In this article, on the basis of astronomical discoveries over the past 25 years, the possible causes of the phenomenon that is perceived as the “acceleration of the expansion of the Universe” are considered. In 1998, in order to confirm the discovery of the “acceleration of the expansion of the Universe”, the specialists of the High-Z SN Search Team tested and rejected the hypothesis about the influence of a local void – the “Hubble bubble”, which was considered an alternative to the positive cosmological constant, based on data on 44 supernovae of type SN Ia. Also in 1998 the author and specialists of the Computing Center of the Russian Academy of Sciences, during the testing of the multidimensional statistical analysis program “MMK-stat M”, according to standard reference data, a divergent dipole anisotropy of the redshift of 383 quasars and radio galaxies along the axis “Virgo – Leo ↔ Eridanus – Aquarius” was detected. In 2007, the problems of anisotropy attracted the attention of cosmologists. In 2016, groups of specialists from the High-Z SN Search Team and the Carnegie-Chicago Hubble program began a discussion about the impasse in cosmology. In the course of additional analysis, it is shown that the redshift dipole anisotropy of not only radio galaxies, but also supernovae of type SN Ia with respect to the quasar anisotropy dipole has an inverse orientation.

The article deals with the problem of assessing the state of remotely controlled complex technical systems using high-level digital twins made on the basis of visualization technologies is considered. An analysis of modern visualization technologies indicates that from the display means already used in the system state assessment loop, there is a transition to new technologies, up to virtual reality technology, which allow solving various kinds of tasks, including management, repair in an interactive mode. An analysis of the scope of visual models showed that models can act either as interpreters or as imitators. In this article, the emphasis is on imitators. Models must be adequate, therefore it is proposed to use modern advances in visualization technologies that allow evaluating a greater number of properties. The degree of adequacy is a monotonically increasing function of the number of properties taken into account when creating a model. Therefore, the more properties of a real object are taken into account in the model, the higher the adequacy of the visual model. The estimation technology is considered; an analyzer action algorithm being developed ensures the virtual presence of the expert at the object being controlled. This technology allows implementation of traditional testing technologies and additional measurements while detecting failures. An example of the technology practical implementation in the interactive analysis and management system is given.

Goniometric methods of measuring the refractive index of optically transparent materials are considered. A modified method for measuring the refractive index of triangular prisms is proposed. In the previous work [1], a modified constant deviation method was proposed for measuring the refractive index, which does not require measuring the refractive angle of the prism. That modification is simple, but its implementation uses low-intensity radiation reflected from the input face of the prism, which creates difficulties in processing signals from a photoelectric receiver and can lead to an increase in measurement error. In this paper, to obtain the reflection of the refracted beam, we used two fixed mirrors, and the refractive index of the prism material was calculated from the solution of a system of equations. This approach makes it possible not to use radiation reflected from the faces of the prism, which makes it possible to increase accuracy by automating the measurement process. The results of an experimental study of a triangular prism made of optical glass using the proposed modified prism method and their comparison with the method of minimum deviation, which has the highest accuracy of determining the refractive index, are presented. The proposed method can be used to study triangular prisms made of optically transparent materials, as well as optically transparent liquids poured in a hollow triangular prism.

The use of a new type of modems with pseudonoise coding and additional tone modulation designed to compare reference time scales over telecommunication geostationary satellites is considered. Experimental studies were carried out on the possibility of comparing time scales of hydrogen keepers from the State primary standard of unit of time, frequency and national time scale using these modems via an optical link. A fiber-optical lines of various lengths were used for a two-way signal transmission. The output radio-frequency signals of the modems connected to the optical transmitters at the ends of the fiber-optical lines were transmitted towards each other on an optical carrier with a wavelength of 1.55 μm. Demodulation of optical signals into the radio frequency range was carried out using optical receivers at the ends of fiber lines. The results of experimental evaluation of type A uncertainty by comparing time scales using fiber-optical lines with 50, 100, and 200 km of length are presented. For the 200 km line, the type A measurement uncertainty does not exceed 3 ps for one day of averaging interval. For the first time, it has been experimentally shown that the implementation of the method of time scales comparison using modems with pseudo-noise coding and additional tone modulation over 200 km of fiber line is possible without the intermediate optical amplifiers. The result opens up the prospect of creating cascaded systems for comparing time scales of remote standards via fiber-optic communication lines with a smaller number of intermediate optical amplifiers.

Problems of a linear mode of thermodynamics with the purpose of studying the change of local entropy rate of production in a non-stationary thermal mode at presence of a gradient of temperature in bodies of the simple form are considered. Article is development of earlier work of authors in which on the basis of experimental thermogram by the electrostatic levitation method received and fixing process of spontaneous cooling of the spherical sample of the molybdenum which is being a solid phase, change of local entropy rate of production from time has been calculated. It has been shown, that in absence of a gradient of temperature on radius of sphere change of local entropy rate of production from time corresponds to a principle of an extremum. In the given work change of local entropy rate of production from time for a case when the non-stationary thermal mode is combined with presence of a gradient of temperature is defined. The task is solved on the basis of known analytical decisions of one-dimensional problems of heating of bodies of the simple form (a unlimited plate, sphere and the unlimited cylinder), under boundary conditions of the second sort which have been received in approach of constant properties. The general meaning of local entropy rate of production is calculated as the sum of the task with gradient of temperature by a making constant in time and the non-stationary task counted in absence of a gradient of temperature. The estimation of the contribution of temperature drop on thickness of a plate in a general meaning of local entropy rate of production is executed, as product of force and a heat flux corresponding force and is widespread to a case of sphere and the cylinder by virtue of equality of temperature drop for all three bodies. The size of a nonstationary component in a general meaning of local entropy rate of production pays off as function of the logarithm, which argument is the relation of two instant temperatures, and the function of the logarithm is divided on a difference the values of time. It is shown, that the non-stationary component in a general meaning of local entropy rate of production also corresponds to a principle of an extremum at increase of Fourier number. For the first time have made comparison a part of non-stationary local entropy rate of production for a plate, sphere and the cylinder which shows, that the principle of an extremum is most brightly shown for sphere.

The problem of obtaining qualitative data on the thermal conductivity of standard rock samples for petrophysical studies is considered. It is shown that the existing instruments for thermal conductivity measurement do not allow one to obtain reliable and accurate values of the thermal conductivity of small-sized rock samples. A laboratory installation for thermal conductivity measurement of standard rock samples with a diameter not less than 30 mm has been created. The installation was assembled and tested on small samples. Possible problems in the development, design and exploitation of the laboratory installation were analyzed. A software that allows automated collection and processing of the data has been developed. The key factors, negatively affecting the accuracy and reliability of thermal conductivity measurement results, are identified and excluded.
There were unshielded thermocouples, potential changes between the hot and cold junctions (due to uneven melting of the water-ice mixture in the Dewar vessel, where the cold junction is immersed), incorrectly selected dimensions and shape of the object of study and the nonequilibrium ratio of the heat input and dissipation. The installation was tested on samples of pure tin standard and brass LS59 with known thermal conductivity. The thermal conductivity of a small-sized rock sample was measured with an error within 5.6 %.

The use of measuring current transformers for the analysis of electrical energy quality indicators requires normalization of their metrological characteristics in the frequency range of 40–2500 Hz, the upper limit of the range corresponds to the value of the 50th harmonic at the frequency of the industrial network of 50 Hz. The metrological support for determining the characteristics of measuring current transformers at the frequency of the industrial network is considered and it is shown that it is necessary to expand the frequency range used, as well as to be able to assess the influence of the harmonic composition of the measured sinusoidal current on the metrological characteristics of these devices. As a result of the work performed, a measuring installation was created to study the metrological characteristics of measuring current transformers in the extended frequency range of 40–2500 Hz. Possible methods of studying the characteristics of measuring current transformers are described and a differential-zero measurement method is selected. A study of the measuring installation was carried out and its characteristics were obtained – the range of reproducible frequencies; the range of reproducible current in the measuring circuit in a given frequency range from 40 to 2500 Hz; uncertainties in the transmission of units of the coefficient and the angle of the scale conversion of the sinusoidal current to measuring current transformers. The results are relevant for assessing the metrological characteristics of current converters used in power engineering and industry, and for the development of metrological support for measuring current transformers in the extended frequency range.

The problem of processing the results of radar measurements of the target motion parameters under conditions of disturbances due to aircraft maneuvers is considered. In order to adapt to the disturbances of measuring procedures, the method of invariant immersion has been modified. The application of the modified method in the case of a linear observation equation leads to a widespread form of a discrete measurement procedure obtained in this paper as a special case of modified invariant immersion equations. On the basis of statistical modeling of digital processing of the results of radar measurements of the movement parameters of the maneuvering target, the efficiency indicators of radar stations are calculated – these are the averaged absolute and relative errors in the measurement of motion parameters, the averaged wiring coefficient and the averaged time of the duration of the breaks of the tracks. Their analysis allows us to assert the high efficiency of using new measuring procedures synthesized using acceleration models in the form of white noise and Singer in the information and measurement systems of radar stations. This becomes possible due to the presence of the matrix coefficient of adaptation in the structure of the modified equations of invariant immersion. The comparison was carried out with Kalman measurement procedures synthesized using these acceleration models. Calculations of performance indicators confirm the reliability of the results obtained, since the wellknown fact of an increase in the error of measuring the height of an aircraft by monopulse radar stations near the surface is demonstrated. The results of the study will be useful in the development of adaptive measurement procedures for information and measurement systems operating under conditions of disturbances of measuring processes, for example, for survey locators.

The issues of providing working standards of the 1st category of metrological organizations of the country with regard to modern needs in the field of ultrasonic measurements in solids are considered. There is presented a modernized reference installation designed for precision measurements of propagation velocities of longitudinal and shear ultrasonic waves and damping coefficient of longitudinal ultrasonic waves in solids. Measurements of acoustic parameters of solid media are made by pulse-echo and resonance methods using contactless broadband capacitive methods of excitation and registration of ultrasonic waves. This installation is used as working standard of the 1st category in accordance with the state verification schedule for measuring instruments of the propagation velocities and damping coefficient of ultrasonic waves in solids. The technical means included in the installation (mechanical and electronic parts) have been improved, analog measuring means have been replaced with digital ones, methods for measuring acoustic parameters of solids based on the use of digital measuring means have been developed and the thickness range of installed ultrasonic measures has been expanded. The composition and main components of the reference installation, the used measurement methods and the principles of operation of the installation in various operating modes are described. The technical and metrological characteristics of the installation are given. Sources of measurement error (uncertainty) were analyzed. The field of application of the results is high-precision measurements of the acoustic characteristics of solid media, metrological ensuring of ultrasonic non-destructive testing and diagnostics.

The relationship between the development of the economy, especially its innovate branches and industry, with the state of measurements, including the level of its uniformity and accuracy, seems obvious. However, for the scientifically based planning of the development of the national measurement system it is necessary to have the numerical data about the relationship between the level of economic development and the parameters of the used fleet of measuring instruments. In this regard, numerous studies were performed by the Russian and foreign scientists, which, however, were fragmentary and did not allow to establish quantitative rules of the relationship between metrology and economics to the required extent. One of the reasons of this situation was the lack of reliable data about the properties and number of measurement means and absence of methods of obtaining such data. The creation of the Federal State Information System “Arshin” and the adoption of relevant regulatory legal acts in the field of ensuring of the uniformity of measurements made it possible in 2021 for the first time to obtain the most complete data on the verifications of measuring instruments applied in the field of state regulation of the uniformity of measurements in the Russian Federation, which number reached more than 90 million records. On the basis of the analysis of this data the model of circulation of the measuring instruments in the sphere of state regulation of the assurance of uniformity of measurements in Russian Federation was designed, and the method of the evaluation of the number of measuring instruments operated in this sphere was elaborated. It is based on the processing of the data about the number of the verification acts of the measuring instruments and its distribution by the interverification interval. It was shown that the upper appraisal of the total number of the measuring instruments has been obtained as a sum of the numbers of the measuring instruments for each interverification interval, which numbers were obtained by multiplying the number of the measuring instruments for each interverification interval in 2021 by the value of the certain interval. An assessment of the influence of factors causing the uncertainty of the number of measuring instruments was carried out. The of the number of measuring instruments used in the sphere of state regulation in the Russian Federation in 2021 was estimated as (420±16) million units. The calculated values of the number of measuring instruments volume are scientifically proved and can be applied in the annual report to the Government of the Russian Federation “On the state of work in the field of ensuring the uniformity of measurements in the Russian Federation”, as well as transmitted to the Federal State Statistics Service. It is reasonable to use it for the elaboration the documents of strategic planning of the development of the system of the ensuring the uniformity of measurements of the Russian Federation.