Synthesis of pyrazoles via electrophilic cyclization

Electrophilic cyclizations of α,β-alkynic hydrazones by molecular iodine were investigated for the synthesis of 4-iodopyrazoles. α,β-Alkynic hydrazones were readily prepared by the reactions of hydrazines with propargyl aldehydes and ketones. When treated with molecular iodine in the presence of sodium bicarbonate, α,β-alkynic hydrazones underwent electrophilic cyclization to afford 4-iodopyrazoles in good to high yields. Iodocyclization was general for a wide range of α,β-alkynic hydrazones and tolerated the presence of aliphatic, aromatic, heteroaromatic, and ferrocenyl moieties with electron-withdrawing and electron-donating substituents.     

Unitary quantum groups,quantum projective spaces andq-oscillators

We discuss the parametrization of quantum groups in terms of independent operators. We find that this consideration leads to the parametrization ofSU _q(2) in terms of aq-oscillator plus a commuting phase. The commuting phase is naturally identified with the subgroupU(1) and the remaining cosetSU _q(2)/U(1)=CP _q(1) consists of aq-oscillator. For unitary quantum groupsSU _q (n), the analogous construction results in the quantum projective spaceSU _q(n+1)/U _q (n)=CP _q (n) being identified with then-dimensionalq-oscillator. This yields a nonlinear action of the quantum groupSU _q(n+1) on then-dimensionalq-oscillator.     

Quantum group invariant fermionic gases: GLp,q(2) and SUp/q(2) invariances

We first investigate the high-temperature behavior of a two-parameter deformed quantum group fermionic gas with GL_p,q(2) symmetry, where (p,q)C×C. We then discuss both the structural and thermodynamical differences between GL_p,q(2)- and SU_r(2)-fermions with r=p/q where (p,q)R×R.     

High temperature bromination. Part 22: Bromination of 1a,2,7,7a-tetrahydro-1H-cyclopropa[b]naphthalene

The high-temperature bromination of 1a,2,7,7a-tetrahydro-1H-cyclopropa[b]naphthalene and its carboethoxy derivative was studied. Reaction of the title compound with 1 mol of bromine in refluxing carbon tetrachloride resulted in the formation of ring-opening products. In the case of the carboethoxy derivative, bromination took place both regio- and stereospecifically at the benzylic positions, the cyclopropane ring did not undergo bond cleavage. A mechanism for the formation of the products and their dehydrobromination reactions is discussed.     

Exponential factor optimization in characteristic function method for electrically charged particles

In this work, the simplest basis function on hyperspherical coordinates with an optimization parameter is used to construct the characteristic function for a system of electrically charged particles. The first three coefficients of the serial expansion of the characteristic function in powers of eigenvalue parameter are evaluated in terms of well-known functions. The construction of a Padé table for this expansion with the aid of these coefficients, a theoretical discussion, the optimization of the exponential parameter, evaluation of ground state energies for certain systems, and finally comparison of accuracy increments due to optimization for several systems complete the work.     

Cycloheptatriene-norcaradiene-equilibrium cycloaddition reactions of the 1.2-benzocycloheptatriene with singlet oxygen and 4-phenyl-1.2.4-triazolin-3.5-dione

Cycloaddition reactions of the 1.2-benzocycloheptatriene with singlet oxygen and 4-phenyl-1.2.4-triazolin-3.5-dione (PTAD) have been studied. For the first time, addition of the PTAD to a cycloheptatriene derivative has been observed.     

A new and convenient synthesis of substituted benzobarrelenes

Bromination of 3-bromo-6,7-benzobicyclo [3.2.1] octa-2,6-diene at ?50°C gave anti-tribromo adduct (5) in essentially quantitative yield. The double dehydrobromination of (5) was achieved using potassium tert.- butoxide to give 2-bromo-benzobarrelene (7). Reaction of (7) with n-BuLi and subsequent quenching with CH₃I, CO₂, and dimethylformamide afforded the corresponding substituted benzobarrelenes in high yield.     

A super AKNS scheme

A super extension of the AKNS scheme is presented by proposing a super sl(2, R) valued connection. A class of super integrable equations, containing the super extension of the Lax hierarchy, is found.     

Multilevel quasi-interpolation on a sparse grid with the Gaussian

Motivated by the recent multilevel sparse kernel-based interpolation (MuSIK) algorithm proposed in Georgoulis et al. (SIAM J. Sci. Comput. 35, 815–832, 2013), we introduce the new quasi-multilevel sparse interpolation with kernels (Q-MuSIK) via the combination technique. The Q-MuSIK scheme achieves better convergence and run time when compared with classical quasi-interpolation. Also, the Q-MuSIK algorithm is generally superior to the MuSIK methods in terms of run time in particular in high-dimensional interpolation problems, since there is no need to solve large algebraic systems. We subsequently propose a fast, low complexity, high-dimensional positive-weight quadrature formula based on Q-MuSIKSapproximation of the integrand. We present the results of numerical experimentation for both quasi-interpolation and quadrature in high dimensions.     

Inventory control with an order-time constraint: optimality,uniqueness and significance

This paper analyzes a stochastic inventory problem with an order-time constraint that restricts the times at which a manufacturer places new orders to a supplier. This constraint stems from the limited upstream capacity in a supply chain, such as production capacity at a supplier or transportation capacity between a supplier and a manufacturer. Consideration of limited upstream capacity extends the classical inventory literature that unrealistically assumes infinite supplier/transporter capacity. But this consideration increases the complexity of the problem. We study the constraint under a Poisson demand process and allow for a fixed ordering cost. In presence of the constraint, we establish the optimality of an (s,S) policy under both the discounted and average cost objectives. Under the average cost objective, we show the uniqueness of the order-up-to level S. We numerically compare our model with the classical unconstrained model. We report significant savings in costs that can be achieved by using our model when the order time is constrained.