recognized as a reliable tool for assessing the hypothalamus-pituitary-adrenal (hpa) axis, measurement of salivary cortisol plays an important role in both the clinical and research settings. to establish a normative data, which forms the basis for the usage of this valuable parameter, we gathered 8:00 h saliva samples from 94 healthy individuals aged 6-14 years. cortisol levels were measured b...

In the theory of wavelets, in the study of subshifts, in the analysis of Julia sets of rational maps of a complex variable, and, more generally, in the study of dynamical systems, we are faced with the problem of building a unitary operator from a mapping r in a compact metric space X. The space X may be a torus, or the state space of subshift dynamical systems, or a Julia set. Our construction...

In the theory of wavelets, in the study of subshifts, in the analysis of Julia sets of rational maps of a complex variable, and, more generally, in the study of dynamical systems, we are faced with the problem of building a unitary operator from a mapping r in a compact metric space X. The space X may be a torus, or the state space of subshift dynamical systems, or a Julia set. Our construction...

We define a Gaussian measure on the space H0 J (M,L N ) of almost holomorphic sections of powers of an ample line bundle L over a symplectic manifold (M,ω), and calculate the joint probability densities of sections taking prescribed values and covariant derivatives at a finite number of points. We prove that they have a universal scaling limit as N → ∞. This result will be used in another paper...

We study the limit distribution of zeros of certain sequences of holomorphic sections of high powers L of a positive holomorphic Hermitian line bundle L over a compact complex manifold M . Our first result concerns ‘random’ sequences of sections. Using the natural probability measure on the space of sequences of orthonormal bases {SN j } of H(M,L ), we show that for almost every sequence {SN j ...

In this paper, we consider in R the Cauchy problem for nonlinear Schrödinger equation with initial data in Sobolev space W s,p for p < 2. It is well known that this problem is ill posed. However, We show that after a linear transformation by the linear semigroup the problem becomes locally well posed in W s,p for 2n n+1 < p < 2 and s > n(1− 1 p ). Moreover, we show that in one space dimension, ...

We consider random Schrödinger equations on R or Z for d ≥ 3 with uncorrelated, identically distributed random potential. Denote by λ the coupling constant and ψt the solution with initial data ψ0. Suppose that the space and time variables scale as x ∼ λ, t ∼ λ with 0 < κ ≤ κ0, where κ0 is a sufficiently small universal constant. We prove that the expectation value of the Wigner distribution of...

In this paper, we consider in R the Cauchy problem for nonlinear Schrödinger equation with initial data in Sobolev space W s,p for p < 2. It is well known that this problem is ill posed. However, We show that after a linear transformation by the linear semigroup the problem becomes locally well posed in W s,p for 2n n+1 < p < 2 and s > n(1− 1 p ). Moreover, we show that in one space dimension, ...

A multiresolution analysis for a Hilbert space realizes the Hilbert space as the direct limit of an increasing sequence of closed subspaces. In a previous paper, we showed how, conversely, direct limits could be used to construct Hilbert spaces which have multiresolution analyses with desired properties. In this paper, we use direct limits, and in particular the universal property which charact...