On Some Inequalities and Their Application to the Cauchy Problem

Derivation of inequalities and application to Cauchy problem for infinite system of equation

In-medium nuclear interactions of low-energy hadrons

Experimental and theoretical developments of the last decade in the study of exotic atoms and some related low-energy reactions are reviewed, in order to provide information on the in-medium hadron-nucleon t matrix over a wide range of densities up to central nuclear densities. In particular, we review pionic deeply bound atomic states and related evidence for partial restoration of chiral symmetry in dense nuclear matter. The case for relatively narrow deeply bound atomic states for antikaons and antiprotons is made, based on the physics of strong nuclear absorption. Recent experimental suggestions for signals of antikaon-nuclear deeply bound states are reviewed, and dynamical models for calculating binding energies, widths and densities of antikaon nuclear states are discussed. Specific features of low-energy in-medium interactions of kaons, antiprotons and of Sigma hyperons are discussed, and suggestions to study experimentally Cascade atoms are reviewed.Comment: 86 pages, 44 figures, slight revisions, references added, Physics Reports (in press

Necrotic tumor growth: an analytic approach

The present paper deals with a free boundary problem modeling the growth process of necrotic multi-layer tumors. We prove the existence of flat stationary solutions and determine the linearization of our model at such an equilibrium. Finally, we compute the solutions of the stationary linearized problem and comment on bifurcation.Comment: 14 pages, 3 figure

Covariant Uniform Acceleration

We show that standard Relativistic Dynamics Equation F=dp/d\tau is only partially covariant. To achieve full Lorentz covariance, we replace the four-force F by a rank 2 antisymmetric tensor acting on the four-velocity. By taking this tensor to be constant, we obtain a covariant definition of uniformly accelerated motion. We compute explicit solutions for uniformly accelerated motion which are divided into four types: null, linear, rotational, and general. For null acceleration, the worldline is cubic in the time. Linear acceleration covariantly extends 1D hyperbolic motion, while rotational acceleration covariantly extends pure rotational motion. We use Generalized Fermi-Walker transport to construct a uniformly accelerated family of inertial frames which are instantaneously comoving to a uniformly accelerated observer. We explain the connection between our approach and that of Mashhoon. We show that our solutions of uniformly accelerated motion have constant acceleration in the comoving frame. Assuming the Weak Hypothesis of Locality, we obtain local spacetime transformations from a uniformly accelerated frame K' to an inertial frame K. The spacetime transformations between two uniformly accelerated frames with the same acceleration are Lorentz. We compute the metric at an arbitrary point of a uniformly accelerated frame. We obtain velocity and acceleration transformations from a uniformly accelerated system K' to an inertial frame K. We derive the general formula for the time dilation between accelerated clocks. We obtain a formula for the angular velocity of a uniformly accelerated object. Every rest point of K' is uniformly accelerated, and its acceleration is a function of the observer's acceleration and its position. We obtain an interpretation of the Lorentz-Abraham-Dirac equation as an acceleration transformation from K' to K.Comment: 36 page