Abstract:
we analyze gauge theories based on abelian p-forms in real compact hyperbolic manifolds. the explicit thermodynamic functions associated with skew-symmetric tensor fields are obtained via zeta-function regularization and the trace tensor kernel formula. thermodynamic quantities in the high-temperature expansions are calculated and the entropy/energy ratios are established.

Abstract:
We analyze gauge theories based on abelian $p-$forms in real compact hyperbolic manifolds. The explicit thermodynamic functions associated with skew--symmetric tensor fields are obtained via zeta--function regularization and the trace tensor kernel formula. Thermodynamic quantities in the high--temperature expansions are calculated and the entropy/energy ratios are established.

Abstract:
A beautiful theorem due to J. L. F. Bertrand concerning the laws of attraction that admit bounded closed orbits for arbitrarily chosen initial conditions is translated from French into English.

Abstract:
The influence of an external constant uniform magnetic field on the Casimir energy density of a Dirac field under antiperiodic (and periodic) boundary condition is computed by applying Schwinger's proper time method. The result thus obtained shows that in principle, under suitable conditions, the magnetic field can enhance the fermionic Casimir energy density.

Abstract:
We discuss the work-kinetic energy theorem and the mechanical energy conservation theorem in the context of general physics courses. The motivation is the fact that all modern texts on introductory mechanics show the same conceptually dangerous statement that besides obliterating the concept of mechanical work, diminishing the importance of the work-kinetic energy theorem, leads to erroneous applications of the energy conservation theorem and at the same eliminates its relationship with the principle of the conservation of the mechanical momentum.

Abstract:
A beautiful theorem due to J. L. F. Bertrand concerning the laws of attraction that admit bounded closed orbits for arbitrarily chosen initial conditions is translated from French into English.

Abstract:
We discuss an alternative non-perturbative proof of Bertrand's theorem that leads in a concise way directly to the two allowed fields: the newtonian and the isotropic harmonic oscillator central fields.