On a uniform estimate for the quaternionic Calabi problem

We establish a C ⁰ a priori bound on the solutions of the quaternionic Calabi-Yau equation (of Monge-Ampère type) on compact HKT manifolds with a locally flat hypercomplex structure. As an intermediate step, we prove a quaternionic version of the Gauduchon theorem.     

Radical Polymerization of the Silene (Me3Si)2SiCR2 by Hydrogen Transfer from a Trimethylsilyl Group

The silene (Me₃Si)₂Si?Ad is polymerized to produce a polycarbosilane with an unusual Si? Si? C repeating backbone, rather than the Si? C or Si? Si? C? C units expected for olefinic radical polymerization. The polymer structure and the polymerization mechanism (see scheme) were studied by GPC, EPR, and NMR spectroscopy and by trapping experiments.

     

Spectroelectrochemical Properties and Catalytic Activity in Cyclohexane Oxidation of the Hybrid Zr/Hf-Phthalocyaninate-Capped Nickel(II) and Iron(II) tris-Pyridineoximates and Their Precursors

The in situ spectroelectrochemical cyclic voltammetric studies of the antimony-monocapped nickel(II) and iron(II) tris-pyridineoximates with a labile triethylantimony cross-linking group and Zr(IV)/Hf(IV) phthalocyaninate complexes were performed in order to understand the nature of the redox events in the molecules of heterodinuclear zirconium(IV) and hafnium(IV) phthalocyaninate-capped derivatives. Electronic structures of their 1e-oxidized and 1e-electron-reduced forms were experimentally studied by electron paramagnetic resonance (EPR) spectroscopy and UV−vis−near-IR spectroelectrochemical experiments and supported by density functional theory (DFT) calculations. The investigated hybrid molecular systems that combine a transition metal (pseudo)clathrochelate and a Zr/Hf-phthalocyaninate moiety exhibit quite rich redox activity both in the cathodic and in the anodic region. These binuclear compounds and their precursors were tested as potential catalysts in oxidation reactions of cyclohexane and the results are discussed.     

Plurisubharmonic Functions on the Octonionic Plane and <Emphasis Type="Italic">Spin</Emphasis>(9)-Invariant Valuations on Convex Sets

A new class of plurisubharmonic functions on the octonionic plane is introduced. An octonionic version of theorems of A.D. Aleksandrov (Vestnik Leningrad. Univ. Ser. Mat. Meh. Astr. 13(1):5–24, 1958) and Chern-Levine-Nirenberg (Global Analysis, pp. 119–139, 1969), and Błocki (Proc. Am. Math. Soc. 128(12):3595–3599, 2000) are proved. These results are used to construct new examples of continuous translation invariant valuations on convex subsets of . In particular, a new example of Spin(9)-invariant valuation on ℝ¹⁶ is given. Partially supported by ISF grant 1369/04.     

Pollicott–Ruelle Resonances for Open Systems

We define Pollicott–Ruelle resonances for geodesic flows on noncompact asymptotically hyperbolic negatively curved manifolds, as well as for more general open hyperbolic systems related to Axiom A flows. These resonances are the poles of the meromorphic continuation of the resolvent of the generator of the flow and they describe decay of classical correlations. As an application, we show that the Ruelle zeta function extends meromorphically to the entire complex plane.     

Individual ergodic theorems in noncommutative Orlicz spaces

For a noncommutative Orlicz space associated with a semifinite von Neumann algebra, a faithful normal semifinite trace and an Orlicz function satisfying \((\delta _2,\Delta _2)\)-condition, an individual ergodic theorem is proved.     

Accuracy of single measurements

Single measurements are widely used in industry, trade and science, yet the problem of the estimation of the accuracy of this type of measurements is neither addressed nor even recognized in traditional Metrology. In particular, the Guide to the Expression of Uncertainty in Measurement is devoted to multiple measurements only and does not mention single measurements. This paper studies the problem of estimating the inaccuracy of single measurements and describes solutions to this problem. The proposed methods are based on metrological characteristics of measuring instruments rated in accordance with Recommendation R34 of International Organization of Legal Metrology (OIML). These characteristics are usually given in manufacturer certificates or provided by calibration laboratories. This paper treats single measurements as the basic type of measurement and multiple measurements as sets of successive single measurements. Presented at the 3rd International Conference on Metrology, November 2006, Tel Aviv, Israel. Papers published in this section do not necessarily reflect the opinion of the Editors, the Editorial Board and the Publisher.     

Spectroscopic evidence for hydrogen diffusion through a several-nanometers-thick titanium carbonitride layer on silicon

Multiple internal reflection Fourier transform infrared spectroscopy, together with other analytical techniques, was used to follow the diffusion of atomic hydrogen through a 10-nm-thick titanium carbonitride layer deposited onto a Si(100)-2x1 surface from tetrakis(dimethylamino)titanium as a chemical vapor deposition precursor. The recombinative desorption of hydrogen from the TiCN/Si interface was shown to coincide with the temperature range where most Ti-based diffusion barriers break down.     

The structure of optimal consumption streams in general incomplete markets

We prove that for any incomplete market and any concave utility function the marginal propensities to consume and to save are always positive. Furthermore, we introduce a class of incomplete markets that includes almost all well known examples of market incompleteness in finance and macroeconomics. Two concrete examples are idiosyncratic income shocks and general, diffusion driven incompleteness. For all markets in our class we explicitly solve the associated utility maximization problem by a recursive construction and derive many important properties. For example, precautionary savings and the diminishing marginal propensity to consume. Effectively, the class is characterized by these two economic properties. We also prove that the growth rate of consumption is always larger when markets are incomplete and that precautionary savings are monotone increasing in the size of idiosyncratic risk. Our construction can be implemented computationally by an efficient, robust numerical scheme. We thank two anonymous referees for useful comments and remarks.