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Journal articles on the topic 'Standard equation'

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Published: 10 December 2022

Last updated: 28 January 2023

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1

Son, Nguyen Quoc, and Nguyen Truong Giang. "Standard gradient models and crack simulation." Vietnam Journal of Mechanics 33, no. 4 (December 12, 2011): 293–301. http://dx.doi.org/10.15625/0866-7136/33/4/261.

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The standard gradient models have been intensively studied in the literature, cf. Fremond (1985) or Gurtin (1991) for various applications in plasticity, damage mechanics and phase change analysis. The governing equations for a solid have been introduced essentially from an extended version of the virtual equation. It is shown here first that these equations can also be derived from the formalism of energy and dissipation potentials and appear as a generalized Biot equation for the solid. In this spirit, the governing equations for higher gradient models can be straightforwardly given. The interest of gradient models is then discussed in the context of damage mechanics and crack simulation. The phenomenon of strain localization in a time-dependent or time-independent process of damage is explored as a convenient numerical method to simulate the propagation of cracks, in relation with some recent works of theliterature, cf. Bourdin & Marigo [3], Lorentz & al [5], Henry & al [12].

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2

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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3

Piccolo, Jack J., Wayne A. Hubert, and Roy A. Whaley. "Standard Weight Equation for Lake Trout." North American Journal of Fisheries Management 13, no. 2 (May 1993): 401–4. http://dx.doi.org/10.1577/1548-8675(1993)013<0401:sweflt>2.3.co;2.

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4

Fatima, Aeeman, Fazal M. Mahomed, and Chaudry Masood Khalique. "Noether symmetries and exact solutions of an Euler–Bernoulli beam model." International Journal of Modern Physics B 30, no. 28n29 (November 10, 2016): 1640011. http://dx.doi.org/10.1142/s0217979216400117.

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In this paper, a Noether symmetry analysis is carried out for an Euler–Bernoulli beam equation via the standard Lagrangian of its reduced scalar second-order equation which arises from the standard Lagrangian of the fourth-order beam equation via its Noether integrals. The Noether symmetries corresponding to the reduced equation is shown to be the inherited Noether symmetries of the standard Lagrangian of the beam equation. The corresponding Noether integrals of the reduced Euler–Lagrange equations are deduced which remarkably allows for three families of new exact solutions of the static beam equation. These are shown to contain all the previous solutions obtained from the standard Lie analysis and more.

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5

ZHANG, YUFENG, HONWAH TAM, and JING ZHAO. "GENERALIZED mKdV EQUATION, LIOUVILLE EQUATION, SINE-GORDON EQUATION AND SINH-GORDON EQUATION AS WELL AS A FORMAL BÄCKLUND TRANSFORMATION." International Journal of Modern Physics B 25, no. 18 (July 20, 2011): 2449–60. http://dx.doi.org/10.1142/s0217979211101387.

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A Lie algebra which consists of linear combinations of one basis of the Lie algebra A1 is presented for which an isospectral Lax pair is exhibited. By using the zero curvature equation, the generalized mKdV equation, Liouville equation and sine-Gordon equation, sinh-Gordon equation are generated via polynomial expansions. Finally, we investigate a kind of formal Bäcklund transformation for the generalized sine-Gordon equation. The explicit Bäcklund transformation of the standard sine-Gordon equation is presented. The other equations given in the paper are obtained similarly.

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6

Leypoldt, John K., and Edward F. Vonesh. "Calculating Standard Kt/V during Hemodialysis Based on Urea Mass Removed." Blood Purification 47, no. 1-3 (October 8, 2018): 62–68. http://dx.doi.org/10.1159/000493178.

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Background/Aims: We derived a novel equation for calculating weekly urea standard Kt/V (stdKt/V) during hemodialysis (HD) based on urea mass removed, comparable to the approach during peritoneal dialysis. Methods: Theoretical consideration of urea mass balance during HD led to the following equation for stdKt/V, namely, stdKt/V = N × (URR + UFV/V), where N is the number of treatments per week, URR is urea reduction ratio per treatment, UFV is ultrafiltration volume per treatment, and V is postdialysis urea distribution volume. URR required corrections for postdialysis rebound and intradialytic urea generation. We compared the accuracy of this approach with previous equations for stdKt/V by numerical simulations using a 2-compartment model of urea kinetics for thrice-weekly and more frequent HD prescriptions. Results: The proposed equation based on urea mass removed predicted values of stdKt/V that are equivalent to those calculated by previous equations for stdKt/V. Conclusion: This work provides a novel approach for calculating stdKt/V during HD and strengthens the theoretical understanding of stdKt/V.

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7

Ogasawara, Haruhiko. "Asymptotic standard errors of estimated standard errors in structural equation modelling." British Journal of Mathematical and Statistical Psychology 55, no. 2 (November 2002): 213–29. http://dx.doi.org/10.1348/000711002760554552.

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8

AHMAD, IBRAHIM TURKI. "Teacher Satisfaction in Jordanian High Schools: The Gold Standard of Structural Equation Modeling." Journal of Research on the Lepidoptera 51, no. 1 (February 28, 2020): 254–65. http://dx.doi.org/10.36872/lepi/v51i1/301022.

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9

Loov, Robert. "A simple equation for axially loaded steel column design curves." Canadian Journal of Civil Engineering 23, no. 1 (February 1, 1996): 272–76. http://dx.doi.org/10.1139/l96-028.

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Clause 13.3 of the Canadian Standards Association Standard CAN/CSA-S16.1-M89 "Limit states design of steel structures" utilizes complex five-piece curves to specify the limiting capacity of axially loaded steel columns. A study of these equations shows that they do not fit smoothly together. The resulting curves are scalloped. It has been found that the five-piece curves can be replaced by one continuous equation which never deviates by more than approximately 3% from the S16.1-M89 values. The proposed equation is applicable to all three column curves of the Structural Stability Research Council with only a change in the value of the exponent. The proposed equation has been adopted in the recently published CAN/CSA-S16.1-94 standard. Key words: axial loads, columns, inelastic analysis, steel columns.

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10

Campos, L. M. B. C. "On the solution of some simple fractional differential equations." International Journal of Mathematics and Mathematical Sciences 13, no. 3 (1990): 481–96. http://dx.doi.org/10.1155/s0161171290000709.

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The differintegration or fractional derivative of complex orderν, is a generalization of the ordinary concept of derivative of ordern, from positive integerν=nto complex values ofν, including also, forν=−na negative integer, the ordinaryn-th primitive. Substituting, in an ordinary differential equation, derivatives of integer order by derivatives of non-integer order, leads to a fractional differential equation, which is generallyaintegro-differential equation. We present simple methods of solution of some classes of fractional differential equations, namely those with constant coefficients (standard I) and those with power type coefficients with exponents equal to the orders of differintegration (standard II). The fractional differential equations of standard I (II), both homogeneous, and inhomogeneous with exponential (power-type) forcing, can be solved in the Liouville (Riemann) systems of differintegration. The standard I (II) is linear with constant (non-constant) coefficients, and some results are also given for a class of non-linear fractional differential equations (standard III).

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11

Baldomá, I., and P. Martín. "The Inner Equation for Generalized Standard Maps." SIAM Journal on Applied Dynamical Systems 11, no. 3 (January 2012): 1062–97. http://dx.doi.org/10.1137/110859932.

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12

Binding, P. A., and H. Volkmer. "Non-standard oscillation theory for multiparameter eigenvalue problems." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 142, no. 4 (August 2012): 673–90. http://dx.doi.org/10.1017/s030821051000154x.

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An eigenvalue problem for k Sturm–Liouville equations coupled by k parameters λ1,…,λk is considered. In contrast to the standard case, for each r, the second-order derivative in the rth equation is multiplied by λr. This problem presents various interesting features. For example, the existence of eigenvalues with oscillation counts beyond a certain (computable) value is obtained without any of the restrictive definiteness conditions known from the standard case. Uniqueness is also analysed, and the results are given greater precision via eigencurve methods in the case of two equations coupled by two parameters.

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13

Bonvechio, Timothy F., Kimberly I. Bonvechio, and Richard L. Cailteux. "Proposed Standard Weight (Ws) Equation and Standard Length Categories for Suwannee Bass." North American Journal of Fisheries Management 30, no. 4 (August 2010): 983–88. http://dx.doi.org/10.1577/m10-034.1.

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14

Wazwaz, Abdul-Majid. "A new (3 + 1)-dimensional Painlevé-integrable Sakovich equation: multiple soliton solutions." International Journal of Numerical Methods for Heat & Fluid Flow 31, no. 9 (January 11, 2021): 3030–35. http://dx.doi.org/10.1108/hff-11-2020-0687.

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Purpose This paper aims to develop a new (3 + 1)-dimensional Painlevée-integrable extended Sakovich equation. This paper formally derives multiple soliton solutions for this developed model. Design/methodology/approach This paper uses the simplified Hirota’s method for deriving multiple soliton solutions. Findings This paper finds that the developed (3 + 1)-dimensional Sakovich model exhibits complete integrability in analogy with the standard Sakovich equation. Research limitations/implications This paper addresses the integrability features of this model via using the Painlevée analysis. This paper reports multiple soliton solutions for this equation by using the simplified Hirota’s method. Practical implications The study reports three non-linear terms added to the standard Sakovich equation. Social implications The study presents useful algorithms for constructing new integrable equations and for handling these equations. Originality/value The paper reports a new Painlevée-integrable extended Sakovich equation, which belongs to second-order partial differential equations. The constructed model does not contain any dispersion term such as uxxx.

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15

KUMAR, SARVESH. "ON THE APPROXIMATION OF INCOMPRESSIBLE MISCIBLE DISPLACEMENT PROBLEMS IN POROUS MEDIA BY MIXED AND STANDARD FINITE VOLUME ELEMENT METHODS." International Journal of Modeling, Simulation, and Scientific Computing 04, no. 03 (August 19, 2013): 1350013. http://dx.doi.org/10.1142/s179396231350013x.

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The incompressible miscible displacement problem in porous media is modeled by a coupled system of two nonlinear partial differential equations, the pressure–velocity equation and the concentration equation. In this paper, we present a mixed finite volume element method (FVEM) for the approximation of the pressure–velocity equation and a standard FVEM for the concentration equation. A priori error estimates in L∞(L2) are derived for velocity, pressure and concentration. Numerical results are presented to substantiate the validity of the theoretical results.

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16

Leary, Rolfe A., and W. Brad Smith. "Test of the TRIM inventory projection methods on Wisconsin jack pine." Canadian Journal of Forest Research 20, no. 6 (June 1, 1990): 774–80. http://dx.doi.org/10.1139/x90-102.

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Reported is a test of the methodology underlying the trim projection system being used in the Resources Planning Act timber assessment. Nine combinations of density standards and relative density change equations were used to estimate annual volume growth of jack pine (Pinusbanksiana Lamb.). Annual volume growth data from remeasured USDA Forest Service inventory plots in two northern Wisconsin survey units and from industrial continuous forest inventory plots were used to evaluate the combinations. The yield table of Gevorkiantz and Duerr for well-stocked jack pine stands combined with a Riccati relative density change equation gave unbiased estimates of annual volume growth on both an absolute and percent error basis. We conclude that the concepts underlying the TRIM methodology are sound. However, for jack pine in northern Wisconsin only well-stocked or normal yield tables as the density standard and locally calibrated relative density change equations provide unbiased estimates of growth. A jack pine empirical yield table combined with the form of the relative density change equation used in the southern timber supply study underestimated growth by 45.4% (1.39 m3/(ha•year)). An empirical yield table enhanced with the STEMS projection system as a density standard used without a relative density change equation underestimated growth by 65.6% (1.67 m3/(ha•year)). Thus, inappropriate combinations of density standards and relative density change equations may lead to large errors in growth estimates.

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17

Lin, Chuen-Sen, and A. G. Erdman. "Singular Conditions and Solutions of the Standard Triad Displacement Equation." Journal of Mechanical Design 112, no. 4 (December 1, 1990): 457–65. http://dx.doi.org/10.1115/1.2912632.

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In the dimensional synthesis of a standard planar triad, if the prescribed angular displacements of two of the three links are the same at all precision positions or the prescribed angular displacements of one link are zero at all precision positions, the standard triad displacement equation will not yield a practical solution: a triad having all links with finite lengths. The displacement equation may also fail to generate a practical solution triad in case that the freely chosen angular displacement of one link equals to zero, or equals to the prescribed angular displacement of another link at the same precision position. In this paper, the special cases in the dimensional synthesis of a standard triad are discussed in detail, the types of triads which can generate the motions corresponding to the special cases are listed, and the solution methods to solve the displacement equations of the special types of triads are developed. Finally a numerical example is given to show the application of one of the special types of triad in the dimensional synthesis of an eight-bar linkage.

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18

Walsh, Ryan. "Comparing enzyme activity modifier equations through the development of global data fitting templates in Excel." PeerJ 6 (December 14, 2018): e6082. http://dx.doi.org/10.7717/peerj.6082.

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The classical way of defining enzyme inhibition has obscured the distinction between inhibitory effect and the inhibitor binding constant. This article examines the relationship between the simple binding curve used to define biomolecular interactions and the standard inhibitory term (1 + ([I]∕Ki)). By understanding how this term relates to binding curves which are ubiquitously used to describe biological processes, a modifier equation which distinguishes between inhibitor binding and the inhibitory effect, is examined. This modifier equation which can describe both activation and inhibition is compared to standard inhibitory equations with the development of global data fitting templates in Excel and via the global fitting of these equations to simulated and previously published datasets. In both cases, this modifier equation was able to match or outperform the other equations by providing superior fits to the datasets. The ability of this single equation to outperform the other equations suggests an over-complication of the field. This equation and the template developed in this article should prove to be useful tools in the study of enzyme inhibition and activation.

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19

Ndogmo, Jean-Claude, and Fazal Mahomed. "On certain properties of linear iterative equations." Open Mathematics 12, no. 4 (April 1, 2014): 648–57. http://dx.doi.org/10.2478/s11533-013-0364-z.

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Abstract An expression for the coefficients of a linear iterative equation in terms of the parameters of the source equation is given both for equations in standard form and for equations in reduced normal form. The operator that generates an iterative equation of a general order in reduced normal form is also obtained and some other properties of iterative equations are established. An expression for the parameters of the source equation of the transformed equation under equivalence transformations is obtained, and this gives rise to the derivation of important symmetry properties for iterative equations. The transformation mapping a given iterative equation to the canonical form is obtained in terms of the simplest determining equation, and several examples of application are discussed.

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20

Arora, Geeta, and Gurpreet Singh Bhatia. "Radial Basis Function Pseudospectral Method for Solving Standard Fitzhugh-Nagumo Equation." International Journal of Mathematical, Engineering and Management Sciences 5, no. 6 (December 1, 2020): 1488–97. http://dx.doi.org/10.33889/ijmems.2020.5.6.110.

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In this article, a pseudospectral approach based on radial basis functions is considered for the solution of the standard Fitzhugh-Nagumo equation. The proposed radial basis function pseudospectral approach is truly mesh free. The standard Fitzhugh-Nagumo equation is approximated into ordinary differential equations with the help of radial kernels. An ODE solver is applied to solve the resultant ODEs. Shape parameter which decides the shape of the radial basis function plays a significant role in the solution. A cross-validation technique which is the extension of the statistical approach leave-one-out-cross-validation is used to find the shape parameter value. The presented method is demonstrated with the help of numerical results which shows a good understanding with the exact solution. The stability of the proposed method is demonstrated with the help of the eigenvalues method numerically.

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21

Vavrukh, M., and D. Dzikovskyi. "The generalized polytropic model for the Sun-like stars." Mathematical Modeling and Computing 10, no. 1 (2023): 1–9. http://dx.doi.org/10.23939/mmc2023.01.001.

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The Eddington method based on simultaneous consideration of gas and light pressures with a homogeneous сhemical composition of stellar matter was generalized for the case of model with a spatially inhomogeneous chemical composition. As a result, it was obtained the equation of state, which is expressed by a generalized polytrope with index n=3. As an example, it was solved the equilibrium equation for the Sun both using the standard polytropic equation of state and generalized polytrope. The coordinate dependence of the Sun characteristics was calculated within two models. Obtained results are compared with the results of numerical calculations for the Sun based on the system of Schwarzschild equations for the standard model. It was shown that the standard polytropic model is applicable only for the Sun of zero-age. The Sun characteristics calculated with help of generalized equation of state are close to the results of numerical calculations based on Schwarzschild equations. It was concluded that the standard polytropic model is applicable for the stars of zero-age main sequence, and the generalized model – for the stars of finite age, in which thermonuclear reactions have already created a significant spatially inhomogeneity of chemical composition inside of the core.

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22

Fach, S., R. Sitzenfrei, and W. Rauch. "Determining the spill flow discharge of combined sewer overflows using rating curves based on computational fluid dynamics instead of the standard weir equation." Water Science and Technology 60, no. 12 (December 1, 2009): 3035–43. http://dx.doi.org/10.2166/wst.2009.752.

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It is state of the art to evaluate and optimise sewer systems with urban drainage models. Since spill flow data is essential in the calibration process of conceptual models it is important to enhance the quality of such data. A wide spread approach is to calculate the spill flow volume by using standard weir equations together with measured water levels. However, these equations are only applicable to combined sewer overflow (CSO) structures, whose weir constructions correspond with the standard weir layout. The objective of this work is to outline an alternative approach to obtain spill flow discharge data based on measurements with a sonic depth finder. The idea is to determine the relation between water level and rate of spill flow by running a detailed 3D computational fluid dynamics (CFD) model. Two real world CSO structures have been chosen due to their complex structure, especially with respect to the weir construction. In a first step the simulation results were analysed to identify flow conditions for discrete steady states. It will be shown that the flow conditions in the CSO structure change after the spill flow pipe acts as a controlled outflow and therefore the spill flow discharge cannot be described with a standard weir equation. In a second step the CFD results will be used to derive rating curves which can be easily applied in everyday practice. Therefore the rating curves are developed on basis of the standard weir equation and the equation for orifice-type outlets. Because the intersection of both equations is not known, the coefficients of discharge are regressed from CFD simulation results. Furthermore, the regression of the CFD simulation results are compared with the one of the standard weir equation by using historic water levels and hydrographs generated with a hydrodynamic model. The uncertainties resulting of the wide spread use of the standard weir equation are demonstrated.

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23

Willis, David W. "Proposed Standard Length–Weight Equation for Northern Pike." North American Journal of Fisheries Management 9, no. 2 (May 1989): 203–8. http://dx.doi.org/10.1577/1548-8675(1989)009<0203:pslwef>2.3.co;2.

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24

Brenden, Travis O., and Brian R. Murphy. "Variance-Covariance Estimation of Standard Weight Equation Coefficients." Journal of Freshwater Ecology 21, no. 1 (March 2006): 1–7. http://dx.doi.org/10.1080/02705060.2006.9664089.

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25

Rybkin, Alexei. "KdV equation beyond standard assumptions on initial data." Physica D: Nonlinear Phenomena 365 (February 2018): 1–11. http://dx.doi.org/10.1016/j.physd.2017.10.005.

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26

Kalisch, Henrik, Darko Mitrovic, and Jan M. Nordbotten. "Non-standard shocks in the Buckley–Leverett equation." Journal of Mathematical Analysis and Applications 428, no. 2 (August 2015): 882–95. http://dx.doi.org/10.1016/j.jmaa.2015.03.041.

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27

Joyce, Robert F., and Martha E. M. Head. "A convolution algorithm for standard parabolic‐equation modeling." Journal of the Acoustical Society of America 86, S1 (November 1989): S54. http://dx.doi.org/10.1121/1.2027555.

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28

Rogers, Kevin B., Lee C. Bergsted, and Eric E. Bergersen. "Management Briefs: Standard Weight Equation for Mountain Whitefish." North American Journal of Fisheries Management 16, no. 1 (February 1996): 207–9. http://dx.doi.org/10.1577/1548-8675(1996)016<0207:mbswef>2.3.co;2.

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29

Neely, Ben C., Martin J. Hamel, and Kirk D. Steffensen. "A Proposed Standard Weight Equation for Blue Suckers." North American Journal of Fisheries Management 28, no. 5 (October 2008): 1450–52. http://dx.doi.org/10.1577/m07-158.1.

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30

Kosi-Ulbl, I. "Equation related to derivations on standard operator algebras." International Mathematical Forum 2 (2007): 273–84. http://dx.doi.org/10.12988/imf.2007.07026.

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31

Rakotoson, Jean-Michel. "Linear equation with data in non standard spaces." Rendiconti Lincei - Matematica e Applicazioni 26, no. 3 (2015): 241–62. http://dx.doi.org/10.4171/rlm/705.

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32

Hall, W. S., and W. H. Robertson. "Standard Helmholtz integral equation calculations near characteristic frequencies." Journal of Sound and Vibration 126, no. 2 (October 1988): 367–68. http://dx.doi.org/10.1016/0022-460x(88)90248-9.

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33

Darouach, M., M. Zasadzinski, and A. Bassong-Onana. "Connection between the three-block generalized Riccati equation and the standard Riccati equation." IEEE Transactions on Automatic Control 39, no. 8 (1994): 1755–58. http://dx.doi.org/10.1109/9.310068.

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34

Jang, T. S. "A Regular Integral Equation Formalism for Solving the Standard Boussinesq’s Equations for Variable Water Depth." Journal of Scientific Computing 75, no. 3 (November 22, 2017): 1721–56. http://dx.doi.org/10.1007/s10915-017-0605-6.

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Abstract This paper begins with a question of existence of a regular integral equation formalism, but different from the existing usual ones, for solving the standard Boussinesq’s equations for variable water depth (or Peregrine’s model). For the question, a pseudo-water depth parameter, suggested by Jang (Commun Nonlinear Sci Numer Simul 43:118–138, 2017), is introduced to alter the standard Boussinesq’s equations into an integral formalism. This enables us to construct a regular (nonlinear) integral equations of second kind (as required), being equivalent to the standard Boussinesq’s equations (of Peregrine’s model). The (constructed) integral equations are, of course, inherently different from the usual integral equation formalisms. For solving them, the successive approximation (or the fixed point iteration) is applied (Jang 2017), whereby a new iterative formula is immediately derived, in this paper, for numerical solutions of the standard Boussinesq’s equations for variable water depth. The formula, semi-analytic and derivative-free, is shown to be useful to observe especially the nonlinear wave phenomena of shallow water waves on a beach. In fact, a numerical experiment is performed on a solitary wave approaching a sloping beach. It shows clearly the main feature of nonlinear wave characteristics, which has reached good agreement with the known (numerical) solutions. Hence, while being theoretical but fundamental in nonlinear computational partial differential equations, the question raised in the study may be solved.

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35

McCarthy, J. M. "The Synthesis of Planar RR and Spatial CC Chains and the Equation of a Triangle." Journal of Mechanical Design 117, B (June 1, 1995): 101–6. http://dx.doi.org/10.1115/1.2836441.

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This paper formulates the planar and spatial versions of an equation that determines one vertex of a triangle in terms of the other two vertices and their interior angles. The fact that a slight modification of Sandor and Erdman’s standard form equation for the design of RR chains yields this planar triangle equation is the basis for identifying the equivalent equation for a spatial triangle as the standard form equation for CC chains. The simultaneous solution of two of the planar equations yields an analytical expression of Burmester’s relationship between the fixed pivot of an RR chain and the relative position poles of its floating link. A similar solution of simultaneous spatial triangle equations yields Roth’s generalization of this insight, specifically, the fixed axis of a CC chain views two relative screw axes in one-half the dual crank rotation angle. These results provide the foundation for generalizing planar linkage synthesis techniques based on complex numbers to the synthesis of spatial linkages.

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McCarthy, J. M. "The Synthesis of Planar RR and Spatial CC Chains and the Equation of a Triangle." Journal of Vibration and Acoustics 117, B (June 1, 1995): 101–6. http://dx.doi.org/10.1115/1.2838647.

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This paper formulates the planar and spatial versions of an equation that determines one vertex of a triangle in terms of the other two vertices and their interior angles. The fact that a slight modification of Sandor and Erdman’s standard form equation for the design of RR chains yields this planar triangle equation is the basis for identifying the equivalent equation for a spatial triangle as the standard form equation for CC chains. The simultaneous solution of two of the planar equations yields an analytical expression of Burmester’s relationship between the fixed pivot of an RR chain and the relative position poles of its floating link. A similar solution of simultaneous spatial triangle equations yields Roth’s generalization of this insight, specifically, the fixed axis of a CC chain views two relative screw axes in one-half the dual crank rotation angle. These results provide the foundation for generalizing planar linkage synthesis techniques based on complex numbers to the synthesis of spatial linkages.

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37

Bonvechio, Timothy F., Kimberly I. Bonvechio, and Steven M. Sammons. "Proposed Standard Weight ( W s ) Equation and Standard Length Categories for Shoal Bass." North American Journal of Fisheries Management 39, no. 5 (August 5, 2019): 933–38. http://dx.doi.org/10.1002/nafm.10325.

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38

de Souza e Silva, Christina G., Leonard A. Kaminsky, Ross Arena, Jeffrey W. Christle, Claudio Gil S. Araújo, Ricardo M. Lima, Euan A. Ashley, and Jonathan Myers. "A reference equation for maximal aerobic power for treadmill and cycle ergometer exercise testing: Analysis from the FRIEND registry." European Journal of Preventive Cardiology 25, no. 7 (March 8, 2018): 742–50. http://dx.doi.org/10.1177/2047487318763958.

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Background Maximal oxygen uptake (VO2max) is a powerful predictor of health outcomes. Valid and portable reference values are integral to interpreting measured VO2max; however, available reference standards lack validation and are specific to exercise mode. This study was undertaken to develop and validate a single equation for normal standards for VO2max for the treadmill or cycle ergometer in men and women. Methods Healthy individuals ( N = 10,881; 67.8% men, 20–85 years) who performed a maximal cardiopulmonary exercise test on either a treadmill or a cycle ergometer were studied. Of these, 7617 and 3264 individuals were randomly selected for development and validation of the equation, respectively. A Brazilian sample (1619 individuals) constituted a second validation cohort. The prediction equation was determined using multiple regression analysis, and comparisons were made with the widely-used Wasserman and European equations. Results Age, sex, weight, height and exercise mode were significant predictors of VO2max. The regression equation was: VO2max (ml kg–1 min–1) = 45.2 – 0.35*Age – 10.9*Sex (male = 1; female = 2) – 0.15*Weight (pounds) + 0.68*Height (inches) – 0.46*Exercise Mode (treadmill = 1; bike = 2) ( R = 0.79, R2 = 0.62, standard error of the estimate = 6.6 ml kg–1 min–1). Percentage predicted VO2max for the US and Brazilian validation cohorts were 102.8% and 95.8%, respectively. The new equation performed better than traditional equations, particularly among women and individuals ≥60 years old. Conclusion A combined equation was developed for normal standards for VO2max for different exercise modes derived from a US national registry. The equation provided a lower average error between measured and predicted VO2max than traditional equations even when applied to an independent cohort. Additional studies are needed to determine its portability.

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39

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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Wu, Jiang Long, and Wei Rong Yang. "Approximate Solutions of Generalized Fifth-Order Korteweg-De Vries (KdV) Equation by the Standard Truncated Expansion Method." Applied Mechanics and Materials 201-202 (October 2012): 246–50. http://dx.doi.org/10.4028/www.scientific.net/amm.201-202.246.

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It is difficult to obtain exact solutions of the nonlinear partial differential equations (PDEs) due to the complexity and nonlinearity, especially for non-integrable systems. In this case, some reasonable approximations of real physics are considered, by means of the standard truncated expansion approach to solve real nonlinear system is proposed. In this paper, a simple standard truncated expansion approach with a quite universal pseudopotential is used for generalized fifth-order Korteweg-de Vries (KdV) equation, we can get two kinds of approximate solutions of the above equation, in some special cases, the approximate solutions may become exact. The same idea can also used to find approximate solutions of other well known nonlinear equations. We find a quite universal expansion approach which is valid for various nonlinear partial differential equations (PDEs).

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Nabi Iskandarov, Elmin Baghishov, Nabi Iskandarov, Elmin Baghishov. "EVALUATION OF UNCERTAINTY OF INFRARED THERMOMETERS WHEN MEASURING BODY TEMPERATURE." PIRETC-Proceeding of The International Research Education & Training Centre 19, no. 02 (May 18, 2022): 21–27. http://dx.doi.org/10.36962/piretc19022022-21.

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As we know from biophysics, infrared tympanic thermometers are easy to use and have a fast response time. They are widely used to measure human body temperature. Measurement accuracy and uncertainty are the most important performance indicators for these measuring instruments. This study evaluated the performance of two infrared tympanic thermometers, the Brown THT-3020 and the OMRON MC-510. The temperature of the temperature calibrator was changed to serve as the standard temperature of the "black body". The measurement errors for the two measuring instruments were reduced by the calibration equation. The predicted values meet the requirements of the ASTM standard. Sources of uncertainty include standard deviations of repetition at constant temperature or predicted values of the calibration equation, reference standard values, and resolution. Uncertainty analysis shows that the uncertainty of the calibration equation is the main source of combined uncertainty. The ambient temperature did not significantly affect the measured performance. The accuracy of infrared tympanic thermometers can be increased by the specified calibration equations. Keywords: infrared tympanic thermometer, metrological support, calibration equation, uncertainty, metrology

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Vas’kovskii, M. M., and I. V. Kachan. "Integration methods of mixed-type stochastic differential equations with fractional Brownian motions." Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series 55, no. 2 (June 28, 2019): 135–51. http://dx.doi.org/10.29235/1561-2430-2019-55-2-135-151.

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In the present, article new methods of exact integration of mixed-type stochastic differential equations with standard Brownian motion, fractional Brownian motion with the Hurst exponent H> 1/2 and the drift term have been constructed. Solutions of these equations are understood in integral sense where, in turn, the standard Brownian motion integral is the Ito integral and the fractional Brownian motion integral is the pathwise Young integral. The constucted integration methods can be attributed to two types. The first-type methods are based on reducing the equations to simpler equations, in particular – to the simplest equations and the linear inhomogeneous equations. In the article, necessary and sufficient conditions of reducing the equations applicable to one-dimensional equations have been obtained and the examples particularly covering the stochastic Bernoulli-type equations have been given. The second-type method is based on going to the Stratonovich equation and is applicable to multidimensional equations. In addition to the mentioned integration methods, the analogues of the differential Kolmogorov equation have been obtained for mathematical expectations and the solution probability density, assuming that coefficients of the mixed-type stochastic differential equation generate commuting flows.

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Guo, Xiu-Rong, Yu-Feng Zhang, Mei Guo, and Zheng-Tao Liu. "A new approach for finding standard heat equation and a special Newell-whitehead equation." Thermal Science 23, no. 3 Part A (2019): 1629–36. http://dx.doi.org/10.2298/tsci181219233g.

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Under a frame of 2 ? 2 matrix Lie algebras, Tu and Meng [9] once established a united integrable model of the Ablowitz-Kaup-Newel-Segur (AKNS) hierarchy, the D-AKNS hierarchy, the Levi hierarchy and the TD hierarchy. Based on this idea, we introduce two block-matrix Lie algebras to present an isospectral problem, whose compatibility condition gives rise to a type of integrable hierarchy which can be reduced to the Levi hierarchy and the AKNS hierarchy, and so on. A united integrable model obtained by us in the paper is different from that given by Tu and Meng. Specially, the main result in the paper can be reduced to two new various integrable couplings of the Levi hierarchy, from which we again obtain the standard heat equation and a special Newell-Whitehead equation.

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Aziz, Faisal, Alexander Christian Reisinger, Felix Aberer, Caren Sourij, Norbert Tripolt, Jolanta M. Siller-Matula, Dirk von-Lewinski, Philipp Eller, Susanne Kaser, and Harald Sourij. "Simplified Acute Physiology Score 3 Performance in Austrian COVID-19 Patients Admitted to Intensive Care Units with and without Diabetes." Viruses 14, no. 4 (April 8, 2022): 777. http://dx.doi.org/10.3390/v14040777.

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This study evaluated and compared the performance of simplified acute physiology score 3 (SAPS 3) for predicting in-hospital mortality in COVID-19 patients admitted to intensive care units (ICUs) with and without diabetes in Austria. The Austrian national public health institute (GÖG) data of COVID-19 patients admitted to ICUs (n = 5850) were analyzed. Three versions of SAPS 3 were used: standard equation, Central European equation, and Austrian equation customized for COVID-19 patients. The observed in-hospital mortality was 38.9%, 42.9%, and 37.3% in all, diabetes, and non-diabetes patients, respectively. The overall C-statistics was 0.69 with an insignificant (p = 0.193) difference between diabetes (0.70) and non-diabetes (0.68) patients. The Brier score was > 0.20 for all SAPS 3 equations in all cohorts. Calibration was unsatisfactory for both standard and Central European equations in all cohorts, whereas it was satisfactory for the Austrian equation in diabetes patients only. The SAPS 3 score demonstrated low discrimination and accuracy in Austrian COVID-19 patients, with an insignificant difference between diabetes and non-diabetes. All equations were miscalibrated particularly in non-diabetes patients, while the Austrian equation showed satisfactory calibration in diabetes patients only. Both uncalibrated and calibrated versions of SAPS 3 should be used with caution in COVID-19 patients.

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Safarov, J., F. Millero, R. Feistel, A. Heintz, and E. Hassel. "Thermodynamic properties of standard seawater." Ocean Science Discussions 6, no. 1 (April 17, 2009): 689–722. http://dx.doi.org/10.5194/osd-6-689-2009.

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Abstract. (p, ρ, T) data of standard seawater with practical salinity S≈35 (corresponding to an absolute salinity SA≈35.16504 g/kg) measured at T=(273.14 to 468.06) K and pressures up to p=140 MPa are reported with an estimated experimental relative combined standard uncertainty of 0.006% in density. The measurements were made with a newly constructed vibration-tube densimeter. The system was calibrated using double-distilled water, methanol and aqueous NaCl solutions. An empirical correlation for the density of standard seawater has been developed as a function of pressure and temperature. This equation of state was used to calculate other volumetric properties such as isothermal compressibility, isobaric thermal expansibility, differences in isobaric and isochoric heat capacities, thermal pressure coefficient, internal pressure and secant bulk modulus. The results can be used to extend the present equation of state of seawater to higher temperature as a function of pressure.

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Yazid, Afiq Witri Muhammad, and Nor Azwadi Che Sidik. "Prediction of the Flow around a Surface-Mounted Cube Using Two-Equation Turbulence Models." Applied Mechanics and Materials 315 (April 2013): 438–42. http://dx.doi.org/10.4028/www.scientific.net/amm.315.438.

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The flow around surface-mounted cube under neutral atmospheric boundary layer was simulated using two-equation turbulence models. The accuracy of two-equation turbulence models to model the flow fields were compared against fully documented experimental data. To build low computational cost, mesh refinements were investigated through mesh independence study by means of standard wall functions for the near wall treatment. All the two-equations turbulence models are shown to be underpredict the separation length and overpredict the reattachment length near the cube wall. In particular, the standardk-εturbulent scheme shows good agreement with experimental data of streamwise velocity flow along the symmetry plane behind the cube.

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MEYER, GUNTER H. "THE BLACK SCHOLES BARENBLATT EQUATION FOR OPTIONS WITH UNCERTAIN VOLATILITY AND ITS APPLICATION TO STATIC HEDGING." International Journal of Theoretical and Applied Finance 09, no. 05 (August 2006): 673–703. http://dx.doi.org/10.1142/s0219024906003755.

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The Black Scholes Barenblatt (BSB) equation for the envelope of option prices with uncertain volatility and interest rate is derived from the Black Scholes equation with the maximum principle for diffusion equations and shown to be equivalent to a readily solvable standard Black Scholes equation with a nonlinear source term. Analogous arguments yield the envelope for the delta of option prices. We then interpret the concept of static hedging for narrowing the envelope in terms of partial differential equations and define the optimal static hedge and computable approximations to it. We apply the BSB equation to find numerically some optimally hedged portfolios of representative European and American options.

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de Marchi, Mario. "Making Marx’s Surplus Equation Work (Within Sraffa’s Standard System)." American Journal of Industrial and Business Management 11, no. 03 (2021): 293–96. http://dx.doi.org/10.4236/ajibm.2021.113018.

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Njamen Njomen, Didier Alain, and Eric Djeutcha. "Solving Black-Schole Equation Using Standard Fractional Brownian Motion." Journal of Mathematics Research 11, no. 2 (March 24, 2019): 142. http://dx.doi.org/10.5539/jmr.v11n2p142.

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In this paper, we emphasize the Black-Scholes equation using standard fractional Brownian motion BHwith the hurst index H ∈ [0,1]. N. Ciprian (Necula, C. (2002)) and Bright and Angela (Bright, O., Angela, I., & Chukwunezu (2014)) get the same formula for the evaluation of a Call and Put of a fractional European with the different approaches. We propose a formula by adapting the non-fractional Black-Scholes model using a λHfactor to evaluate the european option. The price of the option at time t ∈]0,T[ depends on λH(T − t), and the cost of the action St, but not only from t − T as in the classical model. At the end, we propose the formula giving the implied volatility of sensitivities of the option and indicators of the financial market.

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Crothers, Stephen J. "Special relativity: Its inconsistency with the standard wave equation." Physics Essays 31, no. 2 (June 23, 2018): 137–39. http://dx.doi.org/10.4006/0836-1398-31.2.137.

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