After examining the initial value problem for the linear, diocotron response of a long cylinder of pure-electron plasma, the “quasimodes” associated with convex, power-law density profiles are studied. For these profiles, exact, analytic results are available. The “quasimodes,” which are damped by phase mixing, may be characterized by their angular variation, hamess, and the magnitude of the ga...

We present solution generating methods which allow us to construct exact static solutions to the equations of four-dimensional Einstein-MaxwellDilaton gravity starting with arbitrary static solutions to the pure vacuum Einstein equations, Einstein-dilaton or Einstein-Maxwell equations. In four dimensions the field equations of the Einstein-Maxwell-dilaton gravity with arbitrary dilaton coupling...

A function is called an exponential if it is a linear combination of products of polynomials with pure exponentials. In this paper lower and upper bounds for families of spaces of piecewise exponentials are established. In particular, the exact Lp-approximation order (1 _< p _<) is found for a family {Sh}h>O of function spaces when each Sh is generated by an exponential box spline and its multi...

This paper presents an exact solution for the free energy of linear solvation of a dipolar solute in an arbitrary dielectric material with a microscopic spectrum of polarization fluctuations. The solution is given in terms of wave vector-dependent longitudinal and transverse structure factors of the polarization fluctuations in the pure dielectric. Good agreement with computer simulations of di...

A gauge invariant regularisation for dealing with pure Yang-Mills theories within the exact renormalization group approach is proposed. It is based on the reg-ularisation via covariant higher derivatives and includes auxiliary Pauli-Villars fields which amounts to a spontaneously broken SU (N |N) super-gauge theory. We demonstrate perturbatively that the extended theory is ultraviolet finite in...

Quantum mechanics in the Rigged Hilbert Space formulation describes quasistationary phenomena mathematically rigorously in terms of Gamow vectors. We show that these vectors exhibit microphysical irreversibility, related to an intrinsic quantum mechanical arrow of time, which states that preparation of a state has to precede the registration of an observable in this state. Moreover, the Rigged ...

We analyze a class of exact type II solutions of the Robinson–Trautman family which contain pure radiation and (possibly) a cosmological constant. It is shown that these spacetimes exist for any sufficiently smooth initial data, and that they approach the spherically symmetric Vaidya–(anti-)de Sitter metric. We also investigate extensions of the metric, and we demonstrate that their order of sm...

Some exact analytical formulas are presented for the generalized Roche model of rotating star. The gravitational field of the central core is described by the model of two equal-mass point centers placed symmetrically at rotation axis with the pure imaginary z coordinates. The all basic parameters of the critical figure of the rotating massless envelope are presented in analytical form. The exi...

The “entanglement of formation” of a mixed state of a bipartite quantum system can be defined in terms of the number of pure singlets needed to create the state with no further transfer of quantum information. We find an exact formula for the entanglement of formation for all mixed states of two qubits having no more than two non-zero eigenvalues, and we report evidence suggesting that the form...

We present solution generating methods which allow to construct exact static solutions to the equations of four-dimensional Einstein-Maxwell-Dilaton gravity starting with arbitrary static solutions to the pure vacuum Einstein equations, Einstein-dilaton or Einstein-Maxwell equations. In four dimensions the field equations of the Einstein-Maxwell-dilaton gravity with arbitrary dilaton coupling p...