Abstract. Let Gm×n be an m × n real random matrix whose elements are independent and identically distributed standard normal random variables, and let κ2(Gm×n) be the 2-norm condition number of Gm×n. We prove that, for any m ≥ 2, n ≥ 2, and x ≥ |n − m| + 1, κ2(Gm×n) satisfies 1 √ 2π (c/x)|n−m|+1 < P ( κ2(Gm×n) n/(|n−m|+1) > x) < 1 √ 2π (C/x)|n−m|+1, where 0.245 ≤ c ≤ 2.000 and 5.013 ≤ C ≤ 6.414...

with initial conditions r(0) = do and ṙ(0) = vo. If the system is un-damped (C = 0N×N), the free response of the system will not decay with time, and a suitable trial solution to the differential equation (1) is r(t) = r̄ sin(ωnt), where r̄ is a constant vector of dimension N . Differentiating r(t) twice, r̈(t) = −ω2 nr̄ sin(ωnt), and substituting the trial solution into equation (1) we obtain − ω2...

The idea of replacing a divergence constraint by a divergence boundary condition is investigated. The connections between the formulations are considered in detail. It is shown that the most common methods of using divergence boundary conditions do not always work properly. Necessary and sufficient conditions for the equivalence of the formulations are given. ∗This work was supported by the Uni...

This paper uses a fully nonparametric approach to estimate efficiency measures for primary care units incorporating the effect of (exogenous) environmental factors. This methodology allows us to account for different types of variables (continuous and discrete) describing the main characteristics of patients served by those providers. In addition, we use an extension of this nonparametric appro...

We examine the small ball asymptotics for the weak solution X of the stochastic wave equation ∂X ∂t (t, x)− ∂ X ∂x (t, x) = g(X(t, x)) + f(t, x)dW (t, x) on the real line with deterministic initial conditions.

We investigate the viability of a two-stage innationary scenario in the context of super-gravity, so as to resolve the problem of initial conditions for hybrid innation. We allow for non-renormalizable terms in the superpotential and consider the most general form of the KK ahler potential and the gauge kinetic function. We construct a model with two stages of innation, the rst driven by D-term...

Speed humps used as a tool of traffic calming technique that applied to force drivers to reduce their vehicle’ speeds at some locations. For developed countries, the implementations of speed humps are often used within residential areas as well as at locations of schools crossing.  For developing countries (e.g. Iraq), speed humps are used even at urban and urban highways.   This paper investig...

acute respiratory infections, diarrhea and fever are very common in children below the age of five years. all children suffer from these illnesses several times each year. however, during natural disasters like floods children are even more vulnerable to these diseases and death. pneumonia, diarrhea, measles and malaria, and associated malnutrition, are responsible for over 60% deaths in childr...

some 190 specimens of sefidrud loach, oxynoemacheilus bergianus , were collected from aras river (northwestern iran) and age, size, and some biological characteristics of the samples were investigated from march to july 2013. the maximum age was 3 + years. the specimens ranged in size from 42 to 64mm for males and 45 to 61mm for females in total length, weighing from 0.62 to 2.03g for males and...