Dirac Hamiltonian with superstrong Coulomb field

We consider the quantum-mechanical problem of a relativistic Dirac particle moving in the Coulomb field of a point charge $Ze$. In the literature, it is often declared that a quantum-mechanical description of such a system does not exist for charge values exceeding the so-called critical charge with $Z=\alpha ^{-1}=137$ based on the fact that the standard expression for the lower bound state energy yields complex values at overcritical charges. We show that from the mathematical standpoint, there is no problem in defining a self-adjoint Hamiltonian for any value of charge. What is more, the transition through the critical charge does not lead to any qualitative changes in the mathematical description of the system. A specific feature of overcritical charges is a non uniqueness of the self-adjoint Hamiltonian, but this non uniqueness is also characteristic for charge values less than the critical one (and larger than the subcritical charge with $Z=(\sqrt{3}^{-1}=118$). We present the spectra and (generalized) eigenfunctions for all self-adjoint Hamiltonians. The methods used are the methods of the theory of self-adjoint extensions of symmetric operators and the Krein method of guiding functionals. The relation of the constructed one-particle quantum mechanics to the real physics of electrons in superstrong Coulomb fields where multiparticle effects may be of crucial importance is an open question.Comment: 44 pages, LaTex file, to be published in Teor.Mat.Fiz. (Theor.Math.Phys.

Association of Calculation and Designing Subsystems for Engineering of Steam Turbine Equipment

The article describes the integration of the calculation subsystem implemented in PTC Mathcad Prime 3.0 and the design subsystem implemented in the PTC Creo Parametric 3.0 environment when creating design documentation for steam turbine seals.Статья представляет описание интеграции расчетной подсистемы, реализованной в PTC Mathcad Prime 3.0 и проектирующей подсистемы, реализованной в среде PTC Creo Parametric 3.0 при создании конструкторской документации на уплотнения паровой турбины

Toda p-brane black holes and polynomials related to Lie algebras

Black hole generalized p-brane solutions for a wide class of intersection rules are obtained. The solutions are defined on a manifold that contains a product of n - 1 Ricci-flat internal spaces. They are defined up to a set of functions H_s obeying non-linear differential equations equivalent to Toda-type equations with certain boundary conditions imposed. A conjecture on polynomial structure of governing functions H_s for intersections related to semisimple Lie algebras is suggested. This conjecture is proved for Lie algebras: A_m, C_{m+1}, m > 0. For simple Lie algebras the powers of polynomials coincide with the components of twice the dual Weyl vector in the basis of simple coroots. The coefficients of polynomials depend upon the extremality parameter \mu >0. In the extremal case \mu = 0 such polynomials were considered previously by H. L\"u, J. Maharana, S. Mukherji and C.N. Pope. Explicit formulas for A_2-solution are obtained. Two examples of A_2-dyon solutions, i.e. dyon in D = 11 supergravity with M2 and M5 branes intersecting at a point and Kaluza-Klein dyon, are considered.Comment: 24 pages, Latex, typos are eliminated, a correct relation on parameters of special block-orthogonal solution is added in third line after eq. (4.10

The kinetic description of vacuum particle creation in the oscillator representation

The oscillator representation is used for the non-perturbative description of vacuum particle creation in a strong time-dependent electric field in the framework of scalar QED. It is shown that the method can be more effective for the derivation of the quantum kinetic equation (KE) in comparison with the Bogoliubov method of time-dependent canonical transformations. This KE is used for the investigation of vacuum creation in periodical linear and circular polarized electric fields and also in the case of the presence of a constant magnetic field, including the back reaction problem. In particular, these examples are applied for a model illustration of some features of vacuum creation of electron-positron plasma within the planned experiments on the X-ray free electron lasers.Comment: 17 pages, 3 figures, v2: a reference added; some changes in tex

Pharmaceutical technology to be!

The purpose of the study is to study and analyze extemporal formulations for 2022 using the example of one of the production pharmacies in the city of Yekaterinburg, as well as to identify pharmaceutical substances that are not economically feasible to use in the manufacture of drugs.Цель исследования – изучить и проанализировать экстемпоральные рецептуры за 2022 год на примере одной из производственных аптек города Екатеринбурга, а также выявить фармацевтические субстанции, которые экономически нецелесообразно использовать в изготовлении лекарственных препаратов

Measurement of the top quark mass using the matrix element technique in dilepton final states

We present a measurement of the top quark mass in pp¯ collisions at a center-of-mass energy of 1.96 TeV at the Fermilab Tevatron collider. The data were collected by the D0 experiment corresponding to an integrated luminosity of 9.7  fb−1. The matrix element technique is applied to tt¯ events in the final state containing leptons (electrons or muons) with high transverse momenta and at least two jets. The calibration of the jet energy scale determined in the lepton+jets final state of tt¯ decays is applied to jet energies. This correction provides a substantial reduction in systematic uncertainties. We obtain a top quark mass of mt=173.93±1.84  GeV

Ratio of the Isolated Photon Cross Sections at \sqrt{s} = 630 and 1800 GeV

The inclusive cross section for production of isolated photons has been measured in \pbarp collisions at $\sqrt{s} = 630$ GeV with the \D0 detector at the Fermilab Tevatron Collider. The photons span a transverse energy ($E_T$) range from 7-49 GeV and have pseudorapidity $|\eta| < 2.5$. This measurement is combined with to previous \D0 result at $\sqrt{s} = 1800$ GeV to form a ratio of the cross sections. Comparison of next-to-leading order QCD with the measured cross section at 630 GeV and ratio of cross sections show satisfactory agreement in most of the $E_T$ range.Comment: 7 pages. Published in Phys. Rev. Lett. 87, 251805, (2001