On Two Conjectures of Steinhaus

We disprove two conjectures of H. Steinhaus by showing that: (1) there is a convex surface S such that for any point x on S and any point y in the set F _x of farthest points from x, there are at most two segments from x to y; (2) the properties and do not characterize the sphere.     

On the Sunouchi Operator with Respect to the Walsh-Kaczmarz System

Define the operator of Sunouchi (f L ¹) on the Walsh group with respect to the Walsh-Kaczmarz system. In this paper we prove that the operator T is of weak type (1, 1), of type (H ¹, L ¹) and of type (p, p) for all 1 < p 2.     

Phenomenological evidence for gluon depletion in pA collisions

The data of J/psi suppression at large x(F) in pA collisions are used to infer the existence of gluon depletion as the projectile proton traverses the nucleus. The modification of the gluon distribution is studied by use of a convolution equation whose nonperturbative splitting function is determined phenomenologically. The depletion factor at x(1) = 0.8 is found to be about 25% at A = 100.     

From classical mobility to hopping conductivity: charge hopping in an ultracold gas

Studies of charge mobilities in an ultracold gas are reported. Calculations for the Na + Na+ system have been carried out as a function of temperature T and densities, and the conductivity of the ultracold charged gas is obtained. The total charge mobility exhibits a sharp increase as T is lowered, indicating a transition from an almost insulating to a conducting system at few microK. It is shown that the nature of the charge mobility changes with temperature: at high T, the charges are transported by massive centers (i.e., the ions), and at low T, by electrons jumping from neighboring atoms onto the positive ions (the positive holes exhibit hopping conductivity). An experiment is proposed to detect this effect.     

Fresnel diffraction on the edge of causality

Taking advantage of the slow optical response of low-temperature rare earth ion-doped crystal, we explore the similarity between causality and Fresnel diffraction by a straight edge. We relate these features to spectral resolution and selectivity. The concept is illustrated with experimental data.     

Studies on the polymer + plasticizer membrane-electrode-VIII Use of the PVC + tricresyl phosphate membrane as indicating electrode in potentiometric precipitation titration

Results obtained by use of the PVC + tricresyl phosphate membrane-electrode in potentiometric precipitation titration of some halides and pseudohalides are given. Solutions of Ag(+), Tl(+) and Hg(2)(2+) were used as titrants, to which the membrane is responsive. The fast response to Ag(+) ions allowed the determination of iodide by automatic recording of the potentiometric curve (or its derivative).     

Hyperfine fields on59Co in ReCo2

We report⁵⁷Fe Mössbauer measurements in the diluted antiferromagnetic (AF) Fe_xZn_1?xF₂ withx=0.25 at temperatures between 4.2 and 28 K. DC susceptibility measurements show a spin-glass (SG) phase at low temperatures forx?0.3. Our Mössbauer spectra show a competitive coexistence of an SG phase and AF order. We propose an interpretation in terms of clusters in the AF order and some spins exhibiting SG behavior.     

A lower estimate for the achromatic number of irreducible graphs

The achromatic number of a graph is the largest number of independent sets its vertex set can be split into in such a way that the union of any two of these sets is not independent. A graph is irreducible if no two vertices have the same neighborhood. The achromatic number of an irreducible graph with n vertices is shown to be $\text{≥(}\text{1}\text{2}\text{?0(1))log}\text{n?}\text{log log}\text{n,}$ while an example of Erdös shows that it need not be log n/log 2+2 for any n. The proof uses an indiscernibility argument.     

Multiple spin-echoes in a photo-excited triplet state

A Carr-Purcell multiple spin-echo, as modified by Meiboom and Gill, is described for the 3598 MHz zero-field transition of phosphorescent quinoline C₉ND₇ in a durene host. The results show that the dephasing of the electron spins through spectral diffusion may be largely eliminated by the multiple echo technique.     

Soil analysis by thin-film energy-dispersive x-ray fluorescence

Energy-dispersive x-ray fluorescence is advantageous for trace analysis of soils present as thin films. A target thickness of about 2 mg cm^-2 provides a compromise between optimal sensitivity and minimal absorption effect or optimal accuracy. Sample preparation involves only suspending the finely ground soil in water and drying this suspension on a thin mylar foil glued on a ring that fits into the x.r.f. spectrometer. The “effective sample weight” present in the exciting beam area is computed from the scatter peaks, a method that cancels out target heterogeneity problems. High accuracy is demonstrated for many elements in reference soil and rock materials; a precision around 5% and a detection limit around 10 ppm can be achieved. As an illustration, results for 16 trace elements and preliminary interpretation are given for a series of pedologically important soil samples from Brasil.