Gamma-ray angular distribution, linear polarization, Doppler-shift attenuation and γ-γ coincidence measurements have been made in the ⁴⁸Ti(α, nγ)⁵¹Cr reaction. In addition, excitation functions have been measured in the ⁵¹V(p, nγ)⁵¹Cr reaction. A total of 115 γ rays have been assigned as transitions in ⁵¹Cr, and 56 excited levels have been identified in ⁵¹Cr below 4.5 MeV. Previously reported decay schemes of ⁵¹Cr levels have been considerably modified. All the negative parity levels in ⁵¹Cr below 2.8 MeV can be classified into two groups: those which belong to a strongly deformed 1/2⁻ band, and those which belong to the spherical f_7⁄2 configurations. Electromagnetic transitions between these two groups of levels are hindered.

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The characteristics of slow protons and deuterons produced in 400 GeV/c proton interactions with emulsion nuclei have been studied. The results have been compared with those obtained from similar investigations at lower energies and discussed in the light of the existing models on the subject.

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With use of the Wigner representation, the Kramers equation for a Brownian particle in a potential field of external force is extended to the quantum mechanical case. As a simple application of the equation, the rate of jump over a potential barrier is estimated to the lowest order approximation in h. The rate increases due to the quantum mechanical effect by the factor 1+(βhω)²ω²⁄6(η²+ω²), where ω, η and β are the angular frequency of the particle in the potential well, viscosity and the inverse of temperature, respectively.

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To investigate the lattice dynamics of potassium halides a newly proposed 7-parameter bond-bending force model (BBFM) is used. The total potential energy of the system incorporates the short-range forces (radial+bond-bending) as well as the long range Coulombic interactions. The 7 parameters employed in the present treatment are determined by making use of the experimental values of three elastic constants, four critical point phonon frequencies and the lattice equilibrium condition. The model has been applied to calculate the phonon dispersion relations, phonon density of states and the Debye-characteristic temperatures (θ_D) of KCl, KBr, and KI. Theoretical results have been compared with the available experimental data. It is observed that the agreement between theory and experiment is very good and thus gives a confidence in this approach. The remarkable features pertaining to the physical significance of the model have been discussed.

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The thermodynamic quantity [∂(1⁄β)⁄∂P]_T=C, has been studied on the basis of three well-known potential energy functions viz., Born, Born-Mayer and the modified Varshni-Shukla potentials. The computed values have been compared with the observed and other calculated values. A satisfactory agreement is obtained between the calculated and available observed values of C₁. It has also been shown that the expression for C₁ for the Born potential is different from that of Keer (Z. Phys. Chemie, Leipzig 251 (1972) 22; 255 (1974) 808). The relation of C₁, with Grüneisen parameter γ and Anderson-Grüneisen parameter δ has also been studied and the results are compared with the indirect observed values. The agreement between the theory and the experiment is quite satisfactory in view of the approximation involved in the existing theory of inter-ionic forces.

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A random dilute antiferromagnetic system with the fcc lattice, Mg_1−pMn_pTe₂, was studied by means of the susceptibility measurement. The exchange interactions (2J_ijS_i·S_j) are evaluated as J₁=−4.5 K, J₂=−1 K and J₃=−1 K, analyzing the data of very low concentration samples by an isolated cluster method. The ground state spin arrangements in the fcc lattice are derived by taking J₃ into account. The set of J’s lies in the region of the 1 st kind ordering. The critical curve (phase transition temperatures vs concentrations, p) shows ‘terraced form.’ It first decreases linearly with decreasing p (∂(T_cr(p)⁄T_cr(1))⁄∂p=1.4) and abruptly at p=0.5. For 0.5>p>0.35, χ-T curve shows a small peak at low temperatures.

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From the angular dependence of the Cu⁶³ NMR frequency in the magnetically ordered state of (C₂H₅NH₃)₂CuCl₄, the parameters in the Cu⁶³ nuclear spin Hamiltonian are determined as follows; H_x=−28.5 kOe, H_y=−27.7 kOe, H_z=−189.6 kOe, ν_Q=6.00 MHz and η=−0.1. From these values, the Fermi contact, dipolar and orbital fields are separately estimated as H_F=−114 kOe, H_d=+24.4 kOe, H_l⁄⁄=−8.9 kOe and H_l⊥=−6.3 kOe. The disagreement of the dipolar and orbital fields with the theoretical estimations is found and is interpreted as mainly due to the reduction of 3d spin caused by the electron transfer from the Cl⁻ ions. On the contrary, it is shown that the Fermi contact field is hardly affected by the ligand ions.

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The dynamical magnetic susceptibility χ(q, ω) of Cu₂MnAl is evaluated on the basis of the realistic band structure which has been calculated by Mueller’s hybridized T.B.-OPW method. The effective exchange interaction U_eff^d–d is introduced as only one parameter in the present calculation. The theoretical results of the spin wave spectra of Cu₂MnAl are in good agreement with the experimental ones.
It turns out that the transitions from the majority spin bands to the minority spin bands mainly contribute to χ(q, ω). The correlation between the spin density of d-electrons of Mn and that of conduction electrons mainly contributes to the spin waves with small q, while for the spin waves with large q, the correlation between those of Mn is most important.

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Single crystal ESR data are presented for a two-dimensional antiferromagnet, Cu(HCOO)₂·2(NH₂)₂CO·2H₂O. Measurements have been made at 9.4 GHz in the temperature region of 1.3 K to 300 K with a particular attention to the temperature dependences of the linewidth and the resonance field in the short-range ordered region as well as the critical region.
The observed temperature dependence of the linewidth is well fitted to the relation, ΔH=Γ(χT⁄C)+A(1−T⁄T_N)⁻ⁿ by taking account of the two contributions, χT term of q=0 fluctuations at high temperatures and power-law term of q=K₀ fluctuations at low temperatures.
It is suggested that the transition temperature is strongly field-dependent.

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EPR linewidth in KCP was measured in the temperature range between 100 K and 219 K. The linewidth was found to be proportional to T³ and to have an anisotropy with a minimum nearly at an angle of the magnetic field of 50° from the c-axis. The results are interpreted as a superposition of the spin-phonon and the spin-spin relaxation component in a quasi-one-dimensional conductor, within the framework of the ‘mixed-valence-model.’

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Temperature dependences of electrical resistivities in the screw-, ferromagnetic- and fan-phases of MnP have been studied. In the screw phase, T² dependences are observed in the a-, b- and c-axis resistivities up to about 50 K and the coefficients are 4.3, 2.2 and 2.2×10⁻³ μΩcm/deg², respectively. In the ferromagnetic- and fan-phases, too, the T² dependences are observed and the coefficients are 4.0 and 5.2×10⁻³ μΩcm/deg², respectively. The observation of the T² dependence in different magnetic phases and the large value of the coefficients seem to suggest that the electron-electron scattering is dominant at low temperature and the Fermi surfaces are constructed only with the d like electrons. This is consistent with the results of electronic specific heat measurements done before.

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Magnetization of ferromagnetic Mn_1+δSb (0≤δ≤0.22) with NiAs crystal structure decreases linearly with increasing Mn content. In order to study the magnetic disturbance and the lattice strain around the interstitial Mn atom, diffuse scattering of polarized neutrons from a slice of a single crystal of Mn_1.2Sb is measured. It is reconfirmed that the excess Mn atom has no magnetic moment with itself. The reduction of the magnetization around the excess Mn atom is observed to be limited within the first neighboring regular-site Mn atoms.

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The structural energy and the dynamical motions in quasi one-dimensional (1–D) conductors are investigated microscopically from the view point of the pseudo-potential model for such systems developed by the author. When the 1–D Peierls instability is well-developed, the ±2k_F Fourier components of the pseudopotential is absorbed into the unperturbed Hamiltonian. The stabilizing energy of the Peierls state is quartic with respect to the quasi long-range order (QLRO) parameter. Explicit expressions are given for the structural energy including the commensurability energy. Including the effect of the QLRO into the phonon Hamiltonian, the soft phonon (phason mode) and the phonon with an energy gap (amplitude mode) are naturally derived at |q|=2k_F=Q. The phason dispersion near ±Q is derived and compared with the result derived by the conventional method.

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Giant quantum attenuation (GQA) of sound waves in high quality pyrolytic graphites has been measured under the conditions: the longitudinal sound wave vector q is applied along the hexagonal axis and the field H is parallel to a plane containing the hexagonal axis. The line shape of attenuation coefficient versus H curves is well explained by a theory of GQA, except for the highest field peak observed at H=19.2∼20.2 kG for |q∧H|\lesssim20° which is simultaneously contributed from both an electron and a hole Landau level and has an outstandingly large amplitude. Some component of the deformation potential tensor, the Landau level width and others are determined. A discussion is given on the origins of the anomalously large amplitude of the highest field peak.

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The temperature-dependent behavior of the conductivity σ_c perpendicular to the 1–d axis of TMTTF–TCNQ is explained in terms of diffusive hopping process between the Bloch-band electronic states of neighboring 1–d columns. It is pointed out that σ_c can be used to extract the conductivity component σ_SP ascribable to electrons in the single-particle states from the conductivity σ_b along the 1–d axis. The deviation (of about 20%) of σ_b from σ_SP around the maximum-conductivity region is ascribed to the contribution of the charge density waves.

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Diffuse scattering due to short range order (SRO) of the hexagonal ζ phase, Ag–Al, has been studied by X-ray and electron diffraction methods. Intensity distribution was measured in the reciprocal space at room temperature. Peculiar distribution was found such as a thin plate and a hinge shape on h₃=0 and 1 planes in the c^* direction, respectively. The maxima on these planes are shifted from 1/3, 1/3, h₃ and 2/3, 2/3, h₃ positions. SRO parameters α_lmn of a single crystal of Ag-34 at.%Al alloy have been determined by the Fourier transformation of X-ray diffuse intensity. It has been found from the electron diffraction patterns that the shift of the diffuse maxima from 1/3, 1/3, h₃ decreases almost linearly with increasing Al concentration. The Fermi-surface-imaging theory seems to be appropriate to interpret the observations.

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Local and global stabilities of an electron in deformable lattice with dimensionality δ and force range index λ are studied within the adiabatic approximation. Depending on the sign of the stability index: σ=δ−2λ−2, one finds the free state to be locally stable (σ>0) with discontinuous transition to globally stable self-trapped state beyond a critical value of coupling constant g, to be marginal (σ=0) with local (as well as global) stability being governed by g, or to be locally instabilized (σ<0) towards the optimum lattice distortion which grows continuously from zero with increasing g. A phase diagram is presented for an electron interacting simultaneously with two types of phonon fields with σ\lessgtr0. The potential barrier for self-trapping of a Wannier exciton is studied with particular attention to the effect of its internal motion, and is compared with the observation.

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Band structures on the Jones zone boundary are calculated for group V semimetals arsenic and antimony by the pseudopotential method. Jones zone concept is shown to be useful for clear understanding of bonding-antibonding energy gap. Peculiarity of crystal structure is discussed on the basis of the perturbation theory of cohesive energy reinforced with the Jones zone concept. It is shown that the origin of internal displacement of sublattices is, as has been naively expected, in the opening of the gap on the Jones zone surface, but the rhombohedral shear comes from second order, metallic, binding energy.

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We have investigated the quantitative relationship between the polytypes and the direct and indirect exciton gap energies in GaSe_1−xS_x mixed crystals. The X-ray diffraction analysis shows that GaSe_1−xS_x is the ε-type for 0(GaSe)≤x\lesssim0.01, the γ-type for 0.05\lesssimx\lesssim0.4, the β-type for 0.5\lesssimx≤1(GaS), and a mixture of the ε- and γ-types for 0.01\lesssimx\lesssim0.03. The direct and indirect exciton gap energies are determined from optical absorption and luminescence excitation spectra. The plots of the direct and indirect exciton gap energies vs the compositional parameter x show kinks in the neighborhood of x=0.4. Furthermore, a jump in the indirect exciton gap energy is found at around x=0.02. These anomalies at x=0.02 and 0.4 are attributed to the ε-γ and γ-β polytype transformations, respectively.

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By the use of two dye lasers, the spatial dispersion of the excitonic molecule has been studied by the excitation into states of large wave vectors. With the first laser beam ω₁(k₁) an excitonic polariton is created at a large wave vector and an excitonic molecule is formed with the second laser beam ω₂(k₂). The relation between ω₁ and ω₂ is expressed by a straight line of slope 0.57, and the mass of the excitonic molecule is determined to be 2.3 times as much as that of the transverse exciton. In the two different configurations in which the two laser beams are in the same and opposite directions, excitonic molecules are created at k₁±k₂. From the analysis of the relation between ω₁ and ω₂ in the two configurations, the excitonic mass is deduced to be (2.5∼3.0)m₀.

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The absorption and the reflection spectra of the synthetic single crystal of TeO₂ were measured over the photon energy from 1.8 to 5.6 eV for linearly polarized light with the E-vector parallel and perpendicular to the optic axis. From absorption measurement from 80 to 500 K, the fundamental absorption tail was shown to obey the modified Urbach rule with the steepness constatat σ₀=0.69. The optical constants n and k were determined from reflectivity through the Kramers-Kronig calculation. The strong dependence of the reflectivity on the direction of polarization of the incident light was observed, the origin of which was discussed under a model treating of optical transition from a p-like to an s-like state in a tetragonally deformed lattice. The temperature shift of the first reflection peak was estimated to be 2.5×10⁻⁴ eV/K in the temperature range from 80 to 300 K.

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The resonant Brillouin scattering has been investinated in CdS at room temperature by using monochromatic acoustic waves generated by ZnO thin film transducer. Resonant cancellation and enhancement are observed in the allowed configuration, whereas no signals are found in the forbidden configuration in contrast to the results observed by the acoustoelectric domains.

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Under a uniform hydrostatic pressure of about 5 kbar, RbI single crystal undergoes a phase transition from NaCl type to CsCl type polycrystal having preferred orientations. The orientation relation is approximately as follows: [111](CsCl)//[100](NaCl) and [100](CsCl)//[111](NaCl). This orientation relation is different from other types as observed for temperature-induced transition of CsCl or ammonium halides.

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ESR spectra of NH₃⁺ and SeO₃⁻ radicals in γ-irradiated [(NH₄)_1−xR_x]₂SO₄ crystals (R=Rb, Cs) resolving about 4 mol.% SeO₄ were analysed. The intensity of the spectral lines for NH₃⁺(β) was nearly equal to that for NH₃⁺(α) in all the mixed crystals [(MH₄)_1−xRb_x]₂SO₄ examined (x=0.09∼0.75). This fact indicates that the preferential replacement of R⁺ ion to the NH₄⁺(β) ion which has been observed in [(NH₄)_1−xK_x]₂SO₄, was not occurred in [(NH₄)_1−xRb_x]₂SO₄. For [(NH₄)_1−xCs_x]₂SO₄ with larger x, a trend that the NH₄⁺(α) ion was rather easily replaced by Cs⁺ ion, was observed. This result could be explained reasonably by considerig the mean distance from the nearest oxygens surrounding each NH₄⁺ ion. The analysis of SeO₃⁻ radical revealed that SO₄⁻⁻ ion might be deformed below T_c impling that SO₄⁻⁻ ion is responsible for a part of spontaneous polarization in ammonium sulfate and the mixed crystals.

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The optical absorption bandshape for the transition from an s-like ground state to a vibronically coupled p-like set of excited states with spin-orbit coupling is calculated from a numerical approach. The vibronic energy levels and eigenstates of the p-like state are obtained by a numerical diagonalization of the Jahn-Teller plus spin-orbit operators. To explain the experimental band shape in cesium fluoride, it is essential to consider the effect of a T_2g vibrational mode rather than an E_g vibrational mode. The strength of Jahn-Teller coupling and the spin-orbit coupling parameter for the F-center in cesium fluoride are estimated.

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Emission and excitation spectra of Eu²⁺ ions incorporated in MgS, CaS and CaSe were measured at temperatures 300, 80 and 6 K. Both spectra are interpreted as due to the allowed transition between the Eu²⁺ ion’s ground state (⁸S_7⁄2) of 4f⁷ configuration and the excited states of 4f⁶5d configuration, together with the forbidden transition arising from the configuration interaction between 4f⁶5d and 4f⁶6s. From the observed excitation spectra for CaS: Eu²⁺ and CaSe: Eu²⁺ phosphors, ⁸Γ₄(t_2g)-, ⁸Γ₃(e_g)-bands were assigned for lower concentrations of Eu²⁺ ion; besides these bands ⁸Γ₁(6s)- and ⁶Γ₄(t_2g)-bands were assigned for higher concentrations of Eu²⁺ ion. From the assigned ⁸Γ₄(t_2g)- and ⁸Γ₃(e_g)-bands, it has been found that 10Dq for MgS, CaS and CaSe are 19500 cm⁻¹, 18750 cm⁻¹ and 17300 cm⁻¹, respectively.

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The line shapes of the giant two-photon absorption band for the direct generation of excitonic molecules and the molecule luminescence in CuCl have been studied in a temperature region between 6 K and 100 K. The interaction between excitonic molecules and acoustical phonons is found to play an important role for the relaxation mechanism of excitonic molecules at high temperature. For temperatures higher than ∼50 K, the multi-phonon scattering process becomes predominant, and it causes the asymmetry in line shapes of the two-photon absorption band and the relevant two-photon resonant Raman lines.

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The pressure-induced structural change of tellurium has been studied by powder X-ray diffraction using a diamond-anvil and a cubic-anvil apparatus over the pressure range of 40–100 kbar at room temperature. The diffraction pattern for the high-pressure metallic phase at 45 kbar is interpreted as a monoclinic lattice with lattice constants a=3.104 Å, b=7.513 Å, c=4.760 Å, β=92.71° and V=111.0 ų. The coordinates of the four atoms in a unit cell are given by x₁=0.25, y₁=0.23, z₁=0.48; x₂=0.48, y₂=0.0, z₂=0.02, according to the space group C₂², 2a+2a. This atomic arrangement can be viewed as a layer structure. No further structural change was observed up to 100 kbar.

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γ-ray Compton profile measurements of Al metal were made over the temperature range from 25 to 900°C in both the solid and liquid states. The Fermi momentum was determined by the Fourier transform of the Compton profile. It is found that the temperature variation in the Fermi momentum of Al metal corresponds to the change in the electronic density in both the solid and liquid states and that the discontinuous change of the Fermi momentum takes place at the melting point.

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Comton profiles of CVD-crystalline and amorphous Si₃N₄ as well as α- and β-Si₃N₄ were measured using 59.54 keV γ-rays from ²⁴¹Am source and a Ge(Li) detector. The analyses of Compton profiles suggest that the valences of nitrogen and silicon are 3 and 4, respectively, which form the covalent nature of the chemical bond.

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Emission spectra between 2800 and 6000 Å have been observed at the ionic energies from 0.2 to 12 keV. Absolute measurements of emission cross-sections have been made for the emission lines coming from ArII excited states at 4 and 8 keV with a crossed-beam technique. Processes of single-electron capture into the ArII 4p- and 4p′-states, with exothermicity of a few eV, take place dominantly (∼10⁻¹⁵ cm²), while the endothermic processes producing ArII in the 4d- and 5s-states occur with small cross-sections. Sum of the cross-sections for electron capture into the excited states observed is comparable with the total single-electron capture cross-section estimated from attenuation measurements of ion currents. Possible errors and uncertainties are discussed.

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Excitation cross-sections are obtained for each term of the ArII nl-states (nl=4p, 4p′ and 4d) at 4 and 8 keV. The relative population distribution among the terms of a given nl-state can be interpreted in terms of statistics based on the building-up principle of molecule under radial coupling scheme. The relative population distribution among the multiplets in a given term is proportional to their statistical weight; spin-orbit recoupling at large internuclear separations is responsible for the population mechanism. The energy dependence of excitation cross-sections is discussed in connection with the Landau-Zener theory.

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The dissociation energy of the ground state of the AlO radical has been estimated by fitting the Hulburt-Hirschfelder potential curve to the true potential curve. The value of D₀⁰ reported is 120.4 kcal/mole. The applicability of the Hulburt-Hirschfelder function to the X²Σ⁺ state of AlO has been discussed.

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Ab initio SCF–CI calculations have been carried out for the X²Σ⁺, A²Π, B²Σ⁺, D²Σ⁺, ²ΔI, ⁴Σ⁺I, ⁴ΠI and ⁴ΔI states of CaH at four internuclear distances between 3.5 and 4.9 bohr and their potential energy curves are obtained. The calculated spectroscopic parameters are found to be in fair agreement with the observed ones. Present calculation predicts an avoided crossing between the and D²Σ⁺ B²Σ⁺ states occuring in the region of R=3.9∼4.9 bohr.

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A reflex tetrode is proposed to be made on the basis of a new idea that the plasma source is separated from the anode. It is shown that the ion beam is forced to move from the anode toward the virtual cathode in the reflex tetrode. The expressions are derived for the ion-beam current densities which are extracted from reflex tetrodes. Two types of tetrodes, one of which has the ion source and the other has the plasma source, are considered. The analyses are given for the three kinds of geometries; plane, cylindrical and spherical.

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The nonlinear behaviour of the two-dimensional steady-state propagation of the lower hybrid wave near the linear mode-conversion point is investigated in the presence of the density depression due to the ponderomotive force. It is shown that an equation which governs the wave packet near the conversion point can be reduced to the nonlinear Schrödinger equation with a Iinearly increasing potential. Numerical analysis of the model equation visualizes the behaviour of the wave packet in the linear and the nonlinear regimes.

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Cross-field electron heat diffusion due to thermally excited high frequency electrostatic waves propagating almost perpendicular to the magnetic field is studied using a 2–1/2-dimensional simulation code. It is shown that the electron heat diffusion coefficient D_H is an order of magnitude greater than the electron particle diffusion coefficient D_p, which is essentially collisional. The characteristic feature of wave transport is observed, namely an increase of D_H with increasing values of the characteristic temperature scale length L_x. The heat diffusion coefficients D_H^⁄⁄ and D_H^⊥ for the parallel and perpendicular temperatures (D_H\simeqD_H^⁄⁄+D_H^⊥) show quite different magnetic field scalings since D_H^⁄⁄ is due to ion modes while D^⊥_H arises from electron modes. This is also confirmed by treating the ions as an immobile background.

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The space charge wave instability of the spiral beam-plasma system is studied experimentally, under the application of nonuniform magnetic field. The velocity distribution of the spiral electron beam is varied by the mirror effect, which affects the trapping of beam electrons on the potential of the unstable wave. As the results, it is observed that the saturation length and the saturation level of the wave become extremely large, when beam electrons travel with feeling the decreasing magnetic field intensity, and vice versa. The theoretical consideration based on one-dimensional model is given, which explains the experimental results, consistently.

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The Regularized Long Wave (RLW) equation, u_t+u_x+uu_x−μu_xxt=0, has similar properties to the Korteweg-de Vries (KdV) equation. For example, the RLW equation has a stable solitary solution and dispersive property, However, the RLW equation has been found to have only two invariants, while the KdV equation has an infinite number of invariants. The present numerical studies show that the so-called recurrence property (almost-periodicity) for the KdV equation solution does not hold in the case of the RLW equation solution. However, the energy of the RLW solution is shared only among the lower modes of the system (no-thermalization). If the coefficient μ value is large (μ≥1.0), it is found by numerical computations that the recurrence property approximately holds. Some discussions are made on almost-periodicity of the RLW equation with a large value μ. Though the μ-dependence of almost-periodicity of the RLW equation does not become clear, we conjecture that collisions among many solitary waves are not stable for the RLW equation.

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The interaction between short surface waves and long internal waves in a two layer fluid has been investisated by a multiple scale method. When the group velocity of surface waves is equal to the phase velocity of internal wave, the steady solutions that represent the envelope of surface wave group and the internal wave coupling strongly with each other and moving with the same speed have been obtained.
According to the relative magnitude of amplitudes of short and long waves, too different cases, namely, (1) a_l⁄a_s=0(ε), (2) a_l⁄a_s=0(1), where a_l, a_s are amplitudes of long and short waves respectively, have been analysed individually.

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Recently, a class of new solutions have been derived for a number of soliton equations using Hirota’s bilinear forms of these soliton equations (S. Oishi: J. Phys. Soc. Jpn. 47 (1979) 1341). These solutions express solitons in a background of ripples, and are named generalized soliton solutions. In this paper, it is shown that the generalized soliton solutions for the Korteweg-de Vries equation and the Kadomtsev-Petviashvili equation can be transformed into a form of Fredholm’s determinants of the Gel’fand-Levitan-Marchenko integral equation. Using this result, relationship between Hirota’s method and the inverse spectral method is clarified. Moreover, it is also shown that the initial value problems for these two equations can be solved using their generalized soliton solutions.

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A statistical theory is constructed for the turbulent motion of a viscous fluid subject to the Boussinesq convection. The author’s recent approach to the inhomogeneous turbulence is extended to the turbulence of Boussinesq fluid to find general expressions for the velocity covariance and the velocity-scalar (temperature or density) covariance. Results obtained are applied to astrophysical and geophysical phenomena like the stellar convection and the thermocline erosion in the ocean.

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Exact one- and two-periodic wave solutions of a nonlinear integro-differential equation describing the propagation of waves in a stratified fluid of finite depth is presented. The solution reduces to the Korteweg-de Vries (KdV) periodic wave solution in the shallow water limit and to the Benjamin-Ono (B–O) periodic wave solution in the deep water limit.

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The linear stability of periodic permanent roll-wave trains on thin laminar flow of a viscous fluid down an inclined plane wall has been investigated analytically on the basis of a hydraulic model. The analytical result is here confirmed by following numerically the time development of a periodic initial disturbance superimposed upon a basic steady parallel flow into a stable or unstable permanent roll-wave train. Furthermore, it is shown that roll-waves can be generated successively from a localized initial disturbance.

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Exact N-soliton solution of the higher order wave equation for a stratified fluid layer of finite depth is obtained by employing Hirota’s bilinear transformation method. The solution reduces to the N-soliton solution of the higher order Korteweg-de Vries equation in the shallow water limit and to that of the higher order Benjamin-Ono equation in the deep water limit. The asymptotic form of the solution for large time is derived.

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In the present paper we investigate functional integral equations which describe scattering wave functions of effective Hamiltonian for nonlocal potentials, with various applications in defects phenomena of crystals. Particularly for the one dimensional case we study integral kernels of Yamaguchi, Mongan, Hulthen, Gauss and δ-functions.

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Non-radiative components of a local gravitational field can be the origin of noise in gravitational radiation experiments, particularly at low frequencies. The expected noise temperature of an antenna located in the vicinity of moving masses is discussed.

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The average production cross section of ⁵⁵Co in the ⁴⁰Ca+¹⁶O reaction was determined to be at most 1.75±0.5 μb in the energy range E_lab(¹⁶O)=39 to 89 MeV.

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Magnetic hyperfine fields at ¹¹⁹Sn in ferrimagnetic Fe₃O₄ and γ-Fe₂O₃ were measured by means of Mössbauer spectroscopy. The mean values at 4.2 K in Fe₃O₄ and γ-Fe₂O₃ were −241 kOe and −115 kOe respectively. The difference is explained by assuming that the transferred hyperfine contributions from A-site Fe³⁺, B-site Fe³⁺ and B-site Fe²⁺ are −117 kOe/atom, 113 kOe/atom and 40 kOe/atom, respectively.

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