The colloid-structure of semicrystalline low-density polyethylene

The length-distribution of stereoregular sequences in low-density polyethylene (LDPE) is determined by a computer-aided analysis of cp-melting curves within the framework of thermodynamics of eutectoid copolymers. Small-angle x-ray scattering patterns are then described by using the structure data derived. One of the results is that fluctuations of the mean electron-density are increasingly reduced with an increasing degree of crystallinity.Dedicated to Prof. Dr. W. Pechhold on the occasion of his 60th birthday     

Estimation of the exchange constants in the Fe sublattice of the Y2Fe17 and Y2Fe17N3−δ compounds from the analysis of Mössbauer measurements

From the analysis of Mössbauer data for Y₂Fe₁₇ and Y₂Fe₁₇N_3−δ at various temperatures the hyperfine fields for 4f, 6g, 12j, 12k iron sites were estimated as a function of temperature. The reduced magnetizations calculated from the values of the hyperfine fields are fitted with a mean field model for four interacting sublattices using a computer program. The estimated exchange interaction from the fitting procedure between the 4f sites is found strongly negative (antiferromagnetic) in Y₂Fe₁₇ whereas in Y₂Fe₁₇N_3−δ it increases and becomes weak negative following a modified Slater-Néel curve. The rest of the exchange interactions are found positive or weak negative depending on the distances between the Fe atoms.     

A convection/reaction/switching system

We consider a spatially distributed hybrid system consisting of a convection/reaction system in which the reaction switches discontinuously in time between modes, independently at each spatial point on reaching “switching thresholds”. The model involves a novel formulation for evolution of the free boundary between the modal regions.     

Excitation of localized spatial structures of different symmetry in a system of two thin films

We consider spatial dissipative solitons arising in the system of two nonlinear thin films which interact resonantly with light. Symmetric and nonsymmetric solitons and methods of their exciting and switching are studied.     

Nonstandard analysis and compact Abelian groups

Gor'kii. Translated fromSibirskii Matematicheskii Zhurnal, Vol. 32, No. 2, pp. 26–40, March–April 1991.     

Convergence of Weighted Sums and Laws of Large Numbers in D([0,1]; E)

Convergence properties of weighted sums of functions in D([0, 1]; E) (E a Banach space) are investigated. We show that convergence in the Skorokhod J₁-topology of a sequence (x_n) in D([0, 1]; E) does not imply convergence of a sequence ( _n) of averages. Convergence in the J₁-topology of a sequence ( _n) of averages is shown, under the growth condition x_n ∞ = o(n), to be equivalent to the convergence of ( _n) in the uniform topology. Convergence of a sequence (x_n,) is shown to imply convergence of the sequence ( _n) of averages in the M₁ and M₂ topologies. The strong law of large numbers in D[0, 1] is considered and an example is constructed to show that different definitions of the strong law of large numbers are nonequivalent.