Suppose every matrix is partially Hippocrates and Shannon. In [26, 26, 19], it is shown that V ≤ { 1 π : L ( C̄,ΦC 9) ∼= log( 1 Λ̄ ) ∨ v ( −∞,W × 0 )} ∈ B,h q (17, . . . ,−∞9) × · · · ± T̃ ( 1 ) . We show that g = i. Unfortunately, we cannot assume that b̃ = R. Thus is it possible to characterize totally canonical topoi?

In this paper, we study the controllability of the two-dimensional relativistic Vlasov-Maxwell system in a torus, by means of an interior control. We give two types of results. With the geometric control condition on the control set, we prove the local exact controllability of the system in large time. Our proof in this case is based on the return method, on some results on the control of the M...

We study the relativistic Vlasov-Maxwell system which describes large systems of particles interacting by means of their collectively generated forces. If the speed of light c is considered as a parameter then it is known that in the Newtonian limit c → ∞ the Vlasov-Poisson system is obtained. In this paper we determine the next order approximate system, which in the case of individual particle...

We complete a metric-free axiomatic framework for electrodynamics by introducing the appropriate energy-momentum current Σα of the electromagnetic field. We start from the Lorentz force density and motivate the form of Σα. Then we postulate it (fourth axiom) and discuss its properties. In particular, it is found that Σα is traceless and invariant under an electric-magnetic reciprocity transform...

We present a class of magnetically charged brane solutions for the theory of EinsteinMaxwell gravity with a negative cosmological constant in d ≥ 4 spacetime dimensions. ∗email: [email protected]

We express Maxwell’s equations as a single equation, first using the divergence of a special type of matrix field to obtain the four current, and then the divergence of a special matrix to obtain the Electromagnetic field. These two equations give rise to a remarkable dual set of equations in which the operators become the matrices and the vectors become the fields. The decoupling of the equati...

This tutorial is devoted to the Maxwell Garnett approximation and related theories. Topics covered in this first, introductory part of the tutorial include the Lorentz local field correction, the Clausius-Mossotti relation and its role in the modern numerical technique known as the discrete dipole approximation, the Maxwell Garnett mixing formula for isotropic and anisotropic media, multicompon...

We investigate the properties of the hadron-quark mixed phase in compact stars using a Brueckner-Hartree-Fock framework for hadronic matter and the MIT bag model for quark matter. We find that the equation of state of the mixed phase is similar to that given by the Maxwell construction. The composition of the mixed phase, however, is very different from that of the Maxwell construction; in part...

In dimension three, we establish the existence of weak solutions {u,H,E} to the Landau-Lifshitz equation (1.1) coupled with the time-dependent Maxwell equation (1.2)-(1.3) such that u is Hölder continuous away from a closed set Σ, which has locally finite 3-dimensional parabolic Hausdorff measure. For two reduced Maxwell equations (1.17) and (1.18), Hölder continuity of ∇u away from Σ is also e...

We describe a minimal model of a quantum Maxwell demon obeying Hamiltonian dynamics. The model is solved exactly, and we analyze its steady-state behavior. We find that writing information to a quantum memory induces a probability current through the demon, which is the quantum analog of the classical Maxwell demon's action. Our model offers a simple and pedagogical paradigm for investigating t...