Approximation Theorems for Exponentially Bounded <i>a</i>-Times Integrated Cosine Function

Inverse Approximation Theorems for . . .

A Note on Exponentially Bounded Stopping times of Certain One-sample Sequential Rank Order Tests

A simple proof of the exponential boundedness of the stopping time of the one-sample sequential probability ratio tests (SPRT’s) is obtained.

Preservation theorems for bounded formulas

In this paper we naturally define when a theory has bounded quantifier elimination, or is bounded model complete. We give several equivalent conditions for a theory to have each of these properties. These results provide simple proofs for some known results in the model theory of the bounded arithmetic theories like CPV and PV1. We use the mentioned results to obtain some independence results i...

Integrated Cosine Functions

In order to the second order Cauchy problem (CP2): x"(t) Ax(t), z(O) z E D(A"), z"(O) y D(A") on a Banach space, Arendt and Kellermann recently introduced the integrated cosine function. This paper is concerned with its basic theory, which contain some properties, perturbation and approximation theorems, the relationship to analytic integrated semigroups, interpolation and extrapolation theorems.

Bounded Area Theorems for Higher Genus Black Holes Bounded Area Theorems for Higher Genus Black Holes

By a simple modification of Hawking's well-known topology theorems for black hole horizons, we find lower bounds for the areas of smooth apparent horizons and smooth cross-sections of stationary black hole event horizons of genus g > 1 in four dimensions. For a negatively curved Einstein space, the bound is 4π(g−1) −ℓ where ℓ is the cosmological constant of the spacetime. This is complementary ...