On dimensional properties of the generalized Smirnov's spaces

We show that the transfinite inductive dimensions modulo PP-trind and P-trInd introduced in M.G. Charalambous (1997) [2] differ by simple spaces, where P is the absolutely additive Borel class A(α) or the absolutely multiplicative Borel class M(α), 0?α<ω₁.     

Sharkovsky’s program for the classification of triangular maps is almost completed

For a continuous map of the interval, there are more than 50 conditions characterizing zero topological entropy. Some are applicable to the class of triangular maps (x,y)?(f(x),g_x(y)) of the square, but only a few of them are equivalent in this more general setting. In 1989, A.N. Sharkovsky posed the problem of proving or disproving all possible implications between them. During last 20 years, 32 conditions were considered, and most of the work was done. Only 45 relations out of 992 remained not clear. In this paper we give a survey of known results, provide two new examples disproving another 26 possible implications, and spell out the remaining 19 open problems; all but one concern distributional chaos.     

Palladium(II) complexes of Y,C,Y‐chelated phosphines: synthesis,structure, and catalytic activity in Suzuki–Miyaura reaction

The phosphines L¹PPh₂ (1) and L²PPh₂ (2) containing different Y,C,Y‐chelating ligands, L¹ = 2,6‐(^tBuOCH₂)₂C₆H₃^? and L² = 2,6‐(Me₂NCH₂)₂C₆H₃^?, were treated with PdCl₂ and di‐µ‐chloro‐bis[2‐[(N,N‐dimethylamino)methyl]phenyl‐C,N]‐dipalladium(II) and yielded complexes trans‐{[2,6‐(^tBuOCH₂)₂C₆H₃]PPh₂}₂PdCl₂ (3), {[2,6‐(Me₂NCH₂)₂C₆H₃]PPh₂} PdCl₂ (4), {[2,6‐(^tBuOCH₂)₂C₆H₃]PPh₂}Pd(Cl)[2‐(Me₂NCH₂)C₆H₄] (5) and {[2,6‐(Me₂NCH₂)₂C₆H₃]PPh₂}Pd(Cl)[2‐(Me₂NCH₂)C₆H₄] (6) as the result of different ability of starting phosphines 1 and 2 to complex PdCl₂. Compounds 3–6 were characterized by ¹H, ¹³C, ³¹P NMR spectroscopy and ESI‐MS. The molecular structures of 3,4 and 6 were also determined by X‐ray diffraction analysis. The catalytic activity of complexes 3–6 was evaluated in the Suzuki‐Miyaura cross‐coupling reaction. Copyright © 2010 John Wiley & Sons, Ltd.     

Indirect enantioresolution of (R,S)‐mexiletine by reversed‐phase high‐performance liquid chromatography via diastereomerization with [(S,S)‐O,O'‐di‐p‐toluoyl tartaric acid anhydride], (S)‐naproxen and nine chiral reagents synthesized as variants of Marfey's reagent

Eleven chiral derivatizing reagents (CDRs) were used for preparation of diastereomers of (R,S)‐mexiletine containing a primary amino group in close proximity to the stereogenic center. One anhydride, namely [(S,S)‐O,O'‐di‐p‐toluoyl tartaric acid anhydride] was synthesized and (S)‐naproxen was used as such as the chiral derivatizing reagent. The other nine CDRs were synthesized by substituting one of the fluorine atoms in 1,5‐difluoro‐2,4‐dinitrobenzene with six amino acid amides and three amino acids. The diastereomers were separated by reversed‐phase high‐performance liquid chromatography. The method was validated for linearity, accuracy, limit of detection and limit of quantification. The limit of detection was found in the range of 10–30 pmol. Copyright © 2010 John Wiley & Sons, Ltd.     

On the effect of friend feedbacks

Given ?? an (A,B)‐invariant subspace, we prove that the set of friend feedbacks is a linear variety, which can be considered as the direct sum of the feedbacks of the restriction to ?? and the co‐restriction to ??^⊥. In particular, when the natural controllability hypothesis hold, both pole assignments are simultaneously possible by means of a convenient friend feedback. Copyright © 2010 John Wiley & Sons, Ltd.     

Effectivity of Brauer–Manin obstructions on surfaces

We study Brauer–Manin obstructions to the Hasse principle and to weak approximation on algebraic surfaces over number fields. A technique for constructing Azumaya algebra representatives of Brauer group elements is given, and this is applied to the computation of obstructions.     

Geometrically nonlinear continuum thermomechanics with surface energies coupled to diffusion

Surfaces can have a significant influence on the overall response of a continuum body but are often neglected or accounted for in an ad hoc manner. This work is concerned with a nonlinear continuum thermomechanics formulation which accounts for surface structures and includes the effects of diffusion and viscoelasticity. The formulation is presented within a thermodynamically consistent framework and elucidates the nature of the coupling between the various fields, and the surface and the bulk. Conservation principles are used to determine the form of the constitutive relations and the evolution equations. Restrictions on the jump in the temperature and the chemical potential between the surface and the bulk are not a priori assumptions, rather they arise from the reduced dissipation inequality on the surface and are shown to be satisfiable without imposing the standard assumptions of thermal and chemical slavery. The nature of the constitutive relations is made clear via an example wherein the form of the Helmholtz energy is explicitly given.