Distributive lattices of numberings

We study into a semilattice of numberings generated by a given fixed numbering via operations of completion and taking least upper bounds. It is proved that, except for the trivial cases, this semilattice is an infinite distributive lattice every principal ideal in which is finite. The least upper and the greatest lower bounds in the semilattice are invariant under extensions in the semilattice of all numberings. Isomorphism types for the semilattices in question are in one-to-one correspondence with pairs of cardinals the first component of which is equal to the cardinality of a set of non-special elements, and the second — to the cardinality of a set of special elements, of the initial numbering. Supported by INTAS grant No. 00-429. __________ Translated from Algebra i Logika, Vol. 46, No. 1, pp. 83–102, January–February, 2007.     

Proton NMR relaxation in albumin solutions doped with Mn(II)

The aim of this study is to obtain further information about the source of proton relaxation in the Mn(II)-human serum albumin complex. For this purpose, proton relaxation rates in albumin solutions 1/T ₁ and 1/T ₂ were measured versus increasing amounts of manganese [Mn_t]. The fractions of manganese bound to albumin [Mn_b] and free manganese [Mn_f] were then determined from proton relaxation rate enhancement data. Paramagnetic contributions of bound manganese to the observed relaxation rates (1/T _1p^*)_b and (1/T _2p^*)_b were also determined. Finally, the (1/T _2p^*)_b/(1/T _1p^*)_b ratio was used in a derived equation to estimate an effective correlation time τ. Mean τ value of the complex was found to be in the order of 3 ns, while the hydration number of bound manganese q was estimated to be about 4. The 1/τ was found to be the sum of the inverse values of rotational correlation time 1/τ _r, mean residence time of water in hydration spheres of the complex 1/τ _m, and longitudinal electronic relaxation time of manganese 1/τ _s in the complex. In conclusion, the relaxation mechanism in albumin solutions containing Mn(II) can be interpreted through dipolar and scalar interactions modulated by τ _r, τ _m and τ _s. This analysis enables one to get reasonable figures for the τ _r and q of Mn(II) in albumin solution.     

Wavelength tuning in Er3+,Yb3+:glass microchip lasers

The paper presents the investigation results of laser generation around 1.5 μm at different wavelengths. The shifts of the wavelength were achieved by the change of pump power, transmission of an output mirror, and length of an active medium. Mathematical analysis and explanation of this phenomenon was curried out on the basis of the change in relation between the gain and loss lines.     

Effect of crystallographic orientation on the anodic formation of nanoscale pores/tubes in TiO2 films

Self-organized nanopores and nanotubes have been produced in thin films of titanium (Ti) prepared using filtered cathodic vacuum arc (FCVA), DC- and RF-sputter deposition systems. The anodization process was performed using a neutral electrolyte containing fluoride ions with an applied potential between 2 and 20 V (for clarity the results are only presented for 5 V). Scanning electron microscopy (SEM), atomic force microscopy (AFM) and X-ray diffraction (XRD) techniques were used to characterise the films. It was found that the crystallographic orientation of the Ti films played a significant role in determining whether pores or tubes were formed during the anodic etching process.     

A note on the Ramanujan τ-function

Let τ(n) be the Ramanujan τ-function, x ≥ 10 be an integer parameter. We prove that

Short interval asymptotics for a class of arithmetic functions

Summary We provide a general asymptotic formula which permits applications to sums like <InlineEquation ID=IE"1"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"2"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"3"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"4"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"5"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"6"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"7"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"8"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"9"><EquationSource Format="TEX"><![CDATA[$]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>$]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation> \sum_{x< n\le x+y} \big(d(n)\big)^2, \quad \sum_{x< n\le x+y} d(n^3),\quad \sum_{x< n\le x+y}\big(r(n)\big)^2, \quad \sum_{x< n\le x+y}r(n^3), $$ where $d(n)$ and $r(n)$ are the usual arithmetic functions (number of divisors, sums of two squares), and $y$ is small compared to~$x$.     

Optical properties of SrTiO<Subscript>3</Subscript> thin films by pulsed laser deposition

SrTiO₃ thin films were prepared on a fused-quartz substrate by pulsed laser deposition (PLD). Dense and homogeneous films with a thickness of 260 nm were prepared. Optical constants (refractive index n and extinction coefficient k) were determined from the transmittance spectra using the envelope method. The optical band gap energy of the films was found to be 3.58 eV, higher than the 3.22 eV for bulk SrTiO₃, attributable to the film stress exerted by the substrate. The dispersion relation of the refractive index vs. wavelength follows the single electronic oscillator model. The refractive index and the packing density for the PLD-prepared SrTiO₃ thin films are higher than those for the SrTiO₃ films prepared by physical vapor deposition, sol–gel and RF sputtering. Received: 18 March 2002 / Accepted: 7 October 2002 / Published online: 8 January 2003 RID="*" ID="*"Corresponding author. Fax: +86-25/359-5535, E-mail: mszhang@nju.edu.cn     

Efficient two-photon absorption of CdSe-CdS/ZnS core-multishell quantum dots under the excitation of near-infrared femtosecond pulsed laser

We report that two-photon absorption (TPA) properties of semiconductor CdSe-core CdS/ZnS-multishell quantum dots (QDs) in toluene under excitation of femtosecond laser at 800 nm. The results show efficient TPA process and large TPA cross section of three types of size QDs, which is 1900, 5710, and 16060 GM (1 GM = 10⁻⁵⁰ cm⁴ s photon⁻¹), respectively. TPA cross section dramatically increases with increased core size, showing a strong size-dependence effect. Furthermore, two-photon excitation (TPE) fluorescence intensity not only depends on TPA capacity, but also relies on improved quantum yield resulting from passivation of QD surface by different coated monolayers (MLs). These facts in combination with the narrow fluorescence bandwidth make these QDs as promising probes for multicolor two-photon microscopy.     

Electronic structure and X-ray spectra of transition metal sulfides NiS,CuS, and ZnS

A numerical electronic band structure calculations for sulfides NiS, CuS, and ZnS are carried out. Using the results a detailed analysis of a valence states is performed; obtained partial densities of states are compared with X-ray SL _2,3 and $ SK_{\beta _{1,3} } $ SK_{\beta _{1,3} } -emission spectra. We showed that spectrum lineshape depends on hybridization strength between various Me(3d)-orbitals and 3p-states of sulfur. The hybridization strength and the symmetry of hybrid Me(3d)-orbitals are defined by crystal lattice structure. Finally a well splitted in energy bonding and antibonding states Me(3d)-S(3p) appear while weakly hybridized Me(3d)-states mainly contribute to spectra intensity in the energy between them. A good agreement between the theoretical and the experimental spectra of valence band for considered sulfides is obtained.     

Blue organic light-emitting diodes with low driving voltage and maximum enhanced power efficiency based on buffer layer MoO3

Blue organic light-emitting devices based on wide bandgap host material, 2-(t-butyl)-9, 10-di-(2-naphthyl) anthracene (TBADN), blue fluorescent styrylamine dopant, p-bis(p-N,N-diphenyl-amino-styryl)benzene (DSA-Ph) have been realized by using molybdenum oxide (MoO₃) as a buffer layer and 4,7-diphenyl-1,10-phenanthroline (BPhen) as the ETL. The typical device structure used was glass substrate/ITO/MoO₃ (5 nm)/NPB (30 nm)/[TBADN: DSA-Ph (3 wt%)](35 nm)/BPhen (12 nm)/LiF (0.8 nm)/Al (100 nm). It was found that the MoO₃∥BPhen-based device shows the lowest driving voltage and highest power efficiency among the referenced devices. At the current density of 20 mA/cm², its driving voltage and power efficiency are 5.4 V and 4.7 Lm/W, respectively, which is independently reduced 46%, and improved 74% compared with those the m-MTDATA∥Alq₃ is based on, respectively. The J-V curves of ‘hole-only’ devices reveal that a small hole injection barrier between MoO₃∥NPB leads to a strong hole injection, resulting low driving voltage and high power efficiency. The results strongly indicate that carrier injection ability and balance shows a key significance in OLED performance.