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.     

Theory of valuations on manifolds, III. Multiplicative structure in the general case

This is the third part of a series of articles where the theory of valuations on manifolds is constructed. In the second part of this series the notion of a smooth valuation on a manifold was introduced. The goal of this article is to put a canonical multiplicative structure on the space of smooth valuations on general manifolds, thus extending some of the affine constructions from the first author's 2004 paper and, from the first part of this series.

     

Some inequalities for algebraic polynomials with the Laguerre weight

There is a series of publications which have considered inequalities of Markov–Bernstein–Nikolskii type for algebraic polynomials with the Jacobi weight (see [N.K. Bari, A generalization of the Bernstein and Markov inequalities, Izv. Akad. Nauk SSSR Math. Ser. 18 (2) (1954) 159–176; B.D. Bojanov, An extension of the Markov inequality, J. Approx. Theory 35 (1982) 181–190; P. Borwein, T. Erdélyi, Polynomials and Polynomial Inequalities, Springer, New York, 1995; I.K. Daugavet, S.Z. Rafalson, Some inequalities of Markov–Nikolskii type for algebraic polynomials, Vestnik Leningrad. Univ. Mat. Mekh. Astronom. 1 (1972) 15–25; A. Guessab, G.V. Milovanovic, Weighted L²-analogues of Bernstein's inequality and classical orthogonal polynomials, J. Math. Anal. Appl. 182 (1994) 244–249; I.I. Ibragimov, Some inequalities for algebraic polynomials, in: V.I. Smirnov (Ed.), Fizmatgiz, 1961, Research on Modern Problems of Constructive Functions Theory; G.K. Lebed, Inequalities for polynomials and their derivatives, Dokl. Akad. Nauk SSSR 117 (4) (1957) 570–572; G.I. Natanson, To one theorem of Lozinski, Dokl. Akad. Nauk SSSR 117 (1) (1957) 32–35; M.K. Potapov, Some inequalities for polynomials and their derivatives, Vestnik Moskov. Univ. Ser. Mat. Mekh. 2 (1960); E. Schmidt, Über die nebst ihren Ableitungen orthogonalen Polynomsysteme und das zugehörige Extremum, Math. Ann. 119 (1944) 165–209; P. Turán, Remark on a theorem of Erhard Schmidt, Mathematica 2 (25) (1960) 373–378]). In this paper we find an inequality of the same type for algebraic polynomials on (0,∞) with the Laguerre weight function e^-xx^α (α>-1).     

On the index integral transformation with Nicholson's function as the kernel

The integral transformation, which is associated with the Nicholson function as the kernel, is introduced and investigated in the paper. This transformation is an integral, where integration is with respect to an index of the sum of squares of Bessel functions of the first and second kind. Composition representations and relationships with the Meijer K-transform, the Kontorovich-Lebedev transform, the Mellin transform, and the sine Fourier transform are given. We also present boundedness properties, a Parseval type equality, and an inversion formula.     

Harmonic Analysis of Translation Invariant Valuations

The decomposition of the space of continuous and translation-invariant valuations into a sum of SO(n) irreducible subspaces is obtained. A reformulation of this result in terms of a Hadwiger-type theorem for continuous translation-invariant and SO(n)-equivariant tensor valuations is also given. As an application, symmetry properties of rigid-motion invariant and homogeneous bivaluations are established and then used to prove new inequalities of Brunn–Minkowski type for convex body valued valuations.     

A fourier-type transform on translation-invariant valuations on convex sets

Let V be a finite-dimensional real vector space. Let V al ^sm (V) be the space of translation-invariant smooth valuations on convex compact subsets of V. Let Dens(V) be the space of Lebesgue measures on V. The goal of the article is to construct and study an isomorphism $$ \mathbb{F}_V :Val^{sm} (V)\tilde \to Val^{sm} (V^* ) \otimes Dens(V) $$ such that $ \mathbb{F}_V $ commutes with the natural action of the full linear group on both spaces, sends the product on the source (introduced in [5]) to the convolution on the target (introduced in [16]), and satisfies a Planchereltype formula. As an application, a version of the hard Lefschetz theorem for valuations is proved.