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Journal articles on the topic 'Empirical equation'

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Published: 4 June 2021
Last updated: 19 February 2022

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1

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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2

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 (June 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 remaining late in the dissipation process. These residues are important from an environmental point of view and the Hoerl and biexponential equations are more capable of dealing with them.
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3

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 (May 1, 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 the errors resulting from the use of semi-empirical equations.
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4

Wiśniewski, Jerzy Witold. "Empirical Econometric Model of an Enterprise." Folia Oeconomica Stetinensia 16, no. 1 (December 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 equation describing investments in the enterprise. It results from the fact, that during the years 2008–2013 the company suffered meagre investments. Investment output equation, therefore, does not provide any relevant systemic information for the management, since most statistical information in the time series assumes zero values. An empirical model of the company ENERGY is a system of interdependent equations, with statistically significant feedback between labour efficiency (EFEMP) and the average pay per 1 employee (APAY). Additionally, there is recurrence of the relationships between the fixed assets (FIXAS), employment volume (EMP), and the size of the net sales income (SNET). The empirical equations of the model are characterized by a description accuracy of individual endogenous variables. The model also has good decision-making and forecasting qualities.
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5

Lorenzoni, M., D. Giannetto, G. Maio, E. Pizzul, L. Pompei, P. Turin, S. Vincenzi, and A. Crivelli. "Empirical standard mass equation forSalmo marmoratus." Journal of Fish Biology 81, no. 6 (October 19, 2012): 2086–91. http://dx.doi.org/10.1111/j.1095-8649.2012.03459.x.

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6

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

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7

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

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8

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

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9

Leary, Rolfe A. "Near-normal, empirical, and identity yield tables for estimating stand growth." Canadian Journal of Forest Research 21, no. 3 (March 1, 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 inadequacy can be overcome by developing more complex relative density change equations, i.e., by transferring representation burden to the change equation. Introduced in the present paper is the concept of an identity yield table (all entries are one), wherein the entire burden of representing the relations between volume, site, and age is transferred from a density standard to a relative density change equation. Modern whole stand (net) growth models are equivalent to historical relative density change equations based on identity yield tables. The conjecture of a continuum of methods to estimate growth from near-normal to empirical to identity yield tables, each with an appropriate relative density change equation, and each equally accurate, is tested on Wisconsin jack pine (Pinusbanksiana Lamb.). The empirical yield table and its relative density change equation were more biased than near-normal and identity-based projection systems.
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10

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 (December 18, 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 function of coordinates, their derivatives and time variables. We developed a fractional form of this equation over these three variables and finally obtained the most generalized equation of motion, which counts the overall interactions by a fractional form as a variation of two variable. The improved formula, called the stretched Havriliak–Negami equation, has the same form and behavior as the semi-empirical equation and reducible to the Cole–Cole and Cole–Davidson-type of conductivity.
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11

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 (July 11, 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 hydrodynamic (SPH) code. The charges generated in hypervelocity impacts with five different velocities are calculated and verified with the empirical formulas. The influence of a critical velocity for plasma generation is considered in the empirical formula and the parameters are fitted by the numerical results. By comparing with the results in reference, the fitted new empirical formula is verified to be reasonable and useful for a wide range of impact velocity.
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12

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

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13

Zhenyu, Tan, and He Yancai. "An empirical energy loss equation of electrons." Scanning 24, no. 1 (December 6, 2006): 46–51. http://dx.doi.org/10.1002/sca.4950240107.

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14

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

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15

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

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16

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

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17

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

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18

Ferrer, Gerard, Stefan Gschwander, Aran Solé, Camila Barreneche, A. Inés Fernández, Peter Schossig, and Luisa F. Cabeza. "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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19

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 (February 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 different values of sky temperature, using any given correlation for convective heat transfer in the air gap spacings, and for any given values of fluid (air in the present case) properties.
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20

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%. Finally, molar dissolution enthalpy ΔsolH of benzoic acid in organic solvents was determined with the newly obtained empirical equation parameters.
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21

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 porosity. The most satisfactory values of the exponent range from -1 to 1. It has been suggested that firn density, determined primarily by overburdenpressure and firn temperature, contribute to a lesser degree.
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22

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. The most satisfactory values of the exponent range from -1 to 1. It has been suggested that firn density, determined primarily by overburdenpressure and firn temperature, contribute to a lesser degree.
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23

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 (March 2008): 177–89. http://dx.doi.org/10.1007/s10573-008-0024-y.

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24

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 (September 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 theoretically known equation for multiplications less than or equal to two.
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25

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 (February 1, 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 of the simultaneous nitrification and denitrification is discussed and was tested by computer simulation.
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26

Tang, Han, and Wenfei Li. "Empirical study for uncertain finance." Journal of Intelligent & Fuzzy Systems 40, no. 5 (April 22, 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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27

Ye, Hao, Richard J. Beamish, Sarah M. Glaser, Sue C. H. Grant, Chih-hao Hsieh, Laura J. Richards, Jon T. Schnute, and George Sugihara. "Equation-free mechanistic ecosystem forecasting using empirical dynamic modeling." Proceedings of the National Academy of Sciences 112, no. 13 (March 2, 2015): E1569—E1576. http://dx.doi.org/10.1073/pnas.1417063112.

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It is well known that current equilibrium-based models fall short as predictive descriptions of natural ecosystems, and particularly of fisheries systems that exhibit nonlinear dynamics. For example, model parameters assumed to be fixed constants may actually vary in time, models may fit well to existing data but lack out-of-sample predictive skill, and key driving variables may be misidentified due to transient (mirage) correlations that are common in nonlinear systems. With these frailties, it is somewhat surprising that static equilibrium models continue to be widely used. Here, we examine empirical dynamic modeling (EDM) as an alternative to imposed model equations and that accommodates both nonequilibrium dynamics and nonlinearity. Using time series from nine stocks of sockeye salmon (Oncorhynchus nerka) from the Fraser River system in British Columbia, Canada, we perform, for the the first time to our knowledge, real-data comparison of contemporary fisheries models with equivalent EDM formulations that explicitly use spawning stock and environmental variables to forecast recruitment. We find that EDM models produce more accurate and precise forecasts, and unlike extensions of the classic Ricker spawner–recruit equation, they show significant improvements when environmental factors are included. Our analysis demonstrates the strategic utility of EDM for incorporating environmental influences into fisheries forecasts and, more generally, for providing insight into how environmental factors can operate in forecast models, thus paving the way for equation-free mechanistic forecasting to be applied in management contexts.
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28

Band, L. "Field parameterization of an empirical sheetwash transport equation." CATENA 12, no. 1 (January 1985): 281–90. http://dx.doi.org/10.1016/s0341-8162(85)80026-6.

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29

Jović, B., V. Ćirić, M. Kovačević, S. Šeremešić, and B. Kordić. "Empirical equation for preliminary assessment of soil texture." Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 206 (January 2019): 506–11. http://dx.doi.org/10.1016/j.saa.2018.08.039.

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30

Cheng, Yunshuo, and Ana Maria Ferreira da Silva. "Empirical Equation for Determination of Alternate Bar Height." Journal of Hydraulic Engineering 145, no. 11 (November 2019): 04019037. http://dx.doi.org/10.1061/(asce)hy.1943-7900.0001633.

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31

Akimoto, Yutaro, and Keiichi Okajima. "Semi-Empirical Equation of PEMFC Considering Operation Temperature." Energy Technology & Policy 1, no. 1 (January 2014): 91–96. http://dx.doi.org/10.1080/23317000.2014.972480.

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32

Band, Lawrence. "Field parameterization of an empirical sheetwash transport equation." CATENA 12, no. 4 (December 1985): 281–90. http://dx.doi.org/10.1016/0341-8162(85)90019-0.

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33

Chrzanowski, Janusz, and Bohdan Bieg. "Precise, semi-empirical equation for the work function." Applied Surface Science 461 (December 2018): 83–87. http://dx.doi.org/10.1016/j.apsusc.2018.05.120.

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34

Miyashita, T. "Empirical equation about open circuit voltage in SOFC." Journal of Materials Science 40, no. 22 (September 16, 2005): 6027. http://dx.doi.org/10.1007/s10853-005-4560-5.

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35

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 (September 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 in contrast to FAO56-Penman-Monteith equation. The results indicated that the differences observed between the values obtained using the empirical models applied in this study and the values calculated by the FAO56-Penman-Monteith equation were greater than 10%, which means an error of about 0.5 mm.day-1.
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36

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, it’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 shape equation, as it is the only equation that directly links the shoreline positions to the predominant wave direction and the point of diffraction. However, the main limitation with the application of the parabolic bay shape equation is locating the downcoast control point. As a result of research presented in this paper a new equation, based on the hyperbolic tangent shape equation was developed, which eliminates the requirement of placing the down coast control point and relies on defining a minimum beach width instead. This modified equation was incorporated into a new ArcGIS tool.
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37

Meng, Q., Y. Li, and J. Xu. "New empirical stiffness equations for corner-filleted flexure hinges." Mechanical Sciences 4, no. 2 (October 15, 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 minimum thickness of a corner-filleted flexure hinge) to length (l), t/l (0.02 ≤ t/l ≤ 1) and ensure the accuracy for each empirical stiffness equation under large deformation. The errors are within 6% when compared to FEA results.
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38

Dong, Lichun, Yazheng Zhang, Shichun Li, Shun'an Wei, Jianhua Zhang, and Yongli Qi. "AN EMPIRICAL EQUATION TO DIRECTLY CALCULATE PARAMETERB4OF THE MARTIN-HOU EQUATION OF STATE." Chemical Engineering Communications 199, no. 5 (May 2012): 577–86. http://dx.doi.org/10.1080/00986445.2011.599899.

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39

Jayadev, M. "Predictive Power of Financial Risk Factors: An Empirical Analysis of Default Companies." Vikalpa: The Journal for Decision Makers 31, no. 3 (July 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 rating models of the Indian banks and the ratios selected are: current ratio, debt-equity ratio, and operating margin. The second equation is similar to that of Altman's (1968) original equation with a slight modification: instead of debt-to-market value of equity, debt-to-book value of equity is considered. The other three ratios of the second equation are working capital to total assets, retained earnings to total assets, and earnings before interest and taxes to total assets. The third equation is called as Altman, Hartzell and Peck's ‘Emerging Market Score Model.’ Except the asset turnover ratio, all the ratios of the second equation are considered. In all the three equations, the coefficients are estimated by using the development sample of 112 companies. The dominant variables discriminating the default companies from non-default ones are: current ratio, debt-equity ratio, operating margin, working capital to total assets, earnings before interest and tax to total assets, net worth to debt, and asset-turnover ratio. The classification accuracy of the second and the third equations is 82 per cent while that of the first equation is only 57 per cent. It implies that the most widely used two ratios — current ratio and debt-equity ratio — are relatively poor in predicting the default companies. Similarly, the ROC accuracy ratio is the highest for Altman's equation whereas the variables considered in internal credit rating models of banks is having a relatively low accuracy ratio. To test the ability of the model in identifying the defaulting companies correctly, an unbiased diagnostic test of the model is conducted on two separate sets of defaulted firms. The results reveal the following : The Altman's model is capable of predicting default in most of the sample companies. The hold-out sample accuracy results show that the selected variables are capable of predicting default. The analysis shows that the financial risk factors being considered by banks in their internal rating models are not very effective in comparison to other two models in discriminating the firms into default and non-default categories. Banks can map the internal ratings with the Z-scores and scale this up to assign various credit ratings. By arriving at the coefficients on the basis of their own database, banks can develop Z-score calculators for various segments of borrowers.
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40

Fan, P. P., Y. Y. Li, J. B. Evers, B. Ming, C. X. Wang, S. K. Li, and R. Z. Xie. "A new empirical equation to describe the vertical leaf distribution profile of maize." Journal of Agricultural Science 158, no. 8-9 (November 2020): 676–86. http://dx.doi.org/10.1017/s0021859621000010.

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AbstractThe characteristic traits of maize (Zea mays L.) leaves affect light interception and photosynthesis. Measurement or estimation of individual leaf area has been described using discontinuous equations or bell-shaped functions. However, new maize hybrids show different canopy architecture, such as leaf angle in modern maize which is more upright and ear leaf and adjacent leaves which are longer than older hybrids. The original equations and their parameters, which have been used for older maize hybrids and grown at low plant densities, will not accurately represent modern hybrids. Therefore, the aim of this paper was to develop a new empirical equation that captures vertical leaf distribution. To characterize the vertical leaf profile, we conducted a field experiment in Jilin province, Northeast China from 2015 to 2018. Our new equation for the vertical distribution of leaf profile describes leaf length, width or leaf area as a function of leaf rank, using parameters for the maximum value for leaf length, width or area, the leaf rank at which the maximum value is obtained, and the width of the curve. It thus involves one parameter less than the previously used equations. By analysing the characteristics of this new equation, we identified four key leaf ranks (4, 8, 14 and 20) for which leaf parameter values need to be quantified in order to have a good estimation of leaf length, width and area. Together, the method of leaf area estimation proposed here adds versatility for use in modern maize hybrids and simplifies the field measurements by using the four key leaf ranks to estimate vertical leaf distribution in maize canopy instead of all leaf ranks.
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41

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 (July 6, 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 multiple linear regression technique. The performance of the produced equation was compared to five empirical prediction equations of DL selected from literature. It presented correlation coefficient r2 = 0.87, suggesting that this equation is suitable for the estimation of DL in streams. It also presented better results for predicting the DL than the five equations from literature, showing an accuracy of 71%.
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42

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 (January 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 measurement ranges for errors that were lower than 5% for the 100 and 150 mm plates were 30 to 65 m3 h-1 and 70 to 130 m3 h-1 using the theoretical equation and 20 to 65 m3 h-1 and 40 to 130 m3 h-1 using the empirical equation, respectively. The Reader-Harris/Gallagher equation (Method 1) adequately estimated the discharge coefficient of the orifice plates; however, the use of empirical equations (Method 3) demonstrated smaller measurement errors and greater rangeability of the evaluated flow meters.
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Bilous, Andrii, Viktor Myroniuk, Viktor Svynchuk, Oleksandr Soshenskyi, Oleksandr Lesnik, and Yaroslav Kovbasa. "Semi-empirical estimation of log taper using stem profile equations." Journal of Forest Science 67, No. 7 (July 20, 2021): 318–27. http://dx.doi.org/10.17221/209/2020-jfs.

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In January 2019 the forest industry in Ukraine adopted European standards for measuring and grading of round wood based on mid-point diameters, which caused major discrepancies from traditionally used estimates of timber volume using top diameters. To compare methods of merchantable wood volume estimation, we investigated the stem form inside bark for two dominant tree species in Ukraine, i.e. Scots pine (Pinus sylvestris L.) and common oak (Quercus robur L.). We used tree stem measurements to fit stem profile equations, whereas simulation was applied to derive log taper. We found that Newnham's (1992) variable-exponent taper equation performed well for predicting stem taper for both tree species. Then, we simulated the structure of harvested wood, so that it replicated annual distribution of logs by their length and diameters. As a result, the average log taper was estimated at 0.836 ÷ 0.855 cm·m<sup>–1</sup> and 1.180 ÷ 0.121 cm·m<sup>–1</sup> for pine and oak, respectively. The study also indicated that log taper varied along stems. The higher rates of diameter decrease were found for butt logs, for which the taper was 2.5–3.5 times higher than its average for the whole stem. The results of our study ensure the stacked round wood volume conversion between estimates obtained using top and mid-point diameters.
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44

Kaushal, Shaurya, Santosh Ansumali, Bruce Boghosian, and Merek Johnson. "The lattice Fokker–Planck equation for models of wealth distribution." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 378, no. 2175 (June 22, 2020): 20190401. http://dx.doi.org/10.1098/rsta.2019.0401.

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Recent work on agent-based models of wealth distribution has yielded nonlinear, non-local Fokker–Planck equations whose steady-state solutions describe empirical wealth distributions with remarkable accuracy using only a few free parameters. Because these equations are often used to solve the ‘inverse problem’ of determining the free parameters given empirical wealth data, there is much impetus to find fast and accurate methods of solving the ‘forward problem’ of finding the steady state corresponding to given parameters. In this work, we derive and calibrate a lattice Boltzmann equation for this purpose. This article is part of the theme issue ‘Fluid dynamics, soft matter and complex systems: recent results and new methods’.
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Fan, Henghui, and Lingwei Kong. "Empirical equation for evaluating the dispersivity of cohesive soil." Canadian Geotechnical Journal 50, no. 9 (September 2013): 989–94. http://dx.doi.org/10.1139/cgj-2012-0332.

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As indicated by the theory of a clay–water–electrolyte system, the dispersive mechanism of cohesive soil involves three aspects: low clay content, high sodium ion percentage, and strongly alkaline pH. Accordingly, an empirical equation was established with an associated procedure and criteria proposed for evaluating the dispersivity of cohesive soil. The equation consists of four soil physical and chemical indicators: liquid limit (WL), clay content (PC), sodium percentage in the pore water (PS), and pH. The equation is F = 4 − 0.01(2WL + PC − PS) + 0.1 pH, where F is the soil dispersivity value. Compared with the evaluation based on laboratory tests, the empirical equation had higher accuracy for the evaluation of the dispersivity of cohesive soil, and was thus conducive to greater engineering safety. This indicates that the proposed empirical equation is applicable for evaluating the dispersivity of cohesive soil in general engineering.
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46

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 (January 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 flow includes left turns. In the case of Equation 9-20 for gf, the theoretical results are consistently about 5 s larger but otherwise in reasonable agreement with the empirical equation and provide insight into how it could be improved. An analytic approximation is offered either as a replacement or as a framework for an improved empirical model.
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Knackstedt, Mark A., Christoph H. Arns, and W. Val Pinczewski. "Velocity-porosity relationships, 1: Accurate velocity model for clean consolidated sandstones, GEOPHYSICS, 68, 1822–1834." GEOPHYSICS 71, no. 2 (March 2006): Y3. http://dx.doi.org/10.1190/1.2191109.

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48

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 (December 15, 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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Bhatt, Jeewan C., Kuldeep Kholiya, and Ravindra Kumar. "High Pressure Equation of State for Nanomaterials." ISRN Nanotechnology 2013 (June 17, 2013): 1–5. http://dx.doi.org/10.1155/2013/404920.

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Shanker Equation of State is used to study the volume compression of nanocrystalline materials under different pressure. On comparing with the experimental data it gives good results at low pressure, but for higher compression it deviates from the experimental points. Therefore, the Equation of State is modified empirically to study the pressure-volume relation for nanomaterials, namely, n-Rb3C60, n-CdSe (rocksalt phase), n-TiO2 (anatase and rutile phase), Fe-filled nanotube, and γ-Fe2O3, at high pressure. The results obtained from the empirical Equation of State are found to be in better agreement with the available experimental data.
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50

Liu, Yigang, Yingzhong Yuan, Fayuan Zhou, Zhilin Qi, Wei Zhang, Hua Zhang, and Qiuxia Wang. "Analysis on PVT test and empirical formula of Bohai heavy oil with different types of dissolved gases." Journal of Petroleum Exploration and Production Technology 10, no. 8 (August 10, 2020): 3609–17. http://dx.doi.org/10.1007/s13202-020-00973-7.

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Abstract Accurate prediction of PVT properties of heavy oil system is of great significance to the design of injection–production parameters and dynamic analysis of multi-thermal fluid stimulation in heavy oil reservoir. The saturation pressure and viscosity of Bohai heavy oil system at different temperature and different gas oil ratio conditions were tested and analyzed. The functional relations of regression equations for saturation pressure and viscosity are constructed based on classical PVT correlations, but the parameters in the equations different from classical correlations are obtained from present experiment test data with multiple regression method. The empirical formula analysis results indicate that the 2-parameter equation can almost completely fit the experimental data, but its application scope is narrow. Although the 4-parameter equation has an extensive adaptability, its fitting accuracy is very low. The 3-parameter equation can not only better fit the saturation pressure and viscosity of heavy oil for the same gas under different dissolved gas oil ratios and different temperatures, but also has a wide application range. It is recommended to use the 3-parameter equation for physical property analysis and calculation of heavy oil. The research results provide a basis for the accurate prediction of heavy oil PVT parameters.
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