Vojta's Main Conjecture for blowup surfaces

In this paper, we prove Vojta's Main Conjecture for split blowups of products of certain elliptic curves with themselves. We then deduce from the conjecture bounds on the average number of rational points lying on curves on these surfaces, and expound upon this connection for abelian surfaces and rational surfaces.

     

Corrected mirror systems with double reflection

We propose objectives consisting of two mirrors with central holes for passage of a light beam. The optical layout ensures multiple reflection of rays from both mirrors. We consider several approaches to calculating the design parameters for which three and four aberrations do not occur. The objectives can be used in optical devices operating in the UV and IR regions of the spectrum. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 74, No. 2, pp. 267–270, March–April, 2007.     

The Conductance- and Capacitance-Frequency Characteristics of the Rectifying Junctions Formed by Sublimation of Organic Pyronine-B on p-Type Silicon

The rectifying junction characteristics of the organic compound pyronine-B film on a p-type Si substrate has been studied. The pyronine-B has been sublimed on the top of p-Si surface. The barrier height and ideality factor values of 0.79±0.04 and 1.13±0.06 eV for this structure have been obtained from the forward bias current-voltage (I-V) characteristics. From the low capacitance-frequency (C-f) characteristics as well as conductance-frequency (G-f) characteristics, the energy distribution of the interface states and their relaxation time have been determined in the energy range of (0.53−E_v)-(0.79−E_v) eV taking into account the forward bias I-V data. The interface state density N_ss ranges from 4.93×10¹⁰ cm⁻² eV⁻¹ in (0.79−E_v) eV to 3.67×10¹³ cm⁻² eV⁻¹ in (0.53−E_v) eV. Furthermore, the relaxation ranges from 3.80×10⁻³ s in (0.53−E_v) eV to 4.21×10⁻⁴ s in (0.79−E_v) eV. It has been seen that the interface state density has an exponential rise with bias from the midgap towards the top of the valence band. The relaxation time shows a slow exponential rise with bias from the top of the valence band towards the midgap.     

Densité des Points à Coordonnées Multiplicativement Indépendantes

Nous montrons que pour toute sous-variété algébrique d'un tore multiplicatif (non contenue dans un sous-groupe algébrique propre), on peut choisir un ensemble Zariski dense de points algébriques de hauteur contrôlée, dont toutes les coordonnées sont multiplicativement indépendantes. Cet énoncé précise et généralise un théorème de S. Zhang qui lie la hauteur projective d'une varété au minimum essentiel de la hauteur des points algébriques de celle-ci. En tenant compte d'un résultat précédent des auteurs sur le problème de Lehmer généralisé à un tore, nous en déduisons une minoration pour la hauteur normalisée d'une sous-variété d'un tore. Cette dernière est optimale à un «-prés» en le degré géométrique de la variété étudiée (confer une conjecture du second auteur avec P. Philippon).In this article, we prove that on any subvariety of a multiplicative torus which is not contained in a proper algebraic subgroup, one can find a Zariski dense set of algebraic points of small height whose coordinates are multiplicatively independent. This statement generalizes an earlier result of S. Zhang which links the projective height of a variety with the essential minimum of its algebraic points. Taking into account an earlier result of the authors on the Lehmer problem generalized to a multiplicative torus, one deduces a lower bound for the normalized height of subvarieties of multiplicative groups. This lower bound is optimal up to an in the geometric degree of the variety studied (confer a conjecture by the second author and P. Philippon).     

Fission fragment mass yields of Th to Rf even-even nuclei

Fission properties of the actinide nuclei are deduced from theoretical analysis. We investigate potential energy surfaces and fission barriers and predict the fission fragment mass yields of actinide isotopes. The results are compared with experimental data where available. The calculations were performed in the macroscopic-microscopic approximation with the Lublin-Strasbourg Drop (LSD) for the macroscopic part, and the microscopic energy corrections were evaluated in the Yukawa-folded potential. The Fourier nuclear shape parametrization is used to describe the nuclear shape, including the non-axial degree of freedom. The fission fragment mass yields of the nuclei considered are evaluated within a 3D collective model using the Born-Oppenheimer approximation.     

Annealing temperature effect on the structural, optical and electrical properties of ZnS thin films

Zinc sulfide thin films were prepared on glass substrates at room temperature using a chemical bath deposition method. The obtained films were annealed at temperatures ranging from 100 to 500 °C in steps of 100 °C for 1 h. The films were characterized by X-ray diffraction (XRD), Raman spectroscopy, energy dispersive X-ray analysis (EDX), optical absorption spectra, and electrical measurements. X-ray diffraction analysis indicates that the deposited films have an amorphous structure, but after being annealed at 500 °C, they change to slightly polycrystalline. The optical constants such as the refractive index (n_r), the extinction coefficient (k), and the real (ε₁) and imaginary (ε₂) parts of the dielectric constant are calculated depending on the annealing temperature. Aside from the ohmic characteristics of the I-V curve, a nonlinear I-V curve owing to the Schottky contact is also found, and the barrier heights (?_bn) for Au/n-ZnS and In/n-ZnS heterojunctions are calculated. The conductivity type was identified by the hot-probe technique.     

On the exact asymptotic behaviour of the distribution of ladder epochs

Let T₊ denote the first increasing ladder epoch in a random walk with a typical step-length X. It is known that for a large class of random walks with E(X)=0,E(X²)=∞, and the right-hand tail of the distribution function of X asymptotically larger than the left-hand tail, $\text{P}\text{T}{}_{\mathrm{+}}\text{?n∽n}{}^{\mathrm{<mtext>1</mtext><mtext>\beta ?1</mtext>}}\text{L}{}_{\mathrm{+}}\text{(n)}$ as n→∞, with 1<β<2 and L₊ slowly varying, if and only if$\text{P}\text{{X?x}∽ 1/{x}{}^{\mathrm{\beta }}\text{L(x)}}$ as x→+∞, with L slowly varying. In this paper it is shown how the asymptotic behaviour of L determines the asymptotic behaviour of L₊ and vice versa. As a by-product, it follows that a certain class of random walks which are in the domain of attraction of one-sided stable laws is such that the down-going ladder height distribution has finite mean.     

Comparative study of kinetics isomerization of substituted polyacetylene (Cl,F and I): Ab initio and DFT calculations

Ab initio and DFT methods were used to investigate the interconversions of substituted polyacetylene conformers C₁₀H₆X₆ (X=F, Cl and I) in the vapour phase. The rates of this geometrical isomerization have been calculated and the Arrhenius parameters evaluated. In the case of unsubstituted polyacetylene as the reference, the B3LYP Arrhenius parameters obtained are A₁=2.99 × 10¹⁷ s^–1 and E_a=17.30 kcal mol^–1. The values of the equilibrium constant for the reaction have also been determined at various temperatures between 300 and 500 K and the value of the energies change calculated. The results also suggest that the straightforward kinetics characterizing the majority of substituted polyacetylene isomerizations above 300 K. The isomerization energies are positive and the barrier heights ΔE_barrier are expected to be sensitive for the magnitude of halogens effects. According to geometries features the Cis → Trans isomerization in the gas phase occurs by a rotational mechanism.     

Rotational isomerism and barriers to internal rotation in 3-halopropenes byscf-mo methods

Electronic structures of 3 halopropenes have been investigated through semiempiricalscf-mo calculations using valence basis sets of atomic orbitals (ao) constructed from Slater type orbitals (sto). The electronic structures of stable conformers have been predicted and the corresponding calculated dipole moments show good agreement with experimental data. The considerable differences between the dipole moments of various conformers confirm the hindrance to internal rotation about the C−C bond, i.e., the existence of a definite potential barrier to rotation. The barrier heights hindering the internal rotation in each system are also estimated.     

Preferential heights in the growth of Ag islands on Si(1 1 1)-(7 × 7) surfaces

Growth behavior of thin Ag films on Si substrates at room temperature has been investigated by scanning tunneling microscopy and reflection high energy electron diffraction. In the layer-plus-island growth Ag islands show strongly preferred atomic scale heights and flat top. At low coverage (1 ML), islands containing two atomic layers of Ag are overwhelmingly formed. At higher coverages island height distribution shows strong peaks at relative heights corresponding to an even number (2, 4, 6, …) of Ag atomic layers. Beyond some coverage the height preference vanishes due to the appearance of screw dislocations and spiral growth.