Related papers: Hessian measures in the aerodynamic Newton problem
Despite its apparent simplicity, Newtonian Mechanics contains conceptual subtleties that may cause some confusion to the deep-thinking student. These subtleties concern fundamental issues such as, e.g., the number of independent laws needed…
Einstein equations for several matter sources in homogeneous, isotropic metric are shown to reduce to a second order nonlinear ordinary differential equation. An analysis of its solutions is made in an important case.
In this article I present a simple Newtonian heuristic for deriving a weak-field approximation for the spacetime geometry of a point particle. The heuristic is based on Newtonian gravity, the notion of local inertial frames [the Einstein…
We derive the equations of celestial mechanics governing the variations of the orbital elements under a stochastic perturbation generalizing the classical Gauss equations. Explicit formulas are given for the semi-major axis, the…
Quasi-Newton techniques approximate the Newton step by estimating the Hessian using the so-called secant equations. Some of these methods compute the Hessian using several secant equations but produce non-symmetric updates. Other…
We prove the natural weighted Calder\'{o}n and Zygmund estimates for solutions to elliptic and parabolic obstacle problems in nondivergence form with discontinuous coefficients and irregular obstacles. We also obtain Morrey regularity…
We present the quantum measurement problem as a serious physics problem. Serious because without a resolution, quantum theory is not complete, as it does not tell how one should - in principle - perform measurements. It is physical in the…
Many papers have been published over the years that either conjecture or even (claim to) prove the universality of the form of Maxwell's equations. We present yet another derivation of Maxwell's equations and discuss the conclusions…
The notion of the quantum angle is introduced. The quantum angle turns out to be a metric on the set of physical states of a quantum system. Its kinematics and dynamics is studied. The certainty principle for quantum systems is formulated…
According to Heisenberg's uncertainty relation, there is an ultimate limit to how precisely we may predict the outcome of position and momentum measurements on a quantum system. We show that this limit may be violated by an arbitrarily…
There have been recent claims (Anderson et al., EPL, 110, 10002) of a 5.9 year periodicity in measurements of Newton's gravitational constant, $G$, which show a very strong correlation with observed periodic variations in the length of the…
We review some well posed formulations of the evolution part of the Cauchy problem of General Relativity that we have recently obtained. We include also a new first order symmetric hyperbolic system based directly on the Riemann tensor and…
We consider a theory of gravity with a hidden extra-dimension and metric-dependent torsion. A set of physically motivated constraints are imposed on the geometry so that the torsion stays confined to the extra-dimension and the…
Three problems stand in the way of deriving classical theories from quantum mechanics: those of realist interpretation, of classical properties and of quantum measurement. Recently, we have identified some tacit assumptions that lie at the…
We introduce a proposal to modify Einstein's equations by embedding them in a larger symmetric hyperbolic system. The additional dynamical variables of the modified system are essentially first integrals of the original constraints. The…
We are concerned with the energy equality for weak solutions to Newtonian and non-Newtonian incompressible fluids. In particular, the results obtained for non-Newtonian fluids, after restriction to the Newtonian case, equal or improve the…
A novel approach to an old symmetry problem is developed. A new proof is given for the following symmetry problem, studied earlier.
We have solved the Einstein equations of general relativity for a class of metrics with constant spatial curvature and found a non-vanishing Weyl tensor in the presence of an energy-momentum tensor with an anisotropic pressure component.…
We propose a variational approach to approximate measures with measures uniformly distributed over a 1 dimentional set. The problem consists in minimizing a Wasserstein distance as a data term with a regularization given by the length of…
In this work, we have obtained exact solutions of Einstein equations for static and axially symmetric magnetized matter, specifically in plane-symmetric and almost-plane symmetric cases. Although these solutions impose constraints on the…