Asymptotic behaviour of a family of gradient algorithms in ℝ d and Hilbert spaces

The asymptotic behaviour of a family of gradient algorithms (including the methods of steepest descent and minimum residues) for the optimisation of bounded quadratic operators in ℝ^d and Hilbert spaces is analyzed. The results obtained generalize those of Akaike (1959) in several directions. First, all algorithms in the family are shown to have the same asymptotic behaviour (convergence to a two-point attractor), which implies in particular that they have similar asymptotic convergence rates. Second, the analysis also covers the Hilbert space case. A detailed analysis of the stability property of the attractor is provided.     

α-Admissibility of Observation Operators in Discrete and Continuous Time

In this paper a weighted form of the Weiss conjecture is studied. For certain weights, the conjecture is shown to hold for normal contraction operators related to discrete time linear systems. This is proved by an application of the Carleson measure theorem for weighted Dirichlet spaces. The result for discrete time systems is used to show that a weighted form of the Weiss conjecture holds for normal operators generating bounded C₀-semigroups. Previously, weighted admissibility has been characterised for generators of analytic semigroups. No such assumption of analyticity is made here. Additionally, results are presented regarding weighted Carleson measures, fractional powers of normal operators and weighted composition operators.     

Highly Unsaturated Platinum and Palladium Carbenes PtC3 and PdC3 Isolated and Characterized in the Gas Phase

Carbenes of platinum and palladium, PtC₃ and PdC₃, were generated in the gas phase through laser vaporization of a metal target in the presence of a low concentration of a hydrocarbon precursor undergoing supersonic expansion. Rotational spectroscopy and ab initio calculations confirm that both molecules are linear. The geometry of PtC₃ was accurately determined by fitting to the experimental moments of inertia of twenty‐six isotopologues. The results are consistent with the proposal of an autogenic isolobal relationship between O, Au⁺, and Pt atoms.     

Geometry of an Isolated Dimer of Imidazole Characterised by Rotational Spectroscopy and Ab Initio Calculations

An isolated, gas‐phase dimer of imidazole is generated through laser vaporisation of a solid rod containing a 1:1 mixture of imidazole and copper in the presence of an argon buffer gas undergoing supersonic expansion. The complex is characterised through broadband rotational spectroscopy and is shown to have a twisted, hydrogen‐bonded geometry. Calculations at the CCSD(T)(F12*)/cc‐pVDZ‐F12 level of theory confirm this to be the lowest‐energy conformer of the imidazole dimer. The distance between the respective centres of mass of the imidazole monomer subunits is determined to be 5.2751(1) Å, and the twist angle γ describing rotation of one monomer with respect to the other about a line connecting the centres of mass of the monomers is determined to be 87.9(4)°. Four out of six intermolecular parameters in the model geometry are precisely determined from the experimental rotational constants and are consistent with results calculated ab initio.     

A study of biomedical properties of hydrogels based on recombinant spidroin after their sterilization

A comparative analysis of rheological, organoleptic, physical and chemical properties of hydrogels was performed and their biosafety was examined in cell cultures before and after radiation and tyndallization sterilization. It was shown that the radiation sterilization does not destabilize the protein molecules of hydrogels at exposure doses less than 15 kGy, thereby not changing their physical, chemical and biomedical properties and, hence, the operational characteristics of products based on hydrogels.     

Mechanical Properties of Polymeric Emboli for Occlusion of Blood Vessels

Investigations of the formation of solid emboli in an aqueous medium of biocompatible solutions of polymers were carried out. Approaches to the production of solid samples for tensile and compression tests were developed and their mechanical properties were studied. It is shown that the ultimate compressive and tensile strength of emboli formed in an aqueous medium slightly decreases with increasing time of aging in water and increases markedly with increasing polymer concentration in the embolizing solution. All the tested compounds exhibit strength sufficient to not be destroyed by the action of blood flow.     

Determination of amphetamine in rat brain by in vivo microdialysis and ion-pairing liquid chromatography with electrospray tandem mass spectrometry

An ion-pairing liquid chromatography/electrospray tandem mass spectrometry (LC/ES-MS/MS) method with in vivo microdialysis for the determination of amphetamine in rat brain has been developed. A microdialysis probe was surgically implanted into the striatum of the rat and artificial cerebrospinal fluid (aCSF) was used as the perfusion medium. Samples were collected and then analyzed off-line by LC/ES-MS/MS. A reversed-phase C18 column was employed for LC separation and MS/MS was utilized for detection. Trifluoroacetic acid (TFA) was added to the mobile phase (acetonitrile/water) as an ion-pairing reagent. Detection was by ES-MS/MS directly, and no post-column addition of organic modifier was needed. Dual linear ranges were determined from 0.1-0.5 microg/mL and 0.005-0.1 microg/mL, respectively. The detection limit, based on a signal-to-noise ratio of 3, was 0.001 microg/mL (5 nM). Good precision and accuracy were obtained. The applicability of this newly developed method was demonstrated by continuous monitoring of amphetamine concentrations in rat brain. Amphetamine reached a maximum concentration of 0.086 +/- 0.017 microg/mL over 20-40 min after a single 3.0 mg/kg intraperitoneal administration.     

D-nuclear quadrupole and H(D),19F nuclear-spin—nuclear-spin hyperfine coupling constants from rotational spectra of H2O…DF and H2O…HF

The hyperfine structure in the 1₀₁ ← 0₀₀ transitions of H₂O…DF and H₂O…HF arising from D-nuclear quadrupole and H(D),¹⁹F nuclear-spin—nuclear-spin coupling effects have been resolved and measured by the technique of pulsed-nozzle, Fourier-transform microwave spectroscopy to give the following hyperfine coupling constants: ×_aa^D = 263.5(25) kHz, D_aa^DF = ?42.7(25) kHz and D_aa^HF = ?244(5) kHz.