Sensitivity analysis for discrete optimal control problems

We present local sensitivity analysis for discrete optimal control problems with varying endpoints in the case when the customary regularity of boundary conditions can be violated. We study the behavior of the optimal solutions subject to parametric perturbations of the problem.     

Maharam algebras and Cohen reals

We show that the product of any two nonatomic Maharam algebras adds a Cohen real. As a corollary of this and a result of Shelah (1994) we obtain that the product of any two nonatomic ccc Souslin forcing notions adds a Cohen real.

     

Benzannelated analogs of phenanthro[1,2-b]- and [2,1-b]thiophene: Synthesis and structural characterization by two-dimensional NMR and X-ray techniques

Syntheses of benzo[3,4]phenanthro[1,2-b]thiophene, benzo[3,4]phenanthro[2,1-b]thiophene and their 1-methyl analogs are reported as potential constituents of solvent refined coal liquids and for mutagenicity testing. The attempted synthesis of the 13-methyl analogs which gave the 11-methyl isomers is also described. Total assignments of the ¹H- and ¹³C-nmr spectra based on long range optimized heteronuclear protoncarbon two-dimensional chemical shift correlation are reported. Carbon assignments obtained for benzo[3,4]-phenanthro[1,2-b]thiophene using this approach were confirmed with a 125 MHz ¹³C–¹³C INADEQUATE spectrum. X-Ray crystal structures were determined for benzo[3,4]phenanthro[1,2-b]thiophene and 1-methyl-benzo[3,4]phenanthro[2,1-b]thiophene. Both molecules were helically distorted from planarity. Close intramolecular contacts between the bay region H1–H13 and ClMe-H13 of 2.03 and 2.28 Å, respectively, were responsible for the distortions. There were no close intermolecular contacts of <3.5Å. both molecules refined to an R value of <0.05.     

New relationship of displacement signal at quadrant photodiode: Control signal analysis and simulation of a laser tracker

New relationship of displacement signal using opposite sectors on a quadrant photodiode is derived. Standard and new displacement signals are analyzed in details. Through MATLAB^® laser tracking simulation models, based on common and suggested approaches, detailed analysis is performed, and it is shown that better results for the new relationship signal processing are obtained. Within new relationship of displacement signal, the sensitivity of the system to the displacement of the spot increases and, hence, provides better accuracy in positioning up to 30%.     

Asymptotic Cones of Finitely Generated Groups

Answering a question of Gromov [7], we shall present an exampleof a finitely generated group and two non-principal ultrafiltersA, B such that the asymptotic cones Con_A and Con_B are nothomeomorphic. 1991 Mathematics Subject Classification 20F06,20F32.     

Korenblum maximum principle in mixed norm spaces

Archiv der Mathematik - It is well known that the Korenblum maximum principle holds in Bergman spaces $$\mathrm {A}^{p}$$ if and only if $$p\ge 1$$ . In this note, we improve this result by proving...     

Efficient approximation of product distributions

We describe efficient constructions of small probability spaces that approximate the joint distribution of general random variables. Previous work on efficient constructions concentrate on approximations of the joint distribution for the special case of identical, uniformly distributed random variables. © 1998 John Wiley & Sons, Inc. Random Struct. Alg., 13: 1–16, 1998     

Motzkin’s theorem of the alternative: a continuous-time generalization

We revisit Zalmai’s theorem, which is a partial generalization of Motzkin’s theorem of the alternative in the continuous-time setting. In particular, we provide two simple examples demonstrating that its existing proof is incorrect, and we demonstrate that a suitably modified variant of Zalmai’s theorem, concerned with the inconsistency of systems of convex inequalities and affine equalities, can be verified. We also derive two generalized variants of Motzkin’s theorem of the alternative in the continuous-time setting.     

Norm of the Hilbert matrix on Bergman spaces

It is well known that the Hilbert matrix operator H is a bounded operator from the Bergman space $A^p$ into $A^p$ if and only if $2<p<\infty$. In [5] it was shown that the norm of the Hilbert matrix operator H on the Bergman space $A^p$ is equal to $\frac{\pi }{\sin ?\frac{2\pi }{p}}$, when $4\le p<\infty$, and it was also conjectured that

${6H6}_{A^p\to A^p}=\frac{\pi }{\sin ?\frac{2\pi }{p}},$

when $2<p<4$. In this paper we prove this conjecture.     

New aurone epoxide and auronolignan from the heartwood of Cotinus coggygria Scop

New aurone epoxide, 2,10-oxy-10-methoxysulfuretin (14), and new auronolignan (15), named cotinignan A, were isolated by silica gel column and semipreparative HPLC chromatography from the methylene chloride/methanol extract of Cotinus coggygria Scop. heartwood. In addition, thirteen known secondary metabolites namely sulfuretin, 2,3-trans-fustin, fisetin, butin, butein, taxifolin, eriodictyol, 3',5,5',7–tetrahydroxyflavanone, 3',4',7-trihydroxyflavone, 3-O-methyl-2,3-trans-fustin, 3-O-galloyl-2,3-trans-fustin, β-resorcylic acid and 3-O-β-sitosterol glucoside were isolated as well. Their structures were elucidated by 1D and 2D NMR, HR-ESI-MS, IR and UV. Ten out of eleven isolated flavonoids possess 7, 3' and 4' hydroxy groups. These structural features could be considered as chemotaxonomic characteristic of flavonoids from C. coggygria. Cotinignan A (15) represents new subclass of secondary metabolites - auronolignans.