 J. Przeszowski:
Gauge symmetry in models of high temperature superconductors
 S. Poria, C. Mamaloukas, G.C. Layek and H.P. Mazumdar:
Some effects of a transverse magnetic field on the flow
of a viscous conducting fluid produced by an oscillating plane wall
 A. Drzewiecki and B. Maruszewski:
Doping and mass transfer in fullerenes
 E. Radzikowska:
Micropolar model of hightemperature superconductors
 S. Bytner, A. Gałka and B. Gambin:
Effective properties of layered piezoelectric material
with gradient of polarization
 V. Nichoga, P. Dub and Z. Kaczmarek:
Hollow ellipsoid of rotation as a physical model
of tubular cylindrical ferromagnetic core
 J. Cabański:
Exact method of solution of torsional vibrations problem
for discontinuous viscoelastic shaft with oscillators
Brief Notes
 W. Skrzeczanowski, J. Owsik, A. Długaszek,
J. Janucki, M. Nowakowski and A. Zarwalska:
Portable low uncertainty calorimetric standard for energy unit of pulse laser radiation
 J. Przeszowski:
Gauge symmetry in models of high temperature superconductors
 Gauge symmetry which appears in the slavemode approach to the tJ model
of high temperature superconductivity is presented. The mean field analysis of these
microscopic models lead to the continuum gauge field systems with infinitely strong
coupling constant. The viability of the perturbative calculations (with finite coupling
constant) are illustrated with a particularly simple field theory model. Exact
resummation of the perturbation series is discussed for the Heisenberg model of strongly
interacting spins in 1+1 dimensions which is approximated by the Schwinger model.
Contents
 S. Poria, C. Mamaloukas, G.C. Layek and H.P. Mazumdar:
Some effects of a transverse magnetic field on the flow
of a viscous conducting fluid produced by an oscillating plane wall
 In this paper, the unsteady unidirectional motion of an incompressible vicous
fluid, produced by sinusoidal oscillation of a rigid plane wall and subjected to a
uniform magnetic field acting perpendicularly to the flow direction is investigated. The
basic equation, governing the motion of such a flow is expressed in nondimensional form.
It is shown that this equation admits two solutions which satisfy the respective sets of
boundary and initial conditions. The results, showing the development of the velocity
field in time for different values of the magnetic parameter, are presented graphically
and discussed.
Contents
 A. Drzewiecki and B. Maruszewski:
Doping and mass transfer in fullerenes
 A crystalline solid of C_{60} (a fullerene) is expected to be an insulator or
a semiconductor. However, one of the most striking properties of C_{60}  related
materials is the observation of relatively high temperature superconductivity in alkali
metal doped M_{3}C_{60} and in various alkaline earth doped compounds. So, the
interstitial diffusion of impurities considerably influences the superconductivity phase.
The value of the critical temperature below which the superconducting phase exists
strongly depends on many other external influences (electromagnetic, thermal, mechanical,
etc.). The paper deals with construction of a phenomenological macroscopic model of
interactions between physical fields in fullerenes, basing on the extended thermodynamics
with internal variables and with the use of Liu's theorem in order to apply the entropy
inequality. Two types of the mass diffusion have been taken into account constructing the
model.
Contents
 E. Radzikowska:
Micropolar model of hightemperature superconductors
 The micropolar continuum theory is applied to superconductors of type II
containing a vortex lattice. The classical electrodynamic theory of micropolar continua
is supplemented by quantummechanical notions describing the phenomenon of
superconductivity. A variational principle for dissipative processes taking place in
hightemperature superconductors is formulated. The electromagnetic, mechanical and
thermal fields interactions in superconductors are considered. Finally, the complete
system of field equations describing these interactions is obtained together with the
constitutive relations and the jump conditions on the discontinuity surface.
Contents
 S. Bytner, A. Gałka and B. Gambin:
Effective properties of layered piezoelectric material
with gradient of polarization
 In the paper, homogenization of heterogeneous piezoelectricity with
polarization gradient is performed to obtain effective material coefficients. The method
of twoscale asymptotic expansion is used and the layered composite structure is analysed
in details.
Contents
 V. Nichoga, P. Dub and Z. Kaczmarek:
Hollow ellipsoid of rotation as a physical model
of tubular cylindrical ferromagnetic core
 Induction sensors with cores in the shape of hollow cylinder are widely used
because of such advantages as decrease of mass and simplicity of manufacturing cores with
defined geometry. Replacement of a real tubular cylindrical core by the model in the
shape of hollow ellipsoid of rotation with equal values of relative lengths,
ferromagnetic volumes and fluxes, that is proposed in the article, allows to find the
calculation algorithms for determination of electromagnetic parameters of cylindrical rod
with solid and tubular cores. The obtained algorithms take into account the influence of
both the geometry and magnetic properties of core material on the electromagnetic
parameters and are suitable for engineering calculations.
Contents
 J. Cabański:
Exact method of solution of torsional vibrations problem
for discontinuous viscoelastic shaft with oscillators
 In this paper a generalized, exact method for solving the problems of torsional
vibrations of a noncontinuous viscoelastic shaft with oscillators has been presented.
The oscillators are attached to the shaft by means of the viscoelastic constraints. The
vibrations of this compound system are described by the set of conjugated, partial and
ordinary differential equations. The separation of the variables in the complex Hilbert
space, the obtained results from the analysis of the boundaryvalue problems and the
proved generalized orthogonality of complex eigenvectors have been used to obtain the
solution for free vibrations of the system at the arbitrary initial conditions. Finally,
by applying the harmonic moment of the forced vibrations, the problem of the shaft has
been solved. In the herein presented method, the operational generalized principles [6]
have been applied.
Contents
 W. Skrzeczanowski, J. Owsik, A. Długaszek,
J. Janucki, M. Nowakowski and A. Zarwalska:
Portable low uncertainty calorimetric standard for energy unit of pulse laser radiation
 New instrument for metrology applications in measurements of laser pulse energy
is presented. Due to its parameters it can be used as a standard for unit of energy of
pulse laser radiation. The instrument consists of a control unit, three different sources
of laser radiation, two receivers of optical signal, and a laptop. The whole system can
be easily transported enabling one to carry out measurements in situ, at customers, not
only in laboratory conditions. A method of measurement used in operation of the standard
is described. Main characteristics of the standard are shown. Methods of calculation of
uncertainties of measurement during laser energy meters calibration by means of our
standard are also presented.
Contents
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