Assay for urinary estriol during the menstrual cycle based on extraction by a graphitized carbon black cartridge followed by high-performance liquid chromatography

Summary A high-performance liquid chromatography (HPLC) assay for estriol in nonpregnancy urine is described. After Enzymic hydrolysis, the estriol is extracted from urine by the sorbent trap technique utilizing graphitized carbon black (Carbopack B). After some washing steps, estriol is desorbed by a suitable solvent system. After solvent removal, the sample is injected into an HPLC column for estriol quantification. Analytical recovery of estriol was 96.1%. The precision of the method was 2.6 and 4.9% respectively at 145 and 10.6ng/ml of urine. The limit of sensitivity was set at 0.8 ng/ml of urine. The mean contents of estriol in the follicular and luteal phases were respectively 11.3 and 38.8 ng/ml of urine.Dedicated to Prof. Dr. A. Liberti on the occasion of his 70th birthday.     

The wave equation on homogeneous trees

Let be a homogeneous tree, ℒ the Laplace operator of , and b the bottom of its L² spectrum. In this paper we consider the discretised version of the (modified) wave equation (∂ _t ² +ℒ−b)u=0 on . Using methods of spherical Fourier analysis, we study existence and uniqueness of solutions of the corresponding initial value problem, we determine an explicit formula for the solutions in terms of convolution with suitable wave kernels, and describe some of their properties. Entrata in Redazione l'1 gennaio 1997. Work partially supported by the Italian M.U.R.S.T. The first author was supported by a post-doctoral fellowship at the Politecnico di Milano     

On converse H-theorem

In the present paper the so-called weighting process is defined. Conditions on the weights implying the converse H-theorem are given. These conditions are satisfied by the iterated weighting process which contains, as a particular case, the Bayesian model for prediction and retrodiction given by S. Watanabe.     

A stochastic approach for simulating spatially inhomogeneous coagulation dynamics in the gelation regime

We present a stochastic approach for the simulation of coagulation–diffusion dynamics in the gelation regime. The method couples the mass flow algorithm for coagulation processes with a stochastic variant of the diffusion-velocity method in a discretized framework. The simulation of the stochastic processes occurs according to an optimized implementation of the principle of grouping the possible events. A full simulation of a particle system driven by coagulation–diffusion dynamics is performed with a high degree of accuracy. This allows a qualitative and quantitative analysis of the behaviour of the system. The performance of the method becomes more evident especially in the gelation regime, where the computations become usually very time consuming.     

Dependence of electron dynamics on magnetic fields in semiconductor superlattices

Numerical simulation results are presented for a drift-diffusion rate equation model which describes electronic transport due to sequential tunneling between adjacent quantum wells in weakly coupled semiconductor superlattices （SLs）. The electron dynamics is dependent on the external magnetic field perpendicular to the electron motion direction, and a detailed explanation is given. Using different parameters, the system shows different dynamic behaviors, and three distinct phenomena are observed and controlled by increasing magnetic field. （i） For a lower doping density, the system state transfers from stable state to oscillationary state. （ii） An opposite result is obtained to that in the case （i） for an intermediate value of the doping density, and the state changes from oscillationary to stationary. （iii） The state varies between oscillationary and stationary when doping density is large. Then, a detailed theoretical analysis is given to explain these surprise phenomena. The distribution of the electric-field domain along the SLs is plotted. We find the structure of the domain is almost uniform for a lower doping density, and no domain occurs in the SLs. By adding an external ac signal, complex nonlinear behaviors are observed from the Poincaré map and the corresponding phase diagrams when the driving frequency changes.     

Long time heat diffusion on homogeneous trees

Let be a homogeneous tree of degree , , the Laplace operator of and the fundamental solution of the heat equation on . We show that the heat kernel is asymptotically concentrated in an annulus moving to infinity with finite speed . Asymptotic concentration of heat in the norm is also investigated.

     

Higher multipole polarizabilities of hadrons from compton scattering amplitudes (II)

A procedure to derive closed form-sum rules for the hadron generalized electric and magnetic polarizabilities of any multipolar order is presented and discussed. The obtained results complete our previous analysis and may prove useful for a better understanding of the polarizability properties of a spin 0 or $\text{1}\text{2}$ hadron in as far as these show themselves in low energy elastic photon-hadron interactions.     

Optimal sum-rule inequalities for spin-12 compton scattering

A formalism appropriate for model-independent dispersion theoretical investigations of the (not necessarily forward) Compton scattering off $\text{spin}\text{-}\text{1}\text{2}$ hadronic targets, which fully exploits the analyticity properties of the amplitudes (to lowest order in electromagnetism) in ν² at fixed t ($\text{ν =}\text{1}\text{4}\text{(s ? u); s, t}$, u = Mandelstam variables), is developed. It relies on methods which are specific to boundary-value problems for analytic matrix-valued functions. An analytic factorization of the positive definite hermitian matrix associated with the bilinear expression of the unpolarized differential cross section (u.d.c.s.) in terms of the Bardeen-Tung (B.T.) invariant amplitudes is explicitly obtained. For t in a specified portion of the physical region, six new amplitudes describing the process are thereby constructed which have the same good analyticity structure in ν² as the (crossing symmetrized) B.T. amplitudes, while their connection with the usual helicity amplitudes is given by a matrix which is unitary on the unitarity cut. A bound on a certain integral over the u.d.c.s. above the first inelastic threshold, established in terms of the target's charge and anomalous magnetic moment, improves a previous weaker result, being now optimal under the information accepted as known.