New heterocyclic metallomesogens: synthesis,mesomorphic and thermal behaviours of Cu(II) complexes with 1,2,3-triazole-based Schiff bases ligands

Two series of new Cu(II) complexes derived from the reaction of copper acetate with the non-linear 1,2,3-triazole-based Schiff bases have successfully been synthesised. The structures of the ligands and its complexes were elucidated by elemental analysis, FT-IR, ¹H-NMR and UV–visible spectroscopic techniques. The differential scanning calorimetry and polarizing optical microscopy supported the anisotropic properties of uncoordinated ligands in which the focal conic fan-shaped texture and/or broken fan-shaped texture characteristics of respective SmA and SmC phases were recorded. However, not all of their corresponding Cu(II) complexes are mesogenic. Although the iodo-substituted ligands with even parity C₁₀H₂₉ to C₁₄H₃₃ are non-stable and exhibit SmA phase which is not reproducible, the ultimate Cu(II) complexes show exclusively stable SmA phase. This observation can be ascribed to the enhanced colinearity and molecular anisotropic by the presence of Cu-N and Cu-O coordination modes. On the other hand, the comparison studies show that different positions of ortho-hydroxyl group affect the mesomorphic and thermal behaviour of ligands and Cu(II) complexes.     

Heme-protein active site models via self-assembly in water

[structure: see text] Water-soluble models of heme-protein active sites are obtained via the self-assembly of cationic porphyrins 1 and tetrasulfonato calix[4]arene 2 (K(1.2)() = 10(5) M(-)(1)). Selective binding of ligands either outside or inside the cavity of assemblies 1.2 via coordination to the zinc center has been observed. Small ligands such as 4-methylpyridine and 1-methylimidazole are encapsulated, while the bulkier caffeine is bound outside. Assemblies Co-1.2, in which the Zn porphyrin moiety has been replaced by a Co(II) porphyrin, can act as O(2) carriers.     

Selective Spectrophotometric Determination of Copper in Milk with Phenanthraquinone Monothiosemicarbazone

The red complex formed by copper (II) and phenanthraquinone monothiosemicarbazone has an absorption maximum at 530 nm with a molar absorptivity of 14000 cm^?1 mole^?1. The pH range for the determination is 1.1–6.6. Optimum range of concentration for accurate determination is 0.50–3.47 ppm of copper (II) in 50% methanol medium. The limits of interference due to foreign ions have been studied. The method has been successfully employed for the determination of copper in various samples of milk.     

Dual Lukacs regressions for non-commutative variables

Dual Lukacs type characterizations of random variables in free probability are studied here. First, we develop a freeness property satisfied by Lukacs type transformations of free-Poisson and free-binomial non-commutative variables which are free. Second, we give a characterization of non-commutative free-Poisson and free-binomial variables by properties of first two conditional moments, which mimic Lukacs type assumptions known from classical probability. More precisely, our result is a non-commutative version of the following result known in classical probability: if U, V   are independent real random variables, such that E(V(1−U)|UV)$\mathbb{E}(V(1-U)|UV)$ and E(V²(1−U)²|UV)$\mathbb{E}(V^2{(1-U)}^2|UV)$ are non-random then V has a gamma distribution and U has a beta distribution.     

Korovkin type approximation theorem via Ka−convergence on weighted spaces

In this paper, we study the Korovkin type approximation theorem for K_a‐ convergence, which is an interesting convergence method on weighted spaces. We also study the rate of K_a?convergence by using the weighted modulus of continuity and afterwards, we present a nontrivial application.     

Heat kernel estimates for the Bessel differential operator in half‐line

In the paper we consider the Bessel differential operator in half‐line , , and its Dirichlet heat kernel . For , by combining analytical and probabilistic methods, we provide sharp two‐sided estimates of the heat kernel for the whole range of the space parameters and every , which complements the recent results given in 1 , where the case was considered.     

Multiobjective optimization of credit capital allocation in financial institutions

The evolution of international regulation leads to new capital requirements imposed on globally active companies. Financial services firms allocate capital to business lines in order to withstand the materializing credit losses and to measure the performance of various business lines. In this study, we introduce a methodology for optimal credit capital allocation based on operations research approach. In particular, we focus on the efficient allocation of capital to business lines characterized by credit risk losses and cost of capital. We compare different allocation methods and provide a rationale behind using the OR approach. Finally, we formulate a multiobjective optimization model to capital allocation problem and apply it to a real-world case of two financial conglomerates.