Доведено, що зворотна теорема Д'єдоне розповсюджується на замикання різниці двох опуклих множин, тобто достатні умови теореми Д'єдоне для слабкої топології в рефлексивному банаховому твердженні є також і необхідними.

Conditions of <$E GAMMA>-continuity (<$E GAMMA>-discontinuity) of the superposition operator <$E bold roman f> in the space <$E l sub inf> of bounded sequences are investigated. These conditions depend on a set <$E GAMMA> or a function f(n, u) determining the operator <$E bold roman f>. The general form of a weak continuous superposition operator <$E bold roman f> in the space <$E l sub inf> is found. In particular the affiness of a weak continuous superposition operator <$E bold roman f> generated by a function of one variable is proved.

We investigate nonlocal coherent transport in ballistic four-terminal Josephson structures (in which bulk superconductors (terminals) are connected through a clean normal layer, e.g., a two-dimensional electron gas). Coherent anisotropic superposition of macroscopic wave functions of the superconductors in the normal region produces phase slip lines (2D analogs to phase slip centers) and time-reversal symmetry breaking 2D vortex states in it, as well as such effects as phase dragging and magnetic flux transfer. The tunneling density of local Andreev states in the normal layer is shown to contain peaks at the positions controlled by the phase differences between the terminals. We have obtain the general dependence of these effects on the controlling supercurrent/phase differences between the terminals of the ballistic mesoscopic four-terminal SQUID.

Вимірювання питомої електропровідності у разі постійного та змінного струму і термічно вимушеного струму деполяризації (ТВДС) було виконано для кристалу Nd, легованого <$Eroman KGd(WO sub 4 ) sub 2> в інтервалі <$E250~ symbol Ш ~400~ roman K>. Малий максимум, подібний аномалії ТВДС, спектру за 330 К характеризується енергією активації 1,68 еВ. Реверсивний характер малої аномалії температурної залежності діелектричної сталої <$Eepsilon ~(T)> за 330 К показує, що відбувається слабке структурне перетворення в кристалі.

Measurements of the electric conductivity at direct and alternating current and the thermally stimulated depolarization current (TSDC) have been carried out for Nd doped KGd(WO4)2 crystal in the range of 250 ( 400 K. Small maximum-like anomaly of TSDCspectrum at 330 K characterizing by the activation energy 1,68 eV can be associated with the structural defects associated with doped Nd3+ ions. Reversible character of the small anomaly on the temperature dependence of dielectric permittivity ( (T) at 330 K shows also that the weak structure transformation takes place in the crystal

Розглянуто систему рівнянь Нав'є - Стокса - Власова - Пуасона, що описує течію в'язкої нестислової рідини з дрібними твердими зарядженими частками. Доведено існування слабких глобальних розв'язків початково-крайової задачі для цієї системи.

Розглянуто початково-крайову задачу для системи зв'язаних рівнянь Нав'є - Стокса/Фоккера - Планка/Пуассона, яка описує течію в'язкої нестисливої рідини з високодисперсною домішкою твердих заряджених частинок, що піддаються випадковим впливам, які обумовлені тепловим рухом молекул рідини. Доведено існування слабких глобальних розв'язків цієї задачі та вивчено їх властивості.

In the paper, we investigate realizations of a p-dimensional regular weak stationary discrete time stochastic process y(t) as the output data of a passive linear bi-stable discrete time dynamical system. The state x(t) is assumed to tend to zero as t tends to <$E - inf>, and the input data is the m-dimensional white noise. The results are based on author's development of the Darlington method for passive impedance systems with losses of the scattering channels. Here we establish that considering realization for a discrete time process is possible, if the spectral density <$E rho (e sup {i mu})> of the process is a nontangential boundary value of a matrix valued meromorphic function <$E rho (z)> of rank m with bounded Nevanlinna characteristic in the open unit disk. A parameterization of all such realizations is given and minimal, optimal minimal, and <^>*-optimal minimal realizations are obtained. The last two coincide with those which are obtained by Kalman filters. This is a further development of the Lindquist - Picci realization theory.

Роглянуто задачу неопуклого математичного програмування на топологічному просторі в разі обмежень виду нерівностей. Розширену функцію Лагранжа побудовано з використанням слабких субдиференціалів. Показано, що екстремальні значення прямої та подвійної задач є рівними в разі виконання умов стійкості.

The heat capacity of the interstitial solid solution (CH4)0,4C60 has been investigated in the temperature interval 1,4 - 120 K. The contribution of CH4 molecules to the heat capacity of the solution has been separated. The contributions of CH4 and CD4 molecules to the heat capacity of the solutions (CH4)0,40C60 and (CD4)0,40C60 have been compared. It is found that above 90 K the character of the rotational motion of CH4 and CD4 molecules changes from libration to hindered rotation. In the interval 14 - 35 K the heat capacities of CH4 and CD4 molecules are satisfactorily described by contributions of the translational and libration vibrations, as well as the tunnel rotation for the equilibrium distribution of the nuclear spin species. The isotope effect is due to mainly, the difference in the frequencies of local translational and libration vibrations of molecules CH4 and CD4. The contribution of the tunnel rotation of the CH4 and CD4 molecules to the heat capacity is dominant below 8 K. The isotopic effect is caused by the difference between both the conversion rates and the rotational spectra of the nuclear spin species of CH4 and CD4 molecules. The conversion rate of CH4 molecules is several times lower than that of CD4 ones. Weak features observed in the curves of temperature dependencies of the heat capacity of CH4 and CD4 molecules near 6 and 8 K, respectively, are most likely a manifestation of first-order polyamorphic phase transitions in the orientational glasses of these solutions.

The negative-U impurity stripes confining the edge channels of semiconductor quantum wells are shown to allow the effective cooling inside in the process of the spin-dependent transport, with the reduction of the electron-electron interaction. The aforesaid promotes also the creation of composite bosons and fermions by the capture of single magnetic flux quanta on the edge channels under the conditions of low sheet density of carriers, thus opening new opportunities for the registration of the quantum kinetic phenomena in weak magnetic fields at high-temperatures up to the room temperature. As a certain version noted above we present the first findings of the high temperature de Haas-van Alphen, 300 K, quantum Hall, 77 K, effects as well as quantum conductance staircase in the silicon sandwich structure that represents the ultra-narrow, 2 nm, p-type quantum well (Si-QW) confined by the delta barriers heavily doped with boron on the n-type Si (100) surface.

Resistive measurements were made to study the magnetic field-induced antiferromagnetic (AF) - weak ferromagnetic (WF) transition in the La2CuO4 single crystal. The magnetic field (dc or pulsed) was applied normally to the CuO2 layers. The transition manifested itself in a drastic decrease of the resistance in critical fields of 5 - 7 T. The study is the first to display the effect of the AF - WF transition on the conductivity of the La2CuO4 single crystal in the direction parallel to the CuO2 layers. The results provide support for the three-dimensional nature of the hopping conduction of this layered oxide.

Conventional Josephson metal - insulator - metal devices are inherently underdamped and exhibit hysteretic current-voltage response due to a very high subgap resistance compared to that in the normal state. At the same time, overdamped junctions with single-valued characteristics are needed for most superconducting digital applications. The usual way to overcome the hysteretic behavior is to place an external low-resistance normal-metal shunt in parallel with each junction. Unfortunately, such solution results in a considerable complication of the circuitry design and introduces parasitic inductance through the junction. This paper provides a concise overview of some generic approaches that have been proposed in order to realize internal shunting in Josephson heterostructures with a barrier that itself contains the desired resistive component. The main attention is paid to self-shunted devices with local weak-link transmission probabilities that are so strongly disordered in the inter-face plane that transmission probabilities are tiny for the main part of the transition region between two super-conducting electrodes, while a small part of the interface is well transparent. We discuss the possibility of realizing a universal bimodal distribution function and emphasize advantages of such junctions that can be considered as a new class of self-shunted Josephson devices promising for practical applications in superconducting electronics operating at 4,2 K.

The limitation of critical current in high T_c superconducting YBCO thin films has a varied nature according to the quality of YBCO films. Our results showed that in strips from granular films the weak links of superconductor-normal metal-superconductor and superconductor-constriction-superconductor types were responsible for critical current limitation. In the YBCO strips with improved (preferential) crystallographic orientation a flux-creep critical current limitation was found and in the highly oriented YBCO strips the Ginzburg-Landau depairing mechanism approximated the critical current limitation for temperature close to T_c.

The charge carrier overheating effect was studied in the p-type Si0,4Ge0,6/Ge/Si0,4Ge0,6 heterostructure with two subband occupy. The temperature dependences of hole-phonon relaxation time <$E tau sub {h- roman ph}> at weak magnetic fields demonstrated transition of the 2D system from regime of "partial inelasticity" characterized by dependence <$E tau sub {h- roman ph} sup -1~symbol Х~T sup 2> to regime of small-angle scattering, described by dependence <$E tau sub {h- roman ph} sup -1~symbol Х~T sup 5> with temperature increase. But in higher magnetic fields the dependence <$E tau sub {h- roman ph} sup -1~symbol Х~T sup 3> manifests itself on dependences <$E tau sub {h- roman ph} (T sub {h- roman ph})>. The possible explanations of such dependences are discussed.

In this work we introduce a notion of local weakly separability of a topological space, which gives rise to the concepts of separability, local separability and weak separability. It is shown that the notions of local weak separability and local separability coincide when the considered space is a locally compact (in particular, compact Hausdorff), metrizable and linearly ordered space.

For a compact Hausdorff (locally compact Hausdorff, metric, linear ordered) space <$E X> it is shown that <$E wd(X)~=~d(X)>. Some examples of spaces are given, such that <$E wd(X)~symbol Щ~d(X)>.

We review the recent activity in the theoretical description of spin-polarized atomic hydrogen and its isotopes at very low temperatures. Spin-polarized hydrogen is the only system in nature that remains stable in the gas phase even in the zero temperature limit due to its small mass and weak interatomic interaction. Hydrogen and its heavier isotope tritium are bosons, the heavier mass of tritium producing a self-bound (liquid) system at zero temperature. The other isotope, deuterium, is a fermion with nuclear spin one making possible the study of three different quantum systems depending on the population of the three degenerate spin states. From the theoretical point of view, spin-polarized hydrogen is specially appealing because its interatomic potential is very accurately known making possible its precise quantum many-body study. The experimental study of atomic hydrogen has been very difficult due to its high recombination rate, but it finally led to its Bose - Einstein condensate state in 1998. Degeneracy has also been observed in thin films of hydrogen adsorbed on the 4He surface allowing for thepossibility of observing the Berezinskii - Kosterlitz - Thouless superfluid transition.

We show how some notions and results of measurable dynamics can be applied to the theory of Cantor minimal systems. Motivated by measurable dynamics, we study the weak and uniform topologies on full groups and their normalizers. The article develops the approach and ideas of [BK].

The self-consistent band structure calculation of PbSnS3 and PbGeS3 ternary compounds with the mixed cation coordination was performed using the ab initio density functional theory method. It has been found that both compounds are indirect-gap semiconductors. The calculated band-gap widths are Egi = 0,75 eV for PbSnS3 and Egi = 1,96 eV for PbGeS3. It was performed the analysis of partial contributions to the total density of electronic states, which allowed to identify the genetic nature of valence and conduction bands. The feature of the structure of occupied energy bands in these compounds is the presence of isolated quasi-core d-band of lead atoms and the contribution of Pb6s-states of lone-electron pair to the top of valence band as well as to the second occupied subband. The electron density maps in the different planes have been analyzed. They clearly demonstrate presence of covalent-ionic bond character within the infinite chains and ribbons with prevailing charge concentration on Ge-S, Sn-S, Pb-S bonds, and a weak van der Waals bond component with participation of lone-electron pair of lead between layers as well as ribbons.

Relevant is the research of features of market relations formation and development in labour sphere in post-Soviet countries that chose the same Euro-integration path of development with Ukraine. Author provided trend analysis of the competitiveness index and sub-indices in selected countries. By identifying main problems and bottlenecks in the functioning of the selected countries' labour market, we have established common and unique characteristics and, consequently, possible ways to mitigate the significant social risks. Most acute among them are problem of inefficient employment, large-scale prevalence of informal employment, and inadequate system of labour compensation. Comparative analysis shows that for neighbouring countries that are not EU members (Ukraine and Moldova), a characteristic phenomenon is a significant and unjustified differentiation of wages and the incidence of illegal practices in the workplace. In addition to purely economic factors and the almost complete absence of the use of fiscal instruments, which could stimulate the use of the labour services in the economy's formal sector, the weak control function of the respective bodies in these countries should be highlighted. Particularly acute problem of use of informal payments appears to be for Ukraine, which complicates the problem of social and labour sphere. The author used the following methods: statistical, analogy, comparison. Proposed are the measures for the approximation of the minimal wage up to the European standards, reduction of informal employment, and improvement of the social protection system of the unemployed. It is proved that the regulation of the minimum wage, as the most essential regulator of the labour market, has both positive and negative characteristics and consequences for the social and labour sphere. For the comparative analysis of regulatory impacts of the minimum wage Moldova and Ukraine were chosen. Author has studied the peculiarities of structural changes of employment in the neighbouring countries. This allowed validating the change in the sectoral ratios of employment in Ukraine, which is caused not only by economic factors, but also by the integration and disintegration processes, and it explains the phenomenon of deindustrialization and deagrarization of labour in Ukraine.