Equation Formula Research Articles

A general derivation of the classical Doppler effect in 3D space

The classical Doppler effect has already been studied in many textbooks and papers. However, the formula currently used to describe the Doppler effect for a source and a receiver moving with constant velocities is not suitable for practical applications. Indeed, the formula makes use of two angles that depend on the state of the source-receiver system both at the emission instant and at the reception instant of sound, while in most real cases the state of the system is known only at one of the two instants. In this paper, two equivalent formulas are derived for the Doppler shift: one depending solely on the state of the system at the emission instant, and one depending solely on the state of the system at the reception instant. The paper also provides two more general expressions that describe the Doppler shift evolution over time. The expressions derived in this paper are compared with the existing ones in some special cases, obtaining consistent results.

Financial Distress During the COVID-19 Pandemic: Altman and Springate Model Prediction

Background: The retail trade industry has experienced a sharp decline in economic growth during the COVID-19 pandemic. Regulation of social distancing, restrictions on retail shop operating hours, and disruption of online shopping behavior contribute to worsen the financial performance of retail trade companies. </p> <p> Purpose: The purpose of this research is to analyze the prediction of financial distress of retail trade companies. This research chose to use the Altman and Springate Model since both of them are the most accurate and conservative models to predict. </p> <p> Research Methodology: The financial distress analysis technique used is Altman and Springate Model. The calculation of the Altman and Springate Score is based on an equation formula for data in the period before and during the COVID-19 pandemic. The Altman’s Score are grouped in the Safe Zone, Grey Area, and Financial Distress; while the Springate’s Score are grouped in the Safe Zone and Financial Distress categories. </p> <p> Findings: Altman Model Analysis stated that most of the companies experienced a decreased scores, the company’s financial performance during COVID-19 pandemic was predicted financial distress and belong to the Grey Zone category than before COVID-19 pandemic. Springate Model Analysis states that all companies have decreased scores, and the company’s financial performance during COVID-19 pandemic is predicted financial distress than before COVID-19 pandemic. Springate Model revealed a more conservative indicator, but both models stated there were still exist several companies in the Safe Zone category to continue their business. </p> <p> Research limitations: The limitations of this study are only using Altman and Springate Model. The object of this research is the retail trade industry only, then future research may be able to expand the analyzed industry in the new normal conditions. </p> <p> Originality/value: The originality of this research is focused on the retail trade companies as the most affected industry by COVID-19 pandemic. In addition, this research analyzes financial distress based on Altman Z-Score and Springate Model as the most powerful model to predict.

Analysis of magnetostriction of oriented silicon steel under motor magnetic field

The performance requirements of motors are gradually increasing, and anisotropic soft magnetic materials have been applied in motors to improve performance, The magnetostriction of anisotropic soft magnetic materials is one of the main contributors in extensive research on anisotropic soft magnetic material transformers. Compared to transformers, the magnetic field in motors has more complex harmonic and multi-directional characteristics. In this paper, the magnetic field of motors stator teeth under both no-load and load conditions is calculated and analyzed to research magnetostriction of anisotropic soft magnetic materials in motor magnetic field and predict the NVH performance of anisotropic soft magnetic material motors accurately. Furthermore, the magnetostriction in different magnetization angles is investigated for the multi-directional characteristics, and the result is explained from microscopic principles. This paper focuses on a splicing oriented silicon steel (OSS) motor, the magnetization angle of OSS in motor varying from 0° to 90°. Firstly, the equivalent formulas of magnetic field are obtained under the analytical and finite element calculations. After that, the frequency and direction of experiment magnetic field are confirmed and the magnetostriction of OSS in different magnetization angle and frequency is measured. In the end, the variation character of magnetostriction of OSS is summarized.

BASED ON AN INTEGRATIVE APPROACH TO TRIGONOMETRY EXAMPLES AND EXERCISES APPLICATION OF FRACTION PROPERTIES

Recommendations on the method of using fractions,equivalent formulas, series of equivalent ratios, inverse trigonometric functions, the largest and smallest values and finite trigonometric series in order to apply the theoretical part of the science in practice, that is, to increase the skills of solving examples and problems, were highlighted.

A variation of parameters formula for nonautonomous linear impulsive differential equations with piecewise constant arguments of generalized type

A variation of parameters formula for nonautonomous linear impulsive differential equations with piecewise constant arguments of generalized type

Solution formula for generalized two-phase Stokes equations and its applications to maximal regularity: Model problems

<abstract><p>In this paper, we give a solution formula for the two-phase Stokes equations with and without surface tension and gravity over the whole space with a flat interface. The solution formula has already been considered by Shibata and Shimizu. However, we have reconstructed the formula so that we are able to easily prove resolvent and maximal regularity estimates. The previous work required the assumption of additional conditions on normal components. Here, although we consider normal components, the assumption is weaker than before. The method is based on an $ H^\infty $-calculus which has already been applied for the Stokes problems with various boundary conditions in the half-space.</p></abstract>

Nutritional management in critically ill patients with COVID-19: a retrospective multicentre study.

Although nutritional treatment is an established pillar of multidisciplinary care provided in critical illness, there are many concerns regarding this issue in severe COVID-19. This observational, retrospective, multicentre study aimed to analyse the approach to nutritional treatment among selected intensive care units (ICUs) in Poland. The medical records of 129 patients hospitalized in five units due to respiratory failure following COVID-19 were analysed in terms of nutritional management on the eighth day of the ICU stay. The Harris-Benedict equation (HB), Mifflin St. Jeor equation (MsJ) and ESPEN formula (20 kcal kg -1 body weight) were used to estimate the energy target for each patient, and two ESPEN formulas determined the protein target (1 g kg -1 body weight and 1.3 g kg -1 body weight). Evaluation of nutritional therapy was performed in 129 subjects. The fulfilment of caloric requirement considering the HB, MsJ and ESPEN formula was 66%, 66.7% and 62.5%, respectively. Two clinical centres managed to provide 70% or more of daily caloric requirements. According to the ESPEN formula, the implementation of the protein target was 70%; however, one of the investigated units provided a median of 157% of the protein demand. The nutritional management varied in the preferred route of nutrition administration. Neither method nor grade of nutrition supply influenced biochemical parameters on the 8th day of ICU stay. Significant differences in nutritional treatment of critically ill COVID-19 patients in Polish ICUs were noted, which underlines the importance of setting up clear guidelines regarding this issue.

Renal biochemical marker changes in renal protective effects of different doses of Aloe vera on Amphotericin B induced nephrotoxicity in Albino rats: An animal Study

Drug induced nephrotoxicity remains one of the leading causes of acute and chronic kidney diseases in Africa and other developing countries. This can be attributed to environmental pollution due to increased industrialization, poor waste disposal systems, and changes in diets among other factors. The care and treatment of these patients is extremely expensive especially when a patient requires dialysis or kidney transplant. Nephrotoxicity is normally characterized by elevated urea and creatinine levels. The aim of the present study was to evaluate these changes and draw a viable conclusion out of it. In this study a total of 25 rats were used having been calculated using modified resource equation formula. The animals were then systematically sampled and allocated to either pretreatment or treatment groups. Animals in treatment groups were subjected to similar dose of Amphotericin B and different doses of Aloe vera to achieve protection. Later animals were sacrificed humanely and blood collected through cardiac puncture and preserved for renal biochemical analysis. It was noted that there was a significant increase (P=0.0001 and P=0.0001) in both BUN and creatinine respectively in ABG group as compared to pretreatment group. There was a significant reduction (P=0.0001 and P=0.0001) in BUN and creatinine in HDAB group respectively when compared with ABG group. There was no statistical significance (P= 1.000 and P= 1.000) respectively in BUN and creatinine in HDAB group as compared to pretreatment group. It can therefore be concluded that high dose Aloe vera has renal protective benefits in Amphotericin B induced nephrotoxicity as seen in changes of biochemical parameters.

MANAGEMENT OF INVESTMENT PROCESSES OF MUNICIPALITIES - LEGAL AND ECONOMIC ANALYSIS IN THE CONTEXT OF THE INDIVIDUAL DEBT RATIO FORMULA

The new debt limitation rules, which have been in force since 2014, have been a significant setback for most local authorities in planning and managing their local finances. Over the four years of application, a number of drawbacks and inconveniences in the application of the new norms became apparent, and the 'creativity' of the local government financial sector showed that they could be circumvented with relative ease. The construction of the maximum indicator limiting the liabilities on titles defined by the legislator, falling due in a given year, is closely related to the provisions of the Public Finance Act. For the first time, it was applied to the grade of budgets passed in 2014. The essence of this legal regu-lation is the comparison of two indicators, included in the equation (formula) formula. A positive condition for the adoption of the budget is to obtain a relationship in which the left side of the formula (annual commitment repayment ratio) is less than or equal to the right side (maximum commitment repayment ratio).

Reservoir Sedimentation Assessment Using Geospatial Technology: A case Study of Dukan Reservoir, Sulaimani Governorate, Kurdistan Region, Iraq

The accumulation of sediment in reservoirs poses a major challenge that impacts the storage capacity, quality of water, and efficiency of hydroelectric power generation systems. Geospatial methods, including Geographic Information Systems (GIS) and Remote Sensing (RS), were used to assess Dukan Reservoir sediment quantities. Satellite and reservoir water level data from 2010 to 2022 were used for sedimentation assessment. The satellite data was used to analyze the water spread area, employing the Normalized Difference Water Index (NDWI) and Modified Normalized Difference Water Index (MNDWI) to enhance the water surface in the satellite imagery of Dukan Reservoir. The cone formula was employed to calculate the live storage capacity of the reservoir within two elevations. According to the study results, the live storage capacity of Dukan Reservoir at elevation 511.78 m had decreased from 8000 MCM to 7007.77MCM and 6923.53 MCM using NDWI and MNDWI respectively, due to sedimentation, resulting in a capacity loss of 14.59% and 15.83% for NDWI and MNDWI respectively. The annual sedimentation was 13.78 MCM and 14.95 MCM for NDWI and MNDWI, respectively. Joglekar's equation and Khosla's formula have demonstrated that the sedimentation rate in the Dukan reservoir exceeds the critical rate. The findings of this study will inform the development of sediment management strategies aimed at preserving the reservoir's capacity.

Weighing logistics: on the issue of accuracy of determining the weight of the transported goods

Methods. The results are obtained with the following methods: the method of abstractions in determining the essence of the category of «social justice»; general to specific method in establishing the unity of the existing concepts of social justice; standard methods of sociological research in determining the value system of the Ukrainians towards social justice. Results. As a result of the conducted research, the possible value of financial losses during the sale of such goods as sand, wheat, fodder corn, food corn, iron ore pellets, titanium ore, and rolled ferrous metals was determined. These losses can range from hundreds to tens of thousands of hryvnias. The list of available offers of electronic scales for weighing goods on land was analyzed, the value of error when weighing with automobile and wagon scales was determined. The possibility of describing the error using a logarithmic equation has been demonstrated, which proves that the relative weighing error decreases as the mass increases. The equation formula was found by the analytical economic-mathematical method using Microsoft Excel spreadsheets. Based on the use of the properties of the dispersion of weighing, a logistical and organizational method of increasing the accuracy of weighing has been developed, which consists in several repeated weighings and determining the resulting weight as the arithmetic mean of all attempts. A formula was developed to determine the optimal number of repeated weighings to increase accuracy, taking into account the cost of one weighing and losses during a single weighing. The method of weighing cargo on water was analyzed, its limitations were revealed and the need for its improvement was indicated in terms of taking into account such factors as water salinity, through which the draft of the vessel is measured. An analytical dependence has been developed to determine the weight of the goods loaded onto the vessel by its draft depending on the salinity of the water in which the vehicle is located. Novelty. In the process of analyzing exporters’ losses during product weighing, logistical and organizational measures have been developed that are guaranteed to reduce losses. Practical value. Techniques are proposed that will reduce the exporter’s losses when weighing goods both on land and at sea, which will allow adjusting the size of the weighing error with available devices.

A mathematical model for parameter setting in discrete element numerical simulation

To rationalize the setting of joint parameters, model size, and initial value of vertical stress in simulation of mining of steeply inclined coal seams, a fault tree analysis method of discrete element numerical simulation was used and a mathematical model was proposed. A method of eliminating the influences of size-effect errors on the parameters of coal and rock samples was obtained based on previous work. Furthermore, the constitutive equation and eigenvalue determination formula of a joint discontinuity surface were established, and a method of determination of the joint parameters was proposed, forming the complete “coupling chain” between parameters for numerical simulation. In addition, a formula for the initial value of vertical stress was constructed by way of the compression and shear model of the element body. Also, the minimum dimension was determined by means of strength factor analysis of fracture mechanics. Taking the research literature as an example, the model size and initial value of vertical stress were calculated. On this basis, the physical parameters of coal samples, the physical parameters of coal rocks considering the influence of the size effect and the calculated coal rock joint parameters considering the influence of size effect were directly used to comparatively analyze the displacement and stress fields, thus verifying the reasonability and correctness of the mathematical model.

Analysis of the Wireless Power Transfer System Using a Finite Grid of Planar Circular Coils

In this paper was analysed a wireless power transfer system (WPT) with multiple resonators supplying, for example, sensors or LED lighting. Energy is transferred simultaneously using a group of identical planar spiral circular coils acting as transmitters and receivers. These coils were arranged to form transmitting and receiving planes. The receivers were connected to independent power supply circuits of each, e.g., sensor or LED lighting. Higher power reliability and flexibility can be achieved by isolating these circuits. The proposed system was described and discussed. Taking into account the skin effect and mutual couplings, a theoretical analysis was made. A detailed analysis was made at the resonant frequency of the system. The system was modeled using a matrix equation and appropriate formulas. The calculations were verified experimentally for different loads and two distances between transmitters and receivers. The efficiency and receiver power were compared and discussed. The maximum efficiency was about 45% at the small distance between the planes. The maximum efficiency of the WPT system decreased more than two times to less than 20% when the distance between the coils was doubled. The results and discussion of the conducted analysis may provide valuable knowledge when designing this type of system.

Suitability of Torricelli’s Theorem Formulation in Cases of Leaking Reservoirs with Video Analysis Tracker

This study aims to empirically prove the Torricelli equation formula in the case of leaky reservoirs with the help of video tracker analysis. The method used in this research is quantitative descriptive. The experiment was carried out with a simple tool: a 19-liter gallon of water filled with water and dyed, and then three holes were made vertically with different heights. The gallon is filled with water with a constant water level. Next, take a video of each leaking hole. Video is analyzed with Tracker software. Variables observed were the velocity of water exiting from the leak point (v), the time it took for water to gush from the leak point to the bottom (t), and the horizontal distance from the leak point position to the bottom (x). The results obtained based on video analysis with the tracker are that the farther the distance from the surface of the water to the leak point, the farther the horizontal distance of the resulting jet of water will be. This study concludes that theoretical data and experimental data have significant value, so the video analysis tracker software is feasible to use in dynamic and static fluid learning.

Mathematical bounds on Shannon entropy given the abundance of the ith most abundant taxon

The measurement of diversity is a central component of studies in ecology and evolution, with broad uses spanning multiple biological scales. Studies of diversity conducted in population genetics and ecology make use of analogous concepts and even employ equivalent mathematical formulas. For the Shannon entropy statistic, recent developments in the mathematics of diversity in population genetics have produced mathematical constraints on the statistic in relation to the frequency of the most frequent allele. These results have characterized the ways in which standard measures depend on the highest-frequency class in a discrete probability distribution. Here, we extend mathematical constraints on the Shannon entropy in relation to entries in specific positions in a vector of species abundances, listed in decreasing order. We illustrate the new mathematical results using abundance data from examples involving coral reefs and sponge microbiomes. The new results update the understanding of the relationship of a standard measure to the abundance vectors from which it is calculated, potentially contributing to improved interpretation of numerical measurements of biodiversity.

Calculation of ultimate bearing capacity of concrete-filled double steel tubular under compression based on the unified strength theory

Concrete-Filled Steel Tube (CFST) components are widely used in the engineering field due to their superior performance. However, the actual stress state of CFST components under axial compression is complex. As a result, calculations for CFST components are often simplified using material equivalent assumption formulas and empirical equations to determine their load-bearing capacity. These simplifications require the introduction of many coefficients and mechanical performance indicators, and the actual material principal stresses are not adequately considered. This approach weakens the completeness of the theory and adds to the burden of experimental research.The aim of this work is to develop a load-bearing capacity calculation formula for Concrete-Filled Double Steel Tubular (CFDST) components that considers the different stress states of the inner and outer steel tubes, the core concrete, and their interface interactions. This formula is designed to be convenient for engineers to understand and use. By comparing the results of this formula with experimental data collected from domestic and international scholars, it is evident that the results of this formula closely align with the collected experimental data. This validation confirms the accuracy and effectiveness of the formula developed in this paper. Furthermore, when compared with existing axial compression load formulas for CFDST, the formula presented in this paper demonstrates good accuracy. The research results provide a convenient and accurate calculation formula for the axial compression load-bearing capacity of CFDST components, bridging the gap between theoretical derivation and practical application.

Pengaruh Implementasi Kebijakan Dan Mutu Pelayanan Terhadap Kepercayaan Masyarakat Dalam Pembuatan E-KTP Pada Dukcapil Kabupaten Bombana

The problem of this research revolves around, the Influence of Implementation of Service Policies and Quality on Community Trust in Making Electronic KTP at Bombana Regency Population and Civil Registration Office. This study uses a quantitative approach with a description method. Data collected through questionnaires, processed with computers through Excel and SPSS programs, with regression equation formulas, then interpreted analyzed and described in accordance with the research objectives by using a sample of all employees in the district population and civil registration departement of Bombana. From the results of the regression linearity research and data alasysis obtainedfrom the tree hypoteses it turns out that the linear regression population, because the F count is signifikan at alpha =0,05. And the results of the study indicate that all three proposed workyng hypotesis are entirely accepted, this is data by obtaining positive regression coefficients, so that the implementation of the policy of making electronic ID Cards of service quality both separately and in integrated manner affects the trust of the public.To increase public trust better si that it will result in achieving the terget of making electronic ID Cards at the maximum population and civil registration departement of bombana regency, policy implementation and service quality is needed because if the policy implementation is effective and the service quality is good, public trust will tend to increase,conversely if the implementationof policies and service quality is lacking and ineffective then public trust will tend to decrease

Research on the Construction of Innovation and Entrepreneurship Education Model System in Universities Based on Big Data Technology

Abstract This paper aims to build a system of innovation and entrepreneurship education model in colleges and universities. Focusing on the analysis of measurement variables and structural variables in SEM, the evaluation model of college innovation and entrepreneurship education is constructed under the analysis process based on the structural equation model. The path diagram of the standardized solved structural equation model of practice teaching evaluation is outputted through software correction, and the standardized weights of evaluation are determined by combining the structural equation of college innovation and entrepreneurship practice teaching quality evaluation. Apply the evaluation principles to test whether the evaluation model is reasonable. By analyzing the form of innovation and entrepreneurship teaching, the evaluation is conducted according to the structural equation formula to find out the shortcomings in practice for improvement and refinement. The results show that in the dimension of practical teaching preparation, (H1) corresponds to effect coefficients of 0.47, 0.47, 0.60 and 0.53, and the percentages of students who receive innovation and entrepreneurship education courses very systematically are 3.5%, 5%, 6% and 9%. Most of the students were very satisfied and satisfied with the innovation and entrepreneurship courses, with 45% and 40%.

Two-phase Fluid Solid Coupling Modeling: Theory, Numerical Model, and Application

Underground compressed air energy storage (CAES) is seen as an important and promising way for balancing electrical power system. Many large-scale CAES projects (≥300 MW) are being planned in China, some of which have already been permitted for construction. Despite the benefits from CAES, some challenges arise in area of construction technology, operation system, maintenance and monitoring methods. One of the challenges lies in the evaluation of air leakage effect on flow and stress field around the underground cavern. Therefore, considering the actual physical field characteristics, the mathematical formula of mass conservation equations for air and water in porous media, as well as equilibrium equations for solid mechanics are established first and then coupled together for numerical solutions. The constitutive models for solid and porous fluid adopt classical elastic and Darcy’s law respectively, while the air-water interaction adopts classical van-Genuchten model and contributes to solid mechanics by pore pressure. Numerical implementations are based on secondary development to COMSOL software. Then interpretations to simulation results and the comparison with results not taking damage effect into account are made.

Prognostic Significance of Carotid and Lower Extremity Artery Stenosis in Patients With High and Very High Cardiovascular Risk.

Aim To study prognostic significance of the degree of stenosis of carotid and lower-extremity arteries (LEA) in patients at high and very high risk of cardiovascular complications (CVC).Material and methods The study included men and women aged 40-67 years at high and very high risk of CVC. Duplex ultrasound scanning of carotid arteries and LEA was performed for all patients. Laboratory tests included measurements of glucose, glycated hemoglobin, total cholesterol, low-density lipoprotein cholesterol (LDL-C), high-density lipoprotein cholesterol (HDL-C), triglycerides, uric acid, creatinine with estimation of glomerular filtration rate (GFR) using the CKD-EPI Creatinine Equation formula, and high-sensitivity C-reactive protein (hsCRP). Composite endpoint was death from CVC, nonfatal myocardial infarction, nonfatal stroke, and coronary revascularization.Results The study included 214 patients from groups of high and very high risk of CVC. Median age of patients was 59.0 [53.2; 64.0] years. A very high risk was identified in 141 (65.8 %) patients and a high risk of CVC in 73 (34.1 %). Atherosclerotic plaques in at least one vascular bed were found in 191 (89.3 %) patients. Duration of the follow-up period was 32.0 [13.7; 49.1] months. Outcomes comprising the composite endpoint were observed in 36 (16.8 %) patients. Presence of carotid stenosis ≥35 % was not statistically significantly associated with the occurrence of outcomes comprising the composite endpoint (relative risk, RR: 1.22; 95 % confidence interval, CI: 0.56-2.66; p=0.607). In contrast, the presence of LEA stenosis ≥35 % was associated with a 2.51 times increased RR of CVC (95 % CI: 1.02-6.23; p=0.044).Conclusion In patients from the groups of high risk and very high risk of CVC, the presence of LEA stenosis ≥35 % predicted the development of severe CVC with a 69.4% sensitivity and a 61.8% specificity. The presence of LEA stenosis ≥35 %, but not of carotid arteries, was an independent predictor of severe CVC (RR, 2.51; 95 % CI: 1.02-6.23; p=0.044) after adjustments for sex, age, presence of arterial hypertension, diabetes mellitus, ischemic heart disease, obesity, smoking, LDL-C, GFR, and drug therapy.