[en] This paper aims to model the failure pattern of repairable systems in presence of explained and unexplained heterogeneity. The failure pattern of each system is described by a Power Law Process. Part of the heterogeneity among the patterns is explained through the use of a covariate, and the residual unexplained heterogeneity (random effects) is modeled via a joint probability distribution on the PLP parameters. The proposed approach is applied to a real set of failure time data of powertrain systems mounted on 33 buses employed in urban and suburban routes. Moreover, the joint probability distribution on the PLP parameters estimated from the data is used as an informative prior to make Bayesian inference on the future failure process of a generic system belonging to the same population and employed in an urban or suburban route under randomly chosen working conditions. - Highlights: • We describe the failure process of buses powertrain system subject to heterogeneity. • Heterogeneity due to different service types is explained by a covariate. • Random effect is modeled through a joint pdf on failure process parameters. • The powertrain reliability under new future operating conditions is estimated

[en] Method of construction of wave functions approximating eigenfunctions of the L^{^2} operator is proposed for high angular momentum states of few-electron atoms. Basis functions are explicitly correlated Gaussian lobes, projected onto irreducible representations of finite point groups. Variational calculations have been carried out for the lowest states of lithium atom, with quantum number L in the range from 1 to 8. Nonrelativistic energies accurate to several dozens of nanohartree have been obtained. For 2²P, 3²D, and 4²F states they agree well with the reference results. Transition frequencies have been computed and compared with available experimental data

[en] Neutron transport simplified P₃ (SP₃) equation which is an approximation to the neutron transport P_N equation, can be transferred to a format similar to the traditional neutron diffusion equation. Solving the SP₃ equation is implemented by semi-analytic nodal method which is one of the effective nodal method, and also by coarse mesh finite difference (CMFD) method with fine mesh finite difference (FMFD) format. By numerical analysis of NEACRP L-336 benchmark (modified), it is demonstrated that pin-by-pin nodal calculation can obtain almost the same result as FMFD, but pin-by-pin CMFD result has some deviation to the FMFD result. (author)

[en] Three-dimensional (3D), time dependent numerical simulations of flow of matter in stars, now have sufficient resolution to be fully turbulent. The late stages of the evolution of massive stars, leading up to core collapse to a neutron star (or black hole), and often to supernova explosion and nucleosynthesis, are strongly convective because of vigorous neutrino cooling and nuclear heating. Unlike models based on current stellar evolutionary practice, these simulations show a chaotic dynamics characteristic of highly turbulent flow. Theoretical analysis of this flow, both in the Reynolds-averaged Navier-Stokes (RANS) framework and by simple dynamic models, show an encouraging consistency with the numerical results. It may now be possible to develop physically realistic and robust procedures for convection and mixing which (unlike 3D numerical simulation) may be applied throughout the long life times of stars. In addition, a new picture of the presupernova stages is emerging which is more dynamic and interesting (i.e., predictive of new and newly observed phenomena) than our previous one

[en] Non-random event losses due to dead time effect in nuclear radiation detection systems distort the original Poisson process into a new type of distribution. As the characteristics of the distribution depend on physical properties of the detection system, it is possible to estimate the dead time parameters based on time interval analysis, this is the problem investigated in this work. A BF₃ ionization chamber is taken as a case study to check the validity of the method in experiment. The results are compared with the data estimated by power rising experiment performed in Esfahan Heavy Water Zero Power Reactor (EHWZPR). Using Monte Carlo simulation, the problem is elaborately studied and useful range for counting rates of the detector is determined. The proposed method is accurate and applicable for all kinds of radiation detectors with no potential difficulty and no need for any especial nuclear facility. This is not a time consuming method and advanced capability of online examination during normal operation of the detection system is possible

[en] We provide explicit expressions for boundary form factors in the boundary scaling Lee–Yang model for operators with the mildest ultraviolet behavior for all integrable boundary conditions. The form factors of the boundary stress tensor take a determinant form, while the form factors of the boundary primary field contain additional explicit polynomials

[en] The system of partial differential equation for the description of the laminar, steady, axisymmetric flow of an incompressible fluid on a flat horizontal bottom has been derived. The impermeability condition and full slipping condition on the bottom have been used. The reduction of the initial system to an ordinary differential equation for the steam function has been obtained. It has been shown that this equation is reduced under certain conditions to two Chazy equations. The exact solution expressed in terms of Airy functions has been obtained at one value of the parameter in the equation. Three types of the flow of the fluid depending on the values of two arbitrary constants in the solution have been discovered by analyzing this solution

[en] A method for solving systems of linear algebraic equations has been proposed on the basis on the summation of the corresponding continued fractions. The proposed algorithm for solving systems of linear algebraic equations is classified as direct algorithms providing an exact solution in a finite number of operations. Examples of solving systems of linear algebraic equations have been presented and the effectiveness of the algorithm has been estimated

[en] We consider one-dimensional nonlinear delay reaction-diffusion equations with varying transfer coefficients. We describe a few new methods for constructing exact solutions of such equations; these methods are based on using invariant subspaces for the corresponding nonlinear differential operators. A number of new exact generalized and functional separable solutions have been obtained. All of the equations and solutions involve several free parameters. The exact solutions obtained can be used to test approximate analytical and numerical methods for solving nonlinear delay reaction-diffusion equations

[en] A method for approximate determination of roots of a cubic equation that has one real and two complex-conjugate roots and satisfies the conditions of stability has been proposed. The formulas obtained are quite accurate, simple, and convenient for analysis and optimization of systems and objects