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The Newton interpretation of the psi function by rational functions with free poles is studied. A discrete formula for the Rodrigues determinants is obtained and the limit distribution of their zeros is found. The corresponding equilibrium problem of the theory of logarithmic potential is obtained.

Изучается ньютоновская интерполяция пси-функции рациональными функциями со свободными полюсами. Получена дискретная формула Родрига для знаменателей. Найдено предельное распределение их нулей. Получена соответствующая задача равновесия теории логарифмического потенциала. Библиография: 11 названий.

В статье приводится описание автоколебательного гидравлического привода несимметричного действия и стенда для его экспериментальных исследований, позволяющего определить основные динамические параметры исследуемого привода. В работе представлены характеристики привода при работе под нагрузкой и на холостом ходу.

Optical atomic clocks have already overcome the eighteenth decimal digit of instability and uncertainty, demonstrating incredible control over external perturbations of the clock transition frequency. At the same time, there is an increasing demand for atomic (ionic) transitions and new interrogation and readout protocols providing minimal sensitivity to external fields and possessing practical operational wavelengths. One of the goals is to simplify the clock operation while maintaining the relative uncertainty at a low 10−18 level achieved at the shortest averaging time. This is especially important for transportable and envisioned space-based optical clocks. Here, we demonstrate implementation of a synthetic frequency approach for a thulium optical clock with simultaneous optical interrogation of two clock transitions. Our experiment shows suppression of the quadratic Zeeman shift by at least three orders of magnitude. The effect of the tensor lattice Stark shift in thulium can also be reduced to below 10−18 in fractional frequency units. This makes the thulium optical clock almost free from hard-to-control systematic shifts. The “simultaneous” protocol demonstrates very low sensitivity to the cross-talks between individual clock transitions during interrogation and readout., There are continuous efforts in improving the stability and systematic shifts of optical clocks. Here the authors demonstrate thulium optical clock utilizing bicolor scheme involving interrogation of both hyperfine levels and they are able to cancel the quadratic Zeeman shift.

Aim. To assess the efficiency and effectiveness of medical institutions (legal entities) that provide primary health care to the population of Stavropol Region, to form the analytical, scientifically based decision-making base for optimizing the primary health care sector of the Stavropol Region. Methods. The comprehensive analysis of the efficiency and effectiveness of the activities of medical institutions providing primary health care based on the developed technique. Results. The results of the study confirmed the objectivity of the developed system of multi-criteria evaluation of the effectiveness and efficiency of the activities of medical institutions providing primary health care to the population. The results of the assessment became an evidence base for improving the activities of medical institutions providing health care in outpatient settings, and allow providing the comparative analysis of their performance, which is integrated into a single indicator, the well-being index, to form the ratings of medical institutions in the region. Conclusion. The results of the assessment will serve as the evidence base for choosing priority socially important directions and will optimize the activity of providing primary health care to each medical institution of the entire system of outpatient primary health care in Stavropol region.

One of the key systematic effects limiting the performance of state-of-the-art optical clocks is the blackbody radiation (BBR) shift. Here, we demonstrate unusually low sensitivity of a 1.14 μm inner-shell clock transition in neutral Tm atoms to BBR. By direct polarizability measurements, we infer a differential polarizability of the clock levels of −0.063(30) atomic units corresponding to a fractional frequency BBR shift of only 2.3(1.1) × 10−18 at room temperature. This amount is several orders of magnitude smaller than that of the best optical clocks using neutral atoms (Sr, Yb, Hg) and is competitive with that of ion optical clocks (Al+, Lu+). Our results allow the development of lanthanide-based optical clocks with a relative uncertainty at the 10−17 level., Precise and stable optical clocks are important for fundamental science and applications. Here the authors demonstrate a clock transitions in thulium (Tm), which has a small black body radiation frequency shift and is suitable for transportable atomic clocks.

Because of the low sensitivity of a thulium optical clock to black-body radiation and good accuracy and stability estimations, it is considered as a promising transportable optical clock. One of the leading systematic effects for Tm clock transition, i.e., the second-order Zeeman effect, can be canceled by probing two clock transitions between different hyperfine levels of ground and metastable states during clock operation. Herein, we demonstrate efficient optical pumping into the ${m}_{F}=0$ state of both ground hyperfine levels using single-frequency radiation at 418.8 nm. We prepared the atoms in both target states simultaneously and excited two clock transitions alternately. The resulting population of ${m}_{F}=0$ states of ground hyperfine levels was 36% and 3.8% of the initial number of atoms with less than 4% and 0.4% on nonzero magnetic sublevels, respectively. We performed numerical simulations of the optical pumping process, which is able to explain experimental results well.

The asymptotic behavior of the Hermite–Pade approximants of the first type for two beta functions are studied. The results are expressed in terms of equilibrium problems of logarithmic potential theory and in terms of meromorphic functions on Riemann surfaces.

The article describes the developed asymmetric self-oscillating hydraulic drive and a stand for determining its dynamic characteristics. The design feature of the self-oscillating drive is that the switching of the working fluid in the cylinder cavity is made by two spools mounted inside the piston, while the working fluid is supplied to the spools by the hollow rod. The test stand is based on the principle of throttling the working fluid when it flows from one cavity of the loaded hydraulic cylinder to another. Stand tests of the developed drive have shown its reliability at different values of the piston stroke and at different operating pressures. The paper presents the characteristics of the drive when operating under load and at idle..

Currently, there are no sufficiently effective submersible vibrators for the implementation of a promising technology for vibro-seismic impact on oil and gas reservoirs. In this paper, we consider the possibility of using a downhole elastic wave generator based on a two-stage centrifugal nozzle for the vibro-seismic impact technology (VSIT). The equation of non-stationary fluid flow through the nozzle has the form of a nonlinear Van der Pol differential equation. In this paper, when using the method of studying this equation in the Matlab/Simulink application package, the principal possibility of tincture of a well generator to the dominant frequency of an oil reservoir is shown. The result of the study showed that when using an automatic control system, taking into account the hydraulic flow and pressure transmission line, the elastic wave generator can be controlled by the generation frequency with the accuracy necessary for vibro-seismic action on oil and gas formations.

The nitrogen-vacancy (NV) center in diamond has been found to be a powerful tool for various sensing applications. In particular, in ensemble-based sensors, the main ``workhorse'' so far has been optically detected electron resonance. Utilization of the nuclear spin has the potential to significantly improve sensitivity in rotation and magnetic field sensors. Ensemble-based sensors consume a substantial amount of power, leading to noticeable heating of the diamond and thus requiring an understanding of temperature-related shifts. In this paper, we provide a detailed study of the temperature shift of the hyperfine components of the NV center.

Minimization of internal degrees of freedom is an important step in the cooling of atomic species to degeneracy temperature. Here, we report on the loading of 6*10^5 thulium atoms optically polarized at maximum possible magnetic quantum number mf=-4 state into dipole trap operating at 532 nm. The purity of polarizations of the atoms was experimentally verified using a Stern-Gerlach-type experiment. Experimental measured polarization of the state is 3.91(26).

Quickly developing application of nitrogen-vacancy color centers in diamond sets demands on cheap and high optical and spin properties nanodiamonds. Among other types, detonation nanodiamonds are easiest for production but often show no NV color centers inside. In this work we show, that aggregates of detonation nanodiamonds could be as good, or even better in terms of brightness and spin properties, than more expensive single crystal nanodiamonds. This way aggregates of detonation nanodiamonds could efficiently serve as cheap and bright source of single photon radiation or sensitive element of biocompatible sensor.

Ensembles of nitrogen-vacancy color centers in diamond hold promise for ultra-precise magnetometry, competing with superconducting quantum interference device detectors. By utilizing the advantages of dielectric materials, such as very low losses for electromagnetic field, with the potential for creating high Q-factor resonators with strong concentration of the field within it, we implemented a dielectric resonator antenna for coherent manipulation of a large ensemble of nitrogen-vacancy centers in diamond. We reached average Rabi frequency of 10 MHz in a volume of 7 mm3 with a standard deviation of less than 1% at a moderate pump power. The obtained result enables use of large volume low nitrogen-vacancy concentration diamond plates in modern nitrogen-vacancy magnetometers thus improving sensitivity via larger coherence time and higher optical detected magnetic resonance contrast.

We report on the improved measurement of the hyperfine structure of $4f^{12}(^3 H_6)5d_{5/2}6s^2$ $(J=9/2)$ excited state in Tm-169 which is involved in the second-stage laser cooling of Tm. To measure the absolute value of the hyperfine splitting interval we used Doppler-free frequency modulation saturated absorption spectroscopy of Tm atoms in a vapor cell. The sign of the hyperfine constant was determined independently by spectroscopy of laser cooled Tm atoms. The hyperfine constant of the level equals $A_J=-422.112(32)$ MHz that corresponds to the energy difference between two hyperfine sublevels of $-2110.56(16)$~MHz. In relation to the saturated absorption measurement we quantitatively treat contributions of various mechanisms into the line broadening and shift. We consider power broadening in the case when Zeeman sublevels of atomic levels are taken into account. We also discuss the line broadening due to frequency modulation and relative intensities of transitions in saturated-absorption experiments.

Second-stage laser cooling of thulium atoms at the 530.7 nm transition with a natural linewidth of 350 kHz offers an interesting possibility to study different regimes of a magneto-optical trap (MOT). The intermediate value of the spectral linewidth of the cooling transition allows the observation of three distinct regimes depending on intensity and detuning of the cooling beams. Namely, the "bowl-shaped" regime when light pressure force competes with gravity, the "double structure" regime with interplay between Doppler and polarization-gradient (sub-Doppler) cooling, and the "symmetric" regime when Doppler cooling dominates over sub-Doppler cooling and gravity. The polarization-gradient cooling manifests itself by a two-temperature momentum distribution of atoms resulting in a double-structure of the spatial MOT profile consisting of a cold central fraction surrounded by a hot halo. We studied the "double structure" regime at different saturation parameters and compared observations with calculations based on semiclassical and quantum approaches. The quantum treatment adequately reproduces experimental results if the MOT magnetic field is properly taken into account., Comment: 7 pages, 6 figures

We construct multipoint Hermite—Pade approximations for two beta functions generating the Nikishin system with infinite discrete measures and unbounded supports. The asymptotic behavior of the approximants is studied. The result is interpreted in terms of the vector equilibrium problem in logarithmic potential theory in the presence of an external field and constraints on measure.

The effect of temperature on absorption spectra of Rhodamine 6G at concentrations of 10−6 and 10−3 M in water:ethanol solutions of various ethanol content was studied. The dimeric molecular fraction of Rhodamine 6G (10−3 M) was found as a function of temperature and ethanol content in the aqueous solution. It was shown that the absorption spectrum of Rhodamine 6G dimers (10−3 M) is dependent on temperature and ethanol content in the aqueous solution. Based on the relationship between J-and H-bands in the absorption spectrum of Rhodamine 6G dimers, both the angle between planes of associated Rhodamine 6G dye molecules and the free enthalpy of association were calculated. The structure of Rhodamine 6G dimers depends essentially on the ethanol content and aqueous ethanol solution temperature while experiencing the most temperature changes at an ethanol concentration of 25%.

We propose a new method for proving the Zudilin-Rivoal theorem stating, in particular, that the sequence of values of the Dirichlet beta function at even natural points contains infinitely many irrational values. For polylogarithms, we use Hermite—Pade approximations of the first type, invariant with respect to the Klein group. Quantitative additions to this theorem are obtained.

The spreading of the position and momentum probability distributions for the stable free oscillations of a circular membrane of radius l is analyzed by means of the associated Boltzmann–Shannon information entropies in the correspondence principle limit (n → ∞, m fixed), where the numbers (n, m), n ∈ ℕ and m ∈ ℤ, uniquely characterize an oscillation of this two-dimensional system. This is done by solving the short-wave asymptotics of the physical entropies in the two complementary spaces, which boils down to the calculation of the asymptotic behavior of certain entropic integrals of Bessel functions. It is rigorously shown that the position and momentum entropies behave as 2 ln (l) + ln (4π) - 2 and ln (n) - 2 ln (l) + ln (2π3) when n → ∞, respectively. So the total entropy sum has a logarithmic dependence on n and it does not depend on the membrane radius. The former indicates that the ordering of short-wavelength oscillations is exactly identical for the entropic sum and the single-particle energy. The latter holds for all oscillations of the membrane because of the uniform scaling invariance of the entropy sum.

The inverse problem of voice source pulse recovery from a segment of a speech signal is under consideration. A special mathematical model is used for the solution that relates these quantities. A variational method of solving inverse problem of voice source recovery for a new parametric class of sources, that is for piecewise-linear sources (PWL-sources), is proposed. Also, a technique for a posteriori numerical error estimation for obtained solutions is presented. A computer study of the adequacy of adopted speech production model with PWL-sources is performed in solving the inverse problems for various types of voice signals, as well as corresponding study of a posteriori error estimates. Numerical experiments for speech signals show satisfactory properties of proposed a posteriori error estimates, which represent the upper bounds of possible errors in solving the inverse problem. The estimate of the most probable error in determining the source-pulse shapes is about 7-8% for the investigated speech material. It is noted that a posteriori error estimates can be used as a criterion of the quality for obtained voice source pulses in application to speaker recognition.

Further development of quantum emitter based communication and sensing applications intrinsically depends on the availability of robust single-photon detectors. Here, we demonstrate a new generation of superconducting single-photon detectors specifically optimized for the 500–1100 nm wavelength range, which overlaps with the emission spectrum of many interesting solid-state atom-like systems, such as nitrogen-vacancy and silicon-vacancy centers in diamond. The fabricated detectors have a wide dynamic range (up to 350 million counts per second), low dark count rate (down to 0.1 counts per second), excellent jitter (62 ps), and the possibility of on-chip integration with a quantum emitter. In addition to performance characterization, we tested the detectors in real experimental conditions involving nanodiamond nitrogen-vacancy emitters enhanced by a hyperbolic metamaterial.

A matrix continued fraction is defined and used for the approximation of a function F known as a power series in 1/zwith matrix coefficientsp×q, or equivalently by a matrix of functions holomorphic at infinity. It is a generalization of P-fractions, and the sequence of convergents converges to the given function. These convergents have as denominators a matrix, the columns of which are orthogonal with respect to the linear matrix functional associated to F. The case where the algorithm breaks off is characterized in terms of F.