On two comparison tests for linear second-order ordinary differential equations

We prove two comparison tests for second-order linear differential equations. The well-known Sturm comparison theorem is a straightforward corollary of the first of them. The second (integral) test permits one to use specific integral relations between the coefficients of two equations to prove the oscillation of one of the equations assuming the oscillation of the other.     

Derivatives of α,β-dehydro amino acids: VI. Reaction of 4-benzylidene-2-phenyl-1,3-oxazol-5(4H)-one with piperidin-2-ylmethanamine

4-Benzylidene-2-phenyl-1,3-oxazol-5(4H)-one reacts with piperidin-2-ylmethanamine to give N-{(Z)-3-oxo-3-[(piperidin-2-ylmethyl)amino]-1-phenylprop-1-en-2-yl}benzamide, N-(4-benzyl-3-oxooctahydro-2N-pyrido[1,2-a]pyrazin-4-yl)benzamide, or/and (Z)-4-benzylidenehexahydro-2H-pyrido[1,2-a]pyrazin-3(2H)-one, depending on the solvent, temperature, and reaction time. The latter product is formed via three-step tandem process.     

Influence of self-phase modulation on coherent effects in five-level system

The possibility of formation of a coherent dark state in the five-level system in the entire volume of the medium in an adiabatic pulse propagation is investigated. It is shown that the dark state formation is independent on the value of the first two-photon detuning from the resonance, which may be changed during the propagation in the medium. In the case of the M-type system with the equal strengths of oscillators at the extreme transitions it is shown that the self-phase modulation does not influence the coherent effects while in the ladder-type system it may lead to the destruction of the dark state. The estimation of the length of the medium in which the propagation effects are negligible is obtained.     

The <Emphasis Type="Italic">A</Emphasis> dependence of <Emphasis Type="Italic">K</Emphasis><Superscript>0</Superscript> and Λ Neutrinoproduction on nuclei

The A dependence of the production of K ⁰ and Λ is investigated for the first time in neutrino-nuclear reactions using the data obtained with the SKAT bubble chamber. An exponential parametrization (∼A ^β) of the particle yields results in = 0.20 ± 0.05 for V ⁰ particles (K ⁰ and Λ), while for π ⁻ mesons the A dependence is much weaker ( = 0.068 ± 0.007). A nuclear enhancement of the ratio K ⁰/π ⁻ is found; this ratio increases from 0.055 ± 0.013 for vN interactions up to 0.070 ± 0.011 at A ≈ 21 and 0.099 ± 0.011 at A ≈ 45. It is observed that the multiplicity rise of V ⁰ occurs predominantly in the backward hemisphere of the hadronic system. It is shown that the A dependence of the Λ⁰ and π ⁻ yields can be reproduced in the framework of a model incorporating the secondary intranuclear interactions of pions originating from the primary vN interactions. The text was submitted by the authors in English.     

Dielectric properties of perovskite ferroelectrics at the nonequilibrium concentrations of point defects

Dielectric properties of ceramic barium titanate modified by the addition of aluminum oxide are studied via impedance spectroscopy in weak electric fields in frequency range of 0.3–10³ kHz. For better separation of the properties of the inner regions of crystallites and the boundary regions by quenching, an excess concentration of point defects is created, leading to the formation of bulk charge. The experimental results are performed using the Maxwell-Wagner capacitor model and the Schottky barrier model.     

Influence of the external noise intensity on the kinetics of ligands binding to receptors

The average, variance, correlation function and the spectral density of ligand–receptor complexes in the presence of the external Langevin noise are calculated and their characteristics are defined. The analysis of the experimental data using the formulas derived in this work enables one to obtain a new information on the process of forming of ligand–receptor complex, namely, the constants rates of formation and the decay of the ligand–receptor complex.     

Mathematical modelling of the development of mechanical instability in fracturing systems

The dynamics of processes accompanying a loss of stability in a mechanical system are investigated. The mechanical system is in the form of an elastic rod, stretched by an axial load, with one of its lateral surfaces “glued” to a rigid wall. The “glue” is a low-strength elastic material which is subject to brittle fracture at a certain value of the load acting on it. In a fractured segment, the rod surface slides over the wall surface under the action of a dry friction force which is less than the breaking stress. The high sensitivity of the process of the development of instability to small perturbations which initiate the development of instability is established. The system considered is the simplest model of the zone of contact between lithospheric plates which generate earthquakes.     

Form factors and wave functions of vector mesons in holographic QCD

Within the framework of a holographic dual model of QCD, we develop a formalism for calculating form factors of vector mesons. We show that the holographic bound states can be described not only in terms of eigenfunctions of the equation of motion, but also in terms of conjugate wave functions that are close analogues of quantum-mechanical bound state wave functions. We derive a generalized VMD representation for form factors, and find a very specific VMD pattern, in which form factors are essentially given by contributions due to the first two bound states in the Q²-channel. We calculate electric radius of the ρ-meson, finding the value .