Internal magnetic field gradients as information source about porous media characteristics

The geometry of particles is analyzed by the example of a model porous system (filling of glass spheres and glass cylinders) studied by nuclear magnetic resonance. The experimental approach is based on the registration of the <G _int> (ζ) dependences, where <G _int> is the effective (average) internal magnetic field gradient and ζ=<r ²>^1/2<R> is the ratio of the root-mean-square displacement of molecules to the average particle size <R>. It is shown that the dependence <G _int> (ζ) can be approximated by the power law <G _int>(ζ) ∝ ζ^α, where the power index α does not depend on the particle size but is sensitive to its geometry.     

Non-Abelian Vortices,Super Yang–Mills Theory and Spin(7)-Instantons

We consider a complex vector bundle E{\mathcal{E}} endowed with a connection A{\mathcal{A}} over the eight-dimensional manifold \mathbbR²×G/H{\mathbb{R}^2\times G/H}, where G/H = SU(3)/U(1) × U(1) is a homogeneous space provided with a never-integrable almost-complex structure and a family of SU(3)-structures. We establish an equivalence between G-invariant solutions A{\mathcal{A}} of the Spin(7)-instanton equations on \mathbbR²×G/H{\mathbb{R}^2\times G/H} and general solutions of non-Abelian coupled vortex equations on \mathbbR²{\mathbb{R}^2}. These vortices are BPS solitons in a d = 4 gauge theory obtained from N = 1{\mathcal{N} =1} supersymmetric Yang–Mills theory in ten dimensions compactified on the coset space G/H with an SU(3)-structure. The novelty of the obtained vortex equations lies in the fact that Higgs fields, defining morphisms of vector bundles over \mathbbR²{\mathbb{R}^2}, are not holomorphic in the generic case. Finally, we introduce BPS vortex equations in N = 4{\mathcal{N} =4} super Yang–Mills theory and show that they have the same feature.     

Temperature dependence of magnetic properties and change of specific heat in perovskite ErCrO3 chromites

In this paper, the temperature dependence of magnetic properties and specific heat are systematically investigated for perovskite ErCrO₃ chromites. The results show that there exists a strong temperature dependence of magnetic ordering and phase coexistence in the region of low temperature. Specifically, ErCrO₃ possesses the long-range antiferromagnetic ordering and the appearance of weak ferromagnetism, occurring at T _N =133 K. In the range of higher temperature, above 133.0 K, the reciprocal of magnetic susceptibility χ ⁻¹ behaves linearly, indicating a typical Curie–Weiss behavior fitted. The effective magnetic moment μ _eff=10.57μ _B and asymptotic paramagnetic Curie temperature T _cw=−30 K, which suggests the predominance of antiferromagnetic interactions in ErCrO₃ chromites. Around T _SR≈22 K, ErCrO₃ undergoes a spin reorientation from \varGamma ₄(G_x,A_y,F_z;F^R_z)\varGamma _{4}(G_{x},A_{y},F_{z};F^{R}_{z}) to \varGamma ₁(A_x,G_y,C_z;C^R_z)\varGamma _{1}(A_{x},G_{y},C_{z};C^{R}_{z}) or Γ ₁(0). Also, the stability of the ferromagnetic Γ ₄ phase increases with increasing applied field. Furthermore, the ac susceptibilities exhibit frequency-independent anomalies near 133 K and the coexistence of the magnetic configuration \varGamma ₂(F_x,G_y,C_z;F^R_x,C^R_y)\varGamma _{2}(F_{x},G_{y},C_{z};F^{R}_{x},C^{R}_{y}) and Γ ₄. Combining the magnetic properties and the specific-heat measurements, this current magnetization can be interpreted from the interaction between C ^r3+–Cr³⁺, Cr³⁺–Er³⁺ and Er³⁺–Er³⁺.     

Yang-Mills Flows on Nearly Kähler Manifolds and G 2-Instantons

We consider Lie(G)-valued G-invariant connections on bundles over spaces ${G/H,\, \mathbb{R}\times G/H\, {\rm and}\, \mathbb{R}^2\times G/H}We give a geometric construction of the ${\mathcal{W}_{1+\infty}}We consider Lie(G)-valued G-invariant connections on bundles over spaces G/H, \mathbbR×G/H and \mathbbR²×G/H{G/H,\, \mathbb{R}\times G/H\, {\rm and}\, \mathbb{R}^2\times G/H}, where G/H is a compact nearly K?hler six-dimensional homogeneous space, and the manifolds \mathbbR×G/H{\mathbb{R}\times G/H} and \mathbbR²×G/H{\mathbb{R}^2\times G/H} carry G ₂- and Spin(7)-structures, respectively. By making a G-invariant ansatz, Yang-Mills theory with torsion on \mathbbR×G/H{\mathbb{R}\times G/H} is reduced to Newtonian mechanics of a particle moving in a plane with a quartic potential. For particular values of the torsion, we find explicit particle trajectories, which obey first-order gradient or hamiltonian flow equations. In two cases, these solutions correspond to anti-self-dual instantons associated with one of two G ₂-structures on \mathbbR×G/H{\mathbb{R}\times G/H}. It is shown that both G ₂-instanton equations can be obtained from a single Spin(7)-instanton equation on \mathbbR²×G/H{\mathbb{R}^2\times G/H}.     

Nuclear spin-lattice relaxation in the triply rotating frame and ultraslow molecular motions in solids

A method for measuring nuclear magnetic spin-lattice relaxation in solids in the effective field H_e3 acting in the triply rotating frame (TRF) is described. The method advances the previously described techniques whereby nuclear magnetic resonance and relaxation in the rotating (RF) and doubly rotating frames (DRF) are measured directly. In the present work, the RF and DRF are employed for suppressing the secular part of nuclear dipole-dipole (DD) interactions in the first two orders. As a result, the higher-order DD interactions (four- and five-particle ones) were separated, and their contribution to the nuclear spin-lattice relaxation in the TRF was studied experimentally. The experiments were carried out on protons in polycrystalline benzene. With the introduced technique, an overall spin-lattice relaxation decay in the TRF was recorded continuously during a single radio-frequency pulse with a length not exceeding 1 s. The contribution of multiproton nonsecular DD interactions to the proton spin-lattice relaxation in the TRF was observed selectively as a pronounced local minimum in the temperature dependence of the relaxation timeT _1ϱϱϱ. This contribution corresponds to ultraslow motion of benzene molecules with a rate about γH_e3 ≈ 2π · (10¹-10³) s^-1 and is determined quantitatively by specific correlation functions corresponding to the multiparticle nonsecular DD interactions of protons. The prospects of using this method for studying ultraslow atomic and molecular dynamics in solids are discussed.     

Ultraviolet and visible upconversion luminescence of Tm(0.1)Yb(5):FOV oxyfluoride nanophase vitroceramics

The ultraviolet upconversion luminescence of Tm³⁺ ions sensitized by Yb³⁺ ions in oxyfluoride nanophase vitroceramics when excited by a 975 nm diode laser was studied. An ultraviolet upconversion luminescence line positioned at 363.6 nm was found. It was attributed to the fluorescence transition of ¹D₂→³H₆ of Tm³⁺ ion. Several visible upconversion luminescence lines at 450.7 nm, (477.0 nm, 462.5 nm), 648.5 nm, (680.5 nm, 699.5 nm) and (777.2 nm, 800.7 nm) were also found, which result respectively from the fluorescence transitions of ¹D₂→³F₄, ¹G₄→³H₆, ¹G₄→³F₄, ³F₃→³H₆ and ³H₄→³H₆ of Tm³⁺ ion. The careful measurement and analysis of the variation of upconversion luminescence intensity F as a function of the 975 nm pumping laser power P prove that the upconversion luminescence of ¹D₂ state is partly a five-photon upconversion luminescence, and the upconversion luminescence of ¹G₄ state and ³H₄ state are respectively the three-photon and two-photon upconversion luminescence. The theoretical analysis suggested that the upconversion mechanism of the 363.6 nm ¹D₂→³H₆ upconversion luminescence is partly the cross energy transfer of {³H₄(Tm³⁺), ³F₄(Tm³⁺), ¹G₄(Tm³⁺)→¹D₂(Tm³⁺)} and {¹G₄(Tm³⁺)→³F₄(Tm³⁺), ³H₄(Tm³⁺)→¹D₂(Tm³⁺)} between Tm³⁺ ions. In addition, the upconversion luminescence of ¹G₄ and ³H₄ state results respectively from the sequential energy transfer {²F_5/2(Yb³⁺)→²F_7/2(Yb³⁺), ³H₄(Tm³⁺)→¹G₄(Tm³⁺)} and {²F_5/2(Yb³⁺) →²F_7/2(Yb³⁺), ³F₄(Tm³⁺)→³F₂(Tm³⁺)} from Yb³⁺ ions to Tm³⁺ ions. Supported by the National Natural Science Foundation of China (Grant No. 10674019)     

Thermal analysis of InP-based quantum cascade lasers for efficient heat dissipation

We have theoretically investigated the thermal characteristics of double-channel ridge–waveguide InGaAs/InAlAs/InP quantum cascade lasers (QCLs) using a two-dimensional heat dissipation model. The temperature distribution, heat flow, and thermal conductance (G _th) of QCLs were obtained through the thermal simulation. A thick electroplated Au around the laser ridges helps to improve the heat dissipation from devices, being good enough to substitute the buried heterostructure (BH) by InP regrowth for epilayer-up bonded lasers. The effects of the device geometry (i.e., ridge width and cavity length) on the G _th of QCLs were investigated. With 5 μm thick electroplated Au, the G _th is increased with the decrease of ridge width, indicating an improvement from G _th=177 W/K⋅cm² at W=40 μm to G _th=301 W/K⋅cm² at W=9 μm for 2 mm long lasers. For the 9 μm×2 mm epilayer-down bonded laser with 5 μm thick electroplated Au, the use of InP contact layer leads to a further improvement of 13% in G _th, and it was totally raised by 45% corresponding to 436 W/K⋅cm² compared to the epilayer-up bonded laser with InGaAs contact layer. It is found that the epilayer-down bonded 9 μm wide BH laser with InP contact layer leads to the highest G _th=449 W/K⋅cm². The theoretical results were also compared with available obtained experimentally data.     

Structure and phase stability of nanocrystalline Ce1−x Ln x O2−x/2−δ (Ln = Yb, Lu) in oxidizing and reducing atmosphere

The structure and phase evolution of nanocrystalline Ce_{1− x} Ln _x O_{2− x/2−δ} (Ln = Yb, Lu, x = 0 − 1) oxides upon heating in H₂ was studied for the first time. Up to 950 °C the samples were single-phase, with structure changing smoothly with x from fluorite type (F) to bixbyite type (C). For the Lu-doped samples heated at 1100 °C in the air and H₂, phase separation into coexisting F- and C-type structures was observed for ~0.40 < x < ~0.70 and ~0.25 < x < ~0.70, respectively. It was found also that addition of Lu³⁺ and Yb³⁺ strongly hinders the crystallite growth of ceria during heat treatment at 800 and 950 °C in both atmospheres. Valency of Ce and Yb in Ce_0.1Lu_0.9O_1.55−δ and Ce_0.95Yb_0.05O_1.975−δ samples heated at 1100 °C was studied by XANES and magnetic measurements. In the former Ce was dominated by Ce⁴⁺, with small contribution of Ce³⁺ after heating in H₂. In the latter, Yb existed exclusively as 3+ in both O₂ and H₂.     

Perfect fluid bianchi Type-I cosmological models with time varying <Emphasis Type="Italic">G</Emphasis> and Λ

Bianchi Type-I cosmological models containing perfect fluid with time varying G and Λ have been presented. The solutions obtained represent an expansion scalar θ bearing a constant ratio to the anisotropy in the direction of space-like unit vector λ ⁱ . Of the two models obtained, one has negative vacuum energy density, which decays numerically. In this model, we obtain Λ ∼ H ², Λ ∼ R ₄₄/R and Λ ∼ T ⁻² (T is the cosmic time) which is in accordance with the main dynamical laws for the decay of Λ. The second model reduces to a static solution with repulsive gravity.      

Quantum corrections to the conductance of n-GaAs films in a strong magnetic field

The conductance of doped n-GaAs films is studied experimentally as a function of magnetic field and temperature in strong magnetic fields right up to the quantum limit (ħω_c = E _F). The Hall conductance G _xy is virtually independent of temperature T until the transverse conductance G _xx is quite large compared with e ²/h. In strong fields, when G _xx becomes comparable to e ²/h, G _xy starts to depend on T. The difference between the conductances G _xx at the two temperatures 4.2 and 0.35 K depends only weakly on the magnetic field H over a wide range of magnetic fields, while the conductances G _xx themselves vary strongly. The results can be explained by quantum corrections to the conductance as a result of the electron-electron interaction in the diffusion channel. The possibility of quantization of the Hall conductance as a result of the electron-electron interaction is discussed. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 3, 201–206 (10 February 1998)     

Effect of growth rate and Mg content on dendrite tip characteristics of Al–Cu–Mg ternary alloys

An experimental analysis is presented to correlate the secondary dendrite arm spacing λ ₂ and dendrite tip radius R with growth rate V and Mg content C _0-Mg of Al–Cu–Mg ternary alloys. Under constant temperature gradient G (4.84±0.13 K mm⁻¹), a series of directional solidification experiments were performed at five different growth rates V (16.7–83.3 μm/s) and five different Mg contents C _0-Mg in Al–5 wt.% Cu–(0.5–5) wt.% Mg alloys. Solid–liquid interface was investigated from the longitudinal sections of the quenched samples, and λ ₂ and R were measured on the dendrite tips. The dependencies of λ ₂ and R on V and C _0-Mg were determined. The experimental results showed that the values of λ ₂ and R decrease as V and C _0-Mg increase at a constant G. The present exponent values related to V are found to be slightly lower than the values of the theoretical models and previous experimental works; however, C _0-Mg exponent values are found to be much lower than the theoretical models and previous experimental works. The ratio of the secondary dendrite arm spacing to the dendrite tip radius is 2.09±0.15, in good agreement with the scaling law. At a constant C _0-Mg, the values of VR ² were found to slightly increase with the ascending V. However, as C _0-Mg increases, the values of VR ² decrease.     

Contributions to the Gaussian Line Broadening of the Proxyl Spin Probe EPR Spectrum Due to Magnetic-Field Modulation and Unresolved Proton Hyperfine Structure

A simple expression is derived to compute the total Gaussian linewidth of a Voigt line that is broadened by sinusoidal magnetic-field modulation as follows: ΔH^G_pp(H_m)²= ΔH^G_pp(0)²+ κ²H²_m, where ΔH^G_pp(H_m) is the Gaussian linewidth observed with an modulation amplitudeH_m/2 and ΔH^G_pp(0) is the Gaussian linewidth in the limit of zero modulation. The field modulation contributes an additional Gaussian broadening of κH_m, where κ is a constant, which adds in quadrature to ΔH^G_pp(0) to give the total Gaussian linewidth. Denoting the overall linewidth of the Voigt line in the absence of modulation broadening by ΔH⁰_pp(0), it is shown, both by analytical means and by spectral simulation, that the constant κ is equal to 1/2 in the limit ofH_m ΔH⁰_pp(0); however, using values ofH_mas large as ΔH⁰_pp(0) leads to only minor departures from κ = 1/2. The formulation is valid both for Lorentzian and Voigt lines and is tested for 2,2,5,5-tetramethylpyrrolidin-1-oxyl-3-carboxylic acid (3-carboxy proxyl) in CCl₄and in aqueous buffer. This spin probe was studied because the proxyl group is the only major spin-probe moiety whose Gaussian linewidth had not been characterized in the literature. For 3-carboxy proxyl, it is found that ΔH^G_pp(0) = 1.04 ± 0.01 G independent of solvent polarity. Precision values of the¹⁴N hyperfine coupling constant for 3-carboxy proxyl at 9.5°C are as follows: 14.128 ± 0.001 G in CCl₄and 16.230 ± 0.002 G in aqueous buffer. The temperature dependence of ΔH^G_pp(0) and the¹⁴N hyperfine coupling constant are reported as empirical equations. Results of the present work taken together with previously published data permits accurate correction for the effects of inhomogeneous broadening due to unresolved hyperfine structure and modulation broadening for the majority of spin probes in common use.     

Quantum oscillations of the resistivity and hall coefficient and the quantum limit in Bi<Subscript>0.93</Subscript>Sb<Subscript>0.07</Subscript> alloys in a magnetic field along the trigonal axis

The dependences of the electrical resistivity ρ and the Hall coefficient R on the magnetic field have been measured for single-crystal samples of the n-Bi_0.93Sb_0.07 semiconductor alloys with electron concentrations in the range 1 × 10¹⁶ cm⁻³ < n < 2 × 10¹⁸ cm⁻³. It has been found that the measured dependences exhibit Shubnikov-de Haas quantum oscillations. The magnetic fields corresponding to the maxima of the quantum oscillations of the electrical resistivity are in good agreement with the calculated values of the magnetic fields in which the Landau quantum level with the number N intersects the Fermi level. The quantum oscillations of the Hall coefficient with small numbers are characterized by a significant spin splitting. In a magnetic field directed along the trigonal axis, the quantum oscillations of the resistivity ρ and the Hall coefficient R are associated with electrons of the three-valley semiconductor and are in phase with the magnetic field. In the case of a magnetic field directed parallel to the binary axis, the quantum oscillations associated both with electrons of the secondary ellipsoids in weaker magnetic fields and with electrons of the main ellipsoid in strong magnetic fields (after the overflow of electrons from the secondary ellipsoids to the main ellipsoid) are also in phase. In magnetic fields of the quantum limit ħω _c /2 ≥ E _F, the electrical conductivity increases with an increase in the magnetic field: σ₂₂(H) ∼ H ^k . A theoretical evaluation of the exponent in this expression for a nonparabolic semiconductor leads to values of k close to the experimental values in the range 4 ≤ k ≤ 4.6, which were obtained for samples of the semiconductor alloys with different electron concentrations. A further increase in the magnetic field results in a decrease of the exponent k and in the transition to the inequality σ₂₂(H) ≤ σ₂₁(H).     

Ab initio study of the chemical states of water on Cr2O3(0 0 0 1): From the isolated molecule to saturation coverage

The reactivity of the (0 0 0 1)-Cr–Cr₂O₃ surface towards water was studied by means of periodic DFT + U. Several water coverages were studied, from 1.2H₂O/nm² to 14.1H₂O/nm², corresponding to ¼, 1, 2 and 3 water/Cr at the (0 0 0 1)-Cr₂O₃ surface, respectively. With increasing coverage, water gradually completes the coordination sphere of the surface Cr atoms from 3 (dry surface) to 4 (1.2 and 4.7H₂O/nm²), 5 (9.4H₂O/nm²) and 6 (14.1H₂O/nm²). For all studied coverages, water replaces an O atom from the missing above plane. At coverages 1.2 and 4.7H₂O/nm², the Cr–O_s (surface oxygen) acid–base character and bond directionality govern the water adsorption. The adsorption is molecular at the lowest coverage. At 4.7H₂O/nm², molecular and dissociative states are isoenergetic. The activation energy barrier between the two states being as low as 12 kJ/mol, allowing protons exchanges between the OH groups, as evidenced by ab inito molecular dynamics at room temperature. At coverages of 9.4 and 14.1H₂O/nm², 1D- (respectively, 2D-) water networks are formed. The resulting surface terminations are –Cr(OH)₂ and –Cr(OH)₃– like, respectively. The increased stability of those terminations as compared to the previous ones are due to the stabilization of the adsorbed phase through a H-bond network and to the increase in the Cr coordination number, stabilizing the Cr (t_2g) orbitals in the valence band. An atomistic thermodynamic approach allows us to specify the temperature and water pressure domains of prevalence for each surface termination. It is found that the –Cr(OH)₃-like, –Cr(OH)₂ and anhydrous surfaces may be stabilized depending on (T, P) conditions. Calculated energies of adsorption and OH frequencies are in good agreement with published experimental data and support the full hydroxylation model, where the Cr achieves a 6-fold coordination, at saturation.     

Isotope effect in charge transport of LuB12

The galvanomagnetic properties of single-crystal samples with various isotopic boron compositions have been investigated for the first time for the normal state of superconductor LuB₁₂ (T c ≈ 0.44 K). Precision measurements of the resistivity, Hall coefficient, and magnetic susceptibility have been performed over a wide temperature range of 2–300 K in magnetic fields up to 80 kOe. A change of the charge transport regime in this nonmagnetic compound with metallic conduction is shown to occur near T* ≈ 50−70 K. As a result, a sharp peak with significantly different amplitudes for Lu¹⁰B₁₂ and Lu¹¹B₁₂ is recorded in the temperature dependences of the Hall coefficient R _H(T) near T*. A significant (about 10%) difference (in absolute value) of the Hall coefficients R _H for the Lu¹⁰B₁₂ and Lu¹¹B₁₂ compounds at helium and intermediate temperatures has been found and the patterns of behavior of the dependence R _H(H) for T < T* in an external magnetic field H ≤ 80 kOe for Lu¹⁰B₁₂ and Lu¹¹B₁₂ are shown to differ significantly. Analysis of the Curie-Weiss contribution to the magnetic susceptibility χ(T) leads to the conclusion about the formation of magnetic moments μ_eff ≈ (0.13−0.19)μ_B in each unit cell of the fcc structure of LuB₁₂ compounds with various isotopic compositions. The possibility of the realization of an electronic topological 2.5-order transition near T* and the influence of correlation effects in the 5d-band on the formation of a spin polarization near the rare-earth ions in LuB₁₂ is discussed.     

Optical spectra and excited state relaxation dynamics of Sm<Superscript>3+</Superscript> in Gd<Subscript>2</Subscript>SiO<Subscript>5</Subscript> single crystal

Single crystals of gadolinium orthosilicate Gd₂SiO₅ containing 0.5 at% and 5 at% of Sm³⁺ were grown by the Czochralski method. Optical absorption spectra, luminescence spectra and luminescence decay curves were recorded for these systems at 10 K and at room temperature. Comparison of optical spectra recorded in polarized light revealed that the anisotropy of this optically biaxial host affects the intensity distribution within absorption and emission bands related to transitions between multiplets rather than the overall band intensity. It has been found that among four bands of luminescence related to the ⁴G_5/2→⁶H_J (J=5/2–11/2) transitions of Sm³⁺ in the visible and near infrared region the ⁴G_5/2 →⁶H_7/2 one has the highest intensity with a peak emission cross section of 3.54×10⁻²¹ cm² at 601 nm for light polarized parallel to the crystallographic axis c of the crystal. The luminescence decay curve recorded for Gd₂SiO₅:0.5 at% Sm³⁺ follows a single exponential time dependence with a lifetime 1.74 ms, in good agreement with the ⁴G_5/2 radiative lifetime τ _rad=1.78 ms calculated in the framework of Judd-Ofelt theory. Considerably faster and non-exponential luminescence decay recorded for Gd₂SiO₅:5 at% Sm³⁺ sample was fitted to that predicted by the Inokuti-Hirayama theory yielding the microparameter of Sm³⁺–Sm³⁺ energy transfer C _da=1.264×10⁻⁵² cm⁶×s⁻¹.     

Superparamagnetic Ni:SiO<Subscript>2</Subscript>–C nanocomposites films synthesized by a polymeric precursor method

In this work, we report on the magnetic properties of nickel nanoparticles (NP) in a SiO₂–C thin film matrix, prepared by a polymeric precursor method, with Ni content x in the 0–10 wt% range. Microstructural analyses of the films showed that the Ni NP are homogenously distributed in the SiO₂–C matrix and have spherical shape with average diameter of ~10 nm. The magnetic properties reveal features of superparamagnetism with blocking temperatures T _B ~ 10 K. The average diameter of the Ni NP, estimated from magnetization measurements, was found to be ~4 nm for the x = 3 wt% Ni sample, in excellent agreement with X-ray diffraction data. M versus H hysteresis loops indicated that the Ni NP are free from a surrounding oxide layer. We have also observed that coercivity (H _C) develops appreciably below T _B, and follows the H _C ∝ [1 – (T/T _B)^0.5] relationship, a feature expected for randomly oriented and non-interacting nanoparticles. The extrapolation of H _C to 0 K indicates that coercivity decreases with increasing x, suggesting that dipolar interactions may be relevant in films with x > 3 wt% Ni.     

Domain state–dependent magnetic formation of Fe<Subscript>3</Subscript>O<Subscript>4</Subscript> nanoparticles analyzed via magnetic resonance

Magnetic properties, arising from surface exchange and interparticle interactions of the Fe₃O₄ (magnetite) nanoparticles, were investigated in the temperature range of 5–300 and 120–300 K using vibrating sample magnetometer technique and electron spin resonance spectroscopy, respectively. The research was based on to figure out the origin of intraparticle interactions and the change of interparticle interactions in wide size range Fe₃O₄ nanoparticles. The analyses were done for samples having almost same particle size distributions. The average particle sizes were changed in between 30 ± 2 and 34 ± 2 nm. The observed magnetization values were demonstrated the mixture of single-domain size particles, exhibiting both single-domain (SD) and superparamagnetic (SPM) states. The symmetry of resonance curves changed according to the ratio of SD and SPM-stated particles in mixture under located temperature. The changes of anisotropy up to domain state were understood by freezing magnetic moment in glycerol matrix from room temperature to 120 K under 5-kG field. The shift of H _R values to higher magnetic fields and the more symmetric resonance spectrum proved the effect of anisotropy and interparticle interactions fields on magnetic behave. In addition, the origin of intra-interaction was exposed from Fe³⁺ centers and exchange coupling in between Fe²⁺, Fe³⁺, and O⁻, and Fe³⁺ centers found from g factor (g).     

Instantons and Yang–Mills Flows on Coset Spaces

We consider the Yang–Mills flow equations on a reductive coset space G/H and the Yang–Mills equations on the manifold \mathbbR×G/H{\mathbb{R}\times G/H}. On non-symmetric coset spaces G/H one can introduce geometric fluxes identified with the torsion of the spin connection. The condition of G-equivariance imposed on the gauge fields reduces the Yang–Mills equations to f⁴{\phi^4}-kink equations on \mathbbR{\mathbb{R}}. Depending on the boundary conditions and torsion, we obtain solutions to the Yang–Mills equations describing instantons, chains of instanton–anti-instanton pairs or modifications of gauge bundles. For Lorentzian signature on \mathbbR×G/H{\mathbb{R}\times G/H}, dyon-type configurations are constructed as well. We also present explicit solutions to the Yang–Mills flow equations and compare them with the Yang–Mills solutions on \mathbbR×G/H{\mathbb{R}\times G/H}.     

Some asymptotic formulae for one-electron two-center problem

Asymptotic formulae of some expectation values related to the relativistic corrections in inverse powers of the internuclear distance R for the lsσ _g electron state of hydrogen molecular ion H₂⁺ and the lsσ molecule-like state of antiprotonic helium atom He⁺ are obtained with the use of the first-order perturbation function. Using these asymptotic formulae, the relativistic correction of order mα⁶ for these states in reciprocal powers of the internuclear distance R is derived to accuracy of (R ⁻⁴). The article is published in the original.