Factorization of Lipschitz functions and absolute convergence of Vilenkin-Fourier series

LetG be a Vilenkin group (i.e., an infinite, compact, metrizable, zero-dimensional Abelian group). Our main result is a factorization theorem for functions in the Lipschitz spaces \(\mathfrak{L}\mathfrak{i}\mathfrak{p}\) (α,p; G). As colloraries of this theorem, we obtain (i) an extension of a factorization theorem ofY. Uno; (ii) a convolution formula which says that \(\mathfrak{L}\mathfrak{i}\mathfrak{p} (\alpha , r; G) = \mathfrak{L}\mathfrak{i}\mathfrak{p} (\beta , l; G)*\mathfrak{L}\mathfrak{i}\mathfrak{p} (\alpha - \beta , r; G)\) for 0<β<α<∞ and 1≤r≤∞; and (iii) an analogue, valid for allG, of a classical theorem ofHardy andLittlewood. We also present several results on absolute convergence of Fourier series defined onG, extending a theorem ofC. W. Onneweer and four results ofN. Ja. Vilenkin andA. I. Rubinshtein. The fourVilenkin-Rubinshtein results are analogues of classical theorems due, respectively, toO. Szász, S. B. Bernshtein, A. Zygmund, andG. G. Lorentz.     

Deficient generalized Fibonacci maximum path graphs

The structure of an acyclic directed graph with n vertices and m edges, maximizing the number of distinct paths between two given vertices, is studied. In previous work it was shown that there exists such a graph containing a Hamiltonian path joining the two given vertices, thus uniquely ordering the vertices. It was further shown that such a graph contains k ? 1 full levels (an edge (i, j) belongs to level t = j ?i) and some edges of level k—a deficient k-generalized Fibonacci graph. We investigate the distribution of the edges in level 3 in a deficient 3-generalized Fibonacci graph, and develop tools that might be useful in extending the results to higher levels.     

197Au Mössbauer study of Au/Ni artificial multilayers

¹⁹⁷Au Mössbauer measurements have been performed at 16 K on the Au/Ni artificial multilayers having three different thickness of the layers those are 10Å Au/10Å Ni, 30Å Au/30Å Ni and 53Å Au/53Å Ni on a 250Å pure Au buffer layer. Mössbauer spectra obtained can be decomposed into mainly two components. One is an unperturbed component having an identical isomer shift value to the bulk Au metal. The other is the component perturbed strongly by the Ni layer indicating a broad contribution at positive velocity side and its intensity depends on the thickness of the Au layer. The spectrum from 10Å Au/10Å Ni multilayer is an entirely perturbed one and its area ratio to the component rising from pure Au buffer layer indicates the large Debye-Waller-factor suggesting the supermodulus effect in this multilayer.     

On-line nuclear orientation study of184Au

The¹⁸⁴Au→¹⁸⁴Pt decay, studied on-line with the UNISOR facility at HHIRF, is discussed. Gamma-ray and conversion-electron spectroscopy of¹⁸⁴Pt as well as on-line nuclear orientation measurements of¹⁸⁴Au were done. A new low-lying level scheme of¹⁸⁴Pt is proposed. Two coexisting bands with different deformations and their respective γ-vibrational bands are established. Internal conversion coefficients for interband transitions between states with the same spin are extracted from the spectroscopy measurements. The relative E0 contents of the transitions are determined by combining internal conversion coefficients with E2/M1 mixing ratios deduced from gamma-ray anisotropies measured from oriented nuclei.     

T-violation neutron experiment and polarized3He

An experimental scheme of the spin detailed balance in polarized neutron transmission through a polarized nuclear target is discussed for the T-violation test. The value of the spin detailed balance is estimated by using the data of the scattering amplitudes. The nuclear polarizations of proton,³He and¹³⁹La are discussed for the T-violation experiment.     

Collinear fast atomic-beam laser spectroscopy at riken garis/igisol

We have constructed a fast atomic-beam collinear laser spectroscopy system connected to the on-line isotope separator facility GARIS/IGISOL at RIKEN. This system is potentially powerful in studying refractory elements. To test the system, an off-line collinear experiment was made on stable Hf isotopes produced by means of laser ablation technique. For production of radioactive Hf isotopes, the use of the inverse kinematics of a fusion reaction,⁹Be(¹⁶⁶Er,xn)^175-x Hf, was investigated. The radioactive isotope¹⁶⁹Hf was successfully extracted from GARIS/IGISOL and accelerated up to 30 keV.     

Mössbauer effect of iron-57 intercalated in layered compound 2H−Fe0.5TaSe2

⁵⁷Fe Mössbauer effect study has been performed on intercalated compound 2H?Fe_0.5TaSe₂ over a temperature range between 14K and 500K. The highly concentrated intercalation samples 2H?Fe_xTaSe₂ with Fe atoms (x up to 2) are prepared by the electrochemical method for the first time. The Mössbauer measurement shows that iron is in Fe³⁺ high spin state and with the same probability occupies both octahedral and tetrahedral interstices of the Van der Waals gap. The fact that effective masses of iron ions in both sites are close to 57 amu and characteristic temperatures (Θ_M =130K, 107K respectively) are found to be relatively small is attributed to the weak forces on Fe³⁺.     

Calculation of local insulating structure of CaCuO2 with interplanar oxygen defects

The electronic band structures of CaCuO₂ with various planar structures have been computed with the spin polarized, full potential pseudofunction method. The perfect tetragonal structure has metallic bands. If the CuO plane is puckered as proposed on the basis of pulsed neutron experiments, a semi-metallic-like behavior is found. When some of the oxygen atoms are moved from the basal plane into interplanar sites that are coplanar with Ca, an insulating ground state is obtained with antiferromagnetic moments of 0.21 _B . Around this interplanar oxygen defect site, the charge and magnetic moment distributions resemble those of a CuO chain structure with strong coupling to Cu atoms from different basal planes. Small displacements of defect oxygens at interplanar sites along the CaO planar directions produces large changes in band shape near E _F , suggesting strong electron-lattice coupling. The coupling is much weaker for displacements of O atoms within the CuO basal plane. Such interplanar defects could occur in superconducting cuprates and thus create small insulating regions for the pinning of magnetic flux lines.     

Reaction mechanisms in the six-nucleon system with the multi-configuration resonating-group method

The properties of the six-nucleon system are examined with a multi-configuration resonating-group method consisting of thed+ configuration, thep+⁵He andn+⁵Li configurations, and deuteron pseudo-inelastic configurations. The main purpose is to study the reaction mechanisms in this system. The results obtained are quite satisfactory, with the calculatedd+ total reaction cross sections equal to around 90% of the empirically determined values. The one-nucleon transfer process turns out to be significantly more important than the deuteron direct-breakup process; however, the latter process must still be properly taken into consideration, since it does contribute to about one third of thed+ total reaction cross section. The process of one-nucleon transfer is shown to occur mainly in the peripheral region, while the process of deuteron direct-kreakup is found to take place predominantly in the interior region of the compound nucleus. The convergence property with respect to the number of deuteron pseudo-inelastic configurations has also been investigated. Here it is found that, with the dominant configurations included, the number of such configurations required can be rather small, which is an important finding because it greatly simplifies the computational aspects of multi-configuration resonating-group calculations.     

Test of an optical parametric oscillator (OPO) as a compact and fast tunable stokes source in coherent anti-stokes raman spectroscopy (CARS)

An optical parametric oscillator (OPO), as a novel kind of broadband Stokes source, is employed for coherent anti-Stokes Raman spectroscopy (CARS). Compared to the conventional dye laser configuration OPO-CARS offers practical advantages. The tunable OPO allows a fast and comfortable frequency tuning. The excitation bandwidth of about 35 cm^–1 (FWHM) limits the spectral range of effective and stable single pulse CARS generation but can be used to enhance selected spectral structures.