Abstract. There is a family of potentials that minimize the lowest eigenvalue of a Schrödinger eigenvalue under the constraint of a given L norm of the potential. We give effective estimates for the amount by which the eigenvalue increases when the potential is not one of these optimal potentials. Our results are analogous to those for the isoperimetric problem and the Sobolev inequality. We al...

In this lecture, we propose to survey several interesting recent developments on improvements and generalizations of what is popularly known as Steffensen’s integral inequality. Moreover, as a by-product of the investigation presented here, we show how one can correct an error in a recent generalization of Steffensen’s inequality. We also present a brief survey of some old and new inequalities ...

A new constantWD(X) is introduced into any real 2n-dimensional symmetric normed space X . By virtue of this constant, an upper bound of the geometric constant D(X), which is used to measure the difference between Birkhoff orthogonality and isosceles orthogonality, is obtained and further extended to an arbitrarym-dimensional symmetric normed linear space (m≥ 2). As an application, the result is...

Bell's inequality is established based on local realism. The violation of Bell's inequality by quantum mechanics implies either locality or realism or both are untenable. Leggett's inequality is derived based on nonlocal realism. The violation of Leggett's inequality implies that quantum mechanics is neither local realistic nor nonlocal realistic. The incompatibility of nonlocal realism and qua...

OBJECTIVES This study is to cross-map telephone nursing consultation documentations with International Classification for Nursing Practice (ICNP; ver. 1.0 concepts). METHODS The narrative telephone nursing consultation documentations of 170 ophthalmology nursing unit patients were analyzed. The nursing statements were examined and cross-mapped with the Korean version of the ICNP ver. 1.0. If ...

This paper examines the reliability-based stochastic transit assignment problem with elastic demand. A Variational Inequality (VI) model for this problem is developed. The VI model considers capacity, waiting time and in-vehicle travel time as stochastic variables, and includes Spiess and Florian’s (1989) and de Cea and Fernández’s (1993) models as special cases. A reliability-based stochastic ...

In this paper we deal with existence and uniqueness of solution to super-linear problems for the Pucci operator: −M(Du) + |u|u = f(x) in IR, where s > 1 and f satisfies only local integrability conditions. This result is well known when, instead of the Pucci operator, the Laplacian or a divergence form operator is considered. Our existence results use the Alexandroff-Bakelman-Pucci inequality s...

The local galactic cluster, the Great attractor, embeds us in a dimensionless gravitational potential of about −3 × 10. In the solar system this potential is constant to about 1 part in 10. Consequently, planetary orbits, which are determined by the gradient in the gravitational potential, remain unaffected. However, this is not so for the recently introduced flavor-oscillation clocks where the...

1. Introduction There are two divergent views on the proper analysis of Q(uantifier)-float. On one hand, the adverbial position of floated quantifiers (FQs) indicates that they are ver-Q-float in Thai is no exception. Adverbs occur at the right edge of the VP, and this is where we find FQs in Thai as well, as (1b) shows.

1 A 1 < £ < , 5B B SB so that we have the classical theorem of Hurwitz. For other values of r, approximations from both sides are permitted, but the errors allowed on the two sides are different; hence the term unsymmetrical approximation. The result here was new, and is so related to Hurwitz's inequality that one side is strengthened and the other weakened. Notice that the result for r > l is ...