Mathematical Calculation Method Research Articles

Analysis and Design of a High-Frequency Low-Profile Converter for Bendable Equipment

In this article, a 10-MHz low-profile converter for bendable equipment based on aircore inductor is proposed. The mathematical model and inductance calculation method of the bendable planar circular spiral coil under different bending situations is analyzed. An optimal design method of the T type matching network is depicted in detail which helps to guarantee soft-switching characteristics and high efficiency within the whole bending range by realizing weak inductive equivalent input impedance. A 32 V input, 9V/6.3 W output prototype is proposed in the laboratory and the experimental results verify the feasibility of the proposed optimal design methodology, the system efficiency can be improved by 4% than the traditional method.

Carrying Capacity of Land in Bali based on Ecological Footprint

In 2000-2010, based on data from the Population Census in Bali, the average population growth rate was 2.15% per year, this value was greater than the average population growth rate at the national level of 1.49% per year. The increasing number of population growth results in increased development. This causes an increase in the need for land to accommodate these development activities. The reduced availability of productive land because it is used for development facilities has resulted in reduced land carrying capacity in Bali. The purpose of this study was to analyze the value of the carrying capacity of land in Bali using the Ecological Footprint analysis approach. The research methodology is quantitative focusing on secondary data analysis, based on the mathematical calculation method developed by the Global Footprint Network, which has the term biocapacity which means supply and ecological footprint which means demand. After comparing biocapacity and ecological footprint, the results show that the carrying capacity of land in Bali is generally in deficit. Things that can be done to increase the carrying capacity of land are to reduce the rate of population growth, increase land productivity by intensifying agricultural land, and be wiser in carrying out land conversion in the future.

The Application of Probability Theory in Life

Probability theory is a mathematical calculation method that has been continuously summarized and refined in real life. Compared with other subjects, probability theory is more abstract and complicated, and it is relatively difficult for learners. However, this subject is the foundation in many fields, and has obvious guidance and application value in real life. Therefore, proficiency in probability theory is particularly important, which will lay a solid foundation for students to learn statistics. In practical teaching, teachers should actively cultivate students’ good probability and statistics thinking, so that students can better integrate their knowledge through the majors they have learned and apply them to daily life and work.

Numerical simulation of the influence of pillar strength on the internal synergy relationship in the backfill‐pillar system

AbstractThe influence of the strength of the pillar on the bearing characteristics of the backfill‐pillar system (BPS) based on the mechanism of backfill. Quantitative synergy relationships between backfill and pillar were defined and pointed out. There are four kinds of quantitative synergy relationships in the bearing process of the system. To verify the relationship, systems with different strengths of the pillar were selected to carry out numerical simulation experiments, and a mathematical calculation method to quantify synergy relationship in the BPS was designed. The results show that the system under the low strength of the pillar presents the overall increase in bearing characteristics, while the system under the high strength of the pillar presents “N”‐type bearing features. Four kinds of quantitative synergy relationships able to characterise the action mechanism between backfill and pillar in each stage of the bearing of the system. Through analysis and discussion, it was concluded that the essential reason for the difference in bearing characteristics is that the effect of displacement restraint, joint support, and passive compressive weaken with the increase of the strength of pillar. The effect of pillar strength on the internal synergy of BPS is well verified by numerical simulation test.

A System Phase Noise Model for Frequency-Modulated MEMS Gyroscopes

A system phase noise model is proposed in this paper for frequency-modulated (FM) gyroscopes, which gives us a clearly guidance for different noise and how to improve the final performance. The author here introduces a mathematical calculation method to deal with the time domain noise and transforms the time-varying noise into phase modulation paths to analyze the frequency noise effect. Meanwhile, the proposed model reveals the relationships about mechanical vibration noise mechanical additional loop noise and performance indicators. In this way, combing frequency spectrum and Allan variance curves, the weight of each noise can be determined. Here, we get different physical noise sources from actual circuit chip by the proposed phase noise decomposition method and analyze the whole noise contribution. After that, we can clearly understand the performance indicators required to design the circuit. Finally, this work offers a whole theory instructions to quantitate different frequency noise for FM gyroscopes.

COMPUTER SIMULATION OF BIOLOGICAL WASTEWATER TREATMENT PROCESSES IN AEROTANKS WITH PLATES

Purpose. Efficiency determination of the aeration tank at the stage of design or reconstruction of bioreactors in which biological wastewater treatment is carried out requires the use of special mathematical models and calculation methods. The main purpose of the article is to develop CFD models for evaluating the operation efficiency of aeration tanks. Methodology. A numerical model has been developed for the computer calculation of the biological wastewater treatment process in aerotanks, taking into account hydrodynamics. The model is based on two-level mass conservation equations for the substrate and activated sludge and the velocity potential equation. The process of biological transformation of the substrate is calculated based on the Monod model. For the numerical integration of the mass transfer equations of activated sludge and substrate, the alternating-triangular difference splitting scheme is used. In this case, the basic equations are divided into two equations of a more simplified form. For the numerical integration of the equations for the velocity potential, it is split into two one-dimensional equations. Further, each equation is solved according to explicit scheme. For the numerical integration of equations that describe the process of substrate transformation based on the Monod model, the Euler method is used. Findings. The software implementation of the constructed numerical model has been carried out. The results of a computational experiment on the study of the wastewater treatment process in an aeration tank with plates are presented. This leads to the conclusion that the quality control of wastewater treatment in aeration tanks is possible with the help of plates. Originality. A multivariate CFD model has been developed, which makes it possible to quickly assess the efficiency of the aeration tank. A feature of the model is the ability to evaluate the operation of the aeration tank, taking into account its geometric shape and location of additional plates in the construction. Practical value. The constructed numerical model can be used during calculations in the case of designing aeration tanks, or in determining the efficiency of wastewater treatment under new operating conditions.

Effective use of Fire Department Connections

According to the current firefighting facility ordinance, connecting water pipes can be more than five stories in length, and the installation standard is applied to specific objects with a total floor area of > 6,000 m<sup>2</sup> or more than seven stories. This standard is intended to enable fire brigades to quickly move to a fire point and extinguish a fire with extinguishing water supplied smoothly. However, the strict fire safety standards make it possible to install both the connecting water pipe facility and the indoor fire hydrant and sprinkler connecting the water outlet, thus creating a fire extinguishing facility that firefighters cannot use at the fire site. In this study, both domestic and foreign standards and fire cases of consolidated water pipes were reviewed, and various problems were analyzed through field surveys, experiments, and surveys. In addition, using the engineering mathematical calculation method and mathematical calculation program, it was confirmed that direct delivery to the 50th floor is possible with the A1 pump on fire trucks. The fire safety standards have been revised to ensure that fire brigades can extinguish fires under any circumstances, and it is suggested that piping should be installed.

A brief experimental examination of post-exercise hypotension and the impact of calculation method.

There is great variability in the reported values of post-exercise hypotension (PEH), with inconsistent calculation methods employed across primary research. This study aimed to explore the influence of the mathematical calculation method on PEH variability, with the hypothesis that the method of identifying the lowest single reduction point (LSRP) would yield false-positive results. Young, normotensive (108 ± 7/69 ± 5 mmHg), apparently healthy, male (n = 20) were included in this study. Participants completed three random-order experimental sessions, with blood pressure and heart rate measured before (10 min) and after (30 min) an acute bout of either isometric handgrip exercise, aerobic cycling, or a nonexercise control. Three PEH calculation methods were analyzed: LSRP, 30-min average across the full post-exercise recovery, and 15-min binned averages with two recovery windows (0-15 min, 15-30 min). The only calculation method to consistently identify PEH was the LSRP method, which identified PEH for SBP, DBP, and mean arterial pressure, across handgrip exercise, aerobic cycling, and even nonexercise control (P < 0.001). All other calculation methods inconsistently identified PEH across experimental sessions, supporting the hypothesis that LSRP inaccurately overreports PEH. Mathematical calculation method appears to be one source of variability contributing to the inconsistency in reported PEH among young, healthy males. This brief experimental examination reveals that the LSRP method should be avoided as it inaccurately overreports PEH. Alternatively, binned averages of smaller time windows across the recovery period may be a potentially advantageous approach and require further examination to determine to ideal level of granularity.

МОДЕЛЮВАННЯ ПОВЕДІНКИ СТРИЖНЯ З ТРИЛІНІЙНОГО ДВОФАЗНОГО МАТЕРІАЛУ З УРАХУВАННЯМ ТЕМПЕРАТУРИ

В роботі сформульовано феноменологічну модель для опису властивостей сплавів із пам’яттю форм та пам’яттю в точці зміни температури. Встановлено, що класичні матеріальні діаграми – це конверт певного сімейства матеріальних діаграм, побудований за певнимизаконами зміни швидкості та розриву фронту деформації. Для використання феноменологічної моделі з метою дослідження двофазних матеріалів з різними модулями пружності розв’язано додаткову задачу, яка пов’язана з розбудовою миттєвої термомеханічної поверхні. В роботі проведено числове дослідження, як результат показано типову залежність для швидкості розповсюдження фазового переходу від часу. Графік залежності має три ділянки. На першій ділянці швидкість дорівнює нулю, а на третій – досягає постійного значення. Між ними міститься ділянка зі змінною швидкістю. В результаті обчислення дотичного модуля на кожному кроці інтегрування за часом інтегральна діаграма матеріалу, побудована в роботі, теж має три характерні ділянки.

Improving Approach to Conditions’ Statistical Assessment for Ukraine Banking Sector Competitive Development Under the Foreign Banks Presence in the Financial Market

It is substantiated that most of the existing methods and models for assessing the development of the banking sector of the economy do not take into account the competitive conditions for banks of different groups – with national capital and foreign banking groups. This determines the relevance of the study to improve the methodical approach to statistical assessment of competitive conditions in the development of the banking sector in the presence of foreign banks in the financial market.The scientific work proposes to assess the competitive conditions in the banking sector, in particular those created for domestic banks under the influence of foreign presence, by the level of the coefficient of competitive internalization. Eight gradations of the coefficient level were established by the expert method.Due to the use of mathematical calculation method and official statistics, it was found that the level of competitive internalization in the banking sector of Ukraine over the past decade is mostly dangerous, with a tendency to deteriorate. The coefficients of competitive internalization for the banking sectors of the Commonwealth of Independent States and the European Union have been calculated. It is determined that the level of influence of foreign banks in the banking sector of Ukraine can be compared with the conditions of competitive development of national banks of Moldova and Slovenia. The use of competitive internalization coefficient in practice as a statistical data will create a basis for determining the direction of integration processes. We are convinced that the integration of Ukrainian banks into the banking sector of Moldova or Slovenia is possible.

Analysis of static stiffness fluctuation in radially loaded ball and roller bearings

The radial stiffness of rolling bearings is the basis for analyzing the dynamic performance of bearing-rotor systems. The changes of rolling element position may cause continuous change of radial stiffness and relative displacement of inner and outer ring during the operation of the bearing-rotor systems. As a result, the vibration of bearing-rotor systems would be aggravated. In order to accurately study the influence of the changes of rolling element position on radial stiffness, two boundary positions of the inner ring supported by even or odd number of rolling elements are considered in this paper. A mathematical method for rolling bearings modeling and stiffness calculation is proposed based on Hertz elastic contact theory. Then, the differences of radial stiffness under two boundary positions and that of rotor center displacements are studied. The results show that there exist obvious fluctuation of radial stiffness and oscillation of rotor center during the operation of bearing-rotor systems. Moreover, the effect of bearing structure parameters including internal clearance, number of rolling elements on the fluctuation of radial stiffness and oscillation of rotor center has been systematically investigated for ball and roller bearings. Consequently, this paper not only proposes an effective method for the radial stiffness, load distribution and the displacement of rotor center calculation of radially loaded rolling bearings, but also provides a direction for the design of bearing-rotor systems to eliminate vibration.

Statičke karakteristike hidrostatičkog aksijalnog ležaja sa membranskim kompenzatorom pomeranja

The article discusses the design and also presents a mathematical model and method for calculation of static characteristics of a hydrostatic thrust bearing with a membrane-type displacement compensator. Formulae for calculation of compliance and load characteristics of the bearing are also presented, as well as deformation and compliance of the membrane at which zero compliance of the bearing is guaranteed.

Оценка результативности и эффективности системы управления охраной труда на горном предприятии

Overview of the modern Russian and International standards in the field of occupational health and safety management at an enterprise is presented. It is determined that the proactive method of assessing the state of working conditions at the enterprise has advantages over the post-event approaches to the development of corrective actions. The assessment is made concerning the application of the generalized Harrington desirability function, which has such properties as continuity, monotonicity, and smoothness. Based on this function, it is possible to assess the state and conditions of occupational safety and compare the indicators of various mining enterprises. GOST 12.0.230.3—2016 was analyzed, and the number of changes were proposed to the method of mathematical calculation. On the example of data provided by the Russian coal industry enterprise, an assessment was made related to the effectiveness and efficiency of the occupational health and safety management system. The values of the linguistic and numerical assessments of the state of the occupational health and safety management system are obtained. Graphic representation of the Harrington function with numerical and linguistic estimates superimposed on it is presented. The applied practices of internal and external audits of the occupational safety management system allow to identify deviations in its work, but they have rather long intervals between checks — from 1 to 3 years. The result of the performed analytical research is an improved methodology for assessment of the effectiveness and efficiency of the occupational safety management system, which allows to make this work more often, easier, and cheaper. Made calculations of the desirability index for a mining enterprise are an example, but they should be carefully analyzed by senior managers for assessment and decision-making. Practical recommendations on the use of the research results by the employer (head of the organization) to improve and develop the system management of occupational health and safety are presented.

Theoretical and Methodological Calculations of Solar Energy Resource Potentials in the Northern Garagum

The urgency of the issue is the development of the Garagum desert, which occupies 80% of the land resources of Turkmenistan. The aim of the research is to supply the desert regions of the Garagum with energy using solar energy technologies and installations. The research task - to determine the solar-energy resource potential using innovative methods of calculation in the design, creation and implementation of efficient solar energy technology and equipment. Methodology. To determine the gross, technical, economic and ecological potential, the natural and climatic conditions of the Northern Garagum are taken into consideration. Research methodology - used meteorological data, processed by laws of physics and mathematical calculation methods for thermal and photoelectric converters. Research results. The theoretical and methodological calculations of the gross, technical, economic and environmental potentials of solar energy are estimated, the energy efficiency of solar radiation is determined, and the optimal solar collector inclination angles for the Northern Garagum are calculated. Discussion and conclusion. As a result of the research, the resource potentials of solar energy were obtained, converted into thermal and electrical energy, kW•h/m2 per year: gross - 1844.6; technical - 1227.58 and 244.85; economic - 1354.58 and 270.25. Environmental potentials, CO2, kg / year: 784.96 and 156.6. The most effective for the use of solar collectors in the Northern Garagum for months of the year with an angle of inclination is: 60 degrees - January, February, November, December; 45° - March, October; 30° - from April to September.

Investigation of transfer processes in swirling flows in application to vortex furnaces for coal fuel

In this work, the swirling flow structure was studied experimentally and numerically in a wide range of operating parameters at a laboratory model of the promising furnace of pulverized-coal boiler with a four-vortex combustion circuit. The basic aerodynamic features of construction, affecting the efficiency of fuel combustion, were investigated by the example of air under the atmospheric pressure (Re ~ 104) for the isothermal case. The data on distribution of averaged and pulsation velocity characteristics were experimentally obtained in various areas of the model using the non-contact PIV method (Particle Image Velocimetry). The results of measurements carried out in a wide range of initial velocities allow distinguishing three flow regimes (β is the ratio of flow velocities at the outlet of the side and frontal nozzles): the flow regime with regular structure (four symmetric vortices, β ≥ 1.8), the transitional regime (1.8>β > 0.9) and regimes with irregular vortex structure (β ≤ 0.9). It is shown that formation of irregular structures is associated with uneven organization of air supply to the model. In regimes with β < 1.8, the flow becomes sensitive to asymmetry in the input conditions. At the same time, at high β ≥ 1.8, a stable four-vortex flow structure is formed, even if the input conditions are asymmetric within 10% (by velocity). In the transitional regime, when β decreases from 1.8 to 0.9, the flow begins distorting, and this is presented by the flow asymmetry. With a further decrease in β ≤ 0.9, the development of asymmetry is accompanied by the breakdown of large vortices into smaller vortices. A stable four-vortex flow structure at β ≥ 1.8 is important for practical applications, since in this regime, effective “washing” of the heat-exchange surfaces of the boiler will be ensured, thus avoiding their slagging. The results of laboratory measurements obtained in the range of flow regimes, self-similar by the Reynolds number (104<Re < 106), allowed us to verify the mathematical model. Numerical calculations of aerodynamics were performed using the AnsysFluent CFD package. All considered turbulence models (URANS k-w SST, URANS RSM, DES) reproduce well the averaged flow structure in the combustion chamber. The results of numerical calculations are in good agreement with experimental data. The verified mathematical model and calculation method allow us a future transition to simulate the combustion of coal fuel, taking into account all the main processes of heat and mass transfer in the furnace.

Analisis Penurunan Daya Pada Sistem Propulsi Lokomotif Transmisi Diesel Elektrik CC 203 Di Depo Lokomotif

Depo Lokomotif is a work unit that is responsible for locomotive reliability in running the railroad transportation operational business. According to internal monthly report data from February 2019 to February 2020, there were 6 cases of weak locomotive power disruptions that caused operational delays. Analysis was carried out on the CC203 locomotive propulsion system in order to obtain the value of the power reduction in one case of disturbance by comparing the output value against the set standard value. Using mathematical calculation methods from the applicable equations and processing the data on MS.Excell. From the results of the study, the cause of the decrease in locomotive power is due to a decrease in the excitation value so that it affects the output value of the Main Generator at each Notch and has an impact on the motor traction power supply also decreases. The Main Generator can only issue a maximum Horse Power at Notch 8 of 1389.96 HP from 1985.31 HP with a decrease of 595 HP. The electric motion of the generator exciter has the largest decrease at Notch 7 of 6.02 volts from 30.48 volts to 24.46 volts. Motor traction can only output a maximum terminal power of 985.067 Watt from 1407 KWatt. The maximum electromagnetic torque of the Notch 8 motor traction is 2855.48 N.m in the series transition and 3070.21 N.m in the parallel transition. Losses on a series transition of 36886 Watts and a parallel transition of 9122 Watts.

Evaluation of Electromagnetic Environmental Effects for Ship System Based on Impact Degree

The ship system should be compatible with the electromagnetic environment (EME) in which it works. The evaluation of electromagnetic environmental effects (E3) is the premise and means to realize this goal. A method for E3 evaluation of ship system based on impact degree is proposed. The normalized index is used to synthesize the E3 impact degree of different types of E3 elements and different types of susceptible receptors with this method. The mathematical model and calculation method are presented. Through the comparison of the two groups of ship system design schemes before and after the improvement, taking the effects of electromagnetic interference, external radio frequency, radiation field hazards and antenna coverage performance as examples, the numerical results of various effects and the total E3 impact degree are calculated respectively. The results show that the method can support the balance and optimization of ship system E3 multi-index design, and the actual effect is obvious.

A Novel Method for Streamline-Based Tortuosity Calculation and Investigation of Obstacles Shape Effect on Tortuosity in Porous Media with Random Elliptical Obstacles Using Lattice Boltzmann Method

In this research, the lattice Boltzmann method was used to simulate the fluid flow in the random elliptical porous media. Since the tortuosity is one of the most important parameters of porous media and also, the hydraulic tortuosity is more accurate and more realistic than geometric tortuosity, therefore, the hydraulic tortuosity was discussed thoroughly in this study. Contrary to many studies in which the velocity-based method has been used for calculation of tortuosity, one of the novelties in this paper is the application of streamline-based tortuosity including the detailed description of mathematical method for calculation of streamline-based tortuosity and also, the calculation of it numerically and the comparison with velocity-based tortuosity at different porosities and at various aspect ratios. Furthermore, the deviation percentage of velocity-based tortuosity from streamline-based tortuosity was surveyed and depicted. Also, the behavior of streamline-based tortuosity was illustrated as a function of porosity at different aspect ratios and the results were compared with Comiti–Renaud equation and a new equation was proposed. With the structure factor defined as the ratio of porosity to tortuosity, the variation of this quantity with respect to porosity was displayed at different aspect ratios. Also, the formation factor variation versus porosity was discussed at different aspect ratios, too. Finally, the influence of obstacles shape on the tortuosity by varying aspect ratio was investigated and it was concluded that the orientation of elliptical obstacles (vertically or horizontally) has severe effect on the tortuosity.

DRG-Oriented Mathematical Calculation Model and Method of Integrated Medical Service Cost.

In the context of the new round of medical and health reform, in order to alleviate the problem of “difficult to see a doctor and expensive to see a doctor,” the state focuses on reducing the cost of medical services, so it puts forward the calculation and method research of medical costs. The purpose of this study is to calculate and predict the cost of medical services in a DRG-oriented integrated environment. In this study, activity-based costing and weighted moving average methods are used. First, basic data of medical services are collected, then all medical activities are confirmed and all service costs are collected, then a cost database is established, and a calculation model of medical costs is designed. Finally, calculation suggestions and optimization methods are put forward by analyzing the calculated data. The experimental results show that the actual demand of drugs predicted by the general moving average method is relatively insufficient, with the maximum error of 41%, the minimum of 5%, and the average error of 19.8%; the maximum error of drug demand predicted by the weighted moving average method is 24%, the minimum is 2%, and the average is 15.4%. It can be concluded that the prediction effect of the weighted moving average method is better than that of the ordinary moving average method, which plays a good and effective role in the prediction of medical cost. The activity-based costing method is more detailed and organized for the cost calculation and classification of medical services. It provides a certain value for the effective management and control of medical service cost.

Study on Torsional Vibration Characteristics of Cross Shaft Universal Coupling

In this work, the ship propulsion shaft system with cruciform universal coupling is studied. First, based on the analysis of the structure and characteristics of the cross-axis universal coupling, the motion relations and expressions between the components of the universal coupling are established by using the coordinate transformation method. Second, the characteristics of the four submodels of the head mass point element, the end mass point element, the universal coupling mass point element, and other mass point elements are discussed, and the corresponding torsional vibration differential equations of the four submodels are established. On this basis, the mathematical model of the propulsion shafting system and the differential equations of torsional vibration are established by using the modularization method and lumped parameter method. Finally, the torsional vibration modes and response characteristics of the shafts are calculated and analyzed by using the system matrix method when the external load driving torques of the universal coupling, propeller, and diesel engine are considered. At the same time, the correctness of the mathematical model and calculation method is verified by the test and comparative analysis of ship propulsion shafts. It lays a theoretical foundation for further research on torsional vibration characteristics and mechanisms of the ship propulsion shafting system based on universal coupling. Introduction Universal coupling is a common connection component of mechanical shaft system transmission. It is a common mechanism that can be used to transfer motion and torque. Universal coupling has no requirement for neutrality between the two axes connected. It can be used for intersecting, parallel or staggered multiposition relations, and can still ensure the continuous rotation of the two axes connected. Compared with the belt drive and chain drive, universal coupling has the advantages of large transmission range, compact transmission, high transmission efficiency, and convenient maintenance. Therefore, it is widely used in ships, automobiles, lifting and transportation (Avrigean et al. 2015; Chang et al. 2017), engineering machinery, and other equipment. Because of the manufacturing error, assembly error, and the failure to keep synchronous rotation between the driving shaft and the driven shaft in the working process, additional inertia moment of the universal coupling is generated, which causes the vibration of the system and even leads to the fracture of the universal coupling in serious cases.