Directory of Open Access Journals (Sweden)
Garkavenko A. S.
2011-08-01
Full Text Available The rate equations of the exciton laser in the system of interacting excitons have been obtained and the inverted population conditions and generation have been derived. The possibility of creating radically new gamma-ray laser has been shown.
Connecting Related Rates and Differential Equations
Brandt, Keith
2012-01-01
This article points out a simple connection between related rates and differential equations. The connection can be used for in-class examples or homework exercises, and it is accessible to students who are familiar with separation of variables.
Speaking rate effects on locus equation slope
Berry, Jeff; Weismer, Gary
2013-01-01
A locus equation describes a 1st order regression fit to a scatter of vowel steady-state frequency values predicting vowel onset frequency values. Locus equation coefficients are often interpreted as indices of coarticulation. Speaking rate variations with a constant consonant–vowel form are thought to induce changes in the degree of coarticulation. In the current work, the hypothesis that locus slope is a transparent index of coarticulation is examined through the analysis of acoustic samples of large-scale, nearly continuous variations in speaking rate. Following the methodological conventions for locus equation derivation, data pooled across ten vowels yield locus equation slopes that are mostly consistent with the hypothesis that locus equations vary systematically with coarticulation. Comparable analyses between different four-vowel pools reveal variations in the locus slope range and changes in locus slope sensitivity to rate change. Analyses across rate but within vowels are substantially less consistent with the locus hypothesis. Taken together, these findings suggest that the practice of vowel pooling exerts a non-negligible influence on locus outcomes. Results are discussed within the context of articulatory accounts of locus equations and the effects of speaking rate change. PMID:24535890
On Coupled Rate Equations with Quadratic Nonlinearities
Montroll, Elliott W.
1972-01-01
Rate equations with quadratic nonlinearities appear in many fields, such as chemical kinetics, population dynamics, transport theory, hydrodynamics, etc. Such equations, which may arise from basic principles or which may be phenomenological, are generally solved by linearization and application of perturbation theory. Here, a somewhat different strategy is emphasized. Alternative nonlinear models that can be solved exactly and whose solutions have the qualitative character expected from the original equations are first searched for. Then, the original equations are treated as perturbations of those of the solvable model. Hence, the function of the perturbation theory is to improve numerical accuracy of solutions, rather than to furnish the basic qualitative behavior of the solutions of the equations. PMID:16592013
Generating rate equations for complex enzyme systems by a computer-assisted systematic method
Directory of Open Access Journals (Sweden)
Beard Daniel A
2009-08-01
Full Text Available Abstract Background While the theory of enzyme kinetics is fundamental to analyzing and simulating biochemical systems, the derivation of rate equations for complex mechanisms for enzyme-catalyzed reactions is cumbersome and error prone. Therefore, a number of algorithms and related computer programs have been developed to assist in such derivations. Yet although a number of algorithms, programs, and software packages are reported in the literature, one or more significant limitation is associated with each of these tools. Furthermore, none is freely available for download and use by the community. Results We have implemented an algorithm based on the schematic method of King and Altman (KA that employs the topological theory of linear graphs for systematic generation of valid reaction patterns in a GUI-based stand-alone computer program called KAPattern. The underlying algorithm allows for the assumption steady-state, rapid equilibrium-binding, and/or irreversibility for individual steps in catalytic mechanisms. The program can automatically generate MathML and MATLAB output files that users can easily incorporate into simulation programs. Conclusion A computer program, called KAPattern, for generating rate equations for complex enzyme system is a freely available and can be accessed at http://www.biocoda.org.
Directory of Open Access Journals (Sweden)
Ayodele O. Kolawole
2016-01-01
Full Text Available Fish hepatic glutathione transferases are connected with the elimination of intracellular pollutants and detoxification of organic micro-pollutants in their aquatic ecosystem. The two-substrate steady state kinetic mechanism of Silver catfish (Synodontis eupterus major hepatic glutathione transferases purified to apparent homogeneity was explored. The enzyme was dimeric enzyme with a monomeric size of 25.6 kDa. Initial-velocity studies and Product inhibition patterns by methyl glutathione and chloride with respect to GSH-CDNB; GSH-ρ-nitrophenylacetate; and GSH-Ethacrynic acid all conforms to a rapid equilibrium sequential random Bi Bi kinetic mechanism rather than steady state sequential random Bi Bi kinetic. α was 2.96 ± 0.35 for the model. The pH profile of Vmax/KM (with saturating 1-chloro-2,4-dinitrobenzene and variable GSH concentrations showed apparent pKa value of 6.88 and 9.86. Inhibition studies as a function of inhibitor concentration show that the enzyme is a homodimer and near neutral GST. The enzyme poorly conjugates 4-hydroxylnonenal and cumene hydroperoxide and may not be involved in oxidative stress protection. The seGST is unique and overwhelmingly shows characteristics similar to those of homodimeric class Pi GSTs, as was indicated by its kinetic mechanism, substrate specificity and inhibition studies. The rate- limiting step, probably the product release, of the reaction is viscosity-dependent and is consequential if macro-viscosogen or micro-viscosogen.
Representing Rate Equations for Enzyme-Catalyzed Reactions
Ault, Addison
2011-01-01
Rate equations for enzyme-catalyzed reactions are derived and presented in a way that makes it easier for the nonspecialist to see how the rate of an enzyme-catalyzed reaction depends upon kinetic constants and concentrations. This is done with distribution equations that show how the rate of the reaction depends upon the relative quantities of…
Resting metabolic rate prediction equations in teenagers: history and validity
Directory of Open Access Journals (Sweden)
Paulo Henrique Santos da Fonseca
2008-01-01
Full Text Available http://dx.doi.org/10.5007/1980-0037.2008v10n4p405 The resting metabolic rate (RMR has been utilized routinely by clinics to predict the energy necessary for patients. Additionally, governmental agencies and health organizations define the energy necessary for the population and the energy orientation for athletes who play sports. Many recognize the value of the RMR, but it is not always possible to measure it by using calorimetry, so it is suggested to use equations of prediction for this variable. However, RMR prediction equations must be used in such a way that allows its frequent reexamination to guarantee efficiency. This article has three purposes: 1 to analyze the development history of the traditional equations by Harris and Benedict (1919, Schofield (1985, WHO/FAO/UNU (1985, and Henry and Rees (1991 (these authors routinely used the traditional equations to measure the RMR in teenagers; 2 to analyze the studies that tested the validity of these equations in the population of teenagers; 3 to argue and point out possible intervening factors on the RMR results of teenagers, thus guiding to election of independent variables when developing equations for Brazilian’s population. After analyzing the equations, it is possible to conclude that: 1 the equations had been developed by having a given base of compiled evaluations from the beginning of the Twentieth Century; 2 the studies that tested the validity of these equations demonstrated great variability in the results, confirming the impossibility to have a unique/universal equation. This study also showed that new RMR prediction equations must be developed for specific populations taking into consideration the race and where the individual resides.
Modelling of elastic heat conductors via objective rate equations
Morro, Angelo
2018-01-01
A thermoelastic solid is modelled by letting the heat flux be given by a rate equation. As any constitutive property, the rate equation has to be objective and consistent with thermodynamics. Accordingly, firstly a theorem is given that characterizes objective time derivatives. This allows the known objective time derivatives to be viewed as particular elements of the set so specified. Next the thermodynamic consistency is established for the constitutive models involving objective time derivatives within appropriate sets. It emerges that the thermodynamic consistency holds provided the stress contains additively terms quadratic in the heat flux vector in a form that is related to the derivative adopted for the rate of the heat flux.
Ye, Zhengqi; Zetterberg, Craig; Gao, Hong
2017-06-05
Binding of drug molecules to plasma proteins is an important parameter in assessing drug ADME properties. Plasma protein binding (PPB) assays are routinely performed during drug discovery and development. A fully automated PPB assay was developed using rapid equilibrium dialysis (RED) device and Tecan workstation coupled to an automated incubator. The PPB assay was carried out in unsealed RED plates which allowed the assay to be fully automated. The plasma pH was maintained at 7.4 during the 6-h dialysis under 2% CO2 condition. The samples were extracted with acetonitrile and analyzed by liquid chromatography tandem mass spectrometry. The percent bound results of 10 commercial drugs in plasma protein binding were very similar between the automated and manual assays, and were comparable to literature values. The automated assay increases laboratory productivity and is applicable to high-throughput screening of drug protein binding in drug discovery. Copyright © 2017 Elsevier B.V. All rights reserved.
Resting metabolic rate prediction equations in teenagers: history and validity
Directory of Open Access Journals (Sweden)
Paulo Henrique Santos da Fonseca
2008-12-01
Full Text Available The resting metabolic rate (RMR has been utilized routinely by clinics to predict the energy necessary forpatients. Additionally, governmental agencies and health organizations define the energy necessary for the population andthe energy orientation for athletes who play sports. Many recognize the value of the RMR, but it is not always possible tomeasure it by using calorimetry, so it is suggested to use equations of prediction for this variable. However, RMR predictionequations must be used in such a way that allows its frequent reexamination to guarantee efficiency. This article has threepurposes: 1 to analyze the development history of the traditional equations by Harris and Benedict (1919, Schofield (1985,WHO/FAO/UNU (1985, and Henry and Rees (1991 (these authors routinely used the traditional equations to measure theRMR in teenagers; 2 to analyze the studies that tested the validity of these equations in the population of teenagers; 3 toargue and point out possible intervening factors on the RMR results of teenagers, thus guiding to election of independentvariables when developing equations for Brazilian’s population. After analyzing the equations, it is possible to conclude that:1 the equations had been developed by having a given base of compiled evaluations from the beginning of the TwentiethCentury; 2 the studies that tested the validity of these equations demonstrated great variability in the results, confirmingthe impossibility to have a unique/universal equation. This study also showed that new RMR prediction equations must bedeveloped for specific populations taking into consideration the race and where the individual resides.
ECONOMETRIC APPROACH TO DIFFERENCE EQUATIONS MODELING OF EXCHANGE RATES CHANGES
Directory of Open Access Journals (Sweden)
Josip Arnerić
2010-12-01
Full Text Available Time series models that are commonly used in econometric modeling are autoregressive stochastic linear models (AR and models of moving averages (MA. Mentioned models by their structure are actually stochastic difference equations. Therefore, the objective of this paper is to estimate difference equations containing stochastic (random component. Estimated models of time series will be used to forecast observed data in the future. Namely, solutions of difference equations are closely related to conditions of stationary time series models. Based on the fact that volatility is time varying in high frequency data and that periods of high volatility tend to cluster, the most successful and popular models in modeling time varying volatility are GARCH type models and their variants. However, GARCH models will not be analyzed because the purpose of this research is to predict the value of the exchange rate in the levels within conditional mean equation and to determine whether the observed variable has a stable or explosive time path. Based on the estimated difference equation it will be examined whether Croatia is implementing a stable policy of exchange rates.
Melanin binding study of clinical drugs with cassette dosing and rapid equilibrium dialysis inserts.
Pelkonen, Laura; Tengvall-Unadike, Unni; Ruponen, Marika; Kidron, Heidi; Del Amo, Eva M; Reinisalo, Mika; Urtti, Arto
2017-11-15
Melanin pigment is a negatively charged polymer found in pigmented human tissues. In the eye, iris, ciliary body, choroid and retinal pigment epithelium (RPE) are heavily pigmented. Several drug molecules are known to bind to melanin, but larger sets of drugs have not been compared often in similar test conditions. In this study, we introduce a powerful tool for screening of melanin binding. The binding of a set of 34 compounds to isolated porcine RPE melanin was determined by cassette (n-in-one) dosing in rapid equilibrium dialysis inserts and the binding was quantitated with LC-MS/MS analytics. The compounds represented large variety in melanin binding (from 8.6%, ganciclovir) to over 95% bound (ampicillin and ciprofloxacin). The data provides information on melanin binding of small molecular weight compounds that are used for ocular (e.g. brinzolamide, ganciclovir) and systemic (e.g. tizanidine, indomethacin) therapy. Interestingly, competition among compounds was seen for melanin binding and the binding did not show any correlation with plasma protein binding. These results increase the understanding of melanin binding of ocular drugs and can be further exploited to predict pharmacokinetics in the eye. Pigment binding provides an interesting option for improved drug distribution to retina and choroid that are difficult target tissues in drug delivery. Copyright © 2017 Elsevier B.V. All rights reserved.
Ion-beam-driven plasma described by rate equations
Energy Technology Data Exchange (ETDEWEB)
Kaercher, B.; Meyer-ter-Vehn, J. (Max-Planck-Institut fuer Quantenoptik, Garching (Germany, F.R.))
1990-01-01
Ionization distributions and radiation spectra of a dense plasma driven by intense ion beams are studied by solving stationary rate equations. Expressions for the rate coefficients are derived. Optically thin plasmas of hydrogen and carbon are considered neglecting hydrodynamic motion. Results on level populations versus temperature, on power balance and equilibrium states, and also on emission spectra are given. In particular, the transition from beam-determined plasma states to thermal equilibrium states is discussed. Beam parameters are chosen close to those in experiments now being planned. (author).
Empirical rate equation model and rate calculations of hydrogen generation for Hanford tank waste
Energy Technology Data Exchange (ETDEWEB)
HU, T.A.
1999-07-13
Empirical rate equations are derived to estimate hydrogen generation based on chemical reactions, radiolysis of water and organic compounds, and corrosion processes. A comparison of the generation rates observed in the field with the rates calculated for twenty eight tanks shows agreement with in a factor of two to three.
Rate equation analysis of hydrogen uptake on Si (100) surfaces
Inanaga, S.; Rahman, F.; Khanom, F.; Namiki, A.
2005-09-01
We have studied the uptake process of H on Si (100) surfaces by means of rate equation analysis. Flowers' quasiequilibrium model for adsorption and desorption of H [M. C. Flowers, N. B. H. Jonathan, A. Morris, and S. Wright, Surf. Sci. 396, 227 (1998)] is extended so that in addition to the H abstraction (ABS) and β2-channel thermal desorption (TD) the proposed rate equation further includes the adsorption-induced desorption (AID) and β1-TD. The validity of the model is tested by the experiments of ABS and AID rates in the reaction system H+D/Si (100). Consequently, we find it can well reproduce the experimental results, validating the proposed model. We find the AID rate curve as a function of surface temperature Ts exhibits a clear anti-correlation with the bulk dangling bond density versus Ts curve reported in the plasma-enhanced chemical vapor deposition (CVD) for amorphous Si films. The significance of the H chemistry in plasma-enhanced CVD is discussed.
Validation of resting metabolic rate prediction equations for teenagers
Directory of Open Access Journals (Sweden)
Paulo Henrique Santos da Fonseca
2007-09-01
Full Text Available The resting metabolic rate (RMR can be defi ned as the minimum rate of energy spent and represents the main component of the energetic outlay. The purpose of this study is to validate equations to predict the resting metabolic rate in teenagers (103 individuals, being 51 girls and 52 boys, with age between 10 and 17 years from Florianópolis – SC – Brazil. It was measured: the body weight, body height, skinfolds and obtained the lean and body fat mass through bioimpedance. The nonproteic RMR was measured by Weir’s equation (1949, utilizing AeroSport TEEM-100 gas analyzer. The studied equations were: Harry and Benedict (1919, Schofi eld (1985, WHO/FAO/UNU (1985, Henry and Rees (1991, Molnár et al. (1998, Tverskaya et al. (1998 and Müller et al. (2004. In order to study the cross-validation of the RMR prediction equations and its standard measure (Weir 1949, the following statistics procedure were calculated: Pearson’s correlation (r ≥ 0.70, the “t” test with the signifi cance level of p0.05 in relation to the standard measure, with exception of the equations suggested for Tverskaya et al. (1998, and the two models of Müller et al (2004. Even though there was not a signifi cant difference, only the models considered for Henry and Rees (1991, and Molnár et al. (1995 had gotten constant error variation under 5%. All the equations analyzed in the study in girls had not reached criterion of correlation values of 0.70 with the indirect calorimetry. Analyzing the prediction equations of RMR in boys, all of them had moderate correlation coeffi cients with the indirect calorimetry, however below 0.70. Only the equation developed for Tverskaya et al. (1998 presented differences (p ABSTRACT0,05 em relação à medida padrão (Weir 1949, com exceção das equações sugeridas por Tverskaya et al. (1998 e os dois modelos de Müller et al (2004. Mesmo não havendo diferença signifi cativa, somente os modelos propostos por Henry e Rees (1991
Reaction rates for a generalized reaction-diffusion master equation.
Hellander, Stefan; Petzold, Linda
2016-01-01
It has been established that there is an inherent limit to the accuracy of the reaction-diffusion master equation. Specifically, there exists a fundamental lower bound on the mesh size, below which the accuracy deteriorates as the mesh is refined further. In this paper we extend the standard reaction-diffusion master equation to allow molecules occupying neighboring voxels to react, in contrast to the traditional approach, in which molecules react only when occupying the same voxel. We derive reaction rates, in two dimensions as well as three dimensions, to obtain an optimal match to the more fine-grained Smoluchowski model and show in two numerical examples that the extended algorithm is accurate for a wide range of mesh sizes, allowing us to simulate systems that are intractable with the standard reaction-diffusion master equation. In addition, we show that for mesh sizes above the fundamental lower limit of the standard algorithm, the generalized algorithm reduces to the standard algorithm. We derive a lower limit for the generalized algorithm which, in both two dimensions and three dimensions, is of the order of the reaction radius of a reacting pair of molecules.
Laser-rate-equation description of optomechanical oscillators.
Khurgin, J B; Pruessner, M W; Stievater, T H; Rabinovich, W S
2012-06-01
We develop a set of laser rate equations that accurately describes mechanical amplification in optomechanical oscillators driven by photothermal or radiation pressure forces. In the process we introduce a set of parameters describing gain, stored energy, slope efficiency, and saturation power of the mechanical laser. We identify the three-phonon parametric interactions as a microscopic mechanism enabling self-oscillation. Our theory shows remarkable agreement with our experimental data, demonstrating that optomechanical self-oscillation is essentially a "phonon lasing" process in which an optical pump generates coherent acoustic phonons.
Matsushita, K.; Mahmoodi, B.K.; Woodward, M.; Emberson, J.R.; Jafar, T.H.; Jee, S.H.; Polkinghorne, K.R.; Shankar, A.; Smith, D.H.; Tonelli, M.; Warnock, D.G.; Wen, C.P.; Coresh, J.; Gansevoort, R.T.; Hemmelgarn, B.R.; Levey, A.S.; Wetzels, J.F.
2012-01-01
CONTEXT: The Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) equation more accurately estimates glomerular filtration rate (GFR) than the Modification of Diet in Renal Disease (MDRD) Study equation using the same variables, especially at higher GFR, but definitive evidence of its risk
Matsushita, Kunihiro; Mahmoodi, Bakhtawar K.; Woodward, Mark; Emberson, Jonathan R.; Jafar, Tazeen H.; Jee, Sun Ha; Polkinghorne, Kevan R.; Shankar, Anoop; Smith, David H.; Tonelli, Marcello; Warnock, David G.; Wen, Chi-Pang; Coresh, Josef; Gansevoort, Ron T.; Hemmelgarn, Brenda R.; Levey, Andrew S.
2012-01-01
Context The Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) equation more accurately estimates glomerular filtration rate (GFR) than the Modification of Diet in Renal Disease (MDRD) Study equation using the same variables, especially at higher GFR, but definitive evidence of its risk
Kinematic equations for resolved-rate control of an industrial robot arm
Barker, L. K.
1983-01-01
An operator can use kinematic, resolved-rate equations to dynamically control a robot arm by watching its response to commanded inputs. Known resolved-rate equations for the control of a particular six-degree-of-freedom industrial robot arm and proceeds to simplify the equations for faster computations are derived. Methods for controlling the robot arm in regions which normally cause mathematical singularities in the resolved-rate equations are discussed.
Bias and accuracy of resting metabolic rate equations in non-obese and obese adults.
Frankenfield, David C
2013-12-01
Consensus on the best equation for predicting metabolic rate in healthy people remains elusive. New equations continue to appear. The purpose of the current study was to validate several standard and new metabolic rate equations in obese and non-obese adults. Resting metabolic rate was measured with indirect calorimetry and calculated using the Mifflin St. Jeor, Livingston, Harris Benedict, Muller, Vander Weg, WHO equations, and the Oxford variation of WHO. Each equation was compared for accuracy (percent of estimates falling within 10% of measured) and bias (95% confidence intervals of differences between estimate and measured expenditure that excluded zero). Three hundred thirty-seven ambulatory, community-living adults were measured. The Mifflin St. Jeor equation was unbiased (95% confidence interval -26 to +8 kcal/day), the Livingston equation tended to underestimate true metabolic rate (95% confidence interval -63 to -25 kcal/day), while all other equations tended to overestimate true metabolic rate. Accuracy rate was similar between Mifflin St. Jeor and Livingston (82 vs. 79%). Accuracy rate was lower in obese than non-obese volunteers, no matter which equation was used (for example 87 vs. 75% for the Mifflin St. Jeor equation). The Mifflin St. Jeor equation is confirmed as a useful prediction equation for resting metabolic rate in community-living ambulatory adults of various body sizes, though the Livingston equation is similar. Accuracy rate is lower in obese than non-obese people, and so an obesity-specific equation is proposed. This equation needs validation before it is adopted for clinical use. Copyright © 2013 Elsevier Ltd and European Society for Clinical Nutrition and Metabolism. All rights reserved.
Energy Technology Data Exchange (ETDEWEB)
Erjaee, G H [Mathematics and Physics Department, Qatar University, Doha (Qatar)], E-mail: erjaee@qu.edu.qa
2008-02-15
In this article saddle and Hopf bifurcation points of predator-prey fractional differential equations system with a constant rate harvesting are investigated. The numerical results based on Grunwald-Letnikov discretization for fractional differential equations together with the Mickens' non-standard discretization method agree with those found by the corresponding ordinary differential equation system.
Erjaee, G. H.
2008-02-01
In this article saddle and Hopf bifurcation points of predator-prey fractional differential equations system with a constant rate harvesting are investigated. The numerical results based on Grunwald-Letnikov discretization for fractional differential equations together with the Mickens' non-standard discretization method agree with those found by the corresponding ordinary differential equation system.
Quantum-Dot Semiconductor Optical Amplifiers: State Space Model versus Rate Equation Model
Directory of Open Access Journals (Sweden)
Hussein Taleb
2013-01-01
Full Text Available A simple and accurate dynamic model for QD-SOAs is proposed. The proposed model is based on the state space theory, where by eliminating the distance dependence of the rate equation model of the QD-SOA; we derive a state space model for the device. A comparison is made between the rate equation model and the state space model under both steady state and transient regimes. Simulation results demonstrate that the derived state space model not only is much simpler and faster than the rate equation model, but also it is as accurate as the rate equation model.
Vrzheshch, P V
2015-01-01
Quantitative evaluation of the accuracy of the rapid equilibrium assumption in the steady-state enzyme kinetics was obtained for an arbitrary mechanism of an enzyme-catalyzed reaction. This evaluation depends only on the structure and properties of the equilibrium segment, but doesn't depend on the structure and properties of the rest (stationary part) of the kinetic scheme. The smaller the values of the edges leaving equilibrium segment in relation to values of the edges within the equilibrium segment, the higher the accuracy of determination of intermediate concentrations and reaction velocity in a case of the rapid equilibrium assumption.
Beyond the Mincer Equation: The Internal Rate of Return to Higher Education in Colombia
García-Suaza, Andrés Felipe; Guataquí, Juan Carlos; Guerra, José Alberto; Maldonado, Darío
2014-01-01
In order to present an estimation of the internal rate of return (IRR) to higher education in Colombia, we take advantage of recent updates on the methodological approach towards earnings equations. In order to overcome the criticism that surrounds interpretations of the education coefficient of Mincer equations as being the rate of return to…
Derivation and application of hydraulic equation for variable-rate ...
African Journals Online (AJOL)
The variable-rate contour-controlled sprinkler (VRCS) for precision irrigation can throw water on a given shaped area and the flow rate is also varied with the throw distance of the sprinkler for the purpose of high uniformity irrigation. Much of past research work were concentrated on the mechanical availability of ...
Changjie, Guan; Xusheng, Zhu; Feng, He; Shuguang, Qin; Jianwen, Li; Junzhou, Fu
2017-01-01
Performance of equations in elderly with chronic kidney disease (CKD) was debated. We aimed to access the performances of estimating equations for glomerular filtration rate in Chinese elderly population with chronic kidney disease. Participants [N = 218, median age, 82 (range 75-96)] with CKD underwent renal dynamic imaging using technetium-99m diethylene-triamine-penta-acetic acid (99mTc-DTPA). The performances of glomerular filtration rate equations including the Cockcroft-Gault equation, the MDRD (Modification of Diet in Renal Disease) equation for Chinese, 3 CKD-EPI (Chronic Kidney Disease Epidemiology Collaboration) equations, and 2 BIS (Berlin Initiative Study) equations were compared. Median mGFR was 47.62 (3.00-135.00) ml/min/1.73 m(2). Smaller biases were shown in BIS-2 equation and CKD-EPI-Cr equation (0.63 ml/min/1.73 m(2) and -1.22 ml/min/1.73 m(2)). Interquartile range of the differences was least with BIS-2 equation and CKD-EPI-Cr-Cys equation (4.36 ml/min/1.73 m(2) and 9.17 ml/min/1.73 m(2)). For accuracy (percentage of eGFR within 30 % of the mGFR, P30), performance of BIS-2, CKD-EPI-Cr-Cys, and BIS-1 equation was superior (94.50, 89.91, and 88.53 %, respectively). In terms of accuracy (root-mean-square error, RMSE), BIS-2 equation, CKD-EPI-Cr-Cys equation, and BIS-1 equation also performed better (7.21 ml/min/1.73 m(2), 8.87 ml/min/1.73 m(2) and 9.82 ml/min/1.73 m(2)). GFR category misclassification rates were smaller in BIS-2 equation, CKD-EPI-Cr-Cys equation and BIS-1 equation (16.51, 20.64, and 25.69 %, respectively). Compared with other equations, the BIS-2 equation performed better in the estimation of glomerular filtration rate for Chinese elderly with CKD aged 75 or above.
arXiv Status of rates and rate equations for thermal leptogenesis
Biondini, Simone; Brambilla, Nora; Garny, Mathias; Ghiglieri, Jacopo; Hohenegger, Andreas; Laine, Mikko; Mendizabal, Sebastian; Millington, Peter; Salvio, Alberto; Vairo, Antonio
In many realizations of leptogenesis, heavy right-handed neutrinos play the main role in the generation of an imbalance between matter and antimatter in the early Universe. Hence, it is relevant to address quantitatively their dynamics in a hot and dense environment by taking into account the various thermal aspects of the problem at hand. The strong washout regime offers an interesting framework to carry out calculations systematically and reduce theoretical uncertainties. Indeed, any matter-antimatter asymmetry generated when the temperature of the hot plasma $T$ exceeds the right-handed neutrino mass scale $M$ is efficiently erased, and one can focus on the temperature window $T \\ll M$. We review recent progresses in the thermal field theoretic derivation of the key ingredients for the leptogenesis mechanism: the right-handed neutrino production rate, the CP asymmetry in the heavy-neutrino decays and the washout rates. The derivation of evolution equations for the heavy-neutrino and lepton-asymmetry number...
A new approach to model CW CO2 laser using rate equations
Indian Academy of Sciences (India)
The other distinguishing feature of our model is the methodology adopted for carryingout the calculations. For instance, the CW case being a steady state, all the rate equations are thus equated to zero. In the prior works, researchers derived analytical expressions for the vibration level population densities, thatbecomes ...
Cross-validation of recent and longstanding resting metabolic rate prediction equations
Resting metabolic rate (RMR) measurement is time consuming and requires specialized equipment. Prediction equations provide an easy method to estimate RMR; however, their accuracy likely varies across individuals. Understanding the factors that influence predicted RMR accuracy at the individual lev...
Sweat Rate Prediction Equations for Outdoor Exercise with Transient Solar Radiation
2012-01-01
clothing, aerobic fitness, and progressive dehydration . J Therm Biol 22: 331–342, 1997. 25. Matthew WT, Santee WR, Berglund LG. Solar Load Inputs for...code) Sweat rate prediction equations for outdoor exercise with transient solar radiation Richard R. Gonzalez,1 Samuel N. Cheuvront,2 Brett R. Ely,2...Moran DS, Hadid A, Endrusick TL, Sawka MN. Sweat rate prediction equations for outdoor exercise with transient solar radiation. J Appl Phys- iol 112
Derivation of new equations to estimate glomerular filtration rate in pediatric oncology patients.
Millisor, Vanessa E; Roberts, Jessica K; Sun, Yilun; Tang, Li; Daryani, Vinay M; Gregornik, David; Cross, Shane J; Ward, Deborah; Pauley, Jennifer L; Molinelli, Alejandro; Brennan, Rachel C; Stewart, Clinton F
2017-06-02
Monitoring renal function is critical in treating pediatric patients, especially when dosing nephrotoxic agents. We evaluated the validity of the bedside Schwartz and Brandt equations in pediatric oncology patients and developed new equations for estimated glomerular filtration rate (eGFR) in these patients. A retrospective analysis was conducted comparing eGFR using the bedside Schwartz and Brandt equations to measured GFR (mGFR) from technetium-99m diethylenetriamine pentaacetic acid ( 99m Tc-DTPA) between January 2007 and August 2013. An improved equation to estimate GFR was developed, simplified, and externally validated in a cohort of patients studied from September 2013 to June 2015. Carboplatin doses calculated from 99m Tc-DTPA were compared with doses calculated by GFR-estimating equations. Overall, the bedside Schwartz and Brandt equations did not precisely or accurately predict measured GFR (mGFR). Using a data subset, we developed a five-covariate equation, which included height, serum creatinine, age, blood urea nitrogen (BUN), and gender, and a simplified version (two-covariates), which contained height and serum creatinine. These equations were used to estimate GFR in 2036 studies, resulting in precise and accurate predictors of mGFR values. Equations were validated in an external cohort of 570 studies; both new equations were more accurate in calculating carboplatin doses than either the bedside Schwartz or Brandt equation. Two new equations were developed to estimate GFR in pediatric oncology patients, both of which did a better job at estimating mGFR than published equations.
Improved decay rates for solutions for a multidimensional generalized Benjamin-Bona-Mahony equation
Said-Houari, Belkacem
2014-01-01
In this paper, we study the decay rates of solutions for the generalized Benjamin-Bona-Mahony equation in multi-dimensional space. For initial data in some L1-weighted spaces, we prove faster decay rates of the solutions. More precisely, using the Fourier transform and the energy method, we show the global existence and the convergence rates of the solutions under the smallness assumption on the initial data and we give better decay rates of the solutions. This result improves early works in J. Differential Equations 158(2) (1999), 314-340 and Nonlinear Anal. 75(7) (2012), 3385-3392. © 2014-IOS Press.
A comparison of methods for fitting allometric equations to field metabolic rates of animals.
Packard, Gary C; Boardman, Thomas J
2009-02-01
We re-examined data for field metabolic rates of varanid lizards and marsupial mammals to illustrate how different procedures for fitting the allometric equation can lead to very different estimates for the allometric coefficient and exponent. A two-parameter power function was obtained in each case by the traditional method of back-transformation from a straight line fitted to logarithms of the data. Another two-parameter power function was then generated for each data-set by non-linear regression on values in the original arithmetic scale. Allometric equations obtained by non-linear regression described the metabolic rates of all animals in the samples. Equations estimated by back-transformation from logarithms, on the other hand, described the metabolic rates of small species but not large ones. Thus, allometric equations estimated in the traditional way for field metabolic rates of varanids and marsupials do not have general importance because they do not characterize rates for species spanning the full range in body size. Logarithmic transformation of predictor and response variables creates new distributions that may enable investigators to perform statistical analyses in compliance with assumptions underlying the tests. However, statistical models fitted to transformations should not be used to estimate parameters of equations in the arithmetic domain because such equations may be seriously biased and misleading. Allometric analyses should be performed on values expressed in the original scale, if possible, because this is the scale of interest.
Siahkouhian, Marefat; Khodadadi, Davar
2013-09-01
Optimal training intensity and the adequate exercise level for physical fitness is one of the most important interests of coaches and sports physiologists. The aim of this study was to investigate the validity of the Narita et al target heart rate equation for the adequate exercise training level in sedentary young boys. Forty two sedentary young boys (19.07±1.16 years) undertook a blood lactate transition threshold maximal treadmill test to volitional exhaustion with continuous respiratory gas measurements according to the Craig method. The anaerobic threshold (AT) of the participants then was calculated using the Narita target heart rate equation. Hopkin's spreadsheet to obtain confidence limit and the chance of the true difference between gas measurements and Narita target heart rate equation revealed that the Narita equation most likely underestimates the measured anaerobic threshold in sedentary young boys (168.76±15 vs. 130.08±14.36) (Difference ±90% confidence limit: 38.1±18). Intraclass correlation coefficient (ICC) showed a poor agreement between the criterion method and Narita equation (ICC= 0.03). According to the results, the Narita equation underestimates the measured AT. It seems that the Narita equation is a good predictor of aerobic not AT which can be investigated in the future studies.
Directory of Open Access Journals (Sweden)
S. C. Oukouomi Noutchie
2014-01-01
Full Text Available We make use of Laplace transform techniques and the method of characteristics to solve fragmentation equations explicitly. Our result is a breakthrough in the analysis of pure fragmentation equations as this is the first instance where an exact solution is provided for the fragmentation evolution equation with general fragmentation rates. This paper is the key for resolving most of the open problems in fragmentation theory including “shattering” and the sudden appearance of infinitely many particles in some systems with initial finite particles number.
Convergence rates for dispersive approximation schemes to nonlinear Schr\\"odinger equations
Ignat, Liviu; Zuazua, Enrique
2011-01-01
This article is devoted to the analysis of the convergence rates of several nu- merical approximation schemes for linear and nonlinear Schr\\"odinger equations on the real line. Recently, the authors have introduced viscous and two-grid numerical approximation schemes that mimic at the discrete level the so-called Strichartz dispersive estimates of the continuous Schr\\"odinger equation. This allows to guarantee the convergence of numerical approximations for initial data in L2(R), a fact that ...
Almost sure subexponential decay rates of scalar Itô-Volterra equations
Directory of Open Access Journals (Sweden)
John Appleby
2004-08-01
where the random variable $\\Lambda(|\\sigma|\\rightarrow0$ as $\\sigma\\rightarrow\\infty$ a.s. We also prove a decay result for equations with a superlinear diffusion coefficient at zero. If the deterministic equation has solution which is uniformly asymptotically stable, and the kernel is subexponential, the decay rate of the stochastic problem is exactly the same as that of the underlying deterministic problem.
Funakoshi, Yohei; Fujiwara, Yutaka; Kiyota, Naomi; Mukohara, Toru; Shimada, Takanobu; Toyoda, Masanori; Imamura, Yoshinori; Chayahara, Naoko; Umezu, Michio; Otsuki, Naoki; Nibu, Ken-ichi; Minami, Hironobu
2013-03-01
Assessment of renal function is important for safe cancer chemotherapy, and eligibility criteria for clinical trials often include creatinine clearance. However, creatinine clearance overestimates glomerular filtration rate, and various new formulae have been proposed to estimate glomerular filtration rate. Because these were developed mostly in patients with chronic kidney disease, we evaluated their validity in cancer patients without kidney disease. Glomerular filtration rate was measured by inulin clearance in 45 Japanese cancer patients, and compared with creatinine clearance measured by 24-h urine collection as well as that estimated by the Cockcroft-Gault formula, Japanese estimated glomerular filtration rate developed in chronic kidney disease patients, the Modification of Diet in Renal Disease study equation and the Chronic Kidney Disease Epidemiology Collaboration equation. The Modification of Diet in Renal Disease study and Chronic Kidney Disease Epidemiology Collaboration equations were adjusted for the Japanese population by multiplying by 0.808 and 0.813, respectively. The mean inulin clearance was 79.2 ± 18.7 ml/min/1.73 m(2). Bias values to estimate glomerular filtration rate for Japanese estimated glomerular filtration rate, the Cockcroft-Gault formula, creatinine clearance measured by 24-h urine collection, the 0.808 × Modification of Diet in Renal Disease study equation and the 0.813 × Chronic Kidney Disease Epidemiology Collaboration equation were 0.94, 9.75, 29.67, 5.26 and -0.92 ml/min/1.73 m(2), respectively. Precision (root-mean square error) was 14.7, 22.4, 39.8, 16.0 and 14.1 ml/min, respectively. Of the scatter plots of inulin clearance versus each estimation formula, the Japanese estimated glomerular filtration rate correlated most accurately with actual measured inulin clearance. The Japanese estimated glomerular filtration rate and the 0.813 × Chronic Kidney Disease Epidemiology Collaboration equation estimated glomerular
Age-related maximal heart rate: examination and refinement of prediction equations.
Shargal, E; Kislev-Cohen, R; Zigel, L; Epstein, S; Pilz-Burstein, R; Tenenbaum, G
2015-10-01
The aim of this study was to establish the maximal heart rate (HRmax)-age relation with minimal error rate. The records of 28,137 participants (20,691 male and 7446 female, age range between 10 and 80 yrs) who performed a maximal stress test were used in this study. Linear regressions between HRmax and age were used for the entire sample, for the male and female samples, separately, and for each section of the gender-by-age category. The equations were then contrasted to a number of equations reported in the literature. The best fitted equations were then tested on a new sample of 2449 subjects (2091 males and 358 females) for validation purposes. Mean HRmax values were found to decrease at a faster rate in women than in men with age increase. The linear regression functions within each age category were found to be less reliable than the equations derived for the entire sample and for the female and male samples, respectively. The new and updated HRmax prediction equations are as follows: HRmax=208.609-0.716age and 209.273-0.804age for males and females, respectively, and 208.852-0.741age for the entire sample. Those equations along with the other four best equations for predicting HRmax were found to be correlated with the observed HRmax values (validation sample): 0.64 and 0.664 for males and females, respectively. Our equations were derived from a large data set and were found to be highly sensitive for both genders. Therefore, we propose that these new formulas, with their improved accuracy, be used in healthy active and clinical populations.
Liu, Xun; Cheng, Mu-hua; Shi, Cheng-gang; Wang, Cheng; Cheng, Cai-lian; Chen, Jin-xia; Tang, Hua; Chen, Zhu-jiang; Ye, Zeng-chun; Lou, Tan-qi
2012-01-01
Chronic kidney disease (CKD) is recognized worldwide as a public health problem, and its prevalence increases as the population ages. However, the applicability of formulas for estimating the glomerular filtration rate (GFR) based on serum creatinine (SC) levels in elderly Chinese patients with CKD is limited. Based on values obtained with the technetium-99m diethylenetriaminepentaacetic acid ((99m)Tc-DTPA) renal dynamic imaging method, 319 elderly Chinese patients with CKD were enrolled in this study. Serum creatinine was determined by the enzymatic method. The GFR was estimated using the Cockroft-Gault (CG) equation, the Modification of Diet in Renal Disease (MDRD) equations, the Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) equation, the Jelliffe-1973 equation, and the Hull equation. The median of difference ranged from -0.3-4.3 mL/min/1.73 m(2). The interquartile range (IQR) of differences ranged from 13.9-17.6 mL/min/1.73 m(2). Accuracy with a deviation less than 15% ranged from 27.6%-32.9%. Accuracy with a deviation less than 30% ranged from 53.6%-57.7%. Accuracy with a deviation less than 50% ranged from 74.9%-81.5%. None of the equations had accuracy up to the 70% level with a deviation less than 30% from the standard glomerular filtration rate (sGFR). Bland-Altman analysis demonstrated that the mean difference ranged from -3.0-2.4 mL/min/1.73 m(2). However, the agreement limits of all the equations, except the CG equation, exceeded the prior acceptable tolerances defined as 60 mL/min/1.73 m(2). When the overall performance and accuracy were compared in different stages of CKD, GFR estimated using the CG equation showed promising results. Our study indicated that none of these equations were suitable for estimating GFR in the elderly Chinese population investigated. At present, based on overall performance, as well as performance in different CKD stages, the CG equation may be the most accurate for estimating GFR in elderly Chinese patients
On the validity of the Arrhenius equation for electron attachment rate coefficients.
Fabrikant, Ilya I; Hotop, Hartmut
2008-03-28
The validity of the Arrhenius equation for dissociative electron attachment rate coefficients is investigated. A general analysis allows us to obtain estimates of the upper temperature bound for the range of validity of the Arrhenius equation in the endothermic case and both lower and upper bounds in the exothermic case with a reaction barrier. The results of the general discussion are illustrated by numerical examples whereby the rate coefficient, as a function of temperature for dissociative electron attachment, is calculated using the resonance R-matrix theory. In the endothermic case, the activation energy in the Arrhenius equation is close to the threshold energy, whereas in the case of exothermic reactions with an intermediate barrier, the activation energy is found to be substantially lower than the barrier height.
Directory of Open Access Journals (Sweden)
Ary Serpa Neto
2011-09-01
Full Text Available Objective: Considering that the Cockcroft-Gault formula and theequation of diet modification in renal disease are amply used in clinical practice to estimate the glomerular filtration rate, although they seem to have low accuracy in obese patients, the present study intends to evaluate the predictive performance of 12 equations used to estimate the glomerular filtration rate in obese patients. Methods: This is a cross-sectional retrospective study, conducted between 2007 and 2008 and carried out at a university, of 140 patients with severe obesity (mean body mass index 44 ± 4.4 kg/m2. The glomerular filtration rate was determined by means of 24-hour urine samples. Patients were classified into one or more of the four subgroups: impaired glucose tolerance (n = 43, diabetic (n = 24, metabolic syndrome (n = 76, and/or hypertension (n = 66. We used bias, precision, and accuracy to assess the predictive performance of each equation in the entire group and in the subgroups. Results: In renal disease, Cockcroft-Gault’s formula and the diet modification equation are not precise in severely obese patients (precision: 40.9 and 33.4, respectively. Sobh’s equationshowed no bias in the general group or in two subgroups. Salazar-Corcoran’s and Sobh’s equations showed no bias for the entire group(Bias: -5.2, 95% confidence interval (CI = -11.4, 1.0, and 6. 2; 95%CI = -0.3, 12.7, respectively. All the other equations were imprecise for the entire group. Conclusion: Of the equations studied, those of Sobh and Salazar-Corcoran seem to be the best for estimating the glomerular filtration rate in severely obese patients analyzed in our study.
A simple algebraic cancer equation: calculating how cancers may arise with normal mutation rates
Directory of Open Access Journals (Sweden)
Shibata Darryl
2010-01-01
Full Text Available Abstract Background The purpose of this article is to present a relatively easy to understand cancer model where transformation occurs when the first cell, among many at risk within a colon, accumulates a set of driver mutations. The analysis of this model yields a simple algebraic equation, which takes as inputs the number of stem cells, mutation and division rates, and the number of driver mutations, and makes predictions about cancer epidemiology. Methods The equation [p = 1 - (1 - (1 - (1 - udkNm ] calculates the probability of cancer (p and contains five parameters: the number of divisions (d, the number of stem cells (N × m, the number of critical rate-limiting pathway driver mutations (k, and the mutation rate (u. In this model progression to cancer "starts" at conception and mutations accumulate with cell division. Transformation occurs when a critical number of rate-limiting pathway mutations first accumulates within a single stem cell. Results When applied to several colorectal cancer data sets, parameter values consistent with crypt stem cell biology and normal mutation rates were able to match the increase in cancer with aging, and the mutation frequencies found in cancer genomes. The equation can help explain how cancer risks may vary with age, height, germline mutations, and aspirin use. APC mutations may shorten pathways to cancer by effectively increasing the numbers of stem cells at risk. Conclusions The equation illustrates that age-related increases in cancer frequencies may result from relatively normal division and mutation rates. Although this equation does not encompass all of the known complexity of cancer, it may be useful, especially in a teaching setting, to help illustrate relationships between small and large cancer features.
Symmetry analysis of Black-Scholes equation for small values of volatility and rate of return
Directory of Open Access Journals (Sweden)
M. Nadjafikhah
2014-07-01
of volatility and rate of return parameters. A novel method for obtaining the approximate symmetry of a singularly perturbed partial differential equation (PDE is introduced. Further, we compute the optimal system in the singular case. Finally, by combining two methods, a new approach that calculates the approximate generators for admitted Lie groups of asset price is provided.
A new approach to model CW CO2 laser using rate equations
Indian Academy of Sciences (India)
2016-11-11
Nov 11, 2016 ... assumption of the different modes to be in thermal equilibrium. Moore et al [8] and Tychinskii [9] were the first to independently propose these rate equations for the CW CO2 laser. Tyte [10] used such a model to calculate population densities of the vibration lev- els of a CW CO2 laser, in the non-lasing case.
Laser Rate Equation Based Filtering for Carrier Recovery in Characterization and Communication
DEFF Research Database (Denmark)
Piels, Molly; Iglesias Olmedo, Miguel; Xue, Weiqi
2015-01-01
We formulate a semiconductor laser rate equationbased approach to carrier recovery in a Bayesian filtering framework. Filter stability and the effect of model inaccuracies (unknown or un-useable rate equation coefficients) are discussed. Two potential application areas are explored: laser charact......-coupled output power. The extended Kalman filter is also used to recover a 28 GBd DP- 16 QAM signal where a decision-directed phase-locked loop fails....
Validity of predictive equations for resting metabolic rate in healthy older adults.
Itoi, Aya; Yamada, Yosuke; Yokoyama, Keiichi; Adachi, Tetsuji; Kimura, Misaka
2017-12-01
Accurate estimation of energy expenditure in older people is important for nutritional support. The current literature contains controversial or inconsistent data regarding the resting metabolic rate (RMR, or basal metabolic rate) in older adults, including the relationship between the RMR and ethnicity. Little information about the RMR in healthy Asian older adults is available. This study was performed to examine the RMR in healthy Japanese older adults and compare it with previously established 16 equations. Thirty-two community-dwelling, healthy, and active elderly Japanese adults were enrolled (age, 64-87 years; 14 men, 18 women; mean height, 154.9 ± 8.9 cm; mean weight, 53.5 ± 9.1 kg; mean body mass index, 22.2 ± 2.5 kg/m 2 ). The RMR was measured by indirect calorimetry. The measured RMR was compared among 16 equations. Correlation analysis, a paired t test, and a Bland-Altman plot were used to assess the agreement among the equations. The average RMR was 1132 ± 178 kcal/day with 2233 ± 437 kcal/day average total energy expenditure (TEE) measured by doubly labeled water (DLW). The smallest bias was established by De Lorenzo et al.'s equation as bias ±1.96SD = 4 ± 121 kcal/day. De Lorenzo et al. and Ikeda et al.'s equations had no significant average bias both in men and women (P > 0.05). The 1.96SD of bias in six equations was within 160 kcal/day. In contrast, residuals between the measured and predicted RMR were largely correlated with the RMR in four equations. A sex-related difference in the mean bias was observed in many equations. Although the average Japanese healthy older adult has a shorter stature and lower weight than older adults in the Western population, the current data suggest that a similar predictive equation for the RMR can be applied to both Japanese and Western older adults. This study demonstrate that the De Lorenzo et al.'s or Ikeda's equation may be useful for estimating RMR in the community
A differential equation for the flow rate during silo discharge: Beyond the Beverloo rule
Directory of Open Access Journals (Sweden)
Madrid Marcos A.
2017-01-01
Full Text Available We present a differential equation for the flow rate of granular materials during the discharge of a silo. This is based in the energy balance of the variable mass system in contrast with the traditional derivations based on heuristic postulates such as the free fall arch. We show that this new equation is consistent with the well known Beverloo rule, providing an independent estimate for the universal Beverloo prefactor. We also find an analytic expression for the pressure under discharging conditions.
A Globally Convergent Matrix-Free Method for Constrained Equations and Its Linear Convergence Rate
Directory of Open Access Journals (Sweden)
Min Sun
2014-01-01
Full Text Available A matrix-free method for constrained equations is proposed, which is a combination of the well-known PRP (Polak-Ribière-Polyak conjugate gradient method and the famous hyperplane projection method. The new method is not only derivative-free, but also completely matrix-free, and consequently, it can be applied to solve large-scale constrained equations. We obtain global convergence of the new method without any differentiability requirement on the constrained equations. Compared with the existing gradient methods for solving such problem, the new method possesses linear convergence rate under standard conditions, and a relax factor γ is attached in the update step to accelerate convergence. Preliminary numerical results show that it is promising in practice.
Hougardy, J M; Delanaye, P; Le Moine, A; Nortier, J
2014-09-01
The accurate estimation of the glomerular filtration rate (GFR) is a goal of multiple interests regarding clinical, research and public health aspects. The strong relationship between progressive loss of renal function and mortality underlines the need for early diagnosis and close follow-up of renal diseases. Creatinine is the commonest biomarker of GFR in use. By reason of non-renal determinants of GFR, it is required to integrate creatinine values within equations that take in account its most important determinants (i.e., age, sex). The CKD-EPI 2009 equation is now recommended as the first line equation to estimate GFR within the general population. In this indication, it should replace MDRD that tends to overestimate the prevalence of stage 3 chronic kidney disease with GFR around 60 ml/min. However, many questions remain about the accuracy of GFR equations in specific situations such as extremes of age or body weight. The identification of new biomarkers, less determined by non-renal determinants, is of importance. Among these biomarkers, cystatin-C is more accurate to estimate GFR when it is combined to creatinine (i.e., equation CKD-EPI 2012). However the indica. tions for using cystatin-C instead of creatinine alone are still unclear and its use remains limited in routine practice. In conclusion, neither biomarker nor equation gives an accurate estimation for the whole range of GFR and for all patient populations. Limits of prediction are relying on both biomarker's properties and the range of GFR that is concerned, but also rely on the measurement methods. Therefore, it is crucial to interpret the estimated GFR according to the strengths and weaknesses of the equation in use.
Directory of Open Access Journals (Sweden)
Liu X
2012-10-01
Full Text Available Xun Liu,1,2,* Mu-hua Cheng,3,* Cheng-gang Shi,1 Cheng Wang,1 Cai-lian Cheng,1 Jin-xia Chen,1 Hua Tang,1 Zhu-jiang Chen,1 Zeng-chun Ye,1 Tan-qi Lou11Division of Nephrology, Department of Internal Medicine, The Third Affiliated Hospital of Sun Yet-sun University, Guangzhou, China; 2College of Biology Engineering, South China University of Technology, Guangzhou, China; 3Department of Nuclear Medicine, The Third Affiliated Hospital of Sun Yet-sun University, Guangzhou, China *These authors contributed equally to this paperBackground: Chronic kidney disease (CKD is recognized worldwide as a public health problem, and its prevalence increases as the population ages. However, the applicability of formulas for estimating the glomerular filtration rate (GFR based on serum creatinine (SC levels in elderly Chinese patients with CKD is limited.Materials and methods: Based on values obtained with the technetium-99m diethylenetriaminepentaacetic acid (99mTc-DTPA renal dynamic imaging method, 319 elderly Chinese patients with CKD were enrolled in this study. Serum creatinine was determined by the enzymatic method. The GFR was estimated using the Cockroft–Gault (CG equation, the Modification of Diet in Renal Disease (MDRD equations, the Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI equation, the Jelliffe-1973 equation, and the Hull equation.Results: The median of difference ranged from −0.3–4.3 mL/min/1.73 m2. The interquartile range (IQR of differences ranged from 13.9–17.6 mL/min/1.73 m2. Accuracy with a deviation less than 15% ranged from 27.6%–32.9%. Accuracy with a deviation less than 30% ranged from 53.6%–57.7%. Accuracy with a deviation less than 50% ranged from 74.9%–81.5%. None of the equations had accuracy up to the 70% level with a deviation less than 30% from the standard glomerular filtration rate (sGFR. Bland–Altman analysis demonstrated that the mean difference ranged from −3.0–2.4 mL/min/1.73 m2. However, the
The Pandolf equation under-predicts the metabolic rate of contemporary military load carriage.
Drain, Jace R; Aisbett, Brad; Lewis, Michael; Billing, Daniel C
2017-11-01
This investigation assessed the accuracy of error of the Pandolf load carriage energy expenditure equation when simulating contemporary military conditions (load distribution, external load and walking speed). Within-participant design. Sixteen male participants completed 10 trials comprised of five walking speeds (2.5, 3.5, 4.5, 5.5 and 6.5km·h -1 ) and two external loads (22.7 and 38.4kg). The Pandolf equation demonstrated poor predictive precision, with a mean bias of 124.9W and -48.7 to 298.5W 95% limits of agreement. Furthermore, the Pandolf equation systematically under-predicted metabolic rate (pload combinations. Predicted metabolic rate error ranged from 12-33% across all conditions with the 'moderate' walking speeds (i.e. 4.5-5.5km·h -1 ) yielding less prediction error (12-17%) when compared to the slower and faster walking speeds (21-33%). Factors such as mechanical efficiency and load distribution contribute to the impaired predictive accuracy. The authors suggest the Pandolf equation should be applied to military load carriage with caution. Copyright © 2017 Sports Medicine Australia. All rights reserved.
Use of the Burton-prim-slichter Equation at High Growth Rates
Wilcox, W. R.
1984-01-01
The following must be assumed in order to derive the classic Burton-Prim-Slichter equation for segregation during crystal growth: isobaric, isothermal, isopotential or uncharged species, binary, planar interface, steady state, constant diffusion coefficient in fluid, no diffusion in crystal, no lateral convection within fluid film at interface with complete mixing beyond (stagnant film model), and either density, total concentration or partial molar volumes constant in the fluid phase. In addition, the effective distribution coefficient and the interfacial distribution coefficient must be defined properly. The velocity in the equation is the growth rate times a factor correcting for the difference in volumetric properties between crystal and fluid. The stagnant film thickness is found to be a function of freezing rate, with the precise functionality depending on the type of stirring occurring in the growth fluid.
Non-Self-Similar Dead-Core Rate for the Fast Diffusion Equation with Dependent Coefficient
Directory of Open Access Journals (Sweden)
Liping Zhu
2014-01-01
Full Text Available We consider the dead-core problem for the fast diffusion equation with spatially dependent coefficient and show that the temporal dead-core rate is non-self-similar. The proof is based on the standard compactness arguments with the uniqueness of the self-similar solutions and the precise estimates on the single-point final dead-core profile.
Characteristics of quantum dash laser under the rate equation model framework
Khan, Mohammed Zahed Mustafa
2010-09-01
The authors present a numerical model to study the carrier dynamics of InAs/InP quantum dash (QDash) lasers. The model is based on single-state rate equations, which incorporates both, the homogeneous and the inhomogeneous broadening of lasing spectra. The numerical technique also considers the unique features of the QDash gain medium. This model has been applied successfully to analyze the laser spectra of QDash laser. ©2010 IEEE.
Almeida, Inês; Caetano, Francisca; Barra, Sérgio; Madeira, Marta; Mota, Paula; Leitão-Marques, António
2016-06-01
Renal dysfunction is a powerful predictor of adverse outcomes in patients hospitalized for acute coronary syndrome. Three new glomerular filtration rate (GFR) estimating equations recently emerged, based on serum creatinine (CKD-EPIcreat), serum cystatin C (CKD-EPIcyst) or a combination of both (CKD-EPIcreat/cyst), and they are currently recommended to confirm the presence of renal dysfunction. Our aim was to analyse the predictive value of these new estimated GFR (eGFR) equations regarding mid-term mortality in patients with acute coronary syndrome, and compare them with the traditional Modification of Diet in Renal Disease (MDRD-4) formula. 801 patients admitted for acute coronary syndrome (age 67.3±13.3 years, 68.5% male) and followed for 23.6±9.8 months were included. For each equation, patient risk stratification was performed based on eGFR values: high-risk group (eGFRformula, the CKD-EPIcyst equation accurately reclassified a significant percentage of patients into more appropriate risk categories (net reclassification improvement index of 11.9% (p=0.003)). The CKD-EPIcyst equation added prognostic power to the Global Registry of Acute Coronary Events (GRACE) score in the prediction of mid-term mortality. The CKD-EPIcyst equation provides a novel and improved method for assessing the mid-term mortality risk in patients admitted for acute coronary syndrome, outperforming the most widely used formula (MDRD-4), and improving the predictive value of the GRACE score. These results reinforce the added value of cystatin C as a risk marker in these patients. © The European Society of Cardiology 2015.
Chi, Xiao-Hua; Li, Gui-Ping; Wang, Quan-Shi; Qi, Yong-Shuai; Huang, Kai; Zhang, Qian; Xue, Yao-Ming
2017-07-10
The aim of this study was to identify the optimal equation that accurately estimates the glomerular filtration rate (GFR) and the chronic kidney disease (CKD) stage in the Chinese population. A total of 1296 Chinese patients aged 18-65 years old were enrolled in this study. The estimated GFRs (eGFRs) calculated separately by three Diet in Renal Disease (MDRD) equations and three Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) equations were compared with the reference GFR (rGFR) measured by the 99 Tc m -DTPA renal dynamic imaging method. By Bland-Altman analysis, eGFR cys and eGFR scr_cys performed similarly, showing the tightest limits of agreement among the six equations. They also achieved the first and second highest 30% and 50% accuracies. Using a combination of the serum creatinine and cystatin C levels (eGFR scr_cys ) could improve the bias (-0.3 for eGFR scr_cys ) of the equation and achieve the highest diagnostic accuracy for renal insufficiency (AUC 60 , 0.953; P equations predicted stage 3 CKD with moderate accuracy (49.7-51.4%) and stage 5 CKD with good accuracy (90.2-96.4%). For stage 1 CKD, eGFR cys showed a higher percentage of misclassification than the other equations. All equations seemed to perform poorly at predicting stage 2 and 4 CKD, as compared to the other CKD stages. eGFR scr_cys was the best-performing equation in terms of accurate classification of the CKD stage based on the overall performance (kappa value, 0.423). For a Chinese population, the CKD-EPI scr_cys equation seems more suitable for estimating the GFR than the other equations. Each equation had its own advantages in predicting different CKD stages.
Existing creatinine-based equations overestimate glomerular filtration rate in Indians.
Kumar, Vivek; Yadav, Ashok Kumar; Yasuda, Yoshinari; Horio, Masaru; Kumar, Vinod; Sahni, Nancy; Gupta, Krishan L; Matsuo, Seiichi; Kohli, Harbir Singh; Jha, Vivekanand
2018-02-01
Accurate estimation of glomerular filtration rate (GFR) is important for diagnosis and risk stratification in chronic kidney disease and for selection of living donors. Ethnic differences have required correction factors in the originally developed creatinine-based GFR estimation equations for populations around the world. Existing equations have not been validated in the vegetarian Indian population. We examined the performance of creatinine and cystatin-based GFR estimating equations in Indians. GFR was measured by urinary clearance of inulin. Serum creatinine was measured using IDMS-traceable Jaffe's and enzymatic assays, and cystatin C by colloidal gold immunoassay. Dietary protein intake was calculated by measuring urinary nitrogen appearance. Bias, precision and accuracy were calculated for the eGFR equations. A total of 130 participants (63 healthy kidney donors and 67 with CKD) were studied. About 50% were vegetarians, and the remainder ate meat 3.8 times every month. The average creatinine excretion were 14.7 mg/kg/day (95% CI: 13.5 to 15.9 mg/kg/day) and 12.4 mg/kg/day (95% CI: 11.2 to 13.6 mg/kg/day) in males and females, respectively. The average daily protein intake was 46.1 g/day (95% CI: 43.2 to 48.8 g/day). The mean mGFR in the study population was 51.66 ± 31.68 ml/min/1.73m 2 . All creatinine-based eGFR equations overestimated GFR (p equation). However, eGFR by CKD-EPI Cys was not significantly different from mGFR (p = 0.38). The CKD-EPI Cys exhibited lowest bias [mean bias: -3.53 ± 14.70 ml/min/1.73m 2 (95% CI: -0.608 to -0.98)] and highest accuracy (P 30 : 74.6%). The GFR in the healthy population was 79.44 ± 20.19 (range: 41.90-134.50) ml/min/1.73m 2 . Existing creatinine-based GFR estimating equations overestimate GFR in Indians. An appropriately powered study is needed to develop either a correction factor or a new equation for accurate assessment of kidney function in the Indian population.
Montañés Bermúdez, R; Gràcia Garcia, S; Fraga Rodríguez, G M; Escribano Subias, J; Diez de Los Ríos Carrasco, M J; Alonso Melgar, A; García Nieto, V
2014-05-01
The appearance of the K/DOQI guidelines in 2002 on the definition, evaluation and staging of chronic kidney disease (CKD) have led to a major change in how to assess renal function in adults and children. These guidelines, recently updated, recommended that the study of renal function is based, not only on measuring the serum creatinine concentration, but this must be accompanied by the estimation of glomerular filtration rate (GFR) obtained by an equation. However, the implementation of this recommendation in the clinical laboratory reports in the paediatric population has been negligible. Numerous studies have appeared in recent years on the importance of screening and monitoring of patients with CKD, the emergence of new equations for estimating GFR, and advances in clinical laboratories regarding the methods for measuring plasma creatinine and cystatin C, determined by the collaboration between the departments of paediatrics and clinical laboratories to establish recommendations based on the best scientific evidence on the use of equations to estimate GFR in this population. The purpose of this document is to provide recommendations on the evaluation of renal function and the use of equations to estimate GFR in children from birth to 18 years of age. The recipients of these recommendations are paediatricians, nephrologists, clinical biochemistry, clinical analysts, and all health professionals involved in the study and evaluation of renal function in this group of patients. Copyright © 2013 Asociación Española de Pediatría. Published by Elsevier Espana. All rights reserved.
Applicability of a different estimation equation of glomerular filtration rate in Turkey.
Altiparmak, Mehmet Riza; Seyahi, Nurhan; Trabulus, Sinan; Yalin, Serkan Feyyaz; Bolayirli, Murat; Andican, Zeynep Gulnur; Suleymanlar, Gultekin; Serdengecti, Kamil
2013-09-01
We aimed to investigate the performance of various creatinine based glomerular filtration rate estimation equations that were widely used in clinical practice in Turkey and calculate a correction coefficient to obtain a better estimate using the isotope dilution mass spectrometry (IDMS)-traceable Modification of the Diet in Renal Disease (MDRD) formula. This cross-sectional study included adult (>18 years) outpatients and in patients with chronic kidney disease as well as healthy volunteers. Iohexol clearance was measured and the precisions and bias of the various estimation equations were calculated. A correction coefficient for the IDMS-traceable MDRD was also calculated. A total of 229 (113 male/116 female; mean age 53.9 ± 14.4 years) subjects were examined. A median iohexol clearance of 39.21 mL/min/1.73 m(2) (range: 6.01-168.47 mL/min/1.73 m(2)) was found. Bias and random error for the IDMS-traceable MDRD equation were 11.33 ± 8.97 mL/min/1.73 m(2) and 14.21 mL/min/1.73 m(2), respectively. MDRD formula seems to provide the best estimates. To obtain the best agreement with iohexol clearance, a correction factor of 0.804 must be introduced to IDMS-traceable MDRD equation for our study population.
Maximum Rate of Growth of Enstrophy in Solutions of the Fractional Burgers Equation
Yun, Dongfang; Protas, Bartosz
2018-02-01
This investigation is a part of a research program aiming to characterize the extreme behavior possible in hydrodynamic models by analyzing the maximum growth of certain fundamental quantities. We consider here the rate of growth of the classical and fractional enstrophy in the fractional Burgers equation in the subcritical and supercritical regimes. Since solutions to this equation exhibit, respectively, globally well-posed behavior and finite-time blowup in these two regimes, this makes it a useful model to study the maximum instantaneous growth of enstrophy possible in these two distinct situations. First, we obtain estimates on the rates of growth and then show that these estimates are sharp up to numerical prefactors. This is done by numerically solving suitably defined constrained maximization problems and then demonstrating that for different values of the fractional dissipation exponent the obtained maximizers saturate the upper bounds in the estimates as the enstrophy increases. We conclude that the power-law dependence of the enstrophy rate of growth on the fractional dissipation exponent has the same global form in the subcritical, critical and parts of the supercritical regime. This indicates that the maximum enstrophy rate of growth changes smoothly as global well-posedness is lost when the fractional dissipation exponent attains supercritical values. In addition, nontrivial behavior is revealed for the maximum rate of growth of the fractional enstrophy obtained for small values of the fractional dissipation exponents. We also characterize the structure of the maximizers in different cases.
On the Rate of Relaxation for the Landau Kinetic Equation and Related Models
Bobylev, Alexander; Gamba, Irene M.; Zhang, Chenglong
2017-08-01
We study the rate of relaxation to equilibrium for Landau kinetic equation and some related models by considering the relatively simple case of radial solutions of the linear Landau-type equations. The well-known difficulty is that the evolution operator has no spectral gap, i.e. its spectrum is not separated from zero. Hence we do not expect purely exponential relaxation for large values of time t>0. One of the main goals of our work is to numerically identify the large time asymptotics for the relaxation to equilibrium. We recall the work of Strain and Guo (Arch Rat Mech Anal 187:287-339 2008, Commun Partial Differ Equ 31:17-429 2006), who rigorously show that the expected law of relaxation is \\exp (-ct^{2/3}) with some c > 0. In this manuscript, we find an heuristic way, performed by asymptotic methods, that finds this "law of two thirds", and then study this question numerically. More specifically, the linear Landau equation is approximated by a set of ODEs based on expansions in generalized Laguerre polynomials. We analyze the corresponding quadratic form and the solution of these ODEs in detail. It is shown that the solution has two different asymptotic stages for large values of time t and maximal order of polynomials N: the first one focus on intermediate asymptotics which agrees with the "law of two thirds" for moderately large values of time t and then the second one on absolute, purely exponential asymptotics for very large t, as expected for linear ODEs. We believe that appearance of intermediate asymptotics in finite dimensional approximations must be a generic behavior for different classes of equations in functional spaces (some PDEs, Boltzmann equations for soft potentials, etc.) and that our methods can be applied to related problems.
Validation of predictive equations for glomerular filtration rate in the Saudi population
Directory of Open Access Journals (Sweden)
Al Wakeel Jamal
2009-01-01
Full Text Available Predictive equations provide a rapid method of assessing glomerular filtration rate (GFR. To compare the various predictive equations for the measurement of this parameter in the Saudi population, we measured GFR by the Modification of Diet in Renal Disease (MDRD and Cockcroft-Gault formulas, cystatin C, reciprocal of cystatin C, creatinine clearance, reciprocal of creatinine, and inulin clearance in 32 Saudi subjects with different stages of renal disease. We com-pared GFR measured by inulin clearance and the estimated GFR by the equations. The study included 19 males (59.4% and 13 (40.6% females with a mean age of 42.3 ± 15.2 years and weight of 68.6 ± 17.7 kg. The mean serum creatinine was 199 ± 161 μmol/L. The GFR measured by inulin clearance was 50.9 ± 33.5 mL/min, and the estimated by Cockcroft-Gault and by MDRD equations was 56.3 ± 33.3 and 52.8 ± 32.0 mL/min, respectively. The GFR estimated by MDRD revealed the strongest correlation with the measured inulin clearance (r= 0.976, P= 0.0000 followed by the GFR estimated by Cockcroft-Gault, serum cystatin C, and serum creatinine (r= 0.953, P= 0.0000 (r= 0.787, P= 0.0001 (r= -0.678, P= 0.001, respectively. The reciprocal of cystatin C and serum creatinine revealed a correlation coefficient of 0.826 and 0.93, respectively. Cockroft-Gault for-mula overestimated the GFR by 5.40 ± 10.3 mL/min in comparison to the MDRD formula, which exhibited the best correlation with inulin clearance in different genders, age groups, body mass index, renal transplant recipients, chronic kidney disease stages when compared to other GFR predictive equations.
DEFF Research Database (Denmark)
Riisgård, Hans Ulrik; Larsen, Poul Scheel; Pleissner, Daniel
2014-01-01
rate (F, l h-1), W (g), and L (mm) as described by the equations: FW = aWb and FL = cLd, respectively. This is done by using available and new experimental laboratory data on M. edulis obtained by members of the same research team using different methods and controlled diets of cultivated algal cells....... For all data, it was found that FW = 6.773W0.678 and FL = 0.00135L2.088 which are very similar to equations for mussels with ‘medium condition’ (CI = 4–6 mg cm-3): FW = 6.567W0.681 and FL = 0.00150L2.051, with b- and d-values within a few percent of the theoretically expected of 2/3 and 2, respectively...
Rate Equation Analysis of the Dynamics of First-order Exciton Mott Transition
Sekiguchi, Fumiya; Shimano, Ryo
2017-10-01
We perform a rate equation analysis of the dynamics of the exciton Mott transition (EMT) assuming a detailed balance between excitons and unbound electron-hole (e-h) pairs. Using the Saha equation and adopting an empirical expression for the band-gap renormalization effect caused by unbound e-h pairs, we show that the ionization ratio of excitons exhibits bistability as a function of the total e-h pair density at low temperatures. We demonstrate that an incubation time emerges in the dynamics of the EMT from the oversaturated exciton gas phase on the verge of the bistable region. The incubation time shows slowing down behavior when the pair density approaches saddle-node bifurcation of the hysteresis curve of the exciton ionization ratio.
Current use of equations for estimating glomerular filtration rate in Spanish laboratories.
Gràcia-Garcia, Sílvia; Montañés-Bermúdez, Rosario; Morales-García, Luis J; Díez-de Los Ríos, M José; Jiménez-García, Juan Á; Macías-Blanco, Carlos; Martínez-López, Rosalina; Ruiz-Altarejos, Joaquín; Ruiz-Martín, Guadalupe; Sanz-Hernández, Sonia; Ventura-Pedret, Salvador
2012-07-17
In 2006 the Spanish Society of Clinical Biochemistry and Molecular Pathology (SEQC) and the Spanish Society of Nephrology (S.E.N.) developed a consensus document in order to facilitate the diagnosis and monitoring of chronic kidney disease with the incorporation of equations for estimating glomerular filtration rate (eGFR) into laboratory reports. The current national prevalence of eGFR reporting and the degree of adherence to these recommendations among clinical laboratories is unknown. We administered a national survey in 2010-11 to Spanish clinical laboratories. The survey was through e-mail or telephone to laboratories that participated in the SEQC’s Programme for External Quality Assurance, included in the National Hospitals Catalogue 2010, including both primary care and private laboratories. A total of 281 laboratories answered to the survey. Of these, 88.2% reported on the eGFR, with 61.9% reporting on the MDRD equation and 31.6% using the MDRD-IDMS equation. A total of 42.5% of laboratories always reported serum creatinine values, and other variables only when specifically requested. Regarding the way results were presented, 46.2% of laboratories reported the exact numerical value only when the filtration rate was below 60mL/min/1.73m2, while 50.6% reported all values regardless. In 56.3% of the cases reporting eGFR, an interpretive commentary of it was enclosed. Although a high percentage of Spanish laboratories have added eGFR in their reports, this metric is not universally used. Moreover, some aspects, such as the equation used and the correct expression of eGFR results, should be improved.
Directory of Open Access Journals (Sweden)
Anita Nordenson
2010-09-01
Full Text Available Anita Nordenson2, Anne Marie Grönberg1,2, Lena Hulthén1, Sven Larsson2, Frode Slinde11Department of Clinical Nutrition, Sahlgrenska Academy at University of Gothenburg, Göteborg, Sweden; 2Department of Internal Medicine/Respiratory Medicine and Allergology, Sahlgrenska Academy at University of Gothenburg, SwedenAbstract: Malnutrition is a serious condition in chronic obstructive pulmonary disease (COPD. Successful dietary intervention calls for calculations of resting metabolic rate (RMR. One disease-specific prediction equation for RMR exists based on mainly male patients. To construct a disease-specific equation for RMR based on measurements in underweight or weight-losing women and men with COPD, RMR was measured by indirect calorimetry in 30 women and 11 men with a diagnosis of COPD and body mass index <21 kg/m2. The following variables, possibly influencing RMR were measured: length, weight, middle upper arm circumference, triceps skinfold, body composition by dual energy x-ray absorptiometry and bioelectrical impedance, lung function, and markers of inflammation. Relations between RMR and measured variables were studied using univariate analysis according to Pearson. Gender and variables that were associated with RMR with a P value <0.15 were included in a forward multiple regression analysis. The best-fit multiple regression equation included only fat-free mass (FFM: RMR (kJ/day = 1856 + 76.0 FFM (kg. To conclude, FFM is the dominating factor influencing RMR. The developed equation can be used for prediction of RMR in underweight COPD patients.Keywords: pulmonary disease, chronic obstructive, basal metabolic rate, malnutrition, body composition
Directory of Open Access Journals (Sweden)
Abdullah A. Al-Juaid
2016-01-01
Full Text Available The main focus of this paper is in evaluating four constitutive relations which model the strain rate dependency of polymers yield stress. Namely, the two-term power-law, the Ree-Eyring, the cooperative, and the newly modified-Eyring equations are used to fit tensile and compression yield stresses of polycarbonate, which are obtained from the literature. The four equations give good agreement with the experimental data. Despite using only three material constants, the modified-Eyring equation, which considers a strain rate-dependent activation volume, gives slightly worse fit than the three other equations. The two-term power-law and the cooperative equation predict a progressive increase in the strain rate sensitivity of the yield stress. Oppositely, the Ree-Eyring and the modified-Eyring equations show a clear transition between the low and high strain rate ranges. Namely, they predict a linear dependency of the yield stress in terms of the strain rate at the low strain rate range. Crossing a threshold strain rate, the yield stress sensitivity sharply increases as the strain rate increases. Hence, two different behaviors were observed though the four equations fit well the experimental data. More experimental data, mainly at the intermediate strain rate range, are needed to conclude which, of the two behaviors, is more appropriate for polymers.
Ji, Misuk; Lee, Yoon Hee; Hur, Mina; Kim, Hyesun; Cho, Han Ik; Yang, Hyun Suk; Navarin, Silvia; Di Somma, Salvatore
2016-11-01
Estimated glomerular filtration rate (eGFR) is a widely used index of kidney function. Recently, new formulas such as the Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) equations or the Lund-Malmö equation were introduced for assessing eGFR. We compared them with the Modification of Diet in Renal Disease (MDRD) Study equation in the Korean adult population. The study population comprised 1,482 individuals (median age 51 [42-59] yr, 48.9% males) who received annual physical check-ups during the year 2014. Serum creatinine (Cr) and cystatin C (CysC) were measured. We conducted a retrospective analysis using five GFR estimating equations (MDRD Study, revised Lund-Malmö, and Cr and/or CysC-based CKD-EPI equations). Reduced GFR was defined as eGFR EPI(CysC) and -20.5 for CKD-EPI(Cr-CysC)). CysC-based equations decreased the prevalence of reduced GFR by one third (9.4% in the MDRD Study and 2.4% in CKD-EPI(CysC)). Our data shows that there are remarkable differences in eGFR assessment in the Korean population depending on the equation used, especially in normal or mildly decreased categories. Further prospective studies are necessary in various clinical settings.
Utility Rate Equations of Group Population Dynamics in Biological and Social Systems
Yukalov, V I; Sornette, D
2014-01-01
We present a novel system of equations to describe the evolution of self-organized structured societies (biological or human) composed of several trait groups. The suggested approach is based on the combination of ideas employed in the theory of biological populations, system theory, and utility theory. The evolution equations are defined as utility rate equations, whose parameters are characterized by the utility of each group with respect to the society as a whole and by the mutual utilities of groups with respect to each other. We analyze in detail the cases of two groups (cooperators and defectors) and of three groups (cooperators, defectors, and regulators) and find that, in a self-organized society, neither defectors nor regulators can overpass the maximal fractions of about 10% each. This is in agreement with the data for bee and ant colonies. The classification of societies by their distance from equilibrium is proposed. We apply the formalism to rank the countries according to the introduced metric q...
Utility rate equations of group population dynamics in biological and social systems.
Yukalov, Vyacheslav I; Yukalova, Elizaveta P; Sornette, Didier
2013-01-01
We present a novel system of equations to describe the evolution of self-organized structured societies (biological or human) composed of several trait groups. The suggested approach is based on the combination of ideas employed in the theory of biological populations, system theory, and utility theory. The evolution equations are defined as utility rate equations, whose parameters are characterized by the utility of each group with respect to the society as a whole and by the mutual utilities of groups with respect to each other. We analyze in detail the cases of two groups (cooperators and defectors) and of three groups (cooperators, defectors, and regulators) and find that, in a self-organized society, neither defectors nor regulators can overpass the maximal fractions of about [Formula: see text] each. This is in agreement with the data for bee and ant colonies. The classification of societies by their distance from equilibrium is proposed. We apply the formalism to rank the countries according to the introduced metric quantifying their relative stability, which depends on the cost of defectors and regulators as well as their respective population fractions. We find a remarkable concordance with more standard economic ranking based, for instance, on GDP per capita.
Murayama, I; Miyano, A; Sasaki, Y; Hirata, T; Ichijo, T; Satoh, H; Sato, S; Furuhama, K
2013-11-01
This study was performed to clarify whether a formula (Holstein equation) based on a single blood sample and the isotonic, nonionic, iodine contrast medium iodixanol in Holstein dairy cows can apply to the estimation of glomerular filtration rate (GFR) for beef cattle. To verify the application of iodixanol in beef cattle, instead of the standard tracer inulin, both agents were coadministered as a bolus intravenous injection to identical animals at doses of 10 mg of I/kg of BW and 30 mg/kg. Blood was collected 30, 60, 90, and 120 min after the injection, and the GFR was determined by the conventional multisample strategies. The GFR values from iodixanol were well consistent with those from inulin, and no effects of BW, age, or parity on GFR estimates were noted. However, the GFR in cattle weighing less than 300 kg, ageddynamic changes in renal function at young adult ages. Using clinically healthy cattle and those with renal failure, the GFR values estimated from the Holstein equation were in good agreement with those by the multisample method using iodixanol (r=0.89, P=0.01). The results indicate that the simplified Holstein equation using iodixanol can be used for estimating the GFR of beef cattle in the same dose regimen as Holstein dairy cows, and provides a practical and ethical alternative.
Breakdown of the reaction-diffusion master equation with nonelementary rates.
Smith, Stephen; Grima, Ramon
2016-05-01
The chemical master equation (CME) is the exact mathematical formulation of chemical reactions occurring in a dilute and well-mixed volume. The reaction-diffusion master equation (RDME) is a stochastic description of reaction-diffusion processes on a spatial lattice, assuming well mixing only on the length scale of the lattice. It is clear that, for the sake of consistency, the solution of the RDME of a chemical system should converge to the solution of the CME of the same system in the limit of fast diffusion: Indeed, this has been tacitly assumed in most literature concerning the RDME. We show that, in the limit of fast diffusion, the RDME indeed converges to a master equation but not necessarily the CME. We introduce a class of propensity functions, such that if the RDME has propensities exclusively of this class, then the RDME converges to the CME of the same system, whereas if the RDME has propensities not in this class, then convergence is not guaranteed. These are revealed to be elementary and nonelementary propensities, respectively. We also show that independent of the type of propensity, the RDME converges to the CME in the simultaneous limit of fast diffusion and large volumes. We illustrate our results with some simple example systems and argue that the RDME cannot generally be an accurate description of systems with nonelementary rates.
Asymptotics of steady states of a selection–mutation equation for small mutation rate
Calsina, Àngel
2013-12-01
We consider a selection-mutation equation for the density of individuals with respect to a continuous phenotypic evolutionary trait. We assume that the competition term for an individual with a given trait depends on the traits of all the other individuals, therefore giving an infinite-dimensional nonlinearity. Mutations are modelled by means of an integral operator. We prove existence of steady states and show that, when the mutation rate goes to zero, the asymptotic profile of the population is a Cauchy distribution. © Royal Society of Edinburgh 2013.
[Assessment of the new CKD-EPI equation to estimate the glomerular filtration rate].
Montañés Bermúdez, R; Bover Sanjuán, J; Oliver Samper, A; Ballarín Castán, J A; Gràcia García, S
2010-01-01
A recent report by the CKD-EPI Chronic Kidney Disease Epidemiology Collaboration) group describes a new equation to estimate the glomerular filtration rate (GFR). This equation has been developed from a population of 8,254 subjects who had the GFR measured by iothalamate clearance (mean 68 mL/min/1.73 m2, SD 40 mL/min/1.73 m2). It includes variables such as serum creatinine, age, sex and race with different formula according to race, sex and creatinine value. The CKD-EPI equation improved the accuracy and precision results of the current first-choice MDRD-IDMS (Modification of Diet in Renal Disease-Isotopic Dilution Mass Spectrometry) formula, specially for GFR > 60 mL/min/1.73 m2 in a group of 3,896 subjects. The goal of our study was to compare the estimated GFR by using the new equation CKD-EPI with MDRD-IDMS in a wide cohort of 14,427 patients (5,234 women and 9,193 men), and to analyze the impact of the new CKD-EPI formula on the staging of patients with CKD. Mean estimated GFR was 0.6 mL/min/1.73 m2 higher with CKD-EPI as compared to MDRD-IDMS for the whole group, 1.9 mL/min/1.73 m2 higher for women and 0.2 mL/min/1.73 m2 lower for men. The percentage of CKD staging concordancy between equations varied from 79.4 % for stage 3A and 98.6% for stage 5. For those patients younger than 70 years, 18.9 % and 24 % MDRD-IDMS stages 3B and 3A were reclassified as CKD 3A and 2 by CKD-EPI, respectively. For the same stages in the group younger than 70 years, the percentage of reclassified patients increased up to 34.4% and 33.4%, respectively. The new CKD-EPI equation to estimate the GFR reclassifies an important number of patients to higher CKD stages (higher GFR), specially younger women, classified as CKD stage 3 by MDRD-IDMS.
SBMLsqueezer: A CellDesigner plug-in to generate kinetic rate equations for biochemical networks
Directory of Open Access Journals (Sweden)
Schröder Adrian
2008-04-01
Full Text Available Abstract Background The development of complex biochemical models has been facilitated through the standardization of machine-readable representations like SBML (Systems Biology Markup Language. This effort is accompanied by the ongoing development of the human-readable diagrammatic representation SBGN (Systems Biology Graphical Notation. The graphical SBML editor CellDesigner allows direct translation of SBGN into SBML, and vice versa. For the assignment of kinetic rate laws, however, this process is not straightforward, as it often requires manual assembly and specific knowledge of kinetic equations. Results SBMLsqueezer facilitates exactly this modeling step via automated equation generation, overcoming the highly error-prone and cumbersome process of manually assigning kinetic equations. For each reaction the kinetic equation is derived from the stoichiometry, the participating species (e.g., proteins, mRNA or simple molecules as well as the regulatory relations (activation, inhibition or other modulations of the SBGN diagram. Such information allows distinctions between, for example, translation, phosphorylation or state transitions. The types of kinetics considered are numerous, for instance generalized mass-action, Hill, convenience and several Michaelis-Menten-based kinetics, each including activation and inhibition. These kinetics allow SBMLsqueezer to cover metabolic, gene regulatory, signal transduction and mixed networks. Whenever multiple kinetics are applicable to one reaction, parameter settings allow for user-defined specifications. After invoking SBMLsqueezer, the kinetic formulas are generated and assigned to the model, which can then be simulated in CellDesigner or with external ODE solvers. Furthermore, the equations can be exported to SBML, LaTeX or plain text format. Conclusion SBMLsqueezer considers the annotation of all participating reactants, products and regulators when generating rate laws for reactions. Thus, for
Suebmee, Patcharawan; Foocharoen, Chingching; Mahakkanukrauh, Ajanee; Suwannaroj, Siraphop; Theerakulpisut, Daris; Nanagara, Ratanavadee
2016-08-01
Renal involvement in scleroderma is life-threatening. Early detection of a deterioration of the glomerular filtration rate (GFR) is needed to preserve kidney function. To (A) determine the correlation between (1) estimated GFR (eGFR) using 4 different formulae and (2) measured GFR (mGFR) using isotopic renal scan in Thai patients with scleroderma with normal serum creatinine and (B) to define the factors influencing eGFR. A cross-sectional study was performed in adult Thai patients with scleroderma at Srinagarind Hospital, Khon Kaen University, between December 2013 and April 2015. GFR was measured using the gold standard Tc-99m DTPA (Tc-99m diethylenetriaminepentaacetic acid) renal scan. We compared the latter with the eGFR, calculated using the Cockroft-Gault formula, Modification of Diet in Renal Disease (MDRD), Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) equation and creatinine clearance equation. A total of 76 patients with scleroderma (50 women and 26 men) with median age 54.8 years (interquartile range: 47.4 to 58.9) were enrolled. Mean disease duration was 5.6 ± 4.5 years. Median value of mGFR was 100.1 ± 27.6mL/minute/1.73m². There was a correlation between mGFR from the Tc-99m DTPA renal scan and the eGFR using the Cockroft-Gault formula, MDRD and CKD-EPI equation (P = 0.01, formula, MDRD study equation and CKD-EPI were useful formulae for assessing GFR in Thai patients with scleroderma. Higher SBP was associated with a lower GFR. Copyright © 2016 Southern Society for Clinical Investigation. Published by Elsevier Inc. All rights reserved.
Abdullah A. Al-Juaid; Ramzi Othman
2016-01-01
The main focus of this paper is in evaluating four constitutive relations which model the strain rate dependency of polymers yield stress. Namely, the two-term power-law, the Ree-Eyring, the cooperative, and the newly modified-Eyring equations are used to fit tensile and compression yield stresses of polycarbonate, which are obtained from the literature. The four equations give good agreement with the experimental data. Despite using only three material constants, the modified-Eyring equation...
Rigalleau, Vincent; Lasseur, Catherine; Raffaitin, Christelle; Perlemoine, Caroline; Barthe, Nicole; Chauveau, Philippe; Combe, Christian; Gin, Henri
2007-03-01
Although recommended, both the Cockcroft and Gault formula (CG) and the modification of diet in renal disease (MDRD) equation are not ideally predictive of glomerular filtration rate (GFR) in diabetic subjects; we tested whether the new Mayo Clinic Quadratic (MCQ) equation performed better. In 200 diabetic subjects with a wide range of renal function, GFR was measured by 51Cr-EDTA clearance, and compared with the results of the three predictive equations by regression analysis and Bland and Altman procedures. The correlations with body mass index, age and albumin excretion rates were tested. The precisions (absolute difference as percentage), diagnostic accuracies [receiver operating characteristic (ROC) curves for the diagnosis of moderate and severe chronic kidney disease (CKD)], and the results of stratification according to the KDOQ classification were compared. The CG and MCQ overestimated mean GFR, whereas the MDRD underestimated it. Correlation coefficients and areas under the ROC curves were better for the MDRD and the MCQ as compared with the CG, which was biased by body weight (+30% overestimation in obese diabetic subjects). The absolute differences with true GFR were slightly lower for the MDRD than the MCQ, and both better than the CG. Both the MDRD and MCQ correctly stratified 65% of the subjects (CG: 55%, P<0.05). In contrast with the MDRD, the MCQ did not underestimate normal GFR, and its performance for stratification was uniformly good over a wide GFR range. In diabetic subjects, the MCQ has a similar diagnostic performance to the MDRD, but it does not underestimate normal GFR, which is an important advantage.
Groh, Andreas; Kohr, Holger; Louis, Alfred K
2017-02-01
This paper introduces a method to solve the inverse problem of determining an unknown rate function in a partial differential equation (PDE) based on discrete measurements of the modeled quantity. The focus is put on a size-structured population balance equation (PBE) predicting the evolution of the number distribution of a single cell population as a function of the size variable. Since the inverse problem at hand is ill-posed, an adequate regularization scheme is required to avoid amplification of measurement errors in the solution method. The technique developed in this work to determine a rate function in a PBE is based on the approximate inverse method, a pointwise regularization scheme, which employs two key ideas. Firstly, the mollification in the directions of time and size variables are separated. Secondly, instable numerical data derivatives are circumvented by shifting the differentiation to an analytically given function. To examine the performance of the introduced scheme, adapted test scenarios have been designed with different levels of data disturbance simulating the model and measurement errors in practice. The success of the method is substantiated by visualizing the results of these numerical experiments.
Riisgård, Hans Ulrik; Larsen, Poul S.; Pleissner, Daniel
2014-03-01
The relationship between body dry weight ( W) and shell length ( L) of blue mussels, Mytilus edulis, can be expressed by the condition index (CI = W/ L 3) which varies from population to population and during the year. Here, we examine the influence of CI on the relationships between maximum filtration rate ( F, l h-1), W (g), and L (mm) as described by the equations: F W = aW b and F L = cL d , respectively. This is done by using available and new experimental laboratory data on M. edulis obtained by members of the same research team using different methods and controlled diets of cultivated algal cells. For all data, it was found that F W = 6.773 W 0.678 and F L = 0.00135 L 2.088 which are very similar to equations for mussels with `medium condition' (CI = 4-6 mg cm-3): F W = 6.567 W 0.681 and F L = 0.00150 L 2.051, with b- and d-values within a few percent of the theoretically expected of 2/3 and 2, respectively. Further, based on the present data, we propose a correction factor expressed by the empirical relation F W / F L = 0.3562CI2/3 which implies that F W tends to underestimate the actual filtration rate ( F L ) when CI 4.70.
Lainscsek, C.; Rowat, P.; Schettino, L.; Lee, D.; Song, D.; Letellier, C.; Poizner, H.
2012-03-01
Parkinson's disease is a degenerative condition whose severity is assessed by clinical observations of motor behaviors. These are performed by a neurological specialist through subjective ratings of a variety of movements including 10-s bouts of repetitive finger-tapping movements. We present here an algorithmic rating of these movements which may be beneficial for uniformly assessing the progression of the disease. Finger-tapping movements were digitally recorded from Parkinson's patients and controls, obtaining one time series for every 10 s bout. A nonlinear delay differential equation, whose structure was selected using a genetic algorithm, was fitted to each time series and its coefficients were used as a six-dimensional numerical descriptor. The algorithm was applied to time-series from two different groups of Parkinson's patients and controls. The algorithmic scores compared favorably with the unified Parkinson's disease rating scale scores, at least when the latter adequately matched with ratings from the Hoehn and Yahr scale. Moreover, when the two sets of mean scores for all patients are compared, there is a strong (r = 0.785) and significant (p <0.0015) correlation between them.
Directory of Open Access Journals (Sweden)
Yoshimoto Akifumi
2015-01-01
Full Text Available These days, polymer foams, such as polyurethane foam and polystyrene foam, are used in various situations as a thermal insulator or shock absorber. In general, however, their strength is insufficient in high temperature environments because of their low glass transition temperature. Polyimide is a polymer which has a higher glass transition temperature and high strength. Its mechanical properties do not vary greatly, even in low temperature environments. Therefore, polyimide foam is expected to be used in the aerospace industry. Thus, the constitutive equation of polyimide foam that can be applied across a wide range of strain rates and ambient temperature is very useful. In this study, a series of compression tests at various strain rates, from 10−3 to 103 s−1 were carried out in order to examine the effect of strain rate on the compressive properties of polyimide foam. The flow stress of polyimide foam increased rapidly at dynamic strain rates. The effect of ambient temperature on the properties of polyimide foam was also investigated at temperature from − 190 °C to 270°∘C. The flow stress decreased with increasing temperature.
2012-10-01
Currently, the trip generation rates and equations contained in the Institute of Transportation Engineers (ITE) Trip Generation Manual, 8th Edition are based on the information collected at single-use, free-standing sites and cannot be directly appli...
Ito, Kazufumi
1987-01-01
The linear quadratic optimal control problem on infinite time interval for linear time-invariant systems defined on Hilbert spaces is considered. The optimal control is given by a feedback form in terms of solution pi to the associated algebraic Riccati equation (ARE). A Ritz type approximation is used to obtain a sequence pi sup N of finite dimensional approximations of the solution to ARE. A sufficient condition that shows pi sup N converges strongly to pi is obtained. Under this condition, a formula is derived which can be used to obtain a rate of convergence of pi sup N to pi. The results of the Galerkin approximation is demonstrated and applied for parabolic systems and the averaging approximation for hereditary differential systems.
Rate equation model of phototransduction into the membranous disks of mouse rod cells
Takamoto, Rei; Awazu, Akinori
2015-01-01
A theoretical model was developed to investigate the rod phototransduction process in the mouse. In particular, we explored the biochemical reactions of several chemical components that contribute to the signaling process into/around the membranous disks in the outer segments of the rod cells. We constructed a rate equation model incorporating the molecular crowding effects of rhodopsin according to experimental results, which may hinder the diffusion of molecules on the disk mem- brane. The present model could effectively reproduce and explain the mechanisms of the following phenomena observed in experiments. First, the activations and relaxation of the wild-type mouse rod cell progressed more slowly than those of mutant cells containing half the amount of rhodopsin on the disk membrane. Second, the strong photoactivated state of the cell was sustained for a longer period when the light stimuli were strong. Finally, the lifetime of photoactivation exhibited a logarithmic increase with increasing light streng...
Bevc, Sebastjan; Hojs, Nina; Hojs, Radovan; Ekart, Robert; Gorenjak, Maksimiljan; Puklavec, Ludvik
2017-04-01
Estimating glomerular filtration rate (GFR) in elderly patients is a problem, since they are poorly represented in studies developing GFR equations. Serum cystatin C is a better indicator of GFR than serum creatinine in elderly patients. Therefore the aim of our study was to compare frequently used serum cystatin C based GFR equations with a gold standard ( 51 CrEDTA clearance) in elderly chronic kidney disease (CKD) patients. 106 adult Caucasian patients, older than 65 years (58 women, 48 men; mean age 72.5 years), were included. In each patient 51 CrEDTA clearance, serum creatinine (IDMS traceable method) and serum cystatin C (immunonephelometric method) were determined. GFR was estimated using the Simple cystatin C, CKD-EPI cystatin C, CKD-EPI creatinine-cystatin C and BIS2 equation. Mean serum creatinine of our patients was 141.4 ± 41.5 μmol/L, mean serum cystatin C 1.79 ± 0.6 mg/L, mean 51 CrEDTA clearance was 52.2 ± 15.9 mL/min per 1.73 m 2 . Statistically significant correlations between 51 CrEDTA clearance and all formulas were found (P equations were found. Bland-Altman analysis for the same cut-off showed that CKD-EPI creatinine-cystatin C and BIS2 equation underestimated and CKD-EPI cystatin C and Simple cystatin C equation overestimated measured GFR. All equations lacked precision. Analysis of ability to correctly predict patient's GFR below or above 45 mL/min per 1.73 m 2 showed similar ability for all equations (P = 0.24-0.89). All equations are equally accurate for estimating GFR in elderly Caucasian CKD patients. For daily practice Simple cystatin C equation is most practical. © 2017 International Society for Apheresis, Japanese Society for Apheresis, and Japanese Society for Dialysis Therapy.
Xie, Peng; Huang, Jian-Min; Li, Ying; Liu, Huai-Jun; Qu, Yan
2017-06-01
To investigate the application of the new modified Chronic Kidney Disease Epidemiology Collaboration (mCKD-EPI) equation developed by Liu for the measurement of glomerular filtration rate (GFR) in Chinese patients with chronic kidney disease (CKD) and to evaluate whether this modified form is more accurate than the original one in clinical practice. GFR was determined simultaneously by 3 methods: (a) (99m)Tc-diethylene triamine pentaacetic acid ((99m)Tc-DTPA) dual plasma sample clearance method (mGFR), which was used as the reference standard; (b) CKD-EPI equation (eGFRckdepi); (c) modified CKD-EPI equation (eGFRmodified). Concordance correlation and Passing-Bablok regression were used to compare the validity of eGFRckdepi and eGFRmodified. Bias, precision and accuracy were compared to identify which equation showed the better performance in determining GFR. A total of 170 patients were enrolled. Both eGFRckdepi and eGFRmodified correlated well with mGFR (concordance correlation coefficient 0.90 and 0.74, respectively) and the Passing-Bablok regression equation of eGFRckdepi and eGFRmodified against mGFR was mGFR = 0.37 + 1.04 eGFRckdepi and -49.25 + 1.74 eGFRmodified, respectively. In terms of bias, precision and 30 % accuracy, eGFRmodified showed a worse performance compared to eGFRckdepi, in the whole cohort. The new modified CKD-EPI equation cannot replace the original CKD-EPI equation in determining GFR in Chinese patients with CKD.
Flow rate and flow equation of pharmaceutical free-flowable powder excipients.
Sklubalová, Zdenka; Zatloukal, Zdenek
2013-02-01
Basic aspect of powder handling is powder flow which depends on mechanical properties of the solid material. This experimental work presents the results of flowability testing of the free-flowable particle size fraction of 0.0250-0.0315 cm of five powder excipients. The single-point determination of the mass flow rate from a cylindrical, flat-bottomed hopper was primarily influenced by the diameter of a circular orifice. The significant effect of the orifice height was also noted. Increasing the orifice height, the flow under gravity is directed resulting in the sudden acceleration of the flow rate. The critical zone relates to the orifice diameter. The multi-point determination of flowability employed the actual parameters of the flow equation which allows the prediction of the mass flow rate. The precision of the prediction was the basic criterion in optimization of the orifice geometry. Based on the results, the orifice height of 1.6 cm can be recommended for the correction of faster powder flow. For the slower powder flow, an orifice height of 0.2 cm can be used alternatively. In conclusion, the information about the orifice height used should be referred to whenever test the powder flowability and compare the results.
Rigalleau, Vincent; Lasseur, Catherine; Perlemoine, Caroline; Barthe, Nicole; Raffaitin, C; Liu, Chung; Chauveau, Phillipe; Baillet-Blanco, Laurence; Beauvieux, Marie-Christine; Combe, C; Gin, Henri
2005-04-01
The Cockcroft-Gault formula is recommended for the evaluation of renal function in diabetic patients. The more recent Modification of Diet in Renal Disease (MDRD) study equation seems more accurate, but it has not been validated in diabetic patients. This study compares the two methods. In 160 diabetic patients, we compared the Cockcroft-Gault formula and MDRD equation estimations to glomerular filtration rates (GFRs) measured by an isotopic method ((51)Cr-EDTA) by correlation studies and a Bland-Altman procedure. Their accuracy for the diagnosis of moderately (GFR formula (r = 0.74; P formula. Analysis of ROC curves showed that the MDRD equation had a better maximal accuracy for the diagnosis of moderate (areas under the curve [AUCs] 0.868 for the Cockcroft-Gault formula and 0.927 for the MDRD equation; P = 0.012) and severe renal failure (AUC 0.883 for the Cockcroft-Gault formula and 0.962 for the MDRD equation; P = 0.0001). In the 87 patients with renal insufficiency, the MDRD equation estimation was better correlated with isotopic GFR (Cockcroft-Gault formula r = 0.57; the MDRD equation r = 0.78; P < 0.01), and it was not biased as evaluated by the Bland-Altman procedure. Although both equations have imperfections, the MDRD equation is more accurate for the diagnosis and stratification of renal failure in diabetic patients.
Xiao, Guizhen; Xie, Qiuyou; He, Yanbin; Wang, Ziwen; Chen, Yan; Jiang, Mengliu; Ni, Xiaoxiao; Wang, Qinxian; Murong, Min; Guo, Yequn; Qiu, Xiaowen; Yu, Ronghao
2017-10-01
Accurately predicting the basal metabolic rate (BMR) of patients in a vegetative state (VS) or minimally conscious state (MCS) is critical to proper nutritional therapy, but commonly used equations have not been shown to be accurate. Therefore, we compared the BMR measured by indirect calorimetry (IC) to BMR values estimated using common predictive equations in VS and MCS patients. Body composition variables were measured using the bioelectric impedance analysis (BIA) technique. BMR was measured by IC in 82 patients (64 men and 18 women) with VS or MCS. Patients were classified by body mass index as underweight (equations and compared to the measured BMR using Bland-Altman analyses. For the underweight group, there was a significant difference between the measured BMR values and the estimated BMR values calculated using the H-B, Schofield, and Cunningham equations (p equations were different significantly from the measured BMR (p equations, only Schofield was not significantly different from the measured BMR in the normal-weight group. The Schofield equation showed the best concordance (only 41.5%) with the BMR values measured by IC. None of the commonly used equations to estimate BMR were suitable for the VS or MCS populations. Indirect calorimetry is the preferred way to avoid either over or underestimate of BMR values. Copyright © 2016. Published by Elsevier Ltd.
Lewis, Teresa V; Harrison, Donald L; Gildon, Brooke L; Carter, Sandra M; Turman, Martin A
2016-06-01
To determine if significant correlations exist between glomerular filtration rate (GFR) prediction equation values, derived by using the original Schwartz equation and the Chronic Kidney Disease in Children (CKiD) bedside equation with a 24-hour urine creatinine clearance (Clcr ) value normalized to a body surface area of 1.73 m(2) in overweight and obese children. Prospective analysis (20 patients) and retrospective analysis (43 patients). Pediatric inpatient ward and pediatric nephrology clinic at a comprehensive academic medical center. Sixty-three pediatric patients (aged 5-17 years), of whom 27 were overweight (body mass index [BMI] at the 85th percentile or higher) and 36 were not overweight (BMI lower than the 85th percentile [controls]) between 2007 and 2012. Data from the overweight patients were compared with nonoverweight controls. GFR values were calculated by using the original Schwartz equation and the CKiD bedside equation. Each patient's 24-hour urine Clcr value normalized to a body surface area of 1.73 m(2) served as the index value. A Pearson correlation coefficient model was used to determine association between the 24-hour urine Clcr value (index value) with the Schwartz and CKiD GFR estimations. Significant correlation was found to exist between the Schwartz and CKiD bedside GFR estimations relative to the 24-hour urine Clcr in the control subjects (r = 0.85, pSchwartz and CKiD bedside GFR values with the 24-hour urine Clcr value in overweight subjects (r = 0.86, pSchwartz equation estimated average GFR 21.75 ml/minute/1.73 m(2) higher than 24-hour urine Clcr (pSchwartz and CKiD bedside estimations of GFR correlated with 24-hour urine Clcr values in both overweight and nonoverweight children. Compared with the Schwartz equation, which tended to overestimate renal function, the CKiD bedside equation appeared to approximate 24-hour urine Clcr more closely in overweight children with kidney disorder. © 2016 Pharmacotherapy Publications, Inc.
Hight, T K; Brandeau, J F
1983-01-01
The Ramberg-Osgood equation is used to model the viscoplastic properties of compact bone. Because of the exponential nature of this equation a special optimization technique is used to curve fitting. Results are presented for the application of this equation to three sets of strain rate dependent stress-strain curves from the literature. Good to very good curve fits are achieved. This technique holds promise both as a relatively simple means of quantifying the viscoplastic nature of compact bone response and also as a mechanism for mathematically modeling that behavior.
Numerical Estimation of Spectral Properties of Laser Based on Rate Equations
Directory of Open Access Journals (Sweden)
Jan Litvik
2016-01-01
Full Text Available Laser spectral properties are essential to evaluate the performance of optical communication systems. In general, the power spectral density of the phase noise has a crucial impact on spectral properties of the unmodulated laser signal. Here the white Gaussian noise and 1/f-noise are taken into the consideration. By utilizing the time-dependent realizations of the instantaneous optical power and the phase simultaneously, it is possible to estimate the power spectral density or alternatively the power spectrum of an unmodulated laser signal shifted to the baseband and thus estimate the laser linewidth. In this work, we report on the theoretical approach to analyse unmodulated real-valued high-frequency stationary random passband signal of laser, followed by presenting the numerical model of the distributed feedback laser to emulate the time-dependent optical power and the instantaneous phase, as two important time domain laser attributes. The laser model is based on numerical solving the rate equations using fourth-order Runge-Kutta method. This way, we show the direct estimation of the power spectral density and the laser linewidth, when time-dependent laser characteristics are known.
Gaeuman, D.; Andrews, E.D.; Kraus, A.; Smith, W.
2009-01-01
Bed load samples from four locations in the Trinity River of northern California are analyzed to evaluate the performance of the Wilcock-Crowe bed load transport equations for predicting fractional bed load transport rates. Bed surface particles become smaller and the fraction of sand on the bed increases with distance downstream from Lewiston Dam. The dimensionless reference shear stress for the mean bed particle size (t*rm) is largest near the dam, but varies relatively little between the more downstream locations. The relation between t*rm and the reference shear stresses for other size fractions is constant across all locations. Total bed load transport rates predicted with the Wilcock-Crowe equations are within a factor of 2 of sampled transport rates for 68% of all samples. The Wilcock-Crowe equations nonetheless consistently under-predict the transport of particles larger than 128 mm, frequently by more than an order of magnitude. Accurate prediction of the transport rates of the largest particles is important for models in which the evolution of the surface grain size distribution determines subsequent bed load transport rates. Values of term estimated from bed load samples are up to 50% larger than those predicted with the Wilcock-Crowe equations, and sampled bed load transport approximates equal mobility across a wider range of grain sizes than is implied by the equations. Modifications to theWilcock-Crowe equation for determining t*rm and the hiding function used to scale term to other grain size fractions are proposed to achieve the best fit to observed bed load transport in the Trinity River. Copyright 2009 by the American eophysical Union.
Souza, Danielle Ribeiro de; Anjos, Luiz Antonio; Wahrlich, Vivian; Vasconcellos, Mauricio Teixeira Leite de
2015-04-01
The purpose of the present study was to identify energy intake (EI) underreporting and to estimate the impact of using a population specific equation for the basal metabolic rate (BMR) in a probability sample of adults from Niterói, Rio de Janeiro State, Brazil. A sample of 1,726 subjects participated in the study. EI was assessed by a 24-hour dietary recall and EI/BMR was computed with BMR estimated using internationally recommended equations as well as specific equations developed for the adult population of Niterói. Mean EI was 1,570.9 and 2,188.8 kcal.day-1 for women and men, respectively. EI decreased with increasing age in both men and women. BMR estimated by the Brazilian equation was significantly lower than the values estimated by the international equation for all age, sex and nutritional status groups. In general, EI underreporting was found in at least 50% of the population, higher in women, and increased with increasing age and body mass index (BMI). The results of the present study confirm that EI is underreported, even when BMR is estimated using population-specific equations.
Directory of Open Access Journals (Sweden)
Ye XS
2014-09-01
Full Text Available Xiaoshuang Ye,1 Lu Wei,1 Xiaohua Pei,1 Bei Zhu,1 Jianqing Wu,2 Weihong Zhao1 1Division of Nephrology, Department of Geriatrics, The First Affiliated Hospital of Nanjing Medical University, Nanjing, Jiangsu, People’s Republic of China; 2Division of Respiration, Department of Geriatrics, The First Affiliated Hospital of Nanjing Medical University, Nanjing, Jiangsu, People’s Republic of China Background: No conventional creatinine- or cystatin C-based glomerular filtration rate (GFR estimation equation performed consistently outstandingly in elderly Chinese in our previous studies. This research aimed to further evaluate the performance of some recently proposed estimation equations based on creatinine and cystatin C, alone or combined, in this specific population. Materials and methods: The equations were validated in a population totaling 419 participants (median age 68 [range 60–94] years. The estimated GFR (eGFR calculated separately by ten equations was compared with the reference GFR (rGFR measured by the 99mTc-DTPA renal dynamic imaging method. Results: Median serum creatinine, cystatin C, and rGFR levels were 0.93 mg/L, 1.13 mg/L, and 74.20 mL/min/1.73 m2, respectively. The Chinese population-developed creatinine- and cystatin C-based (Cscr-cys equation yielded the least median absolute difference (8.81 vs range 9.53–16.32, P<0.05, vs the Chronic Kidney Disease Epidemiology Collaboration serum creatinine equation, the highest proportion of eGFR within 15% and 30% of rGFR (P15 and P30, 55.13 and 85.44, P<0.05 and P<0.01, vs the Chronic Kidney Disease Epidemiology Collaboration serum creatinine equation, and the lowest root mean square error (14.87 vs range 15.30–22.45 in the whole cohort. A substantial agreement of diagnostic consistency between eGFR and rGFR (with a kappa 0.61–0.80 was also observed with the Cscr-cys equation. Moreover, measures of performance in the Cscr-cys equation were consistent across normal to mildly
Directory of Open Access Journals (Sweden)
A V Mulay
2017-01-01
Full Text Available In clinical practice, serum creatinine-based predicting equations and Gates protocol based on gamma camera imaging of kidneys after injection of Tc99m-diethylenetriaminepentaacetic acid (DTPA are commonly used to assess glomerular filtration rate (GFR. Comparison of these methods, especially the chronic kidney disease-epidemiology collaboration (CKD-EPI equation with gold standard method of assessment of GFR by plasma clearance of Tc-99mDTPA is not well-studied in Indian population. We conducted this study to compare GFR estimation by gamma camera-based Gates protocol and serum creatinine-based predicting equations with GFR measured by plasma clearance of Tc-99mDTPA. One hundred and five patients (65 male and 40 female underwent Tc-99m DTPA renal scan followed by withdrawal of venous blood samples at 2, 3, and 4 h as per predefined protocol. Gates method GFR (GFRs was assessed using standard protocol. GFR by plasma sampling (GFRp was calculated by slope-intercept method with provision for corrections. Estimated GFR was calculated by Cockroft-Gault formula, four variable modification of diet in renal disease (MDRD equation, and CKD-EPI equation (GFRCG, GFRMDRD, GFRCKD-EPI, respectively. GFR measured by gold standard method (GFRp was compared with that estimated by other methods by calculating correlation coefficient, bias, precision, and accuracy. GFR estimated by all three estimating equations correlated better than GFRs with GFRp. For estimating GFRp, GFRCKD-EPI had highest correlation with GFRp with least bias and highest precision. Gamma camera-based Gates protocol was the least precise and least accurate method for estimating GFRp. To conclude, all three estimating equations based on serum creatinine are superior to Tc-99m DTPA scintigraphy for estimating GFR; CKD-EPI equation being the most accurate and precise.
Bach, Aaron J E; Costello, Joseph T; Borg, David N; Stewart, Ian B
2017-03-01
This investigation aimed to quantify metabolic rate when wearing an explosive ordnance disposal (EOD) ensemble (~33kg) during standing and locomotion; and determine whether the Pandolf load carriage equation accurately predicts metabolic rate when wearing an EOD ensemble during standing and locomotion. Ten males completed 8 trials with metabolic rate measured through indirect calorimetry. Walking in EOD at 2.5, 4.0 and 5.5km·h-1 was significantly (p ensemble by 49% (127W), 65% (213W) and 78% (345W), respectively. Mean bias (95% limits of agreement) between predicted and measured metabolism during standing, 2.5, 4 and 5.5km·h-1 were 47W (19 to 75W); -111W (-172 to -49W); -122W (-189 to -54W) and -158W (-245 to -72W), respectively. The Pandolf equation significantly underestimated measured metabolic rate during locomotion. These findings have practical implications for EOD technicians during training and operation and should be considered when developing maximum workload duration models and work-rest schedules. Practitioner Summary: Using a rigorous methodological design we quantified metabolic rate of wearing EOD clothing during locomotion. For the first time we demonstrated that metabolic rate when wearing this ensemble is greater than that predicted by the Pandolf equation. These original findings have significant implications for EOD training and operation.
DEFF Research Database (Denmark)
Orskov, Bjarne; Borresen, Malene L; Feldt-Rasmussen, Bo
2010-01-01
(CKD-EPI) equation, the Cockcroft-Gault equation adjusted for body surface area and the MDRD equation with cystatin C. Performance was evaluated by mean bias, precision and accuracy. RESULTS: The MDRD equation with cystatin C had 97% of GFR estimates within 30% of measured GFR (accuracy). Both the CKD...
Ahmed, Sibtain; Jafri, Lena; Khan, Aysha Habib
2017-07-01
To evaluate the results of 24-hour urinary creatinine clearance (CrCl) with estimated glomerular filtration rate (eGFR) using the Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI), CKD-EPI Pakistan (CKD-EPI Pak), Cockcroft Gault (CG) and 4-variable Modification of Diet in Renal Disease (MDRD) equations. Descriptive, cross-sectional study. Section of Clinical Chemistry, Department of Pathology and Laboratory Medicine, The Aga Khan University, Karachi, from June to October 2013. Laboratory data of subjects ≥18 years ordering 24-hour urinary CrCl from June to October 2013 was retrieved. Statistical comparison of eGFR using CKD-EPI, CKD-EPI Pak, CG and MDRD with the timed urine collection CrCl was done using regression analysis. The mean age of the group (n=670) was 51.3 ±15.4 years with a median of 53 (IQR:22.3) years, 55.7% being males. Median BMI of males and females was 26.98 kg/m2(IQR: 7.09) and 26.16 kg/m2(IQR: 6.97), respectively. Mean GFR using 24-hour creatinine clearance was 57.1 ±35.9 ml/min/1.73m2 with a median of 51 ml/min/1.73m2. Urinary creatinine clearance showed strong correlation with CG, MDRD, CKD-EPI and CKD-EPI Pak, showing r=0.78, r=0.79, r=0.82, and r=0.82, respectively. Sensitivity was highest for the CKD-EPI Pakistan (84.7%). Similarly, CKD-EPI Pakistan equation showed the highest agreement (88.7%) with CrCl compared to the other formulae. The CKD-EPI Pak equation is more accurate and precise than the CG, CKD-EPI and MDRD in estimating GFR in Pakistani population.
Conkar, Seçil; Mir, Sevgi; Karaslan, Fatma Nur; Hakverdi, Gülden
2018-02-27
Glomerular filtration rate (GFR) is the best marker used to assess renal function. Estimated GFR (eGFR) equations have been developed, and the ideal formula is still under discussion. We wanted to find the most practical and reliable GFR in eGFR formulas. We compared serum creatinine (Scr)- and cystatin C (cysC)-based eGFR formulas in the literature. We also aimed to determine the suitability and the reliability of cysC for practical use in determining GFR in children. We have enrolled 238 children in the study. Measurement of 24-hour creatinine clearance was compared with eGFR equations which are based on Scr, cysC, and creatinine plus cysC. Of the patients (n = 238), 117 were males (49.2%), and 121 (50.8%) were females with a median age of 9.0 years. The areas under the ROC curves of Counahan-Barratt and Bedside Schwartz were equal and 0.89 (with a 95% CI 0.80-0.97). The areas under the ROC curves were not significantly different in all cystatin C-based eGFR equations. The highest AUC values for differentiating normal vs abnormal renal functions according to CrCl 24 were for the CKiD-cysC and CKiD-Scr-cysC equations. In our study, compared with creatinine-based ones, the cystatin C-based formulas did not show much superiority in predicting eGFR. Still, we think Bedside Schwartz is a good formula to provide ease of use because, in this equation, the constant k is same for all age groups. However, the most valuable equations in determining chronic kidney disease are the CKiD-cysC and CKiD-Scr-cysC equations. © 2018 Wiley Periodicals, Inc.
Bukabau, Justine B; Sumaili, Ernest K; Cavalier, Etienne; Pottel, Hans; Kifakiou, Bejos; Nkodila, Aliocha; Makulo, Jean Robert R; Mokoli, Vieux M; Zinga, Chantal V; Longo, Augustin L; Engole, Yannick M; Nlandu, Yannick M; Lepira, François B; Nseka, Nazaire M; Krzesinski, Jean Marie; Delanaye, Pierre
2018-01-01
In the estimation of glomerular filtration rate (GFR), ethnicity is an important determinant. However, all existing equations have been built solely from Caucasian and Afro-American populations and they are potentially inaccurate for estimating GFR in African populations. We therefore evaluated the performance of different estimated GFR (eGFR) equations in predicting measured GFR (mGFR). In a cross-sectional study, 93 healthy adults were randomly selected in the general population of Kinshasa, Democratic Republic of the Congo, between June 2015 and April 2016. We compared mGFR by plasma clearance of iohexol with eGFR obtained with the Modified Diet in Renal Disease (MDRD) equation with and without ethnic factor, the Chronic Kidney Disease Epidemiology (CKD-EPI) serum creatinine (SCr)-based equation, with and without ethnic factor, the cystatin C-based CKD-EPI equation (CKD-EPI SCys) and with the combined equation (CKD-EPI SCrCys) with and without ethnic factor. The performance of the equations was studied by calculating bias, precision and accuracy within 30% (P30) of mGFR. There were 48 women and 45 men. Their mean age was 45.0±15.7 years and the average body surface area was 1.68±0.16m2. Mean mGFR was 92.0±17.2 mL/min/1.73m2 (range of 57 to 141 mL/min/1.73m2). Mean eGFRs with the different equations were 105.5±30.1 and 87.2±24.8 mL/min/1.73m2 for MDRD with and without ethnic factor, respectively; 108.8±24.1 and 94.3x20.9 mL/min/1.73m2 for CKD-EPI SCr with and without ethnic factor, respectively, 93.5±18.6 mL/min/1.73m2 for CKD-EPI SCys; 93.5±18.0 and 101±19.6 mL/min/ 1.73m2 for CKD-EPI SCrCys with and without ethnic factor, respectively. All equations slightly overestimated mGFR except MDRD without ethnic factor which underestimated by -3.8±23.0 mL/min /1.73m2. Both CKD-EPI SCr and MDRD with ethnic factors highly overestimated mGFR with a bias of 17.9±19.2 and 14.5±27.1 mL/min/1.73m2, respectively. There was a trend for better P30 for MDRD and CKD
Valente, Mattia A E; Hillege, Hans L; Navis, Gerjan; Voors, Adriaan A; Dunselman, Peter H J M; van Veldhuisen, Dirk J; Damman, Kevin
2014-01-01
The Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) formula estimates glomerular filtration rate (GFR) better than the simplified Modification of Diet in Renal Disease (sMDRD) formula in numerous populations. It has not previously been validated in heart failure patients. The GFR was measured in 120 patients with chronic systolic heart failure (CHF) using [(125)I]iothalamate clearance (GFR(IOTH)) and estimated using the sMDRD and CKD-EPI equations. Accuracy, bias, and prognostic performance were compared. Cockcroft-Gault, CKD-EPI serum cystatin C, and CKD-EPI creatinine-serum cystatin C equations were compared in secondary analyses. Mean age was 59 ± 12 years, 80% were male. Mean LVEF was 29 ± 10%. Mean GFR(IOTH) was 74 ± 27 mL/min/1.73 m(2), and mean estimated GFR was 66 ± 23 mL/min/1.73 m(2) (CKD-EPI) and 63 ± 21 mL/min/1.73m(2) (sMDRD). CKD-EPI showed less bias than sMDRD (-8 ± 15 vs. -11 ± 16 mL/min/1.73 m(2), P heart failure patients, particularly those with preserved or moderately impaired renal function. First published online by Oxford University Press on behalf of the European Society of Cardiology. All rights reserved. © The Author 2013.
Fontseré, Néstor; Bonal, Jordi; Salinas, Isabel; de Arellano, Manel Ramírez; Rios, Jose; Torres, Ferran; Sanmartí, Anna; Romero, Ramón
2008-12-01
To test the Mayo Clinic Quadratic (MCQ) equation against isotopic glomerular filtration rate, compared with the Modification of Diet in Renal Disease (MDRD) and the Cockcroft-Gault formulas, in type 2 diabetes. Based on values obtained with iothalamate, 118 type 2 diabetic patients were divided into three groups according to renal function: hyperfiltration (26), normal function (56), or chronic kidney disease (CKD) stages 3-4 (36). ANOVA, the Bland-Altman procedure, and Lins coefficient (Rc) were performed to study accuracy. In the hyperfiltration and normal function groups, all prediction equations significantly underestimated the value obtained with isotopic glomerular filtration rate (P equations also presented significant differences with the isotopic method. However, MDRD had a bias of -5.3 (Rc 0.452), Cockcroft-Gault formula -0.2 (Rc 0.471), and the MCQ -4.5 (Rc 0.526). The MCQ and prediction equations proved inaccurate (excessive underestimation) in type 2 diabetic patients with hyperfiltration or normal renal function. With regard to CKD, the results obtained provided no evidence of superiority of the MCQ over the MDRD or the Cockcroft-Gault formula.
Crossvalidation of two heart rate-based equations for predicting VO2max in white and black men.
Esco, Michael R; Olson, Michele S; Williford, Henry N; Mugu, Emmanuel M; Bloomquist, Barbara E; McHugh, Aindrea N
2012-07-01
The purpose of this investigation was to crossvalidate 2 equations that use the ratio of maximal heart rate (HRmax) to resting HR (HRrest) for predicting maximal oxygen consumption (VO2max) in white and black men. One hundred and nine white (n = 51) and black (n = 58) men completed a maximal exercise test on a treadmill to determine VO2max. The HRrest and HRmax were used to predict VO2max via the HRindex and HRratio equations. Validity statistics were done to compare the criterion versus predicted VO2max values across the entire cohort and within each race separately. For the entire group, VO2max was significantly overestimated with the HRindex equation, but the HRratio equation yielded no significant difference compared with the criterion. In addition, there were no significant differences shown between VO2max and either HR-based prediction equation for the white subgroup. However, both equations significantly overestimated VO2max in the black group. Furthermore, large standard error of estimates (ranging from 6.92 to 7.90 ml·kg(-1)·min(-1)), total errors (ranging from 8.30 to 8.62 ml·kg(-1)·min(-1)), and limits of agreement (ranging from upper limits of 16.65 to lower limits of -18.25 ml·kg(-1)·min(-1)) were revealed when comparing the predicted to criterion VO2max for both the groups. Considering the results of this investigation, the HRratio and HRindex methods appear to crossvalidate and prove useful for estimating the mean VO2max in white men as a group but not for an age-matched group of black men. However, because of inflated values for error, caution should be exercised when using these methods to predict individual VO2max.
Diego, Elisa; Castro, Pedro; Soy, Dolors; Poch, Esteban; Nicolás, Josep M
2016-02-15
The predictive performance of glomerular filtration rate (GFR) estimation equations based on cystatin C versus serum creatinine (SCr) values in critically ill patients was evaluated. A retrospective observational study was performed in the medical intensive care unit (ICU) of a university hospital from October 2006 through September 2007. All consecutively admitted critically ill patients older than 18 years who stayed in the ICU for more than 48 hours with a urinary bladder catheter in place were included in the study. Data collected included SCr, cystatin C, serum albumin, blood urea nitrogen, and 24-hour urine creatinine clearance [Formula: see text] levels. The following equations were also used to determine the estimated GFR that was compared with the reference [Formula: see text] for all patients in the study: Arnal-Dade using cystatin C, Cockcroft-Gault using actual body weight, Cockcroft-Gault using ideal body weight, Jelliffe, Modification of Diet in Renal Disease (MDRD), and four-variable version MDRD (MDRD-4). This study included 241 measurements corresponding to 131 critically ill patients. The cystatin C-based equation underestimated [Formula: see text], whereas overestimation by every SCr-based formula was observed in the whole cohort and in the [Formula: see text] subgroup; MDRD-4 was the most biased equation in every analysis. There were no significant differences in precision, except for great variability in the subgroup with a [Formula: see text] of Formula: see text]. A retrospective observational study showed no evidence of superiority of a cystatin C-based equation over SCr-based equations to estimate the GFR in an ICU population. Copyright © 2016 by the American Society of Health-System Pharmacists, Inc. All rights reserved.
Grima, R
2010-07-21
Chemical master equations provide a mathematical description of stochastic reaction kinetics in well-mixed conditions. They are a valid description over length scales that are larger than the reactive mean free path and thus describe kinetics in compartments of mesoscopic and macroscopic dimensions. The trajectories of the stochastic chemical processes described by the master equation can be ensemble-averaged to obtain the average number density of chemical species, i.e., the true concentration, at any spatial scale of interest. For macroscopic volumes, the true concentration is very well approximated by the solution of the corresponding deterministic and macroscopic rate equations, i.e., the macroscopic concentration. However, this equivalence breaks down for mesoscopic volumes. These deviations are particularly significant for open systems and cannot be calculated via the Fokker-Planck or linear-noise approximations of the master equation. We utilize the system-size expansion including terms of the order of Omega(-1/2) to derive a set of differential equations whose solution approximates the true concentration as given by the master equation. These equations are valid in any open or closed chemical reaction network and at both the mesoscopic and macroscopic scales. In the limit of large volumes, the effective mesoscopic rate equations become precisely equal to the conventional macroscopic rate equations. We compare the three formalisms of effective mesoscopic rate equations, conventional rate equations, and chemical master equations by applying them to several biochemical reaction systems (homodimeric and heterodimeric protein-protein interactions, series of sequential enzyme reactions, and positive feedback loops) in nonequilibrium steady-state conditions. In all cases, we find that the effective mesoscopic rate equations can predict very well the true concentration of a chemical species. This provides a useful method by which one can quickly determine the
Gerencsér, Máté; Jentzen, Arnulf; Salimova, Diyora
2017-11-01
In a recent article (Jentzen et al. 2016 Commun. Math. Sci.14, 1477-1500 (doi:10.4310/CMS.2016.v14.n6.a1)), it has been established that, for every arbitrarily slow convergence speed and every natural number d∈{4,5,…}, there exist d-dimensional stochastic differential equations with infinitely often differentiable and globally bounded coefficients such that no approximation method based on finitely many observations of the driving Brownian motion can converge in absolute mean to the solution faster than the given speed of convergence. In this paper, we strengthen the above result by proving that this slow convergence phenomenon also arises in two (d=2) and three (d=3) space dimensions.
Horio, M; Yasuda, Y; Kaimori, J; Ichimaru, N; Kakuta, Y; Isaka, Y; Matsuo, S; Takahara, S
2014-01-01
It was reported that the glomerula filtration rate (GFR) equation based on serum creatinine underestimated the GFR in potential kidney donors. Recently, the Japanese GFR equation based on standardized serum cystatin C was reported. Therefore, we assessed the performance of the equation in potential kidney donors. Forty-five potential kidney donors from 2 hospitals were included. GFR was measured (mGFR) using inulin renal clearance. Serum creatinine was measured using the enzymatic method. Serum cystatin C was measured using a nephelometric immunoassay (Siemens) and calibrated to the standardized value traceable to ERM-DA471/IFCC using an equation reported previously. The estimated GFR (eGFR) was calculated using the Japanese GFR equation based on serum creatinine (eGFRcreat) and the Japanese GFR equation based on serum cystatin C (eGFRcys). Bias (mGFR - eGFR) and accuracy (P30) of the equations were evaluated. Inulin clearance, eGFRcreat, and eGFRcys were 91.0 ± 18.2, 78.5 ± 18.8, and 93.3 ± 16.3 mL/min/1.73 m(2), respectively. Bias of eGFRcreat was 12.4 ± 15.8 mL/min/1.73 m(2) and significantly different from zero, indicating underestimation of GFR. Bias of eGFRcys was -2.3 ± 16.3 mL/min/1.73 m(2) and was not significantly different from zero, suggesting better performance. But, the precision (standard deviation [SD] of bias) and accuracy (P30: Percentage of participants with eGFR within 30% of mGFR) of eGFRcys were not better compared with eGFRcreat. Accuracies (P30) of eGFRcreat and eGFRcys were 87% (95% confidence interval [CI], 74-94) and 82% (95% CI, 69-91), respectively. Bias of eGFRcys was better compared with eGFRcreat. But, the precision (SD of bias) and accuracy of eGFRcys were not superior compared with eGFRcreat in potential kidney donors. Copyright © 2014 Elsevier Inc. All rights reserved.
Development of wide-range constitutive equations for calculations of high-rate deformation of metals
Directory of Open Access Journals (Sweden)
Preston D.
2011-01-01
Full Text Available For development of models of strength and compressibility of metals in wide range of pressures (up to several megabar and strain rates ~ 1÷108 s−1, the method of dynamic tests is used. Since direct measurement of strength is impossible under complicated intensive high-rate loading, a formal model is created at first, and then it is updated basing on comparison with many experiments, which are sensitive to shear strength. Elastic-plastic, viscous-elastic-plastic and relaxation integral models became nowadays most commonly used. The basic unsolved problems in simulation of high-rate deformation of metals are mentioned in the paper.
Brand, J.A. van den; Boekel, G.A.J van; Willems, H.L.; Kiemeney, L.A.L.M.; Heijer, M. den; Wetzels, J.F.M.
2011-01-01
BACKGROUND: Chronic kidney disease (CKD) is defined as the presence of kidney damage, albuminuria or a reduction in glomerular filtration rate (GFR). A GFR <60 mL/min/1.73 m(2) alone is sufficient to diagnose CKD Stages III-V. Recently, the new chronic kidney disease epidemiology collaboration
Spatial Moment Equations for a Groundwater Plume with Degradation and Rate-Limited Sorption
In this note, we analytically derive the solution for the spatial moments of groundwater solute concentration distributions simulated by a one-dimensional model that assumes advective-dispersive transport with first-order degradation and rate-limited sorption. Sorption kinetics...
Macroscopic rate equation modeling of trapping/detrapping of hydrogen isotopes in tungsten materials
Energy Technology Data Exchange (ETDEWEB)
Hodille, E.A., E-mail: etienne.hodille@cea.fr [CEA, IRFM, F-13108 Saint Paul lez Durance (France); Bonnin, X. [LSPM-CNRS, Université Paris 13, Sorbonne Paris Cité, F-93430 Villetaneuse (France); Bisson, R.; Angot, T. [Aix-Marseille Université, PIIM, CNRS, UMR 7345, 13397 Marseille (France); Becquart, C.S. [Université Lille I, UMET, UMR 8207, 59655 Villeneuve d’Ascq cédex France (France); Layet, J.M. [Aix-Marseille Université, PIIM, CNRS, UMR 7345, 13397 Marseille (France); Grisolia, C. [CEA, IRFM, F-13108 Saint Paul lez Durance (France)
2015-12-15
Relevant parameters for trapping of Hydrogen Isotopes (HIs) in polycrystalline tungsten are determined with the MHIMS code (Migration of Hydrogen Isotopes in MaterialS) which is used to reproduce Thermal Desorption Spectrometry experiments. Three types of traps are found: two intrinsic traps (detrapping energy of 0.87 eV and 1.00 eV) and one extrinsic trap created by ion irradiation (detrapping energy of 1.50 eV). Then MHIMS is used to simulate HIs retention at different fluences and different implantation temperatures. Simulation results agree well with experimental data. It is shown that at 300 K the retention is limited by diffusion in the bulk. For implantation temperatures above 500 K, the retention is limited by trap creation processes. Above 600 K, the retention drops by two orders of magnitude as compared to the retention at 300 K. With the determined detrapping energies, HIs outgassing at room temperature is predicted. After ions implantation at 300 K, 45% of the initial retention is lost to vacuum in 300 000 s while during this time the remaining trapped HIs diffuse twice as deep into the bulk. - Highlights: • Code development to solve numerically the model equations of diffusion and trapping of hydrogen in metals. • Parametrization of the model trapping parameters (detrapping energies and density): fitting of experimental TDS spectrum. • Confrontation model/experiment: evolution of retention with fluence and implantation temperature. • Investigation of period of rest between implantation and TDS on retention and depth profile.
Directory of Open Access Journals (Sweden)
Salima R. S. Al-Maqbali
2014-05-01
Full Text Available Objectives: Estimated glomerular filtration rate (eGFR is an important component of a patient’s renal function profile. The Modification of Diet in Renal Disease (MDRD equation and the Chronic Kidney Disease-Epidemiology Collaboration (CKD-EPI equation are both commonly used. The aim of this study was to compare the performance of the original MDRD186, revised MDRD175 and CKD-EPI equations in calculating eGFR in type 2 diabetes mellitus (T2DM patients in Oman. Methods: The study included 607 T2DM patients (275 males and 332 females, mean age ± standard deviation 56 ± 12 years who visited primary health centres in Muscat, Oman, during 2011 and whose renal function was assessed based on serum creatinine measurements. The eGFR was calculated using the three equations and the patients were classified based on chronic kidney disease (CKD stages according to the National Kidney Foundation Kidney Disease Outcomes Quality Initiative guidelines. A performance comparison was undertaken using the weighted kappa test. Results: The median eGFR (mL/min/1.73 m2 was 92.9 for MDRD186, 87.4 for MDRD175 and 93.7 for CKD-EPI. The prevalence of CKD stage 1 was 55.4%, 44.7% and 57% while for stages 2 and 3 it was 43.2%, 54% and 41.8%, based on MDRD186, MDRD175 and CKD-EPI, respectively. The agreement between MDRD186 and CKD-EPI (к 0.868 was stronger than MDRD186 and MDRD175 (к 0.753 and MDRD175 and CKD-EPI (к 0.730. Conclusion: The performances of MDRD186 and CKD-EPI were comparable. Considering that CKD-EPI-based eGFR is known to be close to isotopically measured GFR, the use of MDRD186 rather than MDRD175 may be recommended.
Fukuda, Makoto; Yoshimura, Kengo; Namekawa, Koki; Sakai, Kiyotaka
2017-06-01
The objective of the present study is to evaluate the effect of filtration coefficient and internal filtration on dialysis fluid flow and mass transfer coefficient in dialyzers using dimensionless mass transfer correlation equations. Aqueous solution of vitamin B12 clearances were obtained for REXEED-15L as a low flux dialyzer, and APS-15EA and APS-15UA as high flux dialyzers. All the other design specifications were identical for these dialyzers except for filtration coefficient. The overall mass transfer coefficient was calculated, moreover, the exponents of Reynolds number (Re) and film mass transfer coefficient of the dialysis-side fluid (k D) for each flow rate were derived from the Wilson plot and dimensionless correlation equation. The exponents of Re were 0.4 for the low flux dialyzer whereas 0.5 for the high flux dialyzers. Dialysis fluid of the low flux dialyzer was close to laminar flow because of its low filtration coefficient. On the other hand, dialysis fluid of the high flux dialyzers was assumed to be orthogonal flow. Higher filtration coefficient was associated with higher k D influenced by mass transfer rate through diffusion and internal filtration. Higher filtration coefficient of dialyzers and internal filtration affect orthogonal flow of dialysis fluid.
Directory of Open Access Journals (Sweden)
Alaleh Gheissari
2014-01-01
Full Text Available To determine the performance of the updated Schwartz, combined Schwartz and Grubb glomerular filtration rate (GFR equations in a relatively large number of healthy children with no known renal disease, we studied 712 students aged between seven and 18 years from the Isfahan province of Iran by random cluster sampling between 2009 and 2010. Blood investigations included blood urea nitrogen, creatinine and cystatin C. For each participant, GFR was calculated based on the three equations. We used Bland-Altman plots and weighted kappa statistics to compare the performance of the study equations. The mean age of the children was 12.2 ± 2.4 years. A high concordance in estimating GFR (mean difference: 0 ± 12.7 mL/min/1.73 m 2 and a very good agreement in defining chronic kidney disease (CKD and non-CKD individuals (weighted kappa: 0.85; 95% confidence intervals: 0.69-1 were observed between the updated Schwartz and the combined Schwartz equations. Poor agreement was observed between the Grubb equation and two Schwartz equations in estimating GFR and defining CKD. There was no systematic deviation between the updated Schwartz and the combined Schwartz equations in children with normal renal function. The Grubb equation was highly inconsistent with both Schwartz equations in this population. We conclude that the updated Schwartz equation is simpler and more accessible than the combined Schwartz equation in daily clinical practice and CKD screening programs.
Björk, Jonas; Grubb, Anders; Gudnason, Vilmundur; Indridason, Olafur S; Levey, Andrew S; Palsson, Runolfur; Nyman, Ulf
2017-10-05
Validation studies comparing glomerular filtration rate (GFR) equations based on standardized creatinine and cystatin C assays in the elderly are needed. The Icelandic Age, Gene/Environment Susceptibility-Kidney cohort was used to compare two pairs of recently developed GFR equations, the revised Lund-Malmö creatinine equation (LMRCr) and the arithmetic mean of the LMRCr and Caucasian, Asian, Paediatric and Adult cystatin C equations (MEANLMR+CAPA), as well as the Full Age Spectrum creatinine equation (FASCr) and its combination with cystatin C (FASCr+Cys), with the corresponding pair of Chronic Kidney Disease Epidemiology Collaboration equations (CKD-EPICr and CKD-EPICr+Cys). A total of 805 individuals, 74-93 years of age, underwent measurement of GFR (mGFR) using plasma clearance of iohexol. Four metrics were used to compare the performance of the GFR equations: bias, precision, accuracy [including the percentage of participants with estimated GFR (eGFR) within 30% of mGFR (P30)] and the ability to detect mGFR equations had a P30 >90%. LMRCr and FASCr yielded significantly higher precision and P30 than CKD-EPICr, while bias was significantly worse. LMRCr, FASCr and CKD-EPICr showed similar ability to detect mGFR equations. None of the creatinine-based equations was clearly superior overall in this community-dwelling elderly cohort. The addition of cystatin C improved all of the creatinine-based equations.
Mombelli, C A; Giordani, M C; Imperiali, N C; Groppa, S R; Ocampo, L; Elizalde, R I; Schreck, C M; Rosa-Diez, G J
2016-03-01
The Modification of Diet in Renal Disease (MDRD) equation is widely used to estimate glomerular filtration rate (eGFR) in kidney transplant (KT) patients. The novel Chronic Kidney Disease-Epidemiology Collaboration equation (CKD-EPI) could improve accuracy of GFR estimation. Our aim was to compare both equations for staging of CKD in KT patients. In a cohort of KT patients, correlation of eGFR according to MDRD and CKD-EPI with 24-hour creatinine clearance (24h-CrCl) was evaluated. Concordance between both equations for CKD staging was performed. MDRD was used for initial CKD staging. The mean difference of GFR between 24h-CrCl and each equation was calculated and Bland-Altman analysis applied. A cohort of 463 KT patients were studied: 67% female, overall average age 46 ± 14 years, 41% living donor, mean time of transplantation 71 months (3-95), and mean serum creatinine 1.68 ± 1.03 mg/dL. For the whole cohort (all CKD stages), eGFR by CKD-EPI was 5.33 mL/min/1.73 m(2) higher than by MDRD (P EPI - MDRD) were 13.98 ± 3.27, 8.2 ± 1.98, and 5.34 ± 1.32 mL/min/1,73 m(2), respectively. The percentage of patients with eGFR EPI. In women and patients ≤65 years old, eGFR by CKD-EPI was 5.98 and 5.81 mL/min/1.73 m(2) higher, respectively, than by MDRD (P EPI reduces the number of patients with eGFR <60 mL/min/1.73 m(2) and consequently assigns lower CKD stages to our KT population. Copyright © 2016 Elsevier Inc. All rights reserved.
1973-12-01
levels E’ and EC, while molecules with even more symmetry (e.g., those belonging to point group Td or Oh) have in addition to singly degenerate levels A...by: 156 w k 2J + 1 (3.212) rk k ki 0and thus for example for the spontaneous emission rate A mn 0o 64TT4 e 2Vn 3 •n - mn m I- /A )= 4re t• sec (3.2...vB 1+1 +) expk m + (2_J+3)~ 2J exp- MJI(+ 2Vn dJ kT/h j 2 J4 2 ( kT/h jJ ’z 2J2 exp-t i~ dJ -. f~/ i)/ (4.236) 248 K) With (4.236), Eqs. (4.229) through
Tang, Z; Tao, J; Sun, L; Han, Z; Chen, H; Huang, Z; Zhou, W; Zhao, C; Fei, S; Que, H; Li, Y; Tan, R; Gu, M
Currently, there is no dedicated equation to estimate glomerular filtration rate (GFR) for transplanted kidneys. This study aimed to compare the performance of serum creatinine (Scr)- and cystatin C (CysC)-based equations in Chinese renal transplant recipients. A total of 252 stable renal transplant recipients were enrolled in this study. The plasma clearance of 99m Tc-DTPA (rGFR) was used as a reference standard. The Scr, CysC, and rGFR of the patients were measured on the same day. The bias, precision, accuracy (percentage of estimates within 10%, 30%, and 50% of rGFR), and agreements of 8 Scr and 5 CysC eGFR equations were assessed. The factors affecting the accuracy were also evaluated. Among the Scr-based equations, the Japanese Society of Nephrology-Chronic Kidney Disease Initiatives (JSN-CKDI) equation had the best overall performance with a bias of -6.2 mL/min/1.73 m 2 , and 96.1% of its estimates were within 30% of the rGFR. For the CysC-based equations, the Filler equation had the best performance with a bias of -3.9 mL/min/1.73 m 2 , and 93.7% of its estimates were within 30% of the rGFR. Overall, the CysC-based equations showed better performance than the Scr-based equations. In addition, significant differences were observed between bias and gender and between bias and rGFR value in some equations, whereas transplantation time and immunosuppressive regimens were not correlated with the bias. The JSN-CKDI equation provides the best estimation of the GFR equations, and the CysC-based equations performed better than the Scr-based equations in this population. Copyright © 2017. Published by Elsevier Inc.
Boer, P-H
2017-01-01
The purpose of the study was to determine if the regression formula developed for the prediction of maximum heart rate (HR) is valid for adults with Down syndrome (DS). Thirty-six adults with DS (31.7 ± 6.8 years; 20 men, 16 women) completed a maximal aerobic test. Maximum HR and VO2 peak were measured directly on a motorised treadmill with a metabolic analyser. Predicted HR was estimated with the regression equation developed for individuals with DS (Fernhall et al. 2001). Differences between measured versus predicted maximum HR were assessed with a dependent T-test and the relationship with Pearson correlational analyses. Agreement was assessed with Bland-Altman analysis. There was a significant difference between directly measured maximum HR and predicted maximum HR (P measurement bias (+4.7) and large limits of agreement (+26.7 and -17.4) between measured and predicted maximum HR. The Bland-Altman plot also demonstrated the presence of heteroscedasticity. The results indicate that the regression formula developed for individuals with DS was not accurate in this sample of DS adults aged 19 to 46 years. Future studies should develop different prediction equations for more specific age and body mass index categories for individuals with DS. © 2016 MENCAP and International Association of the Scientific Study of Intellectual and Developmental Disabilities and John Wiley & Sons Ltd.
Energy Technology Data Exchange (ETDEWEB)
Pan, Wenxiao; Daily, Michael D.; Baker, Nathan A.
2015-12-01
We demonstrate the accuracy and effectiveness of a Lagrangian particle-based method, smoothed particle hydrodynamics (SPH), to study diffusion in biomolecular systems by numerically solving the time-dependent Smoluchowski equation for continuum diffusion. The numerical method is first verified in simple systems and then applied to the calculation of ligand binding to an acetylcholinesterase monomer. Unlike previous studies, a reactive Robin boundary condition (BC), rather than the absolute absorbing (Dirichlet) boundary condition, is considered on the reactive boundaries. This new boundary condition treatment allows for the analysis of enzymes with "imperfect" reaction rates. Rates for inhibitor binding to mAChE are calculated at various ionic strengths and compared with experiment and other numerical methods. We find that imposition of the Robin BC improves agreement between calculated and experimental reaction rates. Although this initial application focuses on a single monomer system, our new method provides a framework to explore broader applications of SPH in larger-scale biomolecular complexes by taking advantage of its Lagrangian particle-based nature.
Uche, C L; Osegbe, I D
2017-07-01
Homozygous sickle cell patients are prone to renal damage which can be on-going in and out of crises, therefore, there is a need to monitor renal status using glomerular filtration rate. Equations to estimate GFR are readily available. Cockcroft-Gault equation is widely used, while the MDRD formula is the currently accepted equation. The CKD-EPI equation is recently being recommended but has not been validated among HbSS patients. Therefore, we aim to compare estimated GFR using CKD-EPI versus MDRD and Cockcroft-Gault equations among HbSS patients. This was a cross-sectional study of stable HbSS patients. Information on their age, sex, and weight was collected. Their venous blood samples were also obtained for plasma creatinine determination which was used to calculate estimated GFR using Cockcroft-Gault, MDRD and CKD-EPI equations. Student t-test, Pearson correlation, and Bland-Altman difference plots were performed. A p-value of EPI 122 ± 25.1ml/min/1.73m2 (pConclusion: CKD-EPI equation is best for individuals with GFR > 60ml/min/1.73m2. This study has shown that it correlates well with the currently acceptable MDRD equation, therefore, can be used to monitor the renal status of stable HbSS patients. CG gives poor correlation and bias with CKD-EPI. Further validation studies on CKD-EPI equation are needed in different patient populations.
Lee, Chung Sik; Cha, Ran-hui; Lim, Youn-Hee; Kim, Ho; Song, Ka Heon; Gu, Namyi; Yu, Kyung Sang; Lim, Chun Soo; Han, Jin Suk; Kim, Suhnggwon; Kim, Yon Su
2010-11-01
Race and ethnicity are influential in estimating glomerular filtration rate (GFR). We aimed to find the Korean coefficients for the Modification of Diet in Renal Disease (MDRD) study equations and to obtain novel proper estimation equations. Reference GFR was measured by systemic inulin clearance. Serum creatinine (SCr) values were measured by the alkaline picrate Jaffé kinetic method, then, recalibrated to CX3 analyzer and to isotope dilution mass spectrometry (IDMS). The Korean coefficients for the 4 and 6 variable MDRD and IDMS MDRD study equations based on the SCr recalibrated to CX3 and to IDMS were 0.73989/0.74254 and 0.99096/0.9554, respectively. Coefficients for the 4 and 6 variable MDRD equations based on the SCr measured by Jaffé method were 1.09825 and 1.04334, respectively. The modified equations showed better performances than the original equations. The novel 4 variable equations for Korean based on the SCr measured and recalibrated to IDMS were 107.904×SCr(-1.009)×age(-0.02) (×0.667, if woman) and 87.832×SCr(-0.882)×age(0.01) (×0.653, if woman), respectively. Modified estimations of the MDRD and IDMS MDRD study equations with ethnic coefficients and the novel equations improve the performance of GFR estimation for the overall renal function.
Xie, Peng; Huang, Jian-Min; Lin, Hai-ying; Wu, Wei-Jie; Pan, Li-Ping
2013-08-01
To compare the performance of the Chronic Kidney Disease Epidemiology Collaboration (CDK-EPI) equation, the 24-h creatinine clearance rate (24hCCr), Cockroft-Gault (C-G) formula, the abbreviated Modification of Diet in Renal Disease (aMDRD) equation, the modified Modification of Diet in Renal Disease (mMDRD) equation in determining glomerular filtration rate (GFR) in Chinese patients with chronic kidney disease (CKD) and detect the most proper method to measure GFR in clinical practice. One hundred and fifty-four patients with CKD were enrolled in the present study. (99m)Tc-diethylene triamine pentaacetic acid ((99m)Tc-DTPA) plasma clearance method measured by dual plasma sampling method (rGFR) was considered as the reference standard. GFR was estimated simultaneously using five methods: (1) CDK-EPI equation (eGFR1); (2) 24hCCr (eGFR2); (3) C-G formula (eGFR3); (4) abbreviated MDRD equation (eGFR4); (5) mMDRD equation (eGFR5). The comparison of correlation, regression, bias, precision, accuracy, limit of agreement, and receiver-operating characteristics (ROC) for detecting CKD (with a GFR cutoff of 60 mL min(-1) 1.73 m(-2)) among the methods was analyzed to identify the most suitable method. All the equations correlated well with rGFR, and the correlation coefficient of CDK-EPI equation was the highest (reGFR1 = 0.922, P 0.05). However, CDK-EPI equation had the highest accuracy when compared with the other two equations (P < 0.05). And its performance on bias showed no statistically significant difference compared with other four equations. Although its bias and accuracy did not overmatch the other four equations in our patient group, the CDK-EPI equation outperformed the other equations based on creatinine in correlation, precision, limit of agreement, and detecting CKD, and it is very simple, time-saving, and cost-effective. So we recommend intensely that the CDK-EPI equation is the most suitable method in determining GFR in Chinese patients with CKD and can be
Wang, Fang; Yao, Yong; Zhu, Sai-nan; Huang, Jian-ping; Xiao, Hui-jie; Ding, Jie; Sai, Yi-pa
2010-11-01
Accurate and reliable assessment of renal function is important in the management of children with chronic kidney disease (CKD). Glomerular filtration rate (GFR) is the best index of assessing kidney function. For assessment of GFR, both gold standard tests and prediction equations have been used. The well-known 24-hour endogenous creatinine clearance (Ccr), the Schwartz formula and the Filler formula are increasingly used in daily clinical practice. However, there are few studies on the applicability of these prediction equations for estimating GFR in Chinese children with CKD. The aim of this study was to compare these prediction equations estimating GFR with an isotope clearance method [isotope glomerular filtration rate (rGFR)] in such patients. Children aged 1-16 years who underwent isotope (99m)Tc-diethylenetriaminepentaacetic acid ((99m)Tc-DTPA) GFR testing (Gates' method) between the year of 2002 and 2005 were studied retrospectively. GFR was estimated using: (1) 24-hour Ccr, which was calculated using the standard formula: [urine creatinine (milligrammes per millilitre) × 24-hour urine volume/serum creatinine (milligrammes per millilitre) × 1440] × [1.73 (m(2))/body surface area (m(2))]; (2) the Schwartz formula, which is: eGFR (ml/min per 1.73 m(2)) = k × height (centimetres)/serum creatinine (micromoles per litre), where k is 62 in males at 13 years of age and older, 40 in infants, and 49 in all other children; and (3) the Filler formula, which is: logGFR = 1.962 + [1.123 × log(1/Cys C)], where cystatin C is measured in milligrammes per litre. Serum and urinary creatinine levels were detected by alkaline kinetic method. Serum cystatin C was analysed by particle-enhanced immunoturbidimetric assay. Bias and precision were evaluated. Thirty subjects (18 males and 12 females; mean age 9.4 years) fulfilling both inclusion criteria and exclusion criteria were included in this study. The mean (SD) rGFR was 81.57 (36.92) ml/min per 1.73 m(2); 18 subjects
Oya, T.; Yanagimoto, J.; Ito, K.; Uemura, G.; Mori, N.
2017-09-01
In metal forming, progress in material models is required to construct a general and reliable fracture prediction framework because of the increased use of advanced materials and growing demand for higher prediction accuracy. In this study, a fracture prediction framework based on bifurcation theory is constructed. A novel material model based on the stress-rate dependence related to a non-associated flow rule is presented. This model is based on a non-associated flow rule with an arbitrary higher-order yield function and a plastic potential function for any anisotropic material. This formulation is combined with the stress-rate-dependent plastic constitutive equation, which is known as the Ito-Goya rule, to construct a generalized plastic constitutive model in which non-normality and non-associativity are reasonably included. Then, by adopting three-dimensional bifurcation theory, which is referred to the 3D theory, a new theoretical framework for fracture prediction based on the initiation of a shear band is constructed. Using virtual material data, a numerical simulation is carried out to produce a fracture limit diagram, which is used to investigate the characteristics of the proposed methodology.
Simplified method for the computation of parameters of power-law rate equations from time-series.
Díaz-Sierra, R; Fairén, V
2001-05-01
Modeling biological processes from time-series data is a resourceful procedure which has received much attention in the literature. For models established in the context of non-linear differential equations, parameter-dependent phenomenological tentative response functions are tested by comparing would-be solutions of those models to the experimental time-series. Those values of the parameters for which a tested solution is a best fit are then retained. It is done with the help of some appropriate optimization algorithm which simplifies the searching procedure within the range of variability of the parameters that are to be estimated. The procedure works well in problems with a small number of adjustable parameters or/and with narrow searching ranges. However, it may start to be problematic for models with a large number of problem parameters inasmuch as convergence to the best fit is not necessarily ensured. In this case, a reduction in size of the parameter estimation problem must be undertaken. We presently address this issue by proposing a systematic procedure that does so in problems in which the system's response to a sufficiently small pulse perturbation of steady-state can be obtained. The response is then assumed to be a solution of the linearized equations, the Jacobian of which can be retrieved by a simple multilinear regression. The calculated n(2) Jacobian entries provide as many relationships among problem parameters, thus cutting substantially the size of the starting problem. After this preliminary treatment is applied, only (kappa-n(2)) of the initial kappa adjustable parameters are left for evaluation by means of a non-linear optimization procedure. The benefits of the present variant are both in economy of computation and in accuracy in determining the parameter values. The performance of the method is established under different circumstances. It is illustrated in the context of power-law rates, although this does not preclude its applicability
Fernando Bustos-Guadaño; José Luis Martín-Calderón; Juan José Criado-Álvarez; Raquel Muñoz-Jara; Adolfo Cantalejo-Gutiérrez; María Concepción Mena-Moreno
2017-01-01
Background: The evidence of glomerular filtration rate (GFR) estimating with serum creatinine based formulae in the elderly population is scarce. The purpose of this study is to compare CKD-EPI, MRD4-IDMS and BIS1 equations to analyze correlation and concordance in a population older than 85 years old. Patients and methods: We designed a retrospective cross-sectional study, which included data from 600 patients older than 85 years. GFR was estimated by the following equations: CKD-EPI, MDR...
Energy Technology Data Exchange (ETDEWEB)
Isselhardt, B. H.; Prussin, S. G.; Savina, M. R.; Willingham, D. G.; Knight, K. B.; Hutcheon, I. D.
2016-01-01
Resonance Ionization Mass Spectrometry (RIMS) has been developed as a method to measure uranium isotope abundances. In this approach, RIMS is used as an element-selective ionization process between uranium atoms and potential isobars without the aid of chemical purification and separation. The use of broad bandwidth lasers with automated feedback control of wavelength was applied to the measurement of the U-235/U-238 ratio to decrease laser-induced isotopic fractionation. In application, isotope standards are used to identify and correct bias in measured isotope ratios, but understanding laser-induced bias from first-principles can improve the precision and accuracy of experimental measurements. A rate equation model for predicting the relative ionization probability has been developed to study the effect of variations in laser parameters on the measured isotope ratio. The model uses atomic data and empirical descriptions of laser performance to estimate the laser-induced bias expected in experimental measurements of the U-235/U-238 ratio. Empirical corrections are also included to account for ionization processes that are difficult to calculate from first principles with the available atomic data. Development of this model has highlighted several important considerations for properly interpreting experimental results.
Directory of Open Access Journals (Sweden)
Gian Paolo Beretta
2008-08-01
Full Text Available A rate equation for a discrete probability distribution is discussed as a route to describe smooth relaxation towards the maximum entropy distribution compatible at all times with one or more linear constraints. The resulting dynamics follows the path of steepest entropy ascent compatible with the constraints. The rate equation is consistent with the Onsager theorem of reciprocity and the fluctuation-dissipation theorem. The mathematical formalism was originally developed to obtain a quantum theoretical unification of mechanics and thermodinamics. It is presented here in a general, non-quantal formulation as a part of an effort to develop tools for the phenomenological treatment of non-equilibrium problems with applications in engineering, biology, sociology, and economics. The rate equation is also extended to include the case of assigned time-dependences of the constraints and the entropy, such as for modeling non-equilibrium energy and entropy exchanges.
Valente, Mattia A. E.; Hillege, Hans L.; Navis, Gerjan; Voors, Adriaan A.; Dunselman, Peter H. J. M.; van Veldhuisen, Dirk J.; Damman, Kevin
Aims The Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) formula estimates glomerular filtration rate (GFR) better than the simplified Modification of Diet in Renal Disease (sMDRD) formula in numerous populations. It has not previously been validated in heart failure patients. Methods
Directory of Open Access Journals (Sweden)
Ahmed Attia
2012-01-01
Full Text Available We determined the performance of estimated glomerular filtration rate equations (eGFR including MDRD2-Isotope Dilution Mass Spectrometry (MDRD2-IDMS, Cockcroft-Gault (CG and Virga to measure post-transplant chronic kidney disease (CKD stages 1-4, using simultaneous isotope GFR (iGFR measurement. The study was conducted in 97 patients. The eGFR results measured by CG and Virga were normalized to 1.73 m 2 . Analysis of relative and absolute bias, error, scatter, correlation coefficient of variance and accuracy within the 30% range from the reference iGFR result was performed using standard techniques. There were 135, 242, 314 and 82 scans, respectively, in CKD stages 1-4. Bias and accuracy of GFR estimators varied significantly across the CKD stages. In stages 1 and 2, CG had the best error of -12.7 and 0.2 mL/min/1.73 m 2 , respectively, while Virga had the highest accuracy of 74.3% and 85.5, respectively. In stages 3 and 4, MDRD2-IDMS had the best error of -0.52 and 5.8, respectively. Accuracy was the best at 75.1% for Virga in stage 3, while it was the highest of 70.7% for MDRD2-IDMS in stage 4. Virga had the highest accuracy of 75.2% in stage 4. The worst bias was for MDRD2-IDMS in stage 2 (-36.8 mL/min/1.73 m 2 and the best bias was for CG in stage 2 (-0.33 mL/min/1.73 m 2 . The eGFR estimators have inconsistent performances in the various stages of CKD and, thus, another limitation is added to their validity to substitute for the gold standard methods.
Attia, Ahmed; Zahran, Ahmed; Shoker, Ahmed
2012-05-01
We determined the performance of estimated glomerular filtration rate equations (eGFR) including MDRD2-Isotope Dilution Mass Spectrometry (MDRD2-IDMS), Cockcroft-Gault (CG) and Virga to measure post-transplant chronic kidney disease (CKD) stages 1-4, using simultaneous isotope GFR (iGFR) measurement. The study was conducted in 97 patients. The eGFR results measured by CG and Virga were normalized to 1.73 m². Analysis of relative and absolute bias, error, scatter, correlation coefficient of variance and accuracy within the 30% range from the reference iGFR result was performed using standard techniques. There were 135, 242, 314 and 82 scans, respectively, in CKD stages 1-4. Bias and accuracy of GFR estimators varied significantly across the CKD stages. In stages 1 and 2, CG had the best error of -12.7 and 0.2 mL/min/1.73 m², respectively, while Virga had the highest accuracy of 74.3% and 85.5, respectively. In stages 3 and 4, MDRD2-IDMS had the best error of -0.52 and 5.8, respectively. Accuracy was the best at 75.1% for Virga in stage 3, while it was the highest of 70.7% for MDRD2-IDMS in stage 4. Virga had the highest accuracy of 75.2% in stage 4. The worst bias was for MDRD2-IDMS in stage 2 (-36.8 mL/min/1.73 m²) and the best bias was for CG in stage 2 (-0.33 mL/min/1.73 m²). The eGFR estimators have inconsistent performances in the various stages of CKD and, thus, another limitation is added to their validity to substitute for the gold standard methods.
National Research Council Canada - National Science Library
Rognant, Nicolas; Lemoine, Sandrine; Laville, Martine; Hadj-Aïssa, Aoumeur; Dubourg, Laurence
2011-01-01
...), and Chronic Kidney Disease Epidemiology (CKD-EPI) Collaboration equations in 246 diabetic patients by calculating the mean bias and the interquartile range (IQR) of the bias, 10% (P10) and 30% (P30...
Directory of Open Access Journals (Sweden)
Liu X
2013-10-01
Full Text Available Xun Liu,1,2,* Huijuan Ma,1,* Hui Huang,3 Cheng Wang,1 Hua Tang,1 Ming Li,1 Yanni Wang,1 Tanqi Lou1 1Division of Nephrology, Department of Internal Medicine, The Third Affiliated Hospital of Sun Yat-sen University, 2College of Biology Engineering, South China University of Technology, 3Department of Cardiology, Sun Yat-sen Memorial Hospital of Sun Yat-sen University, Guangzhou, People's Republic of China*These authors contributed equally to the paperBackground: We aimed to evaluate the performance of the Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI creatinine–cystatin C equation in a cohort of elderly Chinese participants.Materials and methods: Glomerular filtration rate (GFR was measured in 431 elderly Chinese participants by the technetium-99m diethylene-triamine-penta-acetic acid (99mTc-DTPA renal dynamic imaging method, and was calibrated equally to the dual plasma sample 99mTc-DTPA-GFR. Performance of the CKD-EPI creatinine–cystatin C equation was compared with the Cockroft–Gault equation, the re-expressed 4-variable Modification of Diet in Renal Disease (MDRD equation, and the CKD-EPI creatinine equation.Results: Although the bias of the CKD-EPI creatinine–cystatin C equation was greater than with the other equations (median difference, 5.7 mL/minute/1.73 m2 versus a range from 0.4–2.5 mL/minute/1.73 m2; P<0.001 for all, the precision was improved with the CKD-EPI creatinine–cystatin C equation (interquartile range for the difference, 19.5 mL/minute/1.73 m2 versus a range from 23.0–23.6 mL/minute/1.73 m2; P<0.001 for all comparisons, leading to slight improvement in accuracy (median absolute difference, 10.5 mL/minute/1.73 m2 versus 12.2 and 11.4 mL/minute/1.73 m2 for the Cockcroft–Gault equation and the re-expressed 4-variable MDRD equation, P=0.04 for both; 11.6 mL/minute/1.73 m2 for the CKD-EPI creatinine equation, P=0.11, as the optimal scores of performance (6.0 versus a range from 1.0–2.0 for the other
Energy Technology Data Exchange (ETDEWEB)
Winckler, N., E-mail: n.winckler@gsi.de [GSI Helmholtzzentrum für Schwerionenforschung GmbH, 64291 Darmstadt (Germany); Rybalchenko, A. [GSI Helmholtzzentrum für Schwerionenforschung GmbH, 64291 Darmstadt (Germany); Shevelko, V.P. [P.N. Lebedev Physical Institute, 119991 Moscow (Russian Federation); Al-Turany, M. [GSI Helmholtzzentrum für Schwerionenforschung GmbH, 64291 Darmstadt (Germany); CERN, European Organization for Nuclear Research, 1211 Geneve 23 (Switzerland); Kollegger, T. [GSI Helmholtzzentrum für Schwerionenforschung GmbH, 64291 Darmstadt (Germany); Stöhlker, Th. [GSI Helmholtzzentrum für Schwerionenforschung GmbH, 64291 Darmstadt (Germany); Helmholtz-Institute Jena, D-07743 Jena (Germany); Institut für Optik und Quantenelektronik, Friedrich-Schiller-Universität, D-07743 Jena (Germany)
2017-02-01
A detailed description of a recently developed BREIT computer code (Balance Rate Equations of Ion Transportation) for calculating charge-state fractions of ion beams passing through matter is presented. The code is based on the analytical solutions of the differential balance equations for the charge-state fractions as a function of the target thickness and can be used for calculating the ion evolutions in gaseous, solid and plasma targets. The BREIT code is available on-line and requires the charge-changing cross sections and initial conditions in the input file. The eigenvalue decomposition method, applied to obtain the analytical solutions of the rate equations, is described in the paper. Calculations of non-equilibrium and equilibrium charge-state fractions, performed by the BREIT code, are compared with experimental data and results of other codes for ion beams in gaseous and solid targets. Ability and limitations of the BREIT code are discussed in detail.
Winckler, N; Shevelko, V P; Al-Turany, M; Kollegger, T; Stöhlker, Th
2017-01-01
A detailed description of a recently developed BREIT computer code (Balance Rate Equations of Ion Transportation) for calculating charge-state fractions of ion beams passing through matter is presented. The code is based on the analytical solutions of the differential balance equations for the charge-state fractions as a function of the target thickness and can be used for calculating the ion evolutions in gaseous, solid and plasma targets. The BREIT code is available on-line and requires the charge-changing cross sections and initial conditions in the input file. The eigenvalue decomposition method, applied to obtain the analytical solutions of the rate equations, is described in the paper. Calculations of non-equilibrium and equilibrium charge-state fractions, performed by the BREIT code, are compared with experimental data and results of other codes for ion beams in gaseous and solid targets. Ability and limitations of the BREIT code are discussed in detail.
Directory of Open Access Journals (Sweden)
Luiz Lannes Loureiro
Full Text Available The accurate estimative of energy needs is crucial for an optimal physical performance among athletes and the basal metabolic rate (BMR equations often are not well adjusted for adolescent athletes requiring the use of specific methods, such as the golden standard indirect calorimetry (IC. Therefore, we had the aim to analyse the agreement between the BMR of adolescents pentathletes measured by IC and estimated by commonly used predictive equations.Twenty-eight athletes (17 males and 11 females were evaluated for BMR, using IC and the predictive equations Harris and Benedict (HB, Cunningham (CUN, Henry and Rees (HR and FAO/WHO/UNU (FAO. Body composition was obtained using DXA and sexual maturity data were retrieved through validated questionnaires. The correlations among anthropometric variables an IC were analysed by T-student test and ICC, while the agreement between IC and the predictive equations was analysed according to Bland and Altman and by survival-agreement plotting.The whole sample average BMR measured by IC was significantly different from the estimated by FAO (p<0.05. Adjusting data by gender FAO and HR equations were statistically different from IC (p <0.05 among males, while female differed only for the HR equation (p <0.05.The FAO equation underestimated athletes' BMR when compared with IC (T Test. When compared to the golden standard IC, using Bland and Altman, ICC and Survival-Agreement, the equations underestimated the energy needs of adolescent pentathlon athletes up to 300kcal/day. Therefore, they should be used with caution when estimating individual energy requirements in such populations.
Selistre, Luciano; Rabilloud, Muriel; Cochat, Pierre; de Souza, Vandréa; Iwaz, Jean; Lemoine, Sandrine; Beyerle, Françoise; Poli-de-Figueiredo, Carlos E; Dubourg, Laurence
2016-03-01
Estimating kidney glomerular filtration rate (GFR) is of utmost importance in many clinical conditions. However, very few studies have evaluated the performance of GFR estimating equations over all ages and degrees of kidney impairment. We evaluated the reliability of two major equations for GFR estimation, the CKD-EPI and Schwartz equations, with urinary clearance of inulin as gold standard. The study included 10,610 participants referred to the Renal and Metabolic Function Exploration Unit of Edouard Herriot Hospital (Lyon, France). GFR was measured by urinary inulin clearance (only first measurement kept for analysis) then estimated with isotope dilution mass spectrometry (IDMS)-traceable CKD-EPI and Schwartz equations. The participants' ages ranged from 3 to 90 y, and the measured GFRs from 3 to 160 ml/min/1.73 m2. A linear mixed-effects model was used to model the bias (mean ratio of estimated GFR to measured GFR). Equation reliability was also assessed using precision (interquartile range [IQR] of the ratio) and accuracy (percentage of estimated GFRs within the 10% [P10] and 30% [P30] limits above and below the measured GFR). In the whole sample, the mean ratio with the CKD-EPI equation was significantly higher than that with the Schwartz equation (1.17 [95% CI 1.16; 1.18] versus 1.08 [95% CI 1.07; 1.09], p Schwartz equation were closer to 1 than the mean ratios with the CKD-EPI equation whatever the age class (1.02 [95% CI 1.01; 1.03] versus 1.15 [95% CI 1.13; 1.16], p Schwartz equation had a better precision and was also more accurate than the CKD-EPI equation at GFR values under 60 ml/min/1.73 m2 (IQR: 0.32 [95% CI 0.28; 0.33] versus 0.40 [95% CI 0.36; 0.44]; P30: 81.4 [95% CI 78.1; 84.7] versus 63.8 [95% CI 59.7; 68.0]) and also at GFR values of 60-89 ml/min/1.73 m2. In all patients aged ≥65 y, the CKD-EPI equation performed better than the Schwartz equation (IQR: 0.33 [95% CI 0.31; 0.34] versus 0.40 [95% CI 0.38; 0.41]; P30: 77.6 [95% CI 75.7; 79
Directory of Open Access Journals (Sweden)
Luciano Selistre
2016-03-01
Full Text Available Estimating kidney glomerular filtration rate (GFR is of utmost importance in many clinical conditions. However, very few studies have evaluated the performance of GFR estimating equations over all ages and degrees of kidney impairment. We evaluated the reliability of two major equations for GFR estimation, the CKD-EPI and Schwartz equations, with urinary clearance of inulin as gold standard.The study included 10,610 participants referred to the Renal and Metabolic Function Exploration Unit of Edouard Herriot Hospital (Lyon, France. GFR was measured by urinary inulin clearance (only first measurement kept for analysis then estimated with isotope dilution mass spectrometry (IDMS-traceable CKD-EPI and Schwartz equations. The participants' ages ranged from 3 to 90 y, and the measured GFRs from 3 to 160 ml/min/1.73 m2. A linear mixed-effects model was used to model the bias (mean ratio of estimated GFR to measured GFR. Equation reliability was also assessed using precision (interquartile range [IQR] of the ratio and accuracy (percentage of estimated GFRs within the 10% [P10] and 30% [P30] limits above and below the measured GFR. In the whole sample, the mean ratio with the CKD-EPI equation was significantly higher than that with the Schwartz equation (1.17 [95% CI 1.16; 1.18] versus 1.08 [95% CI 1.07; 1.09], p < 0.001, t-test. At GFR values of 60-89 ml/min/1.73 m2, the mean ratios with the Schwartz equation were closer to 1 than the mean ratios with the CKD-EPI equation whatever the age class (1.02 [95% CI 1.01; 1.03] versus 1.15 [95% CI 1.13; 1.16], p < 0.001, t-test. In young adults (18-40 y, the Schwartz equation had a better precision and was also more accurate than the CKD-EPI equation at GFR values under 60 ml/min/1.73 m2 (IQR: 0.32 [95% CI 0.28; 0.33] versus 0.40 [95% CI 0.36; 0.44]; P30: 81.4 [95% CI 78.1; 84.7] versus 63.8 [95% CI 59.7; 68.0] and also at GFR values of 60-89 ml/min/1.73 m2. In all patients aged ≥65 y, the CKD-EPI equation
Chaurasia, Ramesh Kumar; Agrawal, Rajendra Kumar; Hada, Rajani; Chaurasia, Sweta Kumari; Gurung, Santosh; Basnet, Shakti
2013-01-01
Accurate determination of donor kidney function has important long-term implications for both donor health and recipient outcome. Many centers use 24 hour urinary creatinine clearance or creatinine-based GFR estimations to assess kidney function but their performance when compared with GFR measurements by isotope clearance remains inconclusive. We assessed the performance of creatinine based equations against DTPA GFR for evaluating Nepalese kidney donors. All kidney donors who had undergone both DTPA GFR estimation and 24 hour urine CrCl were included. The performance of the urine-CrCl, CG-CrCl, modiﬁed MDRD GFR against DTPA GFR was evaluated by analyzing global bias, precision (R2),Pearson correlation and accuracy percentage within 30% and 15%. The sensitivity and speciﬁcity of each predictive equation in selecting donor with GFR of ≥80 mL/min/1.73 m2 was also calculated. Of 51 donors analysed, only 18 (35.29%) were male. The mean measured GFR was 102.752±16.71 mL/min/1.73 m2. Of all prediction equations, urine-CrCL has most precision (R2=0.207) with the highest pearson correlation (0.455) and highest accuracy percentage within 30% and 15%. However, predictive performance was poor for all the equations. The urine CrCl had highest sensitivity of 100% for detecting donor with measured GFR>80 mL/min/1.73 m2 with positive predictive value of 92.1%. The performance of all equations was disappointing and even the best performing equation urine-CrCl was suboptimal for donor selection. So considering the potential risk of living kidney donation, other more accurate methods of GFR estimation should be used.
Chaiken, J; Goodisman, J; Kornilov, O
2015-07-09
The Smoluchowski equations provide a rigorous and efficient means for including multiple kinetic pathways when modeling coalescence growth systems. Originally written for a constant temperature and volume system, the equations must be modified if temperature and pressure vary during the coalescence time. In this paper, the equations are generalized, and adaptations appropriate to the situation presented by supersonic nozzle beam expansions are described. Given rate constants for all the cluster-cluster reactions, solution of the Smoluchowski equations would yield the abundances of clusters of all sizes at all times. This is unlikely, but we show that if these rate constants scale with the sizes of the reacting partners, the asymptotic (large size and large time) form of the cluster size distribution can be predicted. Experimentally determined distributions for He fit the predicted asymptotic distribution very well. Deviations between predicted and observed distributions allow identification of special cluster sizes that is, magic numbers. Furthermore, fitting an observed distribution to the theoretical form yields the base agglomeration cross section, from which all cluster-cluster rate constants may be obtained by scaling. Comparing the base cross section to measures of size and reactivity gives information about the coalescence process.
Directory of Open Access Journals (Sweden)
Byung Ha Chung
Full Text Available The aim of this study is to investigate the usefulness of the GFR-estimating equations to predict renal function in kidney donors before and after transplantation. We compared the performance of 24-hour-urine-based creatinine clearance (24 hr urine-CrCl, the Cockcroft-Gault formula (eGFRCG, the Modification of Diet in Renal Disease equation (eGFRMDRD, and the Chronic Kidney Disease Epidemiology Collaboration equation (eGFRCKD-EPI with technetium-diethylenetriaminepentaacetic acid ((99mTc-DTPA clearance (mGFR in 207 potential kidney donors and 108 uninephric donors. Before donation, eGFRCKD-EPI showed minimal bias and did not show a significant difference from mGFR (P = 0.65, respectively while 24 hr urine-CrCl and eGFRMDRD significantly underestimated mGFR (P<0.001 for each. Precision and accuracy was highest in eGFRCKD-EPI and this better performance was more dominant when renal function is higher than 90 mL·min(-1·1.73 m(-2. After kidney donation, eGFRMDRD was superior to other equations in precision and accuracy in contrast to before donation. Within individual analysis, eGFRMDRD showed better performance at post-donation compared to pre-donation, but eGFRCKD-EPI and eGFRCG showed inferior performance at post-donation. In conclusion, eGFRCKD-EPI showed better performance compared to other equations before donation. In a uninephric donor, however, eGFRMDRD is more appropriate for the estimation of renal function than eGFRCKD-EPI.
Deng, Yuzhong; Wong, Harvey; Graham, Richard A; Liu, Wenbin; Shen, Heuy-shin; Shi, Yao; Wang, Laixin; Meng, Min; Malhi, Vikram; Ding, Xiao; Dean, Brian
2011-07-15
A rapid equilibrium dialysis (RED) assay followed by a solid phase extraction (SPE) high-performance liquid chromatography tandem mass spectrometry (LC-MS/MS) assay for the quantitative determination of unbound vismodegib in human plasma was developed and validated. The equilibrium dialysis was carried out using 0.3 mL plasma samples in the single-use plate RED system at 37°C for 6h. The dialysis samples (0.1 mL) were extracted using a Strata-X-C 33u Polymeric Strong Cation SPE plate and the resulting extracts were analyzed using reverse-phase chromatography and positive electrospray ionization (ESI) mass spectrometry. The standard curve, which ranged from 0.100 to 100 ng/mL for vismodegib, was fitted to a 1/x(2) weighted linear regression model. The lower limit of quantitation (LLOQ, 0.100 ng/mL) was sufficient to quantify unbound concentrations of vismodegib after dialysis. The intra-assay precision of the LC-MS/MS assay, based on the four analytical QC levels (LLOQ, low, medium and high), was within 7.7% CV and inter-assay precision was within 5.5% CV. The assay accuracy, expressed as %Bias, was within ±4.0% of the nominal concentration values. Extraction recovery of vismodegib was between 77.9 and 84.0%. The assay provides a means for accurate assessment of unbound vismodegib plasma concentrations in clinical studies. Copyright © 2011 Elsevier B.V. All rights reserved.
Energy Technology Data Exchange (ETDEWEB)
Na, Kyung Hwan; Yun, Eun Sub; Park, Young Sheop [Korea Hydro and Nuclear Power Co., Daejeon (Korea, Republic of)
2009-10-15
Nickel-based austenitic alloys such as Alloy 600 and the weld metals Alloy 82, and 182 have been employed extensively in nuclear power plants (NPPs) in Korea. During the construction of NPPs, it was widely believed that these alloys have high corrosion resistance as well as good mechanical properties. However, since the 2000s, the occurrence of primary water stress corrosion cracking (PWSCC) has been reported in conjunction with these alloys in oversea NPPs and this has received international attention due to its potential effect on the structural integrity of piping in reactor coolant system. Under these circumstances, PWSCC growth rate studies of Alloy 600/82/182 have become important issues, and many studies have been carried out as a result. The Electric Power Research Institute (EPRI) in the United States proposed two crack growth rate (CGR) equations for PWSCC in its MRP-21, and MRP-115 reports. On the other hand, the Nuclear Regulatory Commission (NRC) recommended one equation for this purpose. In the present work, one instance of the initiation of an imaginary crack was assumed to exist at the inner surface of a surge nozzle weld on the hot leg side first. Subsequently, the CGRs were estimated for this initiated crack according to the MRP-21, MRP-115, and NRC equations. Finally, a comparison of the equations was made through their CGR results mainly in terms of their degree of conservatisms.
Chevalier, Michael W; El-Samad, Hana
2014-12-07
Noise and stochasticity are fundamental to biology and derive from the very nature of biochemical reactions where thermal motion of molecules translates into randomness in the sequence and timing of reactions. This randomness leads to cell-to-cell variability even in clonal populations. Stochastic biochemical networks have been traditionally modeled as continuous-time discrete-state Markov processes whose probability density functions evolve according to a chemical master equation (CME). In diffusion reaction systems on membranes, the Markov formalism, which assumes constant reaction propensities is not directly appropriate. This is because the instantaneous propensity for a diffusion reaction to occur depends on the creation times of the molecules involved. In this work, we develop a chemical master equation for systems of this type. While this new CME is computationally intractable, we make rational dimensional reductions to form an approximate equation, whose moments are also derived and are shown to yield efficient, accurate results. This new framework forms a more general approach than the Markov CME and expands upon the realm of possible stochastic biochemical systems that can be efficiently modeled.
Omuse, Geoffrey; Maina, Daniel; Mwangi, Jane; Wambua, Caroline; Kanyua, Alice; Kagotho, Elizabeth; Amayo, Angela; Ojwang, Peter; Erasmus, Rajiv
2017-12-20
Several equations have been developed to estimate glomerular filtration rate (eGFR). The common equations used were derived from populations predominantly comprised of Caucasians with chronic kidney disease (CKD). Some of the equations provide a correction factor for African-Americans due to their relatively increased muscle mass and this has been extrapolated to black Africans. Studies carried out in Africa in patients with CKD suggest that using this correction factor for the black African race may not be appropriate. However, these studies were not carried out in healthy individuals and as such the extrapolation of the findings to an asymptomatic black African population is questionable. We sought to compare the proportion of asymptomatic black Africans reported as having reduced eGFR using various eGFR equations. We further compared the association between known risk factors for CKD with eGFR determined using the different equations. We used participant and laboratory data collected as part of a global reference interval study conducted by the Committee of Reference Intervals and Decision Limits (C-RIDL) under the International Federation of Clinical Chemistry (IFCC). Serum creatinine values were used to calculate eGFR using the Cockcroft-Gault (CG), re-expressed 4 variable modified diet in renal disease (4v-MDRD), full age spectrum (FAS) and chronic kidney disease epidemiology collaboration equations (CKD-EPI). CKD classification based on eGFR was determined for every participant. A total of 533 participants were included comprising 273 (51.2%) females. The 4v-MDRD equation without correction for race classified the least number of participants (61.7%) as having an eGFR equivalent to CKD stage G1 compared to 93.6% for CKD-EPI with correction for race. Only age had a statistically significant linear association with eGFR across all equations after performing multiple regression analysis. The multiple correlation coefficients for CKD risk factors were higher for
Pulkkinen, O
2016-01-01
Many chemical reactions in biological cells occur at very low concentrations of constituent molecules. Thus, transcriptional gene-regulation is often controlled by poorly expressed transcription-factors, such as E.coli lac repressor with few tens of copies. Here we study the effects of inherent concentration fluctuations of substrate-molecules on the seminal Michaelis-Menten scheme of biochemical reactions. We present a universal correction to the Michaelis-Menten equation for the reaction-rates. The relevance and validity of this correction for enzymatic reactions and intracellular gene-regulation is demonstrated. Our analytical theory and simulation results confirm that the proposed variance-corrected Michaelis-Menten equation predicts the rate of reactions with remarkable accuracy even in the presence of large non-equilibrium concentration fluctuations. The major advantage of our approach is that it involves only the mean and variance of the substrate-molecule concentration. Our theory is therefore accessi...
Karimzadeh, Iman; Khalili, Hossein
2016-06-06
Serum cystatin C (Cys C) has a number of advantages over serum creatinine in the evaluation of kidney function. Apart from Cys C level itself, several formulas have also been introduced in different clinical settings for the estimation of glomerular filtration rate (GFR) based upon serum Cys C level. The aim of the present study was to compare a serum Cys C-based equation with Cockcroft-Gault serum creatinine-based formula, both used in the calculation of GFR, in patients receiving amphotericin B. Fifty four adult patients with no history of acute or chronic kidney injury having been planned to receive conventional amphotericin B for an anticipated duration of at least 1 week for any indication were recruited. At three time points during amphotericin B treatment, including days 0, 7, and 14, serum cystatin C as well as creatinine levels were measured. GFR at the above time points was estimated by both creatinine (Cockcroft-Gault) and serum Cys C based equations. There was significant correlation between creatinine-based and Cys C-based GFR values at days 0 (R = 0.606, P = 0.001) and 7 (R = 0.714, P formula at least at the early time period of treatment with amphotericin B. Graphical abstract Comparison between a serum creatinine-and a cystatin C-based glomerular filtration rate equation in patients receiving amphotericin B.
Yao, Chung-Tay; Lai, Ching-Long; Hsieh, Hsiu-Shan; Chi, Chin-Wen; Yin, Shih-Jiun
2010-09-01
Alcohol dehydrogenase (ADH) catalyzes oxidation of ingested ethanol to acetaldehyde, the first step in hepatic metabolism. The purpose of this study was to establish an ex vivo rat liver perfusion system under defined and verified steady states with respect to the metabolites and the metabolic rates, and to quantitatively correlate the observed rates with simulations based on the kinetic mechanism-based rate equations of rat liver ADH. Class I ADH1 was isolated from male Sprague-Dawley rats and characterized by steady-state kinetics in the Krebs-Ringer perfusion buffer with supplements. Nonrecirculating liver perfusion with constant input of ethanol at near physiological hepatic blood flow rate was performed in situ. Ethanol and the related metabolites acetaldehyde, acetate, lactate, and pyruvate in perfusates were determined. Results of the initial velocity, product, and dead-end inhibition studies showed that rat ADH1 conformed to the Theorell-Chance Ordered Bi Bi mechanism. Steady-state metabolism of ethanol in the perfused liver maintained up to 3h as evidenced by the steady-state levels of ethanol and metabolites in the effluent, and the steady-state ethanol disappearance rates and acetate production rates. The changes of the metabolic rates were qualitatively and in general quantitatively correlated to the results from simulations with the kinetic rate equations of ADH1 under a wide range of ethanol, in the presence of competitive inhibitor 4-methylpyrazole and of uncompetitive inhibitor isobutyramide. Preliminary flux control analysis estimated that apparent C(ADH)(J) in the perfused liver may approximate 0.7 at constant infusion with 1-2 mM ethanol, suggesting that ADH plays a major but not the exclusive role in governing hepatic ethanol metabolism. The reported steady-state rat liver perfusion system may potentially be applicable to other drug or drug-ethanol interaction studies. Copyright © 2010 Elsevier Inc. All rights reserved.
Kuster, Nils; Cristol, Jean-Paul; Cavalier, Etienne; Bargnoux, Anne-Sophie; Halimi, Jean-Michel; Froissart, Marc; Piéroni, Laurence; Delanaye, Pierre
2014-01-20
The National Kidney Disease Education Program group demonstrated that MDRD equation is sensitive to creatinine measurement error, particularly at higher glomerular filtration rates. Thus, MDRD-based eGFR above 60 mL/min/1.73 m² should not be reported numerically. However, little is known about the impact of analytical error on CKD-EPI-based estimates. This study aimed at assessing the impact of analytical characteristics (bias and imprecision) of 12 enzymatic and 4 compensated Jaffe previously characterized creatinine assays on MDRD and CKD-EPI eGFR. In a simulation study, the impact of analytical error was assessed on a hospital population of 24084 patients. Ability using each assay to correctly classify patients according to chronic kidney disease (CKD) stages was evaluated. For eGFR between 60 and 90 mL/min/1.73 m², both equations were sensitive to analytical error. Compensated Jaffe assays displayed high bias in this range and led to poorer sensitivity/specificity for classification according to CKD stages than enzymatic assays. As compared to MDRD equation, CKD-EPI equation decreases impact of analytical error in creatinine measurement above 90 mL/min/1.73 m². Compensated Jaffe creatinine assays lead to important errors in eGFR and should be avoided. Accurate enzymatic assays allow estimation of eGFR until 90 mL/min/1.73 m² with MDRD and 120 mL/min/1.73 m² with CKD-EPI equation. Copyright © 2013 Elsevier B.V. All rights reserved.
Directory of Open Access Journals (Sweden)
Amrah Javaid
2015-01-01
Full Text Available To compare the measured glomerular filtration rate (rGFR using [99mTc] diethylene triamine pentacetic acid (DTPA clearance or estimated GFR (eGFR by the Modification of Diet in Renal Disease (MDRD equation in cancer patients with raised serum creatinine level, we studied 100 cancer patients; 50 patients with normal serum creatinine (control group and 50 patients with abnormal serum creatinine (study group. History of patients, including site of cancer, chemotherapy regime and dose of chemotherapy, was recorded. The rGFR and eGFR were increased in the study group as compared with the control group, but the GFR recorded by the MDRD formula or DTPA revealed similar values. It is therefore concluded that the MDRD equation may be recommended for eGFR estimation even with abnormal creatinine, without the need for exposure to radiation.
Cabrerizo-García, José Luis; Díez-Manglano, Jesús; García-Arilla, Ernesto; Revillo-Pinilla, Paz; Ramón-Puertas, José; Sebastián-Royo, Mariano
2015-01-06
The Modification of Diet in Renal Disease (MDRD) equation is recommended by most scientific societies to calculate the estimated glomerular filtration rate (GFR). Recently the group Chronic Kidney Disease Epidemiology Collaboration (CKP-EPI) has published a new, more precise and accurate equation. We have analyzed its behavior in a group of polypathological patients (PP) and compared it with the classic MDRD-4.version Multicenter, observational, descriptive and transversal study. We calculated GFR by MDRD-4 and CKD-EPI in 425 PP. Each stage was assigned according to the GFR: 1:>90; 2: 60-89; 3: 30-59; 4: 15-29; and 5 renal insufficiency, especially in older women. Copyright © 2013 Elsevier España, S.L.U. All rights reserved.
Directory of Open Access Journals (Sweden)
Jia-fu Feng
Full Text Available OBJECTIVE: To establish equations for the estimation of glomerular filtration rates (eGFRs based on serum creatinine (SCr and/or serum cystatin C (SCysC in Chinese patients with chronic kidney disease (CKD, and to compare the new equations with both the reference GFR (rGFR and the literature equations to evaluate their applicability. METHODS: The 788 Chinese CKD patients were randomly divided into two groups, the training group and the testing group, to establish new eGFR-formulas based on serum CysC and to validate the established formulas, respectively. (99mTc-DTPA clearance (as the rGFR, serum Cr, and serum CysC were determined for all patients, and GFR was calculated using the Cockcroft-Gault equation (eGFR1, the MDRD formula (eGFR2, the CKD-EPI formulas (eGFR3, eGFR4, and the Chinese eGFR Investigation Collaboration formulas (eGFR5, eGFR6. The accuracy of each eGFR was compared with the rGFR. RESULTS: The training and testing groups' mean GFRs were 50.84±31.36 mL/min/1.73 m(2 and 54.16±29.45 mL/min/1.73 m(2, respectively. The two newly developed eGFR formulas were fitted using iterative computation: [Formula: see text] and [Formula: see text]. Significant correlation was observed between each eGFR and the rGFR. However, proportional errors and constant errors were observed between rGFR and eGFR1, eGFR2, eGFR4, eGFR5 or eGFR6, and constant errors were observed between eGFR3 and rGFR, as revealed by the Passing & Bablok plot analysis. The Bland-Altman analysis illustrated that the 95% limits of agreement of all equations exceeded the previously accepted limits of <60 mL/min •1.73 m(2, except the equations of eGFR7 and eGFR8. CONCLUSION: The newly developed formulas, eGFR7 and eGFR8, provide precise and accurate GFR estimation using serum CysC detection alone or in combination with serum Cr detection. Differences in detection methods should be carefully considered when choosing literature eGFR equations to avoid misdiagnosis and
Al-Wakeel, Jamal Saleh
2016-01-01
Predictive equations for estimating glomerular filtration rate (GFR) in different clinical conditions should be validated by comparing with the measurement of GFR using inulin clearance, a highly accurate measure of GFR. Our aim was to validate the Chronic Kidney Disease-Epidemiology Collaboration (CKD-EPI) and Modification of Diet in Renal Disease (MDRD) equations by comparing it to the GFR measured using inulin clearance in chronic kidney disease (CKD) patients. Cross-sectional study performed in adult Saudi patients with CKD. King Saud University Affiliated Hospital, Riyadh, Saudi Arabia in 2014. We compared GFR measured by inulin clearance with the estimated GFR calculated using CKD-EPI and MDRD predictive formulas. Correlation, bias, precision and accuracy between the estimated GFR and inulin clearance. Comparisons were made in 31 participants (23 CKD and 8 transplanted), including 19 males (mean age 42.2 [15] years and weight 68.7 [18] kg). GFR using inulin was 51.54 (33.8) mL/min/1.73 m2 in comparison to inulin clearance, the GFR by the predictive equations was: CKD-EPI creatinine 52.6 (34.4) mL/ min/1.73 m2 (P=.490), CKD-EPI cystatin C 41.39 (30.30) mL/min/1.73 m2 (P=.002), CKD creatinine-cystatin C 45.03 (30.9) mL/min/1.73 m2 (P=.004) and MDRD GFR 48.35 (31.5) mL/min/1.73 m2 (P=.028) (statistical comparisons vs inulin). Bland-Altman plots demonstrated that GFR estimated by the CKD-EPI creatinine was the most accurate compared with inulin clearance, having a mean difference (estimated bias) and limits of agreement of -1.1 (15.6,-17.7). By comparison the mean differences for predictive equations were: CKD-EPI cystatin C 10.2 (43.7,-23.4), CKD creatinine-cystatin C 6.5 (29.3,-16.3) and MDRD 3.2 (18.3,-11.9). except for CKD-EPI creatinine, all of the equations underestimated GFR in comparison with inulin clearance. When compared with inulin clearance, the CKD-EPI creatinine equation is the most accurate, precise and least biased equation for estimation of GFR
Pratt, D. T.; Radhakrishnan, K.
1986-01-01
The design of a very fast, automatic black-box code for homogeneous, gas-phase chemical kinetics problems requires an understanding of the physical and numerical sources of computational inefficiency. Some major sources reviewed in this report are stiffness of the governing ordinary differential equations (ODE's) and its detection, choice of appropriate method (i.e., integration algorithm plus step-size control strategy), nonphysical initial conditions, and too frequent evaluation of thermochemical and kinetic properties. Specific techniques are recommended (and some advised against) for improving or overcoming the identified problem areas. It is argued that, because reactive species increase exponentially with time during induction, and all species exhibit asymptotic, exponential decay with time during equilibration, exponential-fitted integration algorithms are inherently more accurate for kinetics modeling than classical, polynomial-interpolant methods for the same computational work. But current codes using the exponential-fitted method lack the sophisticated stepsize-control logic of existing black-box ODE solver codes, such as EPISODE and LSODE. The ultimate chemical kinetics code does not exist yet, but the general characteristics of such a code are becoming apparent.
DEFF Research Database (Denmark)
In this presentation we consider a new method first introduced by Kristensen et al. [1] to improve the model for bacterial growth. Traditionally the substrate dependent growth rate μ(S) is modeled using the Monod expression, however it fails to describe the growth of bacteria in rich media. For P...... contains two state variables, the bacterial and substrate densities. To improve the growth model we initially allow the growth rate μ(S) to vary as a random walk, i.e. we reformulate the SDE model to include μ(S) as an extra state variable which change is described by the Wiener process. We use data from....... aeruginosa we observe a growth pattern far from Monod growth. Therefore a reformulation of the growth expression is necessary. Without any pre-knowledge about the functional dependence between the growth rate and the substrate content and with only limited experimental resources necessary, the proposed...
Pulkkinen, Otto; Metzler, Ralf
2015-12-01
Many chemical reactions in biological cells occur at very low concentrations of constituent molecules. Thus, transcriptional gene-regulation is often controlled by poorly expressed transcription-factors, such as E.coli lac repressor with few tens of copies. Here we study the effects of inherent concentration fluctuations of substrate-molecules on the seminal Michaelis-Menten scheme of biochemical reactions. We present a universal correction to the Michaelis-Menten equation for the reaction-rates. The relevance and validity of this correction for enzymatic reactions and intracellular gene-regulation is demonstrated. Our analytical theory and simulation results confirm that the proposed variance-corrected Michaelis-Menten equation predicts the rate of reactions with remarkable accuracy even in the presence of large non-equilibrium concentration fluctuations. The major advantage of our approach is that it involves only the mean and variance of the substrate-molecule concentration. Our theory is therefore accessible to experiments and not specific to the exact source of the concentration fluctuations.
Osipov, Vladimir Al.; Pullerits, Tõnu
2017-10-01
Application of the phase-modulated pulsed light for advance spectroscopic measurements is the area of growing interest. The phase modulation of the light causes modulation of the signal. Separation of the spectral components of the modulations allows to distinguish the contributions of various interaction pathways. The lasers with high repetition rate used in such experiments can lead to appearance of the accumulation effects, which become especially pronounced in systems with long-living excited states. Recently it was shown that such accumulation effects can be used to evaluate parameters of the dynamical processes in the material. In this work we demonstrate that the accumulation effects are also important in the quantum characteristics measurements provided by modulation spectroscopy. In particular, we consider a model of quantum two-level system driven by a train of phase-modulated light pulses, organized in analogy with the two-dimensional spectroscopy experiments. We evaluate the harmonics' amplitudes in the fluorescent signal and calculate corrections appearing from the accumulation effects. We show that the corrections can be significant and have to be taken into account at analysis of experimental data.
Bar-Sela, Gil; Kaidar-Person, Orit; Mari, Fadi; Assady, Suheir; Haim, Nissim
2012-11-01
The aim of this study was to evaluate the reliability of the Cockroft and Gault (CG) equation for glomerular filtration rate (GFR) estimation in carboplatin dosing based on the Calvert formula. The records of 117 patients with advanced non-small cell lung carcinoma treated with carboplatin were retrospectively analyzed. Theoretical carboplatin doses derived from the Calvert formula using the CG equation were calculated for each chemotherapy cycle. Fluctuations in the theoretical carboplatin doses were analyzed, and discrepancies between actual carboplatin doses prescribed by the physician and theoretical doses were assessed. It was found that, compared with the first-cycle dose, subsequent theoretical doses were more than 10% higher in 79/320 cycles (24.7%) and more than 10% lower in 53/320 cycles (16.6%; P=0.015). A body mass index greater than or equal to 30 was associated with a tendency for increased CG-estimated GFR during subsequent chemotherapy cycles (P=0.009). Physicians tended to lower the prescribed dose (32.2% of the cycles) by using a higher serum creatinine (Scr) level for dose calculation than was actually measured. We concluded that Calvert formula-derived carboplatin doses fluctuate widely during repeated cycles when actual Scr is used for CG-estimated GFR. The measurement of 24-h creatinine clearance is advised as an alternative in selected patients with reduction in serum creatinine observed during treatments.
Blitz, M A; Green, N J B; Shannon, R J; Pilling, M J; Seakins, P W; Western, C M; Robertson, S H
2015-07-16
Rate coefficients for the CH3 + CH3 reaction, over the temperature range 300-900 K, have been corrected for errors in the absorption coefficients used in the original publication ( Slagle et al., J. Phys. Chem. 1988 , 92 , 2455 - 2462 ). These corrections necessitated the development of a detailed model of the B̃(2)A1' (3s)-X̃(2)A2″ transition in CH3 and its validation against both low temperature and high temperature experimental absorption cross sections. A master equation (ME) model was developed, using a local linearization of the second-order decay, which allows the use of standard matrix diagonalization methods for the determination of the rate coefficients for CH3 + CH3. The ME model utilized inverse Laplace transformation to link the microcanonical rate constants for dissociation of C2H6 to the limiting high pressure rate coefficient for association, k∞(T); it was used to fit the experimental rate coefficients using the Levenberg-Marquardt algorithm to minimize χ(2) calculated from the differences between experimental and calculated rate coefficients. Parameters for both k∞(T) and for energy transfer ⟨ΔE⟩down(T) were varied and optimized in the fitting procedure. A wide range of experimental data were fitted, covering the temperature range 300-2000 K. A high pressure limit of k∞(T) = 5.76 × 10(-11)(T/298 K)(-0.34) cm(3) molecule(-1) s(-1) was obtained, which agrees well with the best available theoretical expression.
Bustos-Guadaño, Fernando; Martín-Calderón, José Luis; Criado-Álvarez, Juan José; Muñoz-Jara, Raquel; Cantalejo-Gutiérrez, Adolfo; Mena-Moreno, María Concepción
The evidence of glomerular filtration rate (GFR) estimating with serum creatinine based formulae in the elderly population is scarce. The purpose of this study is to compare CKD-EPI, MRD4-IDMS and BIS1 equations to analyse correlation and concordance in a population older than 85 years old. We designed a retrospective cross-sectional study, which included data from 600 patients older than 85 years. GFR was estimated by the following equations: CKD-EPI, MDR4-IDMS and BIS1, using as variables sex, age and serum creatinine concentration. Statistics analysis included Wilcoxon test, Bland-Altman plot, non-parametric Passing-Bablok method and kappa statistic (simple and weighted). The patients' median (range) age was 87 (interval 85-98). The median GFR (range) was 42.4 (5.2-127.4) mL/min/1.73 m2, when it was estimated with MDRD-IDMS, 40.0 (4.5-93.1) for CKD-EPI and 36.9 (7.6-83.7) for BIS1. The comparison of BIS1 and CKD-EPI and MDRD-IDMS using the Wilcoxon test was significant (PIDMS= 1,025×CKD-EPI+1.360; BIS1= 0.688×CKD-EPI+9.074 and BIS1= 0.666×MDRD-IDMS+8.401. The weighted coefficient was 0.958 for the concordance between MDRD-IDMS and CKD-EPI, 0.812 for the concordance between MDRD-IDMS and BIS1 and 0.846 for CKD-EPI and BIS1. The GFR estimations obtained with BS1 equation are not interchangeable with MDRD-IDMS or CKD-EPI equations. BIS1 estimates lower GFR values than MDRD-IDMS and CKD-EPI and tends to classify the patients in a more advanced chronic kidney disease stage, especially for estimated GFR higher than 29mL/min/1.73 m2. Copyright © 2016 Sociedad Española de Nefrología. Published by Elsevier España, S.L.U. All rights reserved.
Weil, Joyce; Hutchinson, Susan R; Traxler, Karen
2014-11-01
Data from the Women's Health and Aging Study were used to test a model of factors explaining depressive symptomology. The primary purpose of the study was to explore the association between performance-based measures of functional ability and depression and to examine the role of self-rated physical difficulties and perceived instrumental support in mediating the relationship between performance-based functioning and depression. The inclusion of performance-based measures allows for the testing of functional ability as a clinical precursor to disability and depression: a critical, but rarely examined, association in the disablement process. Structural equation modeling supported the overall fit of the model and found an indirect relationship between performance-based functioning and depression, with perceived physical difficulties serving as a significant mediator. Our results highlight the complementary nature of performance-based and self-rated measures and the importance of including perception of self-rated physical difficulties when examining depression in older persons. © The Author(s) 2014.
Singh, Tajinder P; Givertz, Michael M; Gauvreau, Kimberlee
2014-11-15
A new equation for estimating glomerular filtration rate (GFR)-the Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) equation-is better at predicting outcomes in the general population than the Modification of Diet in Renal Disease (MDRD) equation. We compared risk stratification of heart transplant (HT) recipients for early post-HT mortality using estimated GFR from the MDRD and the CKD-EPI equations. We identified all patients 18 years or older who underwent their first HT in the United States between January 2007 and October 2010 (n=6,564). We compared risk stratification for posttransplant in-hospital mortality by GFR estimated by the CKD-EPI equation versus that estimated by the MDRD equation. Posttransplant in-hospital mortality was 4.6%. Lower GFR (mL/min/1.73 m2, MDRD) was associated with higher in-hospital mortality in adjusted analysis (GFR, 60-89; odds ratio [OR], 1.5; 95% confidence interval [CI], 1.0-2.3; GFR, 30-59; OR, 2.2; 95% CI, 1.4-3.3; GFR<30; OR, 3.3; 95% CI, 1.8-6.1; vs. GFR ≥ 90). Glomerular filtration rate estimated using the CKD-EPI equation reclassified 10%, 15%, and 18% of patients, respectively, in GFR categories lower than 30, 30-59, and 60-89 to the next higher GFR category. Using the CKD-EPI equation was not associated with a significant net reclassification improvement for mortality risk in the overall cohort or in GFR subgroups. The risk models of in-hospital mortality developed using the two GFR equations performed similarly for discrimination and calibration. Estimated GFR using the CKD-EPI equation is comparable to estimated GFR using the MDRD equation in risk stratification of HT recipients for early posttransplant mortality.
Magnus, Wilhelm
1979-01-01
The hundreds of applications of Hill's equation in engineering and physics range from mechanics and astronomy to electric circuits, electric conductivity of metals, and the theory of the cyclotron. New applications are continually being discovered and theoretical advances made since Liapounoff established the equation's fundamental importance for stability problems in 1907. Brief but thorough, this volume offers engineers and mathematicians a complete orientation to the subject.""Hill's equation"" connotes the class of homogeneous, linear, second order differential equations with real, period
Schwandt, Anke; Denkinger, Michael; Fasching, Peter; Pfeifer, Martin; Wagner, Christian; Weiland, Jörg; Zeyfang, Andrej; Holl, Reinhard W
2017-09-01
To analyze the performance of Modification of Diet in Renal Disease (MDRD), Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI), Cockcroft-Gault (CG), and CG calculated with ideal bodyweight (CG-IBW) equations to estimate glomerular filtration rate (eGFR) based on serum creatinine in a large diabetic population. 24,516 adults with type-1-diabetes or type-2-diabetes from the multicenter diabetes prospective follow-up registry DPV were analyzed. We compared eGFR and measured GFR (mGFR) based on 24-h urine collection by calculating mean bias (difference), precision (SD of this difference), accuracy (proportion of eGFR within ±10% of mGFR), Bland-Altman-plots. CG overestimates, whereas MDRD, CKD-EPI, and CG-IBW underestimate. Smallest mean bias and highest accuracy (75.3%) were observed for MDRD compared to the other equations (pEPI estimated most accurately in stages 1 (MDRD:57.7%, CKD-EPI:57.3%) and 2 (MDRD:80.2%, CKD-EPI:80.7%). In stages 3 to 5, highest accuracy was observed for the MDRD (stage 3:82.3%, stage 4:77.8%, stage 5:71.0%). Among younger subjects, accuracy was higher using the CKD-EPI (18-<40years:63.7%, 40-<60years:72.8%). Above age 60years, MDRD estimated most accurately (60-<70years:77.3%, ≥70years:78.8%). In males and females, MDRD estimated most accurately (males:75.3%, females:75.3%). In this large diabetic cohort, smallest bias and highest accuracy were observed for the MDRD. Copyright © 2017 Elsevier Inc. All rights reserved.
David-Neto, Elias; Triboni, Ana Heloisa Kamada; Ramos, Fernanda; Agena, Fabiana; Galante, Nelson Zocoler; Altona, Marcelo; Lemos, Francine Brambate Carvalhinho; Sapienza, Marcelo Tatit; Nahas, William Carlos
2016-12-01
Equations to estimate glomerular filtration rate (eGFR) were developed in patients using the variables age, body weight, and serum creatinine, which may be different in the elderly. Elderly renal transplant patients (EG; n=70; mean age 65 ± 4 y) who measured plasma (51) Cr-EDTA-Clearance (mGFR) had mGFR compared to eGFR obtained by the Cockcroft-Gault corrected by body surface area (CG-BSA), the modification of diet in renal disease (MDRD-4), the Berlin Initiative Study (BIS-1), and the chronic kidney disease epidemiology collaboration (CKD-EPI). Results were validated using a cohort of 43, of the 70 elderly recipients, who performed a second (51) Cr-EDTA-Clearance. Mean mGFR was 47 ± 16 mL/min/1.73 m(2) and statistically lower than eGFR by MDRD (52 ± 19, P=.001) and BIS-1 (51 ± 13, P=.007) but not different from the CG-BSA (47 ± 15) and CKD-EPI (49 ± 18). The CKD-EPI and CG-BSA presented the lowest bias but only CKD-EPI also showed the highest 30% and 10% accuracy. The same findings were repeated in the validation set. For a cohort of elderly recipients ≥65 years (n=35, 68 ± 3y), the CKD-EPI performed better with the lowest bias (0 ± 12 mL/min/1.73 m(2) ) and best 30% and 10% accuracy. The CKD-EPI equation is a valuable tool to monitor GFR in the elderly RTx recipients. © 2016 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd.
Lu, Benzhuo; Zhou, Y C
2011-05-18
The effects of finite particle size on electrostatics, density profiles, and diffusion have been a long existing topic in the study of ionic solution. The previous size-modified Poisson-Boltzmann and Poisson-Nernst-Planck models are revisited in this article. In contrast to many previous works that can only treat particle species with a single uniform size or two sizes, we generalize the Borukhov model to obtain a size-modified Poisson-Nernst-Planck (SMPNP) model that is able to treat nonuniform particle sizes. The numerical tractability of the model is demonstrated as well. The main contributions of this study are as follows. 1), We show that an (arbitrarily) size-modified PB model is indeed implied by the SMPNP equations under certain boundary/interface conditions, and can be reproduced through numerical solutions of the SMPNP. 2), The size effects in the SMPNP effectively reduce the densities of highly concentrated counterions around the biomolecule. 3), The SMPNP is applied to the diffusion-reaction process for the first time, to our knowledge. In the case of low substrate density near the enzyme reactive site, it is observed that the rate coefficients predicted by SMPNP model are considerably larger than those by the PNP model, suggesting both ions and substrates are subject to finite size effects. 4), An accurate finite element method and a convergent Gummel iteration are developed for the numerical solution of the completely coupled nonlinear system of SMPNP equations. Copyright © 2011 Biophysical Society. Published by Elsevier Inc. All rights reserved.
Rhee, Jiyoung; Kwon, Jung Mi; Han, Sang Hoon; Kim, Sun Hyung; Park, Chang Hyun; Jeon, Ji Hyeon; Cho, Jong Tae; Lee, Eun Kyoung; Kim, So Mi
2017-12-01
Although the Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) equation has been recommended for accurate estimates of glomerular filtration rate (eGFR), there is little information regarding differences in GFR estimates obtained using the Cockcroft-Gault (CG) or Modification of Diet in Renal Disease (MDRD) equations in East Asian cancer patients. We investigated discrepancies in GFR and toxicities in patients treated with cisplatin-based chemotherapy using three equations equations. A total of 229 patients were retrospectively recruited. We calculated eGFR using the three equations and separated patients into three categories based on GFR 50 (group C) mL/min/1.73m 2 . We analyzed chemotherapy toxicities. The mean eGFR calculated using the CG was the lowest of the values derived using the three equations. Estimates using the MDRD and CKD-EPI equations resulted in reclassifying 32 (71.1%) and 33 (73.3%) of 45 patients, originally placed in group B using the CG into group C. However, only 1 (7.7%) of 13 patients placed in group B using the MDRD were reclassified into group C using the CKD-EPI. Twenty-eight of 45 patients classified into group B using the CG equation were treated with reduced doses of cisplatin. However, these patients did not show significant differences in toxicities compared with other patients taking full doses of cisplatin. The CG equations underestimated GFR compared to the MDRD and CKD-EPI equations. Therefore, when GFR is estimated using CG equations, East Asian cancer patients may receive insufficient doses of chemotherapeutic agents, including cisplatin.
Goharrizi, A. Zandi; Alahyarizadeh, Gh.
2016-08-01
The use of semiconductor lasers is beneficial in long-distance communications. Practical communication systems based on these lasers need high ambient temperature, with temperature changes between 40∘C and 85∘C. The study of the temperature-dependent response of these lasers is important to improve them. This study investigates the effect of temperature on InGaN-based vertical cavity surface emitting lasers (VCSEL). The active region in this structure includes a single quantum well (SQW). The rate equations of carriers and densities are numerically solved. The time variations of carrier density, photon density and output power (N, S and P) at 25∘C and the current injection of 0.04 A are obtained. Values obtained for threshold current and output power include 7 mA and 44 mW, respectively. The effect of temperature on the time variations of N, S and P from 10∘C to 35∘C is studied. Results show that these parameters decrease and the threshold current increases with an increase in temperature. Furthermore, the investigation of the effect of injection current on N, S and P shows that raising the injection current can increase these parameters. Moreover, an increase in the injection current reduces the time response.
Thompson, Dylan; Batterham, Alan M; Bock, Susan; Robson, Claire; Stokes, Keith
2006-04-01
Low-to-moderate intensity physical activity thermogenesis is a highly variable and quantitatively important component of total energy expenditure that is difficult to assess outside the laboratory. Greater precision and accuracy in the measurement of this key contributor to energy balance is a research priority. We developed a laboratory-based protocol that simulated a range of low-to-moderate intensity physical activities. We characterized the bias and random (individual) error in estimating energy expenditure using combined accelerometry and heart rate (AHR) with branched-equation modeling and a simple motion sensor (pedometer) against an indirect calorimetry criterion. Twenty young adult subjects performed a 2-h laboratory-based protocol, simulating 6 low-to-moderate intensity physical activities interspersed with periods of rest. The physical activity level during the laboratory-based protocol reflected an energy expenditure toward the lower end of the active category. We found that AHR-derived energy expenditure showed no evidence of substantial fixed or proportional bias (mean bias 6%), whereas pedometer-derived energy expenditure showed both fixed and proportional bias (bias at minimum, mean, and maximum energy expenditure +11, -20, and -36%, respectively). It appears that AHR provides an accurate estimate of criterion energy expenditure whereas a simple motion sensor (pedometer) does not. It is noteworthy that AHR provides quantitative information about the nature and patterns of physical activity, such as the amount of time and/or energy spent engaged in physical activity above critical health-related thresholds.
Yamwong, Sukit; Kitiyakara, Chagriya; Vathesatogkit, Prin; Saranburut, Krittika; Chittamma, Anchalee; Cheepudomwit, Sayan; Vanavanan, Somlak; Akrawichien, Tawatchai; Sritara, Piyamitr
2016-08-01
There are limited data on the risks of chronic kidney disease (CKD) in Southeast Asian populations. Several GFR estimating equations have been developed in diverse Asian populations, but they produce markedly discrepant results. We investigated the impact of Asian equations on the mortality risk of CKD in a Thai cohort during long term follow-up, and explored the differences between equations grouped according to the reference GFR methods used to develop them. Employees of the Electricity Generating Authority of Thailand (n = 3430) were enrolled in a health survey and followed up for 22 years. The risks for all-cause mortality for each GFR stage classified by CKD-EPI or different Asian equations were assessed by using Cox proportional hazard models. Equations derived from DTPA clearance (Chinese MDRD, Thai GFR, Singapore CKD-EPI) produced higher GFR, whereas equations from inulin clearance (Japanese CKD-EPI, Taiwan MDRD or Taiwan CKD-EPI) produced lower GFR compared to CKD-EPI. (Average ΔGFR: inulin, -14.9 vs. DTPA +5.80 mL/min per 1.73 m(2) , P Chronic kidney disease prevalence and prognosis in Thais varied widely depending on the equation used. Differences in the reference GFR methods could be an important cause for the discrepancies between Asian equations. © 2015 Asian Pacific Society of Nephrology.
Moiseiwitsch, B L
2005-01-01
Two distinct but related approaches hold the solutions to many mathematical problems--the forms of expression known as differential and integral equations. The method employed by the integral equation approach specifically includes the boundary conditions, which confers a valuable advantage. In addition, the integral equation approach leads naturally to the solution of the problem--under suitable conditions--in the form of an infinite series.Geared toward upper-level undergraduate students, this text focuses chiefly upon linear integral equations. It begins with a straightforward account, acco
Energy Technology Data Exchange (ETDEWEB)
Young, C.W. [Applied Research Associates, Inc., Albuquerque, NM (United States)
1997-10-01
In 1967, Sandia National Laboratories published empirical equations to predict penetration into natural earth materials and concrete. Since that time there have been several small changes to the basic equations, and several more additions to the overall technique for predicting penetration into soil, rock, concrete, ice, and frozen soil. The most recent update to the equations was published in 1988, and since that time there have been changes in the equations to better match the expanding data base, especially in concrete penetration. This is a standalone report documenting the latest version of the Young/Sandia penetration equations and related analytical techniques to predict penetration into natural earth materials and concrete. 11 refs., 6 tabs.
Directory of Open Access Journals (Sweden)
Fernando Bustos-Guadaño
2017-03-01
Conclusions: The GFR estimations obtained with BS1 equation are not interchangeable with MDRD-IDMS or CKD-EPI equations. BIS1 estimates lower GFR values than MDRD-IDMS and CKD-EPI and tends to classify the patients in a more advanced chronic kidney disease stage, especially for estimated GFR higher than 29 mL/min/1.73 m2.
Corsonello, Andrea; Pedone, Claudio; Bandinelli, Stefania; Ferrucci, Luigi; Antonelli Incalzi, Raffaele
2017-10-01
The aim was to investigate to what extent chronic kidney disease (CKD) can be staged interchangeably by Chronic Kidney Disease Epidemiological Collaboration (CKD-EPI) and by Berlin Initiative Study (BIS) equations, and to verify whether cystatin C can improve concordance between formulas. Our series consisted of 828 community-dwelling individuals aged 65 years or older enrolled in the Invecchiare in Chianti Study ("Aging in the Chianti Region"). Estimated glomerular filtration rate was calculated using the creatinine-based CKD-EPI, creatinine/cystatin C-based CKD-EPI, creatinine-based BIS and creatinine/cystatin C-based BIS equations. Agreement and sources of discrepancy between equations in identifying people with different degrees of kidney dysfunction was investigated by κ statistic and Bland-Altman plots. Overall, CKD-EPI values were higher than that obtained with BIS equations, especially for eGFR = 30-60 mL/min/1.73 m 2 . A total of 191 out of 828 participants were classified in stage 2 by the creatinine-based CKD-EPI and in stage 3a by the creatinine-based BIS equation, whereas 123 participants were classified in stage 2 by creatinine/cystatin C-based CKD-EPI and in stage 3a by the creatinine/cystatin C-based BIS equation. A total of 27 participants were classified in stage 3a by creatinine-based CKD-EPI and in stage 3b by creatinine-based BIS equation, whereas 18 were classified as stage 3a by creatinine/cystatin C-based CKD-EPI and stage 3b by the creatinine/cystatin C-based BIS equation. Despite a fair overall concordance, the CKD-EPI and BIS equations cannot be considered interchangeable to assess estimated glomerular filtration rate in older people, and using creatinine/cystatin C-based rather than creatinine-based equations only marginally improves the concordance between CKD-EPI and BIS. Disagreement between equations might significantly impact the applications of stage-specific measures for managing CKD among older people
Heim, Lale; Schaal, Susanne
2014-01-01
As a consequence of the 1994 Rwandan genocide, prevalences of mental disorders are elevated in Rwanda. More knowledge about determinants of mental stress can help to improve mental health services and treatment in the east-central African country. The present study aimed to investigate actual rates of mental stress (posttraumatic stress disorder, syndromal depression and syndromal anxiety) in Rwanda and to examine if gender, persecution during the genocide, readiness to reconcile as well as importance given to religiosity and quality of religiosity are predictors of mental stress. The study comprised a community sample of N = 200 Rwandans from Rwanda's capital Kigali, who experienced the Rwandan genocide. By conducting structured interviews, ten local Master level psychologists examined types of potentially lifetime traumatic events, symptoms of posttraumatic stress disorder (PTSD), depression and anxiety, readiness to reconcile and religiosity. Applying non-recursive structural equation modeling (SEM), the associations between gender, persecution, readiness to reconcile, religiosity and mental stress were investigated. Respondents had experienced an average number of 11.38 types of potentially lifetime traumatic events. Of the total sample, 11% met diagnostic criteria for PTSD, 19% presented with syndromal depression and 23% with syndromal anxiety. Female sex, persecution and readiness to reconcile were significant predictors of mental stress. Twofold association was found between centrality of religion (which captures the importance given to religiosity) and mental stress, showing, that higher mental stress provokes a higher centrality and that higher centrality reduces mental stress. The variables positive and negative religious functioning (which determine the quality of religiosity) respectively had an indirect negative and positive effect on mental stress. Study results provide evidence that rates of mental stress are still elevated in Rwanda and that
Tricomi, FG
2013-01-01
Based on his extensive experience as an educator, F. G. Tricomi wrote this practical and concise teaching text to offer a clear idea of the problems and methods of the theory of differential equations. The treatment is geared toward advanced undergraduates and graduate students and addresses only questions that can be resolved with rigor and simplicity.Starting with a consideration of the existence and uniqueness theorem, the text advances to the behavior of the characteristics of a first-order equation, boundary problems for second-order linear equations, asymptotic methods, and diff
Barbu, Viorel
2016-01-01
This textbook is a comprehensive treatment of ordinary differential equations, concisely presenting basic and essential results in a rigorous manner. Including various examples from physics, mechanics, natural sciences, engineering and automatic theory, Differential Equations is a bridge between the abstract theory of differential equations and applied systems theory. Particular attention is given to the existence and uniqueness of the Cauchy problem, linear differential systems, stability theory and applications to first-order partial differential equations. Upper undergraduate students and researchers in applied mathematics and systems theory with a background in advanced calculus will find this book particularly useful. Supplementary topics are covered in an appendix enabling the book to be completely self-contained.
Hochstadt, Harry
2011-01-01
This classic work is now available in an unabridged paperback edition. Hochstatdt's concise treatment of integral equations represents the best compromise between the detailed classical approach and the faster functional analytic approach, while developing the most desirable features of each. The seven chapters present an introduction to integral equations, elementary techniques, the theory of compact operators, applications to boundary value problems in more than dimension, a complete treatment of numerous transform techniques, a development of the classical Fredholm technique, and applicatio
Leion, Felicia; Hegbrant, Josefine; den Bakker, Emil; Jonsson, Magnus; Abrahamson, Magnus; Nyman, Ulf; Björk, Jonas; Lindström, Veronica; Larsson, Anders; Bökenkamp, Arend; Grubb, Anders
2017-09-01
Estimating glomerular filtration rate (GFR) in adults by using the average of values obtained by a cystatin C- (eGFRcystatin C) and a creatinine-based (eGFRcreatinine) equation shows at least the same diagnostic performance as GFR estimates obtained by equations using only one of these analytes or by complex equations using both analytes. Comparison of eGFRcystatin C and eGFRcreatinine plays a pivotal role in the diagnosis of Shrunken Pore Syndrome, where low eGFRcystatin C compared to eGFRcreatinine has been associated with higher mortality in adults. The present study was undertaken to elucidate if this concept can also be applied in children. Using iohexol and inulin clearance as gold standard in 702 children, we studied the diagnostic performance of 10 creatinine-based, 5 cystatin C-based and 3 combined cystatin C-creatinine eGFR equations and compared them to the result of the average of 9 pairs of a eGFRcystatin C and a eGFRcreatinine estimate. While creatinine-based GFR estimations are unsuitable in children unless calibrated in a pediatric or mixed pediatric-adult population, cystatin C-based estimations in general performed well in children. The average of a suitable creatinine-based and a cystatin C-based equation generally displayed a better diagnostic performance than estimates obtained by equations using only one of these analytes or by complex equations using both analytes. Comparing eGFRcystatin and eGFRcreatinine may help identify pediatric patients with Shrunken Pore Syndrome.
Hochstadt, Harry
2012-01-01
Modern approach to differential equations presents subject in terms of ideas and concepts rather than special cases and tricks which traditional courses emphasized. No prerequisites needed other than a good calculus course. Certain concepts from linear algebra used throughout. Problem section at end of each chapter.
First-order partial differential equations
Rhee, Hyun-Ku; Amundson, Neal R
2001-01-01
This first volume of a highly regarded two-volume text is fully usable on its own. After going over some of the preliminaries, the authors discuss mathematical models that yield first-order partial differential equations; motivations, classifications, and some methods of solution; linear and semilinear equations; chromatographic equations with finite rate expressions; homogeneous and nonhomogeneous quasilinear equations; formation and propagation of shocks; conservation equations, weak solutions, and shock layers; nonlinear equations; and variational problems. Exercises appear at the end of mo
Lim, Wai H; Lewis, Joshua R; Wong, Germaine; Turner, Robin M; Lim, Ee M; Thompson, Peter L; Prince, Richard L
2014-01-01
Reduced estimated glomerular filtration rate (eGFR) using the cystatin-C derived equations might be a better predictor of cardiovascular disease (CVD) mortality compared with the creatinine-derived equations, but this association remains unclear in elderly individuals. The aims of this study were to compare the predictive values of the Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI)-creatinine, CKD-EPI-cystatin C and CKD-EPI-creatinine-cystatin C eGFR equations for all-cause mortality and CVD events (hospitalizations±mortality). Prospective cohort study of 1165 elderly women aged>70 years. Associations between eGFR and outcomes were examined using Cox regression analysis. Test accuracy of eGFR equations for predicting outcomes was examined using Receiver Operating Characteristic (ROC) analysis and net reclassification improvement (NRI). Risk of all-cause mortality for every incremental reduction in eGFR determined using CKD-EPI-creatinine, CKD-EPI-cystatin C and the CKD-EPI-creatinine-cystatic C equations was similar. Areas under the ROC curves of CKD-EPI-creatinine, CKD-EPI-cystatin C and CKD-EPI-creatinine-cystatin C equations for all-cause mortality were 0.604 (95%CI 0.561-0.647), 0.606 (95%CI 0.563-0.649; p = 0.963) and 0.606 (95%CI 0.563-0.649; p = 0.894) respectively. For all-cause mortality, there was no improvement in the reclassification of eGFR categories using the CKD-EPI-cystatin C (NRI -4.1%; p = 0.401) and CKD-EPI-creatinine-cystatin C (NRI -1.2%; p = 0.748) compared with CKD-EPI-creatinine equation. Similar findings were observed for CVD events. eGFR derived from CKD-EPI cystatin C and CKD-EPI creatinine-cystatin C equations did not improve the accuracy or predictive ability for clinical events compared to CKD-EPI-creatinine equation in this cohort of elderly women.
MacIsaac, Richard J; Ekinci, Elif I; Premaratne, Erosha; Lu, Zhong X; Seah, Jas-Mine; Li, Yue; Boston, Ray; Ward, Glenn M; Jerums, George
2015-12-03
Our hypothesis was that both the Chronic Kidney Disease-Epidemiology Collaboration (CKD-EPI) and Modification of Diet in Renal Disease (MDRD) equations would underestimate directly measured GFR (mGFR) to a similar extent in people with diabetes and preserved renal function. In a cross-sectional study, bias (eGFR - mGFR) was compared for the CKD-EPI and MDRD equations, after stratification for mGFR levels. We also examined the ability of the CKD-EPI compared with the MDRD equation to correctly classify subjects to various CKD stages. In a longitudinal study of subjects with an early decline in GFR i.e., initial mGFR > 60 ml/min/1.73 m(2) and rate of decline in GFR (ΔmGFR) > 3.3 ml/min/1.73 m(2) per year, ΔmGFR (based on initial and final values) was compared with ΔeGFR by the CKD-EPI and MDRD equations over a mean of 9 years. In the cross-sectional study, mGFR for the whole group was 80 ± 2.2 ml/min/1.73 m(2) (n = 199, 75 % type 2 diabetes). For subjects with mGFR >90 ml/min/1.73 m(2) (mGFR: 112 ± 2.0, n = 76), both equations significantly underestimated mGFR to a similar extent: bias for CKD-EPI: -12 ± 1.4 ml/min/1.73 m(2) (p EPI compared with the MDRD equation did not improve the number of subjects that were correctly classified to a CKD-stage. No biochemical or clinical patient characteristics were identified to account for the under estimation of mGFR values in the normal to high range by the CKD-EPI equation. In the longitudinal study (n = 30, 66 % type 1 diabetes), initial and final mGFR values were 102.8 ± 6 and 54.6 ± 6.0 ml/min/1.73 m(2), respectively. Mean ΔGFR (ml/min/1.73 m(2) per year) was 6.0 by mGFR compared with only 3.0 by MDRD and 3.2 by CKD-EPI (both p EPI and MDRD equations underestimate reference GFR values > 90 ml/min/1.73 m(2) as well as an early decline in GFR to a similar extent in people with diabetes. There is scope to improve methods for estimating an early decline in GFR.
Fontes, R; Ribeiro, J M; Sillero, A
2000-01-01
A combined analysis of enzyme inhibition and activation is presented, based on a rapid equilibrium model assumption in which one molecule of enzyme binds one molecule of substrate (S) and/or one molecule of a modifier X. The modifier acts as activator (essential or non-essential), as inhibitor (total or partial), or has no effect on the reaction rate (v), depending on the values of the equilibrium constants, the rate constants of the limiting velocity steps, and the concentration of substrate ([S]). Different possibilities have been analyzed from an equation written to emphasize that v = f([X]) is, in general and at a fixed [S], a hyperbolic function. Formulas for Su (the value of [S], different from zero, at which v is unaffected by the modifier) and v(su) (v at that particular [S]) were deduced. In Lineweaver-Burk plots, the straight lines related to different [X] generally cross in a point (P) with coordinates (Su, v(su)). In certain cases, point P is located in the first quadrant which implies that X acts as activator, as inhibitor, or has no effect, depending on [S]. Furthermore, we discuss: (1) the apparent Vmax and Km displayed by the enzyme in different situations; (2) the degree of effect (inhibition or activation) observed at different concentrations of substrate and modifier; (3) the concept of Ke, a parameter that depends on the concentration of substrate and helps to evaluate the effect of the modifier: it equals the value of [X] at which the increase or decrease in the reaction rate is half of that achieved at saturating [X]. Equations were deduced for the general case and for particular situations, and used to obtain computer-drawn graphs that are presented and discussed. Formulas for apparent Vmax, Km and Ke have been written in a way making it evident that these parameters can be expressed as pondered means.
Tricomi, Francesco Giacomo
1957-01-01
This classic text on integral equations by the late Professor F. G. Tricomi, of the Mathematics Faculty of the University of Turin, Italy, presents an authoritative, well-written treatment of the subject at the graduate or advanced undergraduate level. To render the book accessible to as wide an audience as possible, the author has kept the mathematical knowledge required on the part of the reader to a minimum; a solid foundation in differential and integral calculus, together with some knowledge of the theory of functions is sufficient. The book is divided into four chapters, with two useful
Stochastic partial differential equations
Chow, Pao-Liu
2014-01-01
Preliminaries Introduction Some Examples Brownian Motions and Martingales Stochastic Integrals Stochastic Differential Equations of Itô Type Lévy Processes and Stochastic IntegralsStochastic Differential Equations of Lévy Type Comments Scalar Equations of First Order Introduction Generalized Itô's Formula Linear Stochastic Equations Quasilinear Equations General Remarks Stochastic Parabolic Equations Introduction Preliminaries Solution of Stochastic Heat EquationLinear Equations with Additive Noise Some Regularity Properties Stochastic Reaction-Diffusion Equations Parabolic Equations with Grad
Dehkordi, Forough Jafarian; Rasuli, Behrouz; Mahmoud-Pashazadeh, Ali
2017-01-01
The main purpose of this study was to investigate dose rate emanating from patients treated with (131)I to evaluate which of the theoretical formulas, inverse-square law (ISL) and International Atomic Energy Agency-International Commission on Radiological Protection (IAEA-ICRP) suggested equation, can provide a sufficiently close approximation of the measured dose rate. Measurements were performed based on the IAEA safety report No. 63 method at 0, 12, 24, and 48 h after administration of radioiodine at a distance of 1 m for 69 patients and for the rest of 67 patients, dose rate was measured at 2, 4, 24, and 48 h at a distance of 2 m. Results revealed that the ISL formula gained better approximation of measured dose rates than the IAEA-ICRP equation with the lesser error. The ISL formula is still more reliable than the novel method of dose calculation in the vicinity of patients. This finding reminded us the prime importance of distance as a radiation protection principle.
Risch, Lorenz; Saely, Christoph H; Neyer, Ulrich; Hoefle, Guenter; Gouya, Ghazaleh; Zerlauth, Manfred; Risch, Gerhard M; Risch, Martin; Drexel, Heinz
2007-03-01
Data on the prevalence of decreased glomerular filtration rate in Europe are limited. Most of the available studies did not employ laboratory methods providing creatinine concentrations traceable to the reference method, i.e. isotope dilution mass spectrometry (IDMS). We therefore conducted a cross-sectional study in the principality of Liechtenstein consecutively enrolling adult patients seeking non-nephrological medical care from whom serum samples were referred for renal function assessment. All measurements were done in one central laboratory. The estimated glomerular filtration rate (eGFR) was calculated based on the determination of IDMS-traceable creatinine by a kinetic Jaffe method (Roche Diagnostics, Switzerland) by means of the MDRD and Mayo Clinic quadratic equations. We further estimated the incidence of end stage renal disease during the next 5 years. For 43% (n=9378) of the entire population>or=25 years renal function assessment was available. An eGFR indicating chronic kidney disease (CKD) stages 3-5 was found in 4.93% when using the MDRD equation and in 3.98 % when using the Mayo Clinic quadratic equation. The two equations had a very good agreement in classifying patients to have an eGFR consistent with CKD stages 3-5 (Cohen's kappa 0.887). Further calculations suggested that among patients aged 80 or younger, annually 42 per 100,000 are going to develop an eGFR<15 ml/min/1.73 m2 over the next 5 years. 4-5% of patients seeking non-nephrological medical advice have an eGFR consistent with CKD stages 3-5, and a considerable number of subjects is expected to develop end stage renal disease over a 5 year period. In order to obtain comparable kidney function estimates among different institutions it is not only important to use standardized methods to measure creatinine but rather to employ standardized methods to calculate a GFR estimate.
Uemura, Osamu; Yokoyama, Hitoshi; Ishikura, Kenji; Gotoh, Yoshimitsu; Sato, Hiroshi; Sugiyama, Hitoshi; Honda, Masataka; Matsuo, Seiichi
2017-06-01
There are two different Japanese serum creatinine-based equations for estimated glomerular filtration rate (eGFR), for adults and paediatric patients, with both equations deemed applicable to 18-year-old subjects. This study assessed the relative accuracy of the two equations in assessing eGFR in patients aged 18 years with chronic kidney disease. A total of 3042 patients (1679 males and 1363 females), aged 2-20 years, who were registered in the Japan Renal Biopsy Registry or the Japan Kidney Disease Registry between 2007 and 2013 were evaluated. eGFR values derived from formulas for children (Uemura's formula) and adults (the 3-variable Japanese formula) were calculated and compared, especially in patients aged 18 years. At all ages, but especially at younger ages, eGFR was significantly higher when calculated with the adult than the paediatric formula. This finding was also observed in 18-year-old adolescents with eGFR <90 mL/min per 1.73 m2 (P = 0.026). However, the mean difference between the two calculated eGFRs was only 2.79 mL/min per 1.73 m2 . These findings indicate that both creatinine-based equations used to calculate eGFR rate in Japanese children and adults with chronic kidney disease could be used to determine eGFR in 18-year-old subjects, with the difference between the two within permissible levels for clinical use. © 2017 Asian Pacific Society of Nephrology.
Order reduction of the chemical master equation via balanced realisation.
Directory of Open Access Journals (Sweden)
Fernando López-Caamal
Full Text Available We consider a Markov process in continuous time with a finite number of discrete states. The time-dependent probabilities of being in any state of the Markov chain are governed by a set of ordinary differential equations, whose dimension might be large even for trivial systems. Here, we derive a reduced ODE set that accurately approximates the probabilities of subspaces of interest with a known error bound. Our methodology is based on model reduction by balanced truncation and can be considerably more computationally efficient than solving the chemical master equation directly. We show the applicability of our method by analysing stochastic chemical reactions. First, we obtain a reduced order model for the infinitesimal generator of a Markov chain that models a reversible, monomolecular reaction. Later, we obtain a reduced order model for a catalytic conversion of substrate to a product (a so-called Michaelis-Menten mechanism, and compare its dynamics with a rapid equilibrium approximation method. For this example, we highlight the savings on the computational load obtained by means of the reduced-order model. Furthermore, we revisit the substrate catalytic conversion by obtaining a lower-order model that approximates the probability of having predefined ranges of product molecules. In such an example, we obtain an approximation of the output of a model with 5151 states by a reduced model with 16 states. Finally, we obtain a reduced-order model of the Brusselator.
Order reduction of the chemical master equation via balanced realisation.
López-Caamal, Fernando; Marquez-Lago, Tatiana T
2014-01-01
We consider a Markov process in continuous time with a finite number of discrete states. The time-dependent probabilities of being in any state of the Markov chain are governed by a set of ordinary differential equations, whose dimension might be large even for trivial systems. Here, we derive a reduced ODE set that accurately approximates the probabilities of subspaces of interest with a known error bound. Our methodology is based on model reduction by balanced truncation and can be considerably more computationally efficient than solving the chemical master equation directly. We show the applicability of our method by analysing stochastic chemical reactions. First, we obtain a reduced order model for the infinitesimal generator of a Markov chain that models a reversible, monomolecular reaction. Later, we obtain a reduced order model for a catalytic conversion of substrate to a product (a so-called Michaelis-Menten mechanism), and compare its dynamics with a rapid equilibrium approximation method. For this example, we highlight the savings on the computational load obtained by means of the reduced-order model. Furthermore, we revisit the substrate catalytic conversion by obtaining a lower-order model that approximates the probability of having predefined ranges of product molecules. In such an example, we obtain an approximation of the output of a model with 5151 states by a reduced model with 16 states. Finally, we obtain a reduced-order model of the Brusselator.
Simple taper: Taper equations for the field forester
David R. Larsen
2017-01-01
"Simple taper" is set of linear equations that are based on stem taper rates; the intent is to provide taper equation functionality to field foresters. The equation parameters are two taper rates based on differences in diameter outside bark at two points on a tree. The simple taper equations are statistically equivalent to more complex equations. The linear...
Dufour, B; Toussaint-Hacquard, M; Kearney-Schwartz, A; Manckoundia, M D P; Laurain, M C; Joly, L; Deibener, J; Wahl, D; Lecompte, T; Benetos, A; Perret-Guillaume, C
2012-07-01
Older people have an increased risk of low molecular weight heparin accumulation leading to an increased bleeding risk. The objective of this study was to assess whether reduced glomerular filtration rate (GFR), estimated by the Cockcroft-Gault or modification of the diet in renal disease (MDRD) equations, indicates drug accumulation by increased anti-Xa levels in older subjects receiving prophylactic enoxaparin treatment. Cohort study. Acute geriatric units in Nancy Hospital. Ninety-two consenting consecutive patients, 65 and older, confined to bed for an acute medical condition requiring enoxaparin for prevention of venous thromboembolism, and hospitalized for at least six days were enrolled. Serum creatinine and peak plasma anti-Xa levels 3 to 4 hours after the daily injection of enoxaparin were measured at days 3, 6, 9 and 12 (first dose of enoxaparin at day one). Analyses of variance for repeated measures were used to evaluate significant predictors of peak anti-Xa activity in univariate and multivariate analyses. A significant correlation was observed between anti-Xa activity and GFR estimated with the Cockcroft formula r=0.43. Following univariate analysis, the three factors associated with higher anti-Xa levels were a lower Cockcroft-Gault GFR (p=0.0002), female gender (p=0.0003) and a lower bodyweight (polder than 65 years old, the Cockcroft-Gault equation, in contrast to the MDRD equation, is able to predict the risk of higher anti-Xa levels.
DEFF Research Database (Denmark)
Mocroft, A; Nielsen, Lene Ryom; Reiss, P
2014-01-01
The aim of this study was to determine whether the Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI)- or Cockcroft-Gault (CG)-based estimated glomerular filtration rates (eGFRs) performs better in the cohort setting for predicting moderate/advanced chronic kidney disease (CKD) or end......-stage renal disease (ESRD)....
Cheuiche, Amanda Veiga; Soares, Ariana Aguiar; Camargo, Eduardo Guimarães; Weinert, Letícia Schwerz; Camargo, Joíza Lins; Silveiro, Sandra Pinho
2013-10-01
The aim of this paper was to compare the agreement between creatinine measured by Jaffe and enzymatic methods and their putative influence on eGFR as calculated by the CKD-EPI (Chronic Kidney Disease Epidemiology Collaboration) equation in healthy and diabetic individuals. Cross-sectional study conducted in 123 adult southern Brazilians with GFR>60 mL/min/1.73 m² (53 patients with type 2 diabetes, 70 healthy volunteers). Mean age was 49±16 years (range of 19-86). Most were female (55%) and white (83%). Creatinine was measured by a traceable Jaffe method (Modular P, Roche Diagnostic) and by an enzymatic method (CREA plus, Roche/Hitachi 917). GFR was measured by the ⁵¹Cr-EDTA single-injection method. Serum creatinine measured by the Jaffe and enzymatic methods was similar in healthy subjects (0.79±0.16 vs. 0.79±0.15 mg/dL, respectively, P=0.76), and diabetic patients (0.96±0.22 vs. 0.92±0.29 mg/dL, respectively, P=0.17). However, the correlation between the two methods was higher in the healthy group (r=0.90 vs. 0.76, P<0.001). The difference between Jaffe creatinine and enzymatic creatinine was <10% in 63% of cases in the healthy group and 40% of cases in the diabetes group (P=0.018). In the subset of patients with diabetes, eGFR based on enzymatic assay results showed better agreement with measured GFR than did eGFR based on Jaffe results. Jaffe and enzymatic creatinine methods show adequate agreement in healthy subjects, but in the presence of diabetes, the enzymatic method performed slightly better. Copyright © 2013 The Canadian Society of Clinical Chemists. Published by Elsevier Inc. All rights reserved.
Tveito, Aslak; Lines, Glenn T; Edwards, Andrew G; McCulloch, Andrew
2016-07-01
Markov models are ubiquitously used to represent the function of single ion channels. However, solving the inverse problem to construct a Markov model of single channel dynamics from bilayer or patch-clamp recordings remains challenging, particularly for channels involving complex gating processes. Methods for solving the inverse problem are generally based on data from voltage clamp measurements. Here, we describe an alternative approach to this problem based on measurements of voltage traces. The voltage traces define probability density functions of the functional states of an ion channel. These probability density functions can also be computed by solving a deterministic system of partial differential equations. The inversion is based on tuning the rates of the Markov models used in the deterministic system of partial differential equations such that the solution mimics the properties of the probability density function gathered from (pseudo) experimental data as well as possible. The optimization is done by defining a cost function to measure the difference between the deterministic solution and the solution based on experimental data. By evoking the properties of this function, it is possible to infer whether the rates of the Markov model are identifiable by our method. We present applications to Markov model well-known from the literature. Copyright © 2016 The Authors. Published by Elsevier Inc. All rights reserved.
Directory of Open Access Journals (Sweden)
Paula Guedes Cocate
2009-10-01
Full Text Available A taxa metabólica de repouso (TMR pode ser determinada por calorimetria indireta (CI. Porém, em função da praticidade, na prática clínica na maioria das vezes esta é estimada por equações de predição, as quais foram desenvolvidas em estudos envolvendo indivíduos não atletas. Apesar de alguns autores terem indicado que tais equações não estimam adequadamente a TMR, estas têm sido bastante utilizadas para calculá-la e prescrever dietas, inclusive para atletas. O objetivo deste estudo foi comparar a TMR determinada por CI com a estimada pelas equações de Harris & Benedict (HB, Schofield, FAO/WHO/UNU e Henry & Rees (HR, em 15 homens ciclistas, de 24,4 ± 3,68 anos, apresentando índice de massa corporal de 21,97 ± 1,46kg/m² e VO2máx de 70,00 ± 5,32mL(kg.min-1. Para comparar a TMR determinada por CI e pelas equações, utilizou-se o tratamento estatístico testes t de Student (variáveis com distribuição normal e de Mann-Whitney (variáveis sem distribuição normal, considerando p The resting metabolic rate (RMR can be determined by indirect calorimetry (IC. However, the clinical estimation of this parameter has been done using mathematical equations, which were developed in studies involving non-athletes. Although some authors have indicated that such equations do not estimate correctly the RMR, they have been constantly used to estimate such parameter and to prescribe diets, including for athletes. The objective of this study was to compare the RMR determined by IC with the ones estimated using the equations proposed by Harris & Benedict (HB, Schofield, FAO/WHO/UNU and Henry & Rees (HR, in 15 male cyclists, aged 24.4±3.68 years, body mass index of 21.97±1.46 kg/m² and VO2max of 70.00±5.32 mL(kg.min-1. Student's t test (when data presented normal distribution and Mann-Whitney (when data did not present normal distribution were used to compare the RMR determined by IC and the ones estimated by the equations. Probability
Mocroft, A; Ryom, L; Reiss, P; Furrer, H; D'Arminio Monforte, A; Gatell, J; de Wit, S; Beniowski, M; Lundgren, J D; Kirk, O
2014-03-01
The aim of this study was to determine whether the Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI)- or Cockcroft-Gault (CG)-based estimated glomerular filtration rates (eGFRs) performs better in the cohort setting for predicting moderate/advanced chronic kidney disease (CKD) or end-stage renal disease (ESRD). A total of 9521 persons in the EuroSIDA study contributed 133 873 eGFRs. Poisson regression was used to model the incidence of moderate and advanced CKD (confirmed eGFR < 60 and < 30 mL/min/1.73 m(2) , respectively) or ESRD (fatal/nonfatal) using CG and CKD-EPI eGFRs. Of 133 873 eGFR values, the ratio of CG to CKD-EPI was ≥ 1.1 in 22 092 (16.5%) and the difference between them (CG minus CKD-EPI) was ≥ 10 mL/min/1.73 m(2) in 20 867 (15.6%). Differences between CKD-EPI and CG were much greater when CG was not standardized for body surface area (BSA). A total of 403 persons developed moderate CKD using CG [incidence 8.9/1000 person-years of follow-up (PYFU); 95% confidence interval (CI) 8.0-9.8] and 364 using CKD-EPI (incidence 7.3/1000 PYFU; 95% CI 6.5-8.0). CG-derived eGFRs were equal to CKD-EPI-derived eGFRs at predicting ESRD (n = 36) and death (n = 565), as measured by the Akaike information criterion. CG-based moderate and advanced CKDs were associated with ESRD [adjusted incidence rate ratio (aIRR) 7.17; 95% CI 2.65-19.36 and aIRR 23.46; 95% CI 8.54-64.48, respectively], as were CKD-EPI-based moderate and advanced CKDs (aIRR 12.41; 95% CI 4.74-32.51 and aIRR 12.44; 95% CI 4.83-32.03, respectively). Differences between eGFRs using CG adjusted for BSA or CKD-EPI were modest. In the absence of a gold standard, the two formulae predicted clinical outcomes with equal precision and can be used to estimate GFR in HIV-positive persons. © 2013 British HIV Association.
Wave equations for pulse propagation
Shore, B. W.
1987-06-01
Theoretical discussions of the propagation of pulses of laser radiation through atomic or molecular vapor rely on a number of traditional approximations for idealizing the radiation and the molecules, and for quantifying their mutual interaction by various equations of propagation (for the radiation) and excitation (for the molecules). In treating short-pulse phenomena it is essential to consider coherent excitation phenomena of the sort that is manifest in Rabi oscillations of atomic or molecular populations. Such processes are not adequately treated by rate equations for excitation nor by rate equations for radiation. As part of a more comprehensive treatment of the coupled equations that describe propagation of short pulses, this memo presents background discussion of the equations that describe the field. This memo discusses the origin, in Maxwell's equations, of the wave equation used in the description of pulse propagation. It notes the separation into lamellar and solenoidal (or longitudinal and transverse) and positive and negative frequency parts. It mentions the possibility of separating the polarization field into linear and nonlinear parts, in order to define a susceptibility or index of refraction and, from these, a phase and group velocity.
Partial Differential Equations
1988-01-01
The volume contains a selection of papers presented at the 7th Symposium on differential geometry and differential equations (DD7) held at the Nankai Institute of Mathematics, Tianjin, China, in 1986. Most of the contributions are original research papers on topics including elliptic equations, hyperbolic equations, evolution equations, non-linear equations from differential geometry and mechanics, micro-local analysis.
Directory of Open Access Journals (Sweden)
Pavithra Sivasamy
Full Text Available A mathematical model of biotransformation of D-methionine into L-methionine in the cascade of the enzymes such as, D-amino acid oxidase (D-AAO, L-phenylalanine dehydrogenase (L-PheDH and formate dehydrogenase (FDH is discussed. The model is based on a system of coupled nonlinear reaction equations under non steady-state conditions for biochemical reactions occurring in the batch reactor that describes the substrate and product concentration within the catalyst. Simple analytical expressions for the concentration of substrate and product have been derived for all values of reaction parameters using the new homotopy perturbation method (NHPM. Enzyme reaction rate in terms of concentration and kinetic parameters are also reported. The analytical results are also compared with experimental and numerical ones and a good agreement is obtained. The graphical procedure for estimating the kinetic parameters is also reported.
Bolton, W
1995-01-01
This book is concerned with linear equations and matrices, with emphasis on the solution of simultaneous linear equations. The solution of simultaneous linear equations is applied to electric circuit analysis and structural analysis.
Exchange Rate Dynamics under Alternative Optimal Interest Rate Rules
Binici, Mahir; Cheung, Yin-Wong
2011-01-01
We explore the role of interest rate policy in the exchange rate determination process. Specifically, we derive exchange rate equations from interest rate rules that are theoretically optimal under a few alternative settings. The exchange rate equation depends on its underlying interest rate rule and its performance could vary across evaluation criteria and sample periods. The exchange rate equation implied by the interest rate rule that allows for interest rate and inflation inertia under co...
Acoustofluidics 1: Governing equations in microfluidics
DEFF Research Database (Denmark)
Bruus, Henrik
2011-01-01
Governing equations for microfluidics and basic flow solutions are presented. Equivalent circuit modeling for determining flow rates in microfluidic networks is introduced.......Governing equations for microfluidics and basic flow solutions are presented. Equivalent circuit modeling for determining flow rates in microfluidic networks is introduced....
Difference equations by differential equation methods
Hydon, Peter E
2014-01-01
Most well-known solution techniques for differential equations exploit symmetry in some form. Systematic methods have been developed for finding and using symmetries, first integrals and conservation laws of a given differential equation. Here the author explains how to extend these powerful methods to difference equations, greatly increasing the range of solvable problems. Beginning with an introduction to elementary solution methods, the book gives readers a clear explanation of exact techniques for ordinary and partial difference equations. The informal presentation is suitable for anyone who is familiar with standard differential equation methods. No prior knowledge of difference equations or symmetry is assumed. The author uses worked examples to help readers grasp new concepts easily. There are 120 exercises of varying difficulty and suggestions for further reading. The book goes to the cutting edge of research; its many new ideas and methods make it a valuable reference for researchers in the field.
Wave equations for pulse propagation
Energy Technology Data Exchange (ETDEWEB)
Shore, B.W.
1987-06-24
Theoretical discussions of the propagation of pulses of laser radiation through atomic or molecular vapor rely on a number of traditional approximations for idealizing the radiation and the molecules, and for quantifying their mutual interaction by various equations of propagation (for the radiation) and excitation (for the molecules). In treating short-pulse phenomena it is essential to consider coherent excitation phenomena of the sort that is manifest in Rabi oscillations of atomic or molecular populations. Such processes are not adequately treated by rate equations for excitation nor by rate equations for radiation. As part of a more comprehensive treatment of the coupled equations that describe propagation of short pulses, this memo presents background discussion of the equations that describe the field. This memo discusses the origin, in Maxwell's equations, of the wave equation used in the description of pulse propagation. It notes the separation into lamellar and solenoidal (or longitudinal and transverse) and positive and negative frequency parts. It mentions the possibility of separating the polarization field into linear and nonlinear parts, in order to define a susceptibility or index of refraction and, from these, a phase and group velocity. The memo discusses various ways of characterizing the polarization characteristics of plane waves, that is, of parameterizing a transverse unit vector, such as the Jones vector, the Stokes vector, and the Poincare sphere. It discusses the connection between macroscopically defined quantities, such as the intensity or, more generally, the Stokes parameters, and microscopic field amplitudes. The material presented here is a portion of a more extensive treatment of propagation to be presented separately. The equations presented here have been described in various books and articles. They are collected here as a summary and review of theory needed when treating pulse propagation.
Directory of Open Access Journals (Sweden)
Tae-Dong Jeong
2013-10-01
Full Text Available Background: We compared the accuracy of the Modification of Diet in Renal Disease (MDRD study and Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI equations in Korean patients and evaluated the difference in CKD prevalence determined using the two equations in the Korean general population. Methods: The accuracy of the two equations was evaluated in 607 patients who underwent a chromium-51-ethylenediaminetetraacetic acid GFR measurement. Additionally, we compared the difference in CKD prevalence determined by the two equations among 5,822 participants in the fifth Korea National Health and Nutrition Examination Survey, 2010. Results: Among the 607 subjects, the median bias of the CKD-EPI equation was significantly lower than that of the MDRD study equation (0.9 vs. 2.2, p=0.020. The accuracy of the two equations was not significantly different in patients with mGFR 2; however, the accuracy of the CKD-EPI equation was significantly higher than that of the MDRD study equation in patients with GFR ≥60 mL/min/1.73m2. The prevalences of the CKD stages 1, 2 and 3 in the Korean general population were 47.56, 49.23, and 3.07%, respectively, for the MDRD study equation; and were 68.48, 28.89, and 2.49%, respectively, for the CKD-EPI equation. Conclusions: These data suggest that the CKD-EPI equation might be more useful in clinical practice than the MDRD study equation in Koreans.
Riccati differential equations
Brolih, Anita
2011-01-01
The intention of this thesis is to present Riccati differential equations, which are used in mathematics and in many other natural sciences. These equations are presented in their basic and in some specific forms and supported with several examples, which make this issue easier to understand. We will introduce mostly Riccati equations of first order and also their correlation with second-order differential equation. At the beginning of solving equations we will sum up the process of solvin...
Kinetic energy equations for the average-passage equation system
Johnson, Richard W.; Adamczyk, John J.
1989-01-01
Important kinetic energy equations derived from the average-passage equation sets are documented, with a view to their interrelationships. These kinetic equations may be used for closing the average-passage equations. The turbulent kinetic energy transport equation used is formed by subtracting the mean kinetic energy equation from the averaged total instantaneous kinetic energy equation. The aperiodic kinetic energy equation, averaged steady kinetic energy equation, averaged unsteady kinetic energy equation, and periodic kinetic energy equation, are also treated.
Introduction to differential equations
Taylor, Michael E
2011-01-01
The mathematical formulations of problems in physics, economics, biology, and other sciences are usually embodied in differential equations. The analysis of the resulting equations then provides new insight into the original problems. This book describes the tools for performing that analysis. The first chapter treats single differential equations, emphasizing linear and nonlinear first order equations, linear second order equations, and a class of nonlinear second order equations arising from Newton's laws. The first order linear theory starts with a self-contained presentation of the exponen
Uraltseva, N N
1995-01-01
This collection focuses on nonlinear problems in partial differential equations. Most of the papers are based on lectures presented at the seminar on partial differential equations and mathematical physics at St. Petersburg University. Among the topics explored are the existence and properties of solutions of various classes of nonlinear evolution equations, nonlinear imbedding theorems, bifurcations of solutions, and equations of mathematical physics (Navier-Stokes type equations and the nonlinear Schrödinger equation). The book will be useful to researchers and graduate students working in p
40 CFR 63.1513 - Equations for determining compliance.
2010-07-01
... 40 Protection of Environment 12 2010-07-01 2010-07-01 true Equations for determining compliance... Compliance Requirements § 63.1513 Equations for determining compliance. (a) THC emission limit. Use Equation... rate, Mg/hr (ton/hr). (b) PM, HCl and D/F emission limits. (1) Use Equation 7 of this section to...
Diffusion phenomenon for linear dissipative wave equations
Said-Houari, Belkacem
2012-01-01
In this paper we prove the diffusion phenomenon for the linear wave equation. To derive the diffusion phenomenon, a new method is used. In fact, for initial data in some weighted spaces, we prove that for {equation presented} decays with the rate {equation presented} [0,1] faster than that of either u or v, where u is the solution of the linear wave equation with initial data {equation presented} [0,1], and v is the solution of the related heat equation with initial data v 0 = u 0 + u 1. This result improves the result in H. Yang and A. Milani [Bull. Sci. Math. 124 (2000), 415-433] in the sense that, under the above restriction on the initial data, the decay rate given in that paper can be improved by t -γ/2. © European Mathematical Society.
Ordinary differential equations
Greenberg, Michael D
2014-01-01
Features a balance between theory, proofs, and examples and provides applications across diverse fields of study Ordinary Differential Equations presents a thorough discussion of first-order differential equations and progresses to equations of higher order. The book transitions smoothly from first-order to higher-order equations, allowing readers to develop a complete understanding of the related theory. Featuring diverse and interesting applications from engineering, bioengineering, ecology, and biology, the book anticipates potential difficulties in understanding the various solution steps
Beginning partial differential equations
O'Neil, Peter V
2014-01-01
A broad introduction to PDEs with an emphasis on specialized topics and applications occurring in a variety of fields Featuring a thoroughly revised presentation of topics, Beginning Partial Differential Equations, Third Edition provides a challenging, yet accessible,combination of techniques, applications, and introductory theory on the subjectof partial differential equations. The new edition offers nonstandard coverageon material including Burger's equation, the telegraph equation, damped wavemotion, and the use of characteristics to solve nonhomogeneous problems. The Third Edition is or
Energy Technology Data Exchange (ETDEWEB)
Ichiguchi, Katsuji [National Inst. for Fusion Science, Toki, Gifu (Japan)
1998-08-01
A new reduced set of resistive MHD equations is derived by averaging the full MHD equations on specified flux coordinates, which is consistent with 3D equilibria. It is confirmed that the total energy is conserved and the linearized equations for ideal modes are self-adjoint. (author)
Fractional Differential Equations
Directory of Open Access Journals (Sweden)
Jianping Zhao
2012-01-01
Full Text Available An extended fractional subequation method is proposed for solving fractional differential equations by introducing a new general ansätz and Bäcklund transformation of the fractional Riccati equation with known solutions. Being concise and straightforward, this method is applied to the space-time fractional coupled Burgers’ equations and coupled MKdV equations. As a result, many exact solutions are obtained. It is shown that the considered method provides a very effective, convenient, and powerful mathematical tool for solving fractional differential equations.
Lanczos's equation to replace Dirac's equation ?
Gsponer, Andre; Gsponer, Andre; Hurni, Jean-Pierre
1994-01-01
Lanczos's quaternionic interpretation of Dirac's equation provides a unified description for all elementary particles of spin 0, 1/2, 1, and 3/2. The Lagrangian formulation given by Einstein and Mayer in 1933 predicts two main classes of solutions. (1) Point like partons which come in two families, quarks and leptons. The correct fractional or integral electric and baryonic charges, and zero mass for the neutrino and the u-quark, are set by eigenvalue equations. The electro-weak interaction of the partons is the same as with the Standard model, with the same two free parameters: e and sin^2 theta. There is no need for a Higgs symmetry breaking mechanism. (2) Extended hadrons for which there is no simple eigenvalue equation for the mass. The strong interaction is essentially non-local. The pion mass and pion-nucleon coupling constant determine to first order the nucleon size, mass and anomalous magnetic moment.
Functional equations with causal operators
Corduneanu, C
2003-01-01
Functional equations encompass most of the equations used in applied science and engineering: ordinary differential equations, integral equations of the Volterra type, equations with delayed argument, and integro-differential equations of the Volterra type. The basic theory of functional equations includes functional differential equations with causal operators. Functional Equations with Causal Operators explains the connection between equations with causal operators and the classical types of functional equations encountered by mathematicians and engineers. It details the fundamentals of linear equations and stability theory and provides several applications and examples.
Stochastic differential equation model to Prendiville processes
Granita, Bahar, Arifah
2015-10-01
The Prendiville process is another variation of the logistic model which assumes linearly decreasing population growth rate. It is a continuous time Markov chain (CTMC) taking integer values in the finite interval. The continuous time Markov chain can be approximated by stochastic differential equation (SDE). This paper discusses the stochastic differential equation of Prendiville process. The work started with the forward Kolmogorov equation in continuous time Markov chain of Prendiville process. Then it was formulated in the form of a central-difference approximation. The approximation was then used in Fokker-Planck equation in relation to the stochastic differential equation of the Prendiville process. The explicit solution of the Prendiville process was obtained from the stochastic differential equation. Therefore, the mean and variance function of the Prendiville process could be easily found from the explicit solution.
Elliptic partial differential equations
Volpert, Vitaly
If we had to formulate in one sentence what this book is about it might be "How partial differential equations can help to understand heat explosion, tumor growth or evolution of biological species". These and many other applications are described by reaction-diffusion equations. The theory of reaction-diffusion equations appeared in the first half of the last century. In the present time, it is widely used in population dynamics, chemical physics, biomedical modelling. The purpose of this book is to present the mathematical theory of reaction-diffusion equations in the context of their numerous applications. We will go from the general mathematical theory to specific equations and then to their applications. Mathematical anaylsis of reaction-diffusion equations will be based on the theory of Fredholm operators presented in the first volume. Existence, stability and bifurcations of solutions will be studied for bounded domains and in the case of travelling waves. The classical theory of reaction-diffusion equ...
Differential equations for dummies
Holzner, Steven
2008-01-01
The fun and easy way to understand and solve complex equations Many of the fundamental laws of physics, chemistry, biology, and economics can be formulated as differential equations. This plain-English guide explores the many applications of this mathematical tool and shows how differential equations can help us understand the world around us. Differential Equations For Dummies is the perfect companion for a college differential equations course and is an ideal supplemental resource for other calculus classes as well as science and engineering courses. It offers step-by-step techniques, practical tips, numerous exercises, and clear, concise examples to help readers improve their differential equation-solving skills and boost their test scores.
Partial differential equations
Evans, Lawrence C
2010-01-01
This text gives a comprehensive survey of modern techniques in the theoretical study of partial differential equations (PDEs) with particular emphasis on nonlinear equations. The exposition is divided into three parts: representation formulas for solutions; theory for linear partial differential equations; and theory for nonlinear partial differential equations. Included are complete treatments of the method of characteristics; energy methods within Sobolev spaces; regularity for second-order elliptic, parabolic, and hyperbolic equations; maximum principles; the multidimensional calculus of variations; viscosity solutions of Hamilton-Jacobi equations; shock waves and entropy criteria for conservation laws; and, much more.The author summarizes the relevant mathematics required to understand current research in PDEs, especially nonlinear PDEs. While he has reworked and simplified much of the classical theory (particularly the method of characteristics), he primarily emphasizes the modern interplay between funct...
Directory of Open Access Journals (Sweden)
Wei Khim Ng
2009-02-01
Full Text Available We construct nonlinear extensions of Dirac's relativistic electron equation that preserve its other desirable properties such as locality, separability, conservation of probability and Poincaré invariance. We determine the constraints that the nonlinear term must obey and classify the resultant non-polynomial nonlinearities in a double expansion in the degree of nonlinearity and number of derivatives. We give explicit examples of such nonlinear equations, studying their discrete symmetries and other properties. Motivated by some previously suggested applications we then consider nonlinear terms that simultaneously violate Lorentz covariance and again study various explicit examples. We contrast our equations and construction procedure with others in the literature and also show that our equations are not gauge equivalent to the linear Dirac equation. Finally we outline various physical applications for these equations.
Differential equations I essentials
REA, Editors of
2012-01-01
REA's Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Differential Equations I covers first- and second-order equations, series solutions, higher-order linear equations, and the Laplace transform.
Directory of Open Access Journals (Sweden)
K. Banoo
1998-01-01
equation in the discrete momentum space. This is shown to be similar to the conventional drift-diffusion equation except that it is a more rigorous solution to the Boltzmann equation because the current and carrier densities are resolved into M×1 vectors, where M is the number of modes in the discrete momentum space. The mobility and diffusion coefficient become M×M matrices which connect the M momentum space modes. This approach is demonstrated by simulating electron transport in bulk silicon.
Ordinary differential equations
Pontryagin, Lev Semenovich
1962-01-01
Ordinary Differential Equations presents the study of the system of ordinary differential equations and its applications to engineering. The book is designed to serve as a first course in differential equations. Importance is given to the linear equation with constant coefficients; stability theory; use of matrices and linear algebra; and the introduction to the Lyapunov theory. Engineering problems such as the Watt regulator for a steam engine and the vacuum-tube circuit are also presented. Engineers, mathematicians, and engineering students will find the book invaluable.
Validating and Improving Interrill Erosion Equations
Zhang, Feng-Bao; Wang, Zhan-Li; Yang, Ming-Yi
2014-01-01
Existing interrill erosion equations based on mini-plot experiments have largely ignored the effects of slope length and plot size on interrill erosion rate. This paper describes a series of simulated rainfall experiments which were conducted according to a randomized factorial design for five slope lengths (0.4, 0.8, 1.2, 1.6, and 2 m) at a width of 0.4 m, five slope gradients (17%, 27%, 36%, 47%, and 58%), and five rainfall intensities (48, 62.4, 102, 149, and 170 mm h−1) to perform a systematic validation of existing interrill erosion equations based on mini-plots. The results indicated that the existing interrill erosion equations do not adequately describe the relationships between interrill erosion rate and its influencing factors with increasing slope length and rainfall intensity. Univariate analysis of variance showed that runoff rate, rainfall intensity, slope gradient, and slope length had significant effects on interrill erosion rate and that their interactions were significant at p = 0.01. An improved interrill erosion equation was constructed by analyzing the relationships of sediment concentration with rainfall intensity, slope length, and slope gradient. In the improved interrill erosion equation, the runoff rate and slope factor are the same as in the interrill erosion equation in the Water Erosion Prediction Project (WEPP), with the weight of rainfall intensity adjusted by an exponent of 0.22 and a slope length term added with an exponent of −0.25. Using experimental data from WEPP cropland soil field interrill erodibility experiments, it has been shown that the improved interrill erosion equation describes the relationship between interrill erosion rate and runoff rate, rainfall intensity, slope gradient, and slope length reasonably well and better than existing interrill erosion equations. PMID:24516624
Indian Academy of Sciences (India)
role in converting the Fokas equation into Hirota's bilinear form. Keywords. Bilinearization; multisoliton solution; Fokas equation; Hirota's bilinear method. PACS Nos 05.45.Yv; 04.20.Jb; 02.30.Jr. 1. Introduction. As pointed out by Drazin and Johnson [1], it is not easy to give a comprehensive and precise definition of a soliton.
Elliptic Quadratic Operator Equations
Ganikhodjaev, Rasul; Mukhamedov, Farrukh; Saburov, Mansoor
2017-01-01
In the present paper is devoted to the study of elliptic quadratic operator equations over the finite dimensional Euclidean space. We provide necessary and sufficient conditions for the existence of solutions of elliptic quadratic operator equations. The iterative Newton-Kantorovich method is also presented for stable solutions.
Directory of Open Access Journals (Sweden)
Hannelore Breckner
2000-01-01
Full Text Available We consider a stochastic equation of Navier-Stokes type containing a noise part given by a stochastic integral with respect to a Wiener process. The purpose of this paper is to approximate the solution of this nonlinear equation by the Galerkin method. We prove the convergence in mean square.
Stochastic Differential Equations
Cecconi, Jaures
2011-01-01
C. Doleans-Dade: Stochastic processes and stochastic differential equations.- A. Friedman: Stochastic differential equations and applications.- D.W. Stroock, S.R.S. Varadhan: Theory of diffusion processes.- G.C. Papanicolaou: Wave propagation and heat conduction in a random medium.- C. Dewitt Morette: A stochastic problem in Physics.- G.S. Goodman: The embedding problem for stochastic matrices.
Indian Academy of Sciences (India)
Abstract. The Raychaudhuri equation is central to the understanding of gravitational attraction in astrophysics and cosmology, and in particular underlies the famous singularity theorems of general relativity theory. This paper reviews the derivation of the equation, and its significance in cosmology.
Differential Equation of Equilibrium
African Journals Online (AJOL)
user
differential equation of equilibrium, comparable to that of beam on elastic foundation, was derived from static principles on the ... tedious and more time saving than the classical method in the solution of the aforementioned differential equation. ... silos, pipelines, bridge arches or wind turbine towers [3]. The objective of this ...
Applied partial differential equations
Logan, J David
2004-01-01
This primer on elementary partial differential equations presents the standard material usually covered in a one-semester, undergraduate course on boundary value problems and PDEs. What makes this book unique is that it is a brief treatment, yet it covers all the major ideas: the wave equation, the diffusion equation, the Laplace equation, and the advection equation on bounded and unbounded domains. Methods include eigenfunction expansions, integral transforms, and characteristics. Mathematical ideas are motivated from physical problems, and the exposition is presented in a concise style accessible to science and engineering students; emphasis is on motivation, concepts, methods, and interpretation, rather than formal theory. This second edition contains new and additional exercises, and it includes a new chapter on the applications of PDEs to biology: age structured models, pattern formation; epidemic wave fronts, and advection-diffusion processes. The student who reads through this book and solves many of t...
Nonlocal higher order evolution equations
Rossi, Julio D.
2010-06-01
In this article, we study the asymptotic behaviour of solutions to the nonlocal operator ut(x, t)1/4(-1)n-1 (J*Id -1)n (u(x, t)), x ∈ ℝN, which is the nonlocal analogous to the higher order local evolution equation vt(-1)n-1(Δ)nv. We prove that the solutions of the nonlocal problem converge to the solution of the higher order problem with the right-hand side given by powers of the Laplacian when the kernel J is rescaled in an appropriate way. Moreover, we prove that solutions to both equations have the same asymptotic decay rate as t goes to infinity. © 2010 Taylor & Francis.
Turbulence kinetic energy equation for dilute suspensions
Abou-Arab, T. W.; Roco, M. C.
1989-01-01
A multiphase turbulence closure model is presented which employs one transport equation, namely the turbulence kinetic energy equation. The proposed form of this equation is different from the earlier formulations in some aspects. The power spectrum of the carrier fluid is divided into two regions, which interact in different ways and at different rates with the suspended particles as a function of the particle-eddy size ratio and density ratio. The length scale is described algebraically. A mass/time averaging procedure for the momentum and kinetic energy equations is adopted. The resulting turbulence correlations are modeled under less retrictive assumptions comparative to previous work. The closures for the momentum and kinetic energy equations are given. Comparisons of the predictions with experimental results on liquid-solid jet and gas-solid pipe flow show satisfactory agreement.
Uncertain differential equations
Yao, Kai
2016-01-01
This book introduces readers to the basic concepts of and latest findings in the area of differential equations with uncertain factors. It covers the analytic method and numerical method for solving uncertain differential equations, as well as their applications in the field of finance. Furthermore, the book provides a number of new potential research directions for uncertain differential equation. It will be of interest to researchers, engineers and students in the fields of mathematics, information science, operations research, industrial engineering, computer science, artificial intelligence, automation, economics, and management science.
Differential equations problem solver
Arterburn, David R
2012-01-01
REA's Problem Solvers is a series of useful, practical, and informative study guides. Each title in the series is complete step-by-step solution guide. The Differential Equations Problem Solver enables students to solve difficult problems by showing them step-by-step solutions to Differential Equations problems. The Problem Solvers cover material ranging from the elementary to the advanced and make excellent review books and textbook companions. They're perfect for undergraduate and graduate studies.The Differential Equations Problem Solver is the perfect resource for any class, any exam, and
Hyperbolic partial differential equations
Witten, Matthew
1986-01-01
Hyperbolic Partial Differential Equations III is a refereed journal issue that explores the applications, theory, and/or applied methods related to hyperbolic partial differential equations, or problems arising out of hyperbolic partial differential equations, in any area of research. This journal issue is interested in all types of articles in terms of review, mini-monograph, standard study, or short communication. Some studies presented in this journal include discretization of ideal fluid dynamics in the Eulerian representation; a Riemann problem in gas dynamics with bifurcation; periodic M
Ordinary differential equations
Miller, Richard K
1982-01-01
Ordinary Differential Equations is an outgrowth of courses taught for a number of years at Iowa State University in the mathematics and the electrical engineering departments. It is intended as a text for a first graduate course in differential equations for students in mathematics, engineering, and the sciences. Although differential equations is an old, traditional, and well-established subject, the diverse backgrounds and interests of the students in a typical modern-day course cause problems in the selection and method of presentation of material. In order to compensate for this diversity,
Fully nonlinear elliptic equations
Caffarelli, Luis A
1995-01-01
The goal of the book is to extend classical regularity theorems for solutions of linear elliptic partial differential equations to the context of fully nonlinear elliptic equations. This class of equations often arises in control theory, optimization, and other applications. The authors give a detailed presentation of all the necessary techniques. Instead of treating these techniques in their greatest generality, they outline the key ideas and prove the results needed for developing the subsequent theory. Topics discussed in the book include the theory of viscosity solutions for nonlinear equa
Beginning partial differential equations
O'Neil, Peter V
2011-01-01
A rigorous, yet accessible, introduction to partial differential equations-updated in a valuable new edition Beginning Partial Differential Equations, Second Edition provides a comprehensive introduction to partial differential equations (PDEs) with a special focus on the significance of characteristics, solutions by Fourier series, integrals and transforms, properties and physical interpretations of solutions, and a transition to the modern function space approach to PDEs. With its breadth of coverage, this new edition continues to present a broad introduction to the field, while also addres
Applied partial differential equations
Logan, J David
2015-01-01
This text presents the standard material usually covered in a one-semester, undergraduate course on boundary value problems and PDEs. Emphasis is placed on motivation, concepts, methods, and interpretation, rather than on formal theory. The concise treatment of the subject is maintained in this third edition covering all the major ideas: the wave equation, the diffusion equation, the Laplace equation, and the advection equation on bounded and unbounded domains. Methods include eigenfunction expansions, integral transforms, and characteristics. In this third edition, text remains intimately tied to applications in heat transfer, wave motion, biological systems, and a variety other topics in pure and applied science. The text offers flexibility to instructors who, for example, may wish to insert topics from biology or numerical methods at any time in the course. The exposition is presented in a friendly, easy-to-read, style, with mathematical ideas motivated from physical problems. Many exercises and worked e...
Applied partial differential equations
DuChateau, Paul
2012-01-01
Book focuses mainly on boundary-value and initial-boundary-value problems on spatially bounded and on unbounded domains; integral transforms; uniqueness and continuous dependence on data, first-order equations, and more. Numerous exercises included.
Fun with Differential Equations
Indian Academy of Sciences (India)
/fulltext/reso/018/06/0543-0557. Keywords. Differential equations; trigonometric functions; elliptic integrals. Author Affiliations. B V Rao1. Chennai Mathematical Institute PlotH1,SIPCOTIT Park Siruseri, Padur Post Chennai 603 103, TN, India.
Saaty, Thomas L
1981-01-01
Covers major types of classical equations: operator, functional, difference, integro-differential, and more. Suitable for graduate students as well as scientists, technologists, and mathematicians. "A welcome contribution." - Math Reviews. 1964 edition.
Tod, Paul
2013-01-01
I review the equations of Conformal Cyclic Cosmology given by Penrose. I suggest a slight modification to Penrose's prescription and show how this works out for FRW cosmologies and for Class A Bianchi cosmologies.
Geometry of differential equations
Khovanskiĭ, A; Vassiliev, V
1998-01-01
This volume contains articles written by V. I. Arnold's colleagues on the occasion of his 60th birthday. The articles are mostly devoted to various aspects of geometry of differential equations and relations to global analysis and Hamiltonian mechanics.
Diophantine Equations and Computation
Davis, Martin
Unless otherwise stated, we’ll work with the natural numbers: N = \\{0,1,2,3, dots\\}. Consider a Diophantine equation F(a1,a2,...,an,x1,x2,...,xm) = 0 with parameters a1,a2,...,an and unknowns x1,x2,...,xm For such a given equation, it is usual to ask: For which values of the parameters does the equation have a solution in the unknowns? In other words, find the set: \\{ mid exists x_1,ldots,x_m [F(a_1,ldots,x_1,ldots)=0] \\} Inverting this, we think of the equation F = 0 furnishing a definition of this set, and we distinguish three classes: a set is called Diophantine if it has such a definition in which F is a polynomial with integer coefficients. We write \\cal D for the class of Diophantine sets.
Nonlinear differential equations
Energy Technology Data Exchange (ETDEWEB)
Dresner, L.
1988-01-01
This report is the text of a graduate course on nonlinear differential equations given by the author at the University of Wisconsin-Madison during the summer of 1987. The topics covered are: direction fields of first-order differential equations; the Lie (group) theory of ordinary differential equations; similarity solutions of second-order partial differential equations; maximum principles and differential inequalities; monotone operators and iteration; complementary variational principles; and stability of numerical methods. The report should be of interest to graduate students, faculty, and practicing scientists and engineers. No prior knowledge is required beyond a good working knowledge of the calculus. The emphasis is on practical results. Most of the illustrative examples are taken from the fields of nonlinear diffusion, heat and mass transfer, applied superconductivity, and helium cryogenics.
Problems in differential equations
Brenner, J L
2013-01-01
More than 900 problems and answers explore applications of differential equations to vibrations, electrical engineering, mechanics, and physics. Problem types include both routine and nonroutine, and stars indicate advanced problems. 1963 edition.
Electromagnetic Interaction Equations
Zinoviev, Yury M.
2009-01-01
For the electromagnetic interaction of two particles the relativistic quantum mechanics equations are proposed. These equations are solved for the case when one particle has a small mass and moves freely. The initial wave functions are supposed to be concentrated at the coordinates origin. The energy spectrum of another particle wave function is defined by the initial wave function of the free moving particle. Choosing the initial wave function of the free moving particle it is possible to ob...
Ordinary differential equations.
Lebl, Jiří
2013-01-01
In this chapter we provide an overview of the basic theory of ordinary differential equations (ODE). We give the basics of analytical methods for their solutions and also review numerical methods. The chapter should serve as a primer for the basic application of ODEs and systems of ODEs in practice. As an example, we work out the equations arising in Michaelis-Menten kinetics and give a short introduction to using Matlab for their numerical solution.
Relativistic Guiding Center Equations
Energy Technology Data Exchange (ETDEWEB)
White, R. B. [PPPL; Gobbin, M. [Euratom-ENEA Association
2014-10-01
In toroidal fusion devices it is relatively easy that electrons achieve relativistic velocities, so to simulate runaway electrons and other high energy phenomena a nonrelativistic guiding center formalism is not sufficient. Relativistic guiding center equations including flute mode time dependent field perturbations are derived. The same variables as used in a previous nonrelativistic guiding center code are adopted, so that a straightforward modifications of those equations can produce a relativistic version.
Modelling conjugation with stochastic differential equations
DEFF Research Database (Denmark)
Philipsen, Kirsten Riber; Christiansen, Lasse Engbo; Hasman, Henrik
2010-01-01
Conjugation is an important mechanism involved in the transfer of resistance between bacteria. In this article a stochastic differential equation based model consisting of a continuous time state equation and a discrete time measurement equation is introduced to model growth and conjugation of two...... Enterococcus faecium strains in a rich exhaustible media. The model contains a new expression for a substrate dependent conjugation rate. A maximum likelihood based method is used to estimate the model parameters. Different models including different noise structure for the system and observations are compared...
Deriving the bond pricing equation
Directory of Open Access Journals (Sweden)
Kožul Nataša
2014-01-01
Full Text Available Given the recent focus on Eurozone debt crisis and the credit rating downgrade not only of US debt, but that of other countries and many UK major banking institutions, this paper aims to explain the concept of bond yield, its different measures and bond pricing equation. Yields on capital market instruments are rarely quoted on the same basis, which makes direct comparison between different as investment choices impossible. Some debt instruments are quoted on discount basis, whilst coupon-bearing ones accrue interest differently, offer different compounding opportunities, have different coupon payment frequencies, and manage non-business day maturity dates differently. Moreover, rules governing debt vary across countries, markets and currencies, making yield calculation and comparison a rather complex issue. Thus, some fundamental concepts applicable to debt instrument yield measurement, with focus on bond equation, are presented here. In addition, bond equation expressed in annuity form and used to apply Newton-Raphson algorithm to derive true bond yield is also shown.
Directory of Open Access Journals (Sweden)
Florian Ion Tiberiu Petrescu
2015-09-01
Full Text Available This paper presents the dynamic, original, machine motion equations. The equation of motion of the machine that generates angular speed of the shaft (which varies with position and rotation speed is deduced by conservation kinetic energy of the machine. An additional variation of angular speed is added by multiplying by the coefficient dynamic D (generated by the forces out of mechanism and or by the forces generated by the elasticity of the system. Kinetic energy conservation shows angular speed variation (from the shaft with inertial masses, while the dynamic coefficient introduces the variation of w with forces acting in the mechanism. Deriving the first equation of motion of the machine one can obtain the second equation of motion dynamic. From the second equation of motion of the machine it determines the angular acceleration of the shaft. It shows the distribution of the forces on the mechanism to the internal combustion heat engines. Dynamic, the velocities can be distributed in the same way as forces. Practically, in the dynamic regimes, the velocities have the same timing as the forces. Calculations should be made for an engine with a single cylinder. Originally exemplification is done for a classic distribution mechanism, and then even the module B distribution mechanism of an Otto engine type.
Introduction to partial differential equations
Greenspan, Donald
2000-01-01
Designed for use in a one-semester course by seniors and beginning graduate students, this rigorous presentation explores practical methods of solving differential equations, plus the unifying theory underlying the mathematical superstructure. Topics include basic concepts, Fourier series, second-order partial differential equations, wave equation, potential equation, heat equation, approximate solution of partial differential equations, and more. Exercises appear at the ends of most chapters. 1961 edition.
Stochastic porous media equations
Barbu, Viorel; Röckner, Michael
2016-01-01
Focusing on stochastic porous media equations, this book places an emphasis on existence theorems, asymptotic behavior and ergodic properties of the associated transition semigroup. Stochastic perturbations of the porous media equation have reviously been considered by physicists, but rigorous mathematical existence results have only recently been found. The porous media equation models a number of different physical phenomena, including the flow of an ideal gas and the diffusion of a compressible fluid through porous media, and also thermal propagation in plasma and plasma radiation. Another important application is to a model of the standard self-organized criticality process, called the "sand-pile model" or the "Bak-Tang-Wiesenfeld model". The book will be of interest to PhD students and researchers in mathematics, physics and biology.
Boussinesq evolution equations
DEFF Research Database (Denmark)
Bredmose, Henrik; Schaffer, H.; Madsen, Per A.
2004-01-01
This paper deals with the possibility of using methods and ideas from time domain Boussinesq formulations in the corresponding frequency domain formulations. We term such frequency domain models "evolution equations". First, we demonstrate that the numerical efficiency of the deterministic...... Boussinesq evolution equations of Madsen and Sorensen [Madsen, P.A., Sorensen, O.R., 1993. Bound waves and triad interactions in shallow water. Ocean Eng. 20 359-388] can be improved by using Fast Fourier Transforms to evaluate the nonlinear terms. For a practical example of irregular waves propagating over...... a submerged bar, it is demonstrated that evolution equations utilising FFT can be solved around 100 times faster than the corresponding time domain model. Use of FFT provides an efficient bridge between the frequency domain and the time domain. We utilise this by adapting the surface roller model for wave...
Quadratic Diophantine equations
Andreescu, Titu
2015-01-01
This monograph treats the classical theory of quadratic Diophantine equations and guides the reader through the last two decades of computational techniques and progress in the area. These new techniques combined with the latest increases in computational power shed new light on important open problems. The authors motivate the study of quadratic Diophantine equations with excellent examples, open problems, and applications. Moreover, the exposition aptly demonstrates many applications of results and techniques from the study of Pell-type equations to other problems in number theory. The book is intended for advanced undergraduate and graduate students as well as researchers. It challenges the reader to apply not only specific techniques and strategies, but also to employ methods and tools from other areas of mathematics, such as algebra and analysis.
Partial differential equations
Agranovich, M S
2002-01-01
Mark Vishik's Partial Differential Equations seminar held at Moscow State University was one of the world's leading seminars in PDEs for over 40 years. This book celebrates Vishik's eightieth birthday. It comprises new results and survey papers written by many renowned specialists who actively participated over the years in Vishik's seminars. Contributions include original developments and methods in PDEs and related fields, such as mathematical physics, tomography, and symplectic geometry. Papers discuss linear and nonlinear equations, particularly linear elliptic problems in angles and gener
Equations of mathematical physics
Tikhonov, A N
2011-01-01
Mathematical physics plays an important role in the study of many physical processes - hydrodynamics, elasticity, and electrodynamics, to name just a few. Because of the enormous range and variety of problems dealt with by mathematical physics, this thorough advanced-undergraduate or graduate-level text considers only those problems leading to partial differential equations. The authors - two well-known Russian mathematicians - have focused on typical physical processes and the principal types of equations deailing with them. Special attention is paid throughout to mathematical formulation, ri
Systematic Equation Formulation
DEFF Research Database (Denmark)
Lindberg, Erik
2007-01-01
A tutorial giving a very simple introduction to the set-up of the equations used as a model for an electrical/electronic circuit. The aim is to find a method which is as simple and general as possible with respect to implementation in a computer program. The “Modified Nodal Approach”, MNA, and th......, and the “Controlled Source Approach”, CSA, for systematic equation formulation are investigated. It is suggested that the kernel of the P Spice program based on MNA is reprogrammed....
Li, Tatsien
2017-01-01
This book focuses on nonlinear wave equations, which are of considerable significance from both physical and theoretical perspectives. It also presents complete results on the lower bound estimates of lifespan (including the global existence), which are established for classical solutions to the Cauchy problem of nonlinear wave equations with small initial data in all possible space dimensions and with all possible integer powers of nonlinear terms. Further, the book proposes the global iteration method, which offers a unified and straightforward approach for treating these kinds of problems. Purely based on the properties of solut ions to the corresponding linear problems, the method simply applies the contraction mapping principle.
Generalized estimating equations
Hardin, James W
2002-01-01
Although powerful and flexible, the method of generalized linear models (GLM) is limited in its ability to accurately deal with longitudinal and clustered data. Developed specifically to accommodate these data types, the method of Generalized Estimating Equations (GEE) extends the GLM algorithm to accommodate the correlated data encountered in health research, social science, biology, and other related fields.Generalized Estimating Equations provides the first complete treatment of GEE methodology in all of its variations. After introducing the subject and reviewing GLM, the authors examine th
Conservation laws for equations related to soil water equations
Directory of Open Access Journals (Sweden)
Khalique C. M.
2005-01-01
Full Text Available We obtain all nontrivial conservation laws for a class of ( 2+1 nonlinear evolution partial differential equations which are related to the soil water equations. It is also pointed out that nontrivial conservation laws exist for certain classes of equations which admit point symmetries. Moreover, we associate symmetries with conservation laws for special classes of these equations.
Test equating methods and practices
Kolen, Michael J
1995-01-01
In recent years, many researchers in the psychology and statistical communities have paid increasing attention to test equating as issues of using multiple test forms have arisen and in response to criticisms of traditional testing techniques This book provides a practically oriented introduction to test equating which both discusses the most frequently used equating methodologies and covers many of the practical issues involved The main themes are - the purpose of equating - distinguishing between equating and related methodologies - the importance of test equating to test development and quality control - the differences between equating properties, equating designs, and equating methods - equating error, and the underlying statistical assumptions for equating The authors are acknowledged experts in the field, and the book is based on numerous courses and seminars they have presented As a result, educators, psychometricians, professionals in measurement, statisticians, and students coming to the subject for...
Differential Equations Models to Study Quorum Sensing.
Pérez-Velázquez, Judith; Hense, Burkhard A
2018-01-01
Mathematical models to study quorum sensing (QS) have become an important tool to explore all aspects of this type of bacterial communication. A wide spectrum of mathematical tools and methods such as dynamical systems, stochastics, and spatial models can be employed. In this chapter, we focus on giving an overview of models consisting of differential equations (DE), which can be used to describe changing quantities, for example, the dynamics of one or more signaling molecule in time and space, often in conjunction with bacterial growth dynamics. The chapter is divided into two sections: ordinary differential equations (ODE) and partial differential equations (PDE) models of QS. Rates of change are represented mathematically by derivatives, i.e., in terms of DE. ODE models allow describing changes in one independent variable, for example, time. PDE models can be used to follow changes in more than one independent variable, for example, time and space. Both types of models often consist of systems (i.e., more than one equation) of equations, such as equations for bacterial growth and autoinducer concentration dynamics. Almost from the onset, mathematical modeling of QS using differential equations has been an interdisciplinary endeavor and many of the works we revised here will be placed into their biological context.
The Statistical Drake Equation
Maccone, Claudio
2010-12-01
We provide the statistical generalization of the Drake equation. From a simple product of seven positive numbers, the Drake equation is now turned into the product of seven positive random variables. We call this "the Statistical Drake Equation". The mathematical consequences of this transformation are then derived. The proof of our results is based on the Central Limit Theorem (CLT) of Statistics. In loose terms, the CLT states that the sum of any number of independent random variables, each of which may be ARBITRARILY distributed, approaches a Gaussian (i.e. normal) random variable. This is called the Lyapunov Form of the CLT, or the Lindeberg Form of the CLT, depending on the mathematical constraints assumed on the third moments of the various probability distributions. In conclusion, we show that: The new random variable N, yielding the number of communicating civilizations in the Galaxy, follows the LOGNORMAL distribution. Then, as a consequence, the mean value of this lognormal distribution is the ordinary N in the Drake equation. The standard deviation, mode, and all the moments of this lognormal N are also found. The seven factors in the ordinary Drake equation now become seven positive random variables. The probability distribution of each random variable may be ARBITRARY. The CLT in the so-called Lyapunov or Lindeberg forms (that both do not assume the factors to be identically distributed) allows for that. In other words, the CLT "translates" into our statistical Drake equation by allowing an arbitrary probability distribution for each factor. This is both physically realistic and practically very useful, of course. An application of our statistical Drake equation then follows. The (average) DISTANCE between any two neighboring and communicating civilizations in the Galaxy may be shown to be inversely proportional to the cubic root of N. Then, in our approach, this distance becomes a new random variable. We derive the relevant probability density
Hypocoercivity for linear kinetic equations conserving mass
Dolbeault, Jean
2015-02-03
We develop a new method for proving hypocoercivity for a large class of linear kinetic equations with only one conservation law. Local mass conservation is assumed at the level of the collision kernel, while transport involves a confining potential, so that the solution relaxes towards a unique equilibrium state. Our goal is to evaluate in an appropriately weighted $ L^2$ norm the exponential rate of convergence to the equilibrium. The method covers various models, ranging from diffusive kinetic equations like Vlasov-Fokker-Planck equations, to scattering models or models with time relaxation collision kernels corresponding to polytropic Gibbs equilibria, including the case of the linear Boltzmann model. In this last case and in the case of Vlasov-Fokker-Planck equations, any linear or superlinear growth of the potential is allowed. - See more at: http://www.ams.org/journals/tran/2015-367-06/S0002-9947-2015-06012-7/#sthash.ChjyK6rc.dpuf
Calculus & ordinary differential equations
Pearson, David
1995-01-01
Professor Pearson's book starts with an introduction to the area and an explanation of the most commonly used functions. It then moves on through differentiation, special functions, derivatives, integrals and onto full differential equations. As with other books in the series the emphasis is on using worked examples and tutorial-based problem solving to gain the confidence of students.
Equational binary decision diagrams
J.F. Groote (Jan Friso); J.C. van de Pol (Jaco)
2000-01-01
textabstractWe incorporate equations in binary decision diagrams (BDD). The resulting objects are called EQ-BDDs. A straightforward notion of ordered EQ-BDDs (EQ-OBDD) is defined, and it is proved that each EQ-BDD is logically equivalent to an EQ-OBDD. Moreover, on EQ-OBDDs satisfiability and
Sonoda, Hidenori
2005-01-01
An application of the exact renormalization group equations to the scalar field theory in three dimensional euclidean space is discussed. We show how to modify the original formulation by J. Polchinski in order to find the Wilson-Fisher fixed point using perturbation theory.
Fay, Temple H.
2010-01-01
Through numerical investigations, we study examples of the forced quadratic spring equation [image omitted]. By performing trial-and-error numerical experiments, we demonstrate the existence of stability boundaries in the phase plane indicating initial conditions yielding bounded solutions, investigate the resonance boundary in the [omega]…
Equational term graph rewriting
Z.M. Ariola (Zena); J.W. Klop (Jan Willem)
1995-01-01
textabstractWe present an equational framework for term graph rewriting with cycles. The usual notion of homomorphism is phrased in terms of the notion of bisimulation, which is well-known in process algebra and concurrency theory. Specifically, a homomorphism is a functional bisimulation. We prove
DEFF Research Database (Denmark)
Dyre, Jeppe
1995-01-01
energies chosen randomly according to a Gaussian. The random-walk model is here derived from Newton's laws by making a number of simplifying assumptions. In the second part of the paper an approximate low-temperature description of energy fluctuations in the random-walk modelthe energy master equation...
Modelling by Differential Equations
Chaachoua, Hamid; Saglam, Ayse
2006-01-01
This paper aims to show the close relation between physics and mathematics taking into account especially the theory of differential equations. By analysing the problems posed by scientists in the seventeenth century, we note that physics is very important for the emergence of this theory. Taking into account this analysis, we show the…
Directory of Open Access Journals (Sweden)
Hatem Mejjaoli
2008-12-01
Full Text Available We introduce and study the Dunkl symmetric systems. We prove the well-posedness results for the Cauchy problem for these systems. Eventually we describe the finite speed of it. Next the semi-linear Dunkl-wave equations are also studied.
Dzhunushaliev, Vladimir
2010-01-01
Stochastic Einstein equations are considered when 3D space metric $\\gamma_{ij}$ are stochastic functions. The probability density for the stochastic quantities is connected with the Perelman's entropy functional. As an example, the Friedman Universe is considered. It is shown that for the Friedman Universe the dynamical evolution is not changed. The connection between general relativity and Ricci flows is discussed.
Partial differential equations
Indian Academy of Sciences (India)
of solutions in the spirit of the work of Gidas–. Ni–Nirenberg, etc. No effort is being made in this writeup to explain their significance in which case the article would go beyond resonable length. References. [1] Brezis H and Nirenberg L 1983 Positive Solutions of nonlinear elliptic equations involving critical Sobolev.
Structural Equation Model Trees
Brandmaier, Andreas M.; von Oertzen, Timo; McArdle, John J.; Lindenberger, Ulman
2013-01-01
In the behavioral and social sciences, structural equation models (SEMs) have become widely accepted as a modeling tool for the relation between latent and observed variables. SEMs can be seen as a unification of several multivariate analysis techniques. SEM Trees combine the strengths of SEMs and the decision tree paradigm by building tree…
Differential Equation of Equilibrium
African Journals Online (AJOL)
user
ABSTRACT. Analysis of underground circular cylindrical shell is carried out in this work. The forth order differential equation of equilibrium, comparable to that of beam on elastic foundation, was derived from static principles on the assumptions of P. L Pasternak. Laplace transformation was used to solve the governing ...
Differential Equations as Actions
DEFF Research Database (Denmark)
Ronkko, Mauno; Ravn, Anders P.
1997-01-01
We extend a conventional action system with a primitive action consisting of a differential equation and an evolution invariant. The semantics is given by a predicate transformer. The weakest liberal precondition is chosen, because it is not always desirable that steps corresponding to differential...
African Journals Online (AJOL)
compaction are two parameters that indicate the degree of compaction in sandstones. When the values are low, the sands are undercompacted, but when they are high the sands are compacted. A number of equations relating porosity and depth in sandstones have been published (Athy,. 1930; Hubbert and Rubey, 1959; ...
ANTHROPOMETRIC PREDICTIVE EQUATIONS FOR ...
African Journals Online (AJOL)
Equations to Estimate Body Composition. Military Medicine. pp. 12-15. Chada, D.S.; Singh, G.P.; Vasdev, V. and Ganjoo, RK. 2006. Anthropometry Correlation of Lipid. Profile in Healthy Aviators. Indian Journal of. Aerospace Med 50 (2), pp. 32 - 36. Dae, J. 2003 . Bodyometryfutrex, http:// www.futrex.com/6100htm/, pp 1-3.
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 15; Issue 8. The Freudenstein Equation - Design of Four-Link Mechanisms. Ashitava Ghosal. General Article Volume 15 Issue 8 August 2010 pp 699-710. Fulltext. Click here to view fulltext PDF. Permanent link:
Problems in Hydrodynamics and Partial Differential Equations.
CALCULUS OF VARIATIONS, RESEARCH MANAGEMENT ), NONLINEAR DIFFERENTIAL EQUATIONS, PARTIAL DIFFERENTIAL EQUATIONS, BOUNDARY VALUE PROBLEMS, EQUATIONS, INEQUALITIES, MEASURE THEORY , INTEGRALS, ABSTRACTS
Lectures on partial differential equations
Petrovsky, I G
1992-01-01
Graduate-level exposition by noted Russian mathematician offers rigorous, transparent, highly readable coverage of classification of equations, hyperbolic equations, elliptic equations and parabolic equations. Wealth of commentary and insight invaluable for deepening understanding of problems considered in text. Translated from the Russian by A. Shenitzer.
Elements of partial differential equations
Sneddon, Ian N
2006-01-01
Geared toward students of applied rather than pure mathematics, this volume introduces elements of partial differential equations. Its focus is primarily upon finding solutions to particular equations rather than general theory.Topics include ordinary differential equations in more than two variables, partial differential equations of the first and second orders, Laplace's equation, the wave equation, and the diffusion equation. A helpful Appendix offers information on systems of surfaces, and solutions to the odd-numbered problems appear at the end of the book. Readers pursuing independent st
Elements of partial differential equations
Sneddon, Ian Naismith
1957-01-01
Geared toward students of applied rather than pure mathematics, this volume introduces elements of partial differential equations. Its focus is primarily upon finding solutions to particular equations rather than general theory.Topics include ordinary differential equations in more than two variables, partial differential equations of the first and second orders, Laplace's equation, the wave equation, and the diffusion equation. A helpful Appendix offers information on systems of surfaces, and solutions to the odd-numbered problems appear at the end of the book. Readers pursuing independent st
Stochastic differential equations and applications
Friedman, Avner
2006-01-01
This text develops the theory of systems of stochastic differential equations, and it presents applications in probability, partial differential equations, and stochastic control problems. Originally published in two volumes, it combines a book of basic theory and selected topics with a book of applications.The first part explores Markov processes and Brownian motion; the stochastic integral and stochastic differential equations; elliptic and parabolic partial differential equations and their relations to stochastic differential equations; the Cameron-Martin-Girsanov theorem; and asymptotic es
Partial difference equations arising from the Cauchy-Riemann equations
Directory of Open Access Journals (Sweden)
S. Haruki
2006-06-01
Full Text Available We consider some functional equations arising from the Cauchy-Riemann equations, and certain related functional equations. First we propose a new functional equation (E.1 below, over a $2$-divisible Abelian group, which is a discrete version of the Cauchy-Riemann equations, and give the general solutions of (E.1. Next we study a functional equation which is equivalent to (E.1. Further we propose and solve partial difference-differential functional equations and nonsymmetric partial difference equations which are also arising from the Cauchy--Riemann equations. [ f(x+t,y- f(x-t,y = - i [f(x,y+t- f(x,y-t]. (E.1
Classical Diophantine equations
1993-01-01
The author had initiated a revision and translation of "Classical Diophantine Equations" prior to his death. Given the rapid advances in transcendence theory and diophantine approximation over recent years, one might fear that the present work, originally published in Russian in 1982, is mostly superseded. That is not so. A certain amount of updating had been prepared by the author himself before his untimely death. Some further revision was prepared by close colleagues. The first seven chapters provide a detailed, virtually exhaustive, discussion of the theory of lower bounds for linear forms in the logarithms of algebraic numbers and its applications to obtaining upper bounds for solutions to the eponymous classical diophantine equations. The detail may seem stark--- the author fears that the reader may react much as does the tourist on first seeing the centre Pompidou; notwithstanding that, Sprind zuk maintainsa pleasant and chatty approach, full of wise and interesting remarks. His emphases well warrant, ...
Numerical Solution of Heun Equation Via Linear Stochastic Differential Equation
Directory of Open Access Journals (Sweden)
Hamidreza Rezazadeh
2014-05-01
Full Text Available In this paper, we intend to solve special kind of ordinary differential equations which is called Heun equations, by converting to a corresponding stochastic differential equation(S.D.E.. So, we construct a stochastic linear equation system from this equation which its solution is based on computing fundamental matrix of this system and then, this S.D.E. is solved by numerically methods. Moreover, its asymptotic stability and statistical concepts like expectation and variance of solutions are discussed. Finally, the attained solutions of these S.D.E.s compared with exact solution of corresponding differential equations.
Shatah, Jalal
2000-01-01
This volume contains notes of the lectures given at the Courant Institute and a DMV-Seminar at Oberwolfach. The focus is on the recent work of the authors on semilinear wave equations with critical Sobolev exponents and on wave maps in two space dimensions. Background material and references have been added to make the notes self-contained. The book is suitable for use in a graduate-level course on the topic.
Differential equations with Mathematica
Abell, Martha L
2004-01-01
The Third Edition of the Differential Equations with Mathematica integrates new applications from a variety of fields,especially biology, physics, and engineering. The new handbook is also completely compatible with recent versions of Mathematica and is a perfect introduction for Mathematica beginners.* Focuses on the most often used features of Mathematica for the beginning Mathematica user* New applications from a variety of fields, including engineering, biology, and physics* All applications were completed using recent versions of Mathematica
Equation with the many fathers
DEFF Research Database (Denmark)
Kragh, Helge
1984-01-01
In this essay I discuss the origin and early development of the first relativistic wave equation, known as the Klein-Gordon equation. In 1926 several physicists, among them Klein, Fock, Schrödinger, and de Broglie, announced this equation as a candidate for a relativistic generalization of the us......In this essay I discuss the origin and early development of the first relativistic wave equation, known as the Klein-Gordon equation. In 1926 several physicists, among them Klein, Fock, Schrödinger, and de Broglie, announced this equation as a candidate for a relativistic generalization...
Bitsadze, A V
1963-01-01
Equations of the Mixed Type compiles a series of lectures on certain fundamental questions in the theory of equations of mixed type. This book investigates the series of problems concerning linear partial differential equations of the second order in two variables, and possessing the property that the type of the equation changes either on the boundary of or inside the considered domain. Topics covered include general remarks on linear partial differential equations of mixed type; study of the solutions of second order hyperbolic equations with initial conditions given along the lines of parab
Coupled Higgs field equation and Hamiltonian amplitude equation ...
Indian Academy of Sciences (India)
Various methods for obtaining exact travelling wave solutions to nonlinear equations, such as the homogeneous ... Once one has determined the symmetry group of a system of differential equations, a number of applications ... Here, we shall perform Lie symmetry analysis for the Higgs field equation. As u is a complex ...
Coupled Higgs field equation and Hamiltonian amplitude equation ...
Indian Academy of Sciences (India)
... involving parameters of the coupled Higgs equation and Hamiltonian amplitude equation using (′/)-expansion methodc, where = () satisfies a second-order linear ordinary differential equation (ODE). The travelling wave solutions expressed by hyperbolic, trigonometric and the rational functions are obtained.
Partial differential equations
Levine, Harold
1997-01-01
The subject matter, partial differential equations (PDEs), has a long history (dating from the 18th century) and an active contemporary phase. An early phase (with a separate focus on taut string vibrations and heat flow through solid bodies) stimulated developments of great importance for mathematical analysis, such as a wider concept of functions and integration and the existence of trigonometric or Fourier series representations. The direct relevance of PDEs to all manner of mathematical, physical and technical problems continues. This book presents a reasonably broad introductory account of the subject, with due regard for analytical detail, applications and historical matters.
Ordinary differential equations
Cox, William
1995-01-01
Building on introductory calculus courses, this text provides a sound foundation in the underlying principles of ordinary differential equations. Important concepts, including uniqueness and existence theorems, are worked through in detail and the student is encouraged to develop much of the routine material themselves, thus helping to ensure a solid understanding of the fundamentals required.The wide use of exercises, problems and self-assessment questions helps to promote a deeper understanding of the material and it is developed in such a way that it lays the groundwork for further
Elliptic partial differential equations
Han, Qing
2011-01-01
Elliptic Partial Differential Equations by Qing Han and FangHua Lin is one of the best textbooks I know. It is the perfect introduction to PDE. In 150 pages or so it covers an amazing amount of wonderful and extraordinary useful material. I have used it as a textbook at both graduate and undergraduate levels which is possible since it only requires very little background material yet it covers an enormous amount of material. In my opinion it is a must read for all interested in analysis and geometry, and for all of my own PhD students it is indeed just that. I cannot say enough good things abo
Hyperbolic partial differential equations
Lax, Peter D
2006-01-01
The theory of hyperbolic equations is a large subject, and its applications are many: fluid dynamics and aerodynamics, the theory of elasticity, optics, electromagnetic waves, direct and inverse scattering, and the general theory of relativity. This book is an introduction to most facets of the theory and is an ideal text for a second-year graduate course on the subject. The first part deals with the basic theory: the relation of hyperbolicity to the finite propagation of signals, the concept and role of characteristic surfaces and rays, energy, and energy inequalities. The structure of soluti
Partial differential equations
Sloan, D; Süli, E
2001-01-01
/homepage/sac/cam/na2000/index.html7-Volume Set now available at special set price ! Over the second half of the 20th century the subject area loosely referred to as numerical analysis of partial differential equations (PDEs) has undergone unprecedented development. At its practical end, the vigorous growth and steady diversification of the field were stimulated by the demand for accurate and reliable tools for computational modelling in physical sciences and engineering, and by the rapid development of computer hardware and architecture. At the more theoretical end, the analytical insight in
Master-equation approach to stochastic neurodynamics
Ohira, Toru; Cowan, Jack D.
1993-09-01
A master-equation approach to the stochastic neurodynamics proposed by Cowan [in Advances in Neural Information Processing Systems 3, edited by R. P. Lippman, J. E. Moody, and D. S. Touretzky (Morgan Kaufmann, San Mateo, 1991), p. 62] is investigated in this paper. We deal with a model neural network that is composed of two-state neurons obeying elementary stochastic transition rates. We show that such an approach yields concise expressions for multipoint moments and an equation of motion. We apply the formalism to a (1+1)-dimensional system. Exact and approximate expressions for various statistical parameters are obtained and compared with Monte Carlo simulations.
Conservational PDF Equations of Turbulence
Shih, Tsan-Hsing; Liu, Nan-Suey
2010-01-01
Recently we have revisited the traditional probability density function (PDF) equations for the velocity and species in turbulent incompressible flows. They are all unclosed due to the appearance of various conditional means which are modeled empirically. However, we have observed that it is possible to establish a closed velocity PDF equation and a closed joint velocity and species PDF equation through conditions derived from the integral form of the Navier-Stokes equations. Although, in theory, the resulted PDF equations are neither general nor unique, they nevertheless lead to the exact transport equations for the first moment as well as all higher order moments. We refer these PDF equations as the conservational PDF equations. This observation is worth further exploration for its validity and CFD application
Singularity: Raychaudhuri equation once again
Indian Academy of Sciences (India)
quantum cosmology as obtained when Raychaudhuri discovered his celebrated equation. We thus need a new analogue of the Raychaudhuri equation in quantum gravity. Keywords. Cosmology; Raychaudhuri equation; Universe; quantum gravity; loop quan- tum gravity; loop quantum cosmology. PACS Nos 04.20.Jb; 04.2 ...
Successfully Transitioning to Linear Equations
Colton, Connie; Smith, Wendy M.
2014-01-01
The Common Core State Standards for Mathematics (CCSSI 2010) asks students in as early as fourth grade to solve word problems using equations with variables. Equations studied at this level generate a single solution, such as the equation x + 10 = 25. For students in fifth grade, the Common Core standard for algebraic thinking expects them to…
Solution of Finite Element Equations
DEFF Research Database (Denmark)
Krenk, Steen
An important step in solving any problem by the finite element method is the solution of the global equations. Numerical solution of linear equations is a subject covered in most courses in numerical analysis. However, the equations encountered in most finite element applications have some special...
Receptor binding kinetics equations: Derivation using the Laplace transform method.
Hoare, Sam R J
Measuring unlabeled ligand receptor binding kinetics is valuable in optimizing and understanding drug action. Unfortunately, deriving equations for estimating kinetic parameters is challenging because it involves calculus; integration can be a frustrating barrier to the pharmacologist seeking to measure simple rate parameters. Here, a well-known tool for simplifying the derivation, the Laplace transform, is applied to models of receptor-ligand interaction. The method transforms differential equations to a form in which simple algebra can be applied to solve for the variable of interest, for example the concentration of ligand-bound receptor. The goal is to provide instruction using familiar examples, to enable investigators familiar with handling equilibrium binding equations to derive kinetic equations for receptor-ligand interaction. First, the Laplace transform is used to derive the equations for association and dissociation of labeled ligand binding. Next, its use for unlabeled ligand kinetic equations is exemplified by a full derivation of the kinetics of competitive binding equation. Finally, new unlabeled ligand equations are derived using the Laplace transform. These equations incorporate a pre-incubation step with unlabeled or labeled ligand. Four equations for measuring unlabeled ligand kinetics were compared and the two new equations verified by comparison with numerical solution. Importantly, the equations have not been verified with experimental data because no such experiments are evident in the literature. Equations were formatted for use in the curve-fitting program GraphPad Prism 6.0 and fitted to simulated data. This description of the Laplace transform method will enable pharmacologists to derive kinetic equations for their model or experimental paradigm under study. Application of the transform will expand the set of equations available for the pharmacologist to measure unlabeled ligand binding kinetics, and for other time
A novel numerical flux for the 3D Euler equations with general equation of state
Toro, Eleuterio F.
2015-09-30
Here we extend the flux vector splitting approach recently proposed in (E F Toro and M E Vázquez-Cendón. Flux splitting schemes for the Euler equations. Computers and Fluids. Vol. 70, Pages 1-12, 2012). The scheme was originally presented for the 1D Euler equations for ideal gases and its extension presented in this paper is threefold: (i) we solve the three-dimensional Euler equations on general meshes; (ii) we use a general equation of state; and (iii) we achieve high order of accuracy in both space and time through application of the semi-discrete ADER methodology on general meshes. The resulting methods are systematically assessed for accuracy, robustness and efficiency on a carefully selected suite of test problems. Formal high accuracy is assessed through convergence rates studies for schemes of up to 4th order of accuracy in both space and time on unstructured meshes.
Cunningham, Kevin
2007-01-01
This article presents an assignment in which students are to research and report on a chemical reaction whose increased or decreased rate is of practical importance. Specifically, students are asked to represent the reaction they have chosen with an acceptable chemical equation, identify a factor that influences its rate and explain how and why it…
Discovering evolution equations with applications
McKibben, Mark
2011-01-01
Most existing books on evolution equations tend either to cover a particular class of equations in too much depth for beginners or focus on a very specific research direction. Thus, the field can be daunting for newcomers to the field who need access to preliminary material and behind-the-scenes detail. Taking an applications-oriented, conversational approach, Discovering Evolution Equations with Applications: Volume 2-Stochastic Equations provides an introductory understanding of stochastic evolution equations. The text begins with hands-on introductions to the essentials of real and stochast
Analyticity estimates for the Navier-Stokes equations
DEFF Research Database (Denmark)
Herbst, I.; Skibsted, Erik
We study spatial analyticity properties of solutions of the Navier-Stokes equation and obtain new growth rate estimates for the analyticity radius. We also study stability properties of strong global solutions of the Navier-Stokes equation with data in and prove a stability result...
Statistical equilibrium equations for trace elements in stellar atmospheres
Kubat, Jiri
2010-01-01
The conditions of thermodynamic equilibrium, local thermodynamic equilibrium, and statistical equilibrium are discussed in detail. The equations of statistical equilibrium and the supplementary equations are shown together with the expressions for radiative and collisional rates with the emphasize on the solution for trace elements.
Directory of Open Access Journals (Sweden)
Vivian Wahrlich
2001-02-01
Full Text Available OBJETIVO: Medir a taxa metabólica basal em mulheres de 20 a 40 anos, não-gestantes ou lactantes, e comparar o valor medido com os valores de taxa metabólica basal estimados por equações de predição. MÉTODOS: A taxa metabólica basal foi medida por calorimetria indireta, pela manhã, durante a fase folicular do ciclo menstrual, em 60 voluntárias residentes no município de Porto Alegre, RS, sob condições padronizadas de jejum, repouso e ambiente. RESULTADOS: A média (± desvio-padrão da taxa metabólica basal medida foi 1.185,3±148,6 kcal em 24 horas. A taxa metabólica basal, estimada por equações, foi significativamente maior (7% a 17% do que a taxa metabólica basal medida. CONCLUSÕES: Os dados evidenciaram que as equações de predição não são adequadas para estimar a taxa metabólica basal nas mulheres avaliadas. O emprego dessas equações podem superestimar os requerimentos energéticos para mulheres com características semelhantes.OBJECTIVE: To measure the basal metabolic rate of women (aged 20 to 40 years living in Porto Alegre, Brazil, and to compare it with estimated values bored on published predictive equations. METHODS: Basal metabolic rate was measured by indirect calorimetry under standard conditions in the follicular phase of the menstrual cycle of 60 volunteers. RESULTS: Mean measured basal metabolic rate (± standard deviation was 1,185.3± 148.6 kcal/24 hours. Estimated basal metabolic rates were significantly greater (7% to 17% than measured basal metabolic rate (p<0.0001. CONCLUSIONS: These results show that predictive equations are not suitable to estimate basal metabolic rate in these groups of women and that the use of estimated basal metabolic rate will lead to an overestimation of energy requirements in women with similar characteristics.
Energy Technology Data Exchange (ETDEWEB)
Gomez, Humberto [Instituto de Fisica - Universidade de São Paulo,Caixa Postal 66318, 05315-970 São Paulo, SP (Brazil); Facultad de Ciencias Basicas, Universidad Santiago de Cali,Calle 5 62-00 Barrio Pampalinda, Cali, Valle (Colombia)
2016-06-17
The CHY representation of scattering amplitudes is based on integrals over the moduli space of a punctured sphere. We replace the punctured sphere by a double-cover version. The resulting scattering equations depend on a parameter Λ controlling the opening of a branch cut. The new representation of scattering amplitudes possesses an enhanced redundancy which can be used to fix, modulo branches, the location of four punctures while promoting Λ to a variable. Via residue theorems we show how CHY formulas break up into sums of products of smaller (off-shell) ones times a propagator. This leads to a powerful way of evaluating CHY integrals of generic rational functions, which we call the Λ algorithm.
Energy Technology Data Exchange (ETDEWEB)
Cardona, Carlos [Physics Division, National Center for Theoretical Sciences, National Tsing-Hua University,Hsinchu, Taiwan 30013 (China); Gomez, Humberto [Instituto de Fisica - Universidade de São Paulo,Caixa Postal 66318, 05315-970 São Paulo, SP (Brazil); Facultad de Ciencias Basicas, Universidad Santiago de Cali,Calle 5 62-00 Barrio Pampalinda, Cali, Valle (Colombia)
2016-06-16
Recently the CHY approach has been extended to one loop level using elliptic functions and modular forms over a Jacobian variety. Due to the difficulty in manipulating these kind of functions, we propose an alternative prescription that is totally algebraic. This new proposal is based on an elliptic algebraic curve embedded in a ℂP{sup 2} space. We show that for the simplest integrand, namely the n−gon, our proposal indeed reproduces the expected result. By using the recently formulated Λ−algorithm, we found a novel recurrence relation expansion in terms of tree level off-shell amplitudes. Our results connect nicely with recent results on the one-loop formulation of the scattering equations. In addition, this new proposal can be easily stretched out to hyperelliptic curves in order to compute higher genus.
New Predictive Equations for Serum Ionized Calcium in Hospitalized Patients.
Mateu-de Antonio, Javier
2016-01-01
To study a new and easy way to calculate equations to predict ionized calcium (Ca2+) for adult hospitalized patients with the usual laboratory and clinical parameters. This retrospective observational study was conducted in a third-level university hospital. An initial learning cohort (cohort L: 269 patients) was selected to derive the new equations. These equations were tested in a validation of another cohort (cohort V: 146 patients). Patients selected were hospitalized adults who had simultaneous determinations of Ca2+ and serum total calcium (CaTot). They were classified using their estimated glomerular filtration rate (GFRe) into normal function, moderate and severe kidney dysfunction. Demographic and biochemical parameters, in addition to comorbidities, were collected from hospital databases. Nine published equations to predict Ca2+ and 2 widely used equations to predict corrected CaTot were also selected to be compared to newer equations for accuracy in detecting serum calcium alterations. New equations were derived by a multiple linear-regression analysis from patients in cohort L. Three equations were derived containing the CaTot square root as the main independent variable. Equation 1: Ca2+ = 0.815 × CaTot(0.5). Equation 2: Ca2+ = 0.826 × CaTot(0.5) - 0.023 × renal function. Equation 3: Ca2+ = 0.813 × CaTot(0.5) - 0.006 × albumin(0.75) + 0.079. These equations performed better than published equations to predict Ca2+ when their error measures were analyzed in cohort V, even in special populations such as critically ill and very old patients. Three new equations predicting Ca2+ were derived requiring easily available clinical and laboratory parameters. They could be valuable in predicting hypocalcemia but are of limited use in hypercalcemia. © 2015 S. Karger AG, Basel.
Mode decomposition evolution equations.
Wang, Yang; Wei, Guo-Wei; Yang, Siyang
2012-03-01
Partial differential equation (PDE) based methods have become some of the most powerful tools for exploring the fundamental problems in signal processing, image processing, computer vision, machine vision and artificial intelligence in the past two decades. The advantages of PDE based approaches are that they can be made fully automatic, robust for the analysis of images, videos and high dimensional data. A fundamental question is whether one can use PDEs to perform all the basic tasks in the image processing. If one can devise PDEs to perform full-scale mode decomposition for signals and images, the modes thus generated would be very useful for secondary processing to meet the needs in various types of signal and image processing. Despite of great progress in PDE based image analysis in the past two decades, the basic roles of PDEs in image/signal analysis are only limited to PDE based low-pass filters, and their applications to noise removal, edge detection, segmentation, etc. At present, it is not clear how to construct PDE based methods for full-scale mode decomposition. The above-mentioned limitation of most current PDE based image/signal processing methods is addressed in the proposed work, in which we introduce a family of mode decomposition evolution equations (MoDEEs) for a vast variety of applications. The MoDEEs are constructed as an extension of a PDE based high-pass filter (Europhys. Lett., 59(6): 814, 2002) by using arbitrarily high order PDE based low-pass filters introduced by Wei (IEEE Signal Process. Lett., 6(7): 165, 1999). The use of arbitrarily high order PDEs is essential to the frequency localization in the mode decomposition. Similar to the wavelet transform, the present MoDEEs have a controllable time-frequency localization and allow a perfect reconstruction of the original function. Therefore, the MoDEE operation is also called a PDE transform. However, modes generated from the present approach are in the spatial or time domain and can be
Relativistic quantum mechanics wave equations
Greiner, Walter
1990-01-01
Relativistic Quantum Mechanics - Wave Equations concentrates mainly on the wave equations for spin-0 and spin-12 particles Chapter 1 deals with the Klein-Gordon equation and its properties and applications The chapters that follow introduce the Dirac equation, investigate its covariance properties and present various approaches to obtaining solutions Numerous applications are discussed in detail, including the two-center Dirac equation, hole theory, CPT symmetry, Klein's paradox, and relativistic symmetry principles Chapter 15 presents the relativistic wave equations for higher spin (Proca, Rarita-Schwinger, and Bargmann-Wigner) The extensive presentation of the mathematical tools and the 62 worked examples and problems make this a unique text for an advanced quantum mechanics course
Integral equations and their applications
Rahman, M
2007-01-01
For many years, the subject of functional equations has held a prominent place in the attention of mathematicians. In more recent years this attention has been directed to a particular kind of functional equation, an integral equation, wherein the unknown function occurs under the integral sign. The study of this kind of equation is sometimes referred to as the inversion of a definite integral. While scientists and engineers can already choose from a number of books on integral equations, this new book encompasses recent developments including some preliminary backgrounds of formulations of integral equations governing the physical situation of the problems. It also contains elegant analytical and numerical methods, and an important topic of the variational principles. Primarily intended for senior undergraduate students and first year postgraduate students of engineering and science courses, students of mathematical and physical sciences will also find many sections of direct relevance. The book contains eig...
Differential equations methods and applications
Said-Houari, Belkacem
2015-01-01
This book presents a variety of techniques for solving ordinary differential equations analytically and features a wealth of examples. Focusing on the modeling of real-world phenomena, it begins with a basic introduction to differential equations, followed by linear and nonlinear first order equations and a detailed treatment of the second order linear equations. After presenting solution methods for the Laplace transform and power series, it lastly presents systems of equations and offers an introduction to the stability theory. To help readers practice the theory covered, two types of exercises are provided: those that illustrate the general theory, and others designed to expand on the text material. Detailed solutions to all the exercises are included. The book is excellently suited for use as a textbook for an undergraduate class (of all disciplines) in ordinary differential equations. .
Introduction to partial differential equations
Borthwick, David
2016-01-01
This modern take on partial differential equations does not require knowledge beyond vector calculus and linear algebra. The author focuses on the most important classical partial differential equations, including conservation equations and their characteristics, the wave equation, the heat equation, function spaces, and Fourier series, drawing on tools from analysis only as they arise.Within each section the author creates a narrative that answers the five questions: (1) What is the scientific problem we are trying to understand? (2) How do we model that with PDE? (3) What techniques can we use to analyze the PDE? (4) How do those techniques apply to this equation? (5) What information or insight did we obtain by developing and analyzing the PDE? The text stresses the interplay between modeling and mathematical analysis, providing a thorough source of problems and an inspiration for the development of methods.
Energy Conservation Equations of Motion
Vinokurov, Nikolay A
2015-01-01
A conventional derivation of motion equations in mechanics and field equations in field theory is based on the principle of least action with a proper Lagrangian. With a time-independent Lagrangian, a function of coordinates and velocities that is called energy is constant. This paper presents an alternative approach, namely derivation of a general form of equations of motion that keep the system energy, expressed as a function of generalized coordinates and corresponding velocities, constant. These are Lagrange equations with addition of gyroscopic forces. The important fact, that the energy is defined as the function on the tangent bundle of configuration manifold, is used explicitly for the derivation. The Lagrangian is derived from a known energy function. A development of generalized Hamilton and Lagrange equations without the use of variational principles is proposed. The use of new technique is applied to derivation of some equations.
Energy Technology Data Exchange (ETDEWEB)
Menikoff, Ralph [Los Alamos National Laboratory
2015-12-15
The JWL equation of state (EOS) is frequently used for the products (and sometimes reactants) of a high explosive (HE). Here we review and systematically derive important properties. The JWL EOS is of the Mie-Grueneisen form with a constant Grueneisen coefficient and a constants specific heat. It is thermodynamically consistent to specify the temperature at a reference state. However, increasing the reference state temperature restricts the EOS domain in the (V, e)-plane of phase space. The restrictions are due to the conditions that P ≥ 0, T ≥ 0, and the isothermal bulk modulus is positive. Typically, this limits the low temperature regime in expansion. The domain restrictions can result in the P-T equilibrium EOS of a partly burned HE failing to have a solution in some cases. For application to HE, the heat of detonation is discussed. Example JWL parameters for an HE, both products and reactions, are used to illustrate the restrictions on the domain of the EOS.
Stochastic partial differential equations
Lototsky, Sergey V
2017-01-01
Taking readers with a basic knowledge of probability and real analysis to the frontiers of a very active research discipline, this textbook provides all the necessary background from functional analysis and the theory of PDEs. It covers the main types of equations (elliptic, hyperbolic and parabolic) and discusses different types of random forcing. The objective is to give the reader the necessary tools to understand the proofs of existing theorems about SPDEs (from other sources) and perhaps even to formulate and prove a few new ones. Most of the material could be covered in about 40 hours of lectures, as long as not too much time is spent on the general discussion of stochastic analysis in infinite dimensions. As the subject of SPDEs is currently making the transition from the research level to that of a graduate or even undergraduate course, the book attempts to present enough exercise material to fill potential exams and homework assignments. Exercises appear throughout and are usually directly connected ...
Galilean equations for massless fields
Niederle, J.; Nikitin, A. G.
2008-01-01
Galilei-invariant equations for massless fields are obtained via contractions of relativistic wave equations. It is shown that the collection of non-equivalent Galilei-invariant wave equations for massless fields with spin equal 1 and 0 is very reach and corresponds to various contractions of the representations of the Lorentz group to those of the Galilei one. It describes many physically consistent systems, e.g., those of electromagnetic fields in various media or Galilean Chern-Simon model...
parabolic equation with integral boundary condition
Directory of Open Access Journals (Sweden)
M. Denche
2001-01-01
Full Text Available In this paper we study the problem of control by the initial conditions of the heat equation with an integral boundary condition. This problem is ill-posed. Perturbing the final condition we obtain an approximate nonlocal problem depending on a small parameter. We show that the approximate problems are well posed. We also obtain estimates of the solutions of the approximate problems and a convergence result of these solutions. Finally, we give explicit convergence rates.
Electronic representation of wave equation
Energy Technology Data Exchange (ETDEWEB)
Veigend, Petr; Kunovský, Jiří, E-mail: kunovsky@fit.vutbr.cz; Kocina, Filip; Nečasová, Gabriela; Valenta, Václav [University of Technology, Faculty of Information Technology, Božetěchova 2, 612 66 Brno (Czech Republic); Šátek, Václav [IT4Innovations, VŠB Technical University of Ostrava, 17. listopadu 15/2172, 708 33 Ostrava-Poruba (Czech Republic); University of Technology, Faculty of Information Technology, Božetěchova 2, 612 66 Brno (Czech Republic)
2016-06-08
The Taylor series method for solving differential equations represents a non-traditional way of a numerical solution. Even though this method is not much preferred in the literature, experimental calculations done at the Department of Intelligent Systems of the Faculty of Information Technology of TU Brno have verified that the accuracy and stability of the Taylor series method exceeds the currently used algorithms for numerically solving differential equations. This paper deals with solution of Telegraph equation using modelling of a series small pieces of the wire. Corresponding differential equations are solved by the Modern Taylor Series Method.
Correct Linearization of Einstein's Equations
Directory of Open Access Journals (Sweden)
Rabounski D.
2006-06-01
Full Text Available Regularly Einstein's equations can be reduced to a wave form (linearly dependent from the second derivatives of the space metric in the absence of gravitation, the space rotation and Christoffel's symbols. As shown here, the origin of the problem is that one uses the general covariant theory of measurement. Here the wave form of Einstein's equations is obtained in the terms of Zelmanov's chronometric invariants (physically observable projections on the observer's time line and spatial section. The obtained equations depend on solely the second derivatives even if gravitation, the space rotation and Christoffel's symbols. The correct linearization proves: the Einstein equations are completely compatible with weak waves of the metric.
Electronic representation of wave equation
Veigend, Petr; Kunovský, Jiří; Kocina, Filip; Nečasová, Gabriela; Šátek, Václav; Valenta, Václav
2016-06-01
The Taylor series method for solving differential equations represents a non-traditional way of a numerical solution. Even though this method is not much preferred in the literature, experimental calculations done at the Department of Intelligent Systems of the Faculty of Information Technology of TU Brno have verified that the accuracy and stability of the Taylor series method exceeds the currently used algorithms for numerically solving differential equations. This paper deals with solution of Telegraph equation using modelling of a series small pieces of the wire. Corresponding differential equations are solved by the Modern Taylor Series Method.
Galilean equations for massless fields
Energy Technology Data Exchange (ETDEWEB)
Niederle, J [Institute of Physics of the Academy of Sciences of the Czech Republic, Na Slovance 2, 182 21 Prague (Czech Republic); Nikitin, A G [Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs' ka Street, Kyiv-4, Ukraine, 01601 (Ukraine)], E-mail: niederle@fzu.cz, E-mail: nikitin@imath.kiev.ua
2009-03-13
Galilei-invariant equations for massless fields are obtained via contractions of relativistic wave equations. It is shown that the collection of non-equivalent Galilei-invariant wave equations for massless fields with spin equal to 1 and 0 is very rich and corresponds to various contractions of the representations of the Lorentz group to those of the Galilei ones. It describes many physically consistent systems, e.g., those of electromagnetic fields in various media or Galilean Chern-Simons models. Finally, classification of all linear and a big group of nonlinear Galilei-invariant equations for massless fields is presented.
Telegrapher's equation for light derived from the transport equation
Hoenders, Bernhard J.; Graaff, R
2005-01-01
Shortcomings of diffusion theory when applied to turbid media such as biological tissue makes the development of more accurate equations desirable. Several authors developed telegrapher's equations in the well known P-1 approximation. The method used in this paper is different: it is based on the
Differential equations a dynamical systems approach ordinary differential equations
Hubbard, John H
1991-01-01
This is a corrected third printing of the first part of the text Differential Equations: A Dynamical Systems Approach written by John Hubbard and Beverly West. The authors' main emphasis in this book is on ordinary differential equations. The book is most appropriate for upper level undergraduate and graduate students in the fields of mathematics, engineering, and applied mathematics, as well as the life sciences, physics and economics. Traditional courses on differential equations focus on techniques leading to solutions. Yet most differential equations do not admit solutions which can be written in elementary terms. The authors have taken the view that a differential equations defines functions; the object of the theory is to understand the behavior of these functions. The tools the authors use include qualitative and numerical methods besides the traditional analytic methods. The companion software, MacMath, is designed to bring these notions to life.
Difference equations theory, applications and advanced topics
Mickens, Ronald E
2015-01-01
THE DIFFERENCE CALCULUS GENESIS OF DIFFERENCE EQUATIONS DEFINITIONS DERIVATION OF DIFFERENCE EQUATIONS EXISTENCE AND UNIQUENESS THEOREM OPERATORS ∆ AND E ELEMENTARY DIFFERENCE OPERATORS FACTORIAL POLYNOMIALS OPERATOR ∆−1 AND THE SUM CALCULUS FIRST-ORDER DIFFERENCE EQUATIONS INTRODUCTION GENERAL LINEAR EQUATION CONTINUED FRACTIONS A GENERAL FIRST-ORDER EQUATION: GEOMETRICAL METHODS A GENERAL FIRST-ORDER EQUATION: EXPANSION TECHNIQUES LINEAR DIFFERENCE EQUATIONSINTRODUCTION LINEARLY INDEPENDENT FUNCTIONS FUNDAMENTAL THEOREMS FOR HOMOGENEOUS EQUATIONSINHOMOGENEOUS EQUATIONS SECOND-ORDER EQUATIONS STURM-LIOUVILLE DIFFERENCE EQUATIONS LINEAR DIFFERENCE EQUATIONS INTRODUCTION HOMOGENEOUS EQUATIONS CONSTRUCTION OF A DIFFERENCE EQUATION HAVING SPECIFIED SOLUTIONS RELATIONSHIP BETWEEN LINEAR DIFFERENCE AND DIFFERENTIAL EQUATIONS INHOMOGENEOUS EQUATIONS: METHOD OF UNDETERMINED COEFFICIENTS INHOMOGENEOUS EQUATIONS: OPERATOR METHODS z-TRANSFORM METHOD SYSTEMS OF DIFFERENCE EQUATIONS LINEAR PARTIAL DIFFERENCE EQUATI...
Derivation and application of hydraulic equation for variable-rate ...
African Journals Online (AJOL)
use
2011-12-12
Dec 12, 2011 ... Square wetted area sprinkler rotation angle (in radian). S q u are w etted area sp rin k ler th eo retical th ro w d istan ce. Figure 4. Square wetted area sprinkler theoretical throw distance in Cartesian coordinate system. Figure 5. Square wetted area sprinkler theoretical discharge in polar coordinate system.
Rate equation simulation of temporal characteristics of a pulsed dye ...
Indian Academy of Sciences (India)
Laser & Plasma Technology Division, Bhabha Atomic Research Centre,. Mumbai 400 085, India ... To design and build high-power, pulsed dye laser MOPA systems, it is necessary to have a detailed knowledge .... qualitative and reasonably good quantitative agreement with experimental results on two separate dye laser ...
Delay dynamic equations with stability
Directory of Open Access Journals (Sweden)
Krueger Robert J
2006-01-01
Full Text Available We first give conditions which guarantee that every solution of a first order linear delay dynamic equation for isolated time scales vanishes at infinity. Several interesting examples are given. In the last half of the paper, we give conditions under which the trivial solution of a nonlinear delay dynamic equation is asymptotically stable, for arbitrary time scales.
Graphical Solution of Polynomial Equations
Grishin, Anatole
2009-01-01
Graphing utilities, such as the ubiquitous graphing calculator, are often used in finding the approximate real roots of polynomial equations. In this paper the author offers a simple graphing technique that allows one to find all solutions of a polynomial equation (1) of arbitrary degree; (2) with real or complex coefficients; and (3) possessing…
Fractals and the Kepler equation
Kasten, Volker
1992-09-01
The application of fractal mathematics to Kepler's equation is addressed. Complex solutions to Kepler's equation are considered along with methods to determine them. The roles of regions of attraction and their boundaries, Julia quantities, Fatou quantities, and fractal quantities in these methods are discussed.
Students' Understanding of Quadratic Equations
López, Jonathan; Robles, Izraim; Martínez-Planell, Rafael
2016-01-01
Action-Process-Object-Schema theory (APOS) was applied to study student understanding of quadratic equations in one variable. This required proposing a detailed conjecture (called a genetic decomposition) of mental constructions students may do to understand quadratic equations. The genetic decomposition which was proposed can contribute to help…
Enclosing Solutions of Integral Equations
DEFF Research Database (Denmark)
Madsen, Kaj; NA NA NA Caprani, Ole; Stauning, Ole
1996-01-01
We present a method for enclosing the solution of an integral equation. It is assumed that a solution exists and that the corresponding integral operator T is a contraction near y. When solving the integral equation by iteration we obtain a result which is normally different from y because...
Kuznetsov equation with variable coefficients
Indian Academy of Sciences (India)
Travelling wave-like solutions of the Zakharov–Kuznetsov equation with vari- able coefficients are studied using the ... exact solutions of nonlinear partial differential equations. Some of the most impor- tant methods are the ... In general, there is no standard method for solving nonlinear. PDEs and more so for PDEs in 2+1 ...
Solving equations by topological methods
Directory of Open Access Journals (Sweden)
Lech Górniewicz
2005-01-01
Full Text Available In this paper we survey most important results from topological fixed point theory which can be directly applied to differential equations. Some new formulations are presented. We believe that our article will be useful for analysts applying topological fixed point theory in nonlinear analysis and in differential equations.
On asymptotics for difference equations
Rafei, M.
2012-01-01
In this thesis a class of nonlinear oscillator equations is studied. Asymptotic approximations of first integrals for nonlinear difference equations are constructed by using the recently developed perturbation method based on invariance vectors. The asymptotic approximations of the solutions of the
Discovering Evolution Equations with Applications, 1 Deterministic Equations
McKibben, Mark A
2010-01-01
Most books written on evolution equations either provide a thorough in-depth treatment of a particular class of equations for beginners or present an assimilation of materials devoted to a very particular timely research direction. This volume offers an engaging, accessible account of a rudimentary core of theoretical results that should be understood by anyone studying evolution equations. The text gradually builds readers' intuition and the material culminates in a discussion of an area of active research. The author's conversational style sets the stage for the next step of theoretical deve
Ozdemir, Burhanettin
2017-01-01
The purpose of this study is to equate Trends in International Mathematics and Science Study (TIMSS) mathematics subtest scores obtained from TIMSS 2011 to scores obtained from TIMSS 2007 form with different nonlinear observed score equating methods under Non-Equivalent Anchor Test (NEAT) design where common items are used to link two or more test…
Stochastic differential equations, backward SDEs, partial differential equations
Pardoux, Etienne
2014-01-01
This research monograph presents results to researchers in stochastic calculus, forward and backward stochastic differential equations, connections between diffusion processes and second order partial differential equations (PDEs), and financial mathematics. It pays special attention to the relations between SDEs/BSDEs and second order PDEs under minimal regularity assumptions, and also extends those results to equations with multivalued coefficients. The authors present in particular the theory of reflected SDEs in the above mentioned framework and include exercises at the end of each chapter. Stochastic calculus and stochastic differential equations (SDEs) were first introduced by K. Itô in the 1940s, in order to construct the path of diffusion processes (which are continuous time Markov processes with continuous trajectories taking their values in a finite dimensional vector space or manifold), which had been studied from a more analytic point of view by Kolmogorov in the 1930s. Since then, this topic has...
Poincar wave equations as Fourier transformations of Galilei wave equations
Gomis Torné, Joaquim; Poch Parés, Agustí; Pons Ràfols, Josep Maria
1980-01-01
The relationship between the Poincar and Galilei groups allows us to write the Poincar wave equations for arbitrary spin as a Fourier transform of the Galilean ones. The relation between the Lagrangian formulation for both cases is also studied.
Interference-exact radiative transfer equation
DEFF Research Database (Denmark)
Partanen, Mikko; Haÿrynen, Teppo; Oksanen, Jani
2017-01-01
Maxwell's equations with stochastic or quantum optical source terms accounting for the quantum nature of light. We show that both the nonlocal wave and local particle features associated with interference and emission of propagating fields in stratified geometries can be fully captured by local damping...... equation (RTE) as a physically transparent interference-exact model that extends the useful range of computationally efficient and quantum optically accurate interference-aware optical models from simple structures to full optical devices.......The Purcell effect, i.e., the modification of the spontaneous emission rate by optical interference, profoundly affects the light-matter coupling in optical resonators. Fully describing the optical absorption, emission, and interference of light hence conventionally requires combining the full...
Cubic nonlinear Schroedinger equation with vorticity
Energy Technology Data Exchange (ETDEWEB)
Caliari, M; Morato, L M; Zuccher, S [Dipartimento di Informatica, Universita di Verona, Ca' Vignal 2, Strada Le Grazie 15, 37134 Verona (Italy); Loffredo, M I [Dipartimento di Scienze Matematiche ed Informatiche, Universita di Siena, Pian dei Mantellini 44, 53100 Siena (Italy)], E-mail: marco.caliari@univr.it, E-mail: loffredo@unisi.it, E-mail: laura.morato@univr.it, E-mail: zuccher@sci.univr.it
2008-12-15
In this paper, we introduce a new class of nonlinear Schroedinger equations (NLSEs), with an electromagnetic potential (A,{phi}), both depending on the wavefunction {psi}. The scalar potential {phi} depends on |{psi}|{sup 2}, whereas the vector potential A satisfies the equation of magnetohydrodynamics with coefficient depending on {psi}. In Madelung variables, the velocity field comes to be not irrotational in general and we prove that the vorticity induces dissipation, until the dynamical equilibrium is reached. The expression of the rate of dissipation is common to all NLSEs in the class. We show that they are a particular case of the one-particle dynamics out of dynamical equilibrium for a system of N identical interacting Bose particles, as recently described within stochastic quantization by Lagrangian variational principle. The cubic case is discussed in particular. Results of numerical experiments for rotational excitations of the ground state in a finite two-dimensional trap with harmonic potential are reported.
On a Fractional Master Equation
Directory of Open Access Journals (Sweden)
Anitha Thomas
2011-01-01
derivative and Caputo derivative of order ,,1<ℜ(≤2 and 1<ℜ(≤2 respectively. In this paper, we derive an analytic solution for the fractional time-independent form of the wave equation or diffusion equation in two dimensions in terms of the Mittag-Leffler function. The solutions to the fractional Poisson and the Laplace equations of the same kind are obtained, again represented by means of the Mittag-Leffler function. In all three cases, the solutions are represented also in terms of Fox's -function.
Integral equation methods for electromagnetics
Volakis, John
2012-01-01
This text/reference is a detailed look at the development and use of integral equation methods for electromagnetic analysis, specifically for antennas and radar scattering. Developers and practitioners will appreciate the broad-based approach to understanding and utilizing integral equation methods and the unique coverage of historical developments that led to the current state-of-the-art. In contrast to existing books, Integral Equation Methods for Electromagnetics lays the groundwork in the initial chapters so students and basic users can solve simple problems and work their way up to the mo
Numerical Solution of Parabolic Equations
DEFF Research Database (Denmark)
Østerby, Ole
These lecture notes are designed for a one-semester course on finite-difference methods for parabolic equations. These equations which traditionally are used for describing diffusion and heat-conduction problems in Geology, Physics, and Chemistry have recently found applications in Finance Theory...... approximations which depend on a step size, such as numerical integration and solution of ordinary and partial differential equations. An integral part of the error estimation is the estimation of the order of the method and can thus satisfy the inquisitive mind: Is the order what we expect it to be from theopry...
Soliton equations and Hamiltonian systems
Dickey, L A
2002-01-01
The theory of soliton equations and integrable systems has developed rapidly during the last 30 years with numerous applications in mechanics and physics. For a long time, books in this field have not been written but the flood of papers was overwhelming: many hundreds, maybe thousands of them. All this output followed one single work by Gardner, Green, Kruskal, and Mizura on the Korteweg-de Vries equation (KdV), which had seemed to be merely an unassuming equation of mathematical physics describing waves in shallow water. Besides its obvious practical use, this theory is attractive also becau
Methods for Equating Mental Tests.
1984-11-01
1983) compared conventional and IRT methods for equating the Test of English as a Foreign Language ( TOEFL ) after chaining. Three conventional and...ID-A149 544 METHODS FOR ’EQUATING MENTAL TESTS (U) ASSESSMENT SYSTEMS 1/2 CORP ST PAUL MN K A GIRLLUCA ET AL. NOV 84 AFHRL-TR-84-35 F4i689-82-C-0023... TEST CHART NATIONAL BUREAU Of STANDARDS- 1963-A -I% AFHRL-TR-84-35 AIR FORCE 0, METHODS FOR EQUATING MENTAL TESTS H U By Kathleen A. Gialluca Leslie I
Hartman-Wintner growth results for sublinear functional differential equations
Directory of Open Access Journals (Sweden)
John A. D. Appleby
2017-01-01
Full Text Available This article determines the rate of growth to infinity of scalar autonomous nonlinear functional and Volterra differential equations. In these equations, the right-hand side is a positive continuous linear functional of f(x. We assume f grows sublinearly, leading to subexponential growth in the solutions. The main results show that the solution of the functional differential equations are asymptotic to that of an auxiliary autonomous ordinary differential equation with right-hand side proportional to f. This happens provided f grows more slowly than l(x=x/log(x. The linear-logarithmic growth rate is also shown to be critical: if f grows more rapidly than l, the ODE dominates the FDE; if f is asymptotic to a constant multiple of l, the FDE and ODE grow at the same rate, modulo a constant non-unit factor; if f grows more slowly than l, the ODE and FDE grow at exactly the same rate. A partial converse of the last result is also proven. In the case when the growth rate is slower than that of the ODE, sharp bounds on the growth rate are determined. The Volterra and finite memory equations can have differing asymptotic behaviour and we explore the source of these differences.
40 CFR 63.1414 - Test methods and emission estimation equations.
2010-07-01
... equations. 63.1414 Section 63.1414 Protection of Environment ENVIRONMENTAL PROTECTION AGENCY (CONTINUED) AIR... § 63.1414 Test methods and emission estimation equations. (a) Test methods. When required to conduct a... rate for a batch emission episode shall be calculated using Equation 1 of this section: ER20JA00.007...
Scaling and the Smoluchowski equations
Goodisman, J.; Chaiken, J.
2006-08-01
The Smoluchowski equations, which describe coalescence growth, take into account combination reactions between a j-mer and a k-mer to form a (j+k)-mer, but not breakup of larger clusters to smaller ones. All combination reactions are assumed to be second order, with rate constants Kjk. The Kjk are said to scale if Kλj,γk=λμγνKjk for j ⩽k. It can then be shown that, for large k, the number density or population of k-mers is given by Akae-bk, where A is a normalization constant (a function of a, b, and time), a =-(μ+ν), and bμ +ν-1 depends linearly on time. We prove this in a simple, transparent manner. We also discuss the origin of odd-even population oscillations for small k. A common scaling arises from the ballistic model, which assumes that the velocity of a k-mer is proportional to 1/√mk (Maxwell distribution), i.e., thermal equilibrium. This does not hold for the nascent distribution of clusters produced from monomers by reactive collisions. By direct calculation, invoking conservation of momentum in collisions, we show that, for this distribution, velocities are proportional to mk-0.577. This leads to μ +ν=0.090, intermediate between the ballistic (0.167) and diffusive (0.000) results. These results are discussed in light of the existence of systems in the experimental literature which apparently correspond to very negative values of μ +ν.
Directory of Open Access Journals (Sweden)
Guillermo J. Rosa-Diez
2011-08-01
Full Text Available La ecuación MDRD para la estimación del índice de filtrado glomerular (IFG, es la estrategia más utilizada para evaluar pacientes con enfermedad renal crónica (ERC. Sin embargo, puede subestimar el IFG con el riesgo de asignar al paciente a estadios más avanzados de ERC. La nueva ecuación CKD-EPI, mejoraría la exactitud y precisión de las estimaciones. Sus autores sugieren que reemplace a la anterior. No habiendo comparaciones de estas ecuaciones aplicadas en un gran número de pacientes en nuestro país, nuestro objetivo fue realizarla en una amplia cohorte de pacientes. Se evaluó la concordancia de asignación en estadios de ERC entre ambas ecuaciones, tomando como referencia los datos surgidos de MDRD. Se calculó la media de las diferencias de los IFG obtenidos empleando ambas ecuaciones y se aplicó el análisis estadístico de Bland-Altman. Se estudió una cohorte de 9 319 pacientes con una media de creatinina sérica de 1.60 ± 1.03 mg/dl, 67% de sexo femenino y edad media 58 ± 20 años. En el grupo total, CKD-EPI presentó una media de IFG 0.61 ml/min/1.73 m² mayor que MDRD (p: NS. En los estadios 2 y 3A las medias del IFG fueron respectivamente 6.95 ± 4.76 y 3.21 ± 3.31, y la concordancia de 81 y 74%. El porcentaje de pacientes con un IFG menor de 60 ml/min/1.73 m², se redujo de 76.3% (MDRD a 70.1% (CKD-EPI. Por lo tanto, la nueva ecuación CKD-EPI disminuye el número de pacientes con IFG debajo de 60 ml/min/1.73 m² y asigna estadios de IFG más elevado a un número mayor de pacientes.The MDRD equation to estimate glomerular filtration rate (GFR is the most widely used strategy to assess chronic kidney disease. Nonetheless, for the individual patient the true GFR can be underestimated with the risk of diagnosing a more elevated CKD stage. This novel CKD-EPI equation would improve accuracy and precision of estimations, and several authors recommend this new equation replace the former. In our country there is only a
Directory of Open Access Journals (Sweden)
Fabiana Andrade Machado
2011-08-01
incrementos de 1 km/h a cada tres minutos. El test se mantuvo hasta el agotamiento voluntario, considerando como FCmáx la mayor frecuencia cardíaca alcanzada durante el test. La FCmáx medida se comparó con los valores previstos por las ecuaciones "220 - edad" y "208 - (0,7 x edad" a través de ANOVA, medidas repetidas. RESULTADOS: Los valores promedios de la FCmáx (lpm fueron: 200,2 ± 8,0 (medida, 207,4 ± 1,5 ("220 - edad" y 199,2 ± 1,1 ("208 - (0,7 x edad". La FCmáx de predicción por la ecuación "220 - edad" fue significantemente mayor (p 0,05. CONCLUSIÓN: La ecuación "220 -edad" supervaloró la FCmáx medida y no se mostró válida para esa población. La ecuación "208 - (0,7 x edad" fue válida presentando resultados bastante próximos a la FCmáx medida. Estudios futuros con muestras mayores podrán comprobar si la FCmáx no depende de la edad para esa población, situación en que el valor constante de 200 lpm sería el más apropiado para la FCmáx.BACKGROUND: There are no studies in the literature to validate equations that predict maximum heart rate (HRmax in children and adolescents. OBJECTIVE: To analyze the validity of the HRmax predictive equations "220 - age" and "208 - (0.7 x age" in boys aged 10 and 16. METHODS: A progressive maximal exertion test was carried out in 69 apparently healthy boys aged 10 to 16. The initial test velocity was 9 km/h, with 1-km/h increments every three minutes. The test was maintained until maximum voluntary exertion was achieved, considering HRmax as the highest heart rate attained during the test. The measured HRmax was compared with the values predicted by the "220 - age" and "208 - (0.7 x age" equations, using ANOVA for repeated measures. RESULTS: The mean values of HRmax (bpm were: 200.2 ± 8.0 (measured, 207.4 ± 1.5 ("220 - age" and 199.2 ± 1.1 ("208 - (0.7 x age". The HRmax predicted by the "220 - age" equation was significantly higher (p 0.05. CONCLUSION: The "220 - age" equation overestimated the measured
Point model equations for neutron correlation counting: Extension of Böhnel's equations to any order
Favalli, Andrea; Croft, Stephen; Santi, Peter
2015-09-01
Various methods of autocorrelation neutron analysis may be used to extract information about a measurement item containing spontaneously fissioning material. The two predominant approaches being the time correlation analysis (that make use of a coincidence gate) methods of multiplicity shift register logic and Feynman sampling. The common feature is that the correlated nature of the pulse train can be described by a vector of reduced factorial multiplet rates. We call these singlets, doublets, triplets etc. Within the point reactor model the multiplet rates may be related to the properties of the item, the parameters of the detector, and basic nuclear data constants by a series of coupled algebraic equations - the so called point model equations. Solving, or inverting, the point model equations using experimental calibration model parameters is how assays of unknown items is performed. Currently only the first three multiplets are routinely used. In this work we develop the point model equations to higher order multiplets using the probability generating functions approach combined with the general derivative chain rule, the so called Faà di Bruno Formula. Explicit expression up to 5th order are provided, as well the general iterative formula to calculate any order. This work represents the first necessary step towards determining if higher order multiplets can add value to nondestructive measurement practice for nuclear materials control and accountancy.
Singularity: Raychaudhuri equation once again
Indian Academy of Sciences (India)
2015-11-27
Keywords. Cosmology; Raychaudhuri equation; Universe; quantum gravity; loop quantum gravity; loop quantum cosmology. ... Proceedings of the International Workshop/Conference on Computational Condensed Matter Physics and Materials Science (IWCCMP-2015). Posted on November 27, 2015. Guest Editors: Anurag ...
Correct Linearization of Einstein's Equations
Directory of Open Access Journals (Sweden)
Rabounski D.
2006-04-01
Full Text Available Routinely, Einstein’s equations are be reduced to a wave form (linearly independent of the second derivatives of the space metric in the absence of gravitation, the space rotation and Christoffel’s symbols. As shown herein, the origin of the problem is the use of the general covariant theory of measurement. Herein the wave form of Einstein’s equations is obtained in terms of Zelmanov’s chronometric invariants (physically observable projections on the observer’s time line and spatial section. The equations so obtained depend solely upon the second derivatives, even for gravitation, the space rotation and Christoffel’s symbols. The correct linearization proves that the Einstein equations are completely compatible with weak waves of the metric.
An Investigation on Quadratic Equations.
Hirst, Keith
1988-01-01
Argues that exploring a familiar topic or examination question in a novel manner is a useful way to find topics for mathematical investigation in the classroom. The example used to illustrate the premise is a quadratic equation. (PK)
Geophysical interpretation using integral equations
Eskola, L
1992-01-01
Along with the general development of numerical methods in pure and applied to apply integral equations to geophysical modelling has sciences, the ability improved considerably within the last thirty years or so. This is due to the successful derivation of integral equations that are applicable to the modelling of complex structures, and efficient numerical algorithms for their solution. A significant stimulus for this development has been the advent of fast digital computers. The purpose of this book is to give an idea of the principles by which boundary-value problems describing geophysical models can be converted into integral equations. The end results are the integral formulas and integral equations that form the theoretical framework for practical applications. The details of mathematical analysis have been kept to a minimum. Numerical algorithms are discussed only in connection with some illustrative examples involving well-documented numerical modelling results. The reader is assu med to have a back...
Solving Differential Equations in R
Although R is still predominantly applied for statistical analysis and graphical representation, it is rapidly becoming more suitable for mathematical computing. One of the fields where considerable progress has been made recently is the solution of differential equations. Here w...
Solutions of Nonlocal -Laplacian Equations
Directory of Open Access Journals (Sweden)
Mustafa Avci
2013-01-01
Full Text Available In view of variational approach we discuss a nonlocal problem, that is, a Kirchhoff-type equation involving -Laplace operator. Establishing some suitable conditions, we prove the existence and multiplicity of solutions.
Comparison of equations for dosing of medications in renal impairment.
Khanal, Aarati; Peterson, Gregory M; Jose, Matthew D; Castelino, Ronald L
2017-06-01
The aim of this study is to determine the concordance among the Cockcroft-Gault, the Modification of Diet in Renal Disease and the Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) equations in hypothetical dosing of renally cleared medications. A total of 2163 patients prescribed at least one of the 31 renally cleared drugs under review were included in the study. Kidney function was estimated using the three equations. We compared actual prescribed dosages of the same drug with recommended dosages based on the kidney function as calculated by each of the equations and applying dosing recommendations in the Australian Medicines Handbook. There was a significant difference in the kidney function values estimated from the three equations (P equations. The CKD-EPI equation non-normalized for body surface area had a greater rate of concordance with the Cockcroft-Gault equation than the Modification of Diet in Renal Disease equation for renal drug dosing. There is need for a long-term multi-centre study in a diverse population to define the clinical effects of the discrepancies among the equations for drug dosing. Given the greater concordance of the non-normalized CKD-EPI equation with the Cockcroft-Gault equation for dosing, the recommendation by Kidney Health Australia and the United States National Kidney Disease Education Program that 'dosing based on either eCrCl or an eGFR with body surface area normalization removed are acceptable' seems suitable and practicable for the purpose of dosing of non-critical drugs in the primary care setting. © 2016 Asian Pacific Society of Nephrology.
Geometrical Solutions of Quadratic Equations.
Grewal, A. S.; Godloza, L.
1999-01-01
Demonstrates that the equation of a circle (x-h)2 + (y-k)2 = r2 with center (h; k) and radius r reduces to a quadratic equation x2-2xh + (h2 + k2 -r2) = O at the intersection with the x-axis. Illustrates how to determine the center of a circle as well as a point on a circle. (Author/ASK)
Feynman integrals and difference equations
Energy Technology Data Exchange (ETDEWEB)
Moch, S. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Schneider, C. [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation
2007-09-15
We report on the calculation of multi-loop Feynman integrals for single-scale problems by means of difference equations in Mellin space. The solution to these difference equations in terms of harmonic sums can be constructed algorithmically over difference fields, the so-called {pi}{sigma}{sup *}-fields. We test the implementation of the Mathematica package Sigma on examples from recent higher order perturbative calculations in Quantum Chromodynamics. (orig.)
Hidden Statistics of Schroedinger Equation
Zak, Michail
2011-01-01
Work was carried out in determination of the mathematical origin of randomness in quantum mechanics and creating a hidden statistics of Schr dinger equation; i.e., to expose the transitional stochastic process as a "bridge" to the quantum world. The governing equations of hidden statistics would preserve such properties of quantum physics as superposition, entanglement, and direct-product decomposability while allowing one to measure its state variables using classical methods.
Approximative solutions of difference equations
Directory of Open Access Journals (Sweden)
Janusz Migda
2014-03-01
\\Delta^m x_n=a_nf(n,x_{\\sigma(n}+b_n $$ are studied. Using the iterated remainder operator and fixed point theorems we obtain sufficient conditions under which for any solution $y$ of the equation $\\Delta^my=b$ and for any real $s\\leq 0$ there exists a solution $x$ of the above equation such that $\\Delta^kx=\\Delta^ky+\\mathrm{o}(n^{s-k}$ for any nonnegative integer $k\\leq m$. Using a discrete variant of the Bihari lemma and a certain new technique we give also sufficient conditions under which for a given real $s\\leq m-1$ all solutions $x$ of the equation satisfy the condition $x=y+\\mathrm{o}(n^s$ where $y$ is a solution of the equation $\\Delta^my=b$. Moreover, we give sufficient conditions under which for a given natural $k
Memory boundary feedback stabilization for Schrodinger equations with variable coefficients
Directory of Open Access Journals (Sweden)
Abdesselam Nawel
2017-05-01
Full Text Available First we consider the boundary stabilization of Schrodinger equations with constant coefficient memory feedback. This is done by using Riemannian geometry methods and the multipliers technique. Then we explore the stabilization limits of Schrodinger equations whose elliptical part has a variable coefficient. We established the exponential decay of solutions using the multipliers techniques. The introduction of dissipative boundary conditions of memory type allowed us to obtain an accurate estimate on the uniform rate of decay of the energy for Schrodinger equations.
The soil moisture velocity equation
Ogden, Fred L.; Allen, Myron B.; Lai, Wencong; Zhu, Jianting; Seo, Mookwon; Douglas, Craig C.; Talbot, Cary A.
2017-06-01
Numerical solution of the one-dimensional Richards' equation is the recommended method for coupling groundwater to the atmosphere through the vadose zone in hyperresolution Earth system models, but requires fine spatial discretization, is computationally expensive, and may not converge due to mathematical degeneracy or when sharp wetting fronts occur. We transformed the one-dimensional Richards' equation into a new equation that describes the velocity of moisture content values in an unsaturated soil under the actions of capillarity and gravity. We call this new equation the Soil Moisture Velocity Equation (SMVE). The SMVE consists of two terms: an advection-like term that accounts for gravity and the integrated capillary drive of the wetting front, and a diffusion-like term that describes the flux due to the shape of the wetting front capillarity profile divided by the vertical gradient of the capillary pressure head. The SMVE advection-like term can be converted to a relatively easy to solve ordinary differential equation (ODE) using the method of lines and solved using a finite moisture-content discretization. Comparing against analytical solutions of Richards' equation shows that the SMVE advection-like term is >99% accurate for calculating infiltration fluxes neglecting the diffusion-like term. The ODE solution of the SMVE advection-like term is accurate, computationally efficient and reliable for calculating one-dimensional vadose zone fluxes in Earth system and large-scale coupled models of land-atmosphere interaction. It is also well suited for use in inverse problems such as when repeat remote sensing observations are used to infer soil hydraulic properties or soil moisture.Plain Language SummarySince its original publication in 1922, the so-called Richards' equation has been the only rigorous way to couple groundwater to the land surface through the unsaturated zone that lies between the water table and land surface. The soil moisture distribution and
Equationally Compact Acts : Coproducts / Peeter Normak
Normak, Peeter
1998-01-01
In this article equational compactness of acts and its generalizations are discussed. As equational compactness does not carry over to coproducts a slight generalization of c-equational campactness is introduced. It is proved that a coproduct of acts is c-equationally compact if and only if all components are c-equationally campact
Costabel, M.; Ervin, V. J.; Stephan, E. P.
1990-07-01
Previously Costabel and Stephan proved the convergence of the collocation method for boundary integral equations on polygonal domains for piecewise linear trial functions which are constant on subintervals next to corners. The convergence and associated error estimates were given in suitable Sobolev spaces with appropriately weighted norms. In this paper we present, for Laplace's equation, the implementation of their method and a slightly modified version. In the latter we use piecewise linear trial functions which are discontinuous at the corners. Of particular note is that the computed experimental convergence rates are in complete agreement with the predicted theoretical rates. In particular, our numerical results underline clearly how the order of convergence depends on the graded mesh.
Complementary equations: a fractional differential equation and a Volterra integral equation
Directory of Open Access Journals (Sweden)
Leigh Becker
2015-03-01
\\] on an interval $(0, T]$ if and only if it satisfies the Volterra integral equation \\[ x(t = x^{0}t^{q-1}+\\frac{1}{\\Gamma (q}\\int_{0}^{t}(t-s^{q-1}f(s, x(s\\,ds \\] on this same interval. In contradistinction to established existence theorems for these equations, no Lipschitz condition is imposed on $f(t,x$. Examples with closed-form solutions illustrate this result.
Stagewise generalized estimating equations with grouped variables.
Vaughan, Gregory; Aseltine, Robert; Chen, Kun; Yan, Jun
2017-12-01
Forward stagewise estimation is a revived slow-brewing approach for model building that is particularly attractive in dealing with complex data structures for both its computational efficiency and its intrinsic connections with penalized estimation. Under the framework of generalized estimating equations, we study general stagewise estimation approaches that can handle clustered data and non-Gaussian/non-linear models in the presence of prior variable grouping structure. As the grouping structure is often not ideal in that even the important groups may contain irrelevant variables, the key is to simultaneously conduct group selection and within-group variable selection, that is, bi-level selection. We propose two approaches to address the challenge. The first is a bi-level stagewise estimating equations (BiSEE) approach, which is shown to correspond to the sparse group lasso penalized regression. The second is a hierarchical stagewise estimating equations (HiSEE) approach to handle more general hierarchical grouping structure, in which each stagewise estimation step itself is executed as a hierarchical selection process based on the grouping structure. Simulation studies show that BiSEE and HiSEE yield competitive model selection and predictive performance compared to existing approaches. We apply the proposed approaches to study the association between the suicide-related hospitalization rates of the 15-19 age group and the characteristics of the school districts in the State of Connecticut. © 2017, The International Biometric Society.
Extremophile Diatoms: Implications to the Drake Equation
Sterrenburg, Frithjof A. S.; Hoover, Richard B.
2011-01-01
Diatoms are unicellular Eukaryotes that (as a group and phylogenetically) are not strictly regarded as extremophiles , since the vast majority of diatoms are mesophilic photoautotrophs. However, among the terrestrial Eukaryotes, diatoms are by far the single group of organisms with the ability to inhabit the greatest range of hostile environments on Earth. They are the dominant eukaryotes in the polar regions; in fumaroles, hot springs and geysers; and in hypersaline and hyperalkaline lakes and pools. Cryophilic species such as Fragilaria sublinearis and Chaetoceras fragilis are able to carry out respiration at extremely low rates at low temperatures in darkness. The Drake Equation refers to the likelihood of there being intelligent life at the technological level of electromagnetic communication. However, consideration of the range of conditions suitable for the habitability of eukaryotic diatoms and prokaryotic extremophiles, the likelihood that life exists elsewhere in the cosmos becomes many orders of magnitude greater than that predicted by the classical Drake Equation. In this paper we review the characteristics of diatoms as eukaryotic extremophiles and consider the implications to adjustments needed to the Drake Equation to assess the possibility that life exists elsewhere in the Universe.
Iterative solution of the Helmholtz equation
Energy Technology Data Exchange (ETDEWEB)
Larsson, E.; Otto, K. [Uppsala Univ. (Sweden)
1996-12-31
We have shown that the numerical solution of the two-dimensional Helmholtz equation can be obtained in a very efficient way by using a preconditioned iterative method. We discretize the equation with second-order accurate finite difference operators and take special care to obtain non-reflecting boundary conditions. We solve the large, sparse system of equations that arises with the preconditioned restarted GMRES iteration. The preconditioner is of {open_quotes}fast Poisson type{close_quotes}, and is derived as a direct solver for a modified PDE problem.The arithmetic complexity for the preconditioner is O(n log{sub 2} n), where n is the number of grid points. As a test problem we use the propagation of sound waves in water in a duct with curved bottom. Numerical experiments show that the preconditioned iterative method is very efficient for this type of problem. The convergence rate does not decrease dramatically when the frequency increases. Compared to banded Gaussian elimination, which is a standard solution method for this type of problems, the iterative method shows significant gain in both storage requirement and arithmetic complexity. Furthermore, the relative gain increases when the frequency increases.
Abstract methods in partial differential equations
Carroll, Robert W
2012-01-01
Detailed, self-contained treatment examines modern abstract methods in partial differential equations, especially abstract evolution equations. Suitable for graduate students with some previous exposure to classical partial differential equations. 1969 edition.
Differential equations with applications in cancer diseases.
Ilea, M; Turnea, M; Rotariu, M
2013-01-01
Mathematical modeling is a process by which a real world problem is described by a mathematical formulation. The cancer modeling is a highly challenging problem at the frontier of applied mathematics. A variety of modeling strategies have been developed, each focusing on one or more aspects of cancer. The vast majority of mathematical models in cancer diseases biology are formulated in terms of differential equations. We propose an original mathematical model with small parameter for the interactions between these two cancer cell sub-populations and the mathematical model of a vascular tumor. We work on the assumption that, the quiescent cells' nutrient consumption is long. One the equations system includes small parameter epsilon. The smallness of epsilon is relative to the size of the solution domain. MATLAB simulations obtained for transition rate from the quiescent cells' nutrient consumption is long, we show a similar asymptotic behavior for two solutions of the perturbed problem. In this system, the small parameter is an asymptotic variable, different from the independent variable. The graphical output for a mathematical model of a vascular tumor shows the differences in the evolution of the tumor populations of proliferating, quiescent and necrotic cells. The nutrient concentration decreases sharply through the viable rim and tends to a constant level in the core due to the nearly complete necrosis in this region. Many mathematical models can be quantitatively characterized by ordinary differential equations or partial differential equations. The use of MATLAB in this article illustrates the important role of informatics in research in mathematical modeling. The study of avascular tumor growth cells is an exciting and important topic in cancer research and will profit considerably from theoretical input. Interpret these results to be a permanent collaboration between math's and medical oncologists.
Hypergeometric solutions to Schr\\"odinger equations for the quantum Painlev\\'e equations
Nagoya, Hajime
2011-01-01
We consider Schr\\"odinger equations for the quantum Painlev\\'e equations. We present hypergeometric solutions of the Schr\\"odinger equations for the quantum Painlev\\'e equations, as particular solutions. We also give a representation theoretic correspondence between Hamiltonians of the Schr\\"odinger equations for the quantum Painlev\\'e equations and those of the KZ equation or the confluent KZ equations.
Fractional complex transform for fractional differential equations
National Research Council Canada - National Science Library
Lİ, Zheng Biao; HE, Ji Huan
2010-01-01
Fractional complex transform is proposed to convert fractional differential equations into ordinary differential equations, so that all analytical methods devoted to advanced calculus can be easily...
Numerical optimization using flow equations.
Punk, Matthias
2014-12-01
We develop a method for multidimensional optimization using flow equations. This method is based on homotopy continuation in combination with a maximum entropy approach. Extrema of the optimizing functional correspond to fixed points of the flow equation. While ideas based on Bayesian inference such as the maximum entropy method always depend on a prior probability, the additional step in our approach is to perform a continuous update of the prior during the homotopy flow. The prior probability thus enters the flow equation only as an initial condition. We demonstrate the applicability of this optimization method for two paradigmatic problems in theoretical condensed matter physics: numerical analytic continuation from imaginary to real frequencies and finding (variational) ground states of frustrated (quantum) Ising models with random or long-range antiferromagnetic interactions.
Introductory course on differential equations
Gorain, Ganesh C
2014-01-01
Introductory Course on DIFFERENTIAL EQUATIONS provides an excellent exposition of the fundamentals of ordinary and partial differential equations and is ideally suited for a first course of undergraduate students of mathematics, physics and engineering. The aim of this book is to present the elementary theories of differential equations in the forms suitable for use of those students whose main interest in the subject are based on simple mathematical ideas. KEY FEATURES: Discusses the subject in a systematic manner without sacrificing mathematical rigour. A variety of exercises drill the students in problem solving in view of the mathematical theories explained in the book. Worked out examples illustrated according to the theories developed in the book with possible alternatives. Exhaustive collection of problems and the simplicity of presentation differentiate this book from several others. Material contained will help teachers as well as aspiring students of different competitive examinations.
Quantum Gross-Pitaevskii Equation
Directory of Open Access Journals (Sweden)
Jutho Haegeman, Damian Draxler, Vid Stojevic, J. Ignacio Cirac, Tobias J. Osborne, Frank Verstraete
2017-07-01
Full Text Available We introduce a non-commutative generalization of the Gross-Pitaevskii equation for one-dimensional quantum gasses and quantum liquids. This generalization is obtained by applying the time-dependent variational principle to the variational manifold of continuous matrix product states. This allows for a full quantum description of many body system ---including entanglement and correlations--- and thus extends significantly beyond the usual mean-field description of the Gross-Pitaevskii equation, which is known to fail for (quasi one-dimensional systems. By linearizing around a stationary solution, we furthermore derive an associated generalization of the Bogoliubov -- de Gennes equations. This framework is applied to compute the steady state response amplitude to a periodic perturbation of the potential.
The respiratory system in equations
Maury, Bertrand
2013-01-01
The book proposes an introduction to the mathematical modeling of the respiratory system. A detailed introduction on the physiological aspects makes it accessible to a large audience without any prior knowledge on the lung. Different levels of description are proposed, from the lumped models with a small number of parameters (Ordinary Differential Equations), up to infinite dimensional models based on Partial Differential Equations. Besides these two types of differential equations, two chapters are dedicated to resistive networks, and to the way they can be used to investigate the dependence of the resistance of the lung upon geometrical characteristics. The theoretical analysis of the various models is provided, together with state-of-the-art techniques to compute approximate solutions, allowing comparisons with experimental measurements. The book contains several exercises, most of which are accessible to advanced undergraduate students.
Integration rules for scattering equations
Energy Technology Data Exchange (ETDEWEB)
Baadsgaard, Christian; Bjerrum-Bohr, N.E.J.; Bourjaily, Jacob L.; Damgaard, Poul H. [Niels Bohr International Academy and Discovery Center,Niels Bohr Institute, University of Copenhagen,Blegdamsvej 17, DK-2100 Copenhagen Ø (Denmark)
2015-09-21
As described by Cachazo, He and Yuan, scattering amplitudes in many quantum field theories can be represented as integrals that are fully localized on solutions to the so-called scattering equations. Because the number of solutions to the scattering equations grows quite rapidly, the contour of integration involves contributions from many isolated components. In this paper, we provide a simple, combinatorial rule that immediately provides the result of integration against the scattering equation constraints for any Möbius-invariant integrand involving only simple poles. These rules have a simple diagrammatic interpretation that makes the evaluation of any such integrand immediate. Finally, we explain how these rules are related to the computation of amplitudes in the field theory limit of string theory.
Dynamics of partial differential equations
Wayne, C Eugene
2015-01-01
This book contains two review articles on the dynamics of partial differential equations that deal with closely related topics but can be read independently. Wayne reviews recent results on the global dynamics of the two-dimensional Navier-Stokes equations. This system exhibits stable vortex solutions: the topic of Wayne's contribution is how solutions that start from arbitrary initial conditions evolve towards stable vortices. Weinstein considers the dynamics of localized states in nonlinear Schrodinger and Gross-Pitaevskii equations that describe many optical and quantum systems. In this contribution, Weinstein reviews recent bifurcations results of solitary waves, their linear and nonlinear stability properties, and results about radiation damping where waves lose energy through radiation. The articles, written independently, are combined into one volume to showcase the tools of dynamical systems theory at work in explaining qualitative phenomena associated with two classes of partial differential equ...
Equating accelerometer estimates among youth
DEFF Research Database (Denmark)
Brazendale, Keith; Beets, Michael W; Bornstein, Daniel B
2016-01-01
OBJECTIVES: Different accelerometer cutpoints used by different researchers often yields vastly different estimates of moderate-to-vigorous intensity physical activity (MVPA). This is recognized as cutpoint non-equivalence (CNE), which reduces the ability to accurately compare youth MVPA across...... percent error was 12.6% (range: 1.3 to 30.1) and the proportion of variance explained ranged from 66.7% to 99.8%. Mean difference for the best performing prediction equation (VC from EV) was -0.110mind(-1) (limits of agreement (LOA), -2.623 to 2.402). The mean difference for the worst performing...... prediction equation (FR3 from PY) was 34.76mind(-1) (LOA, -60.392 to 129.910). CONCLUSIONS: For six different sets of published cutpoints, the use of this equating system can assist individuals attempting to synthesize the growing body of literature on Actigraph, accelerometry-derived MVPA....
Fractional-calculus diffusion equation.
Ajlouni, Abdul-Wali Ms; Al-Rabai'ah, Hussam A
2010-05-21
Sequel to the work on the quantization of nonconservative systems using fractional calculus and quantization of a system with Brownian motion, which aims to consider the dissipation effects in quantum-mechanical description of microscale systems. The canonical quantization of a system represented classically by one-dimensional Fick's law, and the diffusion equation is carried out according to the Dirac method. A suitable Lagrangian, and Hamiltonian, describing the diffusive system, are constructed and the Hamiltonian is transformed to Schrodinger's equation which is solved. An application regarding implementation of the developed mathematical method to the analysis of diffusion, osmosis, which is a biological application of the diffusion process, is carried out. Schrödinger's equation is solved. The plot of the probability function represents clearly the dissipative and drift forces and hence the osmosis, which agrees totally with the macro-scale view, or the classical-version osmosis.
Fractional-calculus diffusion equation
2010-01-01
Background Sequel to the work on the quantization of nonconservative systems using fractional calculus and quantization of a system with Brownian motion, which aims to consider the dissipation effects in quantum-mechanical description of microscale systems. Results The canonical quantization of a system represented classically by one-dimensional Fick's law, and the diffusion equation is carried out according to the Dirac method. A suitable Lagrangian, and Hamiltonian, describing the diffusive system, are constructed and the Hamiltonian is transformed to Schrodinger's equation which is solved. An application regarding implementation of the developed mathematical method to the analysis of diffusion, osmosis, which is a biological application of the diffusion process, is carried out. Schrödinger's equation is solved. Conclusions The plot of the probability function represents clearly the dissipative and drift forces and hence the osmosis, which agrees totally with the macro-scale view, or the classical-version osmosis. PMID:20492677
Equating accelerometer estimates among youth
DEFF Research Database (Denmark)
Brazendale, Keith; Beets, Michael W; Bornstein, Daniel B
2016-01-01
OBJECTIVES: Different accelerometer cutpoints used by different researchers often yields vastly different estimates of moderate-to-vigorous intensity physical activity (MVPA). This is recognized as cutpoint non-equivalence (CNE), which reduces the ability to accurately compare youth MVPA across......,112 Actigraph accelerometer data files from 21 worldwide studies (children 3-18 years, 61.5% female) were used to develop prediction equations for six sets of published cutpoints. Linear and non-linear modeling, using a leave one out cross-validation technique, was employed to develop equations to convert MVPA...... from one set of cutpoints into another. Bland Altman plots illustrate the agreement between actual MVPA and predicted MVPA values. RESULTS: Across the total sample, mean MVPA ranged from 29.7MVPAmind(-1) (Puyau) to 126.1MVPAmind(-1) (Freedson 3 METs). Across conversion equations, median absolute...
On Reducing a System of Equations to a Single Equation
DEFF Research Database (Denmark)
Frandsen, G.S.; Shparlinski, I.E.
2004-01-01
For a system of polynomial equations over Q;p; we present an efficient construction of a single polynomial of quite small degree whose zero set over Q;p; coincides with the zero set over Q;p; of the original system. We also show that the polynomial has some other attractive features such as low...
FMTLxLyLz DIMENSIONAL EQUAT DIMENSIONAL EQUATION ...
African Journals Online (AJOL)
eobe
Filtrate from the sludge started perc through the sand bed by gravitational movemen water downwards. .... (21). By observing the experimental plot of t/V versus V, equation (21) should be re – written as,. = +. (22) where is the intercept of the plot of against V. Since we are working on natural drying bed, the pressure P, under ...
Maxwell's mixing equation revisited: characteristic impedance equations for ellipsoidal cells.
Stubbe, Marco; Gimsa, Jan
2015-07-21
We derived a series of, to our knowledge, new analytic expressions for the characteristic features of the impedance spectra of suspensions of homogeneous and single-shell spherical, spheroidal, and ellipsoidal objects, e.g., biological cells of the general ellipsoidal shape. In the derivation, we combined the Maxwell-Wagner mixing equation with our expression for the Clausius-Mossotti factor that had been originally derived to describe AC-electrokinetic effects such as dielectrophoresis, electrorotation, and electroorientation. The influential radius model was employed because it allows for a separation of the geometric and electric problems. For shelled objects, a special axial longitudinal element approach leads to a resistor-capacitor model, which can be used to simplify the mixing equation. Characteristic equations were derived for the plateau levels, peak heights, and characteristic frequencies of the impedance as well as the complex specific conductivities and permittivities of suspensions of axially and randomly oriented homogeneous and single-shell ellipsoidal objects. For membrane-covered spherical objects, most of the limiting cases are identical to-or improved with respect to-the known solutions given by researchers in the field. The characteristic equations were found to be quite precise (largest deviations typically <5% with respect to the full model) when tested with parameters relevant to biological cells. They can be used for the differentiation of orientation and the electric properties of cell suspensions or in the analysis of single cells in microfluidic systems. Copyright © 2015 The Authors. Published by Elsevier Inc. All rights reserved.
Fundamentals of equations of state
Eliezer, Shalom; Hora, Heinrich
2002-01-01
The equation of state was originally developed for ideal gases, and proved central to the development of early molecular and atomic physics. Increasingly sophisticated equations of state have been developed to take into account molecular interactions, quantization, relativistic effects, etc. Extreme conditions of matter are encountered both in nature and in the laboratory, for example in the centres of stars, in relativistic collisions of heavy nuclei, in inertial confinement fusion (where a temperature of 10 9 K and a pressure exceeding a billion atmospheres can be achieved). A sound knowledg
Einstein Equations from Varying Complexity
Czech, Bartłomiej
2018-01-01
A recent proposal equates the circuit complexity of a quantum gravity state with the gravitational action of a certain patch of spacetime. Since Einstein's equations follow from varying the action, it should be possible to derive them by varying complexity. I present such a derivation for vacuum solutions of pure Einstein gravity in three-dimensional asymptotically anti-de Sitter space. The argument relies on known facts about holography and on properties of tensor network renormalization, an algorithm for coarse-graining (and optimizing) tensor networks.
Applied analysis and differential equations
Cârj, Ovidiu
2007-01-01
This volume contains refereed research articles written by experts in the field of applied analysis, differential equations and related topics. Well-known leading mathematicians worldwide and prominent young scientists cover a diverse range of topics, including the most exciting recent developments. A broad range of topics of recent interest are treated: existence, uniqueness, viability, asymptotic stability, viscosity solutions, controllability and numerical analysis for ODE, PDE and stochastic equations. The scope of the book is wide, ranging from pure mathematics to various applied fields such as classical mechanics, biomedicine, and population dynamics.
Basic linear partial differential equations
Treves, Francois
1975-01-01
Focusing on the archetypes of linear partial differential equations, this text for upper-level undergraduates and graduate students features most of the basic classical results. The methods, however, are decidedly nontraditional: in practically every instance, they tend toward a high level of abstraction. This approach recalls classical material to contemporary analysts in a language they can understand, as well as exploiting the field's wealth of examples as an introduction to modern theories.The four-part treatment covers the basic examples of linear partial differential equations and their
Integral equations on time scales
Georgiev, Svetlin G
2016-01-01
This book offers the reader an overview of recent developments of integral equations on time scales. It also contains elegant analytical and numerical methods. This book is primarily intended for senior undergraduate students and beginning graduate students of engineering and science courses. The students in mathematical and physical sciences will find many sections of direct relevance. The book contains nine chapters and each chapter is pedagogically organized. This book is specially designed for those who wish to understand integral equations on time scales without having extensive mathematical background.
Group analysis of differential equations
Ovsiannikov, L V
1982-01-01
Group Analysis of Differential Equations provides a systematic exposition of the theory of Lie groups and Lie algebras and its application to creating algorithms for solving the problems of the group analysis of differential equations.This text is organized into eight chapters. Chapters I to III describe the one-parameter group with its tangential field of vectors. The nonstandard treatment of the Banach Lie groups is reviewed in Chapter IV, including a discussion of the complete theory of Lie group transformations. Chapters V and VI cover the construction of partial solution classes for the g
Partial differential equations an introduction
Colton, David
2004-01-01
Intended for a college senior or first-year graduate-level course in partial differential equations, this text offers students in mathematics, engineering, and the applied sciences a solid foundation for advanced studies in mathematics. Classical topics presented in a modern context include coverage of integral equations and basic scattering theory. This complete and accessible treatment includes a variety of examples of inverse problems arising from improperly posed applications. Exercises at the ends of chapters, many with answers, offer a clear progression in developing an understanding of
On the Symplectic Dirac Equation
Amorim, R. G. G.; Ulhoa, S. C.; Silva, Edilberto O.
2015-12-01
Symplectic unitary representations for the Poincaré group are studied. The formalism is based on the noncommutative structure of the star-product, and using group theory approach as a guide, a consistent physical theory in phase space is constructed. The state of a quantum mechanics system is described by a quasi-probability amplitude that is in association with the Wigner function. In this context, we derive the Klein-Gordon and Dirac equations. As an application, we study the Dirac equation with electromagnetic interaction in phase space.
Radar equations for modern radar
Barton, David K
2012-01-01
Based on the classic Radar Range-Performance Analysis from 1980, this practical volume extends that work to ensure applicability of radar equations to the design and analysis of modern radars. This unique book helps you identify what information on the radar and its environment is needed to predict detection range. Moreover, it provides equations and data to improve the accuracy of range calculations. You find detailed information on propagation effects, methods of range calculation in environments that include clutter, jamming and thermal noise, as well as loss factors that reduce radar perfo
Stability theory of differential equations
Bellman, Richard Ernest
1953-01-01
Suitable for advanced undergraduates and graduate students, this was the first English-language text to offer detailed coverage of boundedness, stability, and asymptotic behavior of linear and nonlinear differential equations. It remains a classic guide, featuring material from original research papers, including the author's own studies.The linear equation with constant and almost-constant coefficients receives in-depth attention that includes aspects of matrix theory. No previous acquaintance with the theory is necessary, since author Richard Bellman derives the results in matrix theory from
Basic linear partial differential equations
Treves, Francois
2006-01-01
Focusing on the archetypes of linear partial differential equations, this text for upper-level undergraduates and graduate students features most of the basic classical results. The methods, however, are decidedly nontraditional: in practically every instance, they tend toward a high level of abstraction. This approach recalls classical material to contemporary analysts in a language they can understand, as well as exploiting the field's wealth of examples as an introduction to modern theories.The four-part treatment covers the basic examples of linear partial differential equations and their
Sequent Calculus and Equational Programming
Directory of Open Access Journals (Sweden)
Nicolas Guenot
2015-07-01
Full Text Available Proof assistants and programming languages based on type theories usually come in two flavours: one is based on the standard natural deduction presentation of type theory and involves eliminators, while the other provides a syntax in equational style. We show here that the equational approach corresponds to the use of a focused presentation of a type theory expressed as a sequent calculus. A typed functional language is presented, based on a sequent calculus, that we relate to the syntax and internal language of Agda. In particular, we discuss the use of patterns and case splittings, as well as rules implementing inductive reasoning and dependent products and sums.
Rainfall intensity-duration equations
Froehlich, David C.
1988-01-01
A method for rapidly developing a rainfall intensity-duration equation for durations less than one hour and recurrence intervals between 2 and 100 years for any location in the conterminous United States is presented. Optimal parameters of a general rainfall-intensity duration equation are determined using precipitation depths for durations of 5, 10, 15, 30 and 60 minutes obtained from commonly available isopluvial maps. A single set of parameters applies to the entire western U.S. For the central and eastern U.S, a graphical means of determining the parameters is provided.
Navier-Stokes equations on R3 × [0, T
Stenger, Frank; Baumann, Gerd
2016-01-01
In this monograph, leading researchers in the world of numerical analysis, partial differential equations, and hard computational problems study the properties of solutions of the Navier–Stokes partial differential equations on (x, y, z, t) ∈ ℝ3 × [0, T]. Initially converting the PDE to a system of integral equations, the authors then describe spaces A of analytic functions that house solutions of this equation, and show that these spaces of analytic functions are dense in the spaces S of rapidly decreasing and infinitely differentiable functions. This method benefits from the following advantages: The functions of S are nearly always conceptual rather than explicit Initial and boundary conditions of solutions of PDE are usually drawn from the applied sciences, and as such, they are nearly always piece-wise analytic, and in this case, the solutions have the same properties When methods of approximation are applied to functions of A they converge at an exponential rate, whereas methods of approximation ...
Renaissance Learning Equating Study. Report
Sewell, Julie; Sainsbury, Marian; Pyle, Katie; Keogh, Nikki; Styles, Ben
2007-01-01
An equating study was carried out in autumn 2006 by the National Foundation for Educational Research (NFER) on behalf of Renaissance Learning, to provide validation evidence for the use of the Renaissance Star Reading and Star Mathematics tests in English schools. The study investigated the correlation between the Star tests and established tests.…
Wave-equation dispersion inversion
Li, Jing
2016-12-08
We present the theory for wave-equation inversion of dispersion curves, where the misfit function is the sum of the squared differences between the wavenumbers along the predicted and observed dispersion curves. The dispersion curves are obtained from Rayleigh waves recorded by vertical-component geophones. Similar to wave-equation traveltime tomography, the complicated surface wave arrivals in traces are skeletonized as simpler data, namely the picked dispersion curves in the phase-velocity and frequency domains. Solutions to the elastic wave equation and an iterative optimization method are then used to invert these curves for 2-D or 3-D S-wave velocity models. This procedure, denoted as wave-equation dispersion inversion (WD), does not require the assumption of a layered model and is significantly less prone to the cycle-skipping problems of full waveform inversion. The synthetic and field data examples demonstrate that WD can approximately reconstruct the S-wave velocity distributions in laterally heterogeneous media if the dispersion curves can be identified and picked. The WD method is easily extended to anisotropic data and the inversion of dispersion curves associated with Love waves.
Sonar equations for planetary exploration
Ainslie, M.A.; Leighton, T.G.
2016-01-01
The set of formulations commonly known as “the sonar equations” have for many decades been used to quantify the performance of sonar systems in terms of their ability to detect and ocalize objects submerged in seawater. The efficacy of the sonar equations, with individualterms evaluated in decibels,
Equational theories of tropical sernirings
DEFF Research Database (Denmark)
Aceto, Luca; Esik, Zoltan; Ingolfsdottir, Anna
2003-01-01
examples of such structures are the (max,+) semiring and the tropical semiring. It is shown that none of the exotic semirings commonly considered in the literature has a finite basis for its equations, and that similar results hold for the commutative idempotent weak semirings that underlie them. For each...
Indian Academy of Sciences (India)
volving three arbitrary functions for the (2+1)-dimensional KdV equation. Diverse peri- odic wave solutions ... double periodic and possess properties of trigonometric functions. Detailed expla- nations about ... work is to demonstrate that the singular manifold method [12], a powerful method for obtaining the exact solutions to ...
Structural equations in language learning
Moortgat, M.J.
In categorial systems with a fixed structural component, the learning problem comes down to finding the solution for a set of typeassignment equations. A hard-wired structural component is problematic if one want to address issues of structural variation. Our starting point is a type-logical
Pendulum Motion and Differential Equations
Reid, Thomas F.; King, Stephen C.
2009-01-01
A common example of real-world motion that can be modeled by a differential equation, and one easily understood by the student, is the simple pendulum. Simplifying assumptions are necessary for closed-form solutions to exist, and frequently there is little discussion of the impact if those assumptions are not met. This article presents a…
A generalized advection dispersion equation
Indian Academy of Sciences (India)
–Segel equation; Adv. Diff. Eq. 2013, 2013:94, doi:10.1186/1687-1847-2013-94. Abdon Atangana, Aden Ahmed O and Necdet Bıldık 2013. A generalized version of a low velocity impact between a rigid sphere and a transversely isotropic ...
Solving differential equations in R
Soetaert, K.E.R.; Petzoldt, T.; Setzer, R.W.
2010-01-01
Although R is still predominantly applied for statistical analysis and graphical representation, it is rapidly becoming more suitable for mathematical computing. One of the fields where considerable progress has been made recently is the solution of differential equations. Here we give a brief
Quantum adiabatic Markovian master equations
Albash, Tameem; Boixo, Sergio; Lidar, Daniel A.; Zanardi, Paolo
2012-12-01
We develop from first principles Markovian master equations suited for studying the time evolution of a system evolving adiabatically while coupled weakly to a thermal bath. We derive two sets of equations in the adiabatic limit, one using the rotating wave (secular) approximation that results in a master equation in Lindblad form, the other without the rotating wave approximation but not in Lindblad form. The two equations make markedly different predictions depending on whether or not the Lamb shift is included. Our analysis keeps track of the various time and energy scales associated with the various approximations we make, and thus allows for a systematic inclusion of higher order corrections, in particular beyond the adiabatic limit. We use our formalism to study the evolution of an Ising spin chain in a transverse field and coupled to a thermal bosonic bath, for which we identify four distinct evolution phases. While we do not expect this to be a generic feature, in one of these phases dissipation acts to increase the fidelity of the system state relative to the adiabatic ground state.
mixed type partial differential equation
Directory of Open Access Journals (Sweden)
M. Denche
2003-01-01
Full Text Available In this paper, we study a mixed problem with integral boundary conditions for a high order partial differential equation of mixed type. We prove the existence and uniqueness of the solution. The proof is based on energy inequality, and on the density of the range of the operator generated by the considered problem.
Solutions of equations in languages
Hesselink, Wim H.
A context-free grammar corresponds to a system of equations in languages. The language generated by the grammar is the smallest solution of the system. We give a necessary and sufficient condition for an arbitrary solution to be the smallest one. We revive an old criterion to decide that a grammar
Solving Intuitionistic Fuzzy Nonlinear Equations
Directory of Open Access Journals (Sweden)
Mohammad Keyanpour
2014-09-01
Full Text Available In this paper a numerical method is proposed to solve intuitionistic fuzzy nonlinear equations. The method is based on the Midpoint Newton's method in which the intuitionistic fuzzy quantities are presented in parametric form. The efficiency of the proposed method is tested with an illustrative example.
dimensional Jaulent–Miodek equations
Indian Academy of Sciences (India)
Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran,. Babolsar, Iran ... (NLPDEs) are widely used to describe complex phenomena in various fields of sciences particularly, in ... evolution equations plays an important role in nonlinear physical science because these solutions may well ...
Stability of Functional Differential Equations
Lemm, Jeffrey M
1986-01-01
This book provides an introduction to the structure and stability properties of solutions of functional differential equations. Numerous examples of applications (such as feedback systrems with aftereffect, two-reflector antennae, nuclear reactors, mathematical models in immunology, viscoelastic bodies, aeroautoelastic phenomena and so on) are considered in detail. The development is illustrated by numerous figures and tables.
Elizarova, Tatiana G
2009-01-01
This book presents two interconnected mathematical models generalizing the Navier-Stokes system. The models, called the quasi-gas-dynamic and quasi-hydrodynamic equations, are then used as the basis of numerical methods solving gas- and fluid-dynamic problems.
A Versatile Technique for Solving Quintic Equations
Kulkarni, Raghavendra G.
2006-01-01
In this paper we present a versatile technique to solve several types of solvable quintic equations. In the technique described here, the given quintic is first converted to a sextic equation by adding a root, and the resulting sextic equation is decomposed into two cubic polynomials as factors in a novel fashion. The resultant cubic equations are…
Some functional equations originating from number theory
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
We will introduce new functional equations (3) and (4) which are strongly related to well-known formulae (1) and (2) of number theory, and investigate the solutions of the equations. Moreover, we will also study some stability problems of those equations. Keywords. Functional equation; stability; multiplicative function. 1.
General Reducibility and Solvability of Polynomial Equations ...
African Journals Online (AJOL)
A complete work on general reducibility and solvability of polynomial equations by algebraic meansradicals is developed. These equations called, reanegbèd and vic-emmeous are designed by using simple algebraic principles on how systems of equations and polynomials behave. Reanegbèd equations are capable of ...
The Complexity of One-Step Equations
Ngu, Bing
2014-01-01
An analysis of one-step equations from a cognitive load theory perspective uncovers variation within one-step equations. The complexity of one-step equations arises from the element interactivity across the operational and relational lines. The higher the number of operational and relational lines, the greater the complexity of the equations.…
Thermoviscous Model Equations in Nonlinear Acoustics
DEFF Research Database (Denmark)
Rasmussen, Anders Rønne
Four nonlinear acoustical wave equations that apply to both perfect gasses and arbitrary fluids with a quadratic equation of state are studied. Shock and rarefaction wave solutions to the equations are studied. In order to assess the accuracy of the wave equations, their solutions are compared...... to solutions of the basic equations from which the wave equations are derived. A straightforward weakly nonlinear equation is the most accurate for shock modeling. A higher order wave equation is the most accurate for modeling of smooth disturbances. Investigations of the linear stability properties...... of solutions to the wave equations, reveal that the solutions may become unstable. Such instabilities are not found in the basic equations. Interacting shocks and standing shocks are investigated....
A new set of equations describing immiscible two-phase flow in homogeneous porous media
Hansen, Alex; Bedeaux, Dick; Kjelstrup, Signe; Savani, Isha; Vassvik, Morten
2016-01-01
Based on a simple scaling assumption concerning the total flow rate of immiscible two-phase flow in a homogeneous porous medium under steady-state conditions and a constant pressure drop, we derive two new equations that relate the total flow rate to the flow rates of each immiscible fluid. By integrating these equations, we present two integrals giving the flow rate of each fluid in terms of the the total flow rate. If we in addition assume that the flow obeys the relative permeability (generalized Darcy) equations, we find direct expressions for the two relative permeabilities and the capillary pressure in terms of the total flow rate. Hence, only the total flow rate as a function of saturation at constant pressure drop across the porous medium needs to be measured in order to obtain all three quantities. We test the equations on numerical and experimental systems.
Lindblad Equation for the Inelastic Loss of Ultracold Atoms
Braaten, Eric; Lepage, G Peter
2016-01-01
The loss of ultracold trapped atoms due to deeply inelastic reactions has previously been taken into account in effective field theories for low-energy atoms by adding local anti-Hermitian terms to the effective Hamiltonian. Here we show that when multi-atom systems are considered, an additional modification is required in the equation governing the density matrix. We define an effective density matrix by tracing over the states containing high-momentum atoms produced by deeply inelastic reactions. We show that it satisfies a Lindblad equation, with local Lindblad operators determined by the local anti-Hermitian terms in the effective Hamiltonian. We use the Lindblad equation to derive the universal relation for the two-atom inelastic loss rate for fermions with two spin states and the universal relation for the three-atom inelastic loss rate for identical bosons.
MAGNETOHYDRODYNAMIC EQUATIONS (MHD GENERATION CODE
Directory of Open Access Journals (Sweden)
Francisco Frutos Alfaro
2017-04-01
Full Text Available A program to generate codes in Fortran and C of the full magnetohydrodynamic equations is shown. The program uses the free computer algebra system software REDUCE. This software has a package called EXCALC, which is an exterior calculus program. The advantage of this program is that it can be modified to include another complex metric or spacetime. The output of this program is modified by means of a LINUX script which creates a new REDUCE program to manipulate the magnetohydrodynamic equations to obtain a code that can be used as a seed for a magnetohydrodynamic code for numerical applications. As an example, we present part of the output of our programs for Cartesian coordinates and how to do the discretization.
The equations icons of knowledge
Bais, Sander
2005-01-01
For thousands of years mankind has tried to understand nature. Exploring the world on all scales with instruments of ever more ingenuity, we have been able to unravel some of the great mysteries that surround us. While collecting an overwhelming multitude of observational facts, we discovered fundamental laws that govern the structure and evolution of physical reality. We know that nature speaks to us in the language of mathematics. In this language most of our basic understanding of the physical world can be expressed in an unambiguous and concise way. The most artificial language turns out to be the most natural of all. The laws of nature correspond to equations. These equations are the icons of knowledge that mark crucial turning points in our thinking about the world we happen to live in. They form the symbolic representation of most of what we know, and as such constitute an important and robust part of our culture.
BERNULLI DIFFERENTIAL EQUATION AND CHAOS
Directory of Open Access Journals (Sweden)
V. Ye. Belozerov
2013-03-01
Full Text Available Existence conditions of homoclinic orbits for some systems of ordinary quadratic differential equations with singular linear part are founded. A realization of these conditions guarantees the existence of chaotic attractors at 3-D autonomous quadratic systems. In addition, a chaotic behavior of the solutions of these systems is determined by one-dimensional discrete map at some values of parameters. Examples are given.
Equation of State Project Overview
Energy Technology Data Exchange (ETDEWEB)
Crockett, Scott [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2015-09-11
A general overview of the Equation of State (EOS) Project will be presented. The goal is to provide the audience with an introduction of what our more advanced methods entail (DFT, QMD, etc.. ) and how these models are being utilized to better constrain the thermodynamic models. These models substantially reduce our regions of interpolation between the various thermodynamic limits. I will also present a variety example of recent EOS work.
Handbook of structural equation modeling
Hoyle, Rick H
2012-01-01
The first comprehensive structural equation modeling (SEM) handbook, this accessible volume presents both the mechanics of SEM and specific SEM strategies and applications. The editor, contributors, and editorial advisory board are leading methodologists who have organized the book to move from simpler material to more statistically complex modeling approaches. Sections cover the foundations of SEM; statistical underpinnings, from assumptions to model modifications; steps in implementation, from data preparation through writing the SEM report; and basic and advanced applications, inclu
Effective Schroedinger equations on submanifolds
Energy Technology Data Exchange (ETDEWEB)
Wachsmuth, Jakob
2010-02-11
In this thesis the time dependent Schroedinger equation is considered on a Riemannian manifold A with a potential that localizes a certain class of states close to a fixed submanifold C, the constraint manifold. When the potential is scaled in the directions normal to C by a small parameter epsilon, the solutions concentrate in an epsilon-neighborhood of the submanifold. An effective Schroedinger equation on the submanifold C is derived and it is shown that its solutions, suitably lifted to A, approximate the solutions of the original equation on A up to errors of order {epsilon}{sup 3} vertical stroke t vertical stroke at time t. Furthermore, it is proved that, under reasonable conditions, the eigenvalues of the corresponding Hamiltonians below a certain energy coincide upto errors of order {epsilon}{sup 3}. These results holds in the situation where tangential and normal energies are of the same order, and where exchange between normal and tangential energies occurs. In earlier results tangential energies were assumed to be small compared to normal energies, and rather restrictive assumptions were needed, to ensure that the separation of energies is maintained during the time evolution. The most important consequence of this thesis is that now constraining potentials that change their shape along the submanifold can be treated, which is the typical situation in applications like molecular dynamics and quantum waveguides.
Wave equations in higher dimensions
Dong, Shi-Hai
2011-01-01
Higher dimensional theories have attracted much attention because they make it possible to reduce much of physics in a concise, elegant fashion that unifies the two great theories of the 20th century: Quantum Theory and Relativity. This book provides an elementary description of quantum wave equations in higher dimensions at an advanced level so as to put all current mathematical and physical concepts and techniques at the reader’s disposal. A comprehensive description of quantum wave equations in higher dimensions and their broad range of applications in quantum mechanics is provided, which complements the traditional coverage found in the existing quantum mechanics textbooks and gives scientists a fresh outlook on quantum systems in all branches of physics. In Parts I and II the basic properties of the SO(n) group are reviewed and basic theories and techniques related to wave equations in higher dimensions are introduced. Parts III and IV cover important quantum systems in the framework of non-relativisti...
Prediction equation for vehicle-pedestrian crash and safety analysis ...
African Journals Online (AJOL)
On the assumption that negative binomial errors control over dispersion characteristic of the crash data, a Generalized Linear Model was applied to estimate parameters of the predicting equations. Accra accounted for more than 57.6 % of the pedestrian crashes with highest casualty rate of 34 injuries per annum (including ...
Investigating Supervisory Relationships and Therapeutic Alliances Using Structural Equation Modeling
DePue, Mary Kristina; Lambie, Glenn W.; Liu, Ren; Gonzalez, Jessica
2016-01-01
The authors used structural equation modeling to examine the contribution of supervisees' supervisory relationship levels to therapeutic alliance (TA) scores with their clients in practicum. Results showed that supervisory relationship scores positively contributed to the TA. Client and counselor ratings of the TA also differed.
Analogies between Mass-Flux and Reynolds-Averaged Equations
Roode, S.R. de; Duynkerke, P.G.
2000-01-01
In many large-scale models mass-flux parameterizations are applied to prognose the effect of cumulus cloud convection on the large-scale environment. Key parameters in the mass-flux equations are the lateral entrainment and detrainment rates. The physical meaning of these parameters is that they
Assessment of total bed material equations on selected Malaysia rivers
Saleh, A.; Abustan, I.; Mohd Remy Rozainy, M. A. Z.; Sabtu, N.
2017-10-01
Assessment of total sediment load equations on selected Malaysia rivers was done based on 35 sediment loads and hydraulic data. Four rivers were selected to make this assessment which are Sungai Perak, Sungai Kemaman, Sungai Pergau and Sungai Kurau. These rivers can be divided into three categories based on the river width, with Sungai Perak (300-350m) and Sungai Kemaman (150-200m) can categorised as big rivers, meanwhile, Sungai Pergau (30-45m) and Sungai Kurau (10-11m) can categorised as medium and small river respectively. The total sediment load equations used in this assessment are Ackers-White, Brownlie, Engelund-Hansen, Graf, Molinas-Wu, Karim-Kennedy and Yang. This paper also tested the local total sediment load equations by Ariffin and Sinnakaudan et al. to evaluate capabilities of the equations on different rivers in Malaysia. The graphs of the calculated equations versus measured sediment transport rates were plotted to shows the accuracy of the tested equations.
Handbook of differential equations stationary partial differential equations
Chipot, Michel
2006-01-01
This handbook is volume III in a series devoted to stationary partial differential quations. Similarly as volumes I and II, it is a collection of self contained state-of-the-art surveys written by well known experts in the field. The topics covered by this handbook include singular and higher order equations, problems near critically, problems with anisotropic nonlinearities, dam problem, T-convergence and Schauder-type estimates. These surveys will be useful for both beginners and experts and speed up the progress of corresponding (rapidly developing and fascinating) areas of mathematics. Ke
Partial differential equations of mathematical physics and integral equations
Guenther, Ronald B
1996-01-01
This book was written to help mathematics students and those in the physical sciences learn modern mathematical techniques for setting up and analyzing problems. The mathematics used is rigorous, but not overwhelming, while the authors carefully model physical situations, emphasizing feedback among a beginning model, physical experiments, mathematical predictions, and the subsequent refinement and reevaluation of the physical model itself. Chapter 1 begins with a discussion of various physical problems and equations that play a central role in applications. The following chapters take up the t
International Workshop on Elliptic and Parabolic Equations
Schrohe, Elmar; Seiler, Jörg; Walker, Christoph
2015-01-01
This volume covers the latest research on elliptic and parabolic equations and originates from the international Workshop on Elliptic and Parabolic Equations, held September 10-12, 2013 at the Leibniz Universität Hannover. It represents a collection of refereed research papers and survey articles written by eminent scientist on advances in different fields of elliptic and parabolic partial differential equations, including singular Riemannian manifolds, spectral analysis on manifolds, nonlinear dispersive equations, Brownian motion and kernel estimates, Euler equations, porous medium type equations, pseudodifferential calculus, free boundary problems, and bifurcation analysis.
Partial differential equations for scientists and engineers
Farlow, Stanley J
1993-01-01
Most physical phenomena, whether in the domain of fluid dynamics, electricity, magnetism, mechanics, optics, or heat flow, can be described in general by partial differential equations. Indeed, such equations are crucial to mathematical physics. Although simplifications can be made that reduce these equations to ordinary differential equations, nevertheless the complete description of physical systems resides in the general area of partial differential equations.This highly useful text shows the reader how to formulate a partial differential equation from the physical problem (constructing th
Semilinear Schrödinger equations
Cazenave, Thierry
2003-01-01
The nonlinear Schrödinger equation has received a great deal of attention from mathematicians, in particular because of its applications to nonlinear optics. It is also a good model dispersive equation, since it is often technically simpler than other dispersive equations, such as the wave or Korteweg-de Vries equation. Particularly useful tools in studying the nonlinear Schrödinger equation are energy and Strichartz's estimates. This book presents various mathematical aspects of the nonlinear Schrödinger equation. It examines both problems of local nature (local existence of solutions, unique
Using fundamental equations to describe basic phenomena
DEFF Research Database (Denmark)
Jakobsen, Arne; Rasmussen, Bjarne D.
1999-01-01
When the fundamental thermodynamic balance equations (mass, energy, and momentum) are used to describe the processes in a simple refrigeration system, then one finds that the resulting equation system will have a degree of freedom equal to one. Further investigations reveal that it is the equation...... and subcooling are introduced. Since the degree of freedom was equal to one, using both the superheat and subcooling require that one of the fundamental equations must be omitted from the equation system.The main purpose of the paper is to clarify the relation between the fundamental balance equations...
Painleve property for partial differential equations
Energy Technology Data Exchange (ETDEWEB)
Weiss, J.; Tabor, M.; Carnevale, G.
1983-03-01
In this paper we define the Painleve property for partial differential equations and show how it determines, in a remarkably simple manner, the integrability, the Baecklund transforms, the linearizing transforms, and the Lax pairs of three well-known partial differential equations (Burgers' equation, KdV equation, and the modified KdV equation). This indicates that the Painleve property may provide a unified description of integrable behavior in dynamical systems (ordinary and partial differential equations), while, at the same time, providing an efficient method for determining the integrability of particular systems.
Is the new GFR equation using inulin clearance a more accurate method for Asian patients?
Kim, Beom Seok; Lee, Yong Kyu; Choi, Hoon Young; Choi, Seung Ok; Shin, Sug Kyun; Ha, Sung Kyu; Lee, Kang Wook; Kim, Yang Wook; Kim, Yong Lim; Yasuda, Yoshinari; Imai, Enyu; Horio, Masaru; Tomino, Yasuhiko; Matsuo, Seiichi; Lee, Ho Yung
2015-12-01
Recently, a new glomerular filtration rate (GFR) equation for the Japanese population was proposed using measured inulin clearance. To expand its applicability to other Asian populations, we performed a comparative study in the Korean population. Inulin clearance was measured in 166 patients from seven participating medical centers in Korea. Patient's sera and urine were collected, and baseline clinical characteristics were measured to provide an estimated GFR (eGFR) by the Japanese GFR equation using inulin clearance (Japanese-GFR equation), the Modification of Diet in Renal Disease (MDRD) study equation, and the Chronic Kidney Disease - Epidemiology Collaboration (CKD-EPI) equation. We compared the results to determine which equation best estimated the measured GFR (mGFR). Accuracy (95% CI) within 30% of mGFR by the Japanese-GFR equation, the CKD-EPI equation and the MDRD study equation were 66 (58 - 72), 51 (43 - 58), and 55 (47 - 62)%, respectively. Bias (mGFR minus eGFR) were 3.4 ± 22.4, -12.0 ± 22.1, and -9.7 ± 23.8 mL/min/1.73 m2, respectively. The accuracy of the Japanese-GFR equation was significantly better than MDRD study equation in subjects with mGFR < 60 mL/min/1.73 m2 and in total subjects. The bias of the Japanese-GFR equation was significantly smaller compared with other two equations in total subjects. The Japanese-GFR equation has a higher accuracy with less bias than the other equations in estimating GFR in Korean populations. Further studies are required to determine if the current Japanese-GFR equation could represent the standard eGFR for other Asian populations.
Spatiotemporal canards in neural field equations
Avitabile, D.; Desroches, M.; Knobloch, E.
2017-04-01
Canards are special solutions to ordinary differential equations that follow invariant repelling slow manifolds for long time intervals. In realistic biophysical single-cell models, canards are responsible for several complex neural rhythms observed experimentally, but their existence and role in spatially extended systems is largely unexplored. We identify and describe a type of coherent structure in which a spatial pattern displays temporal canard behavior. Using interfacial dynamics and geometric singular perturbation theory, we classify spatiotemporal canards and give conditions for the existence of folded-saddle and folded-node canards. We find that spatiotemporal canards are robust to changes in the synaptic connectivity and firing rate. The theory correctly predicts the existence of spatiotemporal canards with octahedral symmetry in a neural field model posed on the unit sphere.
Savoye, Philippe
2009-01-01
In recent years, I started covering difference equations and z transform methods in my introductory differential equations course. This allowed my students to extend the "classical" methods for (ordinary differential equation) ODE's to discrete time problems arising in many applications.
Chen, Haiwen; Holland, Paul
2010-01-01
In this paper, we develop a new curvilinear equating for the nonequivalent groups with anchor test (NEAT) design under the assumption of the classical test theory model, that we name curvilinear Levine observed score equating. In fact, by applying both the kernel equating framework and the mean preserving linear transformation of…
Application of the simplest equation method to some time-fractional partial differential equations
Directory of Open Access Journals (Sweden)
N. Taghizadeh
2013-12-01
Full Text Available In this paper, we establish exact solutions for some time fractional differential equations. The simplest equation method is used to construct the exact solutions of nonlinear fractional Klein–Gordon equation, Generalized Hirota–Satsuma coupled KdV system of time fractional order and nonlinear fractional Sharma–Tasso–Olever equation. The simplest equation method presents a wide applicability to handling nonlinear wave equations.
Techniques for estimating allometric equations.
Manaster, B J; Manaster, S
1975-11-01
Morphologists have long been aware that differential size relationships of variables can be fo great value when studying shape. Allometric patterns have been the basis of many interpretations of adaptations, biomechanisms, and taxonomies. It is of importance that the parameters of the allometric equation be as accurate estimates as possible since they are so commonly used in such interpretations. Since the error term may come into the allometric relation either exponentially or additively, there are at least two methods of estimating the parameters of the allometric equation. That most commonly used assumes exponentiality of the error term, and operates by forming a linear function by a logarithmic transformation and then solving by the method of ordinary least squares. On the other hand, if the rrror term comes into the equation in an additive way, a nonlinear method may be used, searching the parameter space for those parameters which minimize the sum of squared residuals. Study of data on body weight and metabolism in birds explores the issues involved in discriminating between the two models by working through a specific example and shows that these two methods of estimation can yield highly different results. Not only minimizing the sum of squared residuals, but also the distribution and randomness of the residuals must be considered in determing which model more precisely estimates the parameters. In general there is no a priori way to tell which model will be best. Given the importance often attached to the parameter estimates, it may be well worth considerable effort to find which method of solution is appropriate for a given set of data.
An axiomatic approach to Maxwell's equations
Heras, José A
2016-01-01
This paper suggests an axiomatic approach to Maxwell's equations. The basis of this approach is a theorem formulated for two sets of functions localized in space and time. If each set satisfies a continuity equation then the theorem provides an integral representation for each function. A corollary of this theorem yields Maxwell's equations with magnetic monopoles. It is pointed out that the causality principle and the conservation of electric and magnetic charges are the most fundamental physical axioms underlying these equations. Another application of the corollary yields Maxwell's equations in material media. The theorem is also formulated in the Minkowski space-time and applied to obtain the covariant form of Maxwell's equations with magnetic monopoles and the covariant form of Maxwell's equations in material media. The approach makes use of the infinite-space Green function of the wave equation and is therefore suitable for an advanced course in electrodynamics.
Feedback stabilization of semilinear heat equations
Directory of Open Access Journals (Sweden)
V. Barbu
2003-01-01
Full Text Available This paper is concerned with the internal and boundary stabilization of the steady-state solutions to quasilinear heat equations via internal linear feedback controllers provided by an LQ control problem associated with the linearized equation.
On oscillatory solutions of certain difference equations
Directory of Open Access Journals (Sweden)
Grzegorz Grzegorczyk
2006-01-01
Full Text Available Some difference equations with deviating arguments are discussed in the context of the oscillation problem. The aim of this paper is to present the sufficient conditions for oscillation of solutions of the equations discussed.
Introduction to partial differential equations with applications
Zachmanoglou, E C
1988-01-01
This text explores the essentials of partial differential equations as applied to engineering and the physical sciences. Discusses ordinary differential equations, integral curves and surfaces of vector fields, the Cauchy-Kovalevsky theory, more. Problems and answers.
The Spin-2 Equation on Minkowski Background
Beyer, Florian; Frauendiener, Jörg; Whale, Ben
2014-01-01
The linearised general conformal field equations in their first and second order form are used to study the behaviour of the spin-2 zero-rest-mass equation on Minkowski background in the vicinity of space-like infinity.
Regional Screening Levels (RSLs) - Equations (November 2017 )
Regional Screening Level RSL equations page provides quick access to the equations used in the Chemical Risk Assessment preliminary remediation goal PRG risk based concentration RBC and risk calculator for the assessment of human Health.
Schroedinger equation for bosons and fermions
Energy Technology Data Exchange (ETDEWEB)
Kaniadakis, G. [Politecnico di Torino (Italy). Dipt. di Fisica]|[Istituto Nazionale di Fisica della Materia, Unita del Politecnico di Torino, Turin (Italy)]|[Istituto Nazionale di Fisica Nucleare, Turin (Italy)
1995-10-09
We propose a non-linear Schroedinger equation describing the dynamics of bosons or fermions in an effective external force field. This equation is obtained by quantization of a stochastic Markovian process obeying a generalized exclusion principle. (orig.).
Global existence and decay of solutions of a nonlinear system of wave equations
Said-Houari, Belkacem
2012-03-01
This work is concerned with a system of two wave equations with nonlinear damping and source terms acting in both equations. Under some restrictions on the nonlinearity of the damping and the source terms, we show that our problem has a unique local solution. Also, we prove that, for some restrictions on the initial data, the rate of decay of the total energy is exponential or polynomial depending on the exponents of the damping terms in both equations.
Validation of the Korean coefficient for the modification of diet in renal disease study equation
Oh, Yun Jung; Cha, Ran-hui; Lee, Seung Hwan; Yu, Kyung Sang; Kim, Satbyul Estella; Kim, Ho; Kim, Yon Su
2016-01-01
Background/Aims: Race and ethnicity are important determinants when estimatingglomerular filtration rate (GFR). The Korean coefficients for the isotope dilution mass spectrometry (IDMS) Modification of Diet in Renal Disease (MDRD) Study equations were developed in 2010. However, the coefficients have not been validated. The aim of this study was to validate the performance of the Korean coefficients for the IDMS MDRD Study equations. Methods: Equation development and validation were performed...
PARALLEL SOLUTION METHODS OF PARTIAL DIFFERENTIAL EQUATIONS
Directory of Open Access Journals (Sweden)
Korhan KARABULUT
1998-03-01
Full Text Available Partial differential equations arise in almost all fields of science and engineering. Computer time spent in solving partial differential equations is much more than that of in any other problem class. For this reason, partial differential equations are suitable to be solved on parallel computers that offer great computation power. In this study, parallel solution to partial differential equations with Jacobi, Gauss-Siedel, SOR (Succesive OverRelaxation and SSOR (Symmetric SOR algorithms is studied.
Solutions manual to accompany Ordinary differential equations
Greenberg, Michael D
2014-01-01
Features a balance between theory, proofs, and examples and provides applications across diverse fields of study Ordinary Differential Equations presents a thorough discussion of first-order differential equations and progresses to equations of higher order. The book transitions smoothly from first-order to higher-order equations, allowing readers to develop a complete understanding of the related theory. Featuring diverse and interesting applications from engineering, bioengineering, ecology, and biology, the book anticipates potential difficulties in understanding the various solution steps
Some Aspects of Extended Kinetic Equation
Directory of Open Access Journals (Sweden)
Dilip Kumar
2015-09-01
Full Text Available Motivated by the pathway model of Mathai introduced in 2005 [Linear Algebra and Its Applications, 396, 317–328] we extend the standard kinetic equations. Connection of the extended kinetic equation with fractional calculus operator is established. The solution of the general form of the fractional kinetic equation is obtained through Laplace transform. The results for the standard kinetic equation are obtained as the limiting case.
Notes on the infinity Laplace equation
Lindqvist, Peter
2016-01-01
This BCAM SpringerBriefs is a treaty of the Infinity-Laplace Equation, which has inherited many features from the ordinary Laplace Equation, and is based on lectures by the author. The Infinity.Laplace Equation has delightful counterparts to the Dirichlet integral, the mean value property, the Brownian motion, Harnack's inequality, and so on. This "fully non-linear" equation has applications to image processing and to mass transfer problems, and it provides optimal Lipschitz extensions of boundary values.
Partial differential equations of mathematical physics
Sobolev, S L
1964-01-01
Partial Differential Equations of Mathematical Physics emphasizes the study of second-order partial differential equations of mathematical physics, which is deemed as the foundation of investigations into waves, heat conduction, hydrodynamics, and other physical problems. The book discusses in detail a wide spectrum of topics related to partial differential equations, such as the theories of sets and of Lebesgue integration, integral equations, Green's function, and the proof of the Fourier method. Theoretical physicists, experimental physicists, mathematicians engaged in pure and applied math
Dutta, Gaurav
2016-10-12
Strong subsurface attenuation leads to distortion of amplitudes and phases of seismic waves propagating inside the earth. The amplitude and the dispersion losses from attenuation are often compensated for during prestack depth migration. However, most attenuation compensation or Qcompensation migration algorithms require an estimate of the background Q model. We have developed a wave-equation gradient optimization method that inverts for the subsurface Q distribution by minimizing a skeletonized misfit function ∈, where ∈ is the sum of the squared differences between the observed and the predicted peak/centroid-frequency shifts of the early arrivals. The gradient is computed by migrating the observed traces weighted by the frequency shift residuals. The background Q model is perturbed until the predicted and the observed traces have the same peak frequencies or the same centroid frequencies. Numerical tests determined that an improved accuracy of the Q model by wave-equation Q tomography leads to a noticeable improvement in migration image quality. © 2016 Society of Exploration Geophysicists.
Quantization of Equations of Motion
Directory of Open Access Journals (Sweden)
D. Kochan
2007-01-01
Full Text Available The Classical Newton-Lagrange equations of motion represent the fundamental physical law of mechanics. Their traditional Lagrangian and/or Hamiltonian precursors when available are essential in the context of quantization. However, there are situations that lack Lagrangian and/or Hamiltonian settings. This paper discusses a description of classical dynamics and presents some irresponsible speculations about its quantization by introducing a certain canonical two-form ?. By its construction ? embodies kinetic energy and forces acting within the system (not their potential. A new type of variational principle employing differential two-form ? is introduced. Variation is performed over “umbilical surfaces“ instead of system histories. It provides correct Newton-Lagrange equations of motion. The quantization is inspired by the Feynman path integral approach. The quintessence is to rearrange it into an “umbilical world-sheet“ functional integral in accordance with the proposed variational principle. In the case of potential-generated forces, the new approach reduces to the standard quantum mechanics. As an example, Quantum Mechanics with friction is analyzed in detail.
Sobolev gradients and differential equations
Neuberger, J W
2010-01-01
A Sobolev gradient of a real-valued functional on a Hilbert space is a gradient of that functional taken relative to an underlying Sobolev norm. This book shows how descent methods using such gradients allow a unified treatment of a wide variety of problems in differential equations. For discrete versions of partial differential equations, corresponding Sobolev gradients are seen to be vastly more efficient than ordinary gradients. In fact, descent methods with these gradients generally scale linearly with the number of grid points, in sharp contrast with the use of ordinary gradients. Aside from the first edition of this work, this is the only known account of Sobolev gradients in book form. Most of the applications in this book have emerged since the first edition was published some twelve years ago. What remains of the first edition has been extensively revised. There are a number of plots of results from calculations and a sample MatLab code is included for a simple problem. Those working through a fair p...
Explicit solutions of the Rand Equation
African Journals Online (AJOL)
user
Keywords: Nonlinear partial differential equations, evolution equations, symmetries, similarity solutions, Rand Equation. PACS-Code: ... Classical symmetry analysis - algebraic group properties ... The result is a well-defined system of eight linear homogeneous PDEs (describing the point symmetries) for the infinitesimals. ),(.
Quantum Einstein's equations and constraints algebra
Indian Academy of Sciences (India)
If we are interested in seeing the symmetry breaking at this level, we must look at quantum Einstein's equations. This point is explained in the next section. 3. Quantum Einstein's equations. Previously [5] in the Bohmian quantum gravity framework, we have studied the modifi- cations of Einstein's equations in some special ...
On a Equation in Finite Algebraically Structures
Valcan, Dumitru
2013-01-01
Solving equations in finite algebraically structures (semigroups with identity, groups, rings or fields) many times is not easy. Even the professionals can have trouble in such cases. Therefore, in this paper we proposed to solve in the various finite groups or fields, a binomial equation of the form (1). We specify that this equation has been…
Chaos in discrete fractional difference equations
Indian Academy of Sciences (India)
In the present paper, the chaotic behaviour of fractional difference equations for the tent map, Gauss map and 2x(mod 1) map are studied numerically. We analyse the chaotic behaviour of these fractional difference equations and compare them with their integer counterparts. It is observed that fractional difference equations ...
A reliable treatment for nonlinear Schroedinger equations
Energy Technology Data Exchange (ETDEWEB)
Khani, F. [Department of Mathematics, Ilam University, PO Box 69315516, Ilam (Iran, Islamic Republic of); Department of Mathematics, Bakhtar Institute of Higher Education, PO Box 696, Ilam (Iran, Islamic Republic of)], E-mail: farzad_khani59@yahoo.com; Hamedi-Nezhad, S. [Department of Mathematics, Bakhtar Institute of Higher Education, PO Box 696, Ilam (Iran, Islamic Republic of)], E-mail: s_hamedi2001@yahoo.com; Molabahrami, A. [Department of Mathematics, Ilam University, PO Box 69315516, Ilam (Iran, Islamic Republic of)], E-mail: a_m_bahrami@yahoo.com
2007-11-12
Exp-function method is used to find a unified solution of nonlinear wave equation. Nonlinear Schroedinger equations with cubic and power law nonlinearity are selected to illustrate the effectiveness and simplicity of the method. It is shown that the Exp-function method, with the help of symbolic computation, provides a powerful mathematical tool for solving nonlinear equation.
Some functional equations originating from number theory
Indian Academy of Sciences (India)
We will introduce new functional equations (3) and (4) which are strongly related to well-known formulae (1) and (2) of number theory, and investigate the solutions of the equations. Moreover, we will also study some stability problems of those equations.
Stochastic Evolution Equations with Adapted Drift
Pronk, M.
2013-01-01
In this thesis we study stochastic evolution equations in Banach spaces. We restrict ourselves to the two following cases. First, we consider equations in which the drift is a closed linear operator that depends on time and is random. Such equations occur as mathematical models in for instance
Positive Integer Solutions of Certain Diophantine Equations
Indian Academy of Sciences (India)
29
An important area of number theory is devoted to finding solutions of equations where the solutions are restricted to the set of integers. Diophantine equations get their name from Diophantus of. Alexandria and they are algebraic equations for which rational or integer solutions are sought. Many researchers considered the ...
Functional equations in matrix normed spaces
Indian Academy of Sciences (India)
46] concerning the stability of group homomorphisms. The functional equation f (x + y) = f (x) + f (y) is called the Cauchy additive functional equation. In particular, every solution of the. Cauchy additive functional equation is said to be an additive ...
The Raychaudhuri equations: A brief review
Indian Academy of Sciences (India)
+ l2 (the so-called Ellis wormhole) [21]. 2.3 The equations and the focusing theorem. We now turn towards writing down the evolution equations for the expansion, shear and rotation along the flow representing a time-like geodesic congruence. A fact worth mentioning here is that, these evolution equations (and their ...
On Fractional Duffin-Kemmer-Petiau Equation
Bouzid, N.; Merad, M.; Baleanu, D.
2016-04-01
In this paper we treat a fractional bosonic, scalar and vectorial, time equation namely Duffin-Kemmer-Petiau Equation. The fractional variational principle was used, the fractional Euler-Lagrange equations were presented. The wave functions were determined and expressed in terms of Mittag-Leffler function.
Qualitative mathematical analysis of the Richards equation
Gilding, B.H.
1991-01-01
The Richards equation is widely used as a model for the flow of water in unsaturated soils. For modelling one-dimensional flow in a homogeneous soil, this equation can be cast in the form of a specific nonlinear partial differential equation with a time derivative and one spatial derivative. This