The mechanisms of particle mass generation are discussed within the framework of modern models that generalize the Standard Model of electromagnetic, weak, and strong interactions (hereinafter referred to as generalized models). In generalized models, the structure of the Higgs sector becomes more complicated, resulting in additional Higgs particles. Theoretical works of a number of authors are analyzed and experimental data obtained recently, possibly related to the Higgs sector of generalized models, are presented. Spontaneous violation of gauge symmetry and a possible explanation of the phenomenon of transition to a negative value of the square of the mass of a scalar field, which is used in spontaneous violation, are briefly discussed. The appearance of nonzero mass values of gauge bosons, fermions, and Higgs particles is considered in the framework of the procedure of spontaneous violation of gauge symmetry. The generation of particle masses in generalized models is discussed. Recent data indicating the possible existence of several new scalar particles with masses from tens to hundreds of GeV are considered, which may confirm the more complex structure of the scalar sector of generalized models compared to the structure of the scalar sector of the Standard Model. The results presented in the review can be useful in planning and interpreting the results of experiments on the search for scalar particles, as well as in the development of theoretical generalized models.

The proliferation of ultrasound medical devices and the development of ultrasound diagnostic and therapeutic methods have necessitated metrological control of a wide range of ultrasound medical equipment acoustic output parameters, such as ultrasound pressure and intensity. To ensure the uniformity of high-frequency (0.5–20 MHz) hydroacoustic measurements, as well as to implement metrological traceability of intensity and pressure measurement results obtained using ultrasonic field parameter meters and high-frequency hydrophones, respectively, the State primary standard of the unit of ultrasound power in water, GET 169-2019, has been improved. As a result of these improvements, the State primary standard of the units of ultrasound power, intensity, and pressure in water, GET 169-2025, has been approved. This standard includes two new units: the URTU-1 unit for reproducing and transmitting the unit of ultrasound intensity in water and the URTU-2 unit for reproducing and transmitting the unit of ultrasound pressure in water. The expansion of the list of units reproducible using GET 169-2025 enables metrological traceability of the results of ultrasound power, intensity, and pressure measurements in water, and therefore of devices designed to measure and control the acoustic output parameters of medical ultrasound and other equipment. Amendments have been made to the state verification scheme for ultrasound power measuring instruments in the frequency range from 0.5 to 20 MHz, reflecting the new capabilities of GET 169-2025 and addressing the challenges of distributing working standards to metrology centers across the Russian Federation.

The article discusses the potential use of 3,3,3-trifluoropropene (R1243zf), a new refrigerant with zero ozone-depleting potential and a very low (0.29) global warming potential. In recent years, reliable experimental information has been obtained on the thermodynamic properties (density, pressure, isochoric heat capacity, and speed of sound) of R1243zf both in the single-phase region and on the liquid-vapor saturation line. Using the values of these thermodynamic quantities obtained over a wide range of state parameters, a series of equations of state for this refrigerant have been developed. In contrast to the known equations of state, a unified fundamental equation of state is proposed in this study. The unified fundamental equation of state for R1243zf is developed within the framework of a large-scale theory of critical phenomena and the similarity relation, which makes it possible to obtain reliable data on the equilibrium properties of liquid and gas not only in the regular part of the thermodynamic surface, but also in the asymptotic neighborhood of the critical point. A unified fundamental equation of state was used to calculate the standard reference data, including information on the density, pressure, enthalpy, entropy, speed of sound, isobaric and isochoric heat capacity of 3,3,3-trifl uoropropene in the range of state parameters of 169–420 K and up to 40 MPa. To estimate the uncertainty of the standard reference data, two methods based on the calculation of various statistical characteristics were used. The expanded uncertainties of the following equilibrium properties of R1243zf were obtained: density (0.25 %); pressure (0.35 %); specific heat capacity (1.2 %); speed of sound (0.37 %); saturated vapor and liquid density (0.55 and 0.40 %, respectively). The calculated estimates of the statistical characteristics indicate that the unified fundamental equation of state adequately conveys the equilibrium properties of the refrigerant R1243zf in the above-mentioned range of state parameters. The results of the study can be used in the design of air conditioning and refrigeration systems.

When processing measurement results and evaluating their accuracy, a normal distribution is traditionally used; however, in some cases this approach may be incorrect (for example, if the distribution is significantly asymmetric or it is bounded). Therefore, the selection of a family of distributions is relevant, which would allow the approximation of both traditionally applied normal and uniform laws, as well as encompass distributions of other types that more adequately reflect the specifics of particular measurement tasks. To model measurement data and evaluate accuracy indicators, it is proposed to use the family of two-sided power distributions. The choice of this family is due to the fact that it is described by an extremely simple mathematical model while providing sufficient variety of probability density function shapes, including uniform, bimodal, and unimodal distributions (both symmetric and asymmetric). Methods for fitting (assigning) the distribution law are provided based on both a priori information (using specified accuracy indicators: measured value, standard or expanded uncertainties, coverage interval boundaries for a given probability level) and sample data (including maximum likelihood, the method of moments, and two-sided power distribution fitting via inverse transformation). Metrologically justified criteria for the approximation of continuous distributions by distributions of the family under consideration are proposed, and its application in evaluating the uncertainty of multiple equally precise measurements is described. Software has been developed for transforming distributions, which allows the measurement model to be specified in an analytical form. The results obtained are useful for specialists applying statistical modeling methods when evaluating measurement results, certifying measurement procedures, and processing data from interlaboratory comparisons.

Consideration of the statistical stability of mathematical models of measurement objects, which significantly affects the accuracy of the statistical (probabilistic) estimates used, is considered. This problem is relevant because there is no effective criterion for distinguishing deterministic and random sequences. Accounting is based on a two-level probability distribution density in the form of a conversion formula. The numerator of the formula characterizes the errors of the systematic component of the hypothetical probability distribution as the observed deviations from it of the statistical distribution of measurement data, and the denominator is the unobservable components of the random component. The convergence of a number of repeated measurements is a necessary condition for the correctness of the statistical (probabilistic) estimates obtained. The formulation of such a problem is possible due to the fact that convolution in the form of an inversion formula is considered as the distribution of the sum of two random terms, when the second term characterizes the statistical stability of the first term. The direct solution of the problem by functional transformations of probability distributions leads to very cumbersome results. Within the framework of the interpolation concept, A. N. Kolmogorov's axiomatic approach is adopted, in which probability is represented by a positive real random variable characterized by a probability distribution function, which is a second-order distribution. It is established that the indicator of statistical stability of a mathematical model, the probability of agreement with the data of joint measurements, or kappa, is a reproducibility criterion, summarizes the statistics of the criteria of agreement of A. N. Kolmogorov and N. V. Smirnov – the distances between the distribution functions, and contains the distance according to the variation of V. Feller. The growth trend in the statistics of the probability of agreement with an increase in the sample size for probability distributions directly characterizes the degree of statistical stability of measurement data and the reliability of statistical inference logic in measuring problems of identifying probability distributions, and also complements confi dence probability as a characteristic of the quality of mathematical models of measurement objects.

The efficiency of directional drilling in the Russian Arctic critically depends on the accuracy of magnetic inclinometers. In addition to voltage fluctuations and temperature variations, the metrological characteristics are significantly affected by ionospheric currents during geomagnetic substorms. The superposition of these factors leads to substantial errors in wellbore trajectory determination. Existing compensation methods are predominantly reactive, while proactive risk assessment approaches remain underdeveloped. This paper proposes a statistical framework for the probabilistic assessment of extreme error risks in magnetic inclinometers operating in high-latitude regions. Based on the analysis of magnetic observatory data from the maximum of the 24th solar cycle, it was established that the distributions of magnetic declination and inclination measurement errors follow a lognormal law. It was revealed that the heavy tails of the distributions (up to 19 % of the sample) are accurately described by a Generalized Pareto Distribution, indicating a high risk of extreme events. The probability of exceeding the permissible error threshold is ~6.3 % for azimuthal and ~0.81 % for zenith angles, which is unacceptable for managing the costly drilling process. The obtained results enable the creation of risk maps for integration into decision-support systems when planning drilling operations. This will minimize economic losses and mitigate emergency risks by enabling the advance prediction of periods when the use of magnetic inclinometers is associated with an increased probability of unacceptable errors.

This article addresses a pressing issue in microwave photonics: the development and measurement of the characteristics of ultra-high-frequency optical modulation systems based on Mach-Zehnder modulators. Using ultrahigh-resolution optical spectrometers to measure the spectral composition of a modulator during operation allows us to identify features that cannot be measured after photodetection. Three types of control signal deviations are investigated: operating point setting accuracy, attenuation inequality in the modulator arms, and inequality in the absolute values of signal voltages on different arms of the modulator. The presented spectral compositions of the optical and radio-frequency spectra, obtained through numerical simulation and experiments on modulating radiation with a sinusoidal signal in different operating modes of a standard Mach-Zehnder modulator, allow us to evaluate the infl uence of these effects. It is shown that for deviations less than 1 %, the greatest contribution to spectral distortion is due to the accuracy of the operating point setting. Experimental evaluation methods are proposed for measuring deviation. The obtained results and conclusions provide new opportunities for assessing the manufacturing quality of standard modulators, as well as the accuracy of operating point control systems.

The photochronographic method using image converter streak cameras currently remains the main method for measuring the temporal characteristics of picosecond laser pulses. But the techniques of accounting for sources and estimating measurement uncertainty developed for this method back in the 1970s are outdated and inapplicable to modern streak cameras with digital image registration. As part of the work on updating the metrological support for measurements of laser pulse duration by means of image converter streak cameras, a technique for estimating the laser pulse duration measurement uncertainty has been developed. The developed technique contains a detailed analysis of the sources of uncertainty and an estimation of their contribution to the combined uncertainty of the measurement result. The technique has been implemented in practice to assess the uncertainty of measurement of the duration of a femtosecond laser pulse passed through a fiberoptic stretcher performed using a K016 image converter streak camera. The practical significance of the research lies in the development of metrological support for duration measurement of picosecond optical pulses. Estimating the uncertainty of the laser pulse duration measurement result with the developed technique will make it possible to standardize the metrological characteristics of measuring instruments for the temporal characteristics of optical pulses, used in laser physics and related fields.

Currently, the field of quantum frequency standards based on cold atoms is actively developing. Сold atoms underlie the creation of such quantum gravimetric sensors as atomic gravimeters, atomic gradiometers and atomic gyroscopes. One of the key elements of these sensors is the source of cold atoms, which must provide a sufficient flow of cooled atoms. This paper presents the development of a compact source of Rb87 atoms based on a conical magnetooptical trap, which significantly simplifies the optical scheme by replacing the multipath system with a single conical reflector. The developed compact source is used in fountain-type frequency standards. The scheme, principle of operation, design features and experimental characteristics of a source of slow atoms are given. The results of a study of the operating parameters of a source of slow atoms based on a conical magneto-optical trap and the characteristics of its output atomic beam are presented: the estimated number of trapped atoms in the conical region of the trap, the average atomic flow velocity, and the dependence of the characteristics of the output atomic beam on the operating parameters of the trap. These characteristics demonstrate the possibility of using a conical magneto-optical trap as a source of slow atoms in modern fountain-type frequency standards and other atomic sensors.

This work proposes a improved method for maintaining the thermal regime of heating elements in chemoresistive gas sensor substrates, presenting experimental data on heating inertia modes and heater operation limits during substrate temperature maintenance via pulse-width modulation control. The primary goal was to substantiate pulse-width modulation parameters for substrate temperature control in chemoresistive gas multisensors, addressed through analyzing a generalized microheater-to-pulse-width modulation generator connection diagram, designing and manufacturing a hardware-software unit for controlling substrate heating in multisensors with different microheater characteristics, and conducting experimental research on heating multisensor substrates to 300 °C. The study describes and substantiates approaches for calculating required pulse-width modulation signal parameters, concluding that the pulse-width modulation pulse period depends on the duty cycle percentage determined by generated signal points, defining parameters that ensure stable temperature maintenance and emphasizing the importance of selecting an optimal pulse-width modulation signal frequency.

This paper examines the optimization of one of the most important metrological characteristics of dosimetric X-ray and gamma-ray installations – the geometric size of the uniform field of the gamma radiation field. The influence of the geometric shape of lead attenuators in verification installations on the size of the uniform region of the gamma radiation field is analyzed. It is shown that the use of classically shaped attenuators leads to a significant reduction in the width beam of uniform, which limits the number of simultaneously verified dosimetric instruments designed for measuring the air kerma rate. Experimental measurements of the air kerma rate were conducted using a setup with various attenuator combinations, and a comparison with published data was made. Based on the results, an optimized attenuator shape is proposed, ensuring both the required attenuation factor and maintaining the size of the uniform region of the gamma radiation field. A design implementation of optimized attenuators is presented, protected by a patent from the Eurasian Patent Office, confirming the novelty of the proposed technical solution.

The main problems of creating predictive measurement systems are considered. The role of predictive analytics, digital models and digital twins of measuring systems in predicting the drift of metrological characteristics, estimating the remaining resource and reducing the risk of metrological failure is shown. The key aspects of the development of intelligent measuring systems are considered: requirements for metrological support and features of measuring instruments based on artifi cial intelligence, the infl uence of their multicomponence and opacity of algorithms on the procedures of verifi cation, calibration and metrological self-control. Based on current standards and scientifi c publications, the terminology used in this fi eld is evaluated, and a defi nition of a predictive measuring system is proposed, including functions for predicting both process parameters and the metrological dependability of measuring instruments. Recommendations are formulated to improve methods for assessing the risk of metrological failure and the need to detail the requirements for intelligent measuring systems through the development (revision) of standards is noted.