Global existence and blow-up of solutions to a parabolic system with nonlocal sources and boundaries

This paper deals with a semi-linear parabolic system with nonlinear nonlocal sources and nonlocal boundaries.By using super-and sub-solution techniques,we first give the sufficient conditions that the classical solution exists globally and blows up in a finite time respectively,and then give the necessary and sufficient conditions that two components u and v blow up simultaneously.Finally,the uniform blow-up profiles in the interior are presented.     

Perturbed recurrence relations II the general case

In this paper, we give some new explicit relations between two families of polynomials defined by recurrence relations of all order. These relations allow us to analyze, even in the Sobolev case, how some properties of a family of orthogonal polynomials are affected when the coefficients of the recurrence relation and the order are perturbed. In a paper we have already given a method which allows us to study the polynomials defined by a three-term recurrence relation. Also here some generalizations are given.     

Invar and covar behavior of ferromagnets with allowance for magnetophonon interaction: A thermodynamic simulation

Based on the Landau theory of second-order phase transitions with allowance for interaction between the magnetic subsystem and crystal lattice (magnetophonon interaction, MPI), a consistent thermodynamic model of the invar and covar behavior of ferromagnets with MPI is constructed. Model calculations carried out at real temperatures show that the invar (covar) behavior of ferromagnets results from an optimal relationship between the thermodynamic parameters of the ferromagnetic phase. It is demonstrated that MPI is a fundamentally important factor responsible for the invar and covar effects. With the thermodynamic parameters obeying a certain relationship, the invar behavior of ferromagnets is predicted in a much wider temperature range than in known invars.     

Visions: The coming revolutions in particle physics

We study the branching ratio, CP-violating asymmetry, forward-backward asymmetry and the CP-violating asymmetry in the forward-backward asymmetry for the exclusive decay B → Kτ⁺τ⁻ in the two Higgs doublet model with tree level flavor changing neutral currents (model III). We analyse the dependencies of these quantities on the neutral Higgs boson contributions and the CP parameter sinθ in the model III. We observe that to determine the neutral Higgs boson effects, the measurements of the forward-backward asymmetry and the CP-violating asymmetry in the forward-backward asymmetry for the decay B → Kτ⁺τ⁻ are promising.     

Structural study and electrical properties of Zr-doped Nd<Subscript>2</Subscript>Sn<Subscript>2</Subscript>O<Subscript>7</Subscript> pyrochlore compounds

Nd₂Sn₂O₇ pyrochlores with the substitution of Zr⁴⁺ were prepared by conventional ceramic double sintering technique. The single-phase formation was confirmed by X-ray diffraction and neutron diffraction techniques. Relative intensity calculations for X-ray diffraction analysis were performed for oxygen positional parametersx = 0.331 and 0.375, while Rietveld refinements were employed for neutron diffraction data. The neutron diffraction study revealed that there are only two anion sites with 48f and 8b positions. This indicates that the 8a site, i.e. O(3) sublattice, is completely vacant and the structure is a perfect cubic pyrochlore with space group Fd3m (O _h ⁷ ). From the conductivity measurements, it is observed that the electronic conductivity dominates from room temperature up to about 525 K and forT > 525 K, the oxygen ion conduction dominates the charge transport in these compositions. Complex impedance spectroscopy indicates the existence of grain and grain boundary as two separate elements.     

Scroll codes

We study algebraic geometric codes obtained from rational normal scrolls. We determine the complete weight hierarchy and spectrum of these codes.      

New classes of 2-weight cyclic codes

We introduce new classes of 2-weight cyclic codes which are direct sums of 1-weight irreducible cyclic codes      

Vehicle density and velocity estimation on highways for on-ramp metering control

A scheme for vehicle density and velocity estimation in a stretch of highway based on a modified cell transmission model [C. F. Daganzo, Transportation Research, Part B, 28B(4),269–287, 1994. Elsevier is presented. The scheme is intended for use with on-ramp metering control algorithms, providing local knowledge of densities and velocities that is helpful to improve on-ramp metering control performance. Estimation of density is obtained by nonlinear estimators, while velocity estimation is obtained by gradient algorithms. There is one density–velocity estimator for free traffic flow and other for congested traffic flow. Both estimator schemes work in parallel. The final estimation of density and velocity results from a convex combination of the predictions of the two estimators. This combination depends on occupancy or density measurements at the boundaries of the stretch and is produced by a fuzzy inference system. Stability and convergence of the density and velocity estimation scheme is proved by Lyapunov based techniques. Simulation results comparing measured and estimated traffic data are presented. They confirm good performance of the estimators. Research sponsored by grants UNAM PAPIIT IN110403 and CONACYT 47583.     

Research on Hawking Radiation as Tunneling from Schwarzshild-anti-de Sitter Black Hole

After taking into account energy conservation and the particle’s self-gravitation interaction, Hawking radiation of the massive particle as tunneling from Schwarzshild-anti-de Sitter black hole is studied by using Parikh-Wilczek’s semi-classical quantum tunneling approach. Meanwhile, Hawking radiation as tunneling from the black hole is reexamined by developing Angheben–Nadalini–Vanzo–Zerbini (ANVZ) covariant method to cover energy conservation and the particle’s self-gravitation interaction. Both the results perfectly generalize those obtained by Parikh and Wilczek, and show that the tunneling rate is related to the change of Bekenstein-Hawking entropy, and the factual emission spectrum is not exactly thermal, but satisfies the underlying unitary theory. PACS: 04.70-s, 9760. Lf.