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Academic literature on the topic 'Standard equation'

Author: Grafiati

Published: 10 December 2022

Last updated: 28 January 2023

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Journal articles on the topic "Standard equation"

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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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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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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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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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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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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Dissertations / Theses on the topic "Standard equation"

1

Bendaas, Saïda. "Quelques applications de l'analyse non standard aux équations aux dérivées partielles." Mulhouse, 1994. http://www.theses.fr/1994MULH0298.

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Rakesh, Arora. "Fine properties of solutions for quasi-linear elliptic and parabolic equations with non-local and non-standard growth." Thesis, Pau, 2020. http://www.theses.fr/2020PAUU3021.

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Dans cette thèse, nous étudions les propriétés fines des solutions d'équations elliptiques et paraboliques quasi-linéaires impliquant une croissance non locale et non standard. Nous nous sommes concentrés sur trois différents types d’équations aux dérivées partielles (EDP).Dans un premier temps, nous étudions les propriétés qualitatives des solutions faibles et fortes d’équations d'évolution comportant des termes à croissance non-standard. La motivation de l'étude de ces types d'équations réside dans la modélisation de caractéristiques anisotropes se produisant dans les modèles de fluides électro-rhéologiques, la restauration d'images, le processus de filtration dans les milieux complexes, les problèmes de stratigraphie ou encore les interactions biologiques hétérogènes. Dans cette étude, nous déterminons des conditions suffisantes sur les données initiales pour obtenir l'existence et l'unicité de solution forte. Nous établissons également la régularité de second ordre de la solution forte ainsi que des résultats optimaux d'intégrabilité à l’aide de nouvelles inégalités d'interpolation.Nous étudions en outre les propriétés des solutions faibles de problèmes doublement non-linéaires impliquant premièrement une classe d'opérateurs de type Leray-Lions et une non-linéarité dans la dérivée temporelle. Nous considérons les questions d'existence, d'unicité, de régularité ainsi que de comportement à l’infini des solutions faibles de ces problèmesDans une deuxième étude, nous considérons des systèmes de type Kirchhoff impliquant des opérateurs non-linéaires de type Choquard avec des poids singuliers. Cette classe de problèmes apparaît dans de nombreux phénomènes physiques comme la variation de longueur d’une corde tendue en vibration où le terme de Kirchhoff mesure le changement de tension ou encore la propagation d’ondes électromagnétiques dans le plasma. Motivé par les nombreuses applications physiques, nous étudions cette classe d’équations et nous établissons l'existence et des résultats de non-unicité pour des systèmes impliquant le n-Laplacien et des opérateurs polyharmoniques à l’aide d’inégalités de type Adams, Moser et Trudinger.Enfin, nous étudions des problèmes singuliers impliquant des opérateurs non-locaux comme le p-Laplacien fractionnaire. Nous établissons l'existence et la multiplicité des solutions classiques dans le cas du Laplacien fractionnaire impliquant une non-linéarité exponentielle en utilisant la théorie des bifurcations. Pour caractériser le comportement des grandes solutions, nous étudions en détail les singularités isolées pour l'équation elliptique semi-linéaire singulière. Nous obtenons la symétrie de la solution classique du problème Laplacien fractionnaire grâce à la méthode du plan mobile et d’un principe du maximum. Nous étudions également le problème de p-Laplacian fractionnaire non-linéaire impliquant une non-linéarité singulière et des poids singuliers. Nous montrons l'existence/ non-existence, l'unicité et la régularité holdérienne en exploitant le comportement des solutions proche du bord du domaine et par des méthodes d'approximation
In this thesis, we study the fine properties of solutions to quasilinear elliptic and parabolic equations involving non-local and non-standard growth. We focus on three different types of partial differential equations (PDEs).Firstly, we study the qualitative properties of weak and strong solutions of the evolution equations with non-standard growth. The importance of investigating these kinds of evolutions equations lies in modeling various anisotropic features that occur in electrorheological fluids models, image restoration, filtration process in complex media, stratigraphy problems, and heterogeneous biological interactions. We derive sufficient conditions on the initial data for the existence and uniqueness of a strong solution of the evolution equation with Dirichlet type boundary conditions. We establish the global higher integrability and second-order regularity of the strong solution via proving new interpolation inequalities. We also study the existence, uniqueness, regularity, and stabilization of the weak solution of Doubly nonlinear equation driven by a class of Leray-Lions type operators and non-monotone sub-homogeneous forcing terms. Secondly, we study the Kirchhoff equation and system involving different kinds of non-linear operators with exponential nonlinearity of the Choquard type and singular weights. These type of problems appears in many real-world phenomena starting from the study in the length of the string during the vibration of the stretched string, in the study of the propagation of electromagnetic waves in plasma, Bose-Einstein condensation and many more. Motivating from the abundant physical applications, we prove the existence and multiplicity results for the Kirchhoff equation and system with subcritical and critical exponential non-linearity, that arise out of several inequalities proved by Adams, Moser, and Trudinger. To deal with the system of Kirchhoff equations, we prove new Adams, Moser and Trudinger type inequalities in the Cartesian product of Sobolev spaces.Thirdly, we study the singular problems involving nonlocal operators. We show the existence and multiplicity for the classical solutions of Half Laplacian singular problem involving exponential nonlinearity via bifurcation theory. To characterize the behavior of large solutions, we further study isolated singularities for the singular semi linear elliptic equation. We show the symmetry and monotonicity properties of classical solution of fractional Laplacian problem using moving plane method and narrow maximum principle. We also study the nonlinear fractional Laplacian problem involving singular nonlinearity and singular weights. We prove the existence, uniqueness, non-existence, optimal Sobolev and Holder regularity results via exploiting the C^1,1 regularity of the boundary, barrier arguments and approximation method

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3

Eslick, John. "A Dynamical Study of the Evolution of Pressure Waves Propagating through a Semi-Infinite Region of Homogeneous Gas Combustion Subject to a Time-Harmonic Signal at the Boundary." ScholarWorks@UNO, 2011. http://scholarworks.uno.edu/td/1367.

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In this dissertation, the evolution of a pressure wave driven by a harmonic signal on the boundary during gas combustion is studied. The problem is modeled by a nonlinear, hyperbolic partial differential equation. Steady-state behavior is investigated using the perturbation method to ensure that enough time has passed for any transient effects to have dissipated. The zeroth, first and second-order perturbation solutions are obtained and their moduli are plotted against frequency. It is seen that the first and second-order corrections have unique maxima that shift to the right as the frequency decreases and to the left as the frequency increases. Dispersion relations are determined and their limiting behavior investigated in the low and high frequency regimes. It is seen that for low frequencies, the medium assumes a diffusive-like nature. However, for high frequencies the medium behaves similarly to one exhibiting relaxation. The phase speed is determined and its limiting behavior examined. For low frequencies, the phase speed is approximately equal to sqrt[ω/(n+1)] and for high frequencies, it behaves as 1/(n+1), where n is the mode number. Additionally, a maximum allowable value of the perturbation parameter, ε = 0.8, is determined that ensures boundedness of the solution. The location of the peak of the first-order correction, xmax, as a function of frequency is determined and is seen to approach the limiting value of 0.828/sqrt(ω) as the frequency tends to zero and the constant value of 2 ln 2 as the frequency tends to infinity. Analytic expressions are obtained for the approximate general perturbation solution in the low and high-frequency regimes and are plotted together with the perturbation solution in the corresponding frequency regimes, where the agreement is seen to be excellent. Finally, the solution obtained from the perturbation method is compared with the long-time solution obtained by the finite-difference scheme; again, ensuring that the transient effects have dissipated. Since the finite-difference scheme requires a right boundary, its location is chosen so that the wave dissipates in amplitude enough so that any reflections from the boundary will be negligible. The perturbation solution and the finite-difference solution are found to be in excellent agreement. Thus, the validity of the perturbation method is established.

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4

Dupaigne, Louis. "Equations elliptiques semilineaires avec potentiel singulier." Phd thesis, Université Pierre et Marie Curie - Paris VI, 2001. http://tel.archives-ouvertes.fr/tel-00002721.

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On considère des équations elliptiques semilinéaires simples de la forme Lu = F(x,u), où L est le Laplacien usuel avec condition de Dirichlet sur un ouvert borné régulier de R^n et où F peut être singulière en la variable x. On obtient notemment un critère exact pour l'existence de solutions, qui se traduit par l'apparition d'un nouvel exposant critique dans les applications.

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5

Kuncoro, Andreas. "Employing Quality Management Principles to Improve the Performance of Educational Systems: An Empirical Study of the Effect of ISO 9001 Standard on Teachers and Administrators Performance in the Indonesian Vocational Education System." Doctoral diss., University of Central Florida, 2013. http://digital.library.ucf.edu/cdm/ref/collection/ETD/id/5966.

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ISO 9001 has been world widely implemented in both manufacturing and service organizations. A lot of studies have been conducted to investigate the effects of ISO 9001 implementation on the performance of these organizations. Most of these studies show that ISO 9001 implementation realized positive operational improvements and financial success. Building on the merits of successful implementation of ISO 9001 quality management system in manufacturing and service, educational institutions have been attempted to adopt it in their operations. Even though there are studies relating ISO implementation to education, no research has been done to investigate the effects of ISO 9001 at the individual level. The objective of this research is to investigate the effects of ISO 9001 quality management implementation on the performance of administrators and teachers. The Indonesian vocational education system is selected as a case example as there is a significant number of such institutions in Indonesia that attempt to achieve ISO certification and there is a national need to improve the performance of vocational education. It is a challenge to assess objectively the degree of ISO 9001 implementation in this specific educational context because of the size and diversity. This study relies on survey that measures the respondents' perception. Hence, this study applies a self-reported survey based performance measurement. The questionnaires are developed based on extensive literature review. Partial Least Squares Structural Equation Modeling (PLSSEM) has been used to examine the relationships between the different elements of quality management systems, quality culture; administrator and teacher performances. The study is able to examine multiple interrelated dependence and subsequent relationships simultaneously among examined factors such as teacher and administrator performance, existing quality culture and ISO principles; and to incorporate variables that cannot be directly measured, such as leadership, for example. The findings of this study show that ISO 9001 implementation has positive significant effect on the performance of the vocational school administrator and teacher. The study also identifies key influencing elements of the ISO quality management system and examines their direct and indirect relationships with teacher and administrator performances. This study is expected to improve the current practices in implementing ISO and quality culture in any educational settings, specifically in the case of vocational educational system.
Ph.D.
Doctorate
Industrial Engineering and Management Systems
Engineering and Computer Science
Industrial Engineering

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6

Towler, Kim. "Non-standard discretizations of differential equations." Thesis, University of Kent, 2015. https://kar.kent.ac.uk/66665/.

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This thesis explores non-standard numerical integration methods for a range of non-linear systems of differential equations with a particular interest in looking for the preservation of various features when moving from the continuous system to a discrete setting. Firstly the exsiting non-standard schemes such as one discovered by Hirota and Kimura (and also Kahan) [21, 32] will be presented along with general rules for creating an effective numerical integration scheme devised by Mickens [40]. We then move on to the specific example of the Lotka-Volterra system and present a method for finding the most general forms of a non-standard scheme that is both symplectic and birational. The resulting three schemes found through this method have also been discovered through an alternative method by Roeger in [52]. Next we look at discretizing examples of 3-dimensional bi-Hamiltonian systems from a list given by G¨umral and Nutku [18] using the Hirota-Kimura/Kahan method followed by the same method applied to the H´enon-Heiles case (ii) system. The B¨acklund transformation for the H´enon-Heiles is also considered. Finally chapter 6 looks at systems with cubic vector fields and limit cycles with an aim to find the most general form of a non-standard scheme for two examples. First we look at a trimolecular system and then a Hamiltonian system that has a quartic potential.

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7

Khabir, Mohmed Hassan Mohmed. "Numerical singular perturbation approaches based on spline approximation methods for solving problems in computational finance." Thesis, University of the Western Cape, 2011. http://etd.uwc.ac.za/index.php?module=etd&action=viewtitle&id=gen8Srv25Nme4_7416_1320395978.

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Options are a special type of derivative securities because their values are derived from the value of some underlying security. Most options can be grouped into either of the two categories: European options which can be exercised only on the expiration date, and American options which can be exercised on or before the expiration date. American options are much harder to deal with than European ones. The reason being the optimal exercise policy of these options which led to free boundary problems. Ever since the seminal work of Black and Scholes [J. Pol. Econ. 81(3) (1973), 637-659], the differential equation approach in pricing options has attracted many researchers. Recently, numerical singular perturbation techniques have been used extensively for solving many differential equation models of sciences and engineering. In this thesis, we explore some of those methods which are based on spline approximations to solve the option pricing problems. We show a systematic construction and analysis of these methods to solve some European option problems and then extend the approach to solve problems of pricing American options as well as some exotic options. Proposed methods are analyzed for stability and convergence. Thorough numerical results are presented and compared with those seen in the literature.

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8

Yang, Qianqian. "Novel analytical and numerical methods for solving fractional dynamical systems." Thesis, Queensland University of Technology, 2010. https://eprints.qut.edu.au/35750/1/Qianqian_Yang_Thesis.pdf.

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During the past three decades, the subject of fractional calculus (that is, calculus of integrals and derivatives of arbitrary order) has gained considerable popularity and importance, mainly due to its demonstrated applications in numerous diverse and widespread fields in science and engineering. For example, fractional calculus has been successfully applied to problems in system biology, physics, chemistry and biochemistry, hydrology, medicine, and finance. In many cases these new fractional-order models are more adequate than the previously used integer-order models, because fractional derivatives and integrals enable the description of the memory and hereditary properties inherent in various materials and processes that are governed by anomalous diffusion. Hence, there is a growing need to find the solution behaviour of these fractional differential equations. However, the analytic solutions of most fractional differential equations generally cannot be obtained. As a consequence, approximate and numerical techniques are playing an important role in identifying the solution behaviour of such fractional equations and exploring their applications. The main objective of this thesis is to develop new effective numerical methods and supporting analysis, based on the finite difference and finite element methods, for solving time, space and time-space fractional dynamical systems involving fractional derivatives in one and two spatial dimensions. A series of five published papers and one manuscript in preparation will be presented on the solution of the space fractional diffusion equation, space fractional advectiondispersion equation, time and space fractional diffusion equation, time and space fractional Fokker-Planck equation with a linear or non-linear source term, and fractional cable equation involving two time fractional derivatives, respectively. One important contribution of this thesis is the demonstration of how to choose different approximation techniques for different fractional derivatives. Special attention has been paid to the Riesz space fractional derivative, due to its important application in the field of groundwater flow, system biology and finance. We present three numerical methods to approximate the Riesz space fractional derivative, namely the L1/ L2-approximation method, the standard/shifted Gr¨unwald method, and the matrix transform method (MTM). The first two methods are based on the finite difference method, while the MTM allows discretisation in space using either the finite difference or finite element methods. Furthermore, we prove the equivalence of the Riesz fractional derivative and the fractional Laplacian operator under homogeneous Dirichlet boundary conditions – a result that had not previously been established. This result justifies the aforementioned use of the MTM to approximate the Riesz fractional derivative. After spatial discretisation, the time-space fractional partial differential equation is transformed into a system of fractional-in-time differential equations. We then investigate numerical methods to handle time fractional derivatives, be they Caputo type or Riemann-Liouville type. This leads to new methods utilising either finite difference strategies or the Laplace transform method for advancing the solution in time. The stability and convergence of our proposed numerical methods are also investigated. Numerical experiments are carried out in support of our theoretical analysis. We also emphasise that the numerical methods we develop are applicable for many other types of fractional partial differential equations.

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Davis, Paige N. "Localised structures in some non-standard, singularly perturbed partial differential equations." Thesis, Queensland University of Technology, 2020. https://eprints.qut.edu.au/201835/1/Paige_Davis_Thesis.pdf.

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This thesis addresses the existence and stability of localised solutions in some nonstandard systems of partial differential equations. In particular, it locates the linearised spectrum of a Keller-Segel model for bacterial chemotaxis with logarithmic chemosensitivity, establishes the existence of travelling wave solutions to the Gatenby-Gawlinski model for tumour invasion with the acid-mediation hypothesis using geometric singular perturbation theory, and formulates the Evans function for a trivial defect solution in a general reaction diffusion equation with an added heterogeneous defect. Extending the analysis to these non-standard problems provides a foundation and insight for more general dynamical systems.

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10

Ali, Zakaria Idriss. "Stochastic quasilinear parabolic equations with non standard growth : weak and strong solutions." Thesis, University of Pretoria, 2015. http://hdl.handle.net/2263/53502.

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This thesis consists of two main parts. The rst part concerns the existence of weak probabilistic solutions (called elsewhere martingale solutions) for a stochastic quasilinear parabolic equation of generalized polytropic ltration, characterized by the presence of a nonlinear elliptic part admitting nonstandard growth. The deterministic version of the equation was rst introduced and studied by Samokhin in [178] as a generalized model for polytropic ltration. Our objective is to investigate the corresponding stochastic counterpart in the functional setting of generalized Lebesgue and Sobolev spaces. We establish an existence result of weak probabilistic solutions when the forcing terms do not satisfy Lipschitz conditions and the noise involves cylindrical Wiener processes. The second part is devoted to the existence and uniqueness results for a class of strongly nonlinear stochastic parabolic partial di erential equations. This part aims to treat an important class of higher-order stochastic quasilinear parabolic equations involving unbounded perturbation of zeroth order. The deterministic case was studied by Brezis and Browder (Proc. Natl. Acad. Sci. USA, 76(1): 38-40, 1979). Our main goal is to provide a detailed study of the corresponding stochastic problem. We establish the existence of a probabilistic weak solution and a unique strong probabilistic solution. The main tools used in this part of the thesis are a regularization through a truncation procedure which enables us to adapt the work of Krylov and Rozosvkii (Journal of Soviet Mathematics, 14: 1233-1277, 1981), combined with analytic and probabilistic compactness results (Prokhorov and Skorokhod Theorems), the theory of pseudomonotone operators, and a Banach space version of Yamada-Watanabe's theorem due to R ockner, Schmuland and Zhang. The study undertaken in this thesis is in some sense pioneering since both classes of stochastic partial di erential equations have not been the object of previous investigation, to the best of our knowledge. The results obtained are therefore original and constitute in our view signi cant contribution to the nonlinear theory of stochastic parabolic equations.
Thesis (PhD)--University of Pretoria, 2015.
Mathematics and Applied Mathematics
PhD
Unrestricted

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Books on the topic "Standard equation"

1

Tidriri, M. D. Mathematical analysis of the Navier-Stokes equations with non standard boundary conditions. Hampton, Va: Institute for Computer Applications in Science and Engineering, 1995.

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B, Straughan, ed. Non-standard and improperly posed problems. San Diego, Calif: Academic Press, 1997.

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Daywitt, William C. Horn design equations for the NBS horn-type noise standards. Boulder, Colo: U.S. Dept. of Commerce, National Bureau of Standards, 1987.

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Institute Of Electrical and Electronics Engineers. IEEE standards multivalue logic system for VHDL model interoperability (Std-logic-1164). New York, NY: Institute of Electrical and Electronics Engineers, 1993.

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Zeng, Lingjia. Standard errors of linear equating for the single-group design. Iowa City, Iowa: American College Testing Programs, 1991.

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Zeng, Lingjia. Standard errors of linear equating for the single-group design. Iowa City: American College Testing Program, 1991.

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Fraser, Marlow, ed. The engagement equation: Leadership strategies for an inspired workforce. Hoboken, N.J: Wiley, 2012.

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1962-, Kruse Alfred, ed. Properties of water and steam: The industrial standard IAPWS-IF97 for the thermodynamic properties and supplementary equations for other properties : tables based on these equations. Berlin: Springer-Verlag, 1998.

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Glovackaya, Alevtina. Computational model. ru: INFRA-M Academic Publishing LLC., 2020. http://dx.doi.org/10.12737/1013723.

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The textbook covers the basics of classical numerical methods of computational mathematics used for solving linear and nonlinear equations and systems; interpolation and approximation of functions; numerical integration and differentiation; solutions of ordinary differential equations by methods of one-dimensional and multidimensional optimization. Meets the requirements of the Federal state educational standards of higher education of the latest generation. It is intended for students of higher educational institutions studying in the discipline "Numerical methods".

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Lee, Stuart M. C. Variability of prediction of maximal oxygen consumption on the cycle ergometer using standard equations. Houston, Tx: Lyndon B. Johnson Space Center, 1993.

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Book chapters on the topic "Standard equation"

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Grabowski, Piotr. "Stabilization of Wave Equation Using Standard/Fractional Derivative in Boundary Damping." In Lecture Notes in Electrical Engineering, 101–21. Heidelberg: Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-319-00933-9_9.

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Goble, G. G., and H. Aboumatar. "Determination of wave equation soil constants from the standard penetration test." In Application of Stress-Wave Theory to Piles, 99–103. London: Routledge, 2022. http://dx.doi.org/10.1201/9781315137544-14.

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Agbavon, Koffi Messan, Appanah Rao Appadu, and Bilge İnan. "Comparative Study of Some Numerical Methods for the Standard FitzHugh-Nagumo Equation." In Forum for Interdisciplinary Mathematics, 95–127. Singapore: Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-8498-5_5.

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Percy, Andrew J., and Christoph H. Borchers. "Detailed Method for Performing the ExSTA Approach in Quantitative Bottom-Up Plasma." In Methods in Molecular Biology, 353–84. New York, NY: Springer US, 2021. http://dx.doi.org/10.1007/978-1-0716-1024-4_25.

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AbstractThe use of stable isotope-labeled standards (SIS) is an analytically valid means of quantifying proteins in biological samples. The nature of the labeled standards and their point of insertion in a bottom-up proteomic workflow can vary, with quantification methods utilizing curves in analytically sound practices. A promising quantification strategy for low sample amounts is external standard addition (ExSTA). In ExSTA, multipoint calibration curves are generated in buffer using serially diluted natural (NAT) peptides and a fixed concentration of SIS peptides. Equal concentrations of SIS peptides are spiked into experimental sample digests, with all digests (control and experimental) subjected to solid-phase extraction prior to liquid chromatography tandem mass spectrometry (LC-MS/MS) analysis. Endogenous peptide concentrations are then determined using the regression equation of the standard curves. Given the benefits of ExSTA in large-scale analysis, a detailed protocol is provided herein for quantifying a multiplexed panel of 125 high-to-moderate abundance proteins in undepleted and non-enriched human plasma samples. The procedural details and recommendations for successfully executing all phases of this quantification approach are described. As the proteins have been putatively correlated with various noncommunicable diseases, quantifying these by ExSTA in large-scale studies should help rapidly and precisely assess their true biomarker efficacy.

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Shishkin, G., L. Shishkina, and A. Petrenko. "Standard Difference Scheme for a Singularly Perturbed Convection-Diffusion Equation in the Presence of Perturbations." In Springer Proceedings in Mathematics & Statistics, 41–55. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-06923-4_5.

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Kirk, Mark. "Summary of Work to Develop the Transition Temperature Shift Equation Used in ASTM Standard Guide E900-15." In International Review of Nuclear Reactor Pressure Vessel Surveillance Programs, 432–56. 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959: ASTM International, 2018. http://dx.doi.org/10.1520/stp160320170009.

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Bachmair, Leo. "Standard Completion." In Canonical Equational Proofs, 13–38. Boston, MA: Birkhäuser Boston, 1991. http://dx.doi.org/10.1007/978-1-4684-7118-2_2.

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Stenner, A. Jackson, and Malbert Smith. "Testing Construct Theories." In Explanatory Models, Unit Standards, and Personalized Learning in Educational Measurement, 31–42. Singapore: Springer Nature Singapore, 2022. http://dx.doi.org/10.1007/978-981-19-3747-7_3.

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AbstractThis paper presents and illustrates a novel methodology, construct-specification equations, for examining the construct validity of a psychological instrument. Whereas traditional approaches have focused on the study of between-person variation on the construct, the suggested methodology emphasizes study of the relationships between item characteristics and item scores. The major thesis of the construct-specification-equation approach is that until developers of a psychological instrument understand what item characteristics are determining the item difficulties, the understanding of what is being measured is unsatisfyingly primitive. This method is illustrated with data from the Knox Cube Test which purports to be a measure of visual attention and short-term memory.

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Sanchez-Noguez, Josefina, Carlos Couder-Castañeda, J. J. Hernández-Gómez, and Itzel Navarro-Reyes. "Solving the Heat Transfer Equation by a Finite Difference Method Using Multi-dimensional Arrays in CUDA as in Standard C." In Communications in Computer and Information Science, 221–35. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-04209-6_16.

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Kerr, Nathan M., Iqbal Ike K. Ahmed, Leonard Pinchuk, Omar Sadruddin, and Paul F. Palmberg. "PRESERFLO MicroShunt." In Minimally Invasive Glaucoma Surgery, 91–103. Singapore: Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-5632-6_7.

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Abstract The PRESERFLO® MicroShunt (Santen Pharmaceutical Co. Ltd., Osaka, Japan), formerly called the InnFocus MicroShunt®, is a trans-scleral device that shunts aqueous humour from the anterior chamber to a filtering bleb under the conjunctiva and Tenon’s capsule. Manufactured from an inert biocompatible material called poly(styrene-block-isobutylene-block-styrene), or ‘SIBS’, the device elicits minimal foreign body reaction and inflammation; potentially reducing the risk of bleb-related fibrosis and failure. The MicroShunt is 8.5 mm long with a 70 μm lumen and is designed to minimize hypotony based on the Hagen–Poiseuille equation. Inserted via an ab-externo approach, the MicroShunt eliminates the need for creation of a scleral flap, sclerostomy, iridectomy, scleral flap suturing and postoperative suture lysis. Clinical trials show promising results with the MicroShunt achieving intraocular pressure reduction approaching that of trabeculectomy, the current gold standard for treating refractory glaucoma.

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Conference papers on the topic "Standard equation"

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Lăpădat, Marioara, and Mădălina Paşca. "Approximate solutions of the nonlinear standard Lane–Emden equation using the LSDQ method." In CENTRAL EUROPEAN SYMPOSIUM ON THERMOPHYSICS 2019 (CEST). AIP Publishing, 2019. http://dx.doi.org/10.1063/1.5114376.

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Jefferson-Loveday, Richard, Paul Tucker, V. Nagabhushana Rao, and John Northall. "Differential Equation Specification of Integral Turbulence Length Scales." In ASME Turbo Expo 2012: Turbine Technical Conference and Exposition. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/gt2012-68091.

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A Hamilton-Jacobi differential equation is used to naturally and smoothly (via Dirichlet boundary conditions) set turbulence length scales in separated flow regions based on traditional expected length scales. Such zones occur for example in rim-seals. The approach is investigated using two test cases, flow over a cylinder at a Reynolds number of 140,000 and flow over a rectangular cavity at a Reynolds number of 50,000. The Nee-Kovasznay turbulence model is investigated using this approach. Predicted drag coefficients for the cylinder test-case show significant (15%) improvement over standard steady RANS and are comparable with URANS results. The mean flow-field also shows a significant improvement over URANS. The error in reattachment length is improved by 180% compared with the steady RANS k–ω model. The wake velocity profile at a location downstream shows improvement and the URANS profile is inaccurate in comparison. For the cavity case the HJ-NK approach is generally comparable with the other RANS models for measured velocity profiles. Predicted drag coefficients are compared with large eddy simulation. The new approach shows a 20–30% improvement in predicted drag coefficients compared with standard one and two equation RANS models. The shape of the recirculation region within the cavity is also much improved.

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Karpat, F., S. Ekwaro-Osire, and E. Karpat. "A Virtual Tool for Wear Simulation of Standard and Non-Standard Spur Gears." In ASME 2012 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/imece2012-89759.

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There is an industrial demand for the increased performance of mechanical power transmission devices. This need in high performance is driven by high load capacity, high endurance, low cost, long life, and high speed. New designs and modifications in gears have been investigated to obtain high load carrying capacity and increased life with less volume and weight. Tooth wear is one of the major failure modes in gears. Although there are different classifications of wear mechanisms, wear on gears can be simply classified as mild wear, pitting, and severe wear, depending on the wear rate. These types of wear may lead to power transmission losses, decreased efficiency, increased vibration and noise, and gear tooth failure. This paper deals with the simulation of wear for standard and non-standard gears using an analytical approach. A numerical model for wear prediction of gear pair is developed. A wear model based on Archard’s equation is employed to predict wear depth. A MATLAB-based virtual tool is developed to analyze wear behavior of standard and non-standard spur gears with various gear parameters. In this paper, this virtual tool is introduced by using many numerical examples.

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Onizawa, Takashi, Yuji Nagae, Shigeru Takaya, and Tai Asayama. "Development of 2012 Edition of JSME Code for Design and Construction of Fast Reactors: (3) Development of the Material Strength Standard of Modified 9Cr-1Mo Steel." In ASME 2013 Pressure Vessels and Piping Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/pvp2013-97611.

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This paper describes the material strength standard of Modified 9Cr-1Mo (ASME Gr.91) steel in the design code for fast reactors of 2012 edition published by the Japan Society of Mechanical Engineers. Modified 9Cr-1Mo is to be used for primary and secondary coolant circuits, including intermediate heat exchangers and steam generators for the Japan Sodium Cooled Fast Reactor (JSFR). Modified 9Cr-1Mo steel was developed in Oak Ridge National Laboratory in the United States. Application of Modified 9Cr-1Mo to JSFR needs the material strength standard. Therefore, the authors developed the material strength standard. The material strength standard involved allowable limits such as S0, Sm, Su, Sy, SR and St and so on, environment effects such as sodium effects. In addition, material characteristic equations (Creep rupture equation, creep strain equation and equation of best fit curve for low-cycle fatigue life and so on) necessary for the allowable limits were involved. This paper describes the contents of the material strength standard.

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Onizawa, Takashi, Yuji Nagae, Shigeru Takaya, and Tai Asayama. "Development of 2012 Edition of JSME Code for Design and Construction of Fast Reactors: (2) Development of the Material Strength Standard of 316FR Stainless Steel." In ASME 2013 Pressure Vessels and Piping Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/pvp2013-97608.

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This paper describes the material strength standard of 316FR stainless steel in the design code for fast reactors of 2012 edition published by the Japan Society of Mechanical Engineers. 316FR stainless steel is to be used for a reactor vessel and internals for the Japan Sodium Cooled Fast Reactor (JSFR). 316FR was developed in Japan by optimizing chemical composition within the specifications of SUS316 in the Japanese Industrial Standard which is equivalent to Type 316 stainless steel. The optimization was performed from the viewpoint of maximizing the creep resistance under fast breeder conditions. Application of 316FR stainless steel to JSFR needs the material strength standard. Therefore, the authors developed the material strength standard. The material strength standard involved allowable limits such as S0, Sm, Su, Sy, SR and St and so on, environment effects such as irradiation effects and sodium effects. In addition, material characteristic equations (Creep rupture equation, creep strain equation and equation of best fit curve for low-cycle fatigue life and so on) necessary for the allowable limits were involved. This paper describes the contents of the material strength standard.

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Hung, W. S. Y., A. Fahme, and A. Kubasco. "Development of a Custom Ambient NOx Correction Equation for a Mars SoLoNOx Gas Turbine." In ASME 1994 International Gas Turbine and Aeroengine Congress and Exposition. American Society of Mechanical Engineers, 1994. http://dx.doi.org/10.1115/94-gt-402.

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The United States federal new source performance standards (NSPS) for stationary gas turbines contain NOx limits that are standardized based on the International Standards Organization (ISO) standard for ambient conditions. The measured NOx emissions from stationary gas turbines at test conditions are to be corrected to ISO standard ambient conditions using a recommended equation, which was developed using data from conventional (diffusion flame) combustion systems. It is genearlly expected that this correction equation will require a revision when advanced lean premixed or hybrid combustion system is utilized. At the site of the first Mars 100S SoLoNOx gas turbine, a continuous emissions and gas turbine performance data gathering system has been installed. From the data gathered, the non-applicability of this NOx ambient correction equation is demonstrated. This points to the need to develop a custom NOx ambient correction equation for gas turbines with an advanced lean premixed system. Using a proven NOx model, the humidity effect on NOx emissions from an advanced lean premixed system is determined to be much stronger than that for a conventional combustion system. The humidity effect was determined based on an engineering application of the NOx model. Through statistical analyses, this stronger humidity effect is supported by more than one thousand five hundred data points gathered over a eight-month period at the above customer’s site, covering an ambient temperature range over 100°F (56°C). Using this newly determined humidity effect and a least-square curve fit of the data, a custom NOx ambient correction equation has been developed for this prototype Mars SoLoNOx gas turbine.

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Hunter, A. I. C., R. G. Nyquist, S. Coller, J. Smith, and H. Boice. "Orifice Flow Calculation: Comparison Between Fluid Meter Applications — 6th Edition 1971, ASME PTC 19.5-2004 and ISO 5167 2003." In ASME 2013 Power Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/power2013-98268.

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This paper presents a comparison between existing flow calculations that are currently in use by the authors’ company in its Test Data Reduction System (TDRS) and the latest ASME flow measurement standard. Equations for the current system are referenced from Flow Meter Applications – 6th Edition 1971 [1] and updated equations are referenced from Flow measurement ASME PTC 19.5-2004 [2]. Comparisons were made between mass flow, expansion factor and orifice discharge coefficient calculations. The equations for mass flow and expansion remained unchanged between versions; however a variation in results exists between orifice discharge coefficients. For a diameter ratio, β range of 0.4 to 0.7, the updated 2004 equation for discharge coefficient provides a relatively small change over the 1971 equation. The 2004 equation was also found to be less sensitive to changes in pipe diameter and Reynolds number. A comparison between the ISO 5167 2003 and PTC 19.5-1971 flow calculations was also done. There was a significant difference in the calculation of expansion factor using ISO 5167 2003, which resulted in a significant mass flow variation between the two flow measurement standards.

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Friesen, Sharon. "Using Structural Equation Modeling to Explore the Implementation of the Teaching Quality Standard in Alberta, Canada." In 2021 AERA Annual Meeting. Washington DC: AERA, 2021. http://dx.doi.org/10.3102/1683957.

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Hamad, Ibrahim, and Mardan Pirdawood. "Existence and Uniqueness Theorems in an Infinitesimal Micromonad of an Initial Standard Point and Legendre Equation." In 2018 International Conference on Pure and Applied Science. Koya University, 2018. http://dx.doi.org/10.14500/icpas2018.pma66.

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Zhu, Xian-Kui. "Improved Elastic Compliance Equation and its Inverse Solution for Compact Tension Specimens." In ASME 2017 Pressure Vessels and Piping Conference. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/pvp2017-65406.

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ASTM E1820 is a well-developed fracture test standard and has been used worldwide for fracture toughness testing on ductile materials in terms of the J-integral or J-R curve. This standard recommends the elastic unloading compliance technique for measuring crack length in a single specimen test, and an accurate elastic compliance equation is needed to estimate physical crack length. Compact tension (CT) specimen is one of the most often used standard specimens with crack length ratios of 0.45≤a/W≤0.70 prescribed in E1820 for J-R curve testing. The stress intensity factor K of CT specimens used in E1820 was developed by Srawley (IJF, 1976) and has been commonly accepted as the most accurate solution. The compliance equation of CT specimens was developed by Saxena and Hudak (IJF, 1978) and has been used in ASTM E1820 for decades. However, recent results showed that the load-line displacement (LLD) compliance equation is not consistent with that determined from its K solution, and the maximum error of LLD compliance can be larger than 7% at a/W = 0.32 and ∼ 5% at a/W = 0.45 (E1820 standard crack size). The FEA results confirmed that the K solution in E1820 is indeed very accurate, but its compliance equation is less accurate. Thus, an improved compliance equation with high accuracy is developed from the accurate K solution using the numerical integration technique and shooting method.

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Reports on the topic "Standard equation"

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Kirkham, Harold. Applicability of the ?Gallet equation? to the vegetation clearances of NERC Reliability Standard FAC-003-2. Office of Scientific and Technical Information (OSTI), March 2012. http://dx.doi.org/10.2172/1074327.

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Kirkham, Harold. Follow-on to a report on the Applicability of the ?Gallet equation? to the vegetation clearances of NERC Reliability Standard FAC-003-2. Office of Scientific and Technical Information (OSTI), August 2012. http://dx.doi.org/10.2172/1074328.

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Kott, Phillip S. The Role of Weights in Regression Modeling and Imputation. RTI Press, April 2022. http://dx.doi.org/10.3768/rtipress.2022.mr.0047.2203.

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When fitting observations from a complex survey, the standard regression model assumes that the expected value of the difference between the dependent variable and its model-based prediction is zero, regardless of the values of the explanatory variables. A rarely failing extended regression model assumes only that the model error is uncorrelated with the model’s explanatory variables. When the standard model holds, it is possible to create alternative analysis weights that retain the consistency of the model-parameter estimates while increasing their efficiency by scaling the inverse-probability weights by an appropriately chosen function of the explanatory variables. When a regression model is used to impute for missing item values in a complex survey and when item missingness is a function of the explanatory variables of the regression model and not the item value itself, near unbiasedness of an estimated item mean requires that either the standard regression model for the item in the population holds or the analysis weights incorporate a correctly specified and consistently estimated probability of item response. By estimating the parameters of the probability of item response with a calibration equation, one can sometimes account for item missingness that is (partially) a function of the item value itself.

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Katz, A. R. Issues in defining an equations representation standard. RFC Editor, March 1987. http://dx.doi.org/10.17487/rfc1003.

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Daywitt, William C. Horn design equations for the NBS horn-type noise standards. Gaithersburg, MD: National Bureau of Standards, 1987. http://dx.doi.org/10.6028/nbs.ir.87-3073.

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Kiv, A. E., T. I. Maximova, and V. N. Soloviev. Microstructure of the relaxed (001) Si surface. [б. в.], December 1999. http://dx.doi.org/10.31812/0564/1245.

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We have applied molecular dynamics method and semi-empirical potential [1] to obtain the realistic picture of Si surface layers relaxation.The starting configuration was taken as a parallelepiped containing 864 atoms. There were 12 layers with 72 atoms in each one. Periodic boundary conditions were used in two dimensions. At first all atoms were in normal lattice positions. The relaxation of Si surface, which corresponds to (001) plane was investigated. MD method was applied in its standard form i.e. the equations of motion were solved by using of the central difference scheme. The time-step was 10-14s.

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Williamson, D. L., J. J. Hack, R. Jakob, P. N. Swarztrauber, and J. B. Drake. A standard test set for numerical approximations to the shallow water equations in spherical geometry. Office of Scientific and Technical Information (OSTI), August 1991. http://dx.doi.org/10.2172/5232139.

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Alviarez, Vanessa, and Ayhab Saad. Multinational Production and Intra-firm Trade. Inter-American Development Bank, November 2022. http://dx.doi.org/10.18235/0004566.

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Intra-firm trade, from parents to affiliates, has been combined with standard models of multinational production (MP) to deliver gravity-style predictions for foreign affiliates' sales. Nonetheless, the evidence shows that intra-firm trade is concentrated among a small set of large multinational firms. Using firm-level data from 35 countries, we document that only firms belonging to multinational corporations (MNCs) in the upper tail of the firms size distribution are significantly affected by the distance to their parents. We present a simple framework featuring MNCs selection into intra-firm trade and derive the analytical gravity equations that are consistent with the empirical findings.

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Cheverud, James, Claire C. Gordon, Robert A. Walker, Cashell Jacquish, Luci Kohn, Allen Moore, and Nyuta Yamashita. Anthropometric Survey of US Army Personnel (1988): Correlation Coefficients and Regression Equations. Part 5. Stepwise and Standard Multiple Regression Tables. Fort Belvoir, VA: Defense Technical Information Center, May 1990. http://dx.doi.org/10.21236/ada224990.

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Smith, D. H. INSTD: A Computer Program to Perform Internal Standard Calculations for Isotopic Ratio Mass Spectrometric Data Using General Solutions to the Equations. Office of Scientific and Technical Information (OSTI), November 1985. http://dx.doi.org/10.2172/12203412.

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