We studied the existence and uniqueness of solutions of the following two kinds of nonlinear matrix equations X = Pk−1 l=0 P T l X lPl, and X = Pk−1 l=0 (P T l XPl) αl , and the convergence of the matrix sequences {Xi} recursively defined by Xn+k = Pk−1 l=0 P T l X αl n+lPl, n ≥ 0, and Xn+k = Pk−1 l=0 (P T l Xn+lPl) αl , n ≥ 0, where |αl| ≤ 1 for 0 ≤ l ≤ k − 1 and X0, · · · , Xk−1 are initial p...

Abstract. We define the Ladyzhenskaya-Lions exponent αl(n) = (2 + n)/4 for Navier-Stokes equations with dissipation −(−∆) in R, for all n ≥ 2. We then prove strong global solvability when α ≥ αl(n), given smooth initial data. If the corresponding Euler equations for n > 2 were to allow uncontrolled growth of the enstrophy 1 2 ‖∇u‖ L2 , then no globally controlled coercive quantity is currently ...

We study a model for two-dimensional skyrmions on a sphere of radius L. Such model simulates a skyrmion lattice of density W/(2πL), where W is the skyrmion winding number. We show that, to a very good approximation, physical results depend only on the product αL, where α is the strength of potential term. In the range αL ∼ 3 the order parameter vanishes, there is a uniform distribution of the d...

The ultrasonic relaxation of tellurite glasses xB2O3 – 70 TeO2 (30 x) WO3, 0 ≤ x 30 mol% was investigated by measuring the attenuation (αL) in these thermal range 140–300 K (T) at various frequencies (f). Some characteristics can be obtained from relation αL–T, such as average activation energy (Ep) and attempt frequency (f0). variables Ep f0 are a function B2O3 content. Moreover, αL–T accounts...

We build a new kind of random polynomial model, Massive Algebraic System (MAS), which is equivalent to algebraic polynomial system in solvability. This model focused on Finite Fields, especially on Z2, is NPcomplete. By results of Population Dynamics, we find these systems undergo 1-Replica Symmetry Breaking (1RSB) and high order Replica Symmetry Breaking. This phenomenon indicates subtle struc...

We present an approximate, analytical calculation of the reionized spectra C l of cosmic microwave background radiation (CMB) anisotropies and polarizations generated by relic gravitational waves (RGWs). Three simple models of reionization are explored, whose visibility functions are fitted by gaussian type of functions as approximations. We have derived the analytical polarization βl and tempe...

We show that the mass-segregation solution for the steady state distribution of stars around a massive black hole (MBH) has two branches: the known weak segregation solution (Bahcall & Wolf 1977), and a newly discovered strong segregation solution, presented here. The nature of the solution depends on the heavy-tolight stellar mass ratio MH/ML and on the unbound population number ratio NH/NL, t...

Blood pressure exhibits substantial short- and long-term variability (BPV). We assessed the hypothesis that the complexity of beat-to-beat BPV will be differentially altered in salt-sensitive hypertensive Dahl rats (SS) versus rats protected from salt-induced hypertension (SSBN13) maintained on high-salt versus low-salt diet. Beat-to-beat systolic and diastolic BP series from nine SS and six SS...

Total absorption, defined as the net flux of energy out of a bounded region averaged over one cycle for time harmonic motion, must be non-negative when there are no sources of energy within the region. This passivity condition places constraints on the non-dimensional absorption coefficients of longitudinal and transverse waves, γL and γT, in isotropic linearly viscoelastic materials. Typically...

Quasi-Monte Carlo (QMC) methods are being adopted in statistical applications due to the increasingly challenging nature of numerical integrals that are now routinely encountered. For integrands with d-dimensions and derivatives of order α, an optimal QMC rule converges at a best-possible rate O(N−α/d). However, in applications the value of α can be unknown and/or a rate-optimal QMC rule can be...