Robust Necessary Optimality Conditions for Nondifferentiable Complex Fractional Programming with Uncertain Data

Journal of Optimization Theory and Applications - In this paper, we study robust necessary optimality conditions for a nondifferentiable complex fractional programming with uncertain data. A robust...     

Zero-one integer programs with few constraints —Efficient branch and bound algorithms

The 0–1 integer programming problem and its special case, the 0–1 knapsack problem are frequently encountered in modeling various design and decision making processes. This paper is a follow-up paper to [4] and deals with the development of an effective solution procedure for 0–1 integer programs with few constraints. Detailed computational experiments are carried out and different separation, branching and bounding rules are compared using an experimental branch and bound code. An efficient branch and bound procedure is developed, tested and compared with previously developed optimal algorithms. It is suggested that this procedure may also be used as a heuristic method for large problems by early termination of the tree search. This scheme is tested and found to be very effective.     

On total covers of graphs

A total cover of a graph G is a subset of V(G)E(G) which covers all elements of V(G)E(G). The total covering number ₂(G) of a graph G is the minimum cardinality of a total cover in G. In [1], it is proven that ₂(G)[n/2] for a connected graph G of order n. Here we consider the extremal case and give some properties of connected graphs which have a total covering number [n/2]. We prove that such a graph with even order has a 1-factor and such a graph with odd order is factor-critical.     

A convenient synthesis of amino-substituted 1,3,5-oxadiazinium salts

Diacyl chlorides react with dialkylcyanamide in the presence of a Lewis acid to give amino-substituted bis-1,3,5-oxadiazinium salts in excellent yields. A mechanism leads to the formation of the product has been postulated. All new compounds have been characterized by ¹H-nmr, ¹³C-nmr, ir-spectroscopy and elemental analysis.     

Template synthesis and spectroscopic studies of highly conjugated tetraiminetetraamide macrocyclic complexes from 1,2-diphenylethane-1,2-dione dihydrazone

A new class of tetraiminetetraamide macrocyclic (Ph4[20]tetraene, N8O4, and Ph6[20]tetraene, N8O4) complexes have been prepared through the metal ion controlled reaction of 1,2-diphenylethane-1,2-dione dihydrazone (DPEDDH) with succinic acid [ML1X2] or phthalic acid [ML2X2] [M=Mn, Co, Ni, Cu or Zn; X=Cl or NO3]. The structures of the complexes have been elucidated on the basis of i.r, 1H-n.m.r, e.p.r. and electronic spectral data and conductance, as well as magnetic, properties. An octahedral geometry is assigned for all the complexes, involving coordination of the all-imine nitrogens.     

Structural characterization of polybenzyls by high field 13C-NMR spectroscopy

¹³C-NMR Spectroscopy has been used for the structural characterization of polybenzyls synthesized from the polymerization of benzyl chloride catalyzed by arene chromium tricarbonyls. The ¹³C-chemical shifts for various mono-, di-, tri-, and tetrasubstituted phenyl groups in a polybenzyl have been calculated by the use of additivity parameters and compared with their observed shifts. Although from a theroetical point of view, polysubstitution on a phenyl ring gives rise to a number of isomers, the results indicate the preferential formation of only a few of them due to steric and electronic considerations. Based on quantitative ¹³C-NMR data, several important structural parameters including the percentage of mono-, di-, tri-, and tetrasubstituted phenyl rings in the polybenzyl can be calculated. The extent of branching in a number of polybenzyls prepared under different experimental conditions was determined. The results indicate an increase in branching with the increase in reaction temperature.