The Miura transformations of Kaup's equation and of Mikhailov's equation

Two types of Miura transformations have been found. One relates Kaup's equation to Sawada-Kotera's equation and another relates the generalized Mikhailov equation to a model equation for a shallow water wave.     

Correlation of x-ray chemical shift and bond parameters calculated from levine's theory

The Cu K absorption edge shift in the systems CuCl, CuBr, CuI, CuO, CuS, CuSe, Cu₂O, CuFeS₂ and CuCl₂ · 2H₂O has been studied using a Cauchois-type bent crystal X-ray spectrograph. The bond parameters ionic gap C^μ and average bond gap E^μ_gb calculated from Levine's theory have been correlated with the chemical shift ΔE. The correlation is found to be linear and further it has been observed that distinct separate curves between ΔE and the bond parameters C^μ and E^μ_gb can be drawn for Cu⁺¹ and Cu⁺² ions. The curves have been used to determine bond parameters for the system CuCl₂ · 2H₂O.     

Nonlinear superposition rule for Abel's equation

A nonlinear superposition rule for Abel's cubic differential equation involving four particular solutions can be replaced by a superposition rule involving only two particular solutions. Chiellini's restrictions on the particular solutions are found to be satisfied.     

Generator coordinate calculations of monopole and quadrupole vibrations with Skyrme's interaction

Skyrme's interaction is shown to lead to significant simplifications in generator coordinate calculations. As an illustration monopole and quadrupole modes are calculated in ⁴He, ¹⁶O and ⁴⁰Ca using pure oscillator wave functions.     

Dirac's equation and a new group of external symmetry

It is shown how the handedness of the massless leptons, and the Poincaré invariance of leptonic interactions, can be based on a new group of external symmetry.     

Application of the Green's function method to lattice vibrations in thin films

The Green's function method is used to investigate the lattice vibrations in a simple cubic thin film with nearest neighbour interactions. Appropriate Green's functions for the study of the surface waves for (001) and (011) orientations of the surface are determined. For a thin film with two parallel (001) free surfaces the atomic force tensors at the surface are modified in order to satisfy the rotational invariance condition. The surface waves are determined and a detailed discussion is made for the long wave-length limit k_y = 0 and k_x ? 1. For a given k_x there is a critical thickness below which only an antisymmetrical solution can exist. For the (011) orientation only the case of a single free surface is discussed.     

Relation between generalized idempotency of Dirac's density operator and semigroup property of Bloch's density operator

It is shown that a generalized form of idempotency of Dirac's density operator is a necessary and sufficient condition for semigroup property of Bloch's density operator.     

Calculation of Landau's fermi-liquid parameters in pure neutron matter

The Landau parameters F₀, F₁, G₀ and G₁ have been calculated in pure neutron matter including the interaction induced by exchange of density-density and spin-density excitations at densities up to k_F = 2.5 fm^?1. The main effect of the induced interaction is to make the matter more incompressible.     

Weyl's association,Wigner's function and affine geometry

According to Weyl one may associate a function with a dynamical operator; these functions depend on the parameters p and q and can be displayed in a p, q manifold, the W space. In the classical limit the W space becomes the phase space parametrised by the canonical variables. The function associated in this manner with the density operator is Wigner's function. It turns out that if Wigner's function is a delta function it cannot represent the density operator of a physically realisable state unless the argument of the delta-function is linear in the parameters a and q. In all other cases Wigner's function associated with a physically realisable state has a finite width, proportional to $\text{h}{}^{\mathrm{<mtext>2</mtext><mtext>3</mtext>}}$. Consequently straightness (linear combination of p and q) has a fundamental significance in the W space. Since this property is preserved under linear inhomogeneous transformations the W space will have a geometry generated by these transformations, the affine geometry of Euler, Moebius and Blaschke. In the present note we show how this comes about, how it simplifies the semiclassical approximations of Wigner's function, and makes one understand how in the classical limit this geometry is lost, allowing to be replaced by the geometry of canonical transformations.     

A possible unification of Newton's and Coulomb's forces

We have considered electric charge as the fourth component of the particle momentum in five-dimensional space–time. The fifth dimension has been compactified on a circle with an extremely small radius determined from the fundamental physics constants. First, we have given equations in the framework of five-dimensional special relativity and determined the corresponding reduction to four-dimensional space–time. Then, in order to obtain an appropriate charge-to-mass ratio and to avoid the Fourier modes problem, we have considered the propagation of an off-mass shell particle in the five-dimensional space–time which can be interpreted as the motion of an on-mass shell particle in the four-dimensional world we experience. As an example, we have discussed the five-dimensional kinematic equations associated with the electron-positron annihilation process into two photons. Finally, the consequences on the gravitational interaction between two elementary charged particles has been studied. As a main result, we have obtained a unification of Newton's gravitational and Coulomb's electrostatic forces.     

MacDonald's theorem and Milatz's theorem for multivariate stochastic processes

MacDonald's theorem, which expresses the spectral density of a randomly fluctuating variable α(t) in terms of the finite time average of that variable, α_θ(t), is generalized for multivariate processes. For purely random processes, having a white spectrum, this also yields the corresponding generalization of Milatz's theorem.     

A preliminary examination of rater-determined versus Hayre's voice-based psychological parameters

Rater-determined data on depression, anxiety and mania on some twenty subjects, receiving varying medication in each case, were compared with Hayre's voice-based psychological stress parameter, $\text{H}{}_{\mathrm{<mtext>1</mtext>}}$, determined solely from the voices of the subjects. Each subject was asked by raters to read a given paragraph, from which one word was taken for analysis. The analysis employed spectrum analysis and further processing in order to obtain the raw data for calculating Hayre's voice-based psychological stress parameter, $\text{H}{}_{\mathrm{<mtext>1</mtext>}}$. A comparison of the two results shows that manic measures were not significantly discernible by raters whereas a ratio of depression (D) and anxiety measure (A) seems to be very definitely correlated with Hayre's voice-based parameter, $\text{H}{}_{\mathrm{<mtext>1</mtext>}}$. Further work is continuing since it seems to show considerable promise in quantifying psychological measures obtained solely from the voice of the subject.     

On stationary solutions of the Schrödinger equation with a self-consistent potential satisfying boussinesq's equation

We derive an equation for a dense perturbation valid in a resonance region, M → 1, associated with the Schrödinger equation for a complex amplitude of the high-frequency Langmuir-oscillation electrical field. A solution of the above system in the linear approximation is obtained and discussed.