Geometric Singular Perturbation Theory for Systems with Symmetry

Journal of Dynamics and Differential Equations - In this paper we focus on a class of symmetric vector fields in the context of singularly perturbed fast-slow dynamical systems. Our main question...     

Diastereoselective formation of 2-aryl-3-arenesulfonyl 4-ethyl-1,3-oxazolidines: An X-ray crystallographic and H NMR study

N-Arylsulfonamides of (R)- and (S)-2-amino-1-butanol, on condensation with aromatic aldehydes produced diastereomerically pure 2-aryl-3-arenesulfonyl 4-ethyl-1,3-oxazolidines. The absolute configurations of one enantiomeric pair have been determined from two fully refined X-ray structures, supplemented by nmr data.     

On continuum theories involving quasilinear first order non-conservative systems with involutions and a supplementary inequality

In this note we give a result of hyperbolicity for linearized quasilinear first ordernon-conservative systems with involutions and a supplementary inequality of conservative form. We also indicate some of the circumstances in which, for studying the evolution systems for a class of continua near their equilibria, such result can be applied. Some remarkable examples are the cases of a certain generalization of Landau's two-fluid scheme for superftuid Helium II, of a hyperelastic body acted upon by suitable live body forces, and of various other models appeared in the literature.     

The synthesis, structure, and reactions of some simple unsaturated σ-hydrocarbylplatinum(II) complexes

Trimethyltin compounds Me₃Sn---R(R = CH=CH₂, CF=CF₂, or CCPh) are selective reagents for the synthesis of unsaturated hydrocarbyl derivatives such as trans-PtCl(R)(PPhEt₂)2, by R/Cl exchange or oxidative addition (e.g., to Pt(PPh₃)₃); single crystal X-ray analyses of two such compounds (R = CH=CH₂ or CCPh) show that the trans-influence of R has only a low sensitivity to hybridisation at carbon, with sp³ > sp sp².     

Understanding the factors controlling the photo-oxidation of natural DNA by enantiomerically pure intercalating ruthenium polypyridyl complexes through TA/TRIR studies with polydeoxynucleotides and mixed sequence oligodeoxynucleotides

Ruthenium polypyridyl complexes which can sensitise the photo-oxidation of nucleic acids and other biological molecules show potential for photo-therapeutic applications. In this article a combination of transient visible absorption (TrA) and time-resolved infra-red (TRIR) spectroscopy are used to compare the photo-oxidation of guanine by the enantiomers of [Ru(TAP)₂(dppz)]²⁺ in both polymeric {poly(dG-dC), poly(dA-dT) and natural DNA} and small mixed-sequence duplex-forming oligodeoxynucleotides. The products of electron transfer are readily monitored by the appearance of a characteristic TRIR band centred at ca. 1700 cm⁻¹ for the guanine radical cation and a band centered at ca. 515 nm in the TrA for the reduced ruthenium complex. It is found that efficient electron transfer requires that the complex be intercalated at a G-C base-pair containing site. Significantly, changes in the nucleobase vibrations of the TRIR spectra induced by the bound excited state before electron transfer takes place are used to identify preferred intercalation sites in mixed-sequence oligodeoxynucleotides and natural DNA. Interestingly, with natural DNA, while it is found that quenching is inefficient in the picosecond range, a slower electron transfer process occurs, which is not found with the mixed-sequence duplex-forming oligodeoxynucleotides studied.

Efficient electron transfer requires the complex to be intercalated at a G-C base-pair. Identification of preferred intercalation sites is achieved by TRIR monitoring of the nucleobase vibrations before electron transfer.     

Carbene complexes : IV. Far infrared and 31P NMR spectra of palladium and platinum carbene complexes

Infrared bands mainly associated with v(M—X₂) stretching modes (M = Pd or Pt, and X = Cl, Br, or P) have been identified in the spectra of 35 carbene complexes. Based on these results and on |¹J| (³¹ P—¹⁹⁵ Pt) the trans-influence of the carbene ligands is assessed.     

Mononuclear Pt(II) and Pd(II) 1,4-dithiolato complexes. Crystal structures of [Pt((−) DIOS) (PPh3)2] and [Pd(S(CH2) 4S)(Ph2P(CH2) 3PPh2)]. Application in styrene hydroformylation

Addition of 1,4-dithiols to dichloromethane solutions of [PtCl₂(P-P)] (P-P = (PPh₃)₂, Ph₂P(CH₂)₃PPh₂, Phd₂P(CH₂)₄PPh₂; 1,4-dithiols = HS(CH₂)₄SH, (−)DIOSH₂ (2,3-O-isopropylidene-1,4-dithiol-l-threitol), BINASH₂ (1,1′-dinaphthalene-2,2′-dithiol)) in the presence of NEt₃ yielded the mononuclear complexes [Pt(1,4-dithiolato)(P-P)]. Related palladium(II) complexes [Pd(dithiolato)(P-P)] (P-P=Ph₂P(CH₂)₃PPh₂, Ph₂P(CH₂)₄PPh₂; dithiolato = ⁻S(CH₂)₄S⁻, (−)-DIOS) were prepared by the same method. The structure of [Pt((−)DIOS)(PPh₃)₂] and [Pd(S(CH₂)₄S)(Ph₂P(CH₂)₃PPh₂)] complexes was determined by X-ray diffraction methods. Pt—dithiolato—SnC1₂ systems are active in the hydroformylation of styrene. At 100 atm and 125°C [Pt(dithiolate)(P-P)]/SnCl₂ (Pt:Sn = 20) systems provided aldehyde conversion up to 80%.     

Asymptotic Analysis of Diffraction Integrals in Gevrey Spaces

We present an overview on the state of the art of the research on the asymptotic behavior of diffraction integrals, i.e., the oscillatory integrals employed in the Fresnel theory of optics. We focus on the behavior of such integrals in the presence of standard caustics, in particular the elliptic and the hyperbolic umbilics, adopting the functional setting of Gevrey spaces. We also derive new estimates for the shadow region of the hyperbolic umbilic in terms of the distance from the caustic under symmetry condition in the space of parameters.