Convergence of Anisotropically Decaying Solutions of a Supercritical Semilinear Heat Equation

We consider the Cauchy problem for a semilinear heat equation with a supercritical power nonlinearity. It is known that the asymptotic behavior of solutions in time is determined by the decay rate of their initial values in space. In particular, if an initial value decays like a radial steady state, then the corresponding solution converges to that steady state. In this paper we consider solutions whose initial values decay in an anisotropic way. We show that each such solution converges to a steady state which is explicitly determined by an average formula. For a proof, we first consider the linearized equation around a singular steady state, and find a self-similar solution with a specific asymptotic behavior. Then we construct suitable comparison functions by using the self-similar solution, and apply our previous results on global stability and quasi-convergence of solutions.     

Continuum many Fréchet types of hereditarily strongly infinite-dimensional Cantor manifolds

In this note we construct a family of continuum many hereditarily strongly infinite-dimensional Cantor manifolds such that for every two spaces from this family, no open subset of one is embeddable into the other.

     

On-line coupling of capillary isotachophoresis and zone electrophoresis for the assay of phenolic compounds in plant extracts

The combination of capillary isotachophoresis (ITP) and capillary zone electrophoresis (CZE) in the column coupling configuration was optimized in a mode where the electrolyte for the CZE step is different from the leading and terminating ITP electrolytes. Two colored markers, picric acid and 1-nitroso-2-naphthol, were used for exact timing of the transfer of isotachophoretically stacked analyte zones into the CZE column and for the control of the residual amount of the leading and terminating ITP electrolytes entering the CZE capillary together with the analytes, thus controlling the duration of transient ITP migration in the CZE capillary and ensuring good separation of the analytes and reproducibility of the migration times (relative standard deviations 1%). ITP-CZE was applied to the simultaneous assay of several cinnamic acid derivatives and flavonoids in methanolic extracts of Sambucus flowers and Crataegus leaves and flowers. The preconcentrating and cleansing effect of the ITP step allowed injection of relatively large sample volumes (30 microL). The limits of detection were approximately 20-50 ng x mL(-1) and 100 ng x mL(-1) for the acids and flavonoids, respectively ( thick similar 200-times lower compared to conventional CE) with spectrophotometric detection at 254 nm. The ITP-CZE exhibited satisfactory linearity and precision when using CZE buffer of pseudo "pH" 9.0; 1-nitroso-2-naphthol was employed as the internal standard. The separation took approximately 35 min. The ITP-CZE results for rutin, hyperoside, and vitexin-2-O"-rhamnoside were in good accordance with those obtained previously by high-performance liquid chromatography.     

Theoretical modeling of guided wave propagation in a sandwich plate subjected to transient surface excitations

A fast and efficient two-dimensional (2D) semi-analytical model based on global matrix method is developed to study the general characteristics of guided wave propagation in a honeycomb composite sandwich structure (HCSS) subjected to time-dependent transient surface excitations. The HCSS used in this study has an extremely lightweight and thick nomex honeycomb core, which is sandwiched between two thin graphite woven composite skins. The homogenized material properties of the skin and the core are considered to be elastic and quasi-isotropic in nature. Far-field time history of surface displacements are calculated for vertical and horizontal tone-burst surface excitations that are representative of thickness and radial mode of vibrations of piezoelectric transducers, respectively. Results are compared with those obtained from Finite element modeling (FEM) in LS-DYNA showing good agreement. Wavelet transform is then performed on the time-domain signal to obtain the group velocities of the propagating modes for their accurate identification on the basis of the theoretical dispersion curve. It is found that the response signal is dominated by the first anti-symmetric mode for a vertical excitation, whereas, the signal characteristics are multimodal in nature with dominating higher order symmetric and anti-symmetric modes for a horizontal excitation. The model is expected to be helpful for appropriate guided wave mode tuning and rapid analysis of data for experimental detection of disbonds in these novel structures.     

Precise isotope ratio measurements as a unique tool in modern analytical chemistry

Analytical and Bioanalytical Chemistry -     

Semiempirical SCF theory with “scaled” slater orbitals

A self consistent quantum mechanical treatment of atomic structures is presented. The method which is suitable for molecular calculations involves the optimization (scaling) of exponents of a minimal basis set of Slater orbitals and accounts semiempirically for electron correlation.The calculation of successive ionization potentials as well as that of promotional energies lead to results in satisfactory agreement with experiment.

---

Zusammenfassung Es wird ein selbstkonsistentes quantenmechanisches Verfahren für Atomstrukturen entwickelt, das auch für Moleküle geeignet ist, und eine Optimierung (scaling) der Exponenten von Slaterorbitalen in einem minimalen Satz der Basisvektoren sowie eine semiempirische Berücksichtigung der Elektronenkorrelation beinhaltet. p]Die berechneten Ionisierungs- und Anregungsenergien stimmen gut mit den experimentellen Werten überein.

---

Résumé Un traitement quantique self consistent des structures atomiques est décrit. La méthode qui est aussi valable pour le calcul des molécules introduit l'optimalisation (scaling) des exposents d'un minimal basis set d'orbitales de Slater et prend en considération la corrélation électronique d'une manière semi empirique.Le calcul des potentiels d'ionisations successifs ainsi que celui des énergies de promotion conduit a des résultats en accord satisfaisant avec l'expérience.

     

Paramagnetic silver species in irradiated Ag−NaA zeolites. An EPR and ESEEM study

Several polymeric silver clusters have been observed in Ag_x?NaA zeolite (x=1,6) of varying water content, which was exposed to x-rays at 77 K and annealed at higher temperatures.¹⁰⁹Ag₁?NaA zeolite dehydrated at 130°C yields the dimer¹⁰⁹Ag₂ ⁺ and the trimer¹⁰⁹Ag₃ ²⁺ after irradiation at 77 K and annealing at 240 K. Owing to the use of one Ag isotope the EPR spectra of these species are highly resolved exhibitingg and hyperfine anisotropy. By irradiation of¹⁰⁹Ag_x?NaA zeolite (x=1,6) in hydrated form two new trimeric silver clusters I and II are produced. The ratio between I and II depends on the initial Ag content. ESEEM spectra of these species show interaction with aluminum nuclei of the framework and with distant water molecules. If Ag₆?NaA zeolite dehydrated at 130°C is irradiated the hexameric cluster Ag₆ ⁿ⁺ is formed. The ESEEM spectrum shows interaction only to aluminum nuclei. From ESEEM experiments on Ag₆ ⁿ⁺ with added adsorbates (D₂O, CD₃OD) it could be inferred that Ag₆ ⁿ⁺ is only stable if the neighbouring cages do not contain adsorbate molecules.     

A Monte Carlo study of finite temperature λφ 2, 3 4 ⋆

Zeitschrift für Physik C Particles and Fields - We study the finite temperature behaviour of λφ4 theory in two and three dimensions, using Monte Carlo simulations. We renormalize the...     

Microwave noise radiators

For the purposes of Microwave Active Radiometry (1), three noise radiators were developed and tested. One is a conventional noise diode source in a rectangular R-100 waveguide with a 6-dB horn attached, other two noise radiators are made as half-wave dipoles with noise diodes installed. Excess noise ratio and polarization ratio was estimated for the three designs, and the 3-D radiation pattern determined for the dipole models. For evaluation, radiometers operating at 11.5 GHz and 12.5 GHz were used, but some response was also determined with a radiometer operating at 4 GHz.