Syndiospecific polymerization of styrene with BzCpTiCl3 and methylaluminoxane as cocatalysts

Benzyl cyclopentadienyl titanium trichloride (BzCpTiCl₃) was synthesized from benzyl bromide, cyclopentadienyl lithium, and titanium tetrachloride and used in combination with methylaluminoxane (MAO) for the syndiospecific polymerization of styrene. Kinetic measurements of the polymerization were carried out at different temperatures. The polymerization with BzCpTiCl₃/MAO differs from the polymerization with cyclopentadienyl titanium trichloride in its behavior toward the Al/Ti ratio. In addition, high activities are observed at high Al/Ti ratios. By analyzing the polymerization runs and the physical properties of the polymers with differential scanning calorimetry, ¹³C NMR spectroscopy, wide‐angle X‐ray scattering measurements, and gel permeation chromatography, we found that the phenyl ring coordinates to the titanium atom during polymerization. Other known substitutions of the cyclopentadienyl ring (V. Scholz, Dissertation, University of Hamburg, 1998) in principle influence the polymerization activity. The physical properties of the polymers produced by the catalysts already known are nearly identical. BzCpTiCl₃ is the first catalyst that leads to polystyrene obviously different from the polystyrene produced by other highly active catalysts. © 2001 John Wiley & Sons, Inc. J Polym Sci Part A: Polym Chem 39: 2805–2812, 2001     

Radon gas activity measurements in the frame of an international comparison

In order to validate its original method for the radon gas activity standardization and to assure the international metrological traceability and equivalence, the Radionuclide Metrology Laboratory of IFIN-HH participated recently in the international comparison CCRI(II)-K2.Rn-222, organized by the International Committee for Weights and Measures—CIPM-CCRI(II)-Radionuclide Measurements. The radon gas sample received, the measurement equipment and the experimental procedures are described. Because the comparison is underway, the results are presented only as relative values to the liquid scintillator vial measurement result. The uncertainty budget of the measurements performed is provided.     

Superacid cyclization of esters of some bishomoisoprenoid acids

It is shown that on the superacid cyclization of esters of bishomobicyclogeranylgeranic and E,E-bishomofarnesic acids fully cyclized hydroxyesters are formed in good yield, while on the interaction of esters of 6-hydroxy- and 6-acyloxy-15-bishomobicyclogeranylgeranic acids with a superacid no carbocyclization takes place.     

Existence of rank 3 vector bundles with given chern classes on homogeneous rational 3-folds

One proves that any rank 3 topological vector bundle on a homogeneous rational 3-fold has an algebraic structure. The proof uses extensions of ideals by rank 2 vector bundles. The paper also contains a construction of rank 3 vector bundles on 3-folds using extensions of ideals by rank 2 reflexive sheaves.     

Optimal control for semilinear stochastic evolution equations

Existence, uniqueness, continuous dependence with respect to controls and convergence in the probability of finite differences for controlled semilinear stochastic evolution equations, driven by continuous semimartingales, are considered under Lipschitz and monotone coefficients. The existence of discrete-optimal feedback controls for an associated optimization problem is proved.     

Holomorphic maps preserving parts of the local spectrum

Let x ₀ be a nonzero vector in \({\mathbb{C}^{n}}\) , and let \({U\subseteq \mathcal{M}_{n}}\) be a domain containing the zero matrix. We prove that if φ is a holomorphic map from U into \({\mathcal{M}_{n}}\) such that the local spectrum of T ∈ U at x ₀ and the local spectrum of φ(T) at x ₀ have always a common value, then T and φ(T) have always the same spectrum, and they have the same local spectrum at x ₀ a.e. with respect to the Lebesgue measure on U. If \({\varphi \colon U\rightarrow \mathcal{M}_{n}}\) is holomorphic with φ(0) = 0 such that the local spectral radius of T at x ₀ equals the local spectral radius of φ(T) at x ₀ for all T ∈ U, there exists \({\xi \in \mathbb{C}}\) of modulus one such that ξT and φ(T) have the same spectrum for all T in U. We also prove that if for all T ∈ U the local spectral radius of φ(T) coincides with the local spectral radius of T at each vector x, there exists \({\xi \in \mathbb{C}}\) of modulus one such that φ(T) = ξT on U.     

On the mathematical formulation of the problem of reassembling fragmented objects: two new theorems

In this paper two new theorems are proved in association with the problem of matching three dimensional solid bodies. Rigorous mathematical criteria are given in order to test if two such bodies actually match in a certain position. Since this problem finds important application to the actual problem of reassembling fragmented objects e.g. archaeological, special care is taken to account for small gaps between matching fragments and fuzziness of the matching parameters.