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Journal articles on the topic 'Empirical equation'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Zimdahl, Robert L., Brian K. Cranmer, and Walter W. Stroup. "Use of Empirical Equations to Describe Dissipation of Metribuzin and Pendimethalin." Weed Science 42, no. 2 (1994): 241–48. http://dx.doi.org/10.1017/s0043174500080346.

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Four equations were evaluated as predictors of the rate of herbicide dissipation in soil. A biexponential equation was superior to the first-order equation for metribuzin and pendimethalin dissipation under five moisture levels and three temperatures in laboratory and field studies. The Hoerl function, adapted in the course of this work, is also a good descriptor. The first-order equation predicts slower initial and more rapid later dissipation than actually occurs and these deficiencies are not shared by the biexponential or Hoerl equations. The first-order equation ignores small residues rem

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2

Samdarshi, S. K., and S. C. Mullick. "Analytical Equation for the Top Heat Loss Factor of a Flat-Plate Collector With Double Glazing." Journal of Solar Energy Engineering 113, no. 2 (1991): 117–22. http://dx.doi.org/10.1115/1.2929955.

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An analytical equation for the top heat loss factor of a flat-plate collector with double glazing has been developed. The maximum computational errors resulting from the use of this equation are plus or minus three percent compared to numerical solution of the heat balance equations. The equation is considerably more accurate than the currently used semi-empirical equations over the entire range of variables covered. It is found that the computational errors resulting from simplification of the proposed equation by approximation of the individual heat-transfer coefficients are much lower than

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3

Sabeti, Ramtin, and Mohammad Heidarzadeh. "A new empirical equation for predicting the maximum initial amplitude of submarine landslide-generated waves." Landslides 19, no. 2 (2021): 491–503. http://dx.doi.org/10.1007/s10346-021-01747-w.

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AbstractThe accurate prediction of landslide tsunami amplitudes has been a challenging task given large uncertainties associated with landslide parameters and often the lack of enough information of geological and rheological characteristics. In this context, physical modelling and empirical equations have been instrumental in developing landslide tsunami science and engineering. This study is focused on developing a new empirical equation for estimating the maximum initial landslide tsunami amplitude for solid-block submarine mass movements. We are motivated by the fact that the predictions m

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4

UENO, Masakatsu, and Kametaro ITOH. "Empirical Verification of GROSSMANN'S Equation." Tetsu-to-Hagane 74, no. 5 (1988): 918–24. http://dx.doi.org/10.2355/tetsutohagane1955.74.5_918.

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5

Wiśniewski, Jerzy Witold. "Empirical Econometric Model of an Enterprise." Folia Oeconomica Stetinensia 16, no. 1 (2016): 232–47. http://dx.doi.org/10.1515/foli-2016-0015.

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Abstract This work will present an empirical econometric model describing an enterprise within the category of medium-sized companies (according to European Union classification). The company, code-named ENERGY, carries out a manufacturing, commercial, and service business activity. The statistical data used was in the form of quarterly time series, containing 24 statistical observations from the years 2008–2013. A hypothetical model of the enterprise is a system of interdependent equations. The econometric model is composed of seven stochastic equations. The empirical model is missing the equ

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6

Leary, Rolfe A. "Near-normal, empirical, and identity yield tables for estimating stand growth." Canadian Journal of Forest Research 21, no. 3 (1991): 353–62. http://dx.doi.org/10.1139/x91-043.

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Historically, forest growth was estimated using a normal or near-normal yield table as a density standard, and a relative density change equation to estimate approach to the standard. Although normal yield tables have come under intense criticism, critics have generally ignored the relative density change equation. If a yield table captures the "true" relations between volume, age, and site for a species, the relative density change equation can be a simple function of initial relative density and age. If a yield table does not capture the true relations between volume, site, and age, the inad

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7

Lozano Povis, Arlitt Amy, and Elías Adrián Sanabria Perez. "Experimental Evaluation of an Empirical Equation in a Gaseous Flow." Chemistry & Chemical Technology 18, no. 1 (2024): 57–65. http://dx.doi.org/10.23939/chcht18.01.057.

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In this paper, the estimation error of Dr. Pole's empirical equation was evaluated using copper pipes of different diameters (0.00953, 0.0127, 0.01588 m), under different flow pressure conditions (0, 300, 500, 1000, 1500, 2000, 2500, 3000 L/h). To carry out the experiments, the following instruments were used: an air compressor, 2 flow valves, a needle valve, a gas rotameter, copper piping, pressure gauges and transmitters, a Norus data logger with 4 to 20 mA output signals, thermocouples, and thermoresistors. They allow us to establish that the air pressure drops when the flowing through the

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8

Saglam, Ugur, Kemal Ulutas, Yagmur Parim, Sahin Yakut, and Deniz Deger. "A theoretical approach to conductivity." International Journal of Geometric Methods in Modern Physics 17, no. 01 (2019): 2050004. http://dx.doi.org/10.1142/s0219887820500048.

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In amorphous semiconductors and insulators, the using conductivity formulas are semi-empirical and have no satisfying physical explanations. A conductivity equation has been derived by Debye for the response of ideal materials which is rarely observed in practice, but a general conductivity equation which includes the previous empirical equations via a correct choice of arbitrary parameters and moreover totally theoretical derivation had to be generated. Hence, to determine the motion of electrons in the amorphous environment, we defined the equation of motion including viscous forces as a fun

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9

Awal, Ripendra, Atikur Rahman, Ali Fares, and Hamideh Habibi. "Calibration and Evaluation of Empirical Methods to Estimate Reference Crop Evapotranspiration in West Texas." Water 14, no. 19 (2022): 3032. http://dx.doi.org/10.3390/w14193032.

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Evapotranspiration is an essential component of the hydrologic cycle, and its accurate quantification is crucial for managing crop water requirements and the operation of irrigation systems. Evapotranspiration data is key to hydrological and water management research investigations, including studying the impact of various climatic factors on crop water requirements. It has been estimated as the product of the reference crop evapotranspiration and crop coefficient. Daily reference crop evapotranspiration (ETo) can be determined by several methods and equations. The Food and Agriculture Organiz

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10

Li, Jianqiao, Weidong Song, Jianguo Ning, and Huiping Tang. "Characteristics of impact-generated plasma with different electron temperature and gas temperature." Modern Physics Letters B 28, no. 18 (2014): 1450152. http://dx.doi.org/10.1142/s0217984914501528.

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The characteristics of the plasma with difference between the electron temperature and gas temperature were investigated and the relationship between the plasma ionization degree and the internal energy of a system was obtained. A group of equations included the chemical reaction equilibrium equation, the chemical reaction rate equation and the energy conservation equation were adopted to calculate the electron density, the electron temperature and the atom temperature with a given internal energy. These equations combined with Navier–Stokes (N–S) equations is solved by a smooth particle hydro

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11

Samdarshi, S. K., and S. C. Mullick. "Generalized Analytical Equation for the Top Heat Loss Factor of a Flat-Plate Solar Collector With N Glass Covers." Journal of Solar Energy Engineering 116, no. 1 (1994): 43–46. http://dx.doi.org/10.1115/1.2930064.

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A generalized analytical equation for the top heat loss factor of a flat-plate collector with one or more glass covers has been developed. The maximum computational errors resulting from the use of the analytical equation with several simplifications are ± 5 percent compared to numerical solution of the set of heat balance equations. The analytical equation is considerably more accurate than the available semi-empirical equations over the entire range of variables covered. An additional advantage of the proposed technique over the semi-empirical equations is that results can be obtained for di

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12

Bujak, Damjan, Suzana Ilic, Hanna Miličević, and Dalibor Carević. "Wave Runup Prediction and Alongshore Variability on a Pocket Gravel Beach under Fetch-Limited Wave Conditions." Journal of Marine Science and Engineering 11, no. 3 (2023): 614. http://dx.doi.org/10.3390/jmse11030614.

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Most empirical equations used for wave runup predictions have been developed from measurements at straight sandy beaches in unlimited fetch environments. While there are empirical equations to predict wave runup on gravel beaches, they have not been tested for prediction of wave runup on pocket gravel beaches, in limited-fetch environment, which can be found around Mediterranean. This paper addresses this lack of measurements on this type of beaches and examines the alongshore variability of wave runup. Wave runup measurements were made using video observations along 3 cross-sectional profiles

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13

Al-Saadi, Balsam J. M., and Hussein A. M. Al-Zubaidi. "Reaeration Coefficient Empirical Equation Selection for Water Quality Modeling in Surface Waterbodies: An Integrated Numerical-Modeling-Based Technique with Field Case Study." Limnological Review 25, no. 2 (2025): 15. https://doi.org/10.3390/limnolrev25020015.

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Empirical equations were developed by many investigators to determine the reaeration coefficients (Ka) required for predicting dissolved oxygen concentrations (DO) in surface waters, especially rivers, lakes, and reservoirs. However, these equations yield a wide range of Ka values. In this paper, an integrated numerical-modeling-based technique was developed to check the validity of the equations before using them in water quality modeling for rivers, lakes, and reservoirs. Depending on direct field measurements at the Hilla River headwater (Saddat Al-Hindiyah Reservoir, Iraq), the temporal ox

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14

Lorenzoni, M., D. Giannetto, G. Maio, et al. "Empirical standard mass equation forSalmo marmoratus." Journal of Fish Biology 81, no. 6 (2012): 2086–91. http://dx.doi.org/10.1111/j.1095-8649.2012.03459.x.

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15

Wu, N. S., and W. Wei. "Empirical equation for relative non-overlap." Chromatographia 35, no. 7-8 (1993): 471. http://dx.doi.org/10.1007/bf02278606.

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16

Kolin, Branko, Gradimir Danon, and Tatjana Stevanovic Janezic. "Empirical Equation for Limit of Hygroscopicity." Drying Technology 13, no. 8-9 (1995): 2133–39. http://dx.doi.org/10.1080/07373939508917069.

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17

Wu, N. S., and W. Wei. "Empirical equation for relative non-overlap." Chromatographia 34, no. 9-10 (1992): 450–52. http://dx.doi.org/10.1007/bf02290234.

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18

Cheng, Wen Ting, Shuo Feng, Xiao Qin Cui, and Fang Qin Cheng. "Solubility of Benzoic Acid in Ethanol, Benzene, Acetic Acid and Ethyl Acetate from 291.69 to 356.27 K." Advanced Materials Research 518-523 (May 2012): 3975–79. http://dx.doi.org/10.4028/www.scientific.net/amr.518-523.3975.

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Using a synthetic method designed and installed with laser monitor on line, the solubility values of benzoic acid in ethanol, benzene, acetic acid and ethyl acetate were determined over the temperature range of 291.69-356.27 K. The solubility of benzoic acid in all cases investigated was found to increase with temperature. The two-parameters empirical and λh equations were used successfully to correlate experimental data of benzoic acid solubilities in organic solvents. The mean absolute error σ of 65 data points correlating by two-parameters empirical equation and λh equation was less than 1%

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19

Yuen, Pong Kau, Cheng Man Diana Lau, and Kuok In Gabriel Yuen. "Chemical Formula-based Method for Balancing Organic Combustion and Quantifying Redox Parameters." International Journal of Chemistry 17, no. 2 (2025): 36. https://doi.org/10.5539/ijc.v17n2p36.

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Organic combustion is a classic redox reaction. In the study of stoichiometric organic combustion, structural formula has been given little attention when compared to empirical formula. This article uses the arithmetic method to develop a chemical formula-based molecular organic combustion equation, in which the mean oxidation number of organic carbons is selected to be a redox and structural metric for differentiating empirical formula and structural formula, connecting redox parameters, and balancing organic combustion equations. When any empirical formula of organic matter is given, the org

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20

Watanabe, Yoshimasa, Sumio Masuda, Kiyoshi Nishidome, and Chalermraj Wantawin. "Mathematical Model of Simultaneous Organic Oxidation, Nitrification, and Denitrification in Rotating Biological Contactors." Water Science and Technology 17, no. 2-3 (1985): 385–97. http://dx.doi.org/10.2166/wst.1985.0145.

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Simultaneous organic oxidation and nitrification rates in the RBC are given using a mathematical equation. The equation was derived from a hypothesis stating that intrinsic oxygen uptake rate of the biofilm has a constant value at a fixed temperature , independent of the composition of the aerobic bacteria. Based on this hypothesis, empirical equations are proposed to describe the profile of intrinsic organic oxidation and nitrification rates. Computer simulation of the simultaneous organic oxidation and nitrification was carried out to confirm the empirical equations. The mathematical model o

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21

Galushkin, Nikolai Efimovich, Natal'ya Nikolaevna Yazvinskaya, and Dmitrii Nikolaevich Galushkin. "Capacitance from Discharge Current Depen-dence Modeling in Nickel-Cadmium Batteries." Electrochemical Energetics 12, no. 3 (2012): 147–54. http://dx.doi.org/10.18500/1608-4039-2012-12-3-147-154.

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It was shown by experiments for SAFT batteries of stationary application and medium rate of discharge, that empirical equations Korovin–Skundin’s, Peukert’s generalized equation, probability integral, porous electrode equation allow to describe the dependence capacitance C(i), given by nickel-cadmium batteries, from discharge current with the accuracy sufficient for practical needs (5–6 %) on all the range of discharge currents. Meanwhile the empirical equations of Peukert and Aguf can be used to calculate the capacitance given away only within the discharge currents, starting from the point o

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22

Zhao, Yuyang, and Hongbo Zhao. "Symbolic Regression for the Determination of Joint Roughness Coefficient." Mathematical and Computational Applications 30, no. 1 (2025): 17. https://doi.org/10.3390/mca30010017.

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In this study, a novel symbolic regression-based empirical equation has been developed to compute the joint roughness coefficient (JRC) value based on the statistical parameters of rock joints. The symbolic regression was adopted to map the nonlinear function, which represents the relation between the JRC and statistical parameters of the rock joint, based on the collected rock joint dataset. It is not necessary to presume the mathematical function form of the empirical equation, which is used to fit the rock joint data while using symbolic regression. The collected rock joint samples from the

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23

Hitoshi Shoji, Takao Kameda, Kunio Kawada, Okitsugu Watanabe, and Henrik B. Clausen. "An empirical relation between overburden pressure and firn density." Annals of Glaciology 20 (1994): 87–94. http://dx.doi.org/10.3189/1994aog20-1-87-94.

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Two empirical equations for firn densification have been obtained,considering firn porosity as a function of overburden pressure. In the first equation, thereduction ratio of porosity in firn is assumed to be proportional to the increasing ratioof overburden pressure and the mth power of the porosity. The porosity exponent m should be close to -2, so as to have a best-fit with 14 depth-density profiles fromGreenland and Antarctica. In the second equation, the reduction ratio of porosity wasassumed to increase proportionally to the increment of overburden pressure and thenth power of the porosi

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24

Hitoshi Shoji, Takao Kameda, Kunio Kawada, Okitsugu Watanabe, and Henrik B. Clausen. "An empirical relation between overburden pressure and firn density." Annals of Glaciology 20 (1994): 87–94. http://dx.doi.org/10.1017/s0260305500016281.

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Two empirical equations for firn densification have been obtained,considering firn porosity as a function of overburden pressure. In the first equation, thereduction ratio of porosity in firn is assumed to be proportional to the increasing ratioof overburden pressure and the mth power of the porosity. The porosity exponentmshould be close to -2, so as to have a best-fit with 14 depth-density profiles fromGreenland and Antarctica. In the second equation, the reduction ratio of porosity wasassumed to increase proportionally to the increment of overburden pressure and thenth power of the porosity

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25

DEHWAH, AHMAD H., IDRIS A. AJIA, and JOHN S. MARSLAND. "EMPIRICAL FORMULAE FOR EXCESS NOISE FACTOR WITH DEAD SPACE FOR SINGLE CARRIER MULTIPLICATION." Fluctuation and Noise Letters 10, no. 03 (2011): 315–21. http://dx.doi.org/10.1142/s0219477511000600.

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In this letter, two empirical equations are presented for the calculation of the excess noise factor of an avalanche photodiode for single carrier multiplication including the dead space effect. The first is an equation for calculating the excess noise factor when the multiplication approaches infinity as a function of parameters that describe the degree of the dead space effect. The second equation can be used to find the minimum value of the excess noise factor for any multiplication when the dead space effect is completely dominant, the so called "deterministic" limit. This agrees with the

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26

Dam, Thang Trong, and Bang Xuan Vu. "Research to establish the equation of the principle of claystone breaking under the seabed." Journal of Mining and Earth Sciences 64, no. 5 (2023): 109–19. http://dx.doi.org/10.46326/jmes.2023.64(5).10.

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The rule of breaking rock has practical significance in the process of controlling the blasting for the optimization of mine production or construction of blasting works. The equations describing the particle size distribution after the explosion are established in an experimental form corresponding to the specific conditions of the blasting work. It only has the meaning of a mathematical regression function and does not reflect the characteristics of the rock type, explosive conditions and explosive results. This research has exploited the theory of rock breaking from the point of view of pro

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27

Kemp, Jonathan, Benoit Vandeputte, Thomas Eccleshall, Richard Simons, and Peter Troch. "A MODIFIED HYPERBOLIC TANGENT EQUATION TO DETERMINE EQUILIBRIUM SHAPE OF HEADLAND BAY BEACHES." Coastal Engineering Proceedings, no. 36 (December 30, 2018): 106. http://dx.doi.org/10.9753/icce.v36.papers.106.

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When designing any artificial beach, itâ€™s desirable to avoid (or minimise) future maintenance commitments by arranging the initial beach planshape so that it remains in equilibrium given the incident wave climate. Headlands bays, or embayments, where a sandy beach is held between two erosion resistant headlands, tend to evolve to a stable beach planshape with little movement of the beach contours over time. Several empirical bay shape equations have been derived to fit curves to the shoreline of headland bay beaches. One of the most widely adopted empirical equations is the parabolic bay sha

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28

Fernandes, Lázaro Costa, Célia Maria Paiva, and Otto Corrêa Rotunno Filho. "Evaluation of six empirical evapotranspiration equations - case study: Campos dos Goytacazes/RJ." Revista Brasileira de Meteorologia 27, no. 3 (2012): 272–80. http://dx.doi.org/10.1590/s0102-77862012000300002.

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The evapotranspiration is a component of the water balance constituting a major challenge in its quantification. The complex physical processes involved in its effective determination on a large scale have spurred scientists to often make use of empirical equations, which have inherent limitations with regard to their applicability as descriptors of the evapotranspiration behavior in different regions across the world. This study was performed for the Campos dos Goytacazes region, in Rio de Janeiro state. It is proposed to investigate and to evaluate the performance of six empirical equations

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29

Folmar, Norman D., and Arthur C. Miller. "Development of an Empirical Lag Time Equation." Journal of Irrigation and Drainage Engineering 134, no. 4 (2008): 501–6. http://dx.doi.org/10.1061/(asce)0733-9437(2008)134:4(501).

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30

Saeki, Susumu. "Empirical equation of state for supercritical fluids." Journal of Supercritical Fluids 8, no. 1 (1995): 30–45. http://dx.doi.org/10.1016/0896-8446(95)90048-9.

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31

Ferrer, Gerard, Stefan Gschwander, Aran Solé, et al. "Empirical equation to estimate viscosity of paraffin." Journal of Energy Storage 11 (June 2017): 154–61. http://dx.doi.org/10.1016/j.est.2017.03.002.

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32

Toscani, Siro, and Henri Szwarc. "An empirical equation of state for liquids." Journal of Chemical & Engineering Data 38, no. 4 (1993): 591–97. http://dx.doi.org/10.1021/je00012a031.

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33

Girko, V. L. "Canonical spectral equation for empirical covariance matrices." Ukrainian Mathematical Journal 47, no. 9 (1995): 1341–55. http://dx.doi.org/10.1007/bf01057509.

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34

Zhenyu, Tan, and He Yancai. "An empirical energy loss equation of electrons." Scanning 24, no. 1 (2006): 46–51. http://dx.doi.org/10.1002/sca.4950240107.

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35

Imai, Keisuke, and Eiji Ōsawa. "An empirical extension of the karplus equation." Magnetic Resonance in Chemistry 28, no. 8 (1990): 668–74. http://dx.doi.org/10.1002/mrc.1260280803.

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36

Yuen, Pong Kau, Cheng Man Diana Lau, and Kuok In Gabriel Yuen. "Empirical Buswell’s Equation for Identifying Anaerobic Digestate." International Journal of Chemistry 17, no. 2 (2025): 1. https://doi.org/10.5539/ijc.v17n2p1.

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Anaerobic digestion is a promising circular economic technology. Using organic matters as feedstocks, Buswell&rsquo;s equation can represent anaerobic digestion in accordance with the elemental composition of any organic matter. An organic feedstock is biodegradable to biomethane, biogenetic carbon dioxide, and digestate, but the management of anaerobic digestate encounters some environmental and technological challenges. Currently there is a research gap between Buswell&rsquo;s concept and the general organic elemental composition of unknown anaerobic digestate. To bridge the gap, thi

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37

Bagi, Richárd, Filip Alamaa, and Felix Ryde. "Empirical relations in thermal Comptonization." Monthly Notices of the Royal Astronomical Society 536, no. 1 (2024): 603–8. https://doi.org/10.1093/mnras/stae2664.

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ABSTRACT In many astrophysical systems, photons interact with matter through thermal Comptonization. In these cases, under certain simplifying assumptions, the evolution of the photon spectrum is described by an energy diffusion equation such as the Kompaneets equation, having dependencies on the seed photon temperature, $\theta _i$, the electron temperature, $\theta _e$, and the Compton y-parameter. The resulting steady-state spectrum is characterized by the average photon energy and the Compton temperature, which both lack analytical dependencies on the initial parameters. Here, we present e

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38

Oliveira, Vanessa Vaz de, Marcos Vinícius Mateus, Julio Cesar De Souza Inácio Gonçalves, Alex Garcez Utsumi, and Marcius Fantozzi Giorgetti. "Prediction of the longitudinal dispersion coefficient for small watercourses." Acta Scientiarum. Technology 39, no. 3 (2017): 291. http://dx.doi.org/10.4025/actascitechnol.v39i3.29397.

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Longitudinal dispersion coefficient (DL) is considered an essential physical parameter to water quality modeling in rivers. Therefore, the estimation of this parameter with high accuracy guarantees the reliability of the results of a water quality model. In this study, the observed values of longitudinal dispersion coefficient are determined for natural streams (with discharge less than 2.84 m3s-1), based on sets of measured data from stimulus-response tests using sodium chloride as a tracer. Additionally, a semi-empirical equation for prediction of DL is derived using dimensional analysis and

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39

Zerihun, Yebegaeshet T. "A Study of the Sedimentation and Storage Capacity Depletion of a Reservoir." Slovak Journal of Civil Engineering 31, no. 2 (2023): 37–47. http://dx.doi.org/10.2478/sjce-2023-0011.

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Abstract Theoretical and empirical equations have previously been proposed to compute the sediment trap efficiency of a reservoir. The empirical equations were developed by analyzing a limited amount of field data for reservoirs in selected areas; thus, their suitability is restricted to reservoirs in regions with similar hydrological characteristics. In this study, a sediment trap-efficiency equation, which accounts for the dynamic behavior of sedimentation and the hydraulic conditions of a reservoir, was deduced from the principle of mass conservation. Using this equation, the approximate an

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40

Cano, Nicolas D., Antonio P. de Camargo, Gustavo L. Muniz, Jonesmar de Oliveira, José G. Dalfré Filho, and José A. Frizzone. "Performance of models to determine flow rate using orifice plates." Revista Brasileira de Engenharia Agrícola e Ambiental 25, no. 1 (2021): 10–16. http://dx.doi.org/10.1590/1807-1929/agriambi.v25n1p10-16.

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ABSTRACT This study aimed to evaluate three methodologies for orifice-plate water-flow estimation by quantifying errors in the flow determinations to propose an appropriate measurement range for each evaluated condition. Two orifice-plate models (nominal diameters of 100 and 150 mm) with 50% restriction in the flow section were evaluated. In the theoretical equations, the discharge coefficient was obtained using the Reader-Harris/Gallagher equation (Method 1) and approximated from experimental data using the angular coefficient of a zero-intercept straight line (Method 2). The recommended meas

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41

Tang, Han, and Wenfei Li. "Empirical study for uncertain finance." Journal of Intelligent & Fuzzy Systems 40, no. 5 (2021): 9485–92. http://dx.doi.org/10.3233/jifs-201955.

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Interest rate, stock and option are all important parts of finance. This paper applies uncertain differential equation to the study of the evolution of interest rate and stock price separately. Based on actual observations, we estimate the parameters in uncertain differential equation with the method of moments. Using the introduced interest rate and stock models, we price European options and compare the results with actual observations. Finally, a paradox of the stochastic financial model is stated.

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42

Gordeev, D. G., L. F. Gudarenko, M. V. Zhernokletov, V. G. Kudel’kin, and M. A. Mochalov. "Semi-empirical equation of state of metals. Equation of state of aluminum." Combustion, Explosion, and Shock Waves 44, no. 2 (2008): 177–89. http://dx.doi.org/10.1007/s10573-008-0024-y.

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43

Jayadev, M. "Predictive Power of Financial Risk Factors: An Empirical Analysis of Default Companies." Vikalpa: The Journal for Decision Makers 31, no. 3 (2006): 45–56. http://dx.doi.org/10.1177/0256090920060304.

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This paper provides empirical evidence on the significance of financial risk factors in predicting default companies. Traditionally, credit decision process is built on accounting ratios derived from financial statements of the borrower. Combining various ratios through application of multivariate statistical techniques and testing their predictive power has been popular in credit risk quantification. Altman's Z-score model is the most acceptable model in this category. In this paper, three forms of Z-score models are applied: The first equation is developed by surveying the internal credit ra

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44

Zhao, Ming-Xian, Gui-Ming Le та Jianyong Lu. "Can We Estimate the Intensities of Great Geomagnetic Storms (ΔSYM-H ≤ −200 nT) with the Burton Equation or the O’Brien and McPherron Equation?" Astrophysical Journal 928, № 1 (2022): 18. http://dx.doi.org/10.3847/1538-4357/ac50a8.

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Abstract We input the solar wind parameters responsible for the main phases of 15 great geomagnetic storms (GGSs; ΔSYM-H ≤ −200 nT) into the empirical formulae created by Burton et al. (hereafter the Burton equation) and by OBrien & McPherron (hereafter the OM equation) to evaluate whether these two equations can correctly estimate the intensities of GGSs. The results show that the intensities of most GGSs estimated by the OM equation are much smaller than the observed intensities. The rms error between the intensities estimated by the OM equation and the observed intensities is 203 nT, im

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Hurdle, V. F., and Dominique Lord. "Analysis of Two Left-Turn Equations from the Highway Capacity Manual." Transportation Research Record: Journal of the Transportation Research Board 1646, no. 1 (1998): 71–78. http://dx.doi.org/10.3141/1646-09.

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The left-turn procedures in the Highway Capacity Manual are complex, and some of the equations are presented with little explanation of how they were obtained and the assumptions they embody. This paper is an analytic exploration of two of the four equations used to estimate gq, the amount of green time needed to discharge the opposing queue, and gf, the amount of green time available for through vehicles before the first left-turning vehicle enters the intersection. The investigation reveals surprising hidden assumptions underlying Equation 9-17 for gq, which lead to errors when the opposing

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Meng, Q., Y. Li, and J. Xu. "New empirical stiffness equations for corner-filleted flexure hinges." Mechanical Sciences 4, no. 2 (2013): 345–56. http://dx.doi.org/10.5194/ms-4-345-2013.

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Abstract. This paper investigates the existing stiffness equations for corner-filleted flexure hinges. Three empirical stiffness equations for corner-filleted flexure hinges (each fillet radius, r, equals to 0.1 l; l, the length of a corner-filleted flexure hinge) are formulated based on finite element analysis results for the purpose of overcoming these investigated limitations. Three comparisons made with the existing compliance/stiffness equations and finite element analysis (FEA) results indicate that the proposed empirical stiffness equations enlarge the range of rate of thickness (t, the

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Hosseini, S. M. "Densities and derived properties of nanofluids from new empirical model based on Pack-Cho scheme." High Temperatures-High Pressures 53, no. 4 (2024): 323–38. http://dx.doi.org/10.32908/hthp.v53.1611.

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This work aimed to develop a new empirical model for density and derived properties of nanofluids using a new empirical equation based on Pack-Cho scheme. The previously developed Tammann-Tait based model by the author has suffered a mathematical drawback to properly represent isothermal compressibility and isobaric expansivity confident values with respect to the nanoparticle fraction. Then, that drawback has been fixed through the above-mentioned approach. The base fluid contributions were obtained from Tammann-Tait equation of earlier work, whereas the nanoparticle contribution was expresse

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Khalid, Muhammad Ashraf, Abdul Razzaq Ghumman, and Ghufran Ahmed Pasha. "A Comparative Analysis of Sediment Concentration Using Artificial Intelligence and Empirical Equations." Hydrology 11, no. 5 (2024): 63. http://dx.doi.org/10.3390/hydrology11050063.

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Morphological changes in canals are greatly influenced by sediment load dynamics, whose estimation is a challenging task because of the non-linear behavior of the sediment concentration variables. This study aims to compare different techniques including Artificial Intelligence Models (AIM) and empirical equations for estimating sediment load in Upper Chenab Canal based on 10 years of sediment data from 2012 to 2022. The methodology involves utilization of a newly developed empirical equation, the Ackers and White formula and AIM including 20 neural networks with 10 training functions for both

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Le, Giang Song, and Hung Manh Le. "PRELIMINARY RESULT OF DEVELOPMENT OF 3D NUMERICAL MODEL FOR MORPHOLOGICAL PROCESS." Science and Technology Development Journal 12, no. 18 (2009): 5–11. http://dx.doi.org/10.32508/stdj.v12i18.2376.

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The paper presented a 3D numerical model for calculation of flow and sediment transport in channels. The flow is calculated by solving the Reynolds equation with hydrostatic assumption. Suspended-load is simulated by transport equation while bed-load is calculated using empirical formula. Bed transformation is obtained by solving an overall mass-balance equation. All equations are solved using finite volume method. The model is applied for study of bed deformation of VamNao river in the Mekong delta.

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Soriano, C. M., and P. E. Quinay. "Development of Fragility Curves for the Underground PVC Water Distribution Pipes in Quezon City and Damage Estimation under a Magnitude 7.2 Scenario Earthquake." IOP Conference Series: Earth and Environmental Science 1091, no. 1 (2022): 012005. http://dx.doi.org/10.1088/1755-1315/1091/1/012005.

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Quezon City is traversed by the West Valley Fault System (WVFS) that has the capability of generating a magnitude 7.2 earthquake known as “The Big One”. It has an extensive water distribution network that is very susceptible to damages that will be caused by the ground shaking component of the M 7.2 earthquake. This study focuses on determining the behavior and estimating the damage of underground polyvinyl chloride (PVC) water pipes due to the M 7.2 earthquake by using appropriate empirical repair rates (RR) and developing fragility curves. The appropriate empirical RR equation was determined

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