On sums of Darboux and nowhere constant continuous functions

We show that the property

(P)

for every Darboux function there exists a continuous nowhere constant function such that is Darboux

follows from the following two propositions:

(A)

for every subset of of cardinality there exists a uniformly continuous function such that ,

(B)

for an arbitrary function whose image contains a non-trivial interval there exists an of cardinality such that the restriction of to is uniformly continuous,

which hold in the iterated perfect set model.

     

Helium-antihydrogen interaction: the Born-Oppenheimer potential energy curve

The interaction of atomic antihydrogen with helium has been studied within the Born-Oppenheimer approximation. The linear combination of explicitly correlated Gaussian functions was used as the ansatz for the wave function of light particles. The potential energy curve with the minimum at 3.63 bohr and the barrier at 2.42 bohr has been obtained.     

Efficient generation of flexible-monomer intermolecular potential energy surfaces

A new method of generating flexible-monomer intermolecular interaction potentials has been proposed. The method, based on symmetry-adapted perturbation theory, extends a rigid-monomer potential into a flexible-monomer one at a cost negligible compared to performing calculations on a full-dimensional grid (i.e., including internal degrees of freedom of monomers). The non-rigidity effects are accounted for by density-overlap integrals and by asymptotic expansion coefficients. Results for a model system (Ar-HF) demonstrate that the method recovers a substantial portion of these effects.     

On the number of solutions of an algebraic equation on the curve , and a consequence for o-minimal structures

We prove that every polynomial of degree has at most zeros on the curve . As a consequence we deduce that the existence of a uniform bound for the number of zeros of polynomials of a fixed degree on an analytic curve does not imply that this curve belongs to an o-minimal structure.

     

Identification of a Single Phosphorylation Site Within Octopus Rhodopsin

Abstract— Light-dependent phosphorylation of rhodopsin (Rho) is a first step in the desensitization of the signaling state of the receptor during vertebrate and invertebrate visual transduction. We found that only ³⁵⁸Ser of the photoac-tivated octopus Rho (oRho*) was phosphorylated by octopus rhodopsin kinase (oRK). Tryptic truncation of the C-terminal PPQGY repeats of oRho that follow the phosphorylation region did not influence spectral or G-protein activation properties of oRho but abolished phos phorylation. Despite significant structural differences between oRK and mammalian RK, these results provide i further evidence of the importance of singly phosphorylated species of Rho* in the generation of arrestin binding sites.     

On the degree of cocycles with values in the group<Emphasis Type="Italic">SU</Emphasis>(2)

In this paper are presented some properties of smooth cocycles over irrational rotations on the circle with values in the groupSU(2). It is proved that the degree of anyC ²-cocycle (the notion of degree was introduced in [2]) belongs to 2πℕ (ℕ={0, 1, 2,...}). It is also shown that if the rotation satisfies a Diophantine condition, then everyC ^∞-cocycle with nonzero degree isC ^∞-cohomologous to a cocycle of the form

Radon in well waters in the Kraków area

The method and the results of radon concentration measurements in water samples are presented. Since May 2000, measurements of radon concentration in well waters in the Kraków area have been carried out--both in urban wells (depth above 50 meters) and in other private wells (depth of several meters). The ionisation chamber AlphaGUARD PQ 2000PRO along with the additional special equipment AquaKIT were used for determination of radon concentration in water samples. A total of 45 wells were examined for radon concentration in water--19 urban wells, 21 private ones (from Nowa Huta, Ojcowska, Wola Justowska area--parts of Kraków) and 5 mineral water sources. Wola Justowska is a region where tectonics faults occur and radon can easily migrate from deep basement structure. All the obtained values of radon concentration are below 12 Bq/l. These preliminary results do not show a direct correlation between geological structure and radon concentration in water samples. However, further investigation is needed and is planned to be undertaken.     

Nonrelativistic QED approach to the bound-electron g factor

Within a systematic approach based on nonrelativistic quantum electrodynamics, we derive the one-loop self-energy correction of order alpha(Z alpha)(4) to the bound-electron g factor. In combination with numerical data, this analytic result improves theoretical predictions for the self-energy correction for carbon and oxygen by an order of magnitude. Basing on one-loop calculations, we obtain the logarithmic two-loop contribution of order alpha(2)(Z alpha)(4)ln([(Z alpha)(-2)] and the dominant part of the corresponding constant term. The results obtained improve the accuracy of the theoretical predictions for the 1S bound-electron g factor and influence the value of the electron mass determined from g-factor measurements.     

Three-dimensional reconstruction of biological objects' internal structure heterogeneity from the set of ultrasonic tomograms

The paper presents the method of the three-dimensional reconstruction of biological objects' internal structure heterogeneity based on the ultrasonic examination of a woman's breast biopsy phantom. The phantom is made of quasi-homogeneous dense gel in which drops of lesions, characterized by fixed sizes and two different acoustic impedances, were dipped at random. For the purpose of this research a special measurement setup was elaborated, enabling a non-invasive in vitro imaging of biological objects' internal structure in cross-sections for fixed levels, by means of ultrasound transmission tomography (UTT) using the parallel-ray projection geometry of scanning. The two-dimensional images of the local values of ultrasonic wave's propagation velocity in the phantom's internal structure (ultrasonic tomograms) were reconstructed for fixed levels (by using the convolution and back-projection algorithm) from the measurements of average values of ultrasonic signals' runtime propagated from many directions around the object dipped in water. Analyzing the values of particular pixels and using an appropriate image processing technique, in effect the three-dimensional image of heterogeneity boundaries in the examined phantom's internal structure was computer-reconstructed. The obtained results are compatible with the specification provided by the phantom's producer in terms of sizes and acoustic parameters of lesions, which can simulate pathological changes and of the gel imitating the healthy tissue. It means that the method presented, after an appropriate modification and development of the measurement setup with an aim to accelerate the object scanning process and thus provide an opportunity for non-invasive in vivo examinations, could be applied for detecting and diagnosing tumors in women's breasts.