A Stochastic Subgradient Method for Distributionally Robust Non-convex and Non-smooth Learning

Journal of Optimization Theory and Applications - We consider a distributionally robust formulation of stochastic optimization problems arising in statistical learning, where robustness is with...     

Galerkin method for optimal control of second‐order evolution equations

This paper presents the Galerkin approximation of the optimization problem of a system governed by non‐linear second‐order evolution equation where a non‐linear operator depends on derivative of the state of the system. The control is acting on a non‐linear equation. After giving some results on the existence of optimal control we shall prove the existence of the weak and strong condensation points of a set of solutions of the approximate optimization problems. Each of these points is a solution of the initial optimization problem. Finally we shall give a simple example using the obtained results. Copyright © 2004 John Wiley & Sons, Ltd.     

Optical properties of Fe-doped silica films on Si

Optical properties of Fe-doped silica films on Si were investigated by ellipsometric technique in the region 1-5 eV. Samples were produced by sol-gel method. Precursors were prepared by mixing tetraethoxysilane (TEOS) solution in ethanol and water with aqueous solution of Fe-chloride or Fe-acetate. The coating solution was deposited on Si substrates by spin on technique. The size of Fe-containing nanometric-sized particles depended on technology and varied from 20 to 100 nm. Optical response of complex hybrid samples SiO₂:Fe/Si was interpreted in a multi-layer model. In the inverse problem, the Maxwell equations were solved by transfer matrix technique. Dielectric function of Fe-doped silica layers was calculated in the model of effective media. Analysis of optical data has shown that various Fe-oxides formed. Experimental data for films obtained from precursors with Fe-acetate and annealed in hydrogen were well described by the model calculations taking into account a small contribution 1-5% of metal Fe imbedded in silica. The Fe/Fe-O contribution to optical response increased for samples grown from FeCl₃-precursor. Ellipsometric data for Fe-doped silica films on Si were interpreted taking into account the structural AFM studies as well as the results of magnetic measurements.     

On testing the divisibility of lacunary polynomials by cyclotomic polynomials

An algorithm is described that determines whether a given polynomial with integer coefficients has a cyclotomic factor. The algorithm is intended to be used for sparse polynomials given as a sequence of coefficient-exponent pairs. A running analysis shows that, for a fixed number of nonzero terms, the algorithm runs in polynomial time.

     

Standardization of Methods for Characterizing the Surface Geometry of Solids

Since a comprehensive survey published in 1999 [1] much work was done in standardizing measuring methods to characterize the surface geometry of dispersed and/or porous solids and to certify reference materials. The present paper is an extension of a short communication [2]. It gives a survey on existing standards and reports on new drafts and proposals.     

The representation dimension of domestic weakly symmetric algebras

Auslander’s representation dimension measures how far a finite dimensional algebra is away from being of finite representation type. In [1], M. Auslander proved that a finite dimensional algebra A is of finite representation type if and only if the representation dimension of A is at most 2. Recently, R. Rouquier proved that there are finite dimensional algebras of an arbitrarily large finite representation dimension. One of the exciting open problems is to show that all finite dimensional algebras of tame representation type have representation dimension at most 3. We prove that this is true for all domestic weakly symmetric algebras over algebraically closed fields having simply connected Galois coverings.     

Physicochemical studies on hydrophobic PEO‐PPO‐PEO triblock copolymer micelles in SDS micellar environment

The shape, size, aggregation, hydration, and correlation times of water insoluble PEO‐PPO‐PEO triblock copolymer micelles with sodium dodecylsulfate (SDS) micelles were investigated using transport studies and dynamic light scattering technique. From the conductance of micellar solutions of the polymer in 25 mM SDS and 5 mM NaCl, the hydration of polymer micelles were determined using the principle of obstruction of electrolyte migration by the polymer. The asymmetry of the micellar particles of polymer and polymer‐SDS mixed micellar systems in 5 mM NaCl and their average axial ratios were calculated using intrinsic viscosity and hydration data obeying Simha–Einstein equation. Hydration number and micellar sizes were variable with temperature. The shape of the polymer micelles has been ellipsoidal rather than spherical. The micellar volume, hydrodynamic radius, radius of gyration, diffusional coefficients as well as translational, rotational and effective correlation times have been calculated from the absolute values of the axes. The partial molal volume of polymer micelles has also been determined and its comparison with the molar volume of pure polymer suggested a volume contraction due to immobilization of the water phase by the hydrophilic head groups of the polymer. The thermodynamic activation parameters for viscous flow favor a more ordered water structure around polymer micelles at higher temperatures. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 2410–2420, 2007     

Mittlere Schwingungsamplituden von OTeF 5 −

Summary Mean amplitudes of vibration for OTeF ₅ ^– have been calculated from known spectroscopic and structural data in a wide temperature range. The results are briefly discussed in comparison with those of related species.