行和列和为常量的(0,1)-矩阵的计数

Let fs,t(m,n) be the number of (0,1) - matrices of size m x n such that each row has exactly s ones and each column has exactly t ones (sm = nt). How to determine fs,t(m,n)? As R. P. Stanley has observed (Enumerative CombinatoricsⅠ(1997), Example 1.1.3), the determination of fs,t(m, n) is an unsolved problem, except for very small s, t. In this paper the closed formulas for f2,2(n,n), f3,2(m,n), f4,2(m,n) are given. And recursion formulas and generating functions are discussed.     

(Diazoalkyl)Phosphoranes from [4 + 1]-cycloadditions of tetrahalo-orthobenzoquinones to (diazoalkyl)phosphanes [1]

The (diazoalkyl)phosphanes 4a–e undergo [4 + 1]-cycloaddition reactions with the tetrahalo-orthobenzoquinones 5a,b to furnish the previously unknown (diazoalkyl)phosphoranes 6a–h . The structure of product 6h has been investigated by X-ray crystallography.     

Swelling and fractal heterogeneities in networks

In this paper we revisit old swelling data on polymer networks that have not been interpreted theoretically on a closed molecular basis. If the osmotic pressure of the swollen network is compared to the osmotic pressure of the corresponding uncrosslinked solution unsolved problems appear, when the relative osmotic pressure is plotted against the degree of swelling, i.e. the deformation due to swelling. A significant maximum appears which cannot be explained by any of the recently derived elastic models, such as junction constraint or other entanglement models. It is suggested in this paper that the maximum is a consequence of structural heterogeneities of fractal nature. If such fractal heterogeneities are assumed a strong maximum in the relative osmotic pressure can be reproduced. The physical reason is the different thermodynamic behavior of uncrosslinked linear chains and crosslinked self-similar (non-linear) polymers. The conclusion is supported by numerical (Monte Carlo) simulations.     

Effect of filler networking on the dynamic mechanical properties of crosslinked polymer solids

The strain amplitude dependence of the viscoelastic properties of eight different carbon blacks dispersed in two different rubbery networks is investigated and evaluated within the Cole-Cole approach for the complex elastic modulus at fixed temperature and frequency. This approach is based on the Kraus model of strain-dependent filler agglomeration-deagglomeration rates. We find a non-integer universal shape exponent of the Cole-Cole process that obviously depends only on the surrounding polymer matrix but is independent of the filler grade. The exponent can be related to the fractal dimension of the carbon black surface.     

Dynamic mechanical investigations of different substituted cellulose o-silyl ethers

In contrast to many cellulose derivatives, the cellulose O-silyl ethers with bulky side groups exhibit scarcely a change in glass transition temperature by a variation of the degree of substitution (DS) or degree of polymerization (DP) or by introducing phenyl carbamate groups for the remaining hydroxyls along the main chain. However, a substitution of these hydroxyls by flexible acetate groups lowers the glass transition temperature considerably. The secondary dispersion (relaxation) behavior is strongly influenced by the various substituents and can be correlated to specific motions of the molecules. The dynamic mechanical properties are also dependent on the kind of preconditioning of the samples.     

Thermally Induced Carbohydroxylation of Styrenes with Aryldiazonium Salts

The radical carbohydroxylation of styrenes with aryldiazonium salts has been achieved under mild thermal conditions. A broad range of aryldiazonium salts was tolerated, and the reaction principle based on a radical–polar crossover mechanism could be extended to carboetherification as well as to a two‐step, metal‐free variant of the Meerwein arylation leading to stilbenes.     

A new torsion-rotation fitting program for molecules with a sixfold barrier: Application to the microwave spectrum of toluene

A new program is described for fitting rotation-torsion energy levels in molecules like toluene, in which the frame (C₆H₅) has C_2v symmetry and the methyl top has C_3v symmetry, i.e., for molecules where the internal rotation barrier is expanded in cos6nα, where α is the internal rotation angle and n = 1,2,…. The program is based on the theoretical framework developed by Sørensen and Pedersen in their application of the Longuet-Higgins permutation-inversion group G₁₂ to the microwave spectrum of CH₃NO₂. It is specifically designed for sixfold barrier molecules, and allows the user to select almost any symmetry-allowed torsion-rotation term for inclusion in the fitting Hamiltonian. This program leads to a very successful fit of transitions in the microwave spectrum of toluene characterized by J ? 30, K_a ? 12, and by the free-rotor quantum number ∣m∣ ? 3. In these fits we included both published and rather extensive unpublished new measurements, for which fits using other torsion-rotation programs have not been very successful. The fit presented here uses 28 parameters to give an overall standard deviation of 7.4 kHz for 372 line frequencies, and results in a much improved value for the sixfold barrier for toluene, V₆ = 13.832068(3) cal mol⁻¹.