where n is the exterior normal direction of ∂Ω. In other words, we look for a “best” way to extend the boundary value φ with the prescribed normal derivative ψ. Typical examples of Ω and N are the unit ball and the unit sphere, respectively. In this case, ψ : ∂Ω → TφN means φ (x) · ψ (x) = 0 for all |x| = 1. With the given Dirichlet data φ, the most natural extension is perhaps the harmonic map...

The model of a tired random walker, whose jump-length decays exponentially in time, is proposed and the motion of such a tired random walker is studied systematically in one-, twoand threedimensional continuum. In all cases, the diffusive nature of walker breaks down due to tiring which is quite obvious. In one-dimension, the distribution of the displacement of a tired walker remains Gaussian (...

A proof is given that the maximal Fermi coordinate chart for any comoving observer in a broad class of Robertson-Walker spacetimes consists of all events within the cosmological event horizon, if there is one, or is otherwise global. Exact formulas for the metric coefficients in Fermi coordinates are derived. Sharp universal upper bounds for the proper radii of leaves of the foliation by Fermi ...

Lorentz symmetry breaking effects on relativistic EPR (Einstein–Podolsky–Rosen) correlations are discussed. From the modified Maxwell theory coupled to gravity, we establish a possible scenario of the Lorentz symmetry violation and write an effective metric for the Minkowski spacetime. Then we obtain the Wigner rotation angle via the Fermi–Walker transport of spinors and consider the WKB (Wentz...

Consider nonlinear wave equations in the spatially flat Friedmann-Lema\^itre-Robertson-Walker (FLRW) spacetimes. We show blow-up finite time of solutions and upper bounds lifespan to give FLRW spacetime version Glassey's conjecture for derivative nonlinearity. also results space

Partiendo de la teoŕıa desarrollada en la tesis “Paralelismo y geodésicas en variedades conformes” [5], se utiliza la conexión de Fermi–Walker y el tensor conforme de Schouten para describir los invariantes conformes clásicos asociados a curvas en el espacio conforme plano R. En particular, estos resultados se aplican al estudio de dos ejemplos especiales de curvas: los ćırculos y las hélices. ...

Line A Walker carcinoma differs from line B in that it does not elicit hypercalcemia and hypercalciuria when implanted in rats at various sites (s.c, i.m., intraaortically). However, Walker 256/A, unlike line B, may invade the tibia when implanted i.m. in the adjacent gastrocnemius muscle. This invasion was evaluated by measuring the increased weight of the bone and decreased calcium concentrat...

Sodium acceptors were diffused into ZnO bulk single crystals to a depth of 1 lm, with a near-surface concentration of 10 cm . An O–H local vibrational mode (LVM) was observed at 3304 cm , at a temperature of 9 K, in hydrogenated samples. The LVM is attributed to an O–H bond-stretching mode adjacent to a Na acceptor. When deuterium substitutes for hydrogen, a peak is observed at 2466 cm . The is...

Background: Gonadal dysgenesis, the most common cause of primary amenorrhea, is characterized by absent or underdeveloped ovaries. Although the coexistence of gonadal dysgenesis and Mayer-Rokitansky-Küster-Hauser (MRKH) has been reported, it is still quite infrequent. To the extent that authors searched, just one study reported the association between Rokitansky sequence and Dandy-Walker malfor...