Discrete and Embedded Eigenvalues for One-Dimensional Schrödinger Operators

I present an example of a discrete Schrödinger operator that shows that it is possible to have embedded singular spectrum and, at the same time, discrete eigenvalues that approach the edges of the essential spectrum (much) faster than exponentially. This settles a conjecture of Simon (in the negative). The potential is of von Neumann-Wigner type, with careful navigation around a previously identified borderline situation.     

Algebro-Geometric Approach in the Theory of Integrable Hydrodynamic Type Systems

The algebro-geometric approach for integrability of semi-Hamiltonian hydrodynamic type systems is presented. The class of symmetric hydrodynamic type systems is defined and the calculation of the associated Riemann surfaces is greatly simplified for this class. Many interesting and physically motivated examples are investigated.     

Cluster approach in first-principle calculations for ferroelectrics

It is shown that, proceeding from the first principles, it is possible to separate the contributions from short-and long-range interactions to the lattice dynamics and dielectric properties of crystalline dielectrics. The cluster calculations of local force constants and potentials for the matrix and impurity atoms in ferroelectrics with the perovskite structure were made by the Hartree-Fock MOLCAO-SCF method. The parameters of the Devonshire-Slater-Barrett single-ion model are calculated for barium titanate and potassium niobate. The influence of the quantum statistics on the Curie temperature in these ferroelectrics and the isotope effect in barium titanate are also considered.     

Carbide precipitates in solution-quenched PH13-8 Mo stainless steel: A small-angle neutron scattering investigation

This paper deals with the small-angle neutron scattering (SANS) investigation on solution-quenched PH13-8 Mo stainless steel. From the nature of the variation of the functionality of the profiles for varying specimen thickness and also from the transmission electron microscopy (TEM), it has been established that the small-angle scattering signal predominantly originates from the block-like metallic carbide precipitates in the specimen. The contribution due to double Bragg reflection is not significant in the present case. The single scattering profile has been extracted from the experimental profiles corresponding to different values of specimen thickness. In order to avoid complexity and non-uniqueness of the multi-parameter minimization for randomly oriented polydisperse block-like precipitate model, the data have been analyzed assuming randomly oriented polydisperse cylindrical particle model with a locked aspect ratio.     

Kinetic C<Subscript>(2)-H</Subscript> exchange study of<Emphasis Type="Italic">Cis</Emphasis>-[(en)<Subscript>2</Subscript>Co(HIm)(enH)]Br<Subscript>4</Subscript> by NMR spectroscopy: Evidence for the acidity of C<Subscript>(2)-H</Subscript> proton

C_(2)-H exchange incis-[(en)₂Co(HIm)(enH)]Br₄ (Im, imidazole; en, ethylenediamine) was studied over a pD range of 9.4 to 10.2 at 60°C where thecis-[(en)₂Co(Him)(enH)]⁴⁺ andcis-[(en)₂Co(HIm)(en)]³⁺ are the species present in significant concentrations.Cis-[(en)₂Co(HIm)(enH)]⁴⁺ has pK_a1 7.86 and pK_a2 9.82 with pK_a1 corresponding to coordinated enH ionization and pK_a2 to ImH ionization. The kinetic data may be interpreted in terms of an intramolecular H-D exchange mechanism, where the “dangling”-ND₂CH₂CH₂ND₂ group acts as a base to remove the imidazole C_(2)-H proton from the coordinated DIm moiety.     

<Superscript>6</Superscript>He + <Superscript>6</Superscript>He Clustering of <Superscript>12</Superscript>Be in a Microscopic Algebraic Approach

The norm kernel of the A=12 system composed of two ⁶He clusters, and the L=0 basis functions (in the SU(3) and angular momentum-coupled schemes) are analytically obtained in the Fock-Bargmann space. The norm kernel has a diagonal form in the former basis, but the asymptotic conditions are naturally defined in the latter one. The system is a good illustration for the method of projection of the norm kernel to the basis functions in the presence of SU(3) degeneracy that was proposed by the authors. The coupled-channel problem is considered in the algebraic version of the resonating-group method, with the multiple decay thresholds being properly accounted for. The structure of the ground state of ¹²Be obtained in the approximation of zero-range nuclear force is compared with the shell-model predictions. In the continuum part of the spectrum, the S-matrix is constructed, the asymptotic normalization coefficients are deduced and their energy dependence is analyzed.     

Computation of triple differential cross-sections with the inclusion of exchange effects in atomic K-shell ionization by relativistic electrons for symmetric geometry

The triple differential cross-section for K-shell ionization of silver and copper atoms by relativistic electrons have been computed in the coplanar symmetric geometry with the inclusion of exchange effects following the multiple scattering theory of Das and Seal [1] multiplied by suitable spinors. Present computed results are marginally improved in some cases from the previous computed results [2]. Present results are compared with measured values [3] and with previous computation results [2]. Some other theoretical computational results are also presented here for comparison.      

On a Modification of the Scintillation Method

We solve the problem of diffraction of fluctuating radiation by an optically thin irregular layer (phase screen) with developed turbulent structure. It is shown that in the case of diffraction of radiation with saturated fluctuations and a narrow-band frequency spectrum by a weakly turbulent moving phase screen, the measured frequency spectrum of intensity fluctuations in the observation plane allows one to obtain information on the form of the spectrum of irregularities of an optically thin irregular layer in a wide size range significantly exceeding the size of the first Fresnel zone. Similarly to the well-known phase method of diagnostics of randomly irregular media, the conventional scintillation method modified in such a way yields undistorted information on the form of the irregularity spectrum. However, in contrast to the phase method, it also allows one to obtain data on the drift velocity of irregularities in the studied irregular layer.     

Polarization locking and nonparaxial spatial solitons in media with electronic Kerr nonlinearity

The polarization structure of nonparaxial spatial solitons in a transparent medium with the electronic mechanism of Kerr nonlinearity is studied theoretically. It is demonstrated analytically in the weak nonparaxiality approximation that the regime of polarization locking, in which all the field components have the same propagation constant, is the only stable regime. Estimates of the rate of transition of the initial metastable regime of rotation of the polarization ellipse to the regime of polarization locking are presented. Based on a numerical solution of the nonlinear Maxwell equations, the presence of the nonparaxial regime of polarization locking is confirmed and the main characteristics of the corresponding spatial solitons are obtained.