Dirac constraint analysis and symplectic structure of anti-self-dual Yang-Mills equations

We present the explicit form of the symplectic structure of anti-self-dual Yang-Mills (ASDYM) equations in Yang’s J- and K-gauges in order to establish the bi-Hamiltonian structure of this completely integrable system. Dirac’s theory of constraints is applied to the degenerate Lagrangians that yield the ASDYM equations. The constraints are second class as in the case of all completely integrable systems which stands in sharp contrast to the situation in full Yang-Mills theory. We construct the Dirac brackets and the symplectic 2-forms for both J- and K-gauges. The covariant symplectic structure of ASDYM equations is obtained using the Witten-Zuckerman formalism. We show that the appropriate component of the Witten-Zuckerman closed and conserved 2-form vector density reduces to the symplectic 2-form obtained from Dirac’s theory. Finally, we present the Bäcklund transformation between the J- and K-gauges in order to apply Magri’s theorem to the respective two Hamiltonian structures.     

Semiconvergence in distribution of random closed sets with application to random optimization problems

The paper considers upper semicontinuous behavior in distribution of sequences of random closed sets. Semiconvergence in distribution will be described via convergence in distribution of random variables with values in a suitable topological space. Convergence statements for suitable functions of random sets are proved and the results are employed to derive stability statements for random optimization problems where the objective function and the constraint set are approximated simultaneously. The author is grateful to two anonymous referees for helpful suggestions.     

基于低功耗双边沿D触发器的任意进制异步计数器设计

从D触发器激励表入手，分别给出了采用单边沿D触发器和双边沿D触发器的2^n进制异步加法计数器、减法计数器的设计方法．在此基础上，采用逻辑函数修改技术，通过实例讨论了基于单边沿D触发器和双边沿D触发器的异步任意进制计数器的设计．该设计方法方便，快速，具有一定的实用意义．     

Microwave synthesis of magnetic Fe3O4 nanoparticles used as a precursor of nanocomposites and ferrofluids

Methods to synthesize magnetic Fe₃O₄ nanoparticles and to modify the surface of particles are presented in the present investigation. Fe₃O₄ magnetic nanoparticles were prepared by the co-precipitation of Fe³⁺ and Fe²⁺, NH₃·H₂O was used as the precipitating agent to adjust the pH value, and the aging of Fe₃O₄ magnetic nanoparticles was accelerated by microwave (MW) irradiation. The obtained Fe₃O₄ magnetic nanoparticles were characterized by Fourier transform infrared spectroscopy (FT-IR), transmission electron microscopy (TEM), X-ray powder diffraction (XRD) and vibrating sample magnetometer (VSM). The average size of Fe₃O₄ crystallites was found to be around 8–9 nm. Thereafter, the surface of Fe₃O₄ magnetic nanoparticles was modified by stearic acid. The resultant sample was characterized by FT-IR, scanning electron microscopy (SEM), XRD, lipophilic degree (LD) and sedimentation test. The FT-IR results indicated that a covalent bond was formed by chemical reaction between the hydroxyl groups on the surface of Fe₃O₄ nanoparticles and carboxyl groups of stearic acid, which changed the polarity of Fe₃O₄ nanoparticles. The dispersion of Fe₃O₄ in organic solvent was greatly improved. Effects of reaction time, reaction temperature and concentration of stearic acid on particle surface modification were investigated. In addition, Fe₃O₄/polystyrene (PS) nanocomposite was synthesized by adding surface modified Fe₃O₄ magnetic nanoparticles into styrene monomer, followed by the radical polymerization. The obtained nanocomposite was tested by thermogravimetry (TG), differential scanning calorimetry (DSC) and XRD. Results revealed that the thermal stability of PS was not significantly changed after adding Fe₃O₄ nanoparticles. The Fe₃O₄ magnetic fluid was characterized using UV–vis spectrophotometer, Gouy magnetic balance and laser particle-size analyzer. The testing results showed that the magnetic fluid had excellent stability, and had susceptibility of 4.46×10⁻⁸ and saturated magnetization of 6.56 emu/g. In addition, the mean size d (0.99) of magnetic Fe₃O₄ nanoparticles in the fluid was 36.19 nm.     

Strain-induced modification of magnetic structure and new magnetic phases in rare-earth epitaxial films

Rare earths exhibit complex magnetic phase diagrams resulting from the competition between various contributions to the magnetic energy: exchange, anisotropy and magnetostriction. The epitaxy of a rare-earth film on a substrate induces (i) a clamping to the substrate and (ii) pseudomorphic strains. Both these effects are shown to lead to modifications of the magnetic properties in (0 0 1)Dy, (0 0 1)Tb and (1 1 0)Eu films. In Dy and Tb films, spectacular variations of the Curie temperature have been evidenced. Additionally, Tb films exhibit a new large wavelength magnetic modulation. In Eu films, one of the helical magnetic domains disappears at low temperature whereas the propagation vectors of the other helices are tilted. The link between structural and magnetic properties is underlined via magnetoelastic models. Moreover, molecular beam epitaxy permits the growth of Sm in a metastable dhcp phase. The magnetic structure of dhcp Sm has been elucidated for the first time. In this review, neutron scattering is shown to be a powerful technique to reveal the magnetic structures of rare-earth films.     

Sobolev-Type Classes of Functions with Values in a Metric Space. II

We prove equivalence of the definitions by the author and by Korevaar and Schoen of the Sobolev classes of mappings of a domain of an arithmetic n-dimensional space to a metric space.     

Magnetic hysteresis of the magnetoresistance and the critical current density in polycrystalline YBa2Cu3O7−δ–Ag superconductors

A systematic study of the magnetic hysteresis in transport properties of polycrystalline YBa₂Cu₃O_7−δ–Ag compounds has been made based on two kinds of measurements at 77 K and under applied magnetic fields up to 30 mT: critical current density J_c(B_a) and magnetoresistance R(B_a). The R(B_a) curves show a minimum in their decreasing branch occurring at B=B_min which was found to be both the excitation current I_ex and the maximum applied magnetic field B_am dependent. In addition, for a certain value of B_am>5 mT, we have observed that B_min increases with increasing I_ex and reaches a saturation value. The J_c(B_a) curves show a maximum in decreasing applied magnetic fields occurring at B=B_max. We have also found that B_max increases with increasing B_am and reaches a saturation value. The minimum in the R(B_a) and the maximum in J_c(B_a) curves were found to be related to the trapped flux within the grains. All the experimental results are discussed within the context of the flux dynamics and transport mechanisms in these high-T_c materials.     

Defect clusters in titanium-substituted spinel-related lithium ferrite

The cation distribution in spinel-related titanium-substituted lithium ferrite, Li_0.5+0.5xFe_2.5−1.5xTi_xO₄ has been explored using interatomic potential and ab initio calculations. The results suggest that the cation distribution with Ti⁴⁺ substituting for Fe³⁺ on octahedral B sites and excess Li⁺ substituting for Fe³⁺ on tetrahedral A sites is stabilised by the formation of clusters of two octahedrally coordinated Ti⁴⁺ ions and one tetrahedrally coordinated Li⁺ ion linked through a common oxygen.     

EPR investigations of oxidation effects in (V1−xMox)2−δO3

Electron paramagnetic resonance (EPR) investigations has been carried out on the new family of molybdenum doped vanadium sesquioxides (V_1−xMo_x)_2−δO₃. The oxidation effects were monitored from the rate of paramagnetic V⁴⁺ created when the sample is exposed to the air. The effects of the oxidation time, sample temperature, and annealing at 1000 °C under a diluted hydrogen atmosphere on the EPR signal features are analyzed. The V⁴⁺ concentration in the oxidized samples is determined and the relaxation effects driven by the conduction electrons are pointed out from the thermal behaviour of the EPR line features. EPR spectra of all the oxidized samples also reveal a small ferromagnetic contribution strongly correlated with the V⁴⁺ content.