Approximate Calculation Research Articles

Shear viscosity and electrical conductivity of the relativistic fluid in the presence of a magnetic field: A massless case

We have explored the shear viscosity and electrical conductivity calculations for bosonic and fermionic media, without and with presence of an external magnetic field. For numerical visualisation, we have dealt with their simplified massless expressions. In the presence of a magnetic field, five independent velocity gradient tensors can be designed, and so their corresponding proportional coefficients, connected with the viscous stress tensor, provide us five components of the shear viscosity coefficient. In the existing literature, two sets of viscous stress tensors are available. Starting from them, the present work has obtained expressions for two sets of five shear viscosity coefficients, which can be ultimately classified into three basic components – parallel, perpendicular and Hall components as one get similar expression for the electrical conductivity at the finite magnetic field. Our calculations are based on the kinetic theory approach in relaxation time approximation. Repeating the same mathematical steps under finite magnetic field, which is traditionally practiced in the absence of magnetic field, we have obtained two sets of five shear viscosity components, whose final expressions are in good agreements with earlier references, although a difference in methodology or steps can be noticed. In this context, the present work, for the first time, addresses a detailed calculation of relaxation time approximation (RTA)-based kinetic theory calculations of the second set of five shear viscosity components, which was previously done by Denicol et al (Phys. Rev. D 98, 076009 (2018)) in moment method technique. Realising the massless results of viscosity and conductivity for Maxwell–Boltzmann, Fermi–Dirac and Bose–Einstein distribution functions, we have applied them for massless quark gluon plasma and hadronic matter phases, which can provide us a rough order of strength, within which actual results will vary during quark–hadron phase transition. The present work also indicates that the magnetic field might have some role in building perfect fluid nature in RHIC or LHC matter. The lower bound expectation of shear viscosity to entropy density ratio is also discussed. Here, for the first time, we are addressing an analytic expression of temperature- and magnetic field-dependent relaxation time of the massless fluid, for which perpendicular component of shear viscosity to entropy density ratio can reach its lower bound.

Realizing of cross-polarization conversion for linearly polarized waves in multiband by orthotropic metasurface

A multiband reflective linear-polarization (LP) converter based on an anisotropic metasurface is proposed. The unit cell of the metasurface is composed of a hollow oval sheet and a rectangle patch. Simulation results show that the converter can convert LP wave to its orthogonal state and the polarization conversion ratio (PCR) is above 90% in four frequency bands (4.60–12.27 GHz, 13.79–13.90 GHz, 14.61–14.69 GHz, 15.44–15.52 GHz). Interestingly, the relative bandwidth of first band reaches up to 90.9%, which is even broader than most single-band polarization conversion metasurfaces. Furthermore, we analyze the physical mechanism of polarization conversion of the metasurface, and simplify the derived formulas to make approximate calculations for co- and cross-polarization coefficients. The proposed formulas have better applicability than the equations in previous work. The laboratory sample is fabricated, and we have experimentally characterized our idea in microwave region. This design can advance applications in microwave sensors and mm-wave systems.

Approximate formulas for the evaluation of the mathematical expectation of functionals from the solution to the linear Skorohod equation

This paper is devoted to the construction of approximate formulas for calculating the mathematical expectation of nonlinear functionals from the solution to the linear Skorohod stochastic differential equation with a random initial condition. To calculate the mathematical expectations of nonlinear functionals from random processes, functional analogs of quadrature formulas have been developed, based on the requirement of their accuracy for functional polynomials of a given degree. Most often, formulas are constructed that are exact for polynomials of the third degree [1–9], which are used to obtain an initial approximation and in combination with approximations of the original random process. In the latter case, they are usually also exact for polynomials of a given degree and are called compound formulas. However, in the case of processes specified in the form of compound functions from other random processes the constructed functional quadrature formulas, as a rule, have great computational complexity and cannot be used for computer implementation. This is exactly what happens in the case of functionals from the solutions of stochastic equations. In [1, 2], the approaches to solving this problem were considered for some types of Ito equations in martingales. The solution of the problem is simplified in the cases when the solution of the stochastic equation is found in explicit form: the corresponding approximations were obtained in the cases of the linear equations of Ito, Ito – Levy and Skorohod in [3–11]. In [7, 8, 11], functional quadrature formulas were constructed that are exact for the approximations of the expansions of the solutions in terms of orthonormal functional polynomials and in terms of multiple stochastic integrals. This work is devoted to the approximate calculation of the mathematical expectations of nonlinear functionals from the solution of the linear Skorokhod equation with a leading Wiener process and a random initial condition. A new approach to the construction of quadrature formulas, exact for functional polynomials of the third degree, based on the use of multiple Stieltjes integrals over functions of bounded variation in the sense of Hardy – Krause, is proposed. A composite approximate formula is also constructed, which is exact for second-order functional polynomials, converging to the exact expectation value, based on a combination of the obtained quadrature formula and an approximation of the leading Wiener process. The test examples illustrating the application of the obtained formulas are considered.

Customer segment transition through the customer loyalty program

PurposeThis study presents the applicability of a model-based approach for loyalty program forecasting using smartphone app in the digital strategy of the retail industry.Design/methodology/approachThe authors develop a dynamic model with the cyclical structure of customer segments through customer experience. They use time-series data on the number of members of the loyalty program, “Seven Mile Program” and confirm the validity of the approximate calculation of customer segment share, customer segment sales share and aggregate sales performance. The authors present three medium-term forecast scenarios after the launch of a smartphone payment service linked with the loyalty program.FindingsThe sum of the two customer segment shares for forecasting (the sum of the quasi-excellent and excellent customer ratios) is about 30% in each scenario, consistent with an essential customer loyalty (true loyalty) share obtained in the existing empirical study.Research limitations/implicationsDigital strategy in the retail industry should focus more on estimating and forecasting average amounts of customer segments and the number of aggregated customers through the digitalization on the customer side than on individual customer journeys and responses.Practical implicationsMulti-scenario evaluation through simulation of dynamic models from a systemic view can be used for decision-making in retailing digital strategies.Originality/valueThis study builds a model that integrates the cyclicality of customer segment transition through customer experiences into a loyalty matrix framework, which is a method that has previously been used in the hospitality industry.

Computational Estimation and Mathematics Education: A Narrative Literature Review

Computational estimation, typically construed as an approximate mental calculation of an arithmetical problem, is an important skill in everyday life and a wide range of professional contexts. Despite its importance, textbooks and curricula address it inadequately, with the consequence that many teachers are uncertain as to why and how they should teach it. In this paper, we present a narrative literature review that brings together the extensive research of the cognitive psychologists and the limited research of the mathematics educators to clarify the nature of computational estimation and its development. Focused initially on the strategies used in computational estimation before turning to children’s and adults’ computational estimation competence, the review shows that computational estimation, which develops over time, draws on a wide range of strategies reciprocally dependent on a secure understanding of numbers and arithmetic. It shows that the poor estimation competence of children and adults’ is susceptible to interventions, particularly with respect to addressing a common misconception that the purpose of computational estimation is the mental calculation of exact solutions.

EXACT ANALYTICAL AND APPROXIMATE ASYMPTOTIC CALCULATION METHODS TO DETERMINE THREE-DIMENSIONAL ELECTROMAGNETIC FIELD NEAR CONDUCTING BODY WITH FLAT SURFACE

The analytical solution of the three-dimensional quasi-stationary electromagnetic field problem for a current located near conducting body with a flat surface is considered. The exact and approximate solution of the problem is presented. The exact solution has no restrictions on the external field configuration, physical properties of the medium, and frequency. The approximate solution is based on an expansion in asymptotic series and has limitations: for sinusoidal field, the solution is limited to frequencies above the lower limit; for pulsed field, the solution is limited by the initial time interval of the current pulse. Based on comparison of the results of exact and approximate calculations for nonuniform sinusoidal field at the interface between the media, the admissible value of the introduced small parameter is determined. For pulsed field the proposed choice of the limited time interval for calculating electomagnetic field using the asymptotic method is justified. References 29, figures 7.

Precision Temperature Control for the Laser Gyro Inertial Navigation System in Long-Endurance Marine Navigation.

In the Ring Laser Gyro Inertial Navigation System (RLG INS), the temperature characteristics of the accelerometer can directly influence the measurement results. In order to improve navigation accuracy in long-endurance marine navigation, the operating temperature of the accelerometer should be precisely controlled. Based on thermal studies on the accelerometer, temperature control precision should be better than 0.01 °C to achieve 1 × 10−5 m/s2 output accuracy of the accelerometer. However, this conclusion is obtained by approximate calculations and cannot be directly applied to different inertial navigation systems. In order to verify this thermal conclusion and broaden its application, the Back Propagation Neural Network (BP-NN) algorithm is adopted to validate the feasibility of temperature control in this paper. In addition, a multi-level temperature control system is also set up and carefully designed to support the validation and experiments under different conditions. Test results of the temperature control system prove that operating temperature variation can be reduced to 0.01 °C. Meanwhile, the standard deviation per hundred seconds of the accelerometer outputs, after temperature control, reaches 1 × 10−5 m/s2. Static altitude and navigation results were improved by 41.97% and 62.91%, respectively, with the precision temperature control system, which meets the long-endurance marine navigation requirements.

Design of ALU based on Majority Logic for Low Power Applications

Approximate calculations are a new nanotechnology paradigm for improving efficiency and reducing energy use. Most of the logic extends to many contemporary nanotechnological developments and is used for the design of digital circuits in its basic portion (3 input plurality, MV). This paper suggests implementations of additional compressors and ML multiplicators. An additional bit discovery circuit is used for the proposed compressors. The size of the multiplier is calculated by a control factor for the importance of different extra bits. The designs proposed are tested with hardware (for example, time frame and port complexity) as well as with error calculation. These designs have superior performance in terms of area and delay. The validity of the proposed designs is also shown by case tests of the error resistance implementation.

ABOUT CHOOSING THE METHOD OF EXACT APPROXIMATIONS OF DISCRETE STATISTICS PROBABILITY DISTRIBUTIONS

In the paper, we consider the methods of exact approximations of statistics probabilities distribution. As the exact approximations, we consider ∆-exact distributions. The difference between the ∆-exact distributions and the exact approximations does not exceed a predefined arbitrary small value ∆ that defines the accuracy of the approximations. Besides, we consider the methods of the first and second multiplicity, which use statistic characteristics of samples. The first multiplicity method is based on the properties of the components of the first multiplicity vector, which are nonnegative integer solutions of a linear equation. The linear equation relates the alphabet sign frequency and the sample size. The second multiplicity method is based on the solution of a system of linear equations. The linear equations of the system relate the sample size and the alphabet cardinality with the number of the alphabet signs that have equal frequency in the sample. For the considered methods of exact approximations, we give expressions to estimate the computational complexity of exact approximations of distributions for any sample parameters. To provide the approximations accuracy of 10–5, and the computing resource with the performance of 1018 operations per second, we calculated the sample parameters. For these samples, we can calculate the exact approximations of distributions, using the considered methods, the available computing resource, and the declared accuracy. We formed the parameter regions for the samples, and the exact approximations of distributions can be calculated for these samples with the help of various methods. We compared the regions themselves and with the so-called region of uncertainty, which is limited from above not more than 5-fold excess of the sample size over the alphabet cardinality. On the base of the comparison of the parameter regions of the samples, which are suitable for calculation of the exact approximations of the distributions, we compared their calculation methods. It is shown that owing to the second multiplicity method, we can make calculations for all values of the alphabet cardinality from 2 to 256. In contrast to the second multiplicity method, the first multiplicity method does not allow calculations for the alphabet cardinality over 73. The parameter region of the samples, which are suitable for calculation of the limit approximations of the distributions by the second multiplicity method, contains the complete parameter region of the samples, suitable for calculation of the limit approximations of the distributions by the first multiplicity method, and exceeds it more than in 52 times. Owing to the comparison of the methods of exact approximations, it is proved that if we have the same computing resource, we can calculate the exact approximations with the help of the second multiplicity method for a greater number of samples with the increased parameters in comparison with the first multiplicity method. Hence, to calculate the exact approximations of statistics probability distributions, we choose the second multiplicity method. Practical significance of the research is possibility of calculation of the maximal values of the sample parameters. The current technological level of computer systems allows calculation of the exact approximations of the distributions for these values, which provide the minimal loss of criteria efficiency in comparison with the limit approximations used for the sample parameters. The scientific novelty of the research is the comparative analysis of the methods of exact approximations of distributions for calculation of distributions for the sample parameters, which do not allow calculation of the exact distributions due to their high computational complexity.

КОЛИВАННЯ ІМПУЛЬСНО НАВАНТАЖЕНОГО ОСЦИЛЯТОРА ЗІ СТЕПЕНЕВИМ ПОЗИЦІЙНИМ ТЕРТЯМ

Nonstationary oscillations of the oscillator with nonlinear positional friction caused by an instantaneous force pulse are described. The power dependence of the positional friction force on the displacement of the system, which generalizes the known models, is accepted. The corresponding dynamics problems were solved precisely by the method of adding and approximated by the method of energy balance. In the study, using periodic Ateb-functions, an exact analytical solution of the nonlinear differential equation of motion was constructed. Compact formulas for calculating oscillation ranges and half-cycle durations are derived. It is shown that the decrease in the amplitude of oscillations, as well as under the action of the force of linear viscous resistance, follows the law of geometric progression. The denominator of the progression is less than one and depends on the positional friction constants, in particular on the nonlinearity index. Thus, we have not only a decrease in the amplitude of oscillations, but also an increase in the durations of half-cycles, which is characteristic of nonlinear systems with a rigid force characteristic. Approximate displacement calculations use Pade-type approximations for periodic Ateb-functions. The error of these approximations is less than one percent. From the obtained analytical relations, as separate cases, the known dependences covered in the theory of oscillations for linear positional friction follow. It is shown that even in the case of nonlinear positional friction the process of oscillations caused by an instantaneous momentum has many oscillations and is not limited in time. In the case of power positional friction, the oscillation ranges of the pulse-loaded oscillator can be calculated by elementary formulas. The calculation of displacements in time is associated with the use of periodic Ateb-functions, the values of which are not difficult to determine by known asymptotic formulas. Calculations confirm that the obtained approximate formula does not give large errors. In order to verify the adequacy of the obtained analytical solutions, numerical computer integration of the original nonlinear differential equation of motion was performed. The results of the calculation, which lead to analytical and numerical solutions of the Cauchy problem, are well matched.

СОВРЕМЕННЫЕ ТЕНДЕНЦИИ РАЗВИТИЯ СКЛАДСКОЙ ЛОГИСТИКИ С УЧЕТОМ ПРИМЕНЕНИЯ ДРОНОВ

This article discusses the trend of using drones in various fields of application, in particular, the use of drones (quadcopters) in warehouse logistics. Today, this area of logistics is actively developing, the article provides a brief analysis of the development of the sphere in Russia and the world. An approximate calculation of the inventory speed using a quadcopter was made and an analysis of the solutions on the market was carried out. The article provides a short list of companies that either sell ready-made systems for inventory, or are working on new solutions in this area. In the article, a brief conclusion of this solution is made and an example of the further development of data in general is given, in particular, an example of the implementation of this system for integration into an existing warehouse system is considered, the main advantages of this solution are highlighted. An example of the technical implementation of a drone for performing tasks is given, as well as an example of such software for performing an autonomous flight operation inside a warehouse. Key words: quadrocopters, drone, inventory, warehouse, logistics.

Some applications of the GRAN1 to analyze two-dimensional continuous probability distributions

The article considers the use of GRAN1 software in the analysis of two-dimensional continuous probability distributions. The learning process can be provided by freely distributable software, through the use of cloud technologies, in particular software from the GRAN package. However, the use of any technology in the educational process, including modern information and communication technologies, as well as the content of education, must be pedagogically balanced, which will avoid any negative consequences for the formation of the future member of society, his mental and physical development. Attention is drawn to the fact that children are increasingly looking for entertainment, using mobile devices, sharing new products with their peers and spending time together, playing a variety of online games, and parents cannot control this process. At the same time, teachers conduct lessons using mobile devices to draw attention to the subject, they are teaching. In the process of using computer technology, students can form a special type of thinking, the so-called “clip consciousness”, which leads to fragmentary thinking and the irreversibility of changes in consciousness. Therefore, the problem of excessive use of mobile devices by children requires constant analysis and coverage. The article discusses some examples of using the GRAN1 software to solve problems in probability theory. Examples of approximate calculation of the value of the double integral are given. Tables of values of the corresponding integrals are described. The use of modern information and communication technologies during mathematics lessons is considered.

Approximate calculation of the Caputo-type fractional derivative from inaccurate data. Dynamical approach

Abstract A specific formulation of the “classical” problem of mathematical analysis is considered. This is the problem of calculating the derivative of a function. The purpose of this work is to construct an algorithm for the approximate calculation of the Caputo-type fractional derivative based on the methods of control theory. The input data of the algorithm is represented by inaccurate measured function values at discrete, frequently enough, times. The proposed algorithm is based on two aspects: a local modification of the Tikhonov regularization method from the theory of ill-posed problems and the Krasovskii extremal shift method from the guaranteed control theory, both of which ensure the stability to informational noises and computational errors. Numerical experiments were carried out to illustrate the operation of the algorithm.

Uji Validitas Dan Relibilitas Instrumen Pengukuran Implementasi E-Learning Terhadap Kepuasan Pengguna Pada Masa Pandemi COVID 19 Di Lingkungan Politeknik Negeri Banjarmasin

Implementation of online learning requires adequate preparation and support of resources, first is the software or tools used in online lectures, where Poliban has e-learning that can be used or can use other tools. Both hardware or computer equipment with the required specifications, one of which is a camera used for video conferencing, and what is very important is a stable internet network connection. Therefore, if at least these three things can be fulfilled, then online lectures can be carried out well. However, in reality, there are several problems faced by both lecturers and students, especially related to the unstable internet network signal, so that the implementation of online lectures cannot run optimally. To find out the problems faced by users, a measurement instrument for the implementation of E-learning on user satisfaction is needed. In making a good instrument model, a test is needed to ensure that the indicators used in the instrument used are valid and reliable and have a good level of reliability.
 Based on the problems mentioned above, this research will conduct instrument testing using validity tests and reliability tests where in the analysis process a Partial Least Square (PLS) application framework is used in SEM which is a statistical model that provides an approximate calculation of strength. hypothetical relationships among variables in a theoretical model
 The results of the research that have been carried out show that the results of the validity test of the instrument for measuring the implementation of e-learning on user satisfaction at the Banjarmasin state polytechnic get a loading factor value above 0.5 on the intended construct, these results indicate that the indicators used in this study are valid. or has met convergent validity, then based on the reliability test it shows that the composite reliability value for all constructs is above 0.7 which indicates that all constructs in the estimated model meet the criteria for discriminant validity. The lowest composite reliability value is 0.837 in the System Quality construct, this shows that the test instrument shows a good level of reliability, or in other words, the questionnaire results can be trusted.

Mechanical Behavior of Damaged H-Section Steel Structure

Steel structures are usually damaged by disasters. According to the influence law of the damage on the elastic modulus of steel obtained by the mechanical test of damaged steel, the average elastic moduli of H-section steel members were analyzed. The equations for calculating the average elastic moduli of damaged H-section steel members at different damage degrees were obtained. By using the analytical cross-sectional method, the cross-sectional M-Φ-P relationships and the dimensionless parameter equations of the H-sections in the full-sectional elastic distribution, single-sided plastic distribution, and double-sided plastic distribution were derived. On the basis of the cross-sectional M-Φ-P relationships and dimensionless parameters of actual steel members, the approximate calculation equations for the damaged cross sections were obtained. The Newmark method was used to analyze the deformation of damaged steel columns. Analytical results show good agreement with the test results. The equations and methods proposed in this study have high computational accuracy, and these can be applied to the cross-sectional M-Φ-P relationships and deformation calculation of damaged steel members.

Approximate Calculation Method for Noncentral t-Distribution Quantile

In the process of structural design and structural performance evaluation, the inference of the reliable life of the structure and the representative value of the material strength is a necessary work. The determination of material strength is the presumption of the quantile of the normal distribution, and the determination of the confidence level of the quantile of the normal distribution involves the noncentral t-distribution function. However, the calculation of the quantile is very complicated and is often provided in the form of a numerical table, which often involves multiparameter interpolation calculation, so it is not convenient to apply. The existing approximate calculation methods for noncentral t-distribution quantiles have strict application conditions, and the calculation process is relatively cumbersome. It is still difficult to meet actual needs in terms of fitting accuracy, application range, and convenience. In this paper, a new calculation method for noncentral t-distribution quantiles is proposed by introducing new probability expressions and related approximate distributions, based on theoretical derivation and numerical fitting. The comparative analysis results show that the method not only is convenient for calculation but also has the advantages of higher accuracy and wider application range, and it is more in line with the actual needs of engineering.

MEASUREMENT OF DISTANCE BETWEEN REGULAR EVENTS FOR MULTITAPE AUTOMATA BASED ON A NEW CHARACTERIZATION OF EQUIVALENCE CLASSES

In this paper several problems related to the implementation of the method for the approximate calculation of distance between regular events for multitape finite automata are considered and resolved. An algorithm of matching for the considered regular expressions is suggested and results of the algorithm application to some specific regular expressions are adduced. The proposed method can be used not only for the mentioned implementation, but also separately.

Approximate calculation of 8-point DCT for various scenarios of practical applications

In this paper, based on the parametric model of the matrix of discrete cosine transform (DCT), and using an exhaustive search of the parameters’ space, we seek for the best approximations of 8-point DCT at the given computational complexities by taking into account three different scenarios of practical usage. The possible parameter values are selected in such a way that the resulting transforms are only multiplierless approximations, i.e., only additions and bit-shift operations are required. The considered usage scenarios include such cases where approximation of DCT is used: (i) at the data compression stage, (ii) at the decompression stage, and (iii) both at the compression and decompression stages. The obtained results in effectiveness of generated approximations are compared with results of popular known approximations of 8-point DCT of the same class (i.e., multiplierless approximations). In addition, we perform a series of experiments in lossy compression of natural images using popular JPEG standard. The obtained results are presented and discussed. It should be noted, that in the overwhelming number of cases the generated approximations are better than the known ones, e.g., in asymmetric scenarios even by more than 3 dB starting from entropy of 2 bits per pixel. In the last part of the paper, we investigate the possibility of hardware implementation of generated approximations in Field-Programmable Gate Array (FPGA) circuits. The results in the form of resource and energy consumption are presented and commented. The experiment outcomes confirm the assumption that the considered class of transformations is characterized by low resource utilization.

Ionization Balance in Low-Temperature Plasmas with Nanosized Dust

Ionization mechanisms in the low-temperature thermal plasma, which contains alkali metal atoms as ionizable component and nanosized dust grains, are studied. In such a plasma, electrons are captured by dust grains, because the work function of grains depends on their sizes, and the electron adsorption rate is more than the thermionic emission rate for nanosized grains. Accordingly, an increase of the dust grain number leads to a decrease in the volume ionization and recombination rates, because they depend on the number density of electrons. At the same time, the role of surface processes in the plasma ionization balance is increased, because the total grain surface is increased. The approximate calculation techniques for low and high grain number densities are proposed. The criterions for approximate calculations are specified.

Normal stress distribution of timber-concrete composite panels with an adhesive shear connection under thermal and humidity loadings

Humidity and temperature conditions have a substantial influence on the stresses and total deformation of timber-concrete composite panels, especially in terms of the high rigidity of the shear connection. In the present research, the normal stresses that resulted from the hygrothermal load of timber-concrete composite panels with an adhesive shear connection were analyzed. Three timber-concrete composite panel specimens were placed in controlled climate conditions. Strains in two orthogonal directions were measured. The stress distribution resulted from an approximate analytical calculation model. The results show that the highest stresses occurred near the shear connection. An increase in timber moisture content by 2.1% was predicted to result in exceeding the flexural tensile strength in the concrete perpendicular to the timber grain direction. At an outdoor temperature range, stresses influenced only by the temperature alone will possibly not cause a failure of timber or concrete. Under winter environmental conditions, the stress in timber can possibly reach 12% of the bending strength of the timber used.