Approximate Calculation Research Articles

Russian per capita consumption of fish products in raw mass or marketable product weight: how to recalculate back and forth

Aim. Find a simple way to transfer the average per capita consumption of fish products (kg/person/year) from the raw mass to the mass of marketable products and vice versa.Methods. Statistical processing of official data on the consumption of fish products in the USSR and the Russian Federation, published by Rosstat (Russian Federal State Statistics Service) and FAO (Food and Agriculture Organization of the United Nations) for 58 years, was made using the least squares method.Results. Two-parameter equations are found that best describe the relationship between the average per capita consumption of fish products in the mass of raw fish and in the mass of commercial products ready for consumption, as well as coefficients for simplified approximate quick calculations of the mass of consumed raw fish by the mass of commercial products and the mass of consumed commercial products by mass of raw fish.Novelty. Based on the results of the original analysis of the material, a new method for recalculating the Russian per capita consumption of fish products in the mass of raw fish by the mass of consumed commercial products and vice versa was obtained for the first time.Practical significance. Restoration of long-term series of consumption and targets for food security, the efficiency of the functioning of the fishery complex, and the social policy of the state. The article may be useful to economists, marketers, sociologists, medicals, businessmen, officials and politicians.

Human brain representations of internally generated outcomes of approximate calculation revealed by ultra-high-field brain imaging

Much of human culture’s advanced technology owes its existence to the ability to mentally manipulate quantities. Neuroscience has described the brain regions overall recruited by numerical tasks and the neuronal codes representing individual quantities during perceptual tasks. Nevertheless, it remains unknown how quantity representations are combined or transformed during mental computations and how specific quantities are coded in the brain when generated as the result of internal computations rather than evoked by a stimulus. Here, we imaged the brains of adult human subjects at 7 Tesla during an approximate calculation task designed to disentangle in- and outputs of the computation from the operation itself. While physically presented sample numerosities were distinguished in activity patterns along the dorsal visual pathway and within frontal and occipito-temporal regions, a representation of the internally generated result was most prominently detected in higher order regions such as angular gyrus and lateral prefrontal cortex. Behavioral precision in the task was related to cross-decoding performance between sample and result representations in medial IPS regions. This suggests the transformation of sample into result may be carried out within dorsal stream sensory-motor integration regions, and resulting outputs maintained for task purposes in higher-level regions in a format possibly detached from sensory-evoked inputs.

Research on the output characteristics of photovoltaic arrays under partial shading conditions based on peak point approximate calculation method

Research on the output characteristics of photovoltaic arrays under partial shading conditions based on peak point approximate calculation method

MAIN ASPECTS OF THE TRANSFORMATION OF WORLD TRADE REGIMES AT THE PRESENT STAGE

The article is devoted to the analysis of key aspects of the transformation of world trade regimes at the current stage, such as digital commerce, regional trade agreements, protectionism, trade exchange of services, global supply chains and protection of innovative technologies for international economic stability. It is proved that the study of modern trends and transformations of the world economy is an actual theoretical and applied task, which involves the systematic consolidation of methods and mechanisms of interdisciplinary research. Important factor in modern conditions of globalization of trade relations is the use of information technologies, they become the determining factors of victory in the competitive struggle, it allows you to break traditional supply chains and move to the future. Implementation of digital technologies contributes to significant improvement of business results and significantly accelerates strategic changes in the development of world trade. It is summarized that until recently globalization processes were characterized as stable, mostly positive. But at the current stage, it became clear that the processes of transformation are linear in nature and largely depend on the geopolitical situation in the world, the cyclical nature of global economic development, the geographical location and structure of the economy of the countries of the world. The transformation of the management trade balance changes the form and content of world trade regimes .Accordingly, predicting the future, we understand that we cannot give even approximate calculations or make a more or less accurate analysis. The economic interdependence of different countries should be a guarantee of financial success, but in recent decades it has increasingly transformed and turned into something unusual in world trade. The main focus is on the discussion of forecasts for the current year 2024 of international organizations such as the World Trade Organization (WTO) and the World Trade Organization (WTO), which play a key role in regulating trade relations at this stage.

Formation of images of the future in the USSR in the 1920s.

The article is devoted to the trends in the formation of images of the future in the USSR in the 1920s. The subject of the study is the image of the future as an object of design during the formation of a new state of society, the search for guidelines and practices of social development. Design in a broad context is considered as an active creative activity to shape the image of the future. Design may imply certain deadlines for its implementation, or it may be based on approximate calculations, on some guidelines that do not have a strict time limit. The research methods were historical-analytical, historical-comparative, historical-genetic, system-analytical. The postulates of F. Polak and E. Bloch were adopted as the methodological basis for studying images of the future. The article identifies the subjects of designing images of the future in the period under study, among whom are the leaders and ideologists of the Communist Party, as well as representatives of the urban intelligentsia. The main factors in the formation of images of the future are identified, among which are noted: the “current present”, political programs and ideological attitudes of the power elite, ideological trends of previous decades, scientific achievements, value systems. Projecting images of the future by subjects in the 1920s, experiencing the influence of various factors, led to the formation of images of a predominantly utopian nature, defining the horizons of the “expected” or “possible” future. Given the schematic and vagueness of the political guidelines for communism and the diversity of its author’s figurative variants, the future society was presented in the general categories of collectivism, science-centrism, technocratism, the ideals of a new socially determined person, and the subordination of nature to society.

A time-series analysis of the evolution of scientific and technological concepts in the change of social thinking in modern China

Abstract Exploring the evolutionary process of the concept of science and technology in modern Chinese society is conducive to the innovation of the current path of science education popularization and scientific and technological literacy enhancement. In this paper, we construct a sampling selection algorithm using Bayesian and MCMC and then design a parameter derivation model. Assuming the model prior distribution hyperparameters and using the likelihood function to derive the specific form of the posterior probability distribution, an approximate integral calculation is carried out in order to directly derive the parameters to be estimated, and the BVAR-MCMC model is constructed. Using the model to analyze the temporal changes in the evolution of scientific and technological concepts in modern China, it is finally found that the changes in social and technological concepts during the Republican period were even stronger than those in the late Qing period. Influenced by the increasing scale of cross-cultural exchanges due to the gradual opening up of the gateway, cross-cultural open exchanges have the highest impulse value and the longest duration on the evolution of scientific and technological concepts, with the impulse of the Late Qing and the Republic of China phases above 1, and the duration of the positive influence covers the whole time series. The impulse values of the late Qing and the Republic of China are 2.68 and 3.59, respectively, and the education popularization rate, economic development level, the speed of technological life progress, and the degree of civilization and freedom of the social atmosphere have different degrees of influence on the evolution of scientific and technological concepts in the time series of modern history. This study innovates the statistical research method for modern history and conducts a pioneering exploratory study on the evolutionary process of modern social ideas change.

ПРОБЛЕМЫ ПРОИЗВОДСТВА ЛЕКАРСТВЕННЫХ ПРЕПАРАТОВ

The problems of drug production at one of the pharmaceutical enterprises of the Republic of Tatarstan are analysed. The review of key costs and fixed defects is carried out. The analysis of key costs has shown that the most costly is the process of identifying internal defects and their correction. At that, the main problems arise with one of the most semi-polar medicines - ibuprofen, which has a number of advantages: low price, availability, analgesic and antipyretic effect, with practically no contraindications and no special side effects. The costs of its production for the last three years in comparison with the total costs of the enterprise are the highest. The main types of defects in the production of pharmaceuticals are determined. Consideration of statistical data and reports of the enterprise on quality indicators of products for this period showed that 74% of defects is cracking. The cost of each of the identified types of defects of finished products and ibuprofen, in particular, was determined. The approximate economic calculation of ibuprofen production at the Company was also carried out.

On numerical and approximate analytical modeling of single- and two-photon Young's experiment using the photon coordinate wave function

In modern areas of photonics, the physical description of the interaction of photons with matter in the control, transmission and registration of single-photon and two-photon states implemented in practice is of great importance. An appropriate acceptable description may be faced with the need to take into account various kinds of interference effects associated with these states. Meanwhile, even the most “simple” case of single-photon interference in Young's experiment requires the use of a rather complex apparatus of quantum electrodynamics. This article explains one- and two-photon interference in Young's thought experiment based on the photon wave function (PWF) in coordinate representation. This explanation is illustrated by two examples of wavelengths: 10.6 μm and 1.5 cm. For both examples, two approaches to PWF modeling are used: “purely quantum-mechanical” and “quasi-classical”. In the first approach, a 6-component coordinate PWF is constructed using a spherically symmetric momentum distribution in a wave packet, followed by numerical and approximate analytical calculations. In the second approach, a one-component “quasi-classical” PWF is constructed, which corresponds to either electric dipole radiation or simulated spherically symmetric radiation. In all cases, the same pronounced interference pattern was obtained, which allows us to conclude that not only the quantum-mechanical coordinate PWF is able to explain the phenomena of one- and two-photon interference, but also a much simpler “quasi-classical” PWF. This conclusion sheds light on the theoretical interpretation of the measurement of the coordinate PWF in some recent experiments.

Some Applications of Taylor’s Formula in Approximate Calculations of Quantum Mechanics

Some Applications of Taylor’s Formula in Approximate Calculations of Quantum Mechanics

Quality indicators of roots and tubers stored in the storage facilities

From the technological point of view, it is shown in detail that, how to maintain storage conditions under moderate conditions and the possibility of extending shelf life with less waste and consists of approximate calculations and often does not correspond to practice. To determine the storage method in more detail, firstly a test was conducted on the storages methods tests. Only after the basic technological characteristics of a given storage method have been developed can a conclusion be drawn about its suitability for the task at hand. For example, if you plan to store potatoes or carrots until May-June, you should prepare a refrigerator. If the storage period is set until January, then warehouse with natural ventilation or cooling with outside air using a fan is sufficient.

Primena tehnika vizuelizacije strujanja za određivanje sile otpora projektila

The paper provides an overview of flow visualization methods. From the many ways of classifying flow visualization methods, the chosen method of classification is in accordance with the experimental procedure. Flow visualization methods that involve the addition of foreign material are the simplest, from the point of view of the required material and the experimental setup, in which one tracer and an adequate light source are most often applied, except for layers sensitive to pressure and shear stress. Their application is wide and most methods from this category can be modified very easily depending on the case. Visualization methods that involve addition of energy to the fluid flow use strong sources of electromagnetic radiation, most often lasers, to excite the molecules in the fluid stream, producing an adequate quantum-mechanical effect that enables visualization. Optical methods of flow visualization are based on changes in the refractive index of light caused by the presence of a fluid in motion in the test section, in addition, the principle of superposition of light waves is used in interferometry methods. Optical methods are mainly used in areas of supersonic flow and shock wave studies, but they are also present in exhaust gas propagation studies. As computational fluid dynamics is a separate subject, the physical laws on which CFD is based on are presented, as well as an example of flow visualization, which is an integral part of most calculations performed using this method. In addition to the classification and description of flow visualization methods, the paper provides an explanation of a approximate calculation procedure based on the use of one of the optical methods, Schlieren photography, in order to calculate the resistance force during supersonic projectile flow, as well as a comparison of results based on empirical data.

Comparative analysis of the approximation of a probabilistic indicator of functional stability using Bernstein polynomials and feed­forward neural networks

The use of multi-machine information systems is becoming an increasingly popular component of a wide variety of fields of activity. The increase in the number of problems solved through information systems and the increase in their complexity makes the study of the functional stability of the systems under consideration increasingly relevant. The functional stability of an information system is understood as the ability of this system to perform specified functions under the influence of negative influences. At the moment, a number of indicators have been developed to evaluate functional stability numerically. One such indicator is the convolution of the connectivity matrix. Convolution of the connectivity matrix, despite its completeness, has one very significant drawback: its calculation is a rather complicated procedure. Based on this, the question of approximate calculation of this indicator is logical. Since the convolution of the connectivity matrix can be considered as a function of the probability of serviceability of communication lines, an attempt to use certain methods of approximation theory is obvious. At the moment, methods of approximation theory are quite developed. Some of these methods are quite well researched, while others are just gaining popularity. The first group includes Lagrange interpolation polynomials, Legendre polynomials, Bernstein polynomials, splines, partial sums of series, etc., and the second group includes machine learning models, including feedforward neural networks, regression models, and others. Accordingly, the question immediately arises: which of these methods would allow better approximation of the convolution of the connectivity matrix and under what conditions? This paper provides a comparative analysis of the quality of approximation of the functional connectivity indicator of an information system based on the convolution of the connectivity matrix of this system using often considered feed-forward neural networks and using Bernstein polynomials, which, unfortunately, are not often considered despite their remarkable properties. The specifics of using each of these methods when approaching are also demonstrated and, based on this, it is indicated when which of these methods is better to use.

Optimal cubature formulas for approximate integrals of functions defined on a sphere in three-dimensional space

The development of effective methods of approximate calculation of integrals using optimal cubature formulas and optimal quadrature formulas with trigonometric weights for defined functions on a sphere, the creation of new algorithms for approximate calculation of trigonometric weighted integrals in different classes of functions, as well as the assessment of their errors, is the goal of this work.

Approximate calculation of static mass analyzers based on two-dimensional fields

The concurrent utilization of electric and magnetic fields in static mass analyzers proves highly effective in sparticle separation solely based on their masses, thereby ensuring remarkable analytical capabilities. High-resolution mass analyzers employ an achromatizing electrostatic system to precisely focus ion radiation by energy. Devices featuring zero energy dispersion are created through the collaborative action of electric achromatizing systems and the magnetic field within the analyzer, resulting in ion separation based solely on mass. Expanding the ion beam prior to its magnetic field exposure enhances the overall quality of static mass analyzers. This article delves into a static mass analyzer with dual ion beam focusing, elucidating the ion acceleration and deceleration processes at electrode boundaries, their focalization via a transaxial lens, and the impact of the electrostatic prism's refractive surface on the mass analyzer's "quality" parameter. Additionally, the transition from a sector homogeneous magnetic field to the fields generated by a two-dimensional magnetic prism and a three-electrode transaxial focusing lens is explored to augment the mass analyzer's linear dispersion. To refine ion beam focus pre-magnetic field entry, the proposed adoption of a two-dimensional electrostatic prism promises heightened linear dispersion in the mass analyzer while expanding the beam pre-magnetic field entry. This study also examines the impact of a two-dimensional electric prism on the charged particle beam, presenting an approximate expression for its angular energy dispersion. It is demonstrated that a prism-based mass analyzer integrating two-dimensional electric and magnetic prisms enables energy-focused operations alongside enhanced linear dispersion and reduced linear dimensions.

Study of the Stability of the Mathematical Model of the Bound Pendulums Motion

The article presents a study of the dynamics of an oscillatory dissipative system of two elastically coupled pendulums in a magnetic field. Nonlinear normal modes of oscillation of a pendulum system have been studied, taking into account the resistance to the medium and the damping moment created by the elastic element. A system with two degrees of freedom is considered, in which the masses of the pendulums differ significantly, which leads to the possibility of localization of oscillations. In the following study, the mass ratio is chosen as a small parameter. For approximate calculations of magnetic forces, the Padé approximation is used, which best satisfies the experimental data. This approximation provides a very accurate description of the magnetic excitation. The presence of external influences in the form of magnetic forces and various types of loads that exist in many engineering systems significantly complicates the analysis of vibration modes of nonlinear systems. Studies have been carried out of nonlinear normal modes of oscillations in this system, one of the modes being a coupled mode, and the second being a localized mode. The oscillation modes are constructed using the multiscale method. Both regular and complex behavior when changing system parameters have been studied. The influence of these parameters was studied for small and large initial angles of inclination of the pendulum. Analytical solution based on the fourth order Runge-Kutta method compared with numerical simulation results. The initial conditions for calculating the vibration modes were determined by the analytical solution. Numerical modeling, consisting of constructing phase diagrams, trajectories in configuration space, and amplitude-frequency characteristics, allows one to evaluate the dynamics of a system, which can be either regular or complex. The stability of oscillation modes was studied using numerical analysis tests, which are implementations of the Lyapunov stability criterion. In this case, the stability of the oscillation modes is determined by assessing the orthogonal deviations of the corresponding trajectories of the oscillation modes in the configuration space.

ПРОБЛЕМЫ УЧЕТА ПОСТПЕНИТЕНЦИАРНОГО РЕЦИДИВА

The article deals with one of the problems of modern criminology: the lack of a mechanism for accounting for post-penitentiary recidivism. The paper gives the concepts of post-penitentiary recidivism and post-penitentiary criminality. Analyzing official statistical data, the author concludes that they are insufficient for calculating the scale of post-penitentiary crime and analyzing its characteristics. Modern accounting systems are compared with the Soviet system of special accounting of post-penitentiary recidivism, built on a dynamic model. This provided much more information for calculating real indicators of post-penitentiary recidivism. In Russia, statistics mixes several subtypes of criminological recidivism: penological, post-penological, penitentiary and post-penitentiary recidivism. As a result, there are fewer opportunities to study the causes and factors that provoke each of these types of recidivism. Opportunities to develop an effective system of recidivism prevention are diminished. In addition, the terminology used by different accounting entities differs. Therefore, there is no possibility to study the real scale of both criminal (legal) and subtypes of criminological recidivism (including post-penitentiary). The article offers approximate calculations of the level of post-penitentiary recidivism on the basis of available statistical data. In conclusion, the author’s proposals for improving the systems of recording recidivism are formulated.

Using leave-one-out cross validation (LOO) in a multilevel regression and poststratification (MRP) workflow: A cautionary tale.

In recent decades, multilevel regression and poststratification (MRP) has surged in popularity for population inference. However, the validity of the estimates can depend on details of the model, and there is currently little research on validation. We explore how leave-one-out cross validation (LOO) can be used to compare Bayesian models for MRP. We investigate two approximate calculations of LOO: Pareto smoothed importance sampling (PSIS-LOO) and a survey-weighted alternative (WTD-PSIS-LOO). Using two simulation designs, we examine how accurately these two criteria recover the correct ordering of model goodness at predicting population and small-area estimands. Focusing first on variable selection, we find that neither PSIS-LOO nor WTD-PSIS-LOO correctly recovers the models' order for an MRP population estimand, although both criteria correctly identify the best and worst model. When considering small-area estimation, the best model differs for different small areas, highlighting the complexity of MRP validation. When considering different priors, the models' order seems slightly better at smaller-area levels. These findings suggest that, while not terrible, PSIS-LOO-based ranking techniques may not be suitable to evaluate MRP as a method. We suggest this is due to the aggregation stage of MRP, where individual-level prediction errors average out. We validate these results by applying to the real world National Health and Nutrition Examination Survey (NHANES) data in the United States. Altogether, these results show that PSIS-LOO-based model validation tools need to be used with caution and might not convey the full story when validating MRP as a method.

Estimating the Cardinality of Queries Based on a Sample from a Full Outer Join of Tables

Cardinality estimation (CardEst) plays an important role in creating high-quality query execution plans in the DBMS. In the last decade, a large number of methods have been developed: traditional methods (histograms, samples), machine learning methods based on queries or data. But all of them are based on different restrictions and assumptions, and the cardinality estimation with their help worsens with an increase in the number of joined tables. The article proposes two new methods based on the theory of approximate calculation of aggregates and allowing to remove most of the restrictions. Method 1 fetches blocks after executing the subqueries of the original query and does not require a preliminary analysis of the filter conditions. The condition for joining tables can be arbitrary (not necessarily the equality of attributes). Method 2 allows you to calculate the probabilities of reading blocks based on the metadata accumulated in the process of populating the database. Metadata takes up little memory, and the overhead of maintaining it is low. Method 2, in contrast to method 1, takes into account the true cardinality of the connection of neighboring blocks in the sample obtained from metadata. Therefore, the prospect opens up for a more accurate assessment of the cardinality of joining a large number of tables. Method 1 (EVACAR method) is implemented and compared with modern machine learning methods BayesCard, DeepDB, FLAT on a special STATS test. The results of the experiments confirmed the effectiveness of the EVACAR method. The EVACAR method is more accurate or its maximum q-error is comparable to machine learning methods for 75-88 % of evaluated queries (subplans). In the future, it is planned to implement the 2nd method for assessing the cardinality of queries.

Insight on Gaussian Basis Set Truncation Errors in Weak to Intermediate Magnetic Fields with an Approximate Hamiltonian.

Strong magnetic fields such as those found on white dwarfs have significant effects on the electronic structures of atoms and molecules. However, the vast majority of molecular studies in the literature in such fields are carried out with Gaussian basis sets designed for zero field, leading to large basis set truncation errors [Lehtola et al., Mol. Phys. 2020, 118, e1597989]. In this work, we aim to identify the failures of the Gaussian basis sets in atomic calculations to guide the design of new basis sets for strong magnetic fields. We achieve this by performing fully numerical electronic structure calculations at the complete basis set (CBS) limit for the ground state and low lying excited states of the atoms 1 ≤ Z ≤ 18 in weak to intermediate magnetic fields. We also carry out finite-field calculations for a variety of Gaussian basis sets, introducing a real-orbital approximation for the magnetic-field Hamiltonian. Our primary focus is on the aug-cc-pVTZ basis set, which has been used in many works in the literature. A study of the differences in total energies of the fully numerical CBS limit calculations and the approximate Gaussian basis calculations is carried out to provide insight into basis set truncation errors. Examining a variety of states over the range of magnetic field strengths from B = 0 to B = 0.6B0, we observe significant differences for the aug-cc-pVTZ basis set, while much smaller errors are afforded by the benchmark-quality AHGBSP3-9 basis set [Lehtola, J. Chem. Phys. 2020, 152, 134108]. This suggests that there is considerable room to improve Gaussian basis sets for calculations at finite magnetic fields.

Calculation of the results of basic arithmetic operations with quaternions defined in the interval form

The goal of the work. Creation of an EXCEL-oriented calculator for determining the results of basic arithmetic operations with quaternions, which are given by hyperbolic interval numbers. The subject of research is the set of quaternions and arithmetic operations defined on this set. Research method: Algorithmic and numerical analysis of procedures for performing basic arithmetic operations with quaternions given by hyperbolic interval numbers. The obtained results. The definition of a quaternion, the coefficients of which are interval numbers, is given. It was obtained the ratios for determining in the interval form the following characteristics: quaternion norm, quaternion modulus, quaternion vector part modulus, quaternion argument, quaternion sign was obtained. It was obtained the ratios for determining in the interval form the following basic arithmetic operations: sum of quaternions, difference of quaternions, multiplication of a constant value by a quaternion, scalar product of quaternions, product of vector parts of quaternions, product of quaternions, vector product of quaternions, left and right division of quaternions. The ratio for calculating the determinants of the second order, the elements of which are defined in the interval form, is obtained. The ratio for the approximate calculation of determinants of arbitrary order, the elements of which are defined in the interval form, is obtained. It is shown that the operations of multiplication (division) of interval numbers and raising them to an integer power are expedient to perform when they have a hyperbolic form. It is advisable to perform the addition (subtraction) operation with interval numbers given in the classic form or in the CENTER-RADIUS system. It is better to use the last form in the case of determining the coefficients of the quaternions based on the results of technological calculations. Screenshots of the formulas for determining the vector product of quaternions are given, provided that the coefficients at their orths are represented by interval numbers.