On the harmonic Boltzmannian waves in laser-plasma interaction

We study the permanent regimes of the reduced Vlasov-Maxwell system for laser-plasma interaction. A non-relativistic and two different relativistic models are investigated. We prove the existence of solutions where the distribution function is Boltzmannian and the electromagnetic variables are time-harmonic and circularly polarized

Excise levying on gold products on the Romanian territory

As regards the trade operations with gold products, the tax regime is rather special. The current paper tackles the most significant aspects of excise levying of this products/jewels type in the Romanian system. The focus is on certain framework elements regarding the fiscal status of the operator with gold products. The study relies on the European and national regulations but it also refers to other works which highlight similar problems

The Ising model and Special Geometries

We show that the globally nilpotent G-operators corresponding to the factors of the linear differential operators annihilating the multifold integrals $\chi^{(n)}$ of the magnetic susceptibility of the Ising model ($n \le 6$) are homomorphic to their adjoint. This property of being self-adjoint up to operator homomorphisms, is equivalent to the fact that their symmetric square, or their exterior square, have rational solutions. The differential Galois groups are in the special orthogonal, or symplectic, groups. This self-adjoint (up to operator equivalence) property means that the factor operators we already know to be Derived from Geometry, are special globally nilpotent operators: they correspond to "Special Geometries". Beyond the small order factor operators (occurring in the linear differential operators associated with $\chi^{(5)}$ and $\chi^{(6)}$), and, in particular, those associated with modular forms, we focus on the quite large order-twelve and order-23 operators. We show that the order-twelve operator has an exterior square which annihilates a rational solution. Then, its differential Galois group is in the symplectic group $Sp(12, \mathbb{C})$. The order-23 operator is shown to factorize in an order-two operator and an order-21 operator. The symmetric square of this order-21 operator has a rational solution. Its differential Galois group is, thus, in the orthogonal group $SO(21, \mathbb{C})$.Comment: 33 page

Mining remittances corresponding to metalliferous ores: regulation and budget impact

Economic statistics and forecasting show that Romania has a very favourable potential as far as the metalliferous ores are concerned. As these are owned by the state, once they are allowed to be exploited, they generate considerable amounts for the consolidated public budget. The present paper is meant to conduct a synthetic analysis on the topic of mining remittances from an economic perspective, by considering the juridical framework of capitalizing deposits of ferrous and non-ferrous ores, correlated with the general regulations concerning property and the specific existing regulations of the EU and of the countries that have experience and potential in the mining sector

Subresultants in multiple roots: an extremal case

We provide explicit formulae for the coefficients of the order-d polynomial subresultant of (x-\alpha)^m and (x-\beta)^n with respect to the set of Bernstein polynomials \{(x-\alpha)^j(x-\beta)^{d-j}, \, 0\le j\le d\}. They are given by hypergeometric expressions arising from determinants of binomial Hankel matrices.Comment: 18 pages, uses elsart. Revised version accepted for publication at Linear Algebra and its Application

NuMI Beam Monitoring Simulation and Data Analysis Status and Progress

With the Main Injector Neutrino Oscillation Search (MINOS) experiment decommissioned, muon and hadron monitors became an important diagnostic tool for the NuMI Off-axis v Appearance (NOvA) experiment at Fermilab to monitor the Neutrinos at the Main Injector (NuMI) beam. The goal of this study is to maintain the quality of the monitor signals and to establish correlations with the neutrino beam profile. And we carry out a systematic study of the response of the muon monitors to the changes in the parameters of the proton beam and lattice parameters. We report here on the progress of the beam data analysis and comparison with the simulation results

Holonomic functions of several complex variables and singularities of anisotropic Ising n-fold integrals

Lattice statistical mechanics, often provides a natural (holonomic) framework to perform singularity analysis with several complex variables that would, in a general mathematical framework, be too complex, or could not be defined. Considering several Picard-Fuchs systems of two-variables "above" Calabi-Yau ODEs, associated with double hypergeometric series, we show that holonomic functions are actually a good framework for actually finding the singular manifolds. We, then, analyse the singular algebraic varieties of the n-fold integrals $\chi^{(n)}$, corresponding to the decomposition of the magnetic susceptibility of the anisotropic square Ising model. We revisit a set of Nickelian singularities that turns out to be a two-parameter family of elliptic curves. We then find a first set of non-Nickelian singularities for $\chi^{(3)}$ and $\chi^{(4)}$, that also turns out to be rational or ellipic curves. We underline the fact that these singular curves depend on the anisotropy of the Ising model. We address, from a birational viewpoint, the emergence of families of elliptic curves, and of Calabi-Yau manifolds on such problems. We discuss the accumulation of these singular curves for the non-holonomic anisotropic full susceptibility.Comment: 36 page