On the equitability of multiply-connected monolayered cyclofusene

Multiply-connected monolayered cyclofusene (MMC) is a fused hexacyclic system with an exterior region and at least two interior empty regions called holes, as in figure 1. Each hexacyle has either: (a) two edges belonging to an exterior boundary and at least one hole, or (b) two edges belonging to boundaries of at least two holes. Let G be the graph of a given MMC. We show that G is equitable if and only if the set of vertices belonging to three hexacycles is equitable.     

Colossal magnetoresistance manganites: A new approach

Manganites of the LA_1−x Ca _x MnO₃ family show a variety of new and poorly understood electronic, magnetic and structural effects. Here we outline a new approach recently proposed by us, where we argue that due to strong Jahn-Teller (JT) coupling with phonons the twofold degeneratee _g states at the Mn sites dynamically reorganize themselves into localised, JT polaronsl with exponentially small inter-site hopping, and band-like, nonpolaronic statesb, leading to anew 2-band model for manganites which includes strong Coulomb and Hund’s couplings. We also discuss some results from a dynamical mean-field theory treatment of the model which explains quantitatively a wide variety of experimental results, including insulator-metal transitions and CMR, in terms of the influence of physical conditions on the relative energies and occupation of thel andb states. We argue that this microscopic coexistence of the two types of electronic states, and their relative occupation and spatial correlation is the key to manganite physics. Dedicated to Professor C N R Rao on his 70th birthday     

A tabu search heuristic for solving the CLSP with backlogging and set-up carry-over

In this paper, the multi-item, single-level, capacitated, dynamic lot sizing problem with set-up carry-over and backlogging, abbreviated to CLSP⁺, is considered. The problem is formulated as a mixed integer programming problem. A heuristic method consisting of four elements: (1) a demand shifting rule, (2) lot size determination rules, (3) checking feasibility conditions and (4) set-up carry-over determination, provides us with an initial feasible solution. The resulting feasible solution is improved by adopting the corresponding set-up and set-up carry-over schedule and re-optimizing it by solving a minimum-cost network flow problem. Then the improved solution is used as a starting solution for a tabu search procedure, with the value of moves assessed using the same minimum-cost network problem. Computational results on randomly generated problems show that the algorithm, which is coded in C++, is able to provide optimal solutions or solutions extremely close to optimal. The computational efficiency makes it possible to solve reasonably large problem instances routinely on a personal computer.     

MgBr2·OEt2 mediated protection of alcohols with hexamethyldisilazane: An efficient catalytic route for the preparation of silyl ethers under solvent-free conditions

Various types of alcohols and phenols were rapidly protected by hexamethyldisilazane in good to excellent yields at room temperature in the presence of catalytic amount of magnesium bromide ethyl etherate under solvent-free conditions. Good to excellent chemoselectivity was demonstrated for competitive protection of primary hydroxyls in the presence of secondary and tertiary alcohols. Highly selective protection of phenols in the presence of aromatic amines was also demonstrated successfully.     

Enzyme production and profile by Aspergillus niger during solid substrate fermentation using palm kernel cake as substrate

The oil palm sector is one of the major plantation industries in Malaysia. Palm kernel cake is a byproduct of extracted palm kernel oil. Mostly palm kernel cake is wasted or is mixed with other nutrients and used as animal feed, especially for ruminant animals. Recently, palm kernel cake has been identified as an important ingredient for the formulation of animal feed, and it is also exported especially to Europe, South Korea, and Japan. It can barely be consumed by nonruminant (monogastric) animals owing to the high percentages of hemicellulose and cellulose contents. Palm kernel cake must undergo suitable pretreatment in order to decrease the percentage of hemicellulose and cellulose. One of the methods employed in this study is fermentation with microorganisms, particularly fungi, to partially degrade the hemicellulose and cellulose content. This work focused on the production of enzymes by Aspergillus niger and profiling using palm kernel cake as carbon source.     

A facile synthesis of new 3-(2-benzimidazolyl)-2-alkyl-4-(3H)-quinazolinones under microwave irradiation

Preparation of 2-amino-N-(1-H-benzimidazol-2-yl)benzamide and a variety of new 3-(2-benzimidazolyl)-2-alkyl-4-(3H)-quinazolinones using isatoic anhydride, 2-aminobenzimidazole and orthoesters under microwave irradiation are described.     

Solvation numbers and hydration constant for thorium(IV) in ethanol-water medium

The solvation number and hydration constant of Th⁴⁺ in ethanol-water medium were determined at 25°C using UV-spectral and electrochemical measurements. A solvate formation equilibrium is demonstrated and characterized. Three molecules of ethanol (S) can bond to the metal cation with strengths comparable to that for H₂O to form ThS₃(H₂O) ₃ ⁴⁺ Formation of thorium monochelate with lawsone (2-hydroxy-1,4-naphthoquinone) eliminates bonding with alcohol molecules. The dissociation constant of the chelating agent_sK_a and the formation contant of the monochelated metal ion_sK _f ^* that are essentially independent of the solution composition are evaluated. Hydration titrations involving thorium-lawsone monochelate are performed and the data obtained from the changes of pH with solvent composition are analyzed. The solution independent constant,_sK _f ^* for thorium-lawsone complex formation in mixed aqueous ethanol is given by $$log_s K_f * = vpK_a + log_s K_h - log[LH] - vpH + 3logv$$ where vpK_a is the dissociation constant of the chelating agent LH in the solvent system of ν volume fraction of water and_sK_h is the solution-independent hydration constant of thorium (IV) in the solvent system. Log-values for the constants_sK_h,_sK _f ^* and_sK _a ^* are found to be 7.8±0.02, 11.38±0.04 and ?0.753, respectively.     

New Group 6 metal carbonyl derivatives of 2-(2'(-pyridyl)benzimidazole: synthesis and spectroscopic studies

Reaction of Cr(CO)(6) with 2-(2'-pyridyl)benzimidazole (pbiH) under reduced pressure resulted in the formation of the dinuclear complex [Cr(2)(CO)(6)(pbiH)(2)]. Infra-red (IR) spectroscopy revealed the presence of terminal and bridge Cr-CO bonds. Interaction of M(CO)(6), M=Cr, Mo and W, with pbiH in the presence of 2,2'-bipyridine (bpy) gave the tetracarbonyl complexes [M(CO)(4)(pbiH)].bpy. Spectroscopic studies of the complexes indicated the presence of hydrogen bonding between the bpy nitrogen and the NH group of pbiH. Reactions of M(CO)(6) with pbiH in the presence of PPh(3) gave the tricarbonyl monosubstituted derivatives [M(CO)(3)(PPh(3))(pbiH)]. The spectroscopic studies of the complexes suggested the proposed structures.