Metallocene copolymers of propene and 1‐hexene: The influence of the comonomer content and thermal history on the structure and mechanical properties

The relationships between the structure and properties have been established for copolymers of propylene and 1‐hexene synthesized with an isotactic metallocene catalyst system. The most important factor affecting the structure and properties of these copolymers is the comonomer content. The thermal treatment, that is, the rate of cooling from the melt, is also important. These factors affect the thermal properties, the degree of crystallinity, and therefore the structural parameters and the viscoelastic behavior. A slow cooling from the melt favors the formation of the γ phase instead of the α modification. Regarding the viscoelastic behavior, the β relaxation, associated with the glass‐transition temperature, is shifted to lower temperatures and its intensity is increased as the 1‐hexene content raises. The microhardness values are correlated with those of the storage modulus deduced from dynamic mechanical thermal analysis curves, and good linear relations have been obtained between these parameters. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1253–1267, 2006     

A strange pigeon-hole principle

Using Ramsey theory, we establish the following pigeon-hole type principle: From a large number of random variables (functions, vectors, etc.) one can always select two, X and Y, such that P(X < Y) 1/2. We apply the principle for a poset problem.     

On the error of compound quadrature formulas forr-convex functions

LetC _m be a compound quadrature formula, i.e.C _m is obtained by dividing the interval of integration [a, b] intom subintervals of equal length, and applying the same quadrature formulaQ _n to every subinterval. LetR _m be the corresponding error functional. Iff ^(r) > 0 impliesR _m [f] > 0 (orR _m [f] < 0),=" then=" we=" say=">C _m is positive definite (or negative definite, respectively) of orderr. This is the case for most of the well-known quadrature formulas. The assumption thatf ^(r) > 0 may be weakened to the requirement that all divided differences of orderr off are non-negative. Thenf is calledr-convex. Now letC _m be positive definite or negative definite of orderr, and letf be continuous andr-convex. We prove the following direct and inverse theorems for the errorR _m [f], where , denotes the modulus of continuity of orderr:

On a problem proposed by H. Braß concerning the remainder term in quadrature for convex functions

Summary We prove that the error inn-point Gaussian quadrature, with respect to the standard weight functionw1, is of best possible orderO(n ^–2) for every bounded convex function. This result solves an open problem proposed by H. Braß and published in the problem section of the proceedings of the 2. Conference on Numerical Integration held in 1981 at the Mathematisches Forschungsinstitut Oberwolfach (Hämmerlin 1982; Problem 2). Furthermore, we investigate this problem for positive quadrature rules and for general product quadrature. In particular, for the special class of Jacobian weight functionsw _, (x)=(1–x)(1+x), we show that the above result for Gaussian quadrature is not valid precisely ifw _, is unbounded.Dedicated to Prof. H. Braß on the occasion of his 55th birthday     

Deposition of copper oxide (Cu2O,CuO) thin films at high temperatures by plasma-enhanced CVD

Copper-oxide films are deposited by plasma-enhanced CVD using copper acetylacetonate as a precursor. The influence of various experimental parameters on deposition rate, film composition and resistivity have been studied. The substrate temperature and the bias are the parameters which affect these properties the most. An increase of the substrate temperature changes the phases of the deposit from Cu₂O-CuO over Cu₂O to Cu. At temperatures 500° C the deposition rates are high but the films consist mainly of metallic Cu. A negative bias enhances the deposition rate only slightly but has a strong effect on the film composition and can completely balance the oxygen deficiency. At a bias of –120 V the films consist of pure CuO even at temperatures 500° C.     

Comparison theorems forL-monosplines of minimal norm

Summary LetLM _N be the set of allL-monosplines withN free knots, prescribed by a pair (x;E) of pointsx = {x _i } ₁ ⁿ ,a <x ₁ < ... <x _n <b and an incidence matrixE = (e _ij ) _i=1 ⁿ , _r-1 ^j=0 with Denote byLM _N ^O the subset ofLM _N consisting of theL-monosplines withN simple knots (n=N). We prove that theL-monosplines of minimalL _p-norms inLM _N belong toLM _N ^O .The results are reformulated as comparison theorems for quadrature formulae.     

Convolution quadrature and discretized operational calculus. I

Numerical methods are derived for problems in integral equations (Volterra, Wiener-Hopf equations) and numerical integration (singular integrands, multiple time-scale convolution). The basic tool of this theory is the numerical approximation of convolution integrals

Growth of Ni2Si by rapid thermal annealing: Kinetics and moving species

The growth kinetics is characterized and the moving species is identified for the formation of Ni₂Si by Rapid Thermal Annealing (RTA) of sequentially deposited Si and Ni films on a 100 Si substrate. The interfacial Ni₂Si layer grows as the square root of time, indicating that the suicide growth process is diffusion-limited. The activation energy is 1.25±0.2 eV in the RTA temperature range of 350–450° C. The results extend those of conventional steady-state furnace annealing quite fittingly, and a common activation energy of 1.3±0.2 eV is deduced from 225° to 450° C. The marker experiment shows that Ni is the dominant moving species during Ni₂Si formation by RTA, as is the case for furnace annealing. It is concluded that the two annealing techniques induce the same growth mechanisms in Ni₂Si formation.     

Synthesis of thieno[3.2-<Emphasis Type="Italic">b</Emphasis>]pyrrolenine derivatives under the Fischer reaction conditions

The reaction of alkyl 4-(2-acetylhydrazino)-2-methyl-3-thiophenecarboxylates with 3-methylbutan-2-one was carried out under the Fischer reaction conditions. The influence of Lewis acids and solvents on the process was studied. A convenient method for the synthesis of thieno [3.2-b]pyrrolenine derivatives was proposed.__________Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 3, pp. 725–729, March, 2005.