We define the Dirac-Fock current to hold the current conservation in the momentumdependent Dirac fields, and discuss its effect on the magnetic-moment in the nuclear matter. It is shown that the Dirac-Fock current can largely reduce the magneticmoment even in the isovector case, whose value has been too big due to the small effective mass in the usual relativistic Hartree approximation.

Dirac deformation of Poisson operators of arbitrary rank is considered. The question when Dirac reduction does not destroy linear Poisson pencils is studied. A class of separability preserving Dirac reductions in the corresponding quasi-bi-Hamiltonian systems of Benenti type is discussed. Two examples of such reductions are given. This paper will appear in J. Phys. A: Math. Gen. AMS 2000 Subjec...

We use the spectra of Dirac type operators on the sphere S to produce sharp L inequalities on the sphere. These operators include the Dirac operator on S, the conformal Laplacian and Paenitz operator. We use the Cayley transform, or stereographic projection, to obtain similar inequalities for powers of the Dirac operator and their inverses in R.

The density of states and the AC conductivity of graphene under uniform strain are calculated using a new Dirac Hamiltonian that takes into account the main three ingredients that change the electronic properties of strained graphene: the real displacement of the Fermi energy, the reciprocal lattice strain and the changes in the overlap of atomic orbitals. Our simple analytical expressions for ...

We study the existence of solutions to the fractional elliptic equation (E1) (−∆)u + ǫg(|∇u|) = ν in a bounded regular domain Ω of R (N ≥ 2), subject to the condition (E2) u = 0 in Ω, where ǫ = 1 or −1, (−∆) denotes the fractional Laplacian with α ∈ (1/2, 1), ν is a Radon measure and g : R+ 7→ R+ is a continuous function. We prove the existence of weak solutions for problem (E1)-(E2) when g is ...

We report a method for estimating people’s achievement based on their fame. Earlier we discovered that fame of fighter pilot aces (measured as number of Google hits) grows exponentially with their achievement (number of victories). We hypothesize that the same functional relation between achievement and fame holds for other professions. This allows us to estimate achievement for professions whe...

In 1945, Dirac attempted to develop a “formal probability” distribution to describe quantum operators in terms of two noncommuting variables, such as position x and momentum p [Rev. Mod. Phys. 17, 195 (1945)]. The resulting quasiprobability distribution is a complete representation of the quantum state and can be observed directly in experiments. We measure Dirac’s distribution for the quantum ...

The penalization method is used to take account of obstacles in a tokamak, such as the limiter. We study a non linear hyperbolic system modelling the plasma transport in the area close to the wall. A penalization which cuts the transport term of the momentum is studied. We show numerically that this penalization creates a Dirac measure at the plasma-limiter interface which prevents us from defi...

Consider a Boolean model Σ in R. The centers are given by a homogeneous Poisson point process with intensity λ and the radii of distinct balls are i.i.d. with common distribution ν. The critical covered volume is the proportion of space covered by Σ when the intensity λ is critical for percolation. Previous numerical simulations and heuristic arguments suggest that the critical covered volume m...

Consider two sequences of bounded random variables, a value and a timing process, that satisfy the large deviation principle (LDP) with rate-function J(· , ·) and whose cumulative process satisfies the LDP with rate-function I(·). Under mixing conditions, an LDP for estimates of I constructed by transforming an estimate of J is proved. For the case of cumulative renewal processes it is demonstr...