Optimal controllability in viscoelasticity of rate type

Recently, the control engineers interest turns upon material with structural damping, such as hysteretic effects in elastoplastic systems [27] and flexible space structures [30] and in particular with damping due to the viscoelastic nature of the material, in the sense of Kelvin, [7], [12]. The reason for this renewed interest is the possibility of constructing finite rank compensators with small spillover in the observation [1], [5], [11], [25]. However, a control theory for the infinite system does not seem to exist in the literature. It is shown that the trajectories, initially in a certain subspace, can be steered to rest in any time T > 0 using distributed load controls

1 The reesults are partially contained in [19].

. Furthermore, and perhaps more interesting, the L₂ (0, T, H)-norm of the control decreases as T increases. This gives rise to the problem of time-optimal-controllability and the correlation to the problem of minimum norm controllability. It is shown that the time-optimal control is characterized by a weak “bang-bang” principle.     

Koordinative Verankerung von Nickelkomplexen an Hectorit-Schichtsilicaten mit Hilfe langkettiger Diphenylphosphinogruppen

Coordinative Anchoring of Nickel Complexes on Hectorite-Layer Silicates through long-chain Diphenylphosphine Groups The treatment of sodium and calcium hectorites with 2-diphenylphosphinoethyltriethoxysilane leads, by condensation of free hydroxyl groups, to functionalized layer silicates with long-chain diphenylphosphine groups onto which nickel chloride can be coordinated. In these modified hectorites the fourth coordination site of the tetrahedrally coordinated nickel is occupied by a labile solvent molecule. On the other hand, the complex bis(2-diphenylphosphinoethyltriethoxysilane)nickel(II) chloride prepared beforehand also reacts with sodium hectorite under condensation; but the square-planar coordination of the four stable ligands (two chloride and two phosphor atoms) is maintained. This finds its expression in a significant activity decrease in catalytic reactions as compared to the aforementioned products.     

Heterocyclisation de diols βγ′-alleniques.

The silver nitrate assisted cyclization of the entitled diols $\text{3}$ leads, depending on the substitution of the allenic linkage, specifically to dihydropyranes $\text{4}$, when R is alkyl or to an equimolecular mixture of $\text{4}$ and its tetrahydrofuranyl isomer $\text{5}$ when R is hydrogen.     

Single crystal X- and Q-band EPR spectroscopy of a binuclear Mn(2)(III,IV) complex relevant to the oxygen-evolving complex of photosystem II

The anisotropic g and hyperfine tensors of the Mn di-micro-oxo complex, [Mn(2)(III,IV)O(2)(phen)(4)](PF(6))(3).CH(3)CN, were derived by single-crystal EPR measurements at X- and Q-band frequencies. This is the first simulation of EPR parameters from single-crystal EPR spectra for multinuclear Mn complexes, which are of importance in several metalloenzymes; one of them is the oxygen-evolving complex in photosystem II (PS II). Single-crystal [Mn(2)(III,IV)O(2)(phen)(4)](PF(6))(3).CH(3)CN EPR spectra showed distinct resolved (55)Mn hyperfine lines in all crystal orientations, unlike single-crystal EPR spectra of other Mn(2)(III,IV) di-micro-oxo bridged complexes. We measured the EPR spectra in the crystal ab- and bc-planes, and from these spectra we obtained the EPR spectra of the complex along the unique a-, b-, and c-axes of the crystal. The crystal orientation was determined by X-ray diffraction and single-crystal EXAFS (Extended X-ray Absorption Fine Structure) measurements. In this complex, the three crystallographic axes, a, b, and c, are parallel or nearly parallel to the principal molecular axes of Mn(2)(III,IV)O(2)(phen)(4) as shown in the crystallographic data by Stebler et al. (Inorg. Chem. 1986, 25, 4743). This direct relation together with the resolved hyperfine lines significantly simplified the simulation of single-crystal spectra in the three principal directions due to the reduction of free parameters and, thus, allowed us to define the magnetic g and A tensors of the molecule with a high degree of reliability. These parameters were subsequently used to generate the solution EPR spectra at both X- and Q-bands with excellent agreement. The anisotropic g and hyperfine tensors determined by the simulation of the X- and Q-band single-crystal and solution EPR spectra are as follows: g(x) = 1.9887, g(y) = 1.9957, g(z) = 1.9775, and hyperfine coupling constants are A(III)(x) = |171| G, A(III)(y) = |176| G, A(III)(z) = |129| G, A(IV)(x) = |77| G, A(IV)(y) = |74| G, A(IV)(z) = |80| G.     

QUENCHING OF TYROSINE FLUORESCENCE BY PHOSPHATE IONS: A MODEL STUDY FOR PROTEIN-NUCLEIC ACID COMPLEXES

Abstract— In order to test the ability of phosphate groups to quench the tyrosine fluorescence in nucleic acid-protein complexes, we have studied the effect of several phosphate ions on the fluorescence of tyrosine derivatives. Mono and bianions (H₂PO₄ and HPO₄^2–) which are good proton acceptors quenched the fluorescence of all the phenolic compounds studied except that of O -methyl tyrosine. With the other derivatives (tyrosine, N -acetyl tyrosinamide and lysyl-tyrosyl-α lysine) fluorescence inhibition was accompanied by the appearance of a long wavelength emission (345 nm) attributed to tyrosinate anions. The quenching of tyrosine emission was due to the deprotonation of the phenolic group promoted in the excited state by phosphate ions and leading to the weakly fluorescent tyrosinate ion. Mono and dianions of phosphate mono ester inhibited tyrosine fluorescence as did unesterified phosphates. However, phosphate diester did not have any effect on the fluorescence of tyrosine derivatives. We conclude from this study that in nucleic acid-protein complexes phosphate groups are not able to quench tyrosine fluorescence except at the end of polynucleotide chains. Since monoester and diester monoanions have a different behavior, we propose that quenching of tyrosine fluorescence by monoanions requires the formation of two hydrogen bonds. This complex cannot form with diesters which consequently do not quench tyrosine fluorescence.     

Photochemically induced fluorescence investigation of aβ-cyclodextrin: Azure A inclusion complex and determination of analytical parameters

The photooxidation of Azure A and fluorescence properties of Azure A and its photoproduct have been investigated in aqueous media and in the presence of-cyclodextrin (-CD). The fluorescence intensity of the complex formed between the photoproduct and -CD was found to be three times higher than that of the uncomplexed Azure A photoproduct. A complex formation constant of 110±40 M^–1 was calculated using the Benesi-Hildebrand treatment of the fluorescence emission data. Although the stoichiometry of the Azure A photoproduct: -CD complex was found to be 1: 1, it seems that the Azure A structure is only partially included. Calibration graphs were plotted for the free Azure A photoproduct and the photogenerated product included in -CD. The analytical parameters and quantification limits were determined.     

A general approach toward the synthesis of C-nucleoside pyrazolo[1,5-a]-1,3,5-triazines and their 3',5'-bisphosphate C-nucleotide analogues as the first reported in vivo stable P2Y(1)-receptor antagonists

In our effort to identify potent purinergic P2Y(1) receptor antagonists as potent platelet aggregation inhibitors with enhanced metabolic stability, we developed an efficient route for the large-scale preparation of 2'-deoxy-C-nucleosides of pyrazolo[1,5-a]-1,3,5-triazine. The key strategic elements of this novel synthetic approach involved the following: (i) the use of a novel activating group, the N-methyl-N-phenylamino group, which was easily generated in high yield by treatment of the pyrazolo[1,5-a]-1,3,5-triazin-4-one (5) with phosphorus oxychloride and dimethylaniline under high pressure, (ii) a regio- and stereospecific palladium-mediated coupling reaction of the readily available unprotected glycal 1,4-anhydro-2-deoxy-D-erythro-pent-1-enitol (4b) and the 8-iodo derivative (16), and (iii) the stereoselective reduction of the ketone group of the furanosyl ring followed by the subsequent displacement of the N-methyl-N-phenylamino group upon treatment with methylamine. The beta configuration at the anomeric C-1' position of the glycal moieties was perfectly retained throughout this conversion. This procedure afforded 8-(2'-deoxy-beta-D-ribofuranosyl)-2-methyl-4-(N-methylamino)pyrazolo[1,5-a]-1,3,5-triazine (21) and 8-(2'-deoxy-beta-D-xylofuranosyl)-2-methyl-4-(N-methylamino)pyrazolo[1,5-a]-1,3,5-triazine (24) with an overall yield of 50% and 39%, respectively. Finally, the conversion of nucleosides 21 and 24 to the pyrazolotriazine C-nucleotides 3',5'-bisphosphate 2 and 3',5'-cyclophosphate 26 is also described herein and represents the first reported nucleotide derivatives within the pyrazolo[1,5-a]-1,3,5-triazine series. Preliminary biological testing has shown that compound 2 strongly inhibits ADP-induced human platelet aggregation and shape change and possesses significant efficacies 30 min after injection in rat, highlighting a strong P2Y(1)-receptor antagonist activity in vitro combined with a prolonged duration of action in vivo.     

Wiener-hopf equations for waves scattered by a system of parallel sommerfeld half-planes

A scalar time-harmonic wave (governed by Helmholtz's equation) impinges on N semi-infinite half-planes. The scattered field is sought when first, second, and third-kind boundary conditions or even general linear transmission conditions on the plates ∑_m and their complementary parts ∑ are prescribed. Making use of the Fourier transform a representation formula for H¹ (Ω) solutions is presented. The boundary/transmission problem is shown to be equivalent to a (2N × 2N)-Wiener–Hopf (WH) system for jumps of the Dirichlet–and Neumann–Cauchy data across the semi-infinite screens ∑_m. The (2N × 2N)-Fourier symbol matrix ??_?? contains N block matrices on the diagonal corresponding to Sommerfeld boundary/transmission problems for a single plate. These (2 × 2)-symbol matrices are factorizable and thus the full WH system is invertible by a perturbation argument for not too small spacings of neighbouring screens ∑_m.     

Elastic and inelastic backscattering of slow electrons from silicon

The elastic and inelastic backscattering from Si(111) surfaces and evaporated amorphous silicon were measured as a function of the primary energyE _p (30eVE _p 200eV). A detailed evaluation of the amplitude of the volume plasmon lossA _vp was carried out in the loss spectra. In contrast to single crystals amorphous silicon produces a smooth curve as function of the energy, both for the elastic backscattered electron current and forA _vp (E).To interpret the measured curves for the amorphous Si calculations were made for the elastic scattering and for the excitation probability of the volume plasmon in a randium-jellium-model. In the case of elastic scattering a random distribution of atoms is assumed. In the case of inelastic scattering the free electron model is used. Double scattering processes are included. The comparison between theory and experiment shows satisfactory agreement for elastic scattering. The energy dependent excitation probability of the volume plasmon is excellently represented by this model.