Equation Formula Research Articles

The Effect of Motivation, Competence, Compensation on Employee Performance with Organizational Culture as A Moderating Variable

Motivation, Competence, Compensation, and Organizational Culture have a great influence on the Employee Performance of PT. Adi Dharma Abadi. These four variables prove that this study aims to analyze the influence of motivation, competence, and compensation on employee performance with organizational culture as moderating variables in PT. Adi Dharma Abadi Bogor Regency. The study was conducted at PT. Adi Dharma Abadi Bogor Regency took 35 employees as the research sample, which was calculated using an equation formula through an interaction test often referred to as Moderated Regression Analysis (MRA) with a total population of 35 employees at an error margin of 2.5 %, for the data collection techniques, questionnaires, interviews, and observations. The data is processed using the SPSS version 26 application. The test data used in this research are reliability tests, validity tests, statistical tests, and classical assumption tests. The results of this study show that Motivation, Competence, Compensation, and Organizational Culture have a positive and significant influence on Performance.

Resistance Theory of Asymmetric 2 × n Circuit Network

ABSTRACTThis article proposes a class of asymmetric 2 × n resistor network model which contains multiple independent resistors; the study of asymmetric resistor network models is a challenge. We conducted in‐depth research on this issue using the RT‐V theory (Chinese Physics B, 2017, 26(9): 090503) and achieved new theoretical breakthroughs. This paper derived five original equivalent resistance formulae for this asymmetric 2 × n circuit network and also discusses the analytical expressions for equivalent resistance in different special cases, and several interesting results have been derived, indicating that the original resistance formula has powerful functionality. Finally, visual graphics of two types of equivalent resistances are provided using MATLAB drawing tools, which reveals the law of equivalent resistance changing with resistance variables. The research theory and technology in this article will provide a new theoretical basis for related scientific, engineering, and simulation research.

Research on an Intelligent Vehicle Emergency Avoidance Algorithm Based on User Behaviour Learning

With the development of the Internet of Vehicles and the high-precision lane-level navigation system, vehicles can receive more road details. And the systems will provide conditions for the development of the emergency avoidance function. This paper studies a vehicle automatic emergency avoidance algorithm based on user behaviour learning. The research is based on the Internet of Vehicles to obtain user driving data, generate a user database, and through the analysis of the avoidance track under the user's active operation conditions, generate a track equation or empirical formula, and the vehicle control unit executes the emergency avoidance action according to this. In the algorithm, the emergency avoidance function is defined as based on the vehicle's active safety system to avoid the event of a sudden situation, and the function will briefly disconnect the driver's partial operation when it is intervened, and the trigger conditions are set according to the trigger conditions of the parallel emergency braking function. The track equation is fitted using a sinusoidal signal, and the final output is the vehicle's front wheel angle.

New equivalent resistance formula of \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m\ imes n$$\\end{document} rectangular resistor network represented by Chebyshev polynomials

In the process of exploring the field of circuits, obtaining the exact solution of the equivalent resistance between two nodes in a resistor network has become an important problem. This paper aims to introduce Chebyshev polynomial of the second kind to improve the equivalent resistance formula of \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m\ imes n$$\\end{document} rectangular resistor network, thereby improving the calculation efficiency. Additionally, the discrete sine transform of the first kind (DST-I) is utilized to solve the modeling equation. Under the condition of applying the new equivalent resistance formula, several equivalent resistance formulas with different parameters are given, and three-dimensional views are used to illustrate them. Six comparison tables are provided to showcase the advantages of the improved explicit formula in terms of computational efficiency, as well as the relationship between resistivity and the maximum size of the resistor network that the formula can effectively handle. This may provide more convenient and effective technical support for research and practice in electronic engineering and other related fields.

Solving Algebraic Equations by Completing Powers

We derive the Cardano formula of cubic equations by completing the cube, and provide radical solutions to some algebraic equations of degree greater than 3 by completing powers. The main idea of completing the cube and higher powers arises from David Harrison’s center theory of higher degree forms. Elementary criteria and solving algorithms for such algebraic equations are presented, and the computation amounts to solving linear equations and quadratic equations.

Ferrite formation and decomposition in 316H austenitic stainless steel electro slag remelting ingot for nuclear power applications

316H austenitic stainless steel used in nuclear power has higher requirements for material magnetism, and the main magnetic phase is ferrite. Thus, the ferrite content in 316H steel castings needs to be strictly controlled. This study investigated the ferrite phases in 316H austenitic stainless steel electro-slag remelting (ESR) ingot used in nuclear power applications. The morphology, content and decomposition of ferrite as well as microsegregation in 316H ESR ingot are studied by optical microscopy (OM), scanning electron microscopy (SEM), electron backscatter diffraction (EBSD) and electron probe microanalysis (EPMA). The solidification process is calculated by thermodynamic calculation using Thermo-Calc. Besides, the empirical chromium and nickel equivalent formulas and phase stability diagram are used for prediction of the solidification mode and ferrite content. The experiment results show that the ferrite morphology changes greatly in the direction of the thickness of ESR ingot. From surface to center of the ESR ingot, the ferrite morphology varies as granular → short rod-shaped → blocky → skeletal → parallel short rod-like + network-like. The ferrite content in the thickness direction of the electroslag ingot varied from 1.92 to 3.57 %, showing an “A” shape distribution. There are three kinds of decomposition behavior of ferrite: decomposition into Sigma phase and austenite phase by the eutectoid reaction, transformation into Chi phase in regions enriched with high Mo element along grain boundaries, and direct transformation into secondary austenite phase. In addition, the thermodynamic calculation and most of empirical formulas predicts the solidification mode is FA mode. From the microstructure analysis, the solidification mode of ESR ingots change from AF mode to FA mode from surface to center. Furthermore, the formulas proposed by Hull provides most accurate predictions results in ferrite content.

Analysis of erosion rate in Sleman District using the USLE (Universal Soil Loss Equation) method

Abstract Population growth has resulted in land conversion. One consequence is the potential for erosion. This research is to determine the rate and level of erosion hazard in Sleman Regency. The research was conducted using a survey method. Location determination was carried out purposively, while representative samples were determined using a stratified random sampling method based on land catena which is divided into 4 geomorphic units, namely upper slope, middle slope, lower slope and foot slope. The data obtained were analyzed using the empirical Universal Soil Loss Equation (USLE) formula. The results of the research show that the predicted erosion rate for Sleman Regency in the upper slope geomorphic units is 2.44-331.23 tons/ha/year, belonging to the very light to heavy erosion hazard class. In the middle slope geomorphic unit, it is 0.77-28.34 tons/ha/year with an erosion hazard level that is classified as very light to light. In the lower slope geomorphic unit, it is 0.43-6.62 tons/ha/year with a very light level of erosion hazard, while in the toe slope geomorphic unit it is 0.35-57.05 tons/ha/year with an erosion hazard level classification. which is classified as very light to mild.

Research on temperature performance prediction of vortex tubes based on artificial neural networks

Abstract This study constructs a hybrid neural network model by integrating the physical constraints of the Bernoulli equation and Nikolaev's formula. The model is designed to explore and predict the variation pattern of the cold end temperature in a vortex tube. The input parameters include inlet pressure, inlet temperature, and cold mass fraction, with the cold end temperature as the output parameter. The network employs a multilayer feedforward model and the Levenberg-Marquardt learning algorithm, using a hyperbolic tangent function as the activation function. To evaluate the statistical validity of the developed model, the coefficient of determination (R²) and root mean square error (RMSE) are utilized, along with an analysis of the model's uncertainty and robustness. The hybrid model achieves an R² of 0.9936 and an RMSE of 0.3392, demonstrating strong performance in terms of uncertainty and robustness. These results indicate that the model accurately predicts the cold end temperature variation in the vortex tube. Furthermore, the findings reveal an optimal pressure range (0.49 MPa to 0.76 MPa) and cold mass fraction range (0.1 to 0.2) that minimize the cold end temperature.

Exploration of Changes in Coal Pore Characteristics and Gas Adsorption Characteristics Based on Influence of Stress

As the mining depth increases, the effect of stress on the gas adsorption of coal gradually becomes significant. There are significant differences in the pore volume, specific surface area, and adsorption characteristics of coal before and after stress. In this study, the porosity variation characteristics of coal were studied using axial and confining pressure loading processes, and volumetric stress was introduced to characterize the pore variation law of coal under triaxial stress. By calculating the stress values at different burial depths, gas isothermal adsorption experiments were conducted on coal under different stress effects. The Langmuir equation, D-A equation, and Freundlich empirical formula were used to fit the adsorption experimental results. Combining experiments and models to predict the adsorbed and free gas content under stress, we described the gas adsorption law of coal under different stress effects.

Generalized Itô’s lemma and the stochastic thermodynamics of diffusion with resetting

Abstract Methods from the theory of stochastic processes are increasingly being used to extend classical thermodynamics to mesoscopic non-equilibrium systems. One characteristic feature of these systems is that averaging the stochastic entropy with respect to an ensemble of stochastic trajectories leads to a second law of thermodynamics that quantifies the degree of departure from thermodynamic equilibrium. A well known mechanism for maintaining a diffusing particle out of thermodynamic equilibrium is stochastic resetting. In its simplest form, the position of the particle instantaneously resets to a fixed position x 0 at a sequence of times generated from a Poisson process of constant rate r. Within the context of stochastic thermodynamics, instantaneous resetting to a single point is a unidirectional process that has no time-reversed equivalent. Hence, the average rate of entropy production calculated using the Gibbs–Shannon entropy cannot be related to the degree of time-reversal symmetry breaking. The problem of unidirectionality can be avoided by considering resetting to a random position or diffusion in an intermittent confining potential. In this paper we show how stochastic entropy production along sample paths of diffusion processes with resetting can be analyzed in terms of extensions of Itô’s formula for stochastic differential equations (SDEs) that include both continuous and discrete processes. First, we use the stochastic calculus of jump-diffusion processes to calculate the rate of stochastic entropy production for instantaneous resetting, and show how previous results are recovered upon averaging over sample trajectories. Second, we formulate single-particle diffusion in a switching potential as a hybrid SDE and develop a hybrid extension of Itô’s stochastic calculus to derive a general expression for the rate of stochastic entropy production. We illustrate the theory by considering overdamped Brownian motion in an intermittent harmonic potential. Finally, we calculate the average rate of entropy production for a population of non-interacting Brownian particles moving in a common switching potential. In particular, we show that the latter induces statistical correlations between the particles, which means that the total entropy is not given by the sum of the 1-particle entropies.

Equivalent conversion of different multiaxial stress rupture criteria for creep materials based on skeletal point stresses

Multiaxial creep life prediction of components has been challenging. To cope with the challenge, efforts have been made to develop suitable multiaxial stress rupture criteria (MSRC) based on representative stress concept. Of all MSRCs, the ones due to Sdobyrev and Hayhurst-Leckie (denoted as SHL MSRC), and to Cane (denoted as Cane MSRC) are commonly-used. In this work, the equivalent conversion between the SHL MSRC and the Cane MSRC is investigated based on skeletal point stresses. Equivalent conversion formulae are proposed based on the skeletal point stresses of circumferentially-notched tension (CNT) specimen, and then validated by comparison with the experimental data available in the literature. The equivalent conversion formula between the two MSRCs is found to be dependent on the signs of principal stresses. Therefore, different conversion formulae should be chosen depending on the signs of principal stresses. Afterwards, the applicability of different equivalent conversion formulae is demonstrated for the CNT specimen when skeletal point stresses are available, and for creep crack growth specimen when skeletal point stresses are not available. Finally, the equivalence of the two MSRCs is discussed.

Novel efficient iterative schemes for linear finite element approximations of elliptic optimal control problems with integral constraint on the state

Centering on a distributed optimal control problem governed by elliptic equations with a unilateral integral constraint on the state, we recall the first-order optimality conditions to explore variational formulations. The classical linear finite element method is employed to approximate the equivalent formulae. Taking into account the distinctive structural characteristics of discretized schemes, we divide the discretized optimal conditions into two equivalent matrix schemes. Subsequently, we introduce an efficient iterative algorithm designed to solve the approximation schemes. We demonstrate the convergence of our iterative algorithm and investigate its robustness and uniform optimality under a specified constraint, particularly focusing on small regularization parameters. Finally, numerical tests are conducted using various h and α to illustrate the efficiency of our proposed algorithm. These tests also validate a tremendous reduction in the number of required iterations.

The Carbon Stocks Estimation on Tangga Community Forests of Lombok Utara

Forests are one of the largest carbon dioxide absorbers, the forest's function as a carbon dioxide absorber causes an increase in greenhouse gases in the atmosphere, and carbon dioxide is stored in forest biomass. Forest development to increase carbon dioxide absorption can be carried out in state forest areas or private forests, which also include community forests. This research aims to estimate carbon stocks in the Tangga community forest (HKm) , in the Tangga HKm, Lombok utara, NTB. This research uses quantitative methods. The data collected is standing vegetation data. Standing vegetation data includes saplings, poles and trees by measuring diameter and height using purposive sampling collection techniques. Carbon stocks are estimated using the allometric equation formula. The total carbon reserves in the HKm Tangga obtained from each stand were 9.972,11 ton/ha. The highest carbon stock value is at the tree level with a value of 8.785,08 tons/ha, followed by the sapling level at 731,34 ton/ha, and the pole level at 455,69 tons/ha with the highest amount at the candlenut tree level (Aleurites moluccana) at 2.200,63 ton/ha and the lowest was the breadfruit (Artocarpus altilis) with a value of 1,96 ton/ha.

Recurrence formula for some higher order evolution equations

Riccati’s differential equation is formulated as abstract equation in finite or infinite dimensional Banach spaces. Since the Riccati’s differential equation with the Cole–Hopf transform shows a relation between the first order evolution equations and the second order evolution equations, its generalization suggests the existence of recurrence formula leading to a sequence of differential equations with different order. In conclusion, by means of the logarithmic representation of operators, a transform between the first order evolution equations and the higher order evolution equation is presented. Several classes of evolution equations with different orders are given, and some of them are shown as examples.

Understanding the Role of Economic Education on Generation Z's Lifestyle and Interest in Saving: Why Do Financial Literacy and Circle of Friends Matter?

The lifestyle of the people of a country can also be an illustration of how that country will experience growth in the economic sector. An individual's lifestyle and interest in saving must, of course, be accompanied by knowledge and literacy that can control this. This research aims to determine the influence of economic education on the generation's lifestyle and interest in saving, which is mediated by financial literacy and a circle of friends. The population in this study is generation Z, who live in Petasia District. The sampling technique used the Limeshow equation formula with a determined sample size of 700 respondents. The data collection method uses a questionnaire. The data analysis technique is partial least squares structural equation modeling (PLS-SEM) analysis. The results of this research show that economic education (X) has a positive and significant influence on Generation Z's lifestyle and interest in saving. Then, financial literacy and a circle of friends are able to mediate the influence between economic education and Generation Z's interest in saving. These findings encourage generation Z to optimize economic education, both formal and informal, as well as increase financial literacy, in order to maintain their lifestyle. It is also necessary to optimize learning access and provide great opportunities for Generation Z to increase their financial literacy.

MANAJEMEN STOK PANGAN RUMAH TANGGA PETANI PADI ANGGOTA LUMBUNG PANGAN DI KECAMATAN AMBARAWA KABUPATEN PRINGSEWU

This study aimed firstly to analyze the management of household food stocks and secondly to analyze the various factors affecting household food stocks for rice farmers. All rice farmers were members of the food barn in Ambarawa Sub-district, Pringsewu District. The samples were selected by simple random sampling consisting of 7 granaries with a total of 70 members. The data were collected from January to February 2023. To obtain the first objective, the data were analyzed by using the calculation of food stocks referring to the Chafid equation formula (2017), i.e. the amount of food inventory was subtracted by its sale quantity and its utilization. To obtain the second objective, the data were analyzed by using the multiple linear regression. The results showed that the food stocks of rice farmers who were members of the food barn were 573 kg of MDG in the first season and 450 kg of MDG in the second season, which were not an ideal amount for food stock. This was because the ideal amounts of needs were 586.93 kg of MDG for the first season and 591.51 kg of MDG for the second season. Some of the factors affecting the food stock of the rice farming households incorporated in food barns were land area and household income. Key words: regression analysis, sale delay analysis, stocks, storage.

Feynman-Kac formula for general diffusion equations driven by TFBM with Hurst index H ∈ (0,1)

We consider the general diffusion equation driven by tempered fractional Brownian motion (TFBM)∂u(t,x)∂t=Lu(t,x)+u(t,x)dBH,λ(t)dt,(t,x)∈R+×Rd, where L is the infinitesimal generator of some time-homogeneous Markov process {Xt}t≥0 and {BH,λ(t)}t∈R is a tempered fractional Brownian motion with Hurst index H∈(0,12)∪(12,1) and tempering parameter λ>0 which is independent of {Xt}t≥0. Based on approximating TFBM with a family of Gaussian processes possessing absolutely continuous sample paths, a unified framework of the Feynman-Kac formulau(t,x)=Ex[f(Xt)]eBH,λ(t) is established for the general stochastic diffusion equation driven by TFBM with the initial value f, Hurst index H∈(0,12)∪(12,1) and tempering parameter λ>0. The difficulty is that the Hurst parameter H can be allowed to be less than 1/2. The idea is to explore the above simplest form, to utilize the techniques of Malliavin calculus. By using the properties of TFBM and especially that of the modified Bessel function of the second kind, we prove that the process defined by the Feynman-Kac formula is the mild and weak solutions of the general diffusion equation driven by TFBM. From the Feynman-Kac formula, we exhibit the smoothness of the density of the solution and the sharp Hölder regularity. We further show that limt→∞⁡ln⁡‖u(t,⋅)‖pg(t)=0 in the almost surely sense where p∈R and the function g:R+→R+ grows at least as fast as a linear function. The Feynman-Kac formula for the stochastic general diffusion equation in the Skorohod sense is also achieved by exploring the relationship between the Stratonovich and Skorohod integrals.

One-dimensional analysis of pressure variations induced by trains passing each other in a tunnel

In this study, the asymptotic solutions of the pressure variations induced by two trains passing each other in a tunnel are theoretically investigated. The one-dimensional inviscid compressible airflow is analysed, and two methods to obtain numerically exact solutions and $M_{H}$ expansion formulas for approximate equations are presented, where $M_{H}$ is the Mach number of the high-speed train. The pressure coefficient, corresponding to the maximum value of the magnitude of the pressure, is expressed as $|c_{p}|_{max}=|c_{p,min}|=[({R}/({1-R}))$ $(1+\alpha )^{2}+({R(1-R)}/{(1-2R)^{2}})(1-\alpha )^{2}]+O[M_{H}]$ , where $c_{p,min}<0$ , $\alpha =U_{L}/U_{H}$ and $U_{L}$ and $U_{H}$ denote the speeds of the low- and high-speed trains, respectively, and $R$ is the cross-sectional area ratio of the train to the tunnel. The theoretical results indicate the dependence of the speeds of the two trains on the pressure distribution and that the maximum magnitude of the asymptotic pressure for a fixed value of $M_{H}$ is obtained for $\alpha =1$ and $\alpha =0$ when $R< R_{c}$ and $R>R_{c}$ , respectively, where $R_{c}$ denotes the critical blockage ratio. Because the airflow along the side of the low-speed train, induced by the low-speed train, is along the running direction of the high-speed train and reduces the relative velocity of the high-speed train as the two trains pass each other, $|c_{p}|_{max}$ for $\alpha =0$ is larger than $|c_{p}|_{max}$ for $\alpha =1$ when $R>R_{c}$ . It is theoretically demonstrated that, as conventional high-speed railway systems satisfy $R< R_{c}$ , a conservative pressure estimation can be established assuming $\alpha =1$ .

Feynman–Kac Formulas for Difference-differential Equations of Retarded Type

Feynman–Kac Formulas for Difference-differential Equations of Retarded Type

On the Itô–Alekseev–Gröbner formula for stochastic differential equations

On the Itô–Alekseev–Gröbner formula for stochastic differential equations