Synthesis and crystal structure of bis(2-methylbenzimidazolium) tetrahalocuprate(II)

The crystal structures of 2-methylbenzimidazolium tetrahalocuprates (H2-mebz)₂[CuX₄] (X = Cl and Br) have been detemined. The chloride salt is monoclinic, P2₁/c, with a = 8.540(2) Å, b = 16.591(2) Å, c = 14.303(3) Å, and = 98.69(2)°. The bromide salt is also monoclinic, P2₁/c, with a = 8.316(3) Å, b = 17.436(3) Å, c = 14.747(3) Å, and = 98.82(3)°. Both the compounds contain discrete distorted tetrahedral CuX₄ ^2– anions and almost planar 2-methylbenzimidazolium cations. In the chloride salt, three chloride ions are involved in hydrogen bonding instead of two bromide ions in the bromide salt.     

Kinetics of the interaction of imidazole,benzimidazole and pyrazole with trans-[Pd(PN)2Cl2] (PN = pyridoxine) in dimethyl sulfoxide

The kinetics of the interaction of trans-[Pd(PN)₂Cl₂] (PN = pyridoxine) with nitrogen heterocycles e.g., imidazole, benzimidazole and pyrazole, in dimethyl sulfoxide (DMSO) have been carried out at 30 °C using the stopped-flow technique and u.v.–vis. spectrophotometry. Trans-[Pd(PN)₂(DMSO)₂] was assumed to be the actual reactive species in solution. Four reaction steps can be proposed from an analysis of absorbance-time data and where [Pd(HB)₄]Cl₂ (HB – heterocyclic bases) is the final reaction product. Rate constants for each step have been evaluated and interpreted.     

Kinetics and mechanism of the oxidation of some carboxylates by a nickel (III) oxime-imine complex

The kinetics of the oxidation of formate, oxalate, and malonate by |Ni^III(L¹)|²⁺ (where HL¹ = 15-amino-3-methyl-4,7,10,13-tetraazapentadec-3-en-2-one oxime) were carried out over the regions pH 3.0–5.75, 2.80–5.50, and 2.50–7.58, respectively, at constant ionic strength and temperature 40°C. All the reactions are overall second-order with first-order on both the oxidant and reductant. A general rate law is given as - d/dt|Ni^III(L¹)²⁺| = k_obs|Ni^III(L¹)²⁺| = (k_d + nk_s |R|)|Ni^III(L¹)²⁺|, where k_d is the auto-decomposition rate constant of the complex, k_s is the electron transfer rate constant, n is the stoichiometric factor, and R is either formate, oxalate, or malonate. The reactivity of all the reacting species of the reductants in solution were evaluated choosing suitable pH regions. The reactivity orders are: k_HCOOH > k; k > k > k, and k > k < k for the oxidation of formate, oxalate, and malonate, respectively, and these trends were explained considering the effect of hydrogen bonded adduct formation and thermodynamic potential. © 1997 John Wiley & Sons, Inc. Int J Chem Kinet 29: 225–230, 1997.     

Sum-connectivity index of a graph

Let G be a simple connected graph, and let di be the degree of its i-th vertex. The sum-connectivity index of the graph G is defined as χ(G)=Σvivj∈E(G)? (di+dj)−1/2. We discuss the effect on χ(G) of inserting an edge into a graph. Moreover, we obtain the relations between sum-connectivity index and Randić index.     

Barndorff-Nielsen and Shephard model: oil hedging with variance swap and option

In this paper the Barndorff-Nielsen and Shephard (BN-S) model is implemented to find an optimal hedging strategy for the oil commodity from the Bakken, a new region of oil extraction that is benefiting from fracking technology. The model is analyzed in connection to the quadratic hedging problem and some related analytical results are developed. The results indicate that oil can be optimally hedged with the use of a combination of options and variance swaps. Theoretical results related to the variance process are established and implemented for the analysis of the variance swap. In this paper we also determined the optimal amount of the underlying oil commodity that has to be held for minimizing the hedging error. The model and analysis are used to numerically analyze hedging decisions for managing price risk in Bakken oil commodities. From the numerical results, a number of important features of the usefulness of the Barndorff-Nielsen and Shephard model are illustrated.

     

A versatile ternary ion pair complex of 2′-amino-1,1′-binaphthalen-2-ol for sensing enantiomers and assignment of absolute configuration

2′-Amino-1,1′-binaphthalen-2-ol (NOBIN) serves as a versatile chiral solvating agent (CSA) in the presence of trifluoromethanesulfonic acid (TFMS). The formation of a ternary complex has been established by NMR, UV–Vis, fluorescence and IR studies. The mechanism of interactions among the three components in the ternary complex has been proposed and the ternary complex structures of different diastereomers have been established by DFT based theoretical calculations. The present protocol has its ubiquity not only in the analysis of the enantiomeric composition of molecules possessing diverse functionalities, but also in determining the stereospecific assignment of hydroxy acids.     

Feynman path integrals and asymptotic expansions for transition probability densities of some Lévy driven financial markets

In this paper we implement the method of Feynman path integral for the analysis of option pricing for certain Lévy process driven financial markets. For such markets, we find closed form solutions of transition probability density functions of option pricing in terms of various special functions. Asymptotic analysis of transition probability density functions is provided. We also find expressions for transition probability density functions in terms of various special functions for certain Lévy process driven market where the interest rate is stochastic.