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.     

Ważewski's Principle for retarded functional differential equations

Wa?ewski Principle is an important tool in the study of the asymptotic behavior of solutions of ordinary differential equations. A direct extension of this principle to retarded functional differential equations (RFDEs) can be obtained by noticing that solutions of RFDEs generate processes on C = C([?r, 0], Rⁿ) and by using the general version of Wa?ewski Principle for flows on topological spaces. The resulting method is of little use in applications, due to the infinite-dimensionality of the space C. This paper presents a “Razumikhin-type” extension of Wa?ewski's Principle, which is widely applicable to concrete examples. The main results are Corollaries 3.1 and 3.2. Also, an extension of the method to RFDEs with a merely continuous right-hand side is given, and a few examples illustrate the use of the method. Throughout the paper, a standard notation is used.     

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.     

Thermodynamic properties of liquid silver-antimony alloys determined from emf measurements

The thermodynamic properties of the liquid Ag-Sb alloys were determined using solid oxide galvanic cells with zirconia electrolyte. The emfs of the cells:

     

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.     

Patterns of lepton-flavour violation motivated by decoupling and sneutrino inflation

We present predictions for flavour-violating charged-lepton decays induced by the seesaw mechanism implemented within the constrained minimal supersymmetric standard model (CMSSM) with universal input soft supersymmetry breaking terms. We assume that one heavy singlet neutrino almost decouples from the seesaw mechanism, as suggested by the pattern of light neutrino masses and mixing angles. This is suggested independently by sneutrino inflation with a low reheating temperature, T_RH10⁷ GeV, so as to avoid overproducing gravitinos. This requirement further fixes the mass of the weakly-coupled sneutrino, whose decays may lead to leptogenesis. We find that BR(μ→eγ)10⁻¹³ but BR(τ→μγ)10⁻⁹ in the bulk of the acceptable parameter space, apart from a few isolated points. The ratio BR(μ→eγ)/BR(τ→eγ) depends on only one complex parameter, and is particularly interesting to compare with experiment.     

INVESTIGATION OF THE ATRP OF n-BUTYL METHACRYLATE USING THE Cu(I)/N,N,N'''',N",N"-PENTAMETHYLDIETHYLENETRIAMINE CATALYST SYSTEM

INTRODUCTIONThe atom transfer radical polymerization (ATRP) has become an important method for preparing well-definedmacromolecules. This technique offers control over the molecular weights, the chain end functionalities, and thechain architectures[1-12]. It has been used extensively for the preparation of homopolymers, block, and randomcopolymers[13-39], for the preparation of organic/inorganic hybrid materials[40-54], as well as for combining variousother living polymerization methods …