental analyses, mass, 1H, 31P, 77Se and 13C NMR spectroscopy. The thermal stability of the complexes has also been studie

Dicarbonylrhodium(I) complexes of pyridine alcohol ligands and their catalytic carbonylation reaction

Reaction of dimeric complex [Rh(CO)2Cl]2 with two molar equivalent of pyridine alcohol ligands (L) like 2-hydroxymethylpyridine (a), 3-hydroxymethylpyridine (b) and 4-hydroxymethylpyridine (c) afford the rhodium(I) dicarbonyl complexes [Rh(CO)2ClL](1a–c). The ligands are coordinated to the metal center through N-donor site. The complexes 1 undergo oxidative addition (OA) reactions with various alkyl halides (RI) like CH3I, C2H5I to produce Rh(III)complexes of the type [Rh(CO)(COR)IClL], where R = –CH3(2), –C2H5(3). Kinetic data for the reaction of 1 with CH3I indicate a first order reaction. The catalytic activity of the complexes 1 in the carbonylation of methanol was higher than that of the well known species [Rh(CO)2I2]−

Constrained analytical interrelations in neutrino mixing

Hermitian squared mass matrices of charged leptons and light neutrinos in the flavor basis are studied under general additive lowest order perturbations away from the tribimaximal (TBM) limit in which a weak basis with mass diagonal charged leptons is chosen. Simple analytical expressions are found for the three measurable TBM-deviants in terms of perturbation parameters appearing in the neutrino and charged lepton eigenstates in the flavor basis. Taking unnatural cancellations to be absent and charged lepton perturbation parameters to be small, interrelations are derived among masses, mixing angles and the amount of CP-violation.Comment: To be published in the Springer Proceedings in the Physics Series under the heading of the XXI DAE-BRNS Symposium (Guwahati, India

Thermal stress impaired expression of insulin-like growth factor binding proteins in pigs

This study aimed to investigate the correlation of IGFs, IGFBPs, and IGFBPRs of grower pigs with change in temperature humidity index (THI). THI was calculated to know the months of the year when pigs feel discomfort and samples of feed offered were analyzed to know the nutritional availability/deficit. The calculated average THI was above thermal comfort zone for seven months in a year. It was observed that crude protein (CP) and metabolizable energy (ME) availability to pigs were deficient. Gilts of two months age and similar body weight were randomly divided into two groups (n=6); viz. Con-fed animals (feed offered by the farmer) and For-fed animals (formulated feed supplement + Con-fed). The composition of formulated feed supplement was dried leaf of Moringa oleifera, soybean meal, rice mill waste, and mineral mixture. The plasma cortisol level increased in the experimental animals with accelerated THI as evidenced by the strong positive correlation of THI with HSP70 and HSP90. The level of leptin and ghrelin did not have significant relation with the expression level of HSPs in the present study, however, in the control animals, a low level of leptin was observed. The correlation between the growth factors and HSPs was not significant. During the season, where the THI was above the thermal comfort zone, the IGFBPR and IGFBP concentrations were non-significantly increased along with the increased THI

Grand unification in the minimal left-right symmetric extension of the standard model

The simplest minimal left-right symmetric extension of the standard model is studied in the high energy limit, and some consequences of the grand unification hypothesis are explored assuming that the parity breaking scale is the only relevant energy between the electro-weak scale and the unification point. While the model is shown to be compatible with the observed neutrino phenomenology, the parity breaking scale and the heavy boson masses are predicted to be above 10^7 TeV, quite far from the reach of nowadays experiments. Below that scale only an almost sterile right handed neutrino is allowed with a mass M \approx 100 TeV

Propensity of citric, maleic, oxalic and succnic acids for the acquous solution- vapour interface : Surface tension measurment and molecular dynamics simulations

Behaviour of oxalic, citric, succinic, and maleic acids at the air/water interface is characterized and quantified by surface tension measurements in a broad concentration range and molecular dynamics simulations in slab geometry employing a polarizable force field. The relative order of surface propensities of these atmospherically relevant acids is established in this study with results being also in a very good agreement with previous measurements