An Efficient Method for the Synthesis of 3-Cyano-6-hydroxy-2(1H)-pyridinones under Microwave Irradiation and Solvent-free Conditions

Summary. Three component condensation of alkylacetoacetates, primary amines, and alkyl cyanoacetates catalyzed by solid supports under microwave irradiation gave N-alkyl 3-cyano-6-hydroxy-2(1H)-pyridinones with high yields. Upon carrying out the reaction under the same condition on acidic alumina, zeolite HY, silica gel, and montmorillonite K-10, the best yields were achieved by silica gel. Corresponding author. E-mail: balalaie@yahoo.com Received August 28, 2002; accepted September 3, 2002     

Isolating the most recent entry in a random recursive tree by random cuts

A recursive tree is constructed by starting with a root node and repeatedly adjoining new nodes to one node of the tree already constructed. Such a tree can represent, for example, the heirarchy of a workforce of a company that grows via recruiting. At times of economic depression, the company may decide to lay off participants, and in some cases it is a fair policy to relieve the last senior worker (most recent entry in the tree). If we remove an edge from such a tree then it falls into two subtrees one of which contains the most recent entry. If we continue to remove edges from the successively smaller subtrees that contain the most recent entry, we eventually isolate the most recent entry. We consider how many randomly selected edges must be removed in average before isolating the most recent entry by this procedure.     

Effective and selective aerobic oxidation of primary and secondary alcohols using CoFe2O4@HT@Imine‐CuII and TEMPO in the air atmosphere

In this study, we present a versatile and easy procedure for modifying a cobalt ferrite nanoparticle step by step. A new nanocatalyst was prepared via Cu^II immobilized onto CoFe₂O₄@HT@Imine. The catalyst was fully characterized by Fourier‐transform infrared (FT‐IR), energy‐dispersive X‐ray spectroscopy (EDX), field emission scanning electron microscopy (FE‐SEM), X‐ray diffraction (XRD), and vibrating sample magnetometer (VSM) analyses. The current procedure as a green protocol offers benefits including a simple operational method, an excellent yield of products, mild reaction conditions, minimum chemical wastes, and short reaction times. Without any significant reduction in the catalytic performance, up to five recyclability cycles of the catalyst were obtained. The optimization results suggest that the best condition in the oxidation of benzyl alcohol derivatives is 0.003 g of the CoFe₂O₄@HT@Imine‐Cu^II catalyst, TEMPO, at 70°C under solvent‐free condition and air.     

Green synthesis of the 1-substituted 1H-1, 2, 3, 4-tetrazoles over bifunctional catalyst based on copper intercalated into Mg/Al hydrotalcite modified magnetite nanoparticles

An effective one-pot, convenient process for the synthesis of 1- substituted 1H-tetrazoles from triethyl orthoformate, amines, and sodium azide is described using copper (II) doped and immobilized on functionalized magnetic hydrotalcite (Fe₃O₄/HT-NH₂ Cu^II) as a novel recyclable catalyst. The application of this catalyst allows the synthesis of a variety of tetrazoles in good to excellent yields in water. The new catalyst was characterized using Fourier transform infrared (FT-IR) spectroscopy, X-ray diffraction (XRD), scanning electron microscopy (SEM), energy-dispersive X-ray spectroscopy (EDX), thermogravimetric analysis (TGA), vibration sample magnetometry (VSM) and inductively coupled plasma analysis (ICP-OES). This new procedure offers several advantages such as short operational simplicity, practicability, and applicability to various substrates and the absence of any tedious workup or purification. The loading amount of Cu^II (doped and immobilized) on functionalized magnetic hydrotalcite was indicated to be 4.66 mmol g⁻¹, obtained from the ICP-OES analysis. Also, the excellent catalytic performance, thermal stability, and separation of the catalyst make it an excellent heterogeneous system and a useful alternative to other heterogeneous catalysts. Also, the catalyst could be magnetically separated and reused six times without significant loss of catalytic activity.     

Synthesis, computational study and binding properties of some structurally rigid glycoluril-derived molecular clips

Several new clip-shaped molecules, with different degrees of steric hindrance around their cavities as well as more rigidity on their glycoluril scaffold, have been synthesized and the molecular geometry of their most stable structures has been investigated and optimized with density functional theory (DFT) at the B3LYP level of theory using 6-311G basis set. The affinity of these molecular clips for some dihydroxybenzene derivatives (guests) has been computationally and experimentally studied. The clips having dimethyl-substituted aromatic side walls, showed the best interaction energies towards the mentioned guests. Also, the computational results revealed that the more electron-deficient guest interacts more strongly with the clips (hosts).     

The inverse maximum dynamic flow problem

We consider the inverse maximum dynamic flow (IMDF) problem. IMDF problem can be described as: how to change the capacity vector of a dynamic network as little as possible so that a given feasible dynamic flow becomes a maximum dynamic flow. After discussing some characteristics of this problem, it is converted to a constrained minimum dynamic cut problem. Then an efficient algorithm which uses two maximum dynamic flow algorithms is proposed to solve the problem.     

Writing certain commutators as products of cubes in free groups

Let Cu(γ) be the minimal number of cubes required to express an element γ of a free group F. We establish a method for showing that certain equations do not have solutions in free groups. Using it, we find Cu(γ) for certain elements of the derived subgroup of F. If is the wreath product of F by the infinite cyclic group, we also show that every element of W′ is a product of at most one commutator and three cubes in W.     

A necessary condition for the existence of periodic solutions of certain three dimensional autonomous systems

In this article, we give a necessary condition for the existence of periodic solutions of certain three dimensional autonomous systems. This may become useful in further investigations. Our claims are proved and supported by certain examples for the third order autonomous systems.     

Zeolite HY and Silica Gel as New and Efficient Heterogenous Catalysts for the Synthesis of Triarylimidazoles under Microwave Irradiation

 Zeolite HY and silica gel efficiently catalyzed the three component condensation of benzil, benzaldehyde derivatives, and ammonium acetate under solvent-free conditions and microwave irradiation.