Spherically symmetric thin shell in the presence of a cosmological constant are constructed, applying the Darmois-Israel formalism. An equation governing the behavior of the radial pressure across the junction surface is deduced. The cosmological constant term slows down the collapse of matter. The spherical N-shell model with an appropriate initial condition imitates the FRW universe with Λ = ...

Theorems of the same type with greater constants on the right-hand side of (1.1) were proved by Hartman [3] and Koksma [6]. Recently, the author has shown [1] that the theorem of Uchiyama no longer holds if the constant s14 is replaced by any smaller number. Assuming weaker arithmetical restrictions in (1.2) on numerators and denominators of the approximants, the constant in (1.1) can be dimini...

Let B be a Brownian motion. We show that there is a process H predictable in the natural filtration of B, such that H ·S is a Brownian motion in its own filtration, where St =Bt+t. In other words, H hides the constant drift. This gives a positive answer to a question posed by Marc Yor.

If X is a geodesic metric space and x1, x2, x3 ∈ X, a geodesic triangle T = {x1, x2, x3} is the union of the three geodesics [x1x2], [x2x3] and [x3x1] in X. The space X is δ-hyperbolic (in the Gromov sense) if any side of T is contained in a δneighborhood of the union of the other two sides, for every geodesic triangle T in X. We denote by δ(X) the sharp hyperbolicity constant of X, i.e., δ(X) ...

In over 4 decades of experience with computer-supported learning (CSL), applications have progressed from rote training with primitive computer work stations, to today’s web-based applications for support of online learning communities (OLCs). It is assumed here that the growing focus of CSL applications on OLCs to support collaborative group learning has an inexorable momentum that parallels t...

PURPOSE The aim of this study is to evaluate the feasibility of a telehealthcare application for operable lung cancer (OLC) patients, consisting of ambulant symptom and physical activity monitoring (S&PAM) and a web-accessible home-based exercise program (WEP), and identify possible barriers for successful adoption and implementation. METHODS A two-stage mixed methods design was used, in whic...

Let ζ(s,C) be the partial zeta function attached to a ray class C of a real quadratic field. We study this zeta function at s = 1 and s = 0, combining some ideas and methods due to Zagier and Shintani. The main results are (1) a generalization of Zagier’s formula for the constant term of the Laurent expansion at s = 1, (2) some expressions for the value and the first derivative at s = 0, relate...

Given a smooth complex projective variety X and an ample line bundle L on X. Fix a point x ∈ X. We consider the question, are there conditions which guarantee the maxima of the Seshadri constant of L at x, i.e ε(L, x) = n √ L? We give a partial answer for surfaces and find examples where the answer to our question is negative. If (X,Θ) is a general principal polarized abelian surface, then ε(Θ,...

so ker f ⊂ imh. Hence ker f = imh so the sequence is exact at the middle term. Further, f is injective since Z[X] is a domain, so left multiplication by any element is injective. Finally, h is surjective since the constant polynomials g = a have g(0) = a for every a ∈ Z. Therefore the sequence is exact. The sequence is split over R. The requisite map q : Z→ R so that h ◦ q = 1Z. It is clear tha...

We prove a constant term conjecture of Robbins and Zeilberger (J. Combin. Theory Ser. A 66 (1994), 17–27), by translating the problem into a determinant evaluation problem and evaluating the determinant. This determinant generalizes the determinant that gives the number of all totally symmetric self-complementary plane partitions contained in a (2n)×(2n)×(2n) box and that was used by Andrews (J...