An elementary proof of the Hasse-Weil theorem for hyperelliptic curves

AbstractAn elementary proof is given of the Hasse-Weil theorem about the number of solutions of the hyperelliptic congruence y2 ≡ f(x) (mod p), where the polynomial f(x) has odd degree

Orbit sums and modular vector invariants

[No abstract available

THE ISSUE OF PREGNANCY AND DELIVERY WITH PRENATAL INFECTION OF THE FETUS, HEALTH STATUS OF BABIES ON THE FIRST YEARS OF LIFE

Pregnancy and delivery of 27 women with prenatal infection of the fetus, neonatal period of the babies with prenatal pneumonia, health status of up to 2 children were researched in retrospect. Women with inflammation of the genitals (78,6%) and extragenital pathology of the inflammatory genesis (36,3%) had prenatal infection of the fetus. In the early neonatal period every baby had cerebral ischemia, every third child had haemorrhages in different cerebral structures. All babies have been transferred to children's hospital for treatment where the rehabilitation was carried out during 1-2,5 months. Infantile cerebral paralysis, hydrocephaly, epilepsy, epileptoid attacks were detected in 8 babies on the first year of life (29,6%). 5 babies (18,5%) had atrophy of discs of optic nerves, retinal angiopathy. All babies with local pathology of the central nervous system were premature born on the 26-32 week. Majority has herniae of different localization (55,5%), congenital dysplasia of the hip joint (74%), 26 babies (96,2%) were on the books because of anaemiae, pneumoniae, bronchites, pyelonephrites, septicaemiae. Using the received data we can draw a conclusion: in order to reduce perinatal complications in the maternal organism, in the organism of newborn baby and baby on the first year of life it is necessary to sanify the birth canal, to do preclinical diagnostics and preventive therapy of the prematurely born, gestosis, fetoplacental insufficiency

Numerical study of the centre region acceleration for the RIC-30 cyclotron

The RIC-30 cyclotron was designed for acceleration of protons up to 30 MeV [1]. Since 1994 it has been used for production of radionuclides on internal target installed at a radius of 580 mm, where the beam energy equals 22 MeV. Final radius of acceleration is 655 mm. At present, in the long-time irradiation mode the beam current on target is 190...200 µA [2]. The main objective of the work is to attain a higher beam current due to optimizing configuring of components forming the central ion-optical system of the cyclotron.RIC-30 циклотрон був розроблений для прискорення протонів до 30 МеВ. З 1994 p. він використовувався для виробництва радіонуклідів на внутрішній мішені, встановленої на радіусі 580 мм, де енергія пучка дорівнювала 22 МеВ. Кінцевий радіус прискорення дорівнює 655 мм. В даний час при тривалому режимі опромінення струм пучка на мішені – 190...200 мкА. Основною метою роботи є одержання більш високого струму пучка внаслідок оптимізації конфігурації компонент, що формують центральну іон-оптичну систему циклотрона.RIC-30 циклотрон был разработан для ускорения протонов до 30 МэВ. С 1994 г. он использовался для производства радионуклидов на внутренней мишени, установленной на радиусе 580 мм, где энергия пучка равнялась 22 МэВ. Конечный радиус ускорения равен 655 мм. В настоящее время при длительном режиме облучения ток пучка на мишени – 190...200 мкА. Основной целью работы является получение более высокого тока пучка вследствие оптимизации конфигурации компонент, формирующих центральную ион-оптическую систему циклотрона

Screw dynamo in a time-dependent pipe flow

The kinematic dynamo problem is investigated for the flow of a conducting fluid in a cylindrical, periodic tube with conducting walls. The methods used are an eigenvalue analysis of the steady regime, and the three-dimensional solution of the time-dependent induction equation. The configuration and parameters considered here are close to those of a dynamo experiment planned in Perm, which will use a torus-shaped channel. We find growth of an initial magnetic field by more than 3 orders of magnitude. Marked field growth can be obtained if the braking time is less than 0.2 s and only one diverter is used in the channel. The structure of the seed field has a strong impact on the field amplification factor. The generation properties can be improved by adding ferromagnetic particles to the fluid in order to increase its relative permeability,but this will not be necessary for the success of the dynamo experiment. For higher magnetic Reynolds numbers, the nontrivial evolution of different magnetic modes limits the value of simple `optimistic' and `pessimistic' estimates.Comment: 10 pages, 12 figure

Large negative velocity gradients in Burgers turbulence

We consider 1D Burgers equation driven by large-scale white-in-time random force. The tails of the velocity gradients probability distribution function (PDF) are analyzed by saddle-point approximation in the path integral describing the velocity statistics. The structure of the saddle-point (instanton), that is velocity field configuration realizing the maximum of probability, is studied numerically in details. The numerical results allow us to find analytical solution for the long-time part of the instanton. Its careful analysis confirms the result of [Phys. Rev. Lett. 78 (8) 1452 (1997) [chao-dyn/9609005]] based on short-time estimations that the left tail of PDF has the form ln P(u_x) \propto -|u_x|^(3/2).Comment: 10 pages, RevTeX, 10 figure

Prediction of huge X-ray Faraday rotation at the Gd N_4,5 threshold

X-ray absorption spectra in a wide energy range around the 4d-4f excitation threshold of Gd were recorded by total electron yield from in-plane magnetized Gd metal films. Matching the experimental spectra to tabulated absorption data reveals unprecedented short light absorption lengths down to 3 nm. The associated real parts of the refractive index for circularly polarized light propagating parallel or antiparallel to the Gd magnetization, determined through the Kramers-Kronig transformation, correspond to a magneto-optical Faraday rotation of 0.7 degrees per atomic layer. This finding shall allow the study of magnetic structure and magnetization dynamics of lanthanide elements in nanosize systems and dilute alloys.Comment: 4 pages, 2 figures, final version resubmitted to Phys. Rev. B, Brief Reports. Minor change

The Accidental Terrorist: Okhrana Connections to the Extreme-Right and the Attempt to Assassinate Sergei Witte in 1907

This article represents a case study in the relationship between the tsarist secret police (commonly known as the Okhrana in the West and okhranka in Russia) and acts of political terror perpetrated by the extreme-right in late imperial Russia. This specific case concerns the tangled web of conspiracy, propaganda and controversy that surrounded the attempted assassination of former-Chairman of the Council of Ministers, Sergei Witte, in 1907

Magnetic Fields in the Milky Way

This chapter presents a review of observational studies to determine the magnetic field in the Milky Way, both in the disk and in the halo, focused on recent developments and on magnetic fields in the diffuse interstellar medium. I discuss some terminology which is confusingly or inconsistently used and try to summarize current status of our knowledge on magnetic field configurations and strengths in the Milky Way. Although many open questions still exist, more and more conclusions can be drawn on the large-scale and small-scale components of the Galactic magnetic field. The chapter is concluded with a brief outlook to observational projects in the near future.Comment: 22 pages, 5 figures, to appear in "Magnetic Fields in Diffuse Media", eds. E.M. de Gouveia Dal Pino and A. Lazaria