Розглянуто нейтральне диференційне рівняння з запізненням (p(t)(x(t) + h(t)x(t - eta))')' + q(t)f(x(t - sigma)) = 0, t >= t₀ (*), де p, h, q належать c([t₀, infinity), R), eta і sigma - невід'ємні дійсні числа та f : R -> R неперервно диференціюється так, що uf(u) > 0 для u не дорівнює 0. Поділяючи розв'язки (*) на чотири класи, автори одержали умови існування розв'язків у цих класах.

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.

Equilibrium vortex configuration in conventional type II superconductors containing short-range columnar defects is investigated theoretically. In the bulk superconductor near the upper critical field H_c2 a single defect causes a strong local deformation of the vortex lattice which has C₃ or C₆ point symmetry. The vortices can collapse onto attractive defect, while in the case of repulsion the regions free of vortices appear near a defect. Increasing the applied magnetic field results in an abrupt change of the configuration of vortices related to the formation of multiquantum vortices and giving rise to reentering transitions between configurations with C₃ or C₆ symmetry. In the case of a small concentration of defects these transitions manifest themselves as jumps of magnetization and discontinuities of the magnetic susceptibility. Columnar defects also essentially influence the magnetic properties of a mesoscopic superconducting disc. They help the penetration of vortices into the sample, thereby decreasing the sample magnetization and reducing its upper critical field. Even the presence of weak defects splits a giant vortex state (usually appearing in a clean disc in the vicinity of the transition to a normal state) into a number of vortices with smaller topological charges. In a disc with a sufficient number of strong enough defects vortices are always placed onto defects. The presence of defects lead to the appearance of additional magnetization jumps related to the redistribution of vortices

which are already present on the defects and not to the penetration of new vortices.

Діелектричну проникність epsilon та спектри ЕПР іонів Mn²⁺ досліджено в околі сегнетоелектричного фазового переходу в кристалах Li₂Ge₇O₁₅. Аналіз експериментальних даних дозволив оцінити критичні індекси діелектричної сприйнятливості gamma ~ 1,25, параметра порядку beta ~ 0,32 і кореляційної довжини nu ~ 0,63. Величини критичних індексів, обчислені у досить широкому інтервалі температур поблизу T_c, узгоджуються з теоретичними показниками моделі Ізінга для однокомпонентного неполярного параметра порядку.

The effect of heating and weak pulsed magnetic field on microplastic deformation of high-nitrogen steels is studied. The methods of optic metallography, X-ray analysis, microhardness measurement and internal friction were used. As a result of experimental investigations it is stated that in high-nitrogen Cr - Mn steel at heating (low-temperature range) structure transformations take place. It is shown that at heating from 20 to 300 °C the processes of interaction between nitrogen atoms and extended dislocations take place. Kinetics of processes is similar to kinetics of ageing, but with certain variations. The obtained strucrure is unstable and trends to recovery of the initial state during 10 - 100 h. The influence of TPMF has similar nature. Presumably this process is determined by the redistribution of nitrogen in solid solution-nitrogen phases-dislocation atmospheres system. The authors propose to apply heating up to 400 °C during 4 - 8 h in order to stabilize the dislocation structure.

A generic Hamiltonian, which incorporates the effect of the orbital contraction on the hopping amplitude between nearest sites, is studied both analytically at the weak coupling limit and numerically at the intermediate and strong coupling regimes for a finite atomic cluster. The effect of the orbital contraction due to hole localization at atomic sites is specified with two coupling parameters V and W (multiplicative and additive contraction terms). The singularity of the vertex part of the two-particle Green's function determines the critical temperature T_c and the relaxation rate GAMMA(T) of the order parameter at temperature above T_c. Unlike the case in conventional BCS superconductors, GAMMA has a non-zero imaginary part which may influence the fluctuation conductivity of the superconductor above T_c. We compute the ground state energy as a function of the particle number and magnetic flux through the cluster, and show the existence of the parity gap DELTA appearing at the range of system parameters consistent with the appearance of the Cooper instability. Numeric calculation of the Hubbard model (with U >> 0) at arbitrary occupation does not show any sign of superconductivity in a small cluster.

In an approach of low transparency of the barrier the tunneling of electrons through doubly degenerate local state has been considered with allowance for the Coulomb and electron-phonon interactions. It is shown that in the case of weak electron-phonon and strong electron-electron interactions the dependence of tunneling current on the applied voltage has a step-like character at low temperature. The threshold value of the current was measured for small applied bias. The bistable state of the tunneling current is possible in the region of large bias. In the case of strong electron-phonon and weak electron-electron interactions, the threshold of tunneling current can be bistable. This result is a direct consequence of the electron pairing in local states.

Досліджено розповсюдження нелінійних хвиль в ангармонійному середовищі вздовж системи зв'язаних плоскопаралельних оптичних хвилеводів. Запропоновано ефективний метод розв'язання даної задачі у випадку слабкого зв'язку між хвилеводами.

Исследовано распространение нелинейных волн в ангармонической среде вдоль системы связанных плоскопараллельных оптических волноводов. Предложен эффективный метод для решения этой задачи в пределе слабой связи волноводов.

The propagation of nonlinear waves in an anharmonic medium along an array of coupled parallel plane optical waveguides is considered. The effective method for solving this problem is proposed in the limit of weak waveguide coupling.

A theory is offered for the ballistic 4-terminal Josephson junction. The studied system consists of a mesoscopic two-dimensional normal rectangular layer which іs attached on each side to the bulk superconducting banks (terminals). A relation is obtained between the currents through the different terminals, that is valid for arbitrary temperatures and junction sizes. The nonlocal coupling of the supercurrents leads to a new effect, specific for the mesoscopic weak link between two superconducting rings; an applied magnetic flux through one of the rings produces a magnetic flux in the other ring even in the absence of an external flux through the other one. The phase dependent distributions of the local density of Andreev states, of the supercurrents and of the induced order parameter are obtained. The "interference pattern" for the anomalous average inside the two-dimensional region can be regulated by the applied magnetic fluxes or the transport currents. For some values of the phase differences between the terminals, the current vortex state and the two-dimensional phase slip center appear.

The absorption and resonance Raman spectra of yttrium dimers (Y₂) in argon matrices have been measured for the first time. The absorption spectrum (scattering deplation spectrum SDS) shows a weak, broad transition centered near 485 nm. Resonance Raman spectra obtained by exciting into this absorption band with several visible laser lines (465,5 - 496,5 nm) give a single, sharp progression with up to ten Stokes transitions. These data give omega_e = 184,4(4) cm^-1, with omega_e x_e = 0,30(3) cm^-1, leading to a spectroscopic dissociation energy of D_e = 3,5(4) eV. Comparison of our results with several ab initio calculations adds confirmation to the assignment of the ground state of Y₂ to be ¹SIGMA_g⁺ state.

The Aharonov - Bohm (AB) oscillations of the free energy, critical temperature T_c, magnetization M, and magnetic susceptibility chi as functions of the magnetic flux PHI through the hollow in a stack of mesoscopic superconducting cylinders are studied both analytically and numerically. The shape of these oscillations at low temperature T and small level broadening nu is generally nonsinusoidal and has singularities that depend on the superconducting order parameter DELTA and stacking sequence. The period of the oscillations is equal to the normal flux quantum PHI₀. The harmonic amplitudes of the AB oscillations decrease exponentially if the diameter 2R of the cylinders becomes greater than the coherence length. Further increase of R results in a complete depression of the AB oscillations and the development of the parabolic Little - Parks (LP) oscillations of T_c(PHI), with half the period, PHI_s = PHI₀/2. Therefore a crossover from the AB to LP oscillations takes place as the diameter 2R is increased. It is shown that the temperature behavior of the magnetic susceptibility below the superconducting transition is chi propto exp(-T/T*), where T* = Planck's constant upsilon₀ / 2 pi²R. Such dependence of chi (T) has been observed recently in Ag wires coated with thin Nb layers in a weak external field (upsilon₀ is the Fermi velocity).

Persistent scaling behavior of magnetization in layered high <$E T sub c > superconductors with short-range columnar defects is explained within the Ginzburg-Landau theory. In the weak field region, the scaling function differs from that of a clean sample and the critical temperature is renormalized due to defects. In the strong field region, defects are effectively suppressed and the scaling function, as well as the critical temperature are the same as in a clean superconductor. This picture is consistent with recent experimental results.

On the basis of the functional approach, the conditions of correctness are stated for locally formulated boundary-value problems of the nonlinear theory of isotropic elastic bodies in the three-dimensional statement. We use the known unique existence theorems for the minimum of a functional being lower semicontinuous in the weak topology of a reflexive Banach space.

The photoinduced domino effect for the phase transition dynamics in one-dimensional electron-lattice systems is investigated to clarify the dependence on the friction and interaction between neighboring sites. We find a novel photoinduced domino process in the case of strong intersite interaction and weak friction. In this domino motion, the photoexcited site is still in an excited electronic state, which is in striking contrast to the conventional domino. This mechanism explains the photoinduced phase transitions in systems which have a large-size nucleus of the developing new phase.

Рассмотрены линейные и полулинейные параболические уравнения второго порядка, объединяющие нелокальное условие с условием Ньюмена. Для каждой задачи установлено существование и единственность слабого решения. Такие задачи встречаются в области теплопроводности, химии, биохимии, термоупругости, динамики популяций и других диффузионных процессов.

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.

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.

Досліджено статичну та динамічну діелектричну сприйнятливість псевдоспін-електронної моделі в наближенні хаотичних фаз. У режимі <$E mu~=~roman const> виявлено можливість фазового переходу до однорідної фази, фази з подвійною модуляцією періоду гратки та несумірної фази залежно від значення хімічного потенціалу. Виявлено можливість фазового розшарування на однорідну фазу та фазу з подвоєнням граткового періоду та побудовано фазову діаграму (n, h). Досліджено вплив тунельного розщеплення на фазові переходи. Встановлено присутність у системі псевдоспін-хвильових збуджень, неперервного спектра збуджень і можливість їх взаємоперекриття.

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].

For the first time we present the direct evidence for superconductivity in the ternary magnetic compound <$E roman {YFe sub 4 Al sub 8}> with the <$E roman ThMn sub 12> type structure found via point-contact experiments on contacts between silver needle and single-crystal <$E roman {YFe sub 4 Al sub 8}>, revealing the distinct Andreev-reflection current. The spectra measured prove the existence of normal-superconducting interface and exhibit the triangular-like shape in a vicinity of zero-bias voltage, inferring the unconventional type of superconductivity. The derived dependences of the order parameter versus temperature <$E DELTA (T)> and magnetic field <$E DELTA (H)> are presented. <$E DELTA (T)> follows BCS theory, whereas <$E DELTA (H)> do not satisfy any theoretical predictions. In some cases there exists noticeable superconductivity enhancement by a weak magnetic field. The data obtained imply the very inhomogeneous distribution of superconductivity over the sample volume in spite of its single crystal structure. We assume that the reason is associated with inherent magnetic inhomogeneities of this material. The highest values for the critical temperature <$E T sub c>, upper critical magnetic field <$E H sub c2>, and ratio <$E 2 DELTA (0) "/" kT sub c> are 7,4 K, 5 T, and 7,2, respectively.