On the construction of the matching polynomial for unbranched catacondensed benzenoids

An algorithm for obtaining the matching polynomial of an arbitrary catacondensed unbranched benzenoid molecule is presented. It is based on multiplication of only three 5 x 5 transfer matrices I, J, K, and an appropriate terminal vector. The choice of the matrices is dictated by the history of the growth of the hexagonal “animals” (i.e., by the pattern of the successive fusions of the benzene rings). The approach also gives the number of Kekule valance structures, the count of conjugated circuits, the values of the topological index Z, and the characteristic polynomials.     

Isolation of a new neolignan,magnosalicin, from magnolia salicifolia

A new neolignan named magnosalicin (4) was isolated as a biologically active compound from the buds of $\text{Magnolia salicifolia}$, which have been used as a Chinese medicinal drug, especially for nasal allergy. A unique arrangement of substitution groups on a tetrahydrofuran ring indicates magnosalicin (4) being a neolignan. Its biogenetical formation mechanism is also discussed.     

Lattice path counting andM/M/c queueing systems

We apply the lattice path counting method to the analysis of the transientM/M/c queueing system. A closed-form solution is obtained for the probability of exactlyi arrivals andj departures within a time interval of lengtht in anM/M/c queueing system that is empty at the initial time. The derivation of the probability is based on the counting of paths from the origin to(i,j) on thexy-plane, that have exactly r_d x-steps whose depth from the liney=x isd (d=0,1,...,c–1). The closed-form solution has an expression useful for numerical calculation.     

Synthesis of potent and selective inhibitors against the proliferation of human coronary artery smooth muscle cells

A series of diarylamide urea derivatives were synthesized and evaluated for their inhibitory activities against human coronary artery smooth muscle cells (SMCs) and human coronary artery endothelial cells (ECs). Compound 2h was much superior to Tranilast, in terms of both the potency of its inhibitory activity toward the proliferation of SMCs and the cell selectivity.     

A topological index for the totalπ-electron energy

A modified topological index \(\tilde Z_G \) is proposed to be defined as $$\tilde Z_G = \sum\limits_{k = 0}^{[N/2]} {( - 1)^k } a_{2k} $$ for characterising theπ-electronic system of a conjugated hydrocarbonG withN carbon atoms, wherea _2k is the coefficient of the characteristic polynomial ofG defined as $$P_G (X) = ( - 1)^N \det |A - XE| = \sum\limits_{k = 0}^N { a_k X^{N - k} } $$ with an adjacency matrixA and the unit matrixE. \(\tilde Z_G \) is identical toZ _G for a tree graph, or a chain hydrocarbon.Z _G increases with a (4n+2)-membered ring formation and decreases with a 4n-membered ring formation. The totalπ-electron energyE _π of the Hückel molecular orbital is shown to be related with \(\tilde Z_G \) asE _π =Cln \(\tilde Z_G \) . With this relation generalised and extended Hückel rules for predicting the stability of an arbitrary network are proved.     

Generalized inverse of linear transformations: a geometric approach

A generalized inverse of a linear transformation A:

→

, where

and

are arbitrary finite dimensional vector spaces, is defined using only geometrical concepts of linear transformations. The inverse is uniquely defined in terms of specified subspaces $\text{L}$ ?

, $\text{M}$ ?

and a linear transformation N satisfying some conditions. Such an inverse is called the $\text{LM}$N-inverse. A Moore-Penrose type inverse is obtained by choosing N = 0. Some optimization problems are considered by choosing

and

as inner product spaces. Our results extend without any major modification of proofs to bounded linear operators with closed range on Hilbert spaces.     

Effect of specific adsorbed anions on the electrode kinetics of the V(III)/V(II) and Eu(III)/Eu(II) couples

Electrochemical kinetic parameters of the V(III)/V(II) and Eu(III)/Eu(II) couples in sulfuric, perchloric, hydrochloric, and hydrobromic acids were measured by potentiostatic and double pulse galvanostatic methods. The ₂ potentials in these solutions were calculated from electrocapillary measurements and the effect of the ₂ potentials on the electrode kinetics was discussed. The kinetic data after the Frumkin correction was applied show a very good agreement in H₂SO₄, HClO₄, and HCl solutions, if we assume that the non-complexed ion, which is partially supplied by the dissociation of complex ions, participates in the electrode reaction. The corrected rate constants in the bromide solution were about ten times larger than those to be expected from the ₂ potentials in the case of the V(III)/V(II) couple and a small acceleration effect was observed for the Eu(III)/Eu(II) couple. The greater reaction rate in the bromide solution is explained by the bridging effect.     

Multiresidue analysis of pesticides in vegetables and fruits using a high capacity absorbent polymer for water

A single extraction and a single clean-up procedure was developed for multi-residue analysis of pesticides in non-fatty vegetables and fruits. The method involves the use of a high capacity absorbent polymer for water as a drying agent in extraction from wet food samples and of a graphitized carbon column for clean-up. A homogeneously chopped food sample (20 g) and polymer (3 g) were mixed to absorb water from the sample and then 10 min later the mixture was vigorously extracted with ethyl acetate (100 ml). The extract (50 ml), separated by filtration, was loaded on a graphitized carbon column without concentration. Additional ethyl acetate (50 ml) was also eluted and both eluates were concentrated to 5 ml for analysis. The procedure for sample preparation was completed within 2 h. In a recovery test, 107 pesticides were spiked and average recoveries were more than 80% from asparagus, orange, potato and strawberry. Most pesticides were recovered in the range 70-120% with usually less than a 10% RSD for six experiments. The results indicated that a single extraction with ethyl acetate in the presence of polymer can be applied to the monitoring of pesticide residues in foods.     

Analysis of the π-electronic structure of infinitely large networks. I. Some remarks on the characteristic polynomial and density of states of large polycyclic aromatic hydrocarbons

General expressions of the characteristic polynomials of various series of cyclic and linear polymers of polycyclic aromatic hydrocarbons are presented, i.e., polyacene, zigzag-polyacene, 1,4-dimethylbenzene polymer, polyperylene, etc. The densities of states of cyclic and linear polymers with the same repetitive units are shown. In some cases the allowed region of the energy levels of these polymers is found not to be the same. Several related problems are discussed.