The article presents analytical quadrature expressions for electric field potentials that correspond to radio-frequency straight-axis ion funnels of a general type, specifically, the funnels with a curved channel profile, with multipole diaphragms, and with unequally spaced electrodes. When determining electric fields, the distribution of electric potential over the axis of the device was taken as a basis. The resulting formulae would be appropriate for use in quick, high-quality simulating of radio-frequency devices designed for isolation, conveying and focusing ions, as well as in solving some problems of mathematical physics.

An effective approach to produce an approximate analytical solution to a system of linear ordinary differential equation with polynomial coefficients, is considered. This approach is a modification of the Tau method of C. Lanczos, however, it minimizes an error of the solution, not a residual of the equation. Additionally, by converting a linear ordinary differential equation of n-th order into a system of linear ordinary differential equations of the $1^{\text {st }}$ order it is possible to increase seriously the accuracy of approximate expressions for the derivatives of the approximate solution. The effectiveness of the approach is illustrated by a numerical example.

Principle of similarity of trajectories in electric fields which are homogeneous in Euler terms is an effective instrument in charged particle optics. However, the set of electrical potentials which are homogeneous in Euler terms is not too rich. Weakened principle of similarity (the principle of limited similarity of trajectories) states that trajectories are proportional for a discrete subset of factors only instead of all real factors; it enables to expand significantly the class of electric fields under consideration. Brief theory of discretely homogeneous functions which are a basis of potentials used for the principle of limited similarity of trajectories, is considered here.

This article describes the key achievements over the past 10 years in the microsecond pulsed glow discharge mass spectrometry applied to the analysis of solids and gaseous mixtures. The solid-state analysis allows studying solid materials with different conductivities, including direct simultaneous quantitation of light elements with high ionization energy (N, O, F, Cl, etc.), heavy elements (U, Th, etc.), and isotope analysis. Dielectric materials analysis is considered in details with special emphasis on sample preparation approaches. Particular attention is focused on a new application of the technique for detection of volatile organic and inorganic compounds in gas mixtures (model gas mixtures, ambient air and exhaled air). This approach has prospects for solving medical and environmental problems as well as for process gas monitoring. Several applications (He determination in deuterium, detection of VOCs, Xe and other inorganic compounds in air) are presented as examples. Using the high resolution (6000 for Pb, m/z 208) of Lumas PGD-301 time-of-flight mass spectrometer helps to eliminate most of the interferences and thereby improves the analytical performance. Combination of high energy electron ionization with soft Penning and other ionization mechanisms allows to detect almost all known elements and molecules.

The article considers analytical expressions for electric field potentials that correspond to radio frequency funnels with quadratic, cubic and biquadratic profiles. The funnel electrodes are a sequence of diaphragms with a circular or multipole structure and apertures of variable size. The latter varies along the transport channel according to the desired law. The resulting expressions can be useful for fast, high-quality simulation of radiofrequency devices designed to convey ion beams with simultaneous focusing.

A specialized isotope mass spectrometer for determining the isotopic ratio of lithium by ERIAD (electrospray with atomization in an ion source) is described. The device uses a Mattuha-Herzog-type mass analyzer with double focusing to use ion beams with a large spread in energy and simultaneous registration of signals of both lithium isotopes (6Li and 7Li), and a two-channel receiver based on a doublet of microchannel plates. The gas-dynamic interface is built according to the Kontorowitz-Gray scheme; from the gas-dynamic point of view, it is "long", that is, the distance between the nozzle and the skimmer is 4 times the size of the "Mach barrel" at the operating pressure (200 Pa). The device is desktop, its weight does not exceed 20 kg. The measurement time is 1000 s, sample replacement time is 100 s, measurement accuracy is ~ 0.1%. Keywords: mass spectrometry, electrospray, ion source, isotopes of lithium.

The paper proposes refined definitions for associated homogeneous functions (AHFs) of real variables, which are of great practical importance for a wide range of problems. I. M. Gelfand and Z. Ya. Shapiro were the first in 1955 to introduce AHFs into scientific use. However, the possibilities of using these functions in various applications have not been exhausted to this day. The proposed definitions inherit the basic idea of the original paper to define chains of new functions using the recurrent linear functional relations, where some homogeneous Euler function is the starting point. This makes it possible to apply the corresponding results not only for differentiable and continuous functions, but also for discontinuous functions, including discontinuous ones at all points. The possibility of constructing a detailed consistent theory of AHFs of real variables, defined by a chain of linear recurrent functional relations of a general form, is shown. The basic theorems are formulated and proven. Further ways of generalizing the functions under consideration are discussed.

An effective approach to produce an approximate analytical solution to a linear ordinary differential equation with polynomial coefficients, is considered. This approach is a modification of the Tau method of C. Lanczos, however, it minimizes an error of the solution, not a residual of the equation. The effectiveness of the approach is illustrated by a numerical example. Other similar approaches are discussed briefly.

A study is performed of the physicochemical properties of the aqueous component of the cytoplasm of a living cell and the intercellular fluid associated with their structural organization. As a single coherent system, the structure of the water component of a plant plays a crucial role in its water regime, and therefore determines the development and adaptability of the plant to environmental conditions. Low-frequency L-dielcometry is used for the first time in experimental studies of the water regime of plants. The change in the peak intensities in the spectrum of the dependence of the dielectric loss tangent on the EMF frequency under conditions of artificial drought for different phytotest objects is used to show there are two types of water in living plants: free and self-organized bound. Free water is responsible for the mode of evaporation, while bound water participates in the organization of a complex network of intercellular communications, including the transmission of different signals through putative synapse-like contacts. Results correlate fully with others from plant phytomonitoring with pulsed NMR at the Kazan Scientific School of Phytophysiologist. The conclusion that there are two types of water in a living plant simultaneously is substantiated theoretically on the basis of generalized crystallography using Bulienkov's modular computer design. It is the most important component of the concept of quantum bioenergetics.

The article considers analytical models of high-frequency electric fields which can be used effectively for fast, high-quality simulation of ion flow focusing and transport processes in the radio-frequency funnels. In particular, the use of such devices in the design of a tandem three-quadrupole mass spectrometer increases the amount of ions collected in the forevacuum region of the gas-dynamic interface of the electrospray ion source. The cases of funnels with two- and four-phase electrical voltages (options I and II), as well as with amplitude-modulated electrical voltages providing a pseudopotential mode with an Archimedean wave (III) have been analyzed. As a result, the most preferable design turned out to be option III. The use of such analytical models makes it possible to test effectively promising options and thereby significantly reduce costs for the preliminary selection of a principal scheme of a device with specified characteristics, including similar cases of other mass spectrometric designs.

Integral potential representation is used to design fringing field structures of multipole fields. This approach gives analytical (but integral) form of potential in a space if potential distribution near the multipole axis is known. Equal potential surfaces of fields with different parameters and with given potential distribution specified near the axis are build. Example of trajectory construction in the fields are given.

The article considers numerical algorithms for determining the coefficients of polynomials with a fixed leading coefficient, the algorithms supplying a minimum deviation from zero in a minimax norm with a given weight function. The polynomials serve as a useful tool in many numerical methods, in particular, in the Lanczos' tau method which provides an approximate numerical analytic solution of ordinary differential equations with coefficients as polynomials in the independent variable. The well-known Chebyshev polynomials determined analytically are the special case of such polynomials, however, in most cases of weight functions, such polynomials can only be determined and tabulated numerically.

We developed a specialized mass-spectrometer for measuring the lithium isotopic ratio using electrospray ionization with controlled in-source fragmentation and atomization (in-source atomization, ERIAD). We used a Mattauch–Herzog double-focusing mass analyzer suspended under accelerating voltage; this makes its coupling with the gas-dynamic interface much easier. The mass analyzer is optimized up to the second degree; it can operate with ion beams with a broad energy spread, typical for ERIAD. Both isotopes, 6 Li and 7 Li, are detected simultaneously by a two-channel microchannel plate detector. The gas-dynamic interface is of the Kontorovitz–Gray type; it is gas-dynamically “long”: the nozzle-skimmer distance is four times longer than the Mach barrel at the operation pressure (200 Pa). The instrument is a desktop; it weighs approximately 20 kg. It is suitable for rapid analysis: one run takes 1000 s, and sample replacement takes only 100 s. The measurement precision in a series of 11 LiCl conventional measurements was 0.3%.

Описан специализированный изотопный масс-спектрометр для определения изотопного отношения лития методом ЭРИАД (электрораспыление с атомизацией в источнике ионов). В приборе используются масс-анализатор типа Маттауха-Герцога с двойной фокусировкой для использования пучков ионов с большим разбросом по энергии и одновременной регистрации сигналов обоих изотопов лития (6Li и 7Li) и двухканальный приемник на основе дублета микроканальных пластин. Газодинамический интерфейс построен по схеме Конторовица-Грея (с газодинамической точки зрения он "длинный", т. е. расстояние между соплом и скиммером в 4 раза превышает размер "бочки Маха" при рабочем давлении 200 Pa). Прибор настольный, его вес не превышает 20 kg. Время измерения 1000 s, время замены пробы 100 s, точность измерения содержания изотопа 7Li~ 0.1%. Ключевые слова: масс-спектрометрия, электрораспыление, источник ионов, изотопы лития.

High-resolution low-frequency dielcometry is used to study changes in the structure aqueous solutions of electrolyte salts in the 10−2–10−6 М range of concentrations. Changes are recorded according to differences in tangent $$\tan \delta $$ of dielectric loss, which reflects reactive processes in solution. All experiments are performed at room temperature. Experimental results in the 50–1000 kHz range of frequencies are presented as dependences of the dielectric loss tangent on the logarithm of frequency ω of the excitation of an oscillatory circuit. A glass test tube with the considered solution of electrolyte salt is placed in the inductance coil of the circuit. The observed dependences are of a pronounced spectral nature. The positions of the peaks in the spectra are reliably reproduced and characterize the cationic and anionic composition of a solution. Changes in the concentration in the observed spectra allow aqueous solutions of electrolyte salts to be attributed to classical solutions.

The systematic study of hadronic elliptic flow in various relativistic heavy ion collisions is important for the investigation of the initial geometry influence on the quark gluon plasma characteristics. The φ meson consists of strange and antistrange quarks and has a small interaction cross section with non-strange hadrons. Therefore, φ mesons are barely affected by late hadronic stage and reflect detailed information about hot and dense matter properties. Additionally, the comparison of elliptic flow for φ mesons to those of charged hadrons will provide additional information on the flavor dependence of flow. PHENIX has measured second order azimuthal anisotropy coefficients for φ mesons in Cu+Au collisions at √SNN = 200 GeV and in U+U collisions at √SNN = 193 GeV at midrapidity (| η | < 0.35). The obtained data suggest scaling of elliptic flow for φ mesons with eccentricity of participant nucleons in Cu+Au, U+U, and Au+Au collisions. Viscous hydrodynamic model iEBE-VISHNU provides a simultaneous description of the obtained data.

A new visualization method has been put forward to show the three-dimensional stability zones of a quadrupole mass filter placed in the constant uniform magnetic field directed along the quadrupole axis. The three-dimensional zone was represented by a set of two-dimensional sections each of which being an analogue of a stability two-dimensional zone of an intermittent electric quadrupole. The procedure for redetermining the boundaries of stability regions for the two-dimensional sections was applied. The results obtained can be used both in design of new mass spectrometers and in analyses of periodic dynamic system stability.

The measurements of light hadron production in small collision systems (such as p+Al, p+Au, d+Au, 3He+Au) may allow to explore the quarkgluon plasma formation and to determine the main hadronization mechanism in the considered collisions. Such research has become particularly crucial with the observation of the light hadrons collective behavior in p/d/3He+Au collisions at √SNN = 200 GeV and in p+Al collisions at the same energy at forward and backward rapidities. Among the large variety of light hadrons, ϕ meson is of particular interest since its production is sensitive to the presence of the quark-gluon plasma. The paper presents the comparison of the obtained experimental results on ϕ meson production to different light hadron production in p+Al and 3He+Au at √SNN = 200 GeV at midrapidity. The comparisons of ϕ meson production in p+Al, p+Au, d+Au, and 3He+Au collisions at √SNN = 200 GeV at midrapidity to theoretical models predictions (PYTHIA model and default and string melting versions of the AMPT model) are also provided. The results suggest that the QGP can be formed in p/d/3He+Au collisions, but the volume and lifetime of the produced medium might be insufficient for observation of strangeness enhancement effect. Conceivably, the main hadronization mechanism of ϕ meson production in p+Al collisions is fragmentation, while in p/d/3He+Au collisions this process occurs via coalescence.

The polynomials which give the minimum for the minimax norm are very useful in practical applications of various numerical algorithms. However, except the well-known Chebyshev's polynomials of first and second order there are no such polynomials specified in an explicit algebraic form. The paper considers the numerical algorithm(s) to generate the coefficients of the polynomials which: a) produce an optimal approximation for a given function in a minimax norm with some weight, b) produce an optimal deviation from zero with some weight and with a fixed high order coefficient.

Some mass separating systems use ion optics with periodic supply voltage to separate ions for mass-to-charge ratio. The equation of motion should be linear to guarantee that there is no dependence of stability on initial conditions. To get mass spectrometer stability zone it is possible to overlay stability diagrams of all equations, which are Hill-type ones. Another way to solve this problem when ion equations are not separated is suggested.