The Hadamard Inequality For Convex Function Via Fractional Integrals

In this paper, we establish several inequalities for some differantiable mappings that are connected with the Riemann-Liouville fractional integrals. The analysis used in the proofs is fairly elementary.     

Synthesis, Crystal Structure, Thermal Behavior and IR Characterization of Pentacarbonyl(4-methylpyridine)chromium(0) Complex

Abstract  Pentacarbonyl(4-methylpyridine)chromium(0) complex was isolated from n-hexane solution as yellow plate-like crystals and characterized by using X-ray crystallography. It crystallizes in the orthorhombic system with the space group Cmcm and Z = 4. The unit cell parameters are a = 11.737(1) ?, b = 12.857(2) ?, c = 8.465(1) ?. The single crystal X-ray structure of the complex shows that the coordination sphere around the chromium central atom is slightly distorted octahedron, involving the 4-methylpyridine (4-mp), ligand as a monodentate N-donor ligand and five carbonyl groups. The four equatorial CO groups in the complex, with the Cr–C2 distance of 1.886 Ǻ, are slightly bent away from the 4-methylpyridine ligand with the N–Cr–C2 angle of 91.69°. The pyridine ring plane makes an angle of 135.17° with the Cr–N–CO bond axis. The thermal analysis (differential thermal analysis and thermal gravimetry) and IR spectra of the complex indicated that the compound undergoes complete decomposition to form the Cr₂O₃ as the final decomposition product. Index Abstract  The crystal structure of pentacarbonyl(4-methylpyridine)chromium(0) complex has been determined and its thermal behavior has also been studied.      

Similarity of hybrid numbers

The set of hybrid numbers $𝕂$ is a noncommutative number system that unified and generalized the complex, dual, and double (hyperbolic) numbers with the relation ih =− hi =ε+ i. Two hybrid numbers p and q are said to be similar if there exist a nonlightlike hybrid number x satisfying the equality x ⁻¹ qx = p . And, it is denoted by p ∼ q . In this paper, we study the concept of similarity for hybrid numbers by solving the linear equations px = xq and qx − xp = c for $\text{◂,▸}\mathbf{p},\mathbf{q},\mathbf{c}\in 𝕂\mathbf{.}$     

Surfactant-assisted polyol preparation of nickel powders with different morphologies

Sub-micrometer nickel powders of controlled size and morphology were produced by a surfactant-assisted polyol method, using ethylene glycol (EG) as solvent and reductant in the presence of sodium dodecyl sulfate (SDS) surfactant and NaOH. The resultant Ni powders were characterized by XRD, SEM, EDS, and FTIR. Spherical, hexagonal, and triangular fcc Ni powders from 0.30 to 0.60 μm were obtained in the presence of SDS; irregular spherical fcc Ni powders were obtained in its absence. The concentrations of SDS, NaOH and Ni(CH₃COO)₂·4H₂O greatly influence the product morphology and size.      

Calculations of Isoelectronic Series of He Using Noninteger n‐Slater Type Orbitals in Single and Double Zeta Approximations

Using integer and noninteger n-Slater type orbitals in single- and double-zeta approximations, the Hartree-Fock-Roothaan calculations were performed for the ground states of first ten cationic members of the isoelectronic series of He atom. All the noninteger parameters and orbital exponents were fully optimized. In the case of noninteger n-Slater type orbitals in double zeta basis sets, the results of calculations obtained are more close to the numerical Hatree-Fock values and the average deviations of our ground state energies do not exceed 2×10^－6 hartrees of their numerical results.     

On {\left(1,3 \right) }-Cartan null Bertrand curves in semi-Euclidean 4-space with index 2

In this paper, we study generalized Cartan null Bertrand curves in semi-Euclidean 4-space \({\mathbb{E}_{2}^{4}}\) with index 2.     

Phase equilibria of (water + levulinic acid + dibasic esters) ternary systems

Liquid–liquid equilibrium (LLE) data of the solubility (binodal) curves and tie-line end compositions were examined for mixtures of {(water (1) + levulinic acid (2) + dimethyl succinate or dimethyl glutarate or dimethyl adipate (3)} at 298.15 K and 101.3 ± 0.7 kPa. The reliability of the experimental tie-line data was confirmed by using the Othmer–Tobias correlation. The LLE data of the ternary systems were predicted by UNIFAC method. The LLE data were correlated fairly well with UNIQUAC and NRTL models, indicating the reliability of the UNIQUAC and NRTL equations for these ternary systems. The best results were achieved with the NRTL equation, using non-randomness parameter (α = 0.3) for the correlation. Distribution coefficients and separation factors were measured to evaluate the extracting capability of the solvents.     

Structural and aromatic aspects for tautomerism of (Z)-6-((4-bromophenylamino)methylene)-2,3-dihydroxycyclohexa-2,4-dienone

The molecular and crystal structure of (Z)-6-((4-bromophenylamino)methylene)-2,3-dihydroxycyclohexa-2,4-dienone were determined by single crystal X-ray diffraction and spectroscopic methods. Molecules of the compound can be regarded as a resonance hybrid of cis-keto tautomer and zwitterionic form. Pairs of molecules of the compound generate pseudocyclic centrosymmetric R₂² (10) R_{2}^{2} (10) supramolecular synthons with the aid of O–H···O type intermolecular H-bonds. Stacking of R₂² (10) R_{2}^{2} (10) synthons along b-axis is stabilized by π···π interactions. Changes in both covalent topology and molecular geometry of the compound accompanying proton transfer were monitored by a relaxed PES scan with respect to hydroxyl bond length used as redundant internal coordinate. Quantum chemical studies at 6-311 + G(d,p) level reveal that bond lengths which are indicative to tautomerization process cannot reach their expected values even if proton transfer occurs in gas phase and pseudo-aromatic chelate ring formation has primary effect on the stabilization of NH tautomer. Resonance-assisted intramolecular H-bond affects the electronic state of its neighboring aromatic fragments.