Study of the peak effect phenomenon in single crystals of 2H-NbSe2

The weakly pinned single crystals of the hexagonal 2H-NbSe₂ compound have emerged as prototypes for determining and characterizing the phase boundaries of the possible order-disorder transformations in the vortex matter. We present here a status report based on the ac and dc magnetization measurements of the peak effect phenomenon in three crystals of 2H-NbSe₂, in which the critical current densities vary over two orders of magnitude. We sketch the generic vortex phase diagram of a weakly pinned superconductor, which also utilizes theoretical proposals. We also establish the connection between the metastability effects and pinning.     

Multipliers of convergence in norm of series with respect to multiplicative systems

We prove analogs of the Telyakovskii-Pochuev criteria for multipliers of uniform convergence and of convergence in the integral metric for multiplicative systems with bounded generating sequence.     

The influence of a transverse magnetic field on a subnormal glow discharge in air

In subnormal glow discharge under d.c. excitation at different pressure in a varying transverse magnetic field (0 to 30 G) some measurements have been carried out for various initial average tube currents. The voltage across the discharge increases and average tube current and residual current decreases in the magnetic field. With the help of Beckman’s expression [4] for the axial field and the electron density distribution in a transverse magnetic field the observed variation of current and voltage can be satisfactorily explained. The variation of axial electric field with transverse magnetic field can be represented to a fair degree of accuracy by the derived equation. The behaviour of residual current with magnetic field has been observed in these oscillations.     

Integral equation formulation for buoyancy-driven convection problems

An integral equation formulation for buoyancy-driven convection problems is developed and illustrated. Buoyancy-driven convection in a bounded cylindrical geometry with a free surface is studied for a range of aspect ratios and Nusselt numbers. The critical Rayleigh number, the nature of the cellular motion, and the heat transfer enhancement are computed using linear theory. Green's functions are used to convert the linear problem into linear Fredholm integral equations. Theorems are proved which establish the properties of the eigenvalues and eigenfunctions of the linear integral operator which appears in these equations.     

Fourier transforms in generalized Lipschitz classes

We obtain sufficient conditions for the Fourier transform of a function f ∈ L ₁(?) to belong to generalized Lipschitz classes defined by the modulus of smoothness of order m. The sharpness of these conditions is established in the cases when f(t) ≥ 0 on ? or tf (t) ≥ 0 on ?.     

Generalized fractional integrals in <Emphasis Type="Italic">p</Emphasis>-adic morrey and Herz spaces

For Riesz potential I ^β (f) on p-adic linear space Q _p ⁿ and its modification \(\widetilde{I^\beta }(f)\) we give sufficient conditions of their boundedness from radialMorrey space to anotherMorrey or Campanato space. Also we study the boundedness of modified Riesz potential \(\widetilde{I^\beta }(f)\) from Herz space to special Campanato spaces.     

Generalization of the multiplicative Fourier transform and its properties

We consider a new class of functions on the semiaxis for which the multiplicative Fourier transform can be defined. We prove equalities of Parseval type, an inversion formula and a condition for the validity of representation in the form of the multiplicative Fourier transform.     

Weighted Integrability of Multiple Multiplicative Fourier Transforms

Mathematical Notes - Sufficient conditions for the weighted integrability of multiple multiplicative Fourier transforms of Bernstein–Szasz type involving integral moduli of continuity and of...     

Hausdorff operators on p-adic linear spaces and their properties in Hardy, BMO, and Hölder spaces

Sufficient conditions for the boundedness of p-adic matrix operators in Hardy, Hölder and BMO spaces are obtained. These conditions are expressed in terms of the determinant of the matrix and its norm in a p-adic linear space.