Fano direct products as rationally connected fibrations

Combining the connectedness principle of Shokurov and Kollár, we develop a new technique of studying birational maps of natural Fano fiber spaces. We prove that the only structures of a rationally connected fibration on direct products of typical Fano varieties are projections onto the factors. In particular, the groups of biregular and birational self-maps of Fano direct products coincide. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 10, No. 4, pp. 183–206, 2004.     

Scattering of a Rayleigh wave by monopole-dipole resonators

The problem of scattering of a Rayleigh wave by a chain of identical closely spaced monopole-dipole resonators with friction is considered. The values of resonator parameters that provide the rejection of the Rayleigh wave are found. The conditions under which the Rayleigh wave is much more efficiently reflected by the dipole resonators than by the monopole ones are determined.     

Change in the magnetic state of a surface upon formation of hydrogen bonds during adsorption

It is established that reversible adsorption of water and methyl alcohol molecules, occurring via formation of hydrogen bonds, changes the dynamic properties of domain walls in the surface region of soft ferromagnets, as well as their initial static magnetic susceptibility. A mechanism is proposed for the effects revealed.     

Light scattering by aggregates of magnetite nanoparticles in a magnetic field

The effect of variation of the scattered light intensity in a magnetic fluid with aggregates of magnetite particles several microns in size under the action of a magnetic field is studied. The effect relaxation times are determined when the magnetic field is turned on and off. This effect is found to be caused by the orientation of anisotropically magnetized aggregates. Experimental data are used to calculate the average anisotropy of the magnetic susceptibility of the aggregate and estimate its magnetic permeability.     

The effect of technological microdefects of structure on service life of polymer materials

Within the framework of the kinetic theory of strength, relations for estimation of durability of thermoplastic materials under stationary and non-stationary thermomechanical impacts are obtained It is shown that durability decreases linearly with increase in the natural (Napierian) logarithm of the mean size of microcracks formed during manufacturing of polymer products. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 3–6, July, 2007.     

Semiparametric estimation of the long-range parameter

We study two estimators of the long-range parameter of a covariance stationary linear process. We show that one of the estimators achieve the optimal semiparametric rate of convergence, whereas the other has a rate of convergence as close as desired to the optimal rate. Moreover, we show that the estimators are asymptotically normal with a variance, which does not depend on any unknown parameter, smaller than others suggested in the literature. Finally, a small Monte Carlo study is included to illustrate the finite sample relative performance of our estimators compared to other suggested semiparametric estimators. More specifically, the Monte-Carlo experiment shows the superiority of the proposed estimators in terms of the Mean Squared Error. The first author research was funded by the Economic and Social Research Council (ESRC) reference number: R000238212. The second author research was funded by the Ministry of Education, Culture, Sports and Technology of Japan, reference number: 09CE2002 and B(2)10202202.     

Effect of anions on the phase stability of γ-FeOOH nanoparticles and the magnetic properties of gamma-ferric oxide derived from lepidocrocite

The effect of anions such as Cl⁻, SO₄²⁻, and HPO₄²⁻ on the phase stability of FeOOH (α or γ) during precipitation is investigated. Oxidation of Fe(OH)₂·xH₂O from FeCl₂ solution with high Cl⁻ concentration ([Cl⁻]/[Fe]=R_Cl≥8) or (NH₄)₂Fe(SO₄)₂ (FAS) with [HPO₄²⁻]/[Fe]=R_P≥0.02 yields phase-pure γ-FeOOH. In the medium ranges of R_Cl and R_P, mixed phases of α-FeOOH and γ-FeOOH are obtained. Replacement of OH⁻ by Cl⁻ with the bridging cations or strongly bonded HPO₄²⁻ ions in the matrix of the intermediate phase (Fe_x²⁺Fe_y³⁺(OH)_2x+2y−nz·xH₂O(A)_zⁿ⁻, where A is anions such as Cl⁻, SO₄²⁻, HPO₄²⁻, etc.), promoted the lower density γ-FeOOH. However, the particles are less developed and have poor crystallinity as evidenced from transmission electron microscope and thermogravimetry-differential thermal analysis of the precipitates. Whereas, monophasic, uniformly sized, nano-lath shaped particles with high aspect ratio >10 are obtained when morphology-controlling cation additives such as Pt⁴⁺, Pd²⁺ or Rh³⁺ are present in FeCl₂ (R_Cl≥8) solution. Preferential adsorption of additives on (0k0) and (h00) planes limits the growth in the perpendicular directions leading to high aspect ratios. The effect of these additives are suppressed by the phosphate ion, a strong complexing ligand, giving rise to fibrous aggregate with the length of individual particles as small as 10-30 nm. While most of the Cl⁻ ion is removed from the final precipitates on washing, phosphate remained as HPO₄²⁻ as evidenced from IR absorption spectra. Maghemite obtained by dehydroxylating γ-FeOOH contains randomly distributed micropores bringing in the relaxation effects of spins on the surface atoms as deciphered from Mössbauer spectroscopy. This leads to the low σ_s (44-48 emu/g) and H_c (120-130 Oe) for γ-Fe₂O_3−δ particles. Whereas nearly pore-free single crystalline particles obtained by reduction followed by reoxidation has high value of σ_s (73 emu/g) and H_c (320 Oe), which decreases to 30 emu/g and 75 Oe, respectively, for nanoparticles obtained from phosphate stabilized lepidocrocite. The mobility of iron ions and counter mobility of vacancies during the topotactic transformation of γ-FeOOH to magnetite to γ-Fe₂O_3−δ renders the particles pore-free.     

Graphitic nanofillers in PMMA nanocomposites—An investigation of particle size and dispersion and their influence on nanocomposite properties

Mechanical, thermal, and electrical properties of graphite/PMMA composites have been evaluated as functions of particle size and dispersion of the graphitic nanofiller components via the use of three different graphitic nanofillers: “as received graphite” (ARG), “expanded graphite,” (EG) and “graphite nanoplatelets” (GNPs) EG, a graphitic materials with much lower density than ARG, was prepared from ARG flakes via an acid intercalation and thermal expansion. Subsequent sonication of EG in a liquid yielded GNPs as thin stacks of graphitic platelets with thicknesses of ～10 nm. Solution‐based processing was used to prepare PMMA composites with these three fillers. Dynamic mechanical analysis, thermal analysis, and electrical impedance measurements were carried out on the resulting composites, demonstrating that reduced particle size, high surface area, and increased surface roughness can significantly alter the graphite/polymer interface and enhance the mechanical, thermal, and electrical properties of the polymer matrix. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 2097–2112, 2007