Comparison of the Chronic Kidney Disease Epidemiology Collaboration, the Modification of Diet in Renal Disease study and the Cockcroft-Gault equation in patients with heart failure.

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Szummer, Karolina; Evans, Marie; Carrero, Juan Jesus; Alehagen, Urban; Dahlström, Ulf; Benson, Lina; Lund, Lars H

2017-01-01

It is unknown how the creatinine-based renal function estimations differ for dose adjustment cut-offs and risk prediction in patients with heart failure. The renal function was similar with the Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) (median 59 mL/min/1.73 m 2 , IQR 42 to 77) and Modification of Diet in Renal Disease Study (MDRD) (59 mL/min/1.73 m 2 , IQR 43 to 75) and slightly lower with the Cockcroft-Gault (CG) equation (57 mL/min, IQR 39 to 82). Across the commonly used renal function stages, the CKD-EPI and the MDRD classified patients into the same stage in 87.2% (kappa coefficient 0.83, pFailure Registry (n= 40 736) with standardised creatinine values between 2000 and 2012 had their renal function estimated with the CKD-EPI, the MDRD and the CG. Agreement between the formulas was compared for categories. Prediction of death was assessed with c-statistics and with NRI. The choice of renal function estimation formula has clinical implications and differing results at various cut-off levels. For prognosis, the CG predicts mortality better than the CKD-EPI and MDRD.

Estimating Renal Function in the Elderly Malaysian Patients Attending Medical Outpatient Clinic: A Comparison between Creatinine Based and Cystatin-C Based Equations

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Maisarah Jalalonmuhali

2018-01-01

Full Text Available Background. To assess the performance of different GFR estimating equations, test the diagnostic value of serum cystatin-C, and compare the applicability of cystatin-C based equation with serum creatinine based equation for estimating GFR (eGFR in comparison with measured GFR in the elderly Malaysian patients. Methods. A cross-sectional study recruiting volunteered patients 65 years and older attending medical outpatient clinic. 51 chromium EDTA (51Cr-EDTA was used as measured GFR. The predictive capabilities of Cockcroft-Gault equation corrected for body surface area (CGBSA, four-variable Modification of Diet in Renal Disease (4-MDRD, and Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI equations using serum creatinine (CKD-EPIcr as well as serum cystatin-C (CKD-EPIcys were calculated. Results. A total of 40 patients, 77.5% male, with mean measured GFR 41.2±18.9 ml/min/1.73 m2 were enrolled. Mean bias was the smallest for 4-MDRD; meanwhile, CKD-EPIcr had the highest precision and accuracy with lower limit of agreement among other equations. CKD-EPIcys equation did not show any improvement in GFR estimation in comparison to CKD-EPIcr and MDRD. Conclusion. The CKD-EPIcr formula appears to be more accurate and correlates better with measured GFR in this cohort of elderly patients.

Comparison of the Chronic Kidney Disease Epidemiology Collaboration, the Modification of Diet in Renal Disease study and the Cockcroft-Gault equation in patients with heart failure

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Szummer, Karolina; Evans, Marie; Carrero, Juan Jesus; Alehagen, Urban; Dahlström, Ulf; Benson, Lina; Lund, Lars H

2017-01-01

Background It is unknown how the creatinine-based renal function estimations differ for dose adjustment cut-offs and risk prediction in patients with heart failure. Method and results The renal function was similar with the Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) (median 59 mL/min/1.73 m2, IQR 42 to 77) and Modification of Diet in Renal Disease Study (MDRD) (59 mL/min/1.73 m2, IQR 43 to 75) and slightly lower with the Cockcroft-Gault (CG) equation (57 mL/min, IQR 39 to 82). Across the commonly used renal function stages, the CKD-EPI and the MDRD classified patients into the same stage in 87.2% (kappa coefficient 0.83, pFailure Registry (n= 40 736) with standardised creatinine values between 2000 and 2012 had their renal function estimated with the CKD-EPI, the MDRD and the CG. Agreement between the formulas was compared for categories. Prediction of death was assessed with c-statistics and with NRI. Conclusion The choice of renal function estimation formula has clinical implications and differing results at various cut-off levels. For prognosis, the CG predicts mortality better than the CKD-EPI and MDRD. PMID:28761677

Glomerular filtration rate equations overestimate creatinine clearance in older individuals enrolled in the Baltimore Longitudinal Study on Aging: impact on renal drug dosing.

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Dowling, Thomas C; Wang, En-Shih; Ferrucci, Luigi; Sorkin, John D

2013-09-01

To evaluate the performance of kidney function estimation equations and to determine the frequency of drug dose discordance in an older population. Cross-sectional analysis of data from community-dwelling volunteers randomly selected from the Baltimore Longitudinal Study of Aging from January 1, 2005, to December 31, 2010. A total of 269 men and women with a mean ± SD age of 81 ± 6 years, mean serum creatinine concentration (Scr ) of 1.1 ± 0.4 mg/dl, and mean 24-hour measured creatinine clearance (mClcr ) of 53 ± 13 ml/minute. Kidney function was estimated by using the following equations: Cockcroft-Gault (CG), Modification of Diet in Renal Disease (MDRD), and Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI). The performance of each equation was assessed by measuring bias and precision relative to mClcr . Dose calculation errors (discordance) were determined for 10 drugs requiring renal dosage adjustments to avoid toxicity when compared with the dosages approved by the Food and Drug Administration. The CG equation was the least biased estimate of mClcr . The MDRD and CKD-EPI equations were significantly positively biased compared with CG (mean ± SD 34 ± 20% and 22 ± 15%, respectively, prenal impairment. Thus equations estimating glomerular filtration rate should not be substituted in place of the CG equation in older adults for the purpose of renal dosage adjustments. In addition, the common practice of rounding or replacing low Scr values with an arbitrary value of 1.0 mg/dl for use in the CG equation should be avoided. Additional studies that evaluate alternative eGFR equations in the older populations that incorporate pharmacokinetic and pharmacodynamic outcomes measures are needed. © 2013 Pharmacotherapy Publications, Inc.

Performance of three glomerular filtration rate estimation equations in a population of sub-Saharan Africans with Type 2 diabetes.

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Agoons, D D; Balti, E V; Kaze, F F; Azabji-Kenfack, M; Ashuntantang, G; Kengne, A P; Sobngwi, E; Mbanya, J C

2016-09-01

We evaluated the performance of the Modification of Diet in Renal Disease (MDRD), Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) and Cockcroft-Gault (CG) equations against creatinine clearance (CrCl) to estimate glomerular filtration rate (GFR) in 51 patients with Type 2 diabetes. The CrCl value was obtained from the average of two consecutive 24-h urine samples. Results were adjusted for body surface area using the Dubois formula. Serum creatinine was measured using the kinetic Jaffe method and was calibrated to standardized levels. Bland-Altman analysis and kappa statistic were used to examine agreement between measured and estimated GFR. Estimates of GFR from the CrCl, MDRD, CKD-EPI and CG equations were similar (overall P = 0.298), and MDRD (r = 0.58; 95% CI: 0.36-0.74), CKD-EPI (r = 0.55; 95% CI: 0.33-0.72) and CG (r = 0.61; 95% CI: 0.39-0.75) showed modest correlation with CrCl (all P fair-to-moderate agreement with CrCl (kappa: 0.38-0.51). The c-statistic for all three equations ranged between 0.75 and 0.77 with no significant difference (P = 0.639 for c-statistic comparison). The MDRD equation seems to have a modest advantage over CKD-EPI and CG in estimating GFR and detecting impaired renal function in sub-Saharan African patients with Type 2 diabetes. The overall relatively modest correlation with CrCl, however, suggests the need for context-specific estimators of GFR or context adaptation of existing estimators. © 2015 Diabetes UK.

Comparison of Two Creatinine-Based Equations for Predicting Decline in Renal Function in Type 2 Diabetic Patients with Nephropathy in a Korean Population

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Eun Young Lee

2013-01-01

Full Text Available Aim. To compare two creatinine-based estimated glomerular filtration rate (eGFR equations, the chronic kidney disease epidemiology collaboration (CKD-EPI and the modification of diet in renal disease (MDRD, for predicting the risk of CKD progression in type 2 diabetic patients with nephropathy. Methods. A total of 707 type 2 diabetic patients with 24 hr urinary albumin excretion of more than 30 mg/day were retrospectively recruited and traced until doubling of baseline serum creatinine (SCr levels was noted. Results. During the follow-up period (median, 2.4 years, the CKD-EPI equation reclassified 10.9% of all MDRD-estimated subjects: 9.1% to an earlier stage of CKD and 1.8% to a later stage of CKD. Overall, the prevalence of CKD (eGFR < 60 mL/min/1.73 m2 was lowered from 54% to 51.6% by applying the CKD-EPI equation. On Cox-regression analysis, both equations exhibited significant associations with an increased risk for doubling of SCr. However, only the CKD-EPI equation maintained a significant hazard ratio for doubling of SCr in earlier-stage CKD (eGFR ≥ 45 mL/min/1.73 m2, when compared to stage 1 CKD (eGFR ≥ 90 mL/min/1.73 m2. Conclusion. In regard to CKD progression, these results suggest that the CKD-EPI equation might more accurately stratify earlier-stage CKD among type 2 diabetic patients with nephropathy than the MDRD study equation.

Optimal equation for estimation of glomerular filtration rate in autosomal dominant polycystic kidney disease: influence of tolvaptan.

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Yamaguchi, Tsuyoshi; Higashihara, Eiji; Okegawa, Takatsugu; Miyazaki, Isao; Nutahara, Kikuo

2018-05-22

The reliability of various equations for estimating the GFR in ADPKD patients and the influence of tolvaptan on the resulting estimates have not been examined when GFR is calculated on the basis of inulin clearance. We obtained baseline and on-tolvaptan measured GFRs (mGFRs), calculated on the basis of inulin clearance, in 114 ADPKD, and these mGFRs were compared with eGFRs calculated according to four basic equations: the MDRD, CKD-EPI, and JSN-CKDI equations and the Cockcroft-Gault formula, as well as the influence of tolvaptan and of inclusion of cystatin C on accuracy of the results. Accuracy of each of the seven total equations was evaluated on the basis of the percentage of eGFR values within mGFR ± 30% (P 30 ). mGFRs were distributed throughout CKD stages 1-5. Regardless of the CKD stage, P 30 s of the MDRD, CKD-EPI, and JSN-CKDI equations did not differ significantly between baseline values and on-tolvaptan values. In CKD 1-2 patients, P 30 of the CKD-EPI equation was 100.0%, whether or not the patient was on-tolvaptan. In CKD 3-5 patients, P 30 s of the MDRD, CKD-EPI, and JSN-CKDI equations were similar. For all four equations, regression coefficients and intercepts did not differ significantly between baseline and on-tolvaptan values, but accuracy of the Cockcroft-Gault formula was inferior to that of the other three equations. Incorporation of serum cystatin C reduced accuracy. The CKD-EPI equation is most reliable, regardless of the severity of CKD. Tolvaptain intake has minimal influence and cystatin C incorporation does not improve accuracy.

Estimating glomerular filtration rate in a population-based study

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Anoop Shankar

2010-07-01

Full Text Available Anoop Shankar1, Kristine E Lee2, Barbara EK Klein2, Paul Muntner3, Peter C Brazy4, Karen J Cruickshanks2,5, F Javier Nieto5, Lorraine G Danforth2, Carla R Schubert2,5, Michael Y Tsai6, Ronald Klein21Department of Community Medicine, West Virginia University School of Medicine, Morgantown, WV, USA; 2Department of Ophthalmology and Visual Sciences, 4Department of Medicine, 5Department of Population Health Sciences, University of Wisconsin, School of Medicine and Public Health, Madison, WI, USA; 3Department of Community Medicine, Mount Sinai School of Medicine, NY, USA; 6Department of Laboratory Medicine and Pathology, University of Minnesota, Minneapolis, MN, USABackground: Glomerular filtration rate (GFR-estimating equations are used to determine the prevalence of chronic kidney disease (CKD in population-based studies. However, it has been suggested that since the commonly used GFR equations were originally developed from samples of patients with CKD, they underestimate GFR in healthy populations. Few studies have made side-by-side comparisons of the effect of various estimating equations on the prevalence estimates of CKD in a general population sample.Patients and methods: We examined a population-based sample comprising adults from Wisconsin (age, 43–86 years; 56% women. We compared the prevalence of CKD, defined as a GFR of <60 mL/min per 1.73 m2 estimated from serum creatinine, by applying various commonly used equations including the modification of diet in renal disease (MDRD equation, Cockcroft–Gault (CG equation, and the Mayo equation. We compared the performance of these equations against the CKD definition of cystatin C >1.23 mg/L.Results: We found that the prevalence of CKD varied widely among different GFR equations. Although the prevalence of CKD was 17.2% with the MDRD equation and 16.5% with the CG equation, it was only 4.8% with the Mayo equation. Only 24% of those identified to have GFR in the range of 50–59 mL/min per 1

Renal dysfunction in patients with heart failure with preserved versus reduced ejection fraction

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McAlister, Finlay A; Ezekowitz, Justin; Tarantini, Luigi

2012-01-01

Prior studies in heart failure (HF) have used the Modification of Diet in Renal Disease (MDRD) equation to calculate estimated glomerular filtration rate (eGFR). The Chronic Kidney Disease-Epidemiology Collaboration Group (CKD-EPI) equation provides a more-accurate eGFR than the MDRD when compared...... against the radionuclide gold standard. The prevalence and prognostic import of renal dysfunction in HF if the CKD-EPI equation is used rather than the MDRD is uncertain....

Development and validation of GFR-estimating equations using diabetes, transplant and weight

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Stevens, L.A.; Schmid, C.H.; Zhang, Y.L.

2009-01-01

interactions. Equations were developed in a pooled database of 10 studies [2/3 (N = 5504) for development and 1/3 (N = 2750) for internal validation], and final model selection occurred in 16 additional studies [external validation (N = 3896)]. RESULTS: The mean mGFR was 68, 67 and 68 ml/min/ 1.73 m(2......BACKGROUND: We have reported a new equation (CKD-EPI equation) that reduces bias and improves accuracy for GFR estimation compared to the MDRD study equation while using the same four basic predictor variables: creatinine, age, sex and race. Here, we describe the development and validation...... of this equation as well as other equations that incorporate diabetes, transplant and weight as additional predictor variables. METHODS: Linear regression was used to relate log-measured GFR (mGFR) to sex, race, diabetes, transplant, weight, various transformations of creatinine and age with and without...

Comparison of three empirical formulae for calculating the glomerular filtration rate of patients with chronic kidney disease

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Xiao-mei LUO

2011-07-01

Full Text Available Objective To compare the values of 3 empirical formulae,namely Modification of Diet in Renal Disease(MDRD study equation,Chronic Kidney Disease Epidemiology Collaboration(CKD-EPI equation,and cystatin C(Cys C single variable equations(eGFR-Cys,on predicting the glomerular filtration rate(GFR of patients with chronic kidney disease.Methods Ninety three patients with chronic kidney disease were enrolled in present study.The plasma clearance of 99mTc-diethylenetriamine pentaacetic acid(DTPA was measured the golden standard of GFR(rGFR,and estimated GFR(eGFR was calculated with the MDRD equation,CKD-EPI equation and eGFR-Cys equation,respectively.The result of rGFR with that of various eGFR was compared.Results Compared with rGFR,the mean bias of eGFR in CKD-EPI equation,eGFR-Cys equation and MDRD study equation were-3.4±10.7ml/(min·1.73m2,-4.8±11.9ml/(min·1.73m2 and-5.4±10.4ml/(min·1.73m2,respectively,and no significant difference was noted among the 3 values.The 30% accuracy of 3 equations was 74.2%,72.0% and 64.5%,respectively,no significant difference was found among the 3 values.The 30% accuracy of CKD-EPI equation was higher than that of MDRD study equation(75.7%±5.1% vs 54.1%±7.7%,P 60ml/(min·1.73m2.With 60ml/(min·1.73m2 as the diagnostic cut-off point of GFR damage,the area under receiver operating characteristic(ROC curve was 0.862 in MDRD study equation,0.863 in CKD-EPI equation and 0.877 in eGFR-Cys equation,respectively,and no significant difference was found among the 3 values.Conclusions There are no significant differences among the 3 equations in predicting the GFR of patients with CKD.However,further studies are needed to investigate whether MDRD study equation could be replaced by the CKD-EPI equation and eGFR-Cys equation.

Monitoring of Renal Allograft Function with Different Equations: What are the Differences?

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Bushljetikj Irena Rambabova

2017-06-01

Full Text Available Introduction. Monitoring of graft function by creatinine concentrations in serum and calculated glomerular filtration rate (GFR is recommended after kidney transplantation. KDIGO recommendations on the treatment of transplant patients advocate usage of one of the existing mathematical equations based on serum creatinine. We compared clinical application of three equations based on serum creatinine in monitoring the function of transplanted kidney. Methods. A total number of 55 adult patients who received their first renal allograft from living donors at our transplant center in between 2011-2014 were included into the study. Renal allograft GFR was estimated by the Cockroft-Gault, Nankivell and MDRD formula, and correlated with clinical parameters of donors and recipients. Results. The mean age of recipients was 35.7±9.5 (range 16-58, and the mean age of donors was 55.5±9.0 (34- 77 years. Out of this group of 55 transplant patients, 50(90.91% were on hemodialysis (HD prior to transplantation. HD treatment was shorter than 24 months in 37(74% transplant patients. The calculated GFR with MDRD equation showed the highest mean value at 6 and 12 months (68.46±21.5; 68.39±24.6, respectively and the lowest at 48 months (42.79±12.9. According to the Cockroft&Gault equation GFR was the highest at 12 months (88.91±24.9 and the lowest at 48 months (66.53±18.1 ml/min. The highest mean level (80.53±17.7 of the calculated GFR with the Nankivell equation was obtained at 12 months and the lowest (67.81±16.7 ml/min at 48 months. The values of Pearson’s correlation coefficient between the calculated GFR and the MDRD at 2 years after transplantation according to donor’s age of r=-0.3224, correlation between GFR and the Cockfroft & Gault at 6 and 12 months and donor’s age (r=-0.2735 and r=-0.2818, and correlation between GFR and the Nankivell at 2 years and donor’s age of r=-0.2681, suggested a conclusion that calculated GFR was lower in recipients

Comparison of renal function assessment by cystatin c and creatinine based equations for e-gfr in type 2 diabetics in different stages of albuminuria

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Qamar, A.; Ahmad, T.M.; Hayat, A.; Khan, M.A.; Rehman, S. Z.

2017-01-01

To compare e-GFR estimated by creatinine or cystatin C based and combined creatinine and cystatin C based equations in type 2 diabetics in different stages of albuminuria. Study Design: Comparative cross-sectional study. Place and Duration of Study: Department of Chemical Pathology, Army Medical College Rawalpindi in collaboration with endocrinology outpatient department Military Hospital Rawalpindi, from Nov 2015 to Nov 2016. Material and Methods: A total of 119 type 2 diabetic subjects of either gender, aged 30- 60 years were enrolled in the study with duration of diabetes less than 15 years and were divided into further sub groups on the basis of degree of albuminuria determined by spot urine albumin to creatinine ratio (uACR). Fifty age matched disease free controls with no history of any systemic disease were also included in the study. Known patients of type 1 diabetes, chronic inflammatory disorders, uncontrolled hypertension, thyroid disease, chronic kidney disease, on lipid lowering drugs, steroids, ACE inhibitors and pregnant ladies were excluded from the study. Serum creatinine serum cystatin C were assessed on fully automated chemistry analyzer selectra. E-GFR was calculated by online GFR calculator by National Kidney Foundation. Comparison of means of e-GFR calculated by various equations was carried out by one way ANOVA and post-hoc Tukey tests. Degree of agreement between various equations for the estimation of GFR was assessed by kappa statistics. A p-value less than 0.05 were considered statistically significant. Results: Mean e-GFR (ml/min/1.73m2) was lowest in cystatin C based CKD-EPI equation (89.56 +- 39.84) followed by combined cystatin C and creatinine based CKD-EPI (92.34 +- 37.88). Values of e-GFR by creatinine based CKD-EPI equation (95.84 +- 27.24), and by creatinine based MDRD equation (105.37 +- 64.98) were both higher. In creatinine based MDRD, equation normo albuminuria and micro albuminuria groups did not show statistically

[Differences between MDRD-4 and CG in the prevalence of renal failure and its associated variables in type2 diabetic patients].

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Dalmau Llorca, Maria Rosa; Boira Costa, Míriam; López Pablo, Carlos; Pepió Vilaubí, Josep Maria; Aguilar Martin, Carina; Forcadell Drago, Emma

2016-11-01

To estimate the prevalence of occult renal failure (RF) in DM2, by comparing two formulas for estimating glomerular filtration rate (GFR): Modification of Diet in Renal Disease 4 (MDRD-4) and Cockcroft-Gault (CG), as well as their associated clinical variables. Multicentre analytical cross-sectional. Two basic Primary Care areas in Terres de l'Ebre, in North-Eastern Spain. A total of 493 DM2 patients with age >18years with an assigned doctor in the areas studied. There was a loss of 9 and 11 cases in each formula due to lack of variables necessary for the GFR. Estimated GFR using the two formulas, plasma creatinine values, classification of patients with established RF, occult RF and without RF, and possible clinical-pathological variables associated with RF. Of the total, 45.2% were men, the mean age was 70.4 years, and mean time since onset of diabetes of 7.5 years. The prevalence of occult RF with MDRD-4 was 18%, and 22.6% with CG. The cases detected by GC and not by MDRD-4 were higher, and with lower weight. In both formulas, occult RF patients had more chronic diseases, hypertension, and cardiovascular events (CV) than those without RF. Risk factors associated with occult RF were female, increasing age, and LDL cholesterol. The prevalence of occult RF was 20% in DM2, independently of the formula. A poorer control of cardiovascular risk factors was observed, which makes them a group at higher risk of suffering a CV event. Copyright © 2016 Elsevier España, S.L.U. All rights reserved.

[Estimating glomerular filtration rate in 2012: which adding value for the CKD-EPI equation?].

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Delanaye, Pierre; Mariat, Christophe; Moranne, Olivier; Cavalier, Etienne; Flamant, Martin

2012-07-01

Measuring or estimating glomerular filtration rate (GFR) is still considered as the best way to apprehend global renal function. In 2009, the new Chronic Kidney Disease Epidemiology (CKD-EPI) equation has been proposed as a better estimator of GFR than the Modification of Diet in Renal Disease (MDRD) study equation. This new equation is supposed to underestimate GFR to a lesser degree in higher GFR levels. In this review, we will present and deeply discuss the performances of this equation. Based on articles published between 2009 and 2012, this review will underline advantages, notably the better knowledge of chronic kidney disease prevalence, but also limitations of this new equation, especially in some specific populations. We eventually insist on the fact that all these equations are estimations and nephrologists should remain cautious in their interpretation. Copyright © 2012 Association Société de néphrologie. Published by Elsevier SAS. All rights reserved.

Eficacia de las fórmulas MDRD-abreviada y Cockcroft-Gault para la detección de insuficiencia renal crónica en la atención primaria

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Roberto López Labrada

2014-02-01

Full Text Available Se realizó un estudio comparativo y prospectivo de tipo cohortes, que incluyó a 1038 pacientes, atendidos en el consultorio médico No. 5 de la Policlínica Universitaria "Joel Benítez Borges" de Cauto Cristo, provincia de Granma, desde abril del 2011 hasta noviembre del 2012, a fin de determinar la eficacia de las fórmulas MDRD-abreviada, Cockcroft-Gault y Cockcroft-Gault corregida para la detección de insuficiencia renal crónica en los afectados con creatinina sérica normal. Se comparó el grupo de pacientes con creatinina sérica normal según filtrado glomerular normal o disminuido. La prevalencia de insuficiencia renal crónica fue de 11,9, 10,9 y 11,0 % para las fórmulas MDRD-abreviada, Cockcroft-Gault y Cockcroft-Gault corregida, respectivamente. Se demostró la sencillez y eficacia de la fórmula MDRD-abreviada en el cribaje de la insuficiencia renal crónica, fundamentalmente en mujeres añosas e hipertensas.

Estimated Glomerular Filtration Rate; Laboratory Implementation and Current Global Status.

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Miller, W Greg; Jones, Graham R D

2018-01-01

In 2002, the Kidney Disease Outcomes Quality Initiative guidelines for identifying and treating CKD recommended that clinical laboratories report estimated glomerular filtration rate (eGFR) with every creatinine result to assist clinical practitioners to identify people with early-stage CKD. At that time, the original Modification of Diet in Renal Disease (MDRD) Study equation based on serum creatinine measurements was recommended for calculating eGFR. Because the MDRD Study equation was developed using a nonstandardized creatinine method, a Laboratory Working Group of the National Kidney Disease Education program was formed and implemented standardized calibration traceability for all creatinine methods from global manufacturers by approximately 2010. A modified MDRD Study equation for use with standardized creatinine was developed. The Chronic Kidney Disease Epidemiology Collaboration developed a new equation in 2009 that was more accurate than the MDRD Study equation at values above 60 mL/min/1.73 m 2 . As of 2017, reporting eGFR with creatinine is almost universal in many countries. A reference system for cystatin C became available in 2010, and manufacturers are in the process to standardize cystatin C assays. Equations for eGFR based on standardized cystatin C alone and with creatinine are now available from the Chronic Kidney Disease Epidemiology Collaboration and other groups. Copyright © 2017 National Kidney Foundation, Inc. Published by Elsevier Inc. All rights reserved.

eGFRs from Asian-modified CKD-EPI and Chinese-modified CKD-EPI equations were associated better with hypertensive target organ damage in the community-dwelling elderly Chinese: the Northern Shanghai Study

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Ji H

2017-08-01

Full Text Available Hongwei Ji,1,* Han Zhang,1,* Jing Xiong,1 Shikai Yu,1 Chen Chi,1 Bin Bai,1 Jue Li,2 Jacques Blacher,3 Yi Zhang,1,* Yawei Xu1,* 1Department of Cardiology, Shanghai Tenth People’s Hospital, 2Department of Prevention, Tongji University School of Medicine, Shanghai, People’s Republic of China; 3Paris Descartes University, AP-HP, Diagnosis and Therapeutic Center, Hôtel-Dieu, Paris, France *These authors contributed equally to this work Background: With increasing age, estimated glomerular filtration rate (eGFR decline is a frequent manifestation and is strongly associated with other preclinical target organ damage (TOD. In literature, many equations exist in assessing patients’ eGFR. However, these equations were mainly derived and validated in the population from Western countries, which equation should be used for risk stratification in the Chinese population remains unclear, as well as their comparison. Considering that TOD is a good marker for risk stratification in the elderly, in this analysis, we aimed to investigate whether the recent eGFR equations derived from Asian and Chinese are better associated with preclinical TOD than the other equations in elderly Chinese.Methods: A total of 1,599 community-dwelling elderly participants (age >65 years in northern Shanghai were prospectively recruited from June 2014 to August 2015. Conventional cardiovascular risk factors were assessed, and hypertensive TOD including left ventricular mass index (LVMI, carotid–femoral pulse wave velocity (cf-PWV, carotid intima-media thickness (IMT, ankle–brachial index (ABI and urine albumin to creatinine ratio (UACR was evaluated for each participant. Participant’s eGFR was calculated from the Modification of Diet in Renal Disease (MDRD, Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI, Chinese-abbreviated MDRD (c-aMDRD, Asian-modified CKD-EPI (aCKD-EPI equation and Chinese-modified CKD-EPI (cCKD-EPI equation.Results: In multivariate

Current use of equations for estimating glomerular filtration rate in Spanish laboratories.

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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.

Comparación entre las ecuaciones CKD-EPI y MDRD para la estimación del filtrado glomerular en pacientes con enfermedad renal crónica

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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.

Determination of the best method to estimate glomerular filtration rate from serum creatinine in adult patients with sickle cell disease: a prospective observational cohort study

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Arlet Jean-Benoît

2012-08-01

Full Text Available Abstract Background Sickle cell disease (SCD leads to tissue hypoxia resulting in chronic organ dysfunction including SCD associated nephropathy. The goal of our study was to determine the best equation to estimate glomerular filtration rate (GFR in SCD adult patients. Methods We conducted a prospective observational cohort study. Since 2007, all adult SCD patients in steady state, followed in two medical departments, have had their GFR measured using iohexol plasma clearance (gold standard. The Cockcroft-Gault, MDRD-v4, CKP-EPI and finally, MDRD and CKD-EPI equations without adjustment for ethnicity were tested to estimate GFR from serum creatinine. Estimated GFRs were compared to measured GFRs according to the graphical Bland and Altman method. Results Sixty-four SCD patients (16 men, median age 27.5 years [range 18.0-67.5], 41 with SS-genotype were studied. They were Sub-Saharan Africa and French West Indies natives and predominantly lean (median body mass index: 22 kg/m2 [16-33]. Hyperfiltration (defined as measured GFR >110 mL/min/1.73 m2 was detected in 53.1% of patients. Urinary albumin/creatinine ratio was higher in patients with hyperfiltration than in patients with normal GFR (4.05 mg/mmol [0.14-60] versus 0.4 mg/mmol [0.7-81], p = 0.01. The CKD-EPI equation without adjustment for ethnicity had both the lowest bias and the greatest precision. Differences between estimated GFRs using the CKP-EPI equation and measured GFRs decreased with increasing GFR values, whereas it increased with the Cockcroft-Gault and MDRD-v4 equations. Conclusions We confirm that SCD patients have a high rate of glomerular hyperfiltration, which is frequently associated with microalbuminuria or macroalbuminuria. In non-Afro-American SCD patients, the best method for estimating GFR from serum creatinine is the CKD-EPI equation without adjustment for ethnicity. This equation is particularly accurate to estimate high GFR values, including glomerular

Comparison of the usefulness of selected formulas for GFR estimation in patients with diagnosed chronic kidney disease

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Paweł Wróbel

2018-03-01

Conclusions: CKD-EPI and abbreviated MDRD formulas have a similar usefulness in GFR value estimation in patients with diagnosed chronic kidney disease. Lower eGFR values achieved using abbreviated MDRD formula and CKD-EPI equation in comparison with Bjornsson’s formula may result in an increased number of patients diagnosed with CKD.

Prevalence of chronic kidney disease among adults in a rural community in South India: Results from the kidney disease screening (KIDS project

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Y J Anupama

2014-01-01

Full Text Available Prevalence of chronic kidney disease (CKD appears to be increasing in India. A few studies have studied the prevalence of CKD in urban populations, but there is a paucity of such studies in the rural populations. This project was undertaken to study the prevalence of CKD among adults in a rural population near Shimoga, Karnataka and to study the risk factor profile. Door-to-door screening of 2091 people aged 18 and above was carried out. Demographic and anthropometric data were obtained, urine was analyzed for protein by dipstick and serum creatinine was measured in all participants. Glomerular filtration rate was estimated (eGFR using the 4-variable modification of diet in renal disease (MDRD equation and Cockcroft-Gault equation corrected to the body surface area (CG-BSA. The total number of subjects studied was 2091. Mean age was 39.88 ± 15.87 years. 45.57% were males. The prevalence of proteinuria was 2.8%. CKD was seen in 131 (6.3% subjects when GFR was estimated by MDRD equation. The prevalence of CKD was 16.54% by the CG-BSA method. There was a statistically significant relationship of CKD with gender, advancing age, abdominal obesity, smoking, presence of diabetes and hypertension. The prevalence of CKD is higher compared to the previous studies from rural India and is comparable to that in the studies from the urban Indian populations. The wide difference between the CKD prevalence between MDRD and CG-BSA equations suggests the need for a better measure of kidney function applicable to Indian population.

Creatinine Clearance and Estimated Glomerular Filtration Rate – When are they Interchangeable

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Šimetić, Lucija; Zibar, Lada; Drmić, Sandra; Begić, Ivana; Šerić, Vatroslav

2015-01-01

Study goal was to examine which of glomerular rate equations is most suitable for prediction of creatinine clearance. Using a retrospective review of data from 500 hospital patients we calculated glomerular filtration rate according to Cockcroft-Gault equation (C-G), Modification of Diet in Renal Disease Study equation (MDRD) and Chronic Kidney Disease Epidemiology Collaboration equation (CKD-EPI). We determined if results of these equations were compatible with creatinine clearance, and does...

Prevalence of chronic kidney disease in Nigeria: systematic review of population-based studies

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Chukwuonye II

2018-05-01

Full Text Available Innocent Ijezie Chukwuonye,1 Okechukwu Samuel Ogah,2 Ernest Ndukaife Anyabolu,3 Kenneth Arinze Ohagwu,1 Ogbonna Collins Nwabuko,4 Uwa Onwuchekwa,5 Miracle Erinma Chukwuonye,6 Emmanuel Chukwuebuka Obi,1 Efosa Oviasu7 1Division of Nephrology, Department of Internal Medicine, Federal Medical Centre, Umuahia, Abia State, 2Division of Cardiology, Department of Internal Medicine, University College Hospital Ibadan, Oyo State 3Division of Nephrology, Department of Internal Medicine, Chukwuemeka Odumegwu Ojukwu University Teaching Hospital Awka, Anambra State, 4Department of Haematology, Federal Medical Centre, Umuahia, 5Division of Nephrology, Department of Internal Medicine, Abia State University Teaching Hospital, Aba, 6Department of Family Medicine, Federal Medical Centre, Umuahia, 7Division of Nephrology, Department of Internal Medicine, University of Benin Teaching Hospital, Benin City, Nigeria Background: The aim of this study was to identify and discuss published population-based studies carried out in Nigeria that have information on the prevalence of chronic kidney disease (CKD and have also used the Kidney Disease Outcomes Quality Initiative (KDOQI practice guidelines in defining CKD, with emphasis on the performance of three estimating equations for glomerular filtration rate (GFR – Modification of Diet in Renal Disease (MDRD, Cockcroft–Gault, and CKD epidemiology collaboration (CKD-EPI creatinine equation. Materials and methods: A systematic literature search was carried out in Google, MEDLINE, PubMed, and AJOL database, with the aim of identifying relevant population-based studies with information on the prevalence of CKD in a location in Nigeria. Results: Seven cross-sectional population-based studies were identified. Two of the studies used the Cockcroft–Gault and observed a prevalence of 24.4% and 26%. Four of the studies used the MDRD and the prevalences observed were 12.3%, 14.2%, 2.5%, and 13.4%. One of the studies used the CKD

Is the Chronic Kidney Disease Epidemiology Collaboration creatinine–cystatin C equation useful for glomerular filtration rate estimation in the elderly?

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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

Estimated glomerular filtration rate in patients with type 2 diabetes mellitus

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Paula Caitano Fontela

2014-12-01

Full Text Available Objective: to estimate the glomerular filtration using the Cockcroft-Gault (CG, Modification of Diet in Renal Disease (MDRD, and Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI equations, and serum creatinine in the screening of reduced renal function in patients with type two diabetes (T2DM enrolled in the Family Health Strategy (ESF, Brazilian federal health-care program. Methods: a cross-sectional descriptive and analytical study was conducted. The protocol consisted of sociodemographics, physical examination and biochemical tests. Renal function was analyzed through serum creatinine and glomerular filtration rate (GFR estimated according to the CG, MDRD and CKD-EPI equations, available on the websites of the Brazilian Nephrology Society (SBN and the (NKF. Results: 146 patients aged 60.9±8.9 years were evaluated; 64.4% were women. The prevalence of serum creatinine >1.2 mg/dL was 18.5% and GFR <60 mL/min/1.73m2 totaled 25.3, 36.3 and 34.2% when evaluated by the equations CG, MDRD and CKD-EPI, respectively. Diabetic patients with reduced renal function were older, had long-term T2DM diagnosis, higher systolic blood pressure and higher levels of fasting glucose, compared to diabetics with normal renal function. Creatinine showed strong negative correlation with the glomerular filtration rate estimated using CG, MDRD and CKD-EPI (-0.64, -0.87, -0.89 equations, respectively. Conclusion: the prevalence of individuals with reduced renal function based on serum creatinine was lower, reinforcing the need to follow the recommendations of the SBN and the National Kidney Disease Education Program (NKDEP in estimating the value of the glomerular filtration rate as a complement to the results of serum creatinine to better assess the renal function of patients.

Reliability of estimated glomerular filtration rate in patients treated with platinum containing therapy

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Lauritsen, Jakob; Gundgaard, Maria G; Mortensen, Mette S

2014-01-01

(median percentage error), precision (median absolute percentage error) and accuracy (p10 and p30). The precision of carboplatin dosage based on eGFR was calculated. Data on mGFR, eGFR, and PCr were available in 390 patients, with a total of ∼ 1,600 measurements. Median PCr and mGFR synchronically...... decreased after chemotherapy, yielding high bias and low precision of most estimates. Post-chemotherapy, bias ranged from -0.2% (MDRD after four cycles) to 33.8% (CKD-EPI after five cycles+), precision ranged from 11.6% (MDRD after four cycles) to 33.8% (CKD-EPI after five cycles+) and accuracy (p30) ranged...... from 37.5% (CKD-EPI after five cycles+) to 86.9% (MDRD after four cycles). Although MDRD appeared acceptable after chemotherapy because of high accuracy, this equation underestimated GFR in all other measurements. Before and years after treatment, Cockcroft-Gault and Wright offered best results...

KDIGO 2012 Clinical Practice Guideline CKD classification rules out creatinine clearance 24 hour urine collection?

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Ognibene, A; Grandi, G; Lorubbio, M; Rapi, S; Salvadori, B; Terreni, A; Veroni, F

2016-01-01

The recent guideline for the evaluation and management of Chronic Kidney Disease recommends assessing GFR employing equations based on serum creatinine; despite this, creatinine clearance 24-hour urine collection is used routinely in many settings. In this study we compared the classification assessed from CrCl (creatinine clearance 24h urine collection) and e-GFR calculated with CKD-EPI or MDRD formulas. In this retrospective study we analyze consecutive laboratory data: creatinine clearance 24h urine collection, serum creatinine and demographic data such as sex and age from 15,777 patients >18 years of age collected from 2011 to 2013 in our laboratory at Careggi Hospital. The results were then compared to the estimated GFR calculated with the equations according to the recent treatment guidelines. Consecutive and retrospective laboratory data (creatinine clearance 24h urine collection, serum creatinine and, demographic data such as sex and age) from 15,777 patients >18 years of age seen at Careggi Hospital were collected. Comparison between e-GFR calculated with CKD-EPI or MDRD formulas and GFR according CrCl determinations and bias [95% CI] were 11.34 [-47,4/70.1] and 11.4 [-50.2/73] respectively. The concordance for 18/65 years aged group when compared with e-GFR classification between MDRD vs CKDEPI, MDRD vs CrCl and CKD-EPI vs CrCl were 0.78, 0.34, and 0.41 respectively, while in the 65/110years aged group the concordance Kappas were 0.84, 0.38, and 0.36 respectively. The use of CrCl provides a different classification than the estimation of GFR using a prediction equation. The CrCl is unreliable when it is necessary to identify CKD subjects with decrease of GFR of 5ml/min/1.73m(2)/year. Copyright © 2015 The Canadian Society of Clinical Chemists. Published by Elsevier Inc. All rights reserved.

The Cockcroft-Gault : A Better Predictor of Renal Function in an Overweight and Obese Diabetic Population

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Drion, Iefke; Joosten, Hanneke; Santing, Liane; Logtenberg, Susan J. J.; Groenier, Klaas H.; Lieyerse, Aloysius G.; Kleefstra, Nanne; Bilo, Henk J. G.

2011-01-01

Background: The performance of the Cockcroft-Gault (CG) equation, the Modification of Diet in Renal Disease (MDRD) formula, and the Chronic Kidney Disease Epidemiology Collaboration equation (CKD-EPI) was evaluated in body mass index (BMI) categories. Material and Methods: In this retrospective

Multicenter study of creatinine- and/or cystatin C-based equations for estimation of glomerular filtration rates in Chinese patients with chronic kidney disease.

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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

Assessment of the Renal Function in Potential Donors of Living Kidney Transplants: Expanded Study.

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Macías, L B; Poblet, M S; Pérez, N N; Jerez, R I; Gonzalez Roncero, F M; Blanco, G B; Valdivia, M A P; Benjumea, A S; Gentil Govantes, M A

2015-11-01

It is very important to determine as accurately as possible the renal function in potential living renal transplant donors, especially those with limited renal function (CrCl graphic we have observed that the most dispersed results are obtained with the eGFR using CCr in 24-hour urine and CKD-EPI. By means of Pasing & Bablock, we realized that MDRD-4 and MDRD-6 show the highest approximation to the reference method proposed to be substituted, whereas CCr shows a high dispersion. eGFR using MDRD-4 and MDRD-6 formulas reveal the best adjustment to the measure by EDTA-Cr51. This might represent the best option if a direct eGFR measure is not available. Copyright © 2015 Elsevier Inc. All rights reserved.

Performance of Chronic Kidney Disease Epidemiology Collaboration Creatinine-Cystatin C Equation for Estimating Kidney Function in Cirrhosis

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Mindikoglu, Ayse L.; Dowling, Thomas C.; Weir, Matthew R.; Seliger, Stephen L.; Christenson, Robert H.; Magder, Laurence S.

2013-01-01

Conventional creatinine-based glomerular filtration rate (GFR) equations are insufficiently accurate for estimating GFR in cirrhosis. The Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) recently proposed an equation to estimate GFR in subjects without cirrhosis using both serum creatinine and cystatin C levels. Performance of the new CKD-EPI creatinine-cystatin C equation (2012) was superior to previous creatinine- or cystatin C-based GFR equations. To evaluate the performance of the CKD-EPI creatinine-cystatin C equation in subjects with cirrhosis, we compared it to GFR measured by non-radiolabeled iothalamate plasma clearance (mGFR) in 72 subjects with cirrhosis. We compared the “bias”, “precision” and “accuracy” of the new CKD-EPI creatinine-cystatin C equation to that of 24-hour urinary creatinine clearance (CrCl), Cockcroft-Gault (CG) and previously reported creatinine- and/or cystatin C-based GFR-estimating equations. Accuracy of CKD-EPI creatinine-cystatin C equation as quantified by root mean squared error of difference scores [differences between mGFR and estimated GFR (eGFR) or between mGFR and CrCl, or between mGFR and CG equation for each subject] (RMSE=23.56) was significantly better than that of CrCl (37.69, P=0.001), CG (RMSE=36.12, P=0.002) and GFR-estimating equations based on cystatin C only. Its accuracy as quantified by percentage of eGFRs that differed by greater than 30% with respect to mGFR was significantly better compared to CrCl (P=0.024), CG (P=0.0001), 4-variable MDRD (P=0.027) and CKD-EPI creatinine 2009 (P=0.012) equations. However, for 23.61% of the subjects, GFR estimated by CKD-EPI creatinine-cystatin C equation differed from the mGFR by more than 30%. CONCLUSIONS The diagnostic performance of CKD-EPI creatinine-cystatin C equation (2012) in patients with cirrhosis was superior to conventional equations in clinical practice for estimating GFR. However, its diagnostic performance was substantially worse than

Changes in estimated glomerular filtration rate over time in South African HIV-1-infected patients receiving tenofovir: a retrospective cohort study

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De Waal, Reneé; Cohen, Karen; Fox, Matthew P; Stinson, Kathryn; Maartens, Gary; Boulle, Andrew; Igumbor, Ehimario U; Davies, Mary-Ann

2017-01-01

Abstract Introduction: Tenofovir has been associated with decline in kidney function, but in patients with low baseline kidney function, improvements over time have been reported. Additionally, the magnitude and trajectory of estimated glomerular filtration rate (eGFR) changes may differ according to how eGFR is calculated. We described changes in eGFR over time, and the incidence of, and risk factors for, kidney toxicity, in a South African cohort. Methods: We included antiretroviral-naïve patients ≥16 years old who started tenofovir-containing antiretroviral therapy (ART) between 2002 and 2013. We calculated eGFR using the Modification of Diet in Renal Disease (MDRD), Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI), and Cockcroft-Gault equations. We described changes in eGFR from ART initiation using linear mixed effects regression. We described the incidence of eGFR <30 mL/min on treatment, and identified associations with low eGFR using Cox regression. Results: We included 15156 patients with median age of 35.4 years (IQR 29.9–42.0), median CD4 cell count of 168 cells/µL (IQR 83–243), and median eGFR (MDRD) of 98.6 mL/min (IQR 84.4–115.6). Median duration of follow up on tenofovir was 12.9 months (IQR 5.1–23.3). Amongst those with a baseline and subsequent eGFR  available, mean eGFR change from baseline at 12 months was −4.4 mL/min (95% CI −4.9 to −4.0), −2.3 (−2.5 to −2.1), and 0.6 (0.04 to 1.2) in those with baseline eGFR ≥90 mL/min; and 11.9 mL/min (11.0 to 12.7), 14.6 (13.5 to 15.7), and 11.0 (10.3 to 11.7) in those with baseline eGFR <90 mL/min, according to the MDRD, CKD-EPI (n = 11 112), and Cockcroft-Gault (n = 9 283) equations, respectively. Overall, 292 (1.9%) patients developed eGFR <30 mL/min. Significant associations with low eGFR included older age, baseline eGFR <60 mL/min, CD4 count <200 cells/µL, body weight <60 kg, and concomitant protease inhibitor use. Conclusions: Patients on

Comparison of Cockcroft-Gault and modification of diet in renal disease formulas as predictors of cardiovascular outcomes in patients with myocardial infarction treated with primary percutaneous coronary intervention.

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Ekmekci, Ahmet; Uluganyan, Mahmut; Gungor, Baris; Tufan, Fatih; Cekirdekci, Elif Iclal; Ozcan, Kazim Serhan; Erer, Hatice Betul; Orhan, Ahmet; Osmanov, Damir; Bozbay, Mehmet; Cicek, Gokhan; Sayar, Nurten; Eren, Mehmet

2014-10-01

We prospectively assessed the value of estimated glomerular filtration rate (eGFR) by the Modification of Diet in Renal Disease (MDRD) and Cockcroft-Gault (C-G) equations in predicting inhospital adverse outcomes after primary coronary intervention for acute ST-segment elevation myocardial infarction. We classified 647 patients into 3 categories according to eGFR, 90 mL/min/1.73 m(2). The eGFRC-G classified 17 patients in the >90 mL/min/1.73 m(2) subgroup and 6 and 11 patients in the 60 to 90 and 90 mL/min/1.73 m(2) (P = .01 and P = .01, respectively); the eGFRMDRD was not predictive. Although the MDRD equation more accurately estimates GFR in certain populations, the CG formula may be a better predictor of adverse events. © The Author(s) 2013.

Epidemiology of chronic kidney disease in the Kingdom of Saudi Arabia (SEEK-Saudi investigators) - A pilot study

International Nuclear Information System (INIS)

Abdulkareem O Alsuwaida

2010-01-01

There are no available data about the prevalence of chronic kidney disease (CKD) and its risk factors in the general population of the kingdom of Saudi Arabia. To estimate the prevalence of CKD and its associated risk factors in the Saudi population, we conducted a pilot community-based screening program in commercial centers in Riyadh, Saudi Arabia. Candidates were interviewed and blood and urine samples were collected. Participants were categorized to their CKD stage according to their estimated Modification of Diet in Renal Disease (MDRD3)-based, the new Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) equation and the presence of albuminuria. The sample comprised 491 (49.9% were males) adult Saudi nationals. The mean age was 37.4 ± 11.3 years. The overall prevalence of CKD was 5.7% and 5.3% using the MDRD-3 and CKD-EPI glomerular filtration equations, respectively. Gender, age, smoking status, body mass index, hypertension and diabetes mellitus were not significant predictors of CKD in our cohort. However, CKD was significantly higher in the older age groups, higher serum glucose, waist/hip ratio and blood pressure. Only 7.1% of the CKD patients were aware of their CKD status, while 32.1% were told that they had protein or blood in their urine and 10.7% had known kidney stones in the past. We conclude that prevalence of CKD in the young Saudi population is around 5.7%. Our pilot study demonstrated the feasibility of screening for CKD. Screening of high-risk individuals is likely to be the most cost-effective strategy to detect CKD patients (Author).

Variability of glomerular filtration rate estimation equations in elderly Chinese patients with chronic kidney disease

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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

Combining Cystatin C and Creatinine Yields a Reliable Glomerular Filtration Rate Estimation in Older Adults in Contrast to β-Trace Protein and β2-Microglobulin.

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Werner, Karin; Pihlsgård, Mats; Elmståhl, Sölve; Legrand, Helen; Nyman, Ulf; Christensson, Anders

2017-01-01

The glomerular filtration rate (GFR) is the most important measure of kidney function and chronic kidney disease (CKD). This study aims to validate commonly used equations for estimated GFR (eGFR) based on creatinine (cr), cystatin C (cys), β-trace protein (BTP), and β2-microglobulin (B2M) in older adults. We conducted a validation study with 126 participants aged between 72 and 98 with a mean measured GFR (mGFR) by iohexol clearance of 54 mL/min/1.73 m2. The eGFR equations (CKD-Epidemiology collaboration [CKD-EPI], Berlin Initiative Study [BIS], Full Age Spectrum [FAS], Modification of Diet in Renal Disease [MDRD]cr, Caucasian-Asian-Pediatric-Adult [CAPA]cys, Lund-Malmö Revised [LM-REV]cr, and MEAN-LM-CAPAcr-cys), were assessed in terms of bias (median difference: eGFR-mGFR), precision (interquartile range of the differences), and accuracy (P30: percentage of estimates ±30% of mGFR). The equations were compared to a benchmark equation: CKD-EPIcr-cys. All cystatin C-based equations underestimated the GFR compared to mGFR, whereas bias was mixed for the equations based only on creatinine. Accuracy was the highest for CKD-EPIcr-cys (98%) and lowest for MDRD (82%). Below mGFR 45 mL/min/1.73 m2 only equations incorporating cystatin C reached P30 accuracy >90%. CKD-EPIcr-cys was not significantly more accurate than the other cystatin C-based equations. In contrast, CKD-EPIcr-cys was significantly more accurate than all creatinine-based equations except LM-REVcr. This study confirms that it is reasonable to use equations incorporating cystatin C and creatinine in older patients across a wide spectrum of GFR. However, the results call into question the use of creatinine alone below mGFR 45 mL/min/1.73 m2. B2M and BTP do not demonstrate additional value in eGFR determination in older adults. © 2017 S. Karger AG, Basel.

Chronic renal failure among HIV-1-infected patients

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Mocroft, Amanda; Kirk, Ole; Gatell, Jose

2007-01-01

BACKGROUND: The role of exposure to antiretrovirals in chronic renal failure (CRF) is not well understood. Glomerular filtration rates (GFR) are estimated using the Cockcroft-Gault (CG) or Modification of Diet in Renal Disease (MDRD) equations. METHODS: Baseline was arbitrarily defined as the first...

A comparison of observed versus estimated baseline creatinine for determination of RIFLE class in patients with acute kidney injury

NARCIS (Netherlands)

Bagshaw, Sean M.; Uchino, Shigehiko; Cruz, Dinna; Bellomo, Rinaldo; Morimatsu, Hiroshi; Morgera, Stanislao; Schetz, Miet; Tan, Ian; Bouman, Catherine; Macedo, Etienne; Gibney, Noel; Tolwani, Ashita; Oudemans-van Straaten, Heleen M.; Ronco, Claudio; Kellum, John A.; French, Craig; Mulder, John; Pinder, Mary; Roberts, Brigit; Botha, John; Mudholkar, Pradeen; Holt, Andrew; Hunt, Tamara; Honoré, Patrick Maurice; Clerbaux, Gaetan; Schetz, Miet Maria; Wilmer, Alexander; Yu, Luis; Macedo, Ettiene V.; Laranja, Sandra Maria; Rodrigues, Cassio José; Suassuna, José Hermógenes Rocco; Ruzany, Frederico; Campos, Bruno; Leblanc, Martine; Senécal, Lynne; Gibney, R. T. Noel; Johnston, Curtis; Brindley, Peter; Tan, Ian K. S.; Chen, Hui De; Wan, Li; Rokyta, Richard; Krouzecky, Ales; Neumayer, Hans-Helmut; Detlef, Kindgen-Milles; Mueller, Eckhard; Tsiora, Vicky; Sombolos, Kostas; Mustafa, Iqbal; Suranadi, Iwayan; Bar-Lavie, Yaron; Nakhoul, Farid; Ceriani, Roberto; Bortone, Franco; Zamperetti, Nereo; Pappalardo, Federico; Marino, Giovanni; Calabrese, Prospero; Monaco, Francesco; Liverani, Chiara; Clementi, Stefano; Coltrinari, Rosanna; Marini, Benedetto; Fuke, Nobuo; Miyazawa, Masaaki; Katayama, Hiroshi; Kurasako, Toshiaki; Hirasawa, Hiroyuki; Oda, Shigeto; Tanigawa, Koichi; Tanaka, Keiichi; Oudemans-van Straaten, Helena Maria; de Pont, Anne-Cornelie J. M.; Bugge, Jan Frederik; Riddervold, Fridtjov; Nilsen, Paul Age; Julsrud, Joar; Teixeira e Costa, Fernando; Marcelino, Paulo; Serra, Isabel Maria; Yaroustovsky, Mike; Grigoriyanc, Rachik; Lee, Kang Hoe; Loo, Shi; Singh, Kulgit; Barrachina, Ferran; Llorens, Julio; Sanchez-Izquierdo-Riera, Jose Angel; Toral-Vazquez, Darío; Wizelius, Ivar; Hermansson, Dan; Gaspert, Tomislav; Maggiorini, Marco; Davenport, Andrew; Lombardi, Raúl; Llopart, Teresita; Venkataraman, Ramesh; Kellum, John; Murray, Patrick; Trevino, Sharon; Benjamin, Ernest; Hufanda, Jerry; Paganini, Emil; Warnock, David; Guirguis, Nabil

2009-01-01

The RIFLE classification scheme for acute kidney injury (AKI) is based on relative changes in serum creatinine (SCr) and on urine output. The SCr criteria, therefore, require a pre-morbid baseline value. When unknown, current recommendations are to estimate a baseline SCr by the MDRD equation.

The use of absolute values improves performance of estimation formulae

DEFF Research Database (Denmark)

Redal-Baigorri, Belén; Rasmussen, Knud; Heaf, James Goya

2013-01-01

BACKGROUND: Estimation of Glomerular Filtration Rate (GFR) by equations such as Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) or Modification of Diet in Renal Disease (MDRD) is usually expressed as a Body Surface Area (BSA) indexed value (ml/min per 1.73 m²). This can have severe cl...

Early Acute Kidney Injury in Military Casualties

Science.gov (United States)

2015-05-01

days, because of the high rates of amputations in this patient popu- lation, which may lower creatinine independent of renal func- tion.26 Data on...combat support hospi- tal in Afghanistan. Levels of serum creatinine were collected for up to 14 days and were available in both Afghanistan and...patient did not have a baseline creatinine , then a baseline creatinine was derived using theModification of Diet in Renal Disease (MDRD) study equation

The equationally-defined commutator a study in equational logic and algebra

CERN Document Server

Czelakowski, Janusz

2015-01-01

This monograph introduces and explores the notions of a commutator equation and the equationally-defined commutator from the perspective of abstract algebraic logic.  An account of the commutator operation associated with equational deductive systems is presented, with an emphasis placed on logical aspects of the commutator for equational systems determined by quasivarieties of algebras.  The author discusses the general properties of the equationally-defined commutator, various centralization relations for relative congruences, the additivity and correspondence properties of the equationally-defined commutator, and its behavior in finitely generated quasivarieties. Presenting new and original research not yet considered in the mathematical literature, The Equationally-Defined Commutator will be of interest to professional algebraists and logicians, as well as graduate students and other researchers interested in problems of modern algebraic logic.

Cystatin C, kidney function, and cardiovascular risk factors in primary hypertension Cistatina C, função renal e fatores de risco cardiovascular na hipertensão primária

Directory of Open Access Journals (Sweden)

João Victor Salgado

2013-02-01

Full Text Available OBJECTIVE: To investigate the clinical usefulness of serum cystatin C (Scys and cystatin C-based equations for the screening of chronic kidney disease in primary hypertensive patients, and correlate these markers with risk factors for cardiovascular disease. METHODS: A cross-sectional study was performed in 199 middle-aged adults at a basic health unit. Kidney function assessment included measurements of serum creatinine (Scr and Scys levels, 24-hour microalbuminuria (MA, as well as glomerular filtration rate (GFR through Larsson and Modification of Diet in Renal Disease (MDRD study equations. Bland- Altman plot analysis was used to calculate the agreement between equations. RESULTS: High levels of Scys were found in 22% of the patients, even with normal values of GFR estimated by MDRD study equation. Systolic blood pressure and MA correlated better with Scys than Scr, but there was no correlation between Scys and diastolic blood pressure. Gender, age > 60 years, MA, and uric acid were significantly associated with high Scys levels. After multivariate analysis, only age > 60 yrs (RR = 6.4; p OBJETIVO: Investigar a utilidade clínica da cistatina C sérica (Scys e da equação baseada na cistatina C na triagem da doença renal crônica em pacientes com hipertensão primária e correlacionar esses marcadores com fatores de risco para doença cardiovascular. MÉTODOS: Foi realizado um estudo transversal com 199 adultos de meia-idade em uma unidade básica de saúde. A avaliação da função renal incluiu medidas dos níveis séricos da creatinina (Scr e Scys, microalbuminúria de 24 h (MA, bem como da taxa de filtração glomerular (TFG por meio das equações de Larsson e do estudo MDRD. Foi utilizada a análise Bland-Altman plot para calcular a concordância entre as equações. RESULTADOS: Foram encontrados níveis elevados de Scys em 22% dos pacientes, mesmo com valores normais da TFG estimada pela equação do estudo MDRD. A pressão sist

Differential Equations Models to Study Quorum Sensing.

Science.gov (United States)

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.

Measurement of renal function in a kidney donor: a comparison of creatinine-based and volume-based GFRs

Energy Technology Data Exchange (ETDEWEB)

Choi, Don Kyoung; Choi, See Min; Jeong, Byong Chang; Seo, Seong Il; Jeon, Seong Soo; Lee, Hyun Moo; Choi, Han-Yong; Jeon, Hwang Gyun [Sungkyunkwan University School of Medicine, Department of Urology, Samsung Medical Center, Seoul (Korea, Republic of); Park, Bong Hee [The Catholic University of Korea College of Medicine, Department of Urology, Incheon St. Mary' s Hospital, Seoul (Korea, Republic of)

2015-11-15

We aimed to evaluate the performance of various GFR estimates compared with direct measurement of GFR (dGFR). We also sought to create a new formula for volume-based GFR (new-vGFR) using kidney volume determined by CT. GFR was measured using creatinine-based methods (MDRD, the Cockcroft-Gault equation, CKD-EPI formula, and the Mayo clinic formula) and the Herts method, which is volume-based (vGFR). We compared performance between GFR estimates and created a new vGFR model by multiple linear regression analysis. Among the creatinine-based GFR estimates, the MDRD and C-G equations were similarly associated with dGFR (correlation and concordance coefficients of 0.359 and 0.369 and 0.354 and 0.318, respectively). We developed the following new kidney volume-based GFR formula: 217.48-0.39XA + 0.25XW-0.46XH-54.01XsCr + 0.02XV-19.89 (if female) (A = age, W = weight, H = height, sCr = serum creatinine level, V = total kidney volume). The MDRD and CKD-EPI had relatively better accuracy than the other creatinine-based methods (30.7 % vs. 32.3 % within 10 % and 78.0 % vs. 73.0 % within 30 %, respectively). However, the new-vGFR formula had the most accurate results among all of the analyzed methods (37.4 % within 10 % and 84.6 % within 30 %). The new-vGFR can replace dGFR or creatinine-based GFR for assessing kidney function in donors and healthy individuals. (orig.)

Measurement of renal function in a kidney donor: a comparison of creatinine-based and volume-based GFRs

International Nuclear Information System (INIS)

Choi, Don Kyoung; Choi, See Min; Jeong, Byong Chang; Seo, Seong Il; Jeon, Seong Soo; Lee, Hyun Moo; Choi, Han-Yong; Jeon, Hwang Gyun; Park, Bong Hee

2015-01-01

We aimed to evaluate the performance of various GFR estimates compared with direct measurement of GFR (dGFR). We also sought to create a new formula for volume-based GFR (new-vGFR) using kidney volume determined by CT. GFR was measured using creatinine-based methods (MDRD, the Cockcroft-Gault equation, CKD-EPI formula, and the Mayo clinic formula) and the Herts method, which is volume-based (vGFR). We compared performance between GFR estimates and created a new vGFR model by multiple linear regression analysis. Among the creatinine-based GFR estimates, the MDRD and C-G equations were similarly associated with dGFR (correlation and concordance coefficients of 0.359 and 0.369 and 0.354 and 0.318, respectively). We developed the following new kidney volume-based GFR formula: 217.48-0.39XA + 0.25XW-0.46XH-54.01XsCr + 0.02XV-19.89 (if female) (A = age, W = weight, H = height, sCr = serum creatinine level, V = total kidney volume). The MDRD and CKD-EPI had relatively better accuracy than the other creatinine-based methods (30.7 % vs. 32.3 % within 10 % and 78.0 % vs. 73.0 % within 30 %, respectively). However, the new-vGFR formula had the most accurate results among all of the analyzed methods (37.4 % within 10 % and 84.6 % within 30 %). The new-vGFR can replace dGFR or creatinine-based GFR for assessing kidney function in donors and healthy individuals. (orig.)

Studies on Microwave Heated Drying-rate Equations of Foods

OpenAIRE

呂, 聯通; 久保田, 清; 鈴木, 寛一; 岡崎, 尚; 山下, 洋右

1990-01-01

In order to design various microwave heated drying apparatuses, we must take drying-rate equations which are based on simple drying-rate models. In a previous paper (KUBOTA, et al., 1990), we have studied a convenient microwave heated drying instrument, and studied the simple drying-rate equations of potato and so on by using the simple empirical rate equations that have been reported in previous papers (KUBOTA, 1979-1, 1979-2). In this paper, we studied the microwave drying rate of the const...

Individualizing pharmacotherapy in patients with renal impairment: the validity of the Modification of Diet in Renal Disease formula in specific patient populations with a glomerular filtration rate below 60 ml/min. A systematic review.

Directory of Open Access Journals (Sweden)

Willemijn L Eppenga

Full Text Available The Modification of Diet in Renal Disease (MDRD formula is widely used in clinical practice to assess the correct drug dose. This formula is based on serum creatinine levels which might be influenced by chronic diseases itself or the effects of the chronic diseases. We conducted a systematic review to determine the validity of the MDRD formula in specific patient populations with renal impairment: elderly, hospitalized and obese patients, patients with cardiovascular disease, cancer, chronic respiratory diseases, diabetes mellitus, liver cirrhosis and human immunodeficiency virus.We searched for articles in Pubmed published from January 1999 through January 2014. Selection criteria were (1 patients with a glomerular filtration rate (GFR < 60 ml/min (/1.73 m2, (2 MDRD formula compared with a gold standard and (3 statistical analysis focused on bias, precision and/or accuracy. Data extraction was done by the first author and checked by a second author. A bias of 20% or less, a precision of 30% or less and an accuracy expressed as P30% of 80% or higher were indicators of the validity of the MDRD formula. In total we included 27 studies. The number of patients included ranged from 8 to 1831. The gold standard and measurement method used varied across the studies. For none of the specific patient populations the studies provided sufficient evidence of validity of the MDRD formula regarding the three parameters. For patients with diabetes mellitus and liver cirrhosis, hospitalized patients and elderly with moderate to severe renal impairment we concluded that the MDRD formula is not valid. Limitations of the review are the lack of considering the method of measuring serum creatinine levels and the type of gold standard used.In several specific patient populations with renal impairment the use of the MDRD formula is not valid or has uncertain validity.

Comparing the IRT Pre-equating and Section Pre-equating: A Simulation Study.

Science.gov (United States)

Hwang, Chi-en; Cleary, T. Anne

The results obtained from two basic types of pre-equatings of tests were compared: the item response theory (IRT) pre-equating and section pre-equating (SPE). The simulated data were generated from a modified three-parameter logistic model with a constant guessing parameter. Responses of two replication samples of 3000 examinees on two 72-item…

Numerical study of fractional nonlinear Schrodinger equations

KAUST Repository

Klein, Christian

2014-10-08

Using a Fourier spectral method, we provide a detailed numerical investigation of dispersive Schrödinger-type equations involving a fractional Laplacian in an one-dimensional case. By an appropriate choice of the dispersive exponent, both mass and energy sub- and supercritical regimes can be identified. This allows us to study the possibility of finite time blow-up versus global existence, the nature of the blow-up, the stability and instability of nonlinear ground states and the long-time dynamics of solutions. The latter is also studied in a semiclassical setting. Moreover, we numerically construct ground state solutions of the fractional nonlinear Schrödinger equation.

A functional-analytic method for the study of difference equations

Directory of Open Access Journals (Sweden)

Siafarikas Panayiotis D

2004-01-01

Full Text Available We will give the generalization of a recently developed functional-analytic method for studying linear and nonlinear, ordinary and partial, difference equations in the and spaces, p∈ℕ, . The method will be illustrated by use of two examples concerning a nonlinear ordinary difference equation known as the Putnam equation, and a linear partial difference equation of three variables describing the discrete Newton law of cooling in three dimensions.

Use of cystatin C and serum creatinine for the diagnosis of contrast-induced nephropathy in patients undergoing contrast-enhanced computed tomography at an oncology centre.

Directory of Open Access Journals (Sweden)

Joao Italo Fortalesa Melo

Full Text Available Our aim was to assess renal function using as laboratory measurements serum creatinine and cystatin C concentrations before and after administration of low-osmolarity (nonionic iodinated contrast medium in patients with cancer undergoing computed tomography (CT.This prospective study included 400 oncologic outpatients. Serum creatinine and cystatin C concentrations were measured before and 72 h after contrast administration. Glomerular filtration rates (GFRs were estimated using serum creatinine-based [Modification of Diet in Renal Disease (MDRD and Cockroft-Gault and cystatin C based (Larsson equations. Exploratory data analysis was performed. The nonparametric Wilcoxon test was used to compare pre and post contrast of test results and estimated clearance. The confidence interval used in the analysis was 95%.Compared with the pre-contrast values, the mean serum creatinine concentration was significantly higher and average GFRs estimated using MDRD and Cockcroft-Gault equations were significantly lower after the administration of contrast (p <0.001. It was also observed a significant increase after contrast in the concentration of Cystatin C (p = 0.015. In addition, a decrease in GFR estimated using the average Larsson (p = 0.021 was observed between time points. However, none of the patients presented clinically significant nephropathy.Assessment using serum creatinine and cystatin C concentrations showed changes in renal function among patients with cancer undergoing contrast-enhanced CT examination in this study. No significant renal damage related to the use of low-osmolarity iodinated contrast medium of the type and dosage employed in this study was observed. This contrast medium is thus safe for use in patients with cancer.

Numerical study of the Kadomtsev-Petviashvili equation and dispersive shock waves

Science.gov (United States)

Grava, T.; Klein, C.; Pitton, G.

2018-02-01

A detailed numerical study of the long time behaviour of dispersive shock waves in solutions to the Kadomtsev-Petviashvili (KP) I equation is presented. It is shown that modulated lump solutions emerge from the dispersive shock waves. For the description of dispersive shock waves, Whitham modulation equations for KP are obtained. It is shown that the modulation equations near the soliton line are hyperbolic for the KPII equation while they are elliptic for the KPI equation leading to a focusing effect and the formation of lumps. Such a behaviour is similar to the appearance of breathers for the focusing nonlinear Schrödinger equation in the semiclassical limit.

Study of ODE limit problems for reaction-diffusion equations

Directory of Open Access Journals (Sweden)

Jacson Simsen

2018-01-01

Full Text Available In this work we study ODE limit problems for reaction-diffusion equations for large diffusion and we study the sensitivity of nonlinear ODEs with respect to initial conditions and exponent parameters. Moreover, we prove continuity of the flow and weak upper semicontinuity of a family of global attractors for reaction-diffusion equations with spatially variable exponents when the exponents go to 2 in \\(L^{\\infty}(\\Omega\\ and the diffusion coefficients go to infinity.

A functional-analytic method for the study of difference equations

Directory of Open Access Journals (Sweden)

Panayiotis D. Siafarikas

2004-07-01

Full Text Available We will give the generalization of a recently developed functional-analytic method for studying linear and nonlinear, ordinary and partial, difference equations in the ℓp1 and ℓp2 spaces, p∈ℕ, p≥1. The method will be illustrated by use of two examples concerning a nonlinear ordinary difference equation known as the Putnam equation, and a linear partial difference equation of three variables describing the discrete Newton law of cooling in three dimensions.

Analysis of the magnetohydrodynamic equations and study of the nonlinear solution bifurcations

International Nuclear Information System (INIS)

Morros Tosas, J.

1989-01-01

The nonlinear problems related to the plasma magnetohydrodynamic instabilities are studied. A bifurcation theory is applied and a general magnetohydrodynamic equation is proposed. Scalar functions, a steady magnetic field and a new equation for the velocity field are taken into account. A method allowing the obtention of suitable reduced equations for the instabilities study is described. Toroidal and cylindrical configuration plasmas are studied. In the cylindrical configuration case, analytical calculations are performed and two steady bifurcated solutions are found. In the toroidal configuration case, a suitable reduced equation system is obtained; a qualitative approach of a steady solution bifurcation on a toroidal Kink type geometry is carried out [fr

Analysis of the magnetohydrodynamic equations and study of the nonlinear solution bifurcations

International Nuclear Information System (INIS)

Morros Tosas, J.

1989-05-01

The nonlinear saturation of a plasma magnetohydrodynamic instabilities is studied, by means of a bifurcation theory. The work includes: an accurate mathematical method to study the MHD equations, in which the physical content is clear; and the study of the nonlinear solutions of the branch bifurcations, applied to different unstable plasma models. A scalar function representation is proposed for the MHD equations. This representation is characterized by a reference steady magnetic field and by a velocity field, which allow to write the equations for the scalar functions. An approximation method, leading to the obtention of the reduced equations applied in the instability study, is given. The cylindrical or toroidal plasmas are studied by using the nonlinear solutions bifurcation. Concerning the cylindrical plasma, the representation leads to a reduced system which enables the analytical calculations: two different steady bifurcation solutions are obtained. In the case of the toroidal plasma, an appropriate reduced equations system, is obtained. A qualitative approach of the Kink-type steady solution bifurcation, in a toroidal geometry, is performed [fr

Functional analysis in the study of differential and integral equations

International Nuclear Information System (INIS)

Sell, G.R.

1976-01-01

This paper illustrates the use of functional analysis in the study of differential equations. Our particular starting point, the theory of flows or dynamical systems, originated with the work of H. Poincare, who is the founder of the qualitative theory of ordinary differential equations. In the qualitative theory one tries to describe the behaviour of a solution, or a collection of solutions, without ''solving'' the differential equation. As a starting point one assumes the existence, and sometimes the uniqueness, of solutions and then one tries to describe the asymptotic behaviour, as time t→+infinity, of these solutions. We compare the notion of a flow with that of a C 0 -group of bounded linear operators on a Banach space. We shall show how the concept C 0 -group, or more generally a C 0 -semigroup, can be used to study the behaviour of solutions of certain differential and integral equations. Our main objective is to show how the concept of a C 0 -group and especially the notion of weak-compactness can be used to prove the existence of an invariant measure for a flow on a compact Hausdorff space. Applications to the theory of ordinary differential equations are included. (author)

Development of kinetics equations from the Boltzmann equation; Etablissement des equations de la cinetique a partir de l'equation de Boltzmann

Energy Technology Data Exchange (ETDEWEB)

Plas, R.

1962-07-01

The author reports a study on kinetics equations for a reactor. He uses the conventional form of these equations but by using a dynamic multiplication factor. Thus, constants related to delayed neutrons are not modified by efficiency factors. The author first describes the theoretic kinetic operation of a reactor and develops the associated equations. He reports the development of equations for multiplication factors.

Glomerular filtration rate, cardiovascular risk factors and insulin resistance Filtrado glomerular, riesgo cardiovascular y resistencia a la insulina

Directory of Open Access Journals (Sweden)

Martín R. Salazar

2009-10-01

Full Text Available The aim of this paper was to study the estimated glomerular filtration rate (eGFR, its changes with age, and its association with systolic blood pressure (SBP and diastolic BP (DBP, indicators of obesity, dyslipemia, insulin resistance and inflammation on a random population sample. BP, weight, size and waist circumference (WC were recorded at home. Fasting morning blood samples were analysed. The eGFR was calculated with MDRD (eGFR-MDRD, Cockroft-Gault (eGFR-CG adjusted to 1.73 m² and reciprocal of serum creatinine (100/serum cretinine. A total of 1016 individuals, 722 females (41.97 ± 0.66 years old and 294 males (42.06 ± 0.99 years old, completed the laboratory tests. The mean of 100/Scr was 115.13 ± 0.60 (dl/mg, the mean eGFR-CG was 98.48 ± 0.82 ml/min/1.73 m²; the mean eGFR-MDRD was 85.15 ± 0.58 ml/min/1.73 m². The eGFR-MDRD decreased with age and with the number of risk factors in both sexes. The eGFR-MDRD El objetivo fue evaluar en una muestra poblacional aleatoria el filtrado glomerular estimado (FGe, sus cambios con la edad y su asociación con presión arterial sistólica (PAS y diastólica (PAD, indicadores de obesidad, dislipemia, resistencia a la insulina e inflamación. En cada domicilio fueron medidos presión arterial, peso y talla y perímetro de la cintura (PC. Se analizaron muestras de sangre en ayunas y fue calculado el FGe usando las fórmulas de MDRD (FGe-MDRD y Cockroft-Gault (FGe-CG ajustado a 1.73 m², y la inversa de la creatinina sérica (100/CrS. Completaron el protocolo de laboratorio 1016 sujetos, 722 mujeres (41.97 ± 0.66 años y 294 varones (42.06 ± 0.99 años. La media de 100/Crs fue 115.13 ± 0.60 (dl/mg, la del FGe-CG 98.48 ± 0.82 ml/min/1.73 m² y la del FGe-MDRD 85.15 ± 0.58 ml/min/1.73 m² (CI 95% 84.00-86.29. El FGe-MDRD disminuyó con la edad y con el número de factores de riesgo cardiovascular en ambos sexos. La prevalecencia ajustada de FGe-MDRD < 60 ml/min/1.73 m² fue 6.2 por 100

Age- and sex-specific reference limits for creatinine, cystatin C and the estimated glomerular filtration rate.

Science.gov (United States)

Hannemann, Anke; Friedrich, Nele; Dittmann, Kathleen; Spielhagen, Christin; Wallaschofski, Henri; Völzke, Henry; Rettig, Rainer; Endlich, Karlhans; Lendeckel, Uwe; Stracke, Sylvia; Nauck, Matthias

2011-11-14

Early detection of patients with chronic kidney disease is of great importance. This study developed reference limits for serum creatinine and serum cystatin C concentrations and for the estimated glomerular filtration rate (eGFR) in healthy subjects from the general population aged 25-65 years. This study defined a reference population including 985 subjects from the first follow-up of the Study of Health in Pomerania. Serum creatinine was measured with a modified kinetic Jaffé method. Serum cystatin C was measured with a nephelometric assay. The eGFR was calculated from serum creatinine according to the Cockcroft-Gault (eGFR(CG)) and the Modification of Diet in Renal Disease (eGFR(MDRD)) equation, respectively, as well as from serum cystatin C according to the formula by Larsson (eGFR(Larsson)). Non-parametric quantile regression was used to estimate the reference limits. For serum creatinine and serum cystatin C the 95th percentile and for eGFR(CG), eGFR(MDRD) and eGFR(Larsson) the 5th percentile were selected as reference limits. All data was weighted to reflect the age- and sex-structure of the German population in 2008. The reference limits for serum creatinine (men: 1.11-1.23 mg/dL; women: 0.93-1.00 mg/dL) and serum cystatin C levels (men: 0.92-1.04 mg/L; women: 0.84-1.02 mg/L) increased with advancing age. The reference limits for eGFR decreased with increasing age (eGFR(CG) men: 106.0-64.7 mL/min, women 84.4-57.9 mL/min; eGFR(MDRD) men: 82.5-62.2 mL/min/1.73 m², women 75.0-58.2 mL/min/1.73 m²; eGFR(Larsson) men: 85.5-72.9 mL/min, women 94.5-75.7 mL/min). This study presents age- and sex-specific reference limits for five measures of renal function based on quantile regression models.

Study of nonlinear waves described by the cubic Schroedinger equation

International Nuclear Information System (INIS)

Walstead, A.E.

1980-01-01

The cubic Schroedinger equation (CSE) is ubiquitous as a model equation for the long-time evolution of finite-amplitude near-monochromatic dispersive waves. It incorporates the effects of the radiation field pressure on the constitutive properties of the supporting medium in a self-consistent manner. The properties of the uniformly transiating periodic wave solutions of the one-dimensional CSE are studied here. These (so-called cnoidal) waves are characterized by the values of four parameters. Whitham's averaged variational principle is used to derive a system of quasilinear evolution equations (the modulational equations) for the values of these parameters when they are slowly varying in space and time. Explicit expressions for the characteristic velocities of the modulational equations are obtained for the full set of cnoidal waves. Riemann invariants are obtained for several limits for the stable case, and growth rates are obtained for several limits, including the solitary wave chain, for the unstable case. The results for several nontrivial limiting cases agree with those obtained by independent methods by others. The dynamics of the CSE generalized to two spatial dimensions are studied for the unstable case. A large class of similarity solutions with cylindrical symmetry are obtained systematically using infinitesimal transformation group techniques. The methods are adapted to obtain the symmetries of the action functional of the CSE and to deduce nine integral invariants. A numerical study of the self-similar solutions reveals that they are modulationally unstable and that singularities dominate the dynamics of the CSE in two dimensions. The CSE is derived using perturbation theory for a specific problem in plasma physics: the evolution of the envelope of a near-monochromatic electromagnetic wave in a cold magnetized plasma. 13 figures, 2 tables

Study of nonlinear waves described by the cubic Schroedinger equation

Energy Technology Data Exchange (ETDEWEB)

Walstead, A.E.

1980-03-12

The cubic Schroedinger equation (CSE) is ubiquitous as a model equation for the long-time evolution of finite-amplitude near-monochromatic dispersive waves. It incorporates the effects of the radiation field pressure on the constitutive properties of the supporting medium in a self-consistent manner. The properties of the uniformly transiating periodic wave solutions of the one-dimensional CSE are studied here. These (so-called cnoidal) waves are characterized by the values of four parameters. Whitham's averaged variational principle is used to derive a system of quasilinear evolution equations (the modulational equations) for the values of these parameters when they are slowly varying in space and time. Explicit expressions for the characteristic velocities of the modulational equations are obtained for the full set of cnoidal waves. Riemann invariants are obtained for several limits for the stable case, and growth rates are obtained for several limits, including the solitary wave chain, for the unstable case. The results for several nontrivial limiting cases agree with those obtained by independent methods by others. The dynamics of the CSE generalized to two spatial dimensions are studied for the unstable case. A large class of similarity solutions with cylindrical symmetry are obtained systematically using infinitesimal transformation group techniques. The methods are adapted to obtain the symmetries of the action functional of the CSE and to deduce nine integral invariants. A numerical study of the self-similar solutions reveals that they are modulationally unstable and that singularities dominate the dynamics of the CSE in two dimensions. The CSE is derived using perturbation theory for a specific problem in plasma physics: the evolution of the envelope of a near-monochromatic electromagnetic wave in a cold magnetized plasma. 13 figures, 2 tables.

Serum Cystatin C as an Early Diagnostic Biomarker of Diabetic Kidney Disease in Type 2 Diabetic Patients.

Science.gov (United States)

Qamar, Ayesha; Hayat, Asma; Ahmad, Tariq Mahmood; Khan, Alamgir; Hasnat, Mohammad Najam Ul; Tahir, Sufyan

2018-04-01

To determine the diagnostic accuracy and cut-off values of serum cystatin C as early diagnostic biomarker of diabetic kidney disease. Cross-sectional analytical study. Department of Pathology, Army Medical College, Rawalpindi in collaboration with Endocrinology Department, Military Hospital (MH), Rawalpindi from November 2015 to November 2016. One hundred and nineteen diagnosed patients of type 2 diabetes mellitus were enrolled in the study from the outpatient Endocrinology Department of the MH Rawalpindi. Fifty disease-free controls were also included. Fasting blood samples of the patients and controls were analysed for creatinine by Jaffé's kinetic method and estimated GFR was calculated using MDRD-based equation for GFR. Serum cystatin C was estimated by quantitative turbidimetric method. Serum cystatin C was higher in the diabetic group (mean = 1.022 ±0.33 mg/dl) as compared to the control group (mean = 0.63 ±0.14 mg/dl). ROC curve analysis, keeping less than 60 ml/min/1.73 m2 GFR (CKD-MDRD based) as reference value of the stat variable/gold standard; revealed an area under the curve of 0.914 (95% CI 0.85-0.98) and at optimal sensitivity of 88.2% and specificity of 84.8% the established cut-off of serum cystatin C was 1.26 mg/L. Cystatin C is an accurate biomarker of diabetic kidney disease with good sensitivity and specificity.

Assessing glomerular filtration rate (GFR) in critically ill patients with acute kidney injury - true GFR versus urinary creatinine clearance and estimating equations

Science.gov (United States)

2013-01-01

Introduction Estimation of kidney function in critically ill patients with acute kidney injury (AKI), is important for appropriate dosing of drugs and adjustment of therapeutic strategies, but challenging due to fluctuations in kidney function, creatinine metabolism and fluid balance. Data on the agreement between estimating and gold standard methods to assess glomerular filtration rate (GFR) in early AKI are lacking. We evaluated the agreement of urinary creatinine clearance (CrCl) and three commonly used estimating equations, the Cockcroft Gault (CG), the Modification of Diet in Renal Disease (MDRD) and the Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) equations, in comparison to GFR measured by the infusion clearance of chromium-ethylenediaminetetraacetic acid (51Cr-EDTA), in critically ill patients with early AKI after complicated cardiac surgery. Methods Thirty patients with early AKI were studied in the intensive care unit, 2 to 12 days after complicated cardiac surgery. The infusion clearance for 51Cr-EDTA obtained as a measure of GFR (GFR51Cr-EDTA) was calculated from the formula: GFR (mL/min/1.73m2) = (51Cr-EDTA infusion rate × 1.73)/(arterial 51Cr-EDTA × body surface area) and compared with the urinary CrCl and the estimated GFR (eGFR) from the three estimating equations. Urine was collected in two 30-minute periods to measure urine flow and urine creatinine. Urinary CrCl was calculated from the formula: CrCl (mL/min/1.73m2) = (urine volume × urine creatinine × 1.73)/(serum creatinine × 30 min × body surface area). Results The within-group error was lower for GFR51Cr-EDTA than the urinary CrCl method, 7.2% versus 55.0%. The between-method bias was 2.6, 11.6, 11.1 and 7.39 ml/min for eGFRCrCl, eGFRMDRD, eGFRCKD-EPI and eGFRCG, respectively, when compared to GFR51Cr-EDTA. The error was 103%, 68.7%, 67.7% and 68.0% for eGFRCrCl, eGFRMDRD, eGFRCKD-EPI and eGFRCG, respectively, when compared to GFR51Cr-EDTA. Conclusions The study

Nonlinear Dirac Equations

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.

Five-dimensional Monopole Equation with Hedge-Hog Ansatz and Abel's Differential Equation

OpenAIRE

Kihara, Hironobu

2008-01-01

We review the generalized monopole in the five-dimensional Euclidean space. A numerical solution with the Hedge-Hog ansatz is studied. The Bogomol'nyi equation becomes a second order autonomous non-linear differential equation. The equation can be translated into the Abel's differential equation of the second kind and is an algebraic differential equation.

Equating TIMSS Mathematics Subtests with Nonlinear Equating Methods Using NEAT Design: Circle-Arc Equating Approaches

Science.gov (United States)

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…

Creatinine Versus Cystatin C: Differing Estimates of Renal Function in Hospitalized Veterans Receiving Anticoagulants.

Science.gov (United States)

Wang, Christina Hao; Rubinsky, Anna D; Minichiello, Tracy; Shlipak, Michael G; Price, Erika Leemann

2018-05-31

Current practice in anticoagulation dosing relies on kidney function estimated by serum creatinine using the Cockcroft-Gault equation. However, creatinine can be unreliable in patients with low or high muscle mass. Cystatin C provides an alternative estimation of glomerular filtration rate (eGFR) that is independent of muscle. We compared cystatin C-based eGFR (eGFR cys ) with multiple creatinine-based estimates of kidney function in hospitalized patients receiving anticoagulants, to assess for discordant results that could impact medication dosing. Retrospective chart review of hospitalized patients over 1 year who received non-vitamin K antagonist anticoagulation, and who had same-day measurements of cystatin C and creatinine. Seventy-five inpatient veterans (median age 68) at the San Francisco VA Medical Center (SFVAMC). We compared the median difference between eGFR by the Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) study equation using cystatin C (eGFR cys ) and eGFRs using three creatinine-based equations: CKD-EPI (eGFR EPI ), Modified Diet in Renal Disease (eGFR MDRD ), and Cockcroft-Gault (eGFR CG ). We categorized patients into standard KDIGO kidney stages and into drug-dosing categories based on each creatinine equation and calculated proportions of patients reclassified across these categories based on cystatin C. Cystatin C predicted overall lower eGFR compared to creatinine-based equations, with a median difference of - 7.1 (IQR - 17.2, 2.6) mL/min/1.73 m 2 versus eGFR EPI , - 21.2 (IQR - 43.7, - 8.1) mL/min/1.73 m 2 versus eGFR MDRD , and - 25.9 (IQR - 46.8, - 8.7) mL/min/1.73 m 2 versus eGFR CG . Thirty-one to 52% of patients were reclassified into lower drug-dosing categories using cystatin C compared to creatinine-based estimates. We found substantial discordance in eGFR comparing cystatin C with creatinine in this group of anticoagulated inpatients. Our sample size was limited and included few women. Further

Study of fission dynamics with the three-dimensional Langevin equations

Energy Technology Data Exchange (ETDEWEB)

Eslamizadeh, H. [Persian Gulf University, Department of Physics, Bushehr (Iran, Islamic Republic of)

2011-11-15

The dynamics of fission has been studied by solving one- and three-dimensional Langevin equations with dissipation generated through the chaos weighted wall and window friction formula. The average prescission neutron multiplicities, fission probabilities and the mean fission times have been calculated in a broad range of the excitation energy for compound nuclei {sup 210}Po and {sup 224}Th formed in the fusion-fission reactions {sup 4}He+{sup 206}Pb, {sup 16}O+{sup 208}Pb and results compared with the experimental data. The analysis of the results shows that the average prescission neutron multiplicities, fission probabilities and the mean fission times calculated by one- and three-dimensional Langevin equations are different from each other, and also the results obtained based on three-dimensional Langevin equations are in better agreement with the experimental data. (orig.)

Differential Equations Compatible with KZ Equations

International Nuclear Information System (INIS)

Felder, G.; Markov, Y.; Tarasov, V.; Varchenko, A.

2000-01-01

We define a system of 'dynamical' differential equations compatible with the KZ differential equations. The KZ differential equations are associated to a complex simple Lie algebra g. These are equations on a function of n complex variables z i taking values in the tensor product of n finite dimensional g-modules. The KZ equations depend on the 'dual' variable in the Cartan subalgebra of g. The dynamical differential equations are differential equations with respect to the dual variable. We prove that the standard hypergeometric solutions of the KZ equations also satisfy the dynamical equations. As an application we give a new determinant formula for the coordinates of a basis of hypergeometric solutions

The nonlinear Dirac equation and the study of effective many-particle interactions in QED

International Nuclear Information System (INIS)

Ionescu, D.C.

1987-12-01

The starting point of the discussion was extended Lagrangian density for the classical Dirac field. The considered additional terms we had thereby interpreted as effective interactions because the corresponding field theory was not renormalizable. A scalar coupling as well as a vectorial coupling were put into calculation. The equation of motion for the system was thereby a one-particle equation which separated for s 1/2 and p 1/2 states and led to a system of coupled differential equations for the radial part. The derived radial equations were studied on three different levels. First we considered ordinary systems from atomic physics with ordinal numbers Z ≤ 110 in order to obtain from precision experiments of quantum electrodynamics upper bounds for the coupling constants. Second we have studied the influence of these additional interactions on the energy levels of the superheavy systems with ordinal numbers 110 ≤ Z ≤ 190. Third we have searched for bound states of a nonlinear Dirac equation which should exist only because of the effective interaction. In the further study we have then changed to a field-quantized consideration because our hitherto analysis was purely classical. In this connection we have studied the (e + e - ) 2 system with a (anti ΨΓΨ) 2 interaction. From the corresponding many-particle equation we have then by means of the Hartree-Fock method derived the one-particle equation of the system. Finally we had studied the electron-positron interaction by exchange of a massive intermediate vector boson. (orig./HSI) [de

Detection and prognostic impact of renal dysfunction in patients with chronic heart failure and normal serum creatinine.

Science.gov (United States)

Scrutinio, Domenico; Passantino, Andrea; Lagioia, Rocco; Santoro, Daniela; Cacciapaglia, Erasmo

2011-03-03

Accurate identification of renal dysfunction (RD) is crucial to risk stratification in chronic heart failure (CHF). Patients with CHF are at special risk of having RD despite normal serum creatinine (SCr), owing to a decreased Cr generation. At low levels of SCr, the equations estimating renal function are less accurate. This study was aimed to assess and compare the prognostic value of formulas estimating renal function in CHF patients with normal SCr. We studied 462 patients with systolic CHF and normal SCr. Creatinine clearance was estimated by the Cockcroft-Gault (eCrCl) and glomerular filtration rate by the 4-variable MDRD equation (eGFR); eCrCl normalized for body-surface area (eCrCl(BSA)) was calculated. The primary outcome was all-cause mortality at 2 years. Seventy five patients died. At multivariate Cox regression analysis, only eCrCl(BSA) was significantly associated with mortality (p = 0.006); eGFR (p = 0.24), eCrCl (p = 0.09) and BUN (p = 0.14) were not statistically significant predictors. The patients in the lowest eCrCl(BSA) quartile had an adjusted 2.1-fold (CI: 1.06-4.1) increased risk of mortality, compared with those in the referent quartile. Two-year survival was 70.4% in the lowest eCrCl(BSA) quartile and 89.7% in the referent quartile. Other independent predictors of mortality were ischemic etiology (RR: 2.16 [CI: 1.3-3.5], p = 0.0017), NYHA III/IV class (RR: 2.45 [CI: 1.51-3.97], p = 0.0003), LVEF high-risk subgroup and can more accurately be identified by the CG formula corrected for BSA than the MDRD. Copyright © 2009 Elsevier B.V. All rights reserved.

New treatment for IgA nephropathy: enteric budesonide targeted to the ileocecal region ameliorates proteinuria.

Science.gov (United States)

Smerud, Hilde Kloster; Bárány, Peter; Lindström, Karin; Fernström, Anders; Sandell, Anna; Påhlsson, Peter; Fellström, Bengt

2011-10-01

Systemic corticosteroid treatment has been shown to exert some protection against renal deterioration in IgA nephropathy (IgAN) but is not commonly recommended for long-term use due to the well-known systemic side effects. In this study, we investigated the efficacy and safety of a new enteric formulation of the locally acting glucocorticoid budesonide (Nefecon®), designed to release the active compound in the ileocecal region. The primary objective was to evaluate the efficacy of targeted release budesonide on albuminuria. Budesonide 8 mg/day was given to 16 patients with IgAN for 6 months, followed by a 3-month follow-up period. The efficacy was measured as change in 24-h urine albumin excretion, serum creatinine and estimated glomerular filtration rate (eGFR). The median relative reduction in urinary albumin excretion was 23% during the treatment period (interquartile range: -0.36 to -0.04, P = 0.04) with pretreatment values ranging from 0.3 to 6 g/24 h (median: 1.5 g/24 h). The median reduction in urine albumin peaked at 40% (interquartile range: -0.58 to -0.15) 2 months after treatment discontinuation. Serum creatinine was reduced by 6% (interquartile range: -0.12 to -0.02; P = 0.003), and eGFR [Modification of Diet in Renal Disease (MDRD)] increased ∼8% (interquartile range: 0.02-0.16, P = 0.003) during treatment. No major corticosteroid-related side effects were observed. In the present pilot study, enteric budesonide targeted to the ileocecal region had a significant effect on urine albumin excretion, accompanied by a minor reduction of serum creatinine and a modest increase of eGFR calculated by the MDRD equation, while eGFR calculated from Cockcroft-Gault equation and cystatin C was not changed. Enteric budesonide may represent a new treatment of IgAN warranting further investigation.

Study of a Model Equation in Detonation Theory

KAUST Repository

Faria, Luiz; Kasimov, Aslan R.; Rosales, Rodolfo R.

2014-01-01

Here we analyze properties of an equation that we previously proposed to model the dynamics of unstable detonation waves [A. R. Kasimov, L. M. Faria, and R. R. Rosales, Model for shock wave chaos, Phys. Rev. Lett., 110 (2013), 104104]. The equation

Serum Creatinine in Patients with Advanced Liver Disease Is of Limited Value for Identification of Moderate Renal Dysfunction: Are the Equations for Estimating Renal Function Better?

Directory of Open Access Journals (Sweden)

Jillian MacAulay

2006-01-01

Full Text Available BACKGROUND: The Cockcroft-Gault formula (CGF is used to estimate the glomerular filtration rate (GFR based on serum creatinine (Cr levels, age and sex. A new formula developed by the Modification of Diet in Renal Disease (MDRD Study Group, based on the patient’s Cr levels, age, sex, race and serum urea nitrogen and serum albumin levels, has shown to be more accurate. However, the best formula to identify patients with advanced liver disease (ALD and moderate renal dysfunction (GFR 60 mL/min/1.73 m2 or less is not known. The aim of the present study was to compare calculations of GFR, using published formulas (excluding those requiring urine collections with standard radionuclide measurement of GFR in patients with ALD.

Contribution to the study of the Fokker-planck equation; Contribution a l'etude de l'equation de Fokker-planck

Energy Technology Data Exchange (ETDEWEB)

Blaquiere, A [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires

1963-07-01

In the first paragraphs of this report, the Fokker-Planck equation is presented using the presentation method due to S. Chandrasekhar. Certain conventional resolution methods are given, and then a consideration of the physical interpretation of its various terms leads to a new study method based on the use of Campbell's theorems. This gives a solution to the equation in an integral form. The integral kernel of the solution is a normal centred distribution. Finally, the use of the Laplace transformation leads to a simple determination of the parameters of this integral kernel and connects the present theory to the characteristic function method used in particular in the field of nuclear reactors. The method also makes it possible to calculate the moments of the different orders of the probability distribution without the necessity of solving the Fokker-Planck equation. (author) [French] Dans les premiers paragraphes de ce rapport, l'equation de FOKKER-PLANCK est introduite en utilisant le mode d'expose de S. CHANDRASEKHAR. Puis, apres avoir rappele certaines methodes classiques de resolution, l'interpretation physique de ses differents termes nous conduit a une nouvelle methode d'etude qui repose sur l'utilisation des theoremes de CAMPBELL. On est ainsi conduit a la solution de l'equation sous forme integrale. Le noyau integral de la solution est une distribution normale centree. Enfin l'emploi de la transformation de LAPLACE conduit a une determination simple des parametres de ce noyau integral, et relie la theorie actuelle a la methode de la fonction caracteristique associee, utilisee en particulier dans le domaine des reacteurs nucleaires. Finalement cette methode permet le calcul des moments des differents ordres de la distribution de probabilites, sans passer par la resolution souvent laborieuse de l'equation de FOKKER-PLANCK. (auteur)

Study of the stochastic point reactor kinetic equation

International Nuclear Information System (INIS)

Gotoh, Yorio

1980-01-01

Diagrammatic technique is used to solve the stochastic point reactor kinetic equation. The method gives exact results which are derived from Fokker-Plank theory. A Green's function dressed with the clouds of noise is defined, which is a transfer function of point reactor with fluctuating reactivity. An integral equation for the correlation function of neutron power is derived using the following assumptions: 1) Green's funntion should be dressed with noise, 2) The ladder type diagrams only contributes to the correlation function. For a white noise and the one delayed neutron group approximation, the norm of the integral equation and the variance to mean-squared ratio are analytically obtained. (author)

Ordinary differential equations

CERN Document Server

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

Crossover integral equation theory for the liquid structure study

International Nuclear Information System (INIS)

Lai, S.K.; Chen, H.C.

1994-08-01

The main purpose of this work is to report on a calculation that describes the role of the long-range bridge function [H. Iyetomi and S. Ichimaru, Phys. Rev. A 25, 2434 (1982)] as applied to the study of structure of simple liquid metals. It was found here that this bridge function accounts pretty well for the major part of long-range interactions but is physically inadequate for describing the short-range part of liquid structure. To improve on the theory we have drawn attention to the crossover integral equation method which, in essence, amounts to adding to the above bridge function a short-range correction of bridge diagrams. The suggested crossover procedure has been tested for the case of liquid metal Cs. Remarkably good agreement with experiment was obtained confirming our conjecture that the crossover integral equation approach as stressed in this work is potentially an appropriate theory for an accurate study of liquid structure possibly for the supercooled liquid regime. (author). 21 refs, 3 figs

Reduction of structured population models to threshold-type delay equations and functional differential equations: A case study

Energy Technology Data Exchange (ETDEWEB)

Smith, H.L. (Arizona State Univ., Tempe (United States))

1993-01-01

It is shown by way of a simple example that certain structured population models lead naturally to differential delay equations of the threshold type and that these equations can be transformed in a natural way to functional differential equations. The model examined can be viewed as a model of competition between adults and juveniles of a single population. The results indicate the possibility that this competition leads to instability. 28 refs., 2 figs.

Fractional Schroedinger equation

International Nuclear Information System (INIS)

Laskin, Nick

2002-01-01

Some properties of the fractional Schroedinger equation are studied. We prove the Hermiticity of the fractional Hamilton operator and establish the parity conservation law for fractional quantum mechanics. As physical applications of the fractional Schroedinger equation we find the energy spectra of a hydrogenlike atom (fractional 'Bohr atom') and of a fractional oscillator in the semiclassical approximation. An equation for the fractional probability current density is developed and discussed. We also discuss the relationships between the fractional and standard Schroedinger equations

Interest and limits of glomerular filtration rate (GFR) estimation with formulae using creatinine or cystatin C in the malnourished elderly population.

Science.gov (United States)

Fabre, Emmanuelle E; Raynaud-Simon, Agathe; Golmard, Jean-Louis; Gourgouillon, Nadège; Beaudeux, Jean-Louis; Nivet-Antoine, Valérie

2010-01-01

Renal function is often altered in elderly patients. A lot of formulae are proposed to estimate GFR to adjust drug posology. French guidelines recommend the Cockcroft-Gault formula corrected with the body surface area (cCG), but the initially described unadjusted Cockcroft-Gault equation (CG) is mainly used in geriatric clinical practice. International recommendations have proposed the modification of diet in renal disease (MDRD) formula, since several authors recommended the Rule formula using cystatin C (cystC) in particular population. To appreciate the most accurate GFR estimation for posology adaptation in an elderly polypathological population, a cross-sectional study with prospective inclusion was carried out in Charles Foix Hospital. Plasma glucose levels (PGL), creatinine (CREA) levels and serum cystC, albumin (ALB), transthyretin (TTR), C-reactive protein (CRP), orosomucoid (ORO) total cholesterol (tCHOL) levels were determined among 193 elderly patients aged 70 and older. The results showed that in a malnourished, inflamed old population, CG, MDRD and Rule formulae resulted in different estimations of GFR, depending on nutritional and inflammatory parameters. Only cCG estimation was shown to be independent from these parameters. To conclude, cCG seems to be the most accurate and appropriate formula in a polypathological elderly population to evaluate renal function in order to adapt drug posology. Copyright (c) 2009 Elsevier Ireland Ltd. All rights reserved.

Model Servqual Dengan Pendekatan Structural Equation Modeling (Studi Pada Mahasiswa Sistem Informasi)

OpenAIRE

Nurfaizal, Yusmedi

2015-01-01

Penelitian ini berjudul “MODEL SERVQUAL DENGAN PENDEKATAN STRUCTURAL EQUATION MODELING (Studi Pada Mahasiswa Sistem Informasi)”. Tujuan penelitian ini adalah untuk mengetahui model Servqual dengan pendekatan Structural Equation Modeling pada mahasiswa sistem informasi. Peneliti memutuskan untuk mengambil sampel sebanyak 100 responden. Untuk menguji model digunakan analisis SEM. Hasil penelitian menunjukkan bahwa tangibility, reliability responsiveness, assurance dan emphaty mempunyai pengaruh...

Spirometry Reference Equations from the HCHS/SOL (Hispanic Community Health Study/Study of Latinos).

Science.gov (United States)

LaVange, Lisa; Davis, Sonia M; Hankinson, John; Enright, Paul; Wilson, Rebbecca; Barr, R Graham; Aldrich, Thomas K; Kalhan, Ravi; Lemus, Hector; Ni, Ai; Smith, Lewis J; Talavera, Gregory A

2017-10-15

Accurate reference values for spirometry are important because the results are used for diagnosing common chronic lung diseases such as asthma and chronic obstructive pulmonary disease, estimating physiologic impairment, and predicting all-cause mortality. Reference equations have been established for Mexican Americans but not for others with Hispanic/Latino backgrounds. To develop spirometry reference equations for adult Hispanic/Latino background groups in the United States. The HCHS/SOL (Hispanic Community Health Study/Study of Latinos) recruited a population-based probability sample of 16,415 Hispanics/Latinos aged 18-74 years living in the Bronx, Chicago, Miami, and San Diego. Participants self-identified as being of Puerto Rican, Cuban, Dominican, Mexican, or Central or South American background. Spirometry was performed using standardized methods with central quality control monitoring. Spirometric measures from a subset of 6,425 never-smoking participants without respiratory symptoms or disease were modeled as a function of sex, age, height, and Hispanic/Latino background to produce background-specific reference equations for the predicted value and lower limit of normal. Dominican and Puerto Rican Americans had substantially lower predicted and lower limit of normal values for FVC and FEV 1 than those in other Hispanic/Latino background groups and also than Mexican American values from NHANES III (Third National Health and Nutrition Examination Survey). For patients of Dominican and Puerto Rican background who present with pulmonary symptoms in clinical practice, use of background-specific spirometry reference equations may provide more appropriate predicted and lower limit of normal values, enabling more accurate diagnoses of abnormality and physiologic impairment.

Partial differential equations

CERN Document Server

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...

Equations for studies of feedback stabilization

International Nuclear Information System (INIS)

Boozer, A.H.

1998-01-01

Important ideal magnetohydrodynamic (MHD) instabilities grow slowly when a conducting wall surrounds a toroidal plasma. Feedback stabilization of these instabilities may be required for tokamaks and other magnetic confinement concepts to achieve adequate plasma pressure and self-driven current for practical fusion power. Equations are derived for simulating feedback stabilization, which require the minimum information about an ideal plasma for an exact analysis. The equations are solved in the approximation of one unstable mode, one wall circuit, one feedback circuit, and one sensor circuit. The analysis based on a single unstable mode is shown to be mathematically equivalent to the standard analysis of feedback of the axisymmetric vertical instability of tokamaks. Unlike that analysis, the method presented here applies to multiple modes that are coupled by the wall and to arbitrary toroidal mode numbers. copyright 1998 American Institute of Physics

Integral equation for inhomogeneous condensed bosons generalizing the Gross-Pitaevskii differential equation

International Nuclear Information System (INIS)

Angilella, G.G.N.; Pucci, R.; March, N.H.

2004-01-01

We give here the derivation of a Gross-Pitaevskii-type equation for inhomogeneous condensed bosons. Instead of the original Gross-Pitaevskii differential equation, we obtain an integral equation that implies less restrictive assumptions than are made in the very recent study of Pieri and Strinati [Phys. Rev. Lett. 91, 030401 (2003)]. In particular, the Thomas-Fermi approximation and the restriction to small spatial variations of the order parameter invoked in their study are avoided

Kinetic equations for an unstable plasma; Equations cinetiques d'un plasma instable

Energy Technology Data Exchange (ETDEWEB)

Laval, G; Pellat, R [Commissariat a l' Energie Atomique, Fontenay-aux-Roses (France). Centre d' Etudes Nucleaires

1968-07-01

In this work, we establish the plasma kinetic equations starting from the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy of equations. We demonstrate that relations existing between correlation functions may help to justify the truncation of the hierarchy. Then we obtain the kinetic equations of a stable or unstable plasma. They do not reduce to an equation for the one-body distribution function, but generally involve two coupled equations for the one-body distribution function and the spectral density of the fluctuating electric field. We study limiting cases where the Balescu-Lenard equation, the quasi-linear theory, the Pines-Schrieffer equations and the equations of weak turbulence in the random phase approximation are recovered. At last we generalise the H-theorem for the system of equations and we define conditions for irreversible behaviour. (authors) [French] Dans ce travail nous etablissons les equations cinetiques d'un plasma a partir des equations de la recurrence de Bogoliubov, Born, Green, Kirkwood et Yvon. Nous demontrons qu'entre les fonctions de correlation d'un plasma existent des relations qui permettent de justifier la troncature de la recurrence. Nous obtenons alors les equations cinetiques d'un plasma stable ou instable. En general elles ne se reduisent pas a une equation d'evolution pour la densite simple, mais se composent de deux equations couplees portant sur la densite simple et la densite spectrale du champ electrique fluctuant. Nous etudions le cas limites ou l'on retrouve l'equation de Balescu-Lenard, les equations de la theorie quasi-lineaire, les equations de Pines et Schrieffer et les equations de la turbulence faible dans l'approximation des phases aleatoires. Enfin, nous generalisons le theoreme H pour ce systeme d'equations et nous precisons les conditions d'evolution irreversible. (auteurs)

On the Existence and the Applications of Modified Equations for Stochastic Differential Equations

KAUST Repository

Zygalakis, K. C.

2011-01-01

In this paper we describe a general framework for deriving modified equations for stochastic differential equations (SDEs) with respect to weak convergence. Modified equations are derived for a variety of numerical methods, such as the Euler or the Milstein method. Existence of higher order modified equations is also discussed. In the case of linear SDEs, using the Gaussianity of the underlying solutions, we derive an SDE which the numerical method solves exactly in the weak sense. Applications of modified equations in the numerical study of Langevin equations is also discussed. © 2011 Society for Industrial and Applied Mathematics.

The phase space of the focused cubic Schroedinger equation: A numerical study

Energy Technology Data Exchange (ETDEWEB)

Burlakov, Yuri O. [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

1998-05-01

In a paper of 1988 [41] on statistical mechanics of the nonlinear Schroedinger equation, it was observed that a Gibbs canonical ensemble associated with the nonlinear Schroedinger equation exhibits behavior reminiscent of a phase transition in classical statistical mechanics. The existence of a phase transition in the canonical ensemble of the nonlinear Schroedinger equation would be very interesting and would have important implications for the role of this equation in modeling physical phenomena; it would also have an important bearing on the theory of weak solutions of nonlinear wave equations. The cubic Schroedinger equation, as will be shown later, is equivalent to the self-induction approximation for vortices, which is a widely used equation of motion for a thin vortex filament in classical and superfluid mechanics. The existence of a phase transition in such a system would be very interesting and actually very surprising for the following reasons: in classical fluid mechanics it is believed that the turbulent regime is dominated by strong vortex stretching, while the vortex system described by the cubic Schroedinger equation does not allow for stretching. In superfluid mechanics the self-induction approximation and its modifications have been used to describe the motion of thin superfluid vortices, which exhibit a phase transition; however, more recently some authors concluded that these equations do not adequately describe superfluid turbulence, and the absence of a phase transition in the cubic Schroedinger equation would strengthen their argument. The self-induction approximation for vortices takes into account only very localized interactions, and the existence of a phase transition in such a simplified system would be very unexpected. In this thesis the authors present a numerical study of the phase transition type phenomena observed in [41]; in particular, they find that these phenomena are strongly related to the splitting of the phase space into

Equation of state study of Laser Megajoule capsules ablator materials

International Nuclear Information System (INIS)

Colin-Lalu, Pierre

2016-01-01

This PhD thesis enters the field of inertial confinement fusion studies. In particular, it focuses on the equation of state tables of ablator materials synthesized on LMJ capsules. This work is indeed aims at improving the theoretical models introduced into the equation of state tables. We focused in the Mbar-eV pressure-temperature range because it can be access on kJ-scale laser facilities.In order to achieve this, we used the QEOS model, which is simple to use, configurable, and easily modifiable.First, quantum molecular dynamics (QMD) simulations were performed to generate cold compression curve as well as shock compression curves along the principal Hugoniot. Simulations were compared to QEOS model and showed that atomic bond dissociation has an effect on the compressibility. Results from these simulations are then used to parametrize the Grueneisen parameter in order to generate a tabulated equation of state that includes dissociation. It allowed us to show its influence on shock timing in a hydrodynamic simulation.Second, thermodynamic states along the Hugoniot were measured during three experimental campaigns upon the LULI2000 and GEKKO XII laser facilities. Experimental data confirm QMD simulations.This study was performed on two ablator materials which are an undoped polymer CHO, and a silicon-doped polymer CHOSi. Results showed universal shock compression properties. (author) [fr

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....

Study on state equation for hydrogen storage measurement by volumetric method

International Nuclear Information System (INIS)

Dai Wei; Xu Jiajing; Wang Chaoyang; Tang Yongjian

2014-01-01

Volumetric measurement technique is one of the most popular methods for determining the amount of hydrogen storage. A new state equation was established which extended the limitations from the ideal gas state equation, the van der Waals equation and the Gou equation. The new state equation was then employed to describe the p-V-T character of hydrogen and investigate the adsorption quantity of hydrogen storage in resorcin-formaldehyde aerogel under different temperatures and pressures. The new equation was used to describe the density of hydrogen under different temperatures and pressures. The results are in good agreement with the experimental data. The differences arising from various underlying physics were carefully analyzed. (authors)

Study of the dynamics of an equation with two large different-order delays

International Nuclear Information System (INIS)

Kashchenko, I.S.

2016-01-01

The case where the larger delay is proportional to the square of the smaller delay is studied in detail. Regions of stability and instability of the equilibrium state and critical cases are found. In all critical cases, special evolutionary equations (quasinormal forms) are constructed. Their non-local dynamics determines the local behavior of solutions of the original equation [ru

Theoretical and numerical study of the equations of Vlasov-Maxwell in the covariant formalism

International Nuclear Information System (INIS)

Back, A.

2011-11-01

A new point of view is proposed for the simulation of plasmas using the kinetic model which links the equations of Vlasov for the distribution of particles and the equations of Maxwell for the electromagnetic contribution of fields. We use the following principle: the equations of Physics are mathematical objects which put in relation geometrical objects. To preserve the geometrical properties of the various objects in an equation, we use, for the theoretical and numerical study, the differential geometry. All the equations of Physics can be written with differential forms and this point of view is not dependent on the choice of coordinates. We propose then a discretization of the differential forms by using B-Splines. To be coherent with the theory, we also propose a discretization of the various operations of the differential geometry. We test our scheme, first on the equations of Maxwell with several boundary conditions and since it does not depend on the system of coordinates, we also test it when we change coordinates. Finally, we apply the same method to the equations of Vlasov-Poisson in one-dimension and we propose several numerical schemes. (author)

A single-equation study of US petroleum consumption: The role of model specificiation

International Nuclear Information System (INIS)

Jones, C.T.

1993-01-01

The price responsiveness of US petroleum consumption began to attract a great deal of attention following the unexpected and substantial oil price increases of 1973-74. There have been a number of large, multi-equation econometric studies of US energy demand since then which have focused primarily on estimating short run and long run price and income elasticities of individual energy resources (coal, oil, natural gas ampersand electricity) for various consumer sectors (residential, industrial, commercial). Following these early multi-equation studies there have been several single-equation studies of aggregate US petroleum consumption. When choosing an economic model specification for a single-equation study of aggregate US petroleum consumption, an easily estimated model that will provide unbiased price and income elasticity estimates and yield accurate forecasts is needed. Using Hendry's general-to-simple specification search technique and annual data to obtain a restricted, data-acceptable simplification of a general ADL model yielded GNP and short run price elasticities near the consensus estimates, but a long run price elasticity substantially smaller than existing estimates. Comparisons with three other seemingly acceptable simple-to-general models showed that popular model specifications often involve untested, unacceptable parameter restrictions. These models may also demonstrate poorer forecasting performance. Based on results, the general-to-simple approach appears to offer a more accurate methodology for generating superior forecast models of petroleum consumption and other energy use patterns

Exact Solutions to Nonlinear Schroedinger Equation and Higher-Order Nonlinear Schroedinger Equation

International Nuclear Information System (INIS)

Ren Ji; Ruan Hangyu

2008-01-01

We study solutions of the nonlinear Schroedinger equation (NLSE) and higher-order nonlinear Schroedinger equation (HONLSE) with variable coefficients. By considering all the higher-order effect of HONLSE as a new dependent variable, the NLSE and HONLSE can be changed into one equation. Using the generalized Lie group reduction method (GLGRM), the abundant solutions of NLSE and HONLSE are obtained

Singular stochastic differential equations

CERN Document Server

Cherny, Alexander S

2005-01-01

The authors introduce, in this research monograph on stochastic differential equations, a class of points termed isolated singular points. Stochastic differential equations possessing such points (called singular stochastic differential equations here) arise often in theory and in applications. However, known conditions for the existence and uniqueness of a solution typically fail for such equations. The book concentrates on the study of the existence, the uniqueness, and, what is most important, on the qualitative behaviour of solutions of singular stochastic differential equations. This is done by providing a qualitative classification of isolated singular points, into 48 possible types.

A Comparison of Kernel Equating and Traditional Equipercentile Equating Methods and the Parametric Bootstrap Methods for Estimating Standard Errors in Equipercentile Equating

Science.gov (United States)

Choi, Sae Il

2009-01-01

This study used simulation (a) to compare the kernel equating method to traditional equipercentile equating methods under the equivalent-groups (EG) design and the nonequivalent-groups with anchor test (NEAT) design and (b) to apply the parametric bootstrap method for estimating standard errors of equating. A two-parameter logistic item response…

p-Euler equations and p-Navier-Stokes equations

Science.gov (United States)

Li, Lei; Liu, Jian-Guo

2018-04-01

We propose in this work new systems of equations which we call p-Euler equations and p-Navier-Stokes equations. p-Euler equations are derived as the Euler-Lagrange equations for the action represented by the Benamou-Brenier characterization of Wasserstein-p distances, with incompressibility constraint. p-Euler equations have similar structures with the usual Euler equations but the 'momentum' is the signed (p - 1)-th power of the velocity. In the 2D case, the p-Euler equations have streamfunction-vorticity formulation, where the vorticity is given by the p-Laplacian of the streamfunction. By adding diffusion presented by γ-Laplacian of the velocity, we obtain what we call p-Navier-Stokes equations. If γ = p, the a priori energy estimates for the velocity and momentum have dual symmetries. Using these energy estimates and a time-shift estimate, we show the global existence of weak solutions for the p-Navier-Stokes equations in Rd for γ = p and p ≥ d ≥ 2 through a compactness criterion.

Equating error in observed-score equating

NARCIS (Netherlands)

van der Linden, Willem J.

2006-01-01

Traditionally, error in equating observed scores on two versions of a test is defined as the difference between the transformations that equate the quantiles of their distributions in the sample and population of test takers. But it is argued that if the goal of equating is to adjust the scores of

Methods for Equating Mental Tests.

Science.gov (United States)

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...three IRT equating methods were examined in this study; two sections of TOEFL were each (separately) equated. The IRT methods included the following: (a...group. A separate base form was established for each of the six equating methods. Instead of equating the base-form TOEFL to itself, the last (eighth

Semilinear Schrödinger equations

CERN Document Server

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

Nonlinear diffusion equations

CERN Document Server

Wu Zhuo Qun; Li Hui Lai; Zhao Jun Ning

2001-01-01

Nonlinear diffusion equations, an important class of parabolic equations, come from a variety of diffusion phenomena which appear widely in nature. They are suggested as mathematical models of physical problems in many fields, such as filtration, phase transition, biochemistry and dynamics of biological groups. In many cases, the equations possess degeneracy or singularity. The appearance of degeneracy or singularity makes the study more involved and challenging. Many new ideas and methods have been developed to overcome the special difficulties caused by the degeneracy and singularity, which

A numerical study of adaptive space and time discretisations for Gross–Pitaevskii equations

Science.gov (United States)

Thalhammer, Mechthild; Abhau, Jochen

2012-01-01

As a basic principle, benefits of adaptive discretisations are an improved balance between required accuracy and efficiency as well as an enhancement of the reliability of numerical computations. In this work, the capacity of locally adaptive space and time discretisations for the numerical solution of low-dimensional nonlinear Schrödinger equations is investigated. The considered model equation is related to the time-dependent Gross–Pitaevskii equation arising in the description of Bose–Einstein condensates in dilute gases. The performance of the Fourier-pseudo spectral method constrained to uniform meshes versus the locally adaptive finite element method and of higher-order exponential operator splitting methods with variable time stepsizes is studied. Numerical experiments confirm that a local time stepsize control based on a posteriori local error estimators or embedded splitting pairs, respectively, is effective in different situations with an enhancement either in efficiency or reliability. As expected, adaptive time-splitting schemes combined with fast Fourier transform techniques are favourable regarding accuracy and efficiency when applied to Gross–Pitaevskii equations with a defocusing nonlinearity and a mildly varying regular solution. However, the numerical solution of nonlinear Schrödinger equations in the semi-classical regime becomes a demanding task. Due to the highly oscillatory and nonlinear nature of the problem, the spatial mesh size and the time increments need to be of the size of the decisive parameter 0Fourier pseudo-spectral and the finite element method. Nevertheless, for smaller parameter values locally adaptive time discretisations facilitate to determine the time stepsizes sufficiently small in order that the numerical approximation captures correctly the behaviour of the analytical solution. Further illustrations for Gross–Pitaevskii equations with a focusing nonlinearity or a sharp Gaussian as initial condition, respectively

Hyperbolic partial differential equations

CERN Document Server

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

Numerical study of traveling-wave solutions for the Camassa-Holm equation

International Nuclear Information System (INIS)

Kalisch, Henrik; Lenells, Jonatan

2005-01-01

We explore numerically different aspects of periodic traveling-wave solutions of the Camassa-Holm equation. In particular, the time evolution of some recently found new traveling-wave solutions and the interaction of peaked and cusped waves is studied

Study on the creep constitutive equation of Hastelloy X, (1)

International Nuclear Information System (INIS)

Hada, Kazuhiko; Mutoh, Yasushi

1983-01-01

A creep constitutive equation of Hastelloy X was obtained from available experimental data. A sensitivity analysis of this creep constitutive equation was carried out. As the result, the following were revealed: (i) Variations in creep behavior with creep constitutive equation are not small. (ii) In a simpler stress change pattern, variations in creep behavior are similar to those in the corresponding fundamental creep characteristics (creep strain curve, stress relaxation curve, etc.). (iii) Cumulative creep damage estimated in accordance with ASME Boiler and Pressure Vessel Code Case N-47 from a stress history predicted by ''the standard creep constitutive equation'' which predicts the average behavior of creep strain curve data is not thought to be on the safe side on account of uncertainties in creep damage caused by variations in creep strain curve. (author)

Factors affecting the incidence of contrast-induced nephropathy in patients undergoing computed tomography.

Science.gov (United States)

Heras Benito, M; Garrido Blázquez, M; Gómez Sanz, Y; Bernardez Mardomingo, M; Ruiz Cacho, J; Rodríguez Recio, F J; Fernández-Reyes Luis, M J

2018-05-17

To analyze the incidence of contrast-induced nephropathy in a cohort of patients undergoing computed tomography (CT) with intravenous iodinated contrast material. To evaluate the efficacy of N-acetylcysteine in preventing contrast-induced nephropathy. This prospective observational study was carried out in the months comprising March 2016 through July 2016. We selected the first five patients scheduled to undergo CT examination each day who agreed to participate and signed the informed consent form. We recorded patients' cardiovascular histories, chronic treatments, and indications for the CT examination. We measured blood levels of creatinine and urea before and after the CT examination. We used the Modification of Diet in Renal Disease (MDRD-4) equation to estimate the glomerular filtration rate. We analyzed the type and dose of contrast material. We recorded whether N-acetylcysteine was administered before the CT examination. We used SPSS 15.0 ® to compare means and proportions. Statistical significance was set at p < 0.05. No incidents of contrast-induced nephropathy were detected in any of the 202 patients included [mean age, 63.92 ± 12 years (range 22-87); 57.4% male; 21.8% diabetic; 39.6% hypertensive; 87.1% had MDRD4 ≥ 60 ml/min/1.73 m 2 (89.45 ± 14, range 62.36-134.14) and 12.9% had MDRD4 < 60 ml/min/1.73 m 2 (45.38 ± 11, range 9.16-58.90)]. The most common indication for CT examinations was oncologic (81.2%). The only contrast agent administered was iopamidol; the mean dose was 107.83 ± 11 ml (range 70-140). The mean interval between pre-CT and post-CT laboratory tests was 4.06 ± 1 days. Only 13 patients received N-acetylcysteine; 9 of these had MDRD < 60 ml/min/1.73 m 2 and 4 had MDRD4 ≥ 60 ml/min/1.73 m 2 (p = 0.000). The incidence of contrast-induced nephropathy was not significant in patients with glomerular filtration rates greater than 30 ml/min/1.73 m 2 : these favorable results might be due to

Numerical resolution of Navier-Stokes equations coupled to the heat equation

International Nuclear Information System (INIS)

Zenouda, Jean-Claude

1970-08-01

The author proves a uniqueness theorem for the time dependent Navier-Stokes equations coupled with heat flow in the two-dimensional case. He studies stability and convergence of several finite - difference schemes to solve these equations. Numerical experiments are done in the case of a square domain. (author) [fr

A generalized fractional sub-equation method for fractional differential equations with variable coefficients

International Nuclear Information System (INIS)

Tang, Bo; He, Yinnian; Wei, Leilei; Zhang, Xindong

2012-01-01

In this Letter, a generalized fractional sub-equation method is proposed for solving fractional differential equations with variable coefficients. Being concise and straightforward, this method is applied to the space–time fractional Gardner equation with variable coefficients. As a result, many exact solutions are obtained including hyperbolic function solutions, trigonometric function solutions and rational solutions. It is shown that the considered method provides a very effective, convenient and powerful mathematical tool for solving many other fractional differential equations in mathematical physics. -- Highlights: ► Study of fractional differential equations with variable coefficients plays a role in applied physical sciences. ► It is shown that the proposed algorithm is effective for solving fractional differential equations with variable coefficients. ► The obtained solutions may give insight into many considerable physical processes.

Numerical Study of Two-Dimensional Volterra Integral Equations by RDTM and Comparison with DTM

Directory of Open Access Journals (Sweden)

Reza Abazari

2013-01-01

Full Text Available The two-dimensional Volterra integral equations are solved using more recent semianalytic method, the reduced differential transform method (the so-called RDTM, and compared with the differential transform method (DTM. The concepts of DTM and RDTM are briefly explained, and their application to the two-dimensional Volterra integral equations is studied. The results obtained by DTM and RDTM together are compared with exact solution. As an important result, it is depicted that the RDTM results are more accurate in comparison with those obtained by DTM applied to the same Volterra integral equations. The numerical results reveal that the RDTM is very effective, convenient, and quite accurate compared to the other kind of nonlinear integral equations. It is predicted that the RDTM can be found widely applicable in engineering sciences.

Differential equations problem solver

CERN Document Server

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

Solution and Study of the Two-Dimensional Nodal Neutron Transport Equation

International Nuclear Information System (INIS)

Panta Pazos, Ruben; Biasotto Hauser, Eliete; Tullio de Vilhena, Marco

2002-01-01

In the last decade Vilhena and coworkers reported an analytical solution to the two-dimensional nodal discrete-ordinates approximations of the neutron transport equation in a convex domain. The key feature of these works was the application of the combined collocation method of the angular variable and nodal approach in the spatial variables. By nodal approach we mean the transverse integration of the SN equations. This procedure leads to a set of one-dimensional S N equations for the average angular fluxes in the variables x and y. These equations were solved by the old version of the LTS N method, which consists in the application of the Laplace transform to the set of nodal S N equations and solution of the resulting linear system by symbolic computation. It is important to recall that this procedure allow us to increase N the order of S N up to 16. To overcome this drawback we step forward performing a spectral painstaking analysis of the nodal S N equations for N up to 16 and we begin the convergence of the S N nodal equations defining an error for the angular flux and estimating the error in terms of the truncation error of the quadrature approximations of the integral term. Furthermore, we compare numerical results of this approach with those of other techniques used to solve the two-dimensional discrete approximations of the neutron transport equation. (authors)

The Correlation Between Urinary 8-Iso-Prostaglandin F2α and Hydrogen Peroxide Toward Renal Function in T2DM Patients Consuming Sulfonylurea and Combination of Metformin-Sulfonylurea.

Science.gov (United States)

Sauriasari, Rani; Wulandari, Fitri; Nurifahmi, Rahmaningtyas; Sekar, Andisyah P; Susilo, Veronika Y

2018-01-01

Renal dysfunction is a common complication in type 2 diabetes mellitus patients associated with oxidative damage which could be characterized by 8-iso-prostaglandin F2α and hydrogen peroxide level as oxidative stress markers. The aim of our study is to determine if there is a difference in 8-iso-prostaglandin F2α and hydrogen peroxide levels between sulfonylurea and combination of metformin-sulfonylurea in diabetic patients. We also wanted to determine if these oxidative stress markers correlate with the estimated Glomerular Filtration Rate (eGFR). We conducted a cross-sectional study with inclusion of 55 patients with type 2 diabetes mellitus in Dr. Sitanala Tangerang Hospital, Indonesia with purposive sampling. The value of eGFR was obtained by serum creatinine levels, while the level of 8-iso-prostaglandin F2α was measured by ELISA and urinary hydrogen peroxide using FOX-1 (Ferrous Ion Oxidation Xylenol Orange 1). There was no difference in 8-iso-prostaglandin F2α and hydrogen peroxide level between the two groups (p=0.088 and p=0.848). Moreover, there was no difference in eGFR values between the two groups, measured by Cockroft-Gault, MDRD, and CKD-EPI. 8-iso-prostaglandin F2α (n=55) was positively correlated with eGFR based on Cockroft-Gault (r=0.382; p=0.009), whereas urinary hydrogen peroxide (n=47) also generate significant positive correlation with eGFR based on the MDRD equation (r=0.326; p=0.021). Linear regression analysis showed that 8-iso-prostaglandin F2α is the most predictive factor and the only significant factor for eGFR in Cockroft-Gault, MDRD and also CKDEPI, even after controlled by gender, age, BMI, HbA1c, systole, and H2O2. The two treatments did not have any significant differences in antioxidant activity. However, an increase of urinary 8-iso-prostaglandin F2. and hydrogen peroxide which correlates with eGFR in the total sample may play a significant role in the pathophysiology of diabetic nephropathy. Copyright© Bentham Science

Analytical studies on the Benney-Luke equation in mathematical physics

Science.gov (United States)

Islam, S. M. Rayhanul; Khan, Kamruzzaman; Woadud, K. M. Abdul Al

2018-04-01

The enhanced (G‧/G)-expansion method presents wide applicability to handling nonlinear wave equations. In this article, we find the new exact traveling wave solutions of the Benney-Luke equation by using the enhanced (G‧/G)-expansion method. This method is a useful, reliable, and concise method to easily solve the nonlinear evaluation equations (NLEEs). The traveling wave solutions have expressed in term of the hyperbolic and trigonometric functions. We also have plotted the 2D and 3D graphics of some analytical solutions obtained in this paper.

Solutions of system of P1 equations without use of auxiliary differential equations coupled

International Nuclear Information System (INIS)

Martinez, Aquilino Senra; Silva, Fernando Carvalho da; Cardoso, Carlos Eduardo Santos

2000-01-01

The system of P1 equations is composed by two equations coupled itself one for the neutron flux and other for the current. Usually this system is solved by definitions of two integrals parameters, which are named slowing down densities of the flux and the current. Hence, the system P1 can be change from integral to only two differential equations. However, there are two new differentials equations that may be solved with the initial system. The present work analyzes this procedure and studies a method, which solve the P1 equations directly, without definitions of slowing down densities. (author)

Numerical study of fractional nonlinear Schrodinger equations

KAUST Repository

Klein, Christian; Sparber, Christof; Markowich, Peter A.

2014-01-01

Using a Fourier spectral method, we provide a detailed numerical investigation of dispersive Schrödinger-type equations involving a fractional Laplacian in an one-dimensional case. By an appropriate choice of the dispersive exponent, both mass

Incidence of chronic kidney disease among people with diabetes: a systematic review of observational studies.

Science.gov (United States)

Koye, D N; Shaw, J E; Reid, C M; Atkins, R C; Reutens, A T; Magliano, D J

2017-07-01

The aim was to systematically review published articles that reported the incidence of chronic kidney disease among people with diabetes. A systematic literature search was performed using MEDLINE, Embase and CINAHL databases. The titles and abstracts of all publications identified by the search were reviewed and 10 047 studies were retrieved. A total of 71 studies from 30 different countries with sample sizes ranging from 505 to 211 132 met the inclusion criteria. The annual incidence of microalbuminuria and albuminuria ranged from 1.3% to 3.8% for Type 1 diabetes. For Type 2 diabetes and studies combining both diabetes types, the range was from 3.8% to 12.7%, with four of six studies reporting annual rates between 7.4% and 8.6%. In studies reporting the incidence of eGFR Disease (MDRD) equation, apart from one study which reported an annual incidence of 8.9%, the annual incidence ranged from 1.9% to 4.3%. The annual incidence of end-stage renal disease ranged from 0.04% to 1.8%. The annual incidence of microalbuminuria and albuminuria is ~ 2-3% in Type 1 diabetes, and ~ 8% in Type 2 diabetes or mixed diabetes type. The incidence of developing eGFR kidney disease, there was only modest variation in incidence rates. These findings may be useful in clinical settings to help understand the risk of developing kidney disease among those with diabetes. © 2017 Diabetes UK.

Degenerate nonlinear diffusion equations

CERN Document Server

Favini, Angelo

2012-01-01

The aim of these notes is to include in a uniform presentation style several topics related to the theory of degenerate nonlinear diffusion equations, treated in the mathematical framework of evolution equations with multivalued m-accretive operators in Hilbert spaces. The problems concern nonlinear parabolic equations involving two cases of degeneracy. More precisely, one case is due to the vanishing of the time derivative coefficient and the other is provided by the vanishing of the diffusion coefficient on subsets of positive measure of the domain. From the mathematical point of view the results presented in these notes can be considered as general results in the theory of degenerate nonlinear diffusion equations. However, this work does not seek to present an exhaustive study of degenerate diffusion equations, but rather to emphasize some rigorous and efficient techniques for approaching various problems involving degenerate nonlinear diffusion equations, such as well-posedness, periodic solutions, asympt...

INVARIANTS OF GENERALIZED RAPOPORT-LEAS EQUATIONS

Directory of Open Access Journals (Sweden)

Elena N. Kushner

2018-01-01

Full Text Available For the generalized Rapoport-Leas equations, algebra of differential invariants is constructed with respect to point transformations, that is, transformations of independent and dependent variables. The finding of a general transformation of this type reduces to solving an extremely complicated functional equation. Therefore, following the approach of Sophus Lie, we restrict ourselves to the search for infinitesimal transformations which are generated by translations along the trajectories of vector fields. The problem of finding these vector fields reduces to the redefined system decision of linear differential equations with respect to their coefficients. The Rapoport-Leas equations arise in the study of nonlinear filtration processes in porous media, as well as in other areas of natural science: for example, these equations describe various physical phenomena: two-phase filtration in a porous medium, filtration of a polytropic gas, and propagation of heat at nuclear explosion. They are vital topic for research: in recent works of Bibikov, Lychagin, and others, the analysis of the symmetries of the generalized Rapoport-Leas equations has been carried out; finite-dimensional dynamics and conditions of attractors existence have been found. Since the generalized RapoportLeas equations are nonlinear partial differential equations of the second order with two independent variables; the methods of the geometric theory of differential equations are used to study them in this paper. According to this theory differential equations generate subvarieties in the space of jets. This makes it possible to use the apparatus of modern differential geometry to study differential equations. We introduce the concept of admissible transformations, that is, replacements of variables that do not derive equations outside the class of the Rapoport-Leas equations. Such transformations form a Lie group. For this Lie group there are differential invariants that separate

equateIRT: An R Package for IRT Test Equating

Directory of Open Access Journals (Sweden)

Michela Battauz

2015-12-01

Full Text Available The R package equateIRT implements item response theory (IRT methods for equating different forms composed of dichotomous items. In particular, the IRT models included are the three-parameter logistic model, the two-parameter logistic model, the one-parameter logistic model and the Rasch model. Forms can be equated when they present common items (direct equating or when they can be linked through a chain of forms that present common items in pairs (indirect or chain equating. When two forms can be equated through different paths, a single conversion can be obtained by averaging the equating coefficients. The package calculates direct and chain equating coefficients. The averaging of direct and chain coefficients that link the same two forms is performed through the bisector method. Furthermore, the package provides analytic standard errors of direct, chain and average equating coefficients.

Study on the creep constitutive equation of Hastelloy X, (1)

International Nuclear Information System (INIS)

Suzuki, Kazuhiko; Mutoh, Yasushi

1983-01-01

In order to carry out the structural design of high temperature pipings, intermediate heat exchangers and isolating valves for a multipurpose high temperature gas-cooled reactor, in which coolant temperature reaches 1000 deg C, the creep characteristics of Hastelloy X used as the heat resistant material must be clarified. In addition to usual creep rupture life and the time to reach a specified creep strain, the dependence of creep strain curves on time, temperature and stress must be determined and expressed with equations. Therefore, using the creep data of Hastelloy X given in the literatures, the creep constitutive equation was made. Since the creep strain curves under the same test condition were different according to heats, the sensitivity analysis of the creep constitutive equation was performed. The form of the creep constitutive equation was determined to be Garofalo type. The result of the sensitivity analysis is reported. (Kako, I.)

Quadratic Diophantine equations

CERN Document Server

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.

Analytic study of solutions for a (3 + 1) -dimensional generalized KP equation

Science.gov (United States)

Gao, Hui; Cheng, Wenguang; Xu, Tianzhou; Wang, Gangwei

2018-03-01

The (3 + 1) -dimensional generalized KP (gKP) equation is an important nonlinear partial differential equation in theoretical and mathematical physics which can be used to describe nonlinear wave motion. Through the Hirota bilinear method, one-solition, two-solition and N-solition solutions are derived via symbolic computation. Two classes of lump solutions, rationally localized in all directions in space, to the dimensionally reduced cases in (2 + 1)-dimensions, are constructed by using a direct method based on the Hirota bilinear form of the equation. It implies that we can derive the lump solutions of the reduced gKP equation from positive quadratic function solutions to the aforementioned bilinear equation. Meanwhile, we get interaction solutions between a lump and a kink of the gKP equation. The lump appears from a kink and is swallowed by it with the change of time. This work offers a possibility which can enrich the variety of the dynamical features of solutions for higher-dimensional nonlinear evolution equations.

Random walk and the heat equation

CERN Document Server

Lawler, Gregory F

2010-01-01

The heat equation can be derived by averaging over a very large number of particles. Traditionally, the resulting PDE is studied as a deterministic equation, an approach that has brought many significant results and a deep understanding of the equation and its solutions. By studying the heat equation by considering the individual random particles, however, one gains further intuition into the problem. While this is now standard for many researchers, this approach is generally not presented at the undergraduate level. In this book, Lawler introduces the heat equation and the closely related notion of harmonic functions from a probabilistic perspective. The theme of the first two chapters of the book is the relationship between random walks and the heat equation. The first chapter discusses the discrete case, random walk and the heat equation on the integer lattice; and the second chapter discusses the continuous case, Brownian motion and the usual heat equation. Relationships are shown between the two. For exa...

Complex centers of polynomial differential equations

Directory of Open Access Journals (Sweden)

Mohamad Ali M. Alwash

2007-07-01

Full Text Available We present some results on the existence and nonexistence of centers for polynomial first order ordinary differential equations with complex coefficients. In particular, we show that binomial differential equations without linear terms do not have complex centers. Classes of polynomial differential equations, with more than two terms, are presented that do not have complex centers. We also study the relation between complex centers and the Pugh problem. An algorithm is described to solve the Pugh problem for equations without complex centers. The method of proof involves phase plane analysis of the polar equations and a local study of periodic solutions.

A numerical study of adaptive space and time discretisations for Gross-Pitaevskii equations.

Science.gov (United States)

Thalhammer, Mechthild; Abhau, Jochen

2012-08-15

As a basic principle, benefits of adaptive discretisations are an improved balance between required accuracy and efficiency as well as an enhancement of the reliability of numerical computations. In this work, the capacity of locally adaptive space and time discretisations for the numerical solution of low-dimensional nonlinear Schrödinger equations is investigated. The considered model equation is related to the time-dependent Gross-Pitaevskii equation arising in the description of Bose-Einstein condensates in dilute gases. The performance of the Fourier-pseudo spectral method constrained to uniform meshes versus the locally adaptive finite element method and of higher-order exponential operator splitting methods with variable time stepsizes is studied. Numerical experiments confirm that a local time stepsize control based on a posteriori local error estimators or embedded splitting pairs, respectively, is effective in different situations with an enhancement either in efficiency or reliability. As expected, adaptive time-splitting schemes combined with fast Fourier transform techniques are favourable regarding accuracy and efficiency when applied to Gross-Pitaevskii equations with a defocusing nonlinearity and a mildly varying regular solution. However, the numerical solution of nonlinear Schrödinger equations in the semi-classical regime becomes a demanding task. Due to the highly oscillatory and nonlinear nature of the problem, the spatial mesh size and the time increments need to be of the size of the decisive parameter [Formula: see text], especially when it is desired to capture correctly the quantitative behaviour of the wave function itself. The required high resolution in space constricts the feasibility of numerical computations for both, the Fourier pseudo-spectral and the finite element method. Nevertheless, for smaller parameter values locally adaptive time discretisations facilitate to determine the time stepsizes sufficiently small in order that

Linear integral equations and soliton systems

International Nuclear Information System (INIS)

Quispel, G.R.W.

1983-01-01

A study is presented of classical integrable dynamical systems in one temporal and one spatial dimension. The direct linearizations are given of several nonlinear partial differential equations, for example the Korteweg-de Vries equation, the modified Korteweg-de Vries equation, the sine-Gordon equation, the nonlinear Schroedinger equation, and the equation of motion for the isotropic Heisenberg spin chain; the author also discusses several relations between these equations. The Baecklund transformations of these partial differential equations are treated on the basis of a singular transformation of the measure (or equivalently of the plane-wave factor) occurring in the corresponding linear integral equations, and the Baecklund transformations are used to derive the direct linearization of a chain of so-called modified partial differential equations. Finally it is shown that the singular linear integral equations lead in a natural way to the direct linearizations of various nonlinear difference-difference equations. (Auth.)

Computing generalized Langevin equations and generalized Fokker-Planck equations.

Science.gov (United States)

Darve, Eric; Solomon, Jose; Kia, Amirali

2009-07-07

The Mori-Zwanzig formalism is an effective tool to derive differential equations describing the evolution of a small number of resolved variables. In this paper we present its application to the derivation of generalized Langevin equations and generalized non-Markovian Fokker-Planck equations. We show how long time scales rates and metastable basins can be extracted from these equations. Numerical algorithms are proposed to discretize these equations. An important aspect is the numerical solution of the orthogonal dynamics equation which is a partial differential equation in a high dimensional space. We propose efficient numerical methods to solve this orthogonal dynamics equation. In addition, we present a projection formalism of the Mori-Zwanzig type that is applicable to discrete maps. Numerical applications are presented from the field of Hamiltonian systems.

Studying language change using price equation and Pólya-urn dynamics.

Science.gov (United States)

Gong, Tao; Shuai, Lan; Tamariz, Mónica; Jäger, Gerhard

2012-01-01

Language change takes place primarily via diffusion of linguistic variants in a population of individuals. Identifying selective pressures on this process is important not only to construe and predict changes, but also to inform theories of evolutionary dynamics of socio-cultural factors. In this paper, we advocate the Price equation from evolutionary biology and the Pólya-urn dynamics from contagion studies as efficient ways to discover selective pressures. Using the Price equation to process the simulation results of a computer model that follows the Pólya-urn dynamics, we analyze theoretically a variety of factors that could affect language change, including variant prestige, transmission error, individual influence and preference, and social structure. Among these factors, variant prestige is identified as the sole selective pressure, whereas others help modulate the degree of diffusion only if variant prestige is involved. This multidisciplinary study discerns the primary and complementary roles of linguistic, individual learning, and socio-cultural factors in language change, and offers insight into empirical studies of language change.

Novel equations to predict body fat percentage of Brazilian professional soccer players: A case study

Directory of Open Access Journals (Sweden)

Luiz Fernando Novack

2014-12-01

Full Text Available This study analyzed classical and developed novel mathematical models to predict body fat percentage (%BF in professional soccer players from the South Brazilian region using skinfold thicknesses measurement. Skinfolds of thirty one male professional soccer players (age of 21.48 ± 3.38 years, body mass of 79.05 ± 9.48 kg and height of 181.97 ± 8.11 cm were introduced into eight mathematical models from the literature for the prediction of %BF; these results were then compared to Dual-energy X-ray Absorptiometry (DXA. The classical equations were able to account from 65% to 79% of the variation of %BF in DXA. Statistical differences between most of the classical equations (seven of the eight classic equations and DXA were found, rendering their widespread use in this population useless. We developed three new equations for prediction of %BF with skinfolds from: axils, abdomen, thighs and calves. Theses equations accounted for 86.5% of the variation in %BF obtained with DXA.

Lie symmetries in differential equations

International Nuclear Information System (INIS)

Pleitez, V.

1979-01-01

A study of ordinary and Partial Differential equations using the symmetries of Lie groups is made. Following such a study, an application to the Helmholtz, Line-Gordon, Korleweg-de Vries, Burguer, Benjamin-Bona-Mahony and wave equations is carried out [pt

Sourcing for Parameter Estimation and Study of Logistic Differential Equation

Science.gov (United States)

Winkel, Brian J.

2012-01-01

This article offers modelling opportunities in which the phenomena of the spread of disease, perception of changing mass, growth of technology, and dissemination of information can be described by one differential equation--the logistic differential equation. It presents two simulation activities for students to generate real data, as well as…

Nuclear structure information studied through Dirac equation with deformed mean fields

International Nuclear Information System (INIS)

Dudek, J.

2000-01-01

Complete text of publication follows. Relativistic mean-field theory provides a formal expression for the Dirac equation for the nucleonic motion in an atomic nucleus. The 'potentials' within such a formalism are given in terms of the meson fields, the latter obtained through a coupled system of equations of the Klein-Grodon type. Usually the whole system is being solved by using a Hartree approximation by employing an iterative selfonsistent algorithms. On a more phenomenological level one can parametrize the potentials that enter into a Dirac equation rather than obtain the selfconsistently; such a simplification was suggested some time ago by the Munich group. We introduce a Woods-Saxon type parametrisation and verify by a non-linear search routine what are the 'best fit potential parameters' that reproduce the single particle excitations in the double-magic spherical nuclei as well as the band-head properties in some hundreds of deformed nuclei. Next, by introducing a low-energy reduction of the Dirac equation, one may obtain in a natural way a Pauli Schrodinger type equation with a position dependent effective mass. The role of the corresponding term in a description of single particle energies of the nucleons is illustrated and the implications for the cranking equation are discussed in some detail. (author)

Parallels between control PDE's (Partial Differential Equations) and systems of ODE's (Ordinary Differential Equations)

Science.gov (United States)

Hunt, L. R.; Villarreal, Ramiro

1987-01-01

System theorists understand that the same mathematical objects which determine controllability for nonlinear control systems of ordinary differential equations (ODEs) also determine hypoellipticity for linear partial differentail equations (PDEs). Moreover, almost any study of ODE systems begins with linear systems. It is remarkable that Hormander's paper on hypoellipticity of second order linear p.d.e.'s starts with equations due to Kolmogorov, which are shown to be analogous to the linear PDEs. Eigenvalue placement by state feedback for a controllable linear system can be paralleled for a Kolmogorov equation if an appropriate type of feedback is introduced. Results concerning transformations of nonlinear systems to linear systems are similar to results for transforming a linear PDE to a Kolmogorov equation.

Fundamental equations for two-phase flow. Part 1: general conservation equations. Part 2: complement and remarks; Equations fondamentales des ecoulements diphasiques. Premiere partie: equations generales de conservation. Deuxieme partie: complements et remarques

Energy Technology Data Exchange (ETDEWEB)

Delhaye, J M [Commissariat a l' Energie Atomique, 38 - Grenoble (France). Centre d' Etudes Nucleaires

1968-12-01

This report deals with the general equations of mass conservation, of momentum conservation, and energy conservation in the case of a two-phase flow. These equations are presented in several forms starting from integral equations which are assumed initially a priori. 1. Equations with local instantaneous variables, and interfacial conditions; 2. Equations with mean instantaneous variables in a cross-section, and practical applications: these equations include an important experimental value which is the ratio of the cross-section of passage of one phase to the total cross-section of a flow-tube. 3. Equations with a local statistical mean, and equations averaged over a period of time: A more advanced attempt to relate theory and experiment consists in taking the statistical averages of local equations. Equations are then obtained involving variables which are averaged over a period of time with the help of an ergodic assumption. 4. Combination of statistical averages and averages over a cross-section: in this study are considered the local variables averaged statistically, then averaged over the cross-section, and also the variables averaged over the section and then averaged statistically. 5. General equations concerning emulsions: In this case a phase exists in a locally very finely divided form. This peculiarity makes it possible to define a volume concentration, and to draw up equations which have numerous applications. - Certain points arising in the first part of this report concerning general mass conservation equations for two-phase flow have been completed and clarified. The terms corresponding to the interfacial tension have been introduced into the general equations. The interfacial conditions have thus been generalized. A supplementary step has still to be carried out: it has, in effect, been impossible to take the interfacial tension into account in the case of emulsions. It was then appeared interesting to compare this large group of fundamental

Fundamental equations for two-phase flow. Part 1: general conservation equations. Part 2: complement and remarks; Equations fondamentales des ecoulements diphasiques. Premiere partie: equations generales de conservation. Deuxieme partie: complements et remarques

Energy Technology Data Exchange (ETDEWEB)

Delhaye, J.M. [Commissariat a l' Energie Atomique, 38 - Grenoble (France). Centre d' Etudes Nucleaires

1968-12-01

This report deals with the general equations of mass conservation, of momentum conservation, and energy conservation in the case of a two-phase flow. These equations are presented in several forms starting from integral equations which are assumed initially a priori. 1. Equations with local instantaneous variables, and interfacial conditions; 2. Equations with mean instantaneous variables in a cross-section, and practical applications: these equations include an important experimental value which is the ratio of the cross-section of passage of one phase to the total cross-section of a flow-tube. 3. Equations with a local statistical mean, and equations averaged over a period of time: A more advanced attempt to relate theory and experiment consists in taking the statistical averages of local equations. Equations are then obtained involving variables which are averaged over a period of time with the help of an ergodic assumption. 4. Combination of statistical averages and averages over a cross-section: in this study are considered the local variables averaged statistically, then averaged over the cross-section, and also the variables averaged over the section and then averaged statistically. 5. General equations concerning emulsions: In this case a phase exists in a locally very finely divided form. This peculiarity makes it possible to define a volume concentration, and to draw up equations which have numerous applications. - Certain points arising in the first part of this report concerning general mass conservation equations for two-phase flow have been completed and clarified. The terms corresponding to the interfacial tension have been introduced into the general equations. The interfacial conditions have thus been generalized. A supplementary step has still to be carried out: it has, in effect, been impossible to take the interfacial tension into account in the case of emulsions. It was then appeared interesting to compare this large group of fundamental

Exact results for the Boltzmann equation and Smoluchowski's coagulation equation

International Nuclear Information System (INIS)

Hendriks, E.M.

1983-01-01

Almost no analytical solutions have been found for realistic intermolecular forces, largely due to the complicated structure of the collision term which calls for the construction of simplified models, in which as many physical properties are maintained as possible. In the first three chapters of this thesis such model Boltzmann equations are studied. Only spatially homogeneous gases with isotropic distribution functions are considered. Chapter I considers transition kernels, chapter II persistent scattering models and chapter III very hard particles. The second part of this dissertation deals with Smoluchowski's coagulation equation for the size distribution function in a coagulating system, with chapters devoted to the following topics: kinetics of gelation and universality, coagulation equations with gelation and exactly soluble models of nucleation. (Auth./C.F.)

Differential equations I essentials

CERN Document Server

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.

Monge-Ampere equations and tensorial functors

International Nuclear Information System (INIS)

Tunitsky, Dmitry V

2009-01-01

We consider differential-geometric structures associated with Monge-Ampere equations on manifolds and use them to study the contact linearization of such equations. We also consider the category of Monge-Ampere equations (the morphisms are contact diffeomorphisms) and a number of subcategories. We are chiefly interested in subcategories of Monge-Ampere equations whose objects are locally contact equivalent to equations linear in the second derivatives (semilinear equations), linear in derivatives, almost linear, linear in the second derivatives and independent of the first derivatives, linear, linear and independent of the first derivatives, equations with constant coefficients or evolution equations. We construct a number of functors from the category of Monge-Ampere equations and from some of its subcategories to the category of tensorial objects (that is, multi-valued sections of tensor bundles). In particular, we construct a pseudo-Riemannian metric for every generic Monge-Ampere equation. These functors enable us to establish effectively verifiable criteria for a Monge-Ampere equation to belong to the subcategories listed above.

Comparative study of the two-fluid momentum equations for multi-dimensional bubbly flows: Modification of Reynolds stress

Energy Technology Data Exchange (ETDEWEB)

Lee, Seung Jun; Park, Ik Kyu; Yoon, Han Young [Thermal-Hydraulic Safety Research Division, Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of); Jae, Byoung [School of Mechanical Engineering, Chungnam National University, Daejeon (Korea, Republic of)

2017-01-15

Two-fluid equations are widely used to obtain averaged behaviors of two-phase flows. This study addresses a problem that may arise when the two-fluid equations are used for multi-dimensional bubbly flows. If steady drag is the only accounted force for the interfacial momentum transfer, the disperse-phase velocity would be the same as the continuous-phase velocity when the flow is fully developed without gravity. However, existing momentum equations may show unphysical results in estimating the relative velocity of the disperse phase against the continuous-phase. First, we examine two types of existing momentum equations. One is the standard two-fluid momentum equation in which the disperse-phase is treated as a continuum. The other is the averaged momentum equation derived from a solid/ fluid particle motion. We show that the existing equations are not proper for multi-dimensional bubbly flows. To resolve the problem mentioned above, we modify the form of the Reynolds stress terms in the averaged momentum equation based on the solid/fluid particle motion. The proposed equation shows physically correct results for both multi-dimensional laminar and turbulent flows.

A critical assessment of capillary condensation and evaporation equations: a computer simulation study.

Science.gov (United States)

Wongkoblap, A; Do, D D; Birkett, G; Nicholson, D

2011-04-15

Grand Canonical Monte Carlo simulation (GCMC) is used to study the capillary condensation and evaporation of argon adsorption in finite-length carbon cylindrical nanopores. From the simulation results of local density distributions in the radial and axial directions we obtain the contact angle and the core radii just before condensation and just after evaporation. These are then used in the Kelvin equation (evaporation) and Cohan equation (condensation) to obtain the product of surface tension and liquid molar volume. This product is found to be always greater than for the bulk liquid. We test this deviation with pores of different length and radius and find that both affect the derived product of surface tension and liquid molar volume. The implication of this finding is that if the values of surface tension and liquid molar volume of the bulk phase are used in the Kelvin equation the pore radius will be underestimated. For argon adsorption in cylindrical pores we propose that the Kelvin and Cohan equations should be modified to take account of the difference between the fluid in the adsorbed phase in the confined space and that in the bulk phase. Copyright © 2011 Elsevier Inc. All rights reserved.

About the solvability of matrix polynomial equations

OpenAIRE

Netzer, Tim; Thom, Andreas

2016-01-01

We study self-adjoint matrix polynomial equations in a single variable and prove existence of self-adjoint solutions under some assumptions on the leading form. Our main result is that any self-adjoint matrix polynomial equation of odd degree with non-degenerate leading form can be solved in self-adjoint matrices. We also study equations of even degree and equations in many variables.

An interpolation between the wave and diffusion equations through the fractional evolution equations Dirac like

International Nuclear Information System (INIS)

Pierantozzi, T.; Vazquez, L.

2005-01-01

Through fractional calculus and following the method used by Dirac to obtain his well-known equation from the Klein-Gordon equation, we analyze a possible interpolation between the Dirac and the diffusion equations in one space dimension. We study the transition between the hyperbolic and parabolic behaviors by means of the generalization of the D'Alembert formula for the classical wave equation and the invariance under space and time inversions of the interpolating fractional evolution equations Dirac like. Such invariance depends on the values of the fractional index and is related to the nonlocal property of the time fractional differential operator. For this system of fractional evolution equations, we also find an associated conserved quantity analogous to the Hamiltonian for the classical Dirac case

Simple equation method for nonlinear partial differential equations and its applications

Directory of Open Access Journals (Sweden)

Taher A. Nofal

2016-04-01

Full Text Available In this article, we focus on the exact solution of the some nonlinear partial differential equations (NLPDEs such as, Kodomtsev–Petviashvili (KP equation, the (2 + 1-dimensional breaking soliton equation and the modified generalized Vakhnenko equation by using the simple equation method. In the simple equation method the trial condition is the Bernoulli equation or the Riccati equation. It has been shown that the method provides a powerful mathematical tool for solving nonlinear wave equations in mathematical physics and engineering problems.

Development of a predictive energy equation for maintenance hemodialysis patients: a pilot study.

Science.gov (United States)

Byham-Gray, Laura; Parrott, J Scott; Ho, Wai Yin; Sundell, Mary B; Ikizler, T Alp

2014-01-01

The study objectives were to explore the predictors of measured resting energy expenditure (mREE) among a sample of maintenance hemodialysis (MHD) patients, to generate a predictive energy equation (MHDE), and to compare such models to another commonly used predictive energy equation in nutritional care, the Mifflin-St. Jeor equation (MSJE). The study was a retrospective, cross-sectional cohort design conducted at the Vanderbilt University Medical Center. Study subjects were adult MHD patients (N = 67). Data collected from several clinical trials were analyzed using Pearson's correlation and multivariate linear regression procedures. Demographic, anthropometric, clinical, and laboratory data were examined as potential predictors of mREE. Limits of agreement between the MHDE and the MSJE were evaluated using Bland-Altman plots. The a priori α was set at P lean body mass [LBM]) of mREE included (R(2) = 0.489) FFM, ALB, age, and CRP. Two additional models (MHDE-CRP and MHDE-CR) with acceptable predictability (R(2) = 0.460 and R(2) = 0.451) were derived to improve the clinical utility of the developed energy equation (MHDE-LBM). Using Bland-Altman plots, the MHDE over- and underpredicted mREE less often than the MSJE. Predictive models (MHDE) including selective demographic, clinical, and anthropometric data explained less than 50% variance of mREE but had better precision in determining energy requirements for MHD patients when compared with MSJE. Further research is necessary to improve predictive models of mREE in the MHD population and to test its validity and clinical application. Copyright © 2014 National Kidney Foundation, Inc. Published by Elsevier Inc. All rights reserved.

Series solutions to partial differential equations. A study of the singularities, expansions, and solutions of Schroedinger's equation for the helium atom

International Nuclear Information System (INIS)

Mahlab, M.S.

1975-01-01

All the presently available techniques for solving Schroedinger's differential equation for helium-like atoms display poor convergence of the wave function in the neighborhood of the singularities of the Hamiltonian operator. In general most of the methods of solving this equation will converge in the appropriate limit to the exact wave function; however, convergence is slow, especially near the singularities of this differential equation. These difficulties become readily apparent from local energy studies. A technique is presented that avoids these difficulties. The wave function it produces is specifically most accurate at the singularities of the Hamiltonian. The novel aspect of this treatment is the subdivision of the space spanned by the wave function. Different expansions are picked such that they converge rapidly in each of the different subdivisions. These expansions may be constructed in such a way that they obey the boundary conditions in their respective subdivision. Most importantly, all the information available from the recursion relations associated with the differential equation may be incorporated into these expansions. A systematic procedure is presented such that these expansions may be brought together to form a wave function that satisfies all the continuity requirements. An S-state helium wave function was constructed to demonstrate that this method of treatment is feasible, and capable of indefinite systematic improvement. A discussion of several new asymptotic expansions that were constructed for the helium wave function, as well as an improved functional form for the small electron-nucleus wave function, is included in this presentation

Some remarks on unilateral matrix equations

International Nuclear Information System (INIS)

Cerchiai, Bianca L.; Zumino, Bruno

2001-01-01

We briefly review the results of our paper LBNL-46775: We study certain solutions of left-unilateral matrix equations. These are algebraic equations where the coefficients and the unknown are square matrices of the same order, or, more abstractly, elements of an associative, but possibly noncommutative algebra, and all coefficients are on the left. Recently such equations have appeared in a discussion of generalized Born-Infeld theories. In particular, two equations, their perturbative solutions and the relation between them are studied, applying a unified approach based on the generalized Bezout theorem for matrix polynomials

Study of a Model Equation in Detonation Theory

KAUST Repository

Faria, Luiz

2014-04-24

Here we analyze properties of an equation that we previously proposed to model the dynamics of unstable detonation waves [A. R. Kasimov, L. M. Faria, and R. R. Rosales, Model for shock wave chaos, Phys. Rev. Lett., 110 (2013), 104104]. The equation is ut+ 1/2 (u2-uu (0-, t))x=f (x, u (0-, t)), x > 0, t < 0. It describes a detonation shock at x = 0 with the reaction zone in x > 0. We investigate the nature of the steady-state solutions of this nonlocal hyperbolic balance law, the linear stability of these solutions, and the nonlinear dynamics. We establish the existence of instability followed by a cascade of period-doubling bifurcations leading to chaos. © 2014 Society for Industrial and Applied Mathematics.

Dealing with Dependent Uncertainty in Modelling: A Comparative Study Case through the Airy Equation

Directory of Open Access Journals (Sweden)

J.-C. Cortés

2013-01-01

Full Text Available The consideration of uncertainty in differential equations leads to the emergent area of random differential equations. Under this approach, inputs become random variables and/or stochastic processes. Often one assumes that inputs are independent, a hypothesis that simplifies the mathematical treatment although it could not be met in applications. In this paper, we analyse, through the Airy equation, the influence of statistical dependence of inputs on the output, computing its expectation and standard deviation by Fröbenius and Polynomial Chaos methods. The results are compared with Monte Carlo sampling. The analysis is conducted by the Airy equation since, as in the deterministic scenario its solutions are highly oscillatory, it is expected that differences will be better highlighted. To illustrate our study, and motivated by the ubiquity of Gaussian random variables in numerous practical problems, we assume that inputs follow a multivariate Gaussian distribution throughout the paper. The application of Fröbenius method to solve Airy equation is based on an extension of the method to the case where inputs are dependent. The numerical results show that the existence of statistical dependence among the inputs and its magnitude entails changes on the variability of the output.

Extended rate equations

International Nuclear Information System (INIS)

Shore, B.W.

1981-01-01

The equations of motion are discussed which describe time dependent population flows in an N-level system, reviewing the relationship between incoherent (rate) equations, coherent (Schrodinger) equations, and more general partially coherent (Bloch) equations. Approximations are discussed which replace the elaborate Bloch equations by simpler rate equations whose coefficients incorporate long-time consequences of coherence

On Volatility Induced Stationarity for Stochastic Differential Equations

DEFF Research Database (Denmark)

Albin, J.M.P.; Astrup Jensen, Bjarne; Muszta, Anders

2006-01-01

This article deals with stochastic differential equations with volatility induced stationarity. We study of theoretical properties of such equations, as well as numerical aspects, together with a detailed study of three examples.......This article deals with stochastic differential equations with volatility induced stationarity. We study of theoretical properties of such equations, as well as numerical aspects, together with a detailed study of three examples....

Augmented renal clearance is not a risk factor for mortality in Enterobacteriaceae bloodstream infections treated with appropriate empiric antimicrobials.

Science.gov (United States)

Burnham, Jason P; Micek, Scott T; Kollef, Marin H

2017-01-01

The main objective of the study was to assess whether augmented renal clearance was a risk factor for mortality in a cohort of patients with Enterobacteriaceae sepsis, severe sepsis, or septic shock that all received appropriate antimicrobial therapy within 12 hours. Using a retrospective cohort from Barnes-Jewish Hospital, a 1,250-bed teaching hospital, we collected data on individuals with Enterobacteriaceae sepsis, severe sepsis, and septic shock who received appropriate initial antimicrobial therapy between June 2009 and December 2013. Clinical outcomes were compared according to renal clearance, as assessed by Modification of Diet in Renal Disease (MDRD) and Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) formulas, sepsis classification, demographics, severity of illness, and comorbidities. We identified 510 patients with Enterobacteriaceae bacteremia and sepsis, severe sepsis, or septic shock. Sixty-seven patients (13.1%) were nonsurvivors. Augmented renal clearance was uncommon (5.1% of patients by MDRD and 3.0% by CKD-EPI) and was not associated with increased mortality. Our results are limited by the absence of prospective determination of augmented renal clearance. However, in this small cohort, augmented renal clearance as assessed by MDRD and CKD-EPI does not seem to be a risk factor for mortality in patients with Enterobacteriaceae sepsis. Future studies should assess this finding prospectively.

Attractors for equations of mathematical physics

CERN Document Server

Chepyzhov, Vladimir V

2001-01-01

One of the major problems in the study of evolution equations of mathematical physics is the investigation of the behavior of the solutions to these equations when time is large or tends to infinity. The related important questions concern the stability of solutions or the character of the instability if a solution is unstable. In the last few decades, considerable progress in this area has been achieved in the study of autonomous evolution partial differential equations. For a number of basic evolution equations of mathematical physics, it was shown that the long time behavior of their soluti

Nonlinear hydrodynamic equations for superfluid helium in aerogel

International Nuclear Information System (INIS)

Brusov, Peter N.; Brusov, Paul P.

2003-01-01

Aerogel in superfluids is studied very intensively during last decade. The importance of these systems is connected to the fact that this allows to investigate the influence of impurities on superfluidity. We have derived for the first time nonlinear hydrodynamic equations for superfluid helium in aerogel. These equations are generalization of McKenna et al. equations for nonlinear hydrodynamics case and could be used to study sound propagation phenomena in aerogel-superfluid system, in particular--to study sound conversion phenomena. We have obtained two alternative sets of equations, one of which is a generalization of a traditional set of nonlinear hydrodynamics equations for the case of an aerogel-superfluid system and, the other one represents a la Putterman equations (equation for v→ s is replaced by equation for A→=((ρ n )/(ρσ))w→, where w→=v→ n -v→ s )

Fundamental equations for two-phase flow. Part 1: general conservation equations. Part 2: complement and remarks

International Nuclear Information System (INIS)

Delhaye, J.M.

1968-12-01

This report deals with the general equations of mass conservation, of momentum conservation, and energy conservation in the case of a two-phase flow. These equations are presented in several forms starting from integral equations which are assumed initially a priori. 1. Equations with local instantaneous variables, and interfacial conditions; 2. Equations with mean instantaneous variables in a cross-section, and practical applications: these equations include an important experimental value which is the ratio of the cross-section of passage of one phase to the total cross-section of a flow-tube. 3. Equations with a local statistical mean, and equations averaged over a period of time: A more advanced attempt to relate theory and experiment consists in taking the statistical averages of local equations. Equations are then obtained involving variables which are averaged over a period of time with the help of an ergodic assumption. 4. Combination of statistical averages and averages over a cross-section: in this study are considered the local variables averaged statistically, then averaged over the cross-section, and also the variables averaged over the section and then averaged statistically. 5. General equations concerning emulsions: In this case a phase exists in a locally very finely divided form. This peculiarity makes it possible to define a volume concentration, and to draw up equations which have numerous applications. - Certain points arising in the first part of this report concerning general mass conservation equations for two-phase flow have been completed and clarified. The terms corresponding to the interfacial tension have been introduced into the general equations. The interfacial conditions have thus been generalized. A supplementary step has still to be carried out: it has, in effect, been impossible to take the interfacial tension into account in the case of emulsions. It was then appeared interesting to compare this large group of fundamental

ON DIFFERENTIAL EQUATIONS, INTEGRABLE SYSTEMS, AND GEOMETRY

OpenAIRE

Enrique Gonzalo Reyes Garcia

2004-01-01

ON DIFFERENTIAL EQUATIONS, INTEGRABLE SYSTEMS, AND GEOMETRY Equations in partial derivatives appeared in the 18th century as essential tools for the analytic study of physical models and, later, they proved to be fundamental for the progress of mathematics. For example, fundamental results of modern differential geometry are based on deep theorems on differential equations. Reciprocally, it is possible to study differential equations through geometrical means just like it was done by o...

On matrix fractional differential equations

Directory of Open Access Journals (Sweden)

Adem Kılıçman

2017-01-01

Full Text Available The aim of this article is to study the matrix fractional differential equations and to find the exact solution for system of matrix fractional differential equations in terms of Riemann–Liouville using Laplace transform method and convolution product to the Riemann–Liouville fractional of matrices. Also, we show the theorem of non-homogeneous matrix fractional partial differential equation with some illustrative examples to demonstrate the effectiveness of the new methodology. The main objective of this article is to discuss the Laplace transform method based on operational matrices of fractional derivatives for solving several kinds of linear fractional differential equations. Moreover, we present the operational matrices of fractional derivatives with Laplace transform in many applications of various engineering systems as control system. We present the analytical technique for solving fractional-order, multi-term fractional differential equation. In other words, we propose an efficient algorithm for solving fractional matrix equation.

Integral equations and their applications

CERN Document Server

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...

Cystatin C levels in healthy kidney donors and its correlation with GFR by creatinine clearance

International Nuclear Information System (INIS)

Ayub, S.; Khan, S.; Zafar, M.N.

2014-01-01

Objective: To determine Serum Cystatin C (S.CysC) levels in healthy potential kidney donors and its correlation with Serum Creatinine (S.Cr), Glomerular filtration rate (GFR) by 24 hour urinary Creatinine clearance (CCL) and GFR by formulae of Cockcroft Gault (CCG) and Modification of diet in Renal Disease (MDRD). Methods: A Cross sectional study was conducted at Sindh Institute of Urology and Transplantation (SIUT), Karachi, between June and December 2012. One hundred and three potential healthy kidney donors were enrolled in the study to measure their S.CysC and correlate it with S.Cr, CCL and GFR by CCG and MDRD. Statistical analysis was done by SPSS 17. Results: The mean age of the healthy kidney donors was 32.19+8.27 years with a M:F ratio of 1.86:1. The mean Serum Creatinine (S.Cr) was 0.86+0.18 mg/dl and mean S.CysC was 0.88+0.12 mg/dl. S.CysC showed significant correlation with S.Cr (r = 0.78, p<0.001), CCL (r = 0.67, p<0.001), GFR CCG (r = 0.54, p<0.001) and GFR MDRD (r = 0.67, p<0.001). Correlation of S.CysC was better than S.Cr for CCL, S.Cr (0.60) vs S.CysC (0.67) and GFR CCG, S.Cr (0.41) vs S.CysC (0.54). Correlation was comparable for MDRD, S.Cr (0.67) vs S.Cys (0.67). Conclusion: S.CysC is better marker of kidney function in potential healthy kidney donors. It is a reliable, convenient and economical marker that can be used especially in routine clinical practice. (author)

Studies on the movement of radioactive debris across the equator

International Nuclear Information System (INIS)

Rangarajan, C.; Gopalakrishnan, S.

1975-01-01

Short-lived fission products from the French tests of Polynesia (22 0 S) carried out during the summer period 1966-1971 have indicated a travel time of 15-21 days to the west coast of India. It has also been noted that the levels of activity on the west coast of India are an order of magnitude higher than at other areas of the northern hemisphere. Comparison with the activity from the Chinese tests of northern hemisphere (40 0 N) shows that the levels on the west coast of India are comparable to other areas of the northern hemisphere. From these data it can be concluded that there is a heavy influx of air masses across the equator in the West Indian Ocean by way of the monsoon. An idea of the magnitude of this influx can be had by comparing the levels at Bombay and Thumba with those at Pretoria. It is also concluded from these studies that the source of the summer monsoon should be to the south of the equator. (author)

Numerical Solution of Heun Equation Via Linear Stochastic Differential Equation

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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.

A comparative study of diffraction of shallow-water waves by high-level IGN and GN equations

Energy Technology Data Exchange (ETDEWEB)

Zhao, B.B. [College of Shipbuilding Engineering, Harbin Engineering University, 150001 Harbin (China); Ertekin, R.C. [Department of Ocean and Resources Engineering, University of Hawai' i, Honolulu, HI 96822 (United States); College of Shipbuilding Engineering, Harbin Engineering University, 150001 Harbin (China); Duan, W.Y., E-mail: duanwenyangheu@hotmail.com [College of Shipbuilding Engineering, Harbin Engineering University, 150001 Harbin (China)

2015-02-15

This work is on the nonlinear diffraction analysis of shallow-water waves, impinging on submerged obstacles, by two related theories, namely the classical Green–Naghdi (GN) equations and the Irrotational Green–Naghdi (IGN) equations, both sets of equations being at high levels and derived for incompressible and inviscid flows. Recently, the high-level Green–Naghdi equations have been applied to some wave transformation problems. The high-level IGN equations have also been used in the last decade to study certain wave propagation problems. However, past works on these theories used different numerical methods to solve these nonlinear and unsteady sets of differential equations and at different levels. Moreover, different physical problems have been solved in the past. Therefore, it has not been possible to understand the differences produced by these two sets of theories and their range of applicability so far. We are thus motivated to make a direct comparison of the results produced by these theories by use of the same numerical method to solve physically the same wave diffraction problems. We focus on comparing these two theories by using similar codes; only the equations used are different but other parts of the codes, such as the wave-maker, damping zone, discretion method, matrix solver, etc., are exactly the same. This way, we eliminate many potential sources of differences that could be produced by the solution of different equations. The physical problems include the presence of various submerged obstacles that can be used for example as breakwaters or to represent the continental shelf. A numerical wave tank is created by placing a wavemaker on one end and a wave absorbing beach on the other. The nonlinear and unsteady sets of differential equations are solved by the finite-difference method. The results are compared with different equations as well as with the available experimental data.

Rayleigh-Plesset equation of the bubble stable cavitation in water: A nonequilibrium all-atom molecular dynamics simulation study

Science.gov (United States)

Man, Viet Hoang; Li, Mai Suan; Derreumaux, Philippe; Nguyen, Phuong H.

2018-03-01

The Rayleigh-Plesset (RP) equation was derived from the first principles to describe the bubble cavitation in liquids in terms of macroscopic hydrodynamics. A number of nonequilibrium molecular dynamics studies have been carried out to validate this equation in describing the bubble inertial cavitation, but their results are contradictory and the applicability of the RP equation still remains to be examined, especially for the stable cavitation. In this work, we carry out nonequilibrium all-atom simulation to validate the applicability of the RP equation in the description of the stable cavitation of nano-sized bubbles in water. We show that although microscopic effects are not explicitly included, this equation still describes the dynamics of subnano-bubbles quite well as long as the contributions of various terms including inertial, surface tension, and viscosity are correctly taken into account. These terms are directly and inversely proportional to the amplitude and period of the cavitation, respectively. Thus, their contributions to the RP equation depend on these two parameters. This may explain the discrepancy between the current results obtained using different parameters. Finally, the accuracy of the RP equation in the current mathematical modeling studies of the ultrasound-induced blood-brain-barrier experiments is discussed in some detail.

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.

Lean body mass-based standardized uptake value, derived from a predictive equation, might be misleading in PET studies

International Nuclear Information System (INIS)

Erselcan, Taner; Turgut, Bulent; Dogan, Derya; Ozdemir, Semra

2002-01-01

The standardized uptake value (SUV) has gained recognition in recent years as a semiquantitative evaluation parameter in positron emission tomography (PET) studies. However, there is as yet no consensus on the way in which this index should be determined. One of the confusing factors is the normalisation procedure. Among the proposed anthropometric parameters for normalisation is lean body mass (LBM); LBM has been determined by using a predictive equation in most if not all of the studies. In the present study, we assessed the degree of agreement of various LBM predictive equations with a reference method. Secondly, we evaluated the impact of predicted LBM values on a hypothetical value of 2.5 SUV, normalised to LBM (SUV LBM ), by using various equations. The study population consisted of 153 women, aged 32.3±11.8 years (mean±SD), with a height of 1.61±0.06 m, a weight of 71.1±17.5 kg, a body surface area of 1.77±0.22 m 2 and a body mass index of 27.6±6.9 kg/m 2 . LBM (44.2±6.6 kg) was measured by a dual-energy X-ray absorptiometry (DEXA) method. A total of nine equations from the literature were evaluated, four of them from recent PET studies. Although there was significant correlation between predicted and measured LBM values, 95% limits of agreement determined by the Bland and Altman method showed a wide range of variation in predicted LBM values as compared with DEXA, no matter which predictive equation was used. Moreover, only one predictive equation was not statistically different in the comparison of means (DEXA and predicted LBM values). It was also shown that the predictive equations used in this study yield a wide range of SUV LBM values from 1.78 to 5.16 (29% less or 107% more) for an SUV of 2.5. In conclusion, this study suggests that estimation of LBM by use of a predictive equation may cause substantial error for an individual, and that if LBM is chosen for the SUV normalisation procedure, it should be measured, not predicted. (orig.)

Community-based study on CKD subjects and the associated risk factors.

Science.gov (United States)

Chen, Nan; Wang, Weiming; Huang, Yanping; Shen, Pingyan; Pei, Daoling; Yu, Haijin; Shi, Hao; Zhang, Qianying; Xu, Jing; Lv, Yilun; Fan, Qishi

2009-07-01

The study was performed to investigate the prevalence, awareness and the risk factors of chronic kidney disease (CKD) in the community population in Shanghai, China. A total of 2596 residents were randomly recruited from the community population in Shanghai, China. All were screened for albuminuria, haematuria, morning spot urine albumin-to-creatinine ratio and renal function. Serum creatinine, uric acid, cholesterol, triglyceride and haemoglobin were assessed. A simplified MDRD equation was used to estimate the glomerular filtration rate (eGFR). All studied subjects were screened by kidney ultrasound. Haematuria, if present in the morning spot urine dipstick test, was confirmed by microscopy. The associations among the demographic characteristics, health characteristics and indicators of kidney damage were examined. Two thousand five hundred and fifty-four residents (n = 2554), after giving informed consent and with complete data, were entered into this study. Albuminuria and haematuria were detected in 6.3% and 1.2% of all the studied subjects, respectively, whereas decreased kidney function was found in 5.8% of all studied subjects. Approximately 11.8% of subjects had at least one indicator of kidney damage. The rate of awareness of CKD was 8.2%. The logistic regression model showed that age, central obesity, hypertension, diabetes, anaemia, hyperuricaemia and nephrolithiasis each contributed to the development of CKD. This is the first Shanghai community-based epidemiological study data on Chinese CKD patients. The prevalence of CKD in the community population in Shanghai is 11.8%, and the rate of awareness of CKD is 8.2%. All the factors including age, central obesity, hypertension, diabetes, anaemia, hyperuricaemia and nephrolithiasis are positively correlated with the development of CKD in our studied subjects.

A generalization of the simplest equation method and its application to (3+1)-dimensional KP equation and generalized Fisher equation

International Nuclear Information System (INIS)

Zhao, Zhonglong; Zhang, Yufeng; Han, Zhong; Rui, Wenjuan

2014-01-01

In this paper, the simplest equation method is used to construct exact traveling solutions of the (3+1)-dimensional KP equation and generalized Fisher equation. We summarize the main steps of the simplest equation method. The Bernoulli and Riccati equation are used as simplest equations. This method is straightforward and concise, and it can be applied to other nonlinear partial differential equations

Alternative equations of gravitation

International Nuclear Information System (INIS)

Pinto Neto, N.

1983-01-01

It is shown, trough a new formalism, that the quantum fluctuation effects of the gravitational field in Einstein's equations are analogs to the effects of a continuum medium in Maxwell's Electrodynamics. Following, a real example of the applications of these equations is studied. Qunatum fluctuations effects as perturbation sources in Minkowski and Friedmann Universes are examined. (L.C.) [pt

Solution of radial spin-1 field equation in Robertson-Walker space-time via Heun's equation

International Nuclear Information System (INIS)

Zecca, A.

2010-01-01

The spin-1 field equation is considered in Robertson-Walker spacetime. The problem of the solution of the separated radial equations, previously discussed in the flat space-time case, is solved also for both the closed and open curvature case. The radial equation is reduced to Heun's differential equation that recently has been widely reconsidered. It is shown that the solution of the present Heun equation does not fall into the class of polynomial-like or hypergeometric functions. Heun's operator results also non-factorisable. The properties follow from application of general theorems and power series expansion. In the positive curvature case of the universe a discrete energy spectrum of the system is found. The result follows by requiring a polynomial-like behaviour of at least one component of the spinor field. Developments and applications of the theory suggest further study of the solution of Heun's equation.

Study of the Bellman equation in a production model with unstable demand

Science.gov (United States)

Obrosova, N. K.; Shananin, A. A.

2014-09-01

A production model with allowance for a working capital deficit and a restricted maximum possible sales volume is proposed and analyzed. The study is motivated by the urgency of analyzing well-known problems of functioning low competitive macroeconomic structures. The original formulation of the task represents an infinite-horizon optimal control problem. As a result, the model is formalized in the form of a Bellman equation. It is proved that the corresponding Bellman operator is a contraction and has a unique fixed point in the chosen class of functions. A closed-form solution of the Bellman equation is found using the method of steps. The influence of the credit interest rate on the firm market value assessment is analyzed by applying the developed model.

Analysis of discrete reaction-diffusion equations for autocatalysis and continuum diffusion equations for transport

Energy Technology Data Exchange (ETDEWEB)

Wang, Chi-Jen [Iowa State Univ., Ames, IA (United States)

2013-01-01

In this thesis, we analyze both the spatiotemporal behavior of: (A) non-linear “reaction” models utilizing (discrete) reaction-diffusion equations; and (B) spatial transport problems on surfaces and in nanopores utilizing the relevant (continuum) diffusion or Fokker-Planck equations. Thus, there are some common themes in these studies, as they all involve partial differential equations or their discrete analogues which incorporate a description of diffusion-type processes. However, there are also some qualitative differences, as shall be discussed below.

Higher order field equations. II

International Nuclear Information System (INIS)

Tolhoek, H.A.

1977-01-01

In a previous paper wave propagation was studied according to a sixth-order partial differential equation involving a complex mass M. The corresponding Yang-Feldman integral equations (indicated as SM-YF-equations), were formulated using modified Green's functions Gsub(R)sup(M)(x) and Gsub(A)sup(M)(x), which then incorporate the partial differential equation together with certain boundary conditions. In this paper certain limit properties of these modified Green's functions are derived: (a) It is shown that for mod(M)→infinity the Green's functions Gsub(R)sup(M)(x) and Gsub(A)sup(M)(x) approach the Green's functions Δsub(R)(x) and Δsub(A)(x) of the corresponding KG-equation (Klein-Gordon equation). (b) It is further shown that the asymptotic behaviour of Gsub(R)sup(M)(x) and Gsub(A)sup(M)(x) is the same as of Δsub(R)(x) and Δsub(A)(x)-and also the same as for Dsub(R)(x) and Dsub(A)(x) for t→+-infinity;, where Dsub(R) and Dsub(A) are the Green's functions for the KG-equation with mass zero. It is essential to take limits in the sense of distribution theory in both cases (a) and (b). The property (b) indicates that the wave propagation properties of the SM-YF-equations, the KG-equation with finite mass and the KG-equation with mass zero are closely related in an asymptotic sense. (Auth.)

On matrix fractional differential equations

OpenAIRE

Adem Kılıçman; Wasan Ajeel Ahmood

2017-01-01

The aim of this article is to study the matrix fractional differential equations and to find the exact solution for system of matrix fractional differential equations in terms of Riemann–Liouville using Laplace transform method and convolution product to the Riemann–Liouville fractional of matrices. Also, we show the theorem of non-homogeneous matrix fractional partial differential equation with some illustrative examples to demonstrate the effectiveness of the new methodology. The main objec...

Numerical solutions of diffusive logistic equation

International Nuclear Information System (INIS)

Afrouzi, G.A.; Khademloo, S.

2007-01-01

In this paper we investigate numerically positive solutions of a superlinear Elliptic equation on bounded domains. The study of Diffusive logistic equation continues to be an active field of research. The subject has important applications to population migration as well as many other branches of science and engineering. In this paper the 'finite difference scheme' will be developed and compared for solving the one- and three-dimensional Diffusive logistic equation. The basis of the analysis of the finite difference equations considered here is the modified equivalent partial differential equation approach, developed from many authors these years

Development and validation of risk prediction equations to estimate survival in patients with colorectal cancer: cohort study

OpenAIRE

Hippisley-Cox, Julia; Coupland, Carol

2017-01-01

Objective: To develop and externally validate risk prediction equations to estimate absolute and conditional survival in patients with colorectal cancer. \\ud \\ud Design: Cohort study.\\ud \\ud Setting: General practices in England providing data for the QResearch database linked to the national cancer registry.\\ud \\ud Participants: 44 145 patients aged 15-99 with colorectal cancer from 947 practices to derive the equations. The equations were validated in 15 214 patients with colorectal cancer ...

Study of coupled nonlinear partial differential equations for finding exact analytical solutions.

Science.gov (United States)

Khan, Kamruzzaman; Akbar, M Ali; Koppelaar, H

2015-07-01

Exact solutions of nonlinear partial differential equations (NPDEs) are obtained via the enhanced (G'/G)-expansion method. The method is subsequently applied to find exact solutions of the Drinfel'd-Sokolov-Wilson (DSW) equation and the (2+1)-dimensional Painlevé integrable Burgers (PIB) equation. The efficiency of this method for finding these exact solutions is demonstrated. The method is effective and applicable for many other NPDEs in mathematical physics.

Organizational Cynicism, School Culture, and Academic Achievement: The Study of Structural Equation Modeling

Science.gov (United States)

Karadag, Engin; Kilicoglu, Gökhan; Yilmaz, Derya

2014-01-01

The purpose of this study is to explain constructed theoretical models that organizational cynicism perceptions of primary school teachers affect school culture and academic achievement, by using structural equation modeling. With the assumption that there is a cause-effect relationship between three main variables, the study was constructed with…

Modeling and Implementing Nonlinear Equations in Solid-State Lasers for Studying their Performance

Directory of Open Access Journals (Sweden)

Ali Roudehghat Shotorbani

2018-05-01

Full Text Available In this paper, the effect of radius variation of beam light on output efficacy of SFD Yttrium aluminium borate laser doped with Neodymium ion, which is simultaneously a non-linear and active laser crystal, is investigated in a double-pass cavity. This is done with a concave lens that concentrates (Reduction of optical radius within nonlinear material as much optical laser as possible, resulting in increasing the laser efficiency, second harmonic and the population inversion difference. In this study, we first developed five discrete differential equations describing the interactions of 807 nm pump beam, 1060nm laser beam and 530nm second harmonic beam. Output efficiencies of laser and second harmonic beams at pumping power of Pp =20W and beam radius of 5μm have been presented. Meanwhile, in this paper, the first experiment for creating second harmonic in solid state lasers was fully described with a figure and its procedure was investigated and then the equations (second harmonic and laser and population inversion were studied. Radius variation of beam light aims at increasing laser output efficacy and improving second harmonic and population inversion. The analytic methods which have been solved the discrete differential equations via Matlab.

Analysis of wave equation in electromagnetic field by Proca equation

International Nuclear Information System (INIS)

Pamungkas, Oky Rio; Soeparmi; Cari

2017-01-01

This research is aimed to analyze wave equation for the electric and magnetic field, vector and scalar potential, and continuity equation using Proca equation. Then, also analyze comparison of the solution on Maxwell and Proca equation for scalar potential and electric field, both as a function of distance and constant wave number. (paper)

Comparison of Kernel Equating and Item Response Theory Equating Methods

Science.gov (United States)

Meng, Yu

2012-01-01

The kernel method of test equating is a unified approach to test equating with some advantages over traditional equating methods. Therefore, it is important to evaluate in a comprehensive way the usefulness and appropriateness of the Kernel equating (KE) method, as well as its advantages and disadvantages compared with several popular item…

Integral equations

CERN Document Server

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

Extremal Kähler metrics and Bach-Merkulov equations

Science.gov (United States)

Koca, Caner

2013-08-01

In this paper, we study a coupled system of equations on oriented compact 4-manifolds which we call the Bach-Merkulov equations. These equations can be thought of as the conformally invariant version of the classical Einstein-Maxwell equations. Inspired by the work of C. LeBrun on Einstein-Maxwell equations on compact Kähler surfaces, we give a variational characterization of solutions to Bach-Merkulov equations as critical points of the Weyl functional. We also show that extremal Kähler metrics are solutions to these equations, although, contrary to the Einstein-Maxwell analogue, they are not necessarily minimizers of the Weyl functional. We illustrate this phenomenon by studying the Calabi action on Hirzebruch surfaces.

Minimal solution for inconsistent singular fuzzy matrix equations

Directory of Open Access Journals (Sweden)

M. Nikuie

2013-10-01

Full Text Available The fuzzy matrix equations $Ailde{X}=ilde{Y}$ is called a singular fuzzy matrix equations while the coefficients matrix of its equivalent crisp matrix equations be a singular matrix. The singular fuzzy matrix equations are divided into two parts: consistent singular matrix equations and inconsistent fuzzy matrix equations. In this paper, the inconsistent singular fuzzy matrix equations is studied and the effect of generalized inverses in finding minimal solution of an inconsistent singular fuzzy matrix equations are investigated.

Partial Differential Equations

CERN Document Server

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.

Nonlinear evolution equations

CERN Document Server

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

FMTLxLyLz DIMENSIONAL EQUAT DIMENSIONAL EQUATION ...

African Journals Online (AJOL)

eobe

plant made of 12mm thick steel plate was used in de steel plate ... water treatment plant. ... ameters affecting filtration processes were used to derive an equation usin ..... system. However, in deriving the equation onl terms are incorporated.

An inverse problem in a parabolic equation

Directory of Open Access Journals (Sweden)

Zhilin Li

1998-11-01

Full Text Available In this paper, an inverse problem in a parabolic equation is studied. An unknown function in the equation is related to two integral equations in terms of heat kernel. One of the integral equations is well-posed while another is ill-posed. A regularization approach for constructing an approximate solution to the ill-posed integral equation is proposed. Theoretical analysis and numerical experiment are provided to support the method.

Study of coupled nonlinear partial differential equations for finding exact analytical solutions

Science.gov (United States)

Khan, Kamruzzaman; Akbar, M. Ali; Koppelaar, H.

2015-01-01

Exact solutions of nonlinear partial differential equations (NPDEs) are obtained via the enhanced (G′/G)-expansion method. The method is subsequently applied to find exact solutions of the Drinfel'd–Sokolov–Wilson (DSW) equation and the (2+1)-dimensional Painlevé integrable Burgers (PIB) equation. The efficiency of this method for finding these exact solutions is demonstrated. The method is effective and applicable for many other NPDEs in mathematical physics. PMID:26587256

A study of fractional Schrödinger equation composed of Jumarie ...

Indian Academy of Sciences (India)

In this paper we have derived the fractional-order Schrödinger equation composed of Jumarie fractional derivative. The solution of this fractional-order Schrödinger equation is obtained in terms of Mittag–Leffler function with complex arguments, and fractional trigonometric functions. A few important properties of the ...

Formal truncations of connected kernel equations

International Nuclear Information System (INIS)

Dixon, R.M.

1977-01-01

The Connected Kernel Equations (CKE) of Alt, Grassberger and Sandhas (AGS); Kouri, Levin and Tobocman (KLT); and Bencze, Redish and Sloan (BRS) are compared against reaction theory criteria after formal channel space and/or operator truncations have been introduced. The Channel Coupling Class concept is used to study the structure of these CKE's. The related wave function formalism of Sandhas, of L'Huillier, Redish and Tandy and of Kouri, Krueger and Levin are also presented. New N-body connected kernel equations which are generalizations of the Lovelace three-body equations are derived. A method for systematically constructing fewer body models from the N-body BRS and generalized Lovelace (GL) equations is developed. The formally truncated AGS, BRS, KLT and GL equations are analyzed by employing the criteria of reciprocity and two-cluster unitarity. Reciprocity considerations suggest that formal truncations of BRS, KLT and GL equations can lead to reciprocity-violating results. This study suggests that atomic problems should employ three-cluster connected truncations and that the two-cluster connected truncations should be a useful starting point for nuclear systems

equate: An R Package for Observed-Score Linking and Equating

Directory of Open Access Journals (Sweden)

Anthony D. Albano

2016-10-01

Full Text Available The R package equate contains functions for observed-score linking and equating under single-group, equivalent-groups, and nonequivalent-groups with anchor test(s designs. This paper introduces these designs and provides an overview of observed-score equating with details about each of the supported methods. Examples demonstrate the basic functionality of the equate package.

ON THE EQUIVALENCE OF THE ABEL EQUATION

Institute of Scientific and Technical Information of China (English)

无

2006-01-01

This article uses the reflecting function of Mironenko to study some complicated differential equations which are equivalent to the Abel equation. The results are applied to discuss the behavior of solutions of these complicated differential equations.

The parabolic equation method for outdoor sound propagation

DEFF Research Database (Denmark)

Arranz, Marta Galindo

The parabolic equation method is a versatile tool for outdoor sound propagation. The present study has focused on the Cranck-Nicolson type Parabolic Equation method (CNPE). Three different applications of the CNPE method have been investigated. The first two applications study variations of the g......The parabolic equation method is a versatile tool for outdoor sound propagation. The present study has focused on the Cranck-Nicolson type Parabolic Equation method (CNPE). Three different applications of the CNPE method have been investigated. The first two applications study variations...

Partial differential equations of mathematical physics

CERN Document Server

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

Neoclassical MHD equations for tokamaks

International Nuclear Information System (INIS)

Callen, J.D.; Shaing, K.C.

1986-03-01

The moment equation approach to neoclassical-type processes is used to derive the flows, currents and resistive MHD-like equations for studying equilibria and instabilities in axisymmetric tokamak plasmas operating in the banana-plateau collisionality regime (ν* approx. 1). The resultant ''neoclassical MHD'' equations differ from the usual reduced equations of resistive MHD primarily by the addition of the important viscous relaxation effects within a magnetic flux surface. The primary effects of the parallel (poloidal) viscous relaxation are: (1) Rapid (approx. ν/sub i/) damping of the poloidal ion flow so the residual flow is only toroidal; (2) addition of the bootstrap current contribution to Ohm's laws; and (3) an enhanced (by B 2 /B/sub theta/ 2 ) polarization drift type term and consequent enhancement of the perpendicular dielectric constant due to parallel flow inertia, which causes the equations to depend only on the poloidal magnetic field B/sub theta/. Gyroviscosity (or diamagnetic vfiscosity) effects are included to properly treat the diamagnetic flow effects. The nonlinear form of the neoclassical MHD equations is derived and shown to satisfy an energy conservation equation with dissipation arising from Joule and poloidal viscous heating, and transport due to classical and neoclassical diffusion

Exact traveling wave solutions of modified KdV-Zakharov-Kuznetsov equation and viscous Burgers equation.

Science.gov (United States)

Islam, Md Hamidul; Khan, Kamruzzaman; Akbar, M Ali; Salam, Md Abdus

2014-01-01

Mathematical modeling of many physical systems leads to nonlinear evolution equations because most physical systems are inherently nonlinear in nature. The investigation of traveling wave solutions of nonlinear partial differential equations (NPDEs) plays a significant role in the study of nonlinear physical phenomena. In this article, we construct the traveling wave solutions of modified KDV-ZK equation and viscous Burgers equation by using an enhanced (G '/G) -expansion method. A number of traveling wave solutions in terms of unknown parameters are obtained. Derived traveling wave solutions exhibit solitary waves when special values are given to its unknown parameters. 35C07; 35C08; 35P99.

Polygons of differential equations for finding exact solutions

International Nuclear Information System (INIS)

Kudryashov, Nikolai A.; Demina, Maria V.

2007-01-01

A method for finding exact solutions of nonlinear differential equations is presented. Our method is based on the application of polygons corresponding to nonlinear differential equations. It allows one to express exact solutions of the equation studied through solutions of another equation using properties of the basic equation itself. The ideas of power geometry are used and developed. Our approach has a pictorial interpretation, which is illustrative and effective. The method can be also applied for finding transformations between solutions of differential equations. To demonstrate the method application exact solutions of several equations are found. These equations are: the Korteveg-de Vries-Burgers equation, the generalized Kuramoto-Sivashinsky equation, the fourth-order nonlinear evolution equation, the fifth-order Korteveg-de Vries equation, the fifth-order modified Korteveg-de Vries equation and the sixth-order nonlinear evolution equation describing turbulent processes. Some new exact solutions of nonlinear evolution equations are given

Stochastic Differential Equations and Kondratiev Spaces

Energy Technology Data Exchange (ETDEWEB)

Vaage, G.

1995-05-01

The purpose of this mathematical thesis was to improve the understanding of physical processes such as fluid flow in porous media. An example is oil flowing in a reservoir. In the first of five included papers, Hilbert space methods for elliptic boundary value problems are used to prove the existence and uniqueness of a large family of elliptic differential equations with additive noise without using the Hermite transform. The ideas are then extended to the multidimensional case and used to prove existence and uniqueness of solution of the Stokes equations with additive noise. The second paper uses functional analytic methods for partial differential equations and presents a general framework for proving existence and uniqueness of solutions to stochastic partial differential equations with multiplicative noise, for a large family of noises. The methods are applied to equations of elliptic, parabolic as well as hyperbolic type. The framework presented can be extended to the multidimensional case. The third paper shows how the ideas from the second paper can be extended to study the moving boundary value problem associated with the stochastic pressure equation. The fourth paper discusses a set of stochastic differential equations. The fifth paper studies the relationship between the two families of Kondratiev spaces used in the thesis. 102 refs.

Chemical Equation Balancing.

Science.gov (United States)

Blakley, G. R.

1982-01-01

Reviews mathematical techniques for solving systems of homogeneous linear equations and demonstrates that the algebraic method of balancing chemical equations is a matter of solving a system of homogeneous linear equations. FORTRAN programs using this matrix method to chemical equation balancing are available from the author. (JN)

Estimated glomerular filtration rate is an early biomarker of cardiac surgery-associated acute kidney injury.

Science.gov (United States)

Candela-Toha, Ángel; Pardo, María Carmen; Pérez, Teresa; Muriel, Alfonso; Zamora, Javier

2018-04-20

and objective Acute kidney injury (AKI) diagnosis is still based on serum creatinine and diuresis. However, increases in creatinine are typically delayed 48h or longer after injury. Our aim was to determine the utility of routine postoperative renal function blood tests, to predict AKI one or 2days in advance in a cohort of cardiac surgery patients. Using a prospective database, we selected a sample of patients who had undergone major cardiac surgery between January 2002 and December 2013. The ability of the parameters to predict AKI was based on Acute Kidney Injury Network serum creatinine criteria. A cohort of 3,962 cases was divided into 2groups of similar size, one being exploratory and the other a validation sample. The exploratory group was used to show primary objectives and the validation group to confirm results. The ability to predict AKI of several kidney function parameters measured in routine postoperative blood tests, was measured with time-dependent ROC curves. The primary endpoint was time from measurement to AKI diagnosis. AKI developed in 610 (30.8%) and 623 (31.4%) patients in the exploratory and validation samples, respectively. Estimated glomerular filtration rate using the MDRD-4 equation showed the best AKI prediction capacity, with values for the AUC ROC curves between 0.700 and 0.946. We obtained different cut-off values for estimated glomerular filtration rate depending on the degree of AKI severity and on the time elapsed between surgery and parameter measurement. Results were confirmed in the validation sample. Postoperative estimated glomerular filtration rate using the MDRD-4 equation showed good ability to predict AKI following cardiac surgery one or 2days in advance. Copyright © 2018 Sociedad Española de Nefrología. Published by Elsevier España, S.L.U. All rights reserved.

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.

A new auxiliary equation and exact travelling wave solutions of nonlinear equations

International Nuclear Information System (INIS)

Sirendaoreji

2006-01-01

A new auxiliary ordinary differential equation and its solutions are used for constructing exact travelling wave solutions of nonlinear partial differential equations in a unified way. The main idea of this method is to take full advantage of the auxiliary equation which has more new exact solutions. More new exact travelling wave solutions are obtained for the quadratic nonlinear Klein-Gordon equation, the combined KdV and mKdV equation, the sine-Gordon equation and the Whitham-Broer-Kaup equations

Review on mathematical basis for thermal conduction equation

Energy Technology Data Exchange (ETDEWEB)

Park, D. G.; Kim, H. M

2007-10-15

In the view point of thermal conductivity measurement technology, It is very useful to understand mathematical theory of thermal conduction equation in order to evaluation of measurement data and to solve diverse technical problem in measurement. To approach this mathematical theory, thermal conduction equation is derived by Fourier thermal conduction law. Since thermal conduction equation depends on the Lapacian operator basically, mathematical meaning of Lapalacian and various diffusion equation including Laplacian have been studied. Stum-Liouville problem and Bessel function were studied in this report to understand analytical solution of various diffusion equation.

Review on mathematical basis for thermal conduction equation

International Nuclear Information System (INIS)

Park, D. G.; Kim, H. M.

2007-10-01

In the view point of thermal conductivity measurement technology, It is very useful to understand mathematical theory of thermal conduction equation in order to evaluation of measurement data and to solve diverse technical problem in measurement. To approach this mathematical theory, thermal conduction equation is derived by Fourier thermal conduction law. Since thermal conduction equation depends on the Lapacian operator basically, mathematical meaning of Lapalacian and various diffusion equation including Laplacian have been studied. Stum-Liouville problem and Bessel function were studied in this report to understand analytical solution of various diffusion equation

Local p-Adic Differential Equations

NARCIS (Netherlands)

Put, Marius van der; Taelman, Lenny

2006-01-01

This paper studies divergence in solutions of p-adic linear local differential equations. Such divergence is related to the notion of p-adic Liouville numbers. Also, the influence of the divergence on the differential Galois groups of such differential equations is explored. A complete result is

Numerical solution of Boltzmann's equation

International Nuclear Information System (INIS)

Sod, G.A.

1976-04-01

The numerical solution of Boltzmann's equation is considered for a gas model consisting of rigid spheres by means of Hilbert's expansion. If only the first two terms of the expansion are retained, Boltzmann's equation reduces to the Boltzmann-Hilbert integral equation. Successive terms in the Hilbert expansion are obtained by solving the same integral equation with a different source term. The Boltzmann-Hilbert integral equation is solved by a new very fast numerical method. The success of the method rests upon the simultaneous use of four judiciously chosen expansions; Hilbert's expansion for the distribution function, another expansion of the distribution function in terms of Hermite polynomials, the expansion of the kernel in terms of the eigenvalues and eigenfunctions of the Hilbert operator, and an expansion involved in solving a system of linear equations through a singular value decomposition. The numerical method is applied to the study of the shock structure in one space dimension. Numerical results are presented for Mach numbers of 1.1 and 1.6. 94 refs, 7 tables, 1 fig

The Convergence Study of the Homotopy Analysis Method for Solving Nonlinear Volterra-Fredholm Integrodifferential Equations

Directory of Open Access Journals (Sweden)

Behzad Ghanbari

2014-01-01

Full Text Available We aim to study the convergence of the homotopy analysis method (HAM in short for solving special nonlinear Volterra-Fredholm integrodifferential equations. The sufficient condition for the convergence of the method is briefly addressed. Some illustrative examples are also presented to demonstrate the validity and applicability of the technique. Comparison of the obtained results HAM with exact solution shows that the method is reliable and capable of providing analytic treatment for solving such equations.

On a functional equation related to the intermediate long wave equation

International Nuclear Information System (INIS)

Hone, A N W; Novikov, V S

2004-01-01

We resolve an open problem stated by Ablowitz et al (1982 J. Phys. A: Math. Gen. 15 781) concerning the integral operator appearing in the intermediate long wave equation. We explain how this is resolved using the perturbative symmetry approach introduced by one of us with Mikhailov. By solving a certain functional equation, we prove that the intermediate long wave equation and the Benjamin-Ono equation are the unique integrable cases within a particular class of integro-differential equations. Furthermore, we explain how the perturbative symmetry approach is naturally extended to treat equations on a periodic domain. (letter to the editor)

Some New Integrable Equations from the Self-Dual Yang-Mills Equations

International Nuclear Information System (INIS)

Ivanova, T.A.; Popov, A.D.

1994-01-01

Using the symmetry reductions of the self-dual Yang-Mills (SDYM) equations in (2+2) dimensions, we introduce new integrable equations which are 'deformations' of the chiral model in (2+1) dimensions, generalized nonlinear Schroedinger, Korteweg-de Vries, Toda lattice, Garnier, Euler-Arnold, generalized Calogero-Moser and Euler-Calogero-Moser equations. The Lax pairs for all of these equations are derived by the symmetry reductions of the Lax pair for the SDYM equations. 34 refs

Auxiliary equation method for solving nonlinear partial differential equations

International Nuclear Information System (INIS)

Sirendaoreji,; Jiong, Sun

2003-01-01

By using the solutions of an auxiliary ordinary differential equation, a direct algebraic method is described to construct several kinds of exact travelling wave solutions for some nonlinear partial differential equations. By this method some physically important nonlinear equations are investigated and new exact travelling wave solutions are explicitly obtained with the aid of symbolic computation

Students' Understanding of Quadratic Equations

Science.gov (United States)

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…

A Comparison between Linear IRT Observed-Score Equating and Levine Observed-Score Equating under the Generalized Kernel Equating Framework

Science.gov (United States)

Chen, Haiwen

2012-01-01

In this article, linear item response theory (IRT) observed-score equating is compared under a generalized kernel equating framework with Levine observed-score equating for nonequivalent groups with anchor test design. Interestingly, these two equating methods are closely related despite being based on different methodologies. Specifically, when…

Ultradiscrete sine-Gordon Equation over Symmetrized Max-Plus Algebra, and Noncommutative Discrete and Ultradiscrete sine-Gordon Equations

Directory of Open Access Journals (Sweden)

Kenichi Kondo

2013-11-01

Full Text Available Ultradiscretization with negative values is a long-standing problem and several attempts have been made to solve it. Among others, we focus on the symmetrized max-plus algebra, with which we ultradiscretize the discrete sine-Gordon equation. Another ultradiscretization of the discrete sine-Gordon equation has already been proposed by previous studies, but the equation and the solutions obtained here are considered to directly correspond to the discrete counterpart. We also propose a noncommutative discrete analogue of the sine-Gordon equation, reveal its relations to other integrable systems including the noncommutative discrete KP equation, and construct multisoliton solutions by a repeated application of Darboux transformations. Moreover, we derive a noncommutative ultradiscrete analogue of the sine-Gordon equation and its 1-soliton and 2-soliton solutions, using the symmetrized max-plus algebra. As a result, we have a complete set of commutative and noncommutative versions of continuous, discrete, and ultradiscrete sine-Gordon equations.

New solutions of the confluent Heun equation

Directory of Open Access Journals (Sweden)

Harold Exton

1998-05-01

Full Text Available New compact triple series solutions of the confluent Heun equation (CHE are obtained by the appropriate applications of the Laplace transform and its inverse to a suitably constructed system of soluble differential equations. The computer-algebra package MAPLE V is used to tackle an auxiliary system of non-linear algebraic equations. This study is partly motivated by the relationship between the CHE and certain Schrödininger equations.

Dunkl Hyperbolic Equations

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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.

Optimal Control for Stochastic Delay Evolution Equations

Energy Technology Data Exchange (ETDEWEB)

Meng, Qingxin, E-mail: mqx@hutc.zj.cn [Huzhou University, Department of Mathematical Sciences (China); Shen, Yang, E-mail: skyshen87@gmail.com [York University, Department of Mathematics and Statistics (Canada)

2016-08-15

In this paper, we investigate a class of infinite-dimensional optimal control problems, where the state equation is given by a stochastic delay evolution equation with random coefficients, and the corresponding adjoint equation is given by an anticipated backward stochastic evolution equation. We first prove the continuous dependence theorems for stochastic delay evolution equations and anticipated backward stochastic evolution equations, and show the existence and uniqueness of solutions to anticipated backward stochastic evolution equations. Then we establish necessary and sufficient conditions for optimality of the control problem in the form of Pontryagin’s maximum principles. To illustrate the theoretical results, we apply stochastic maximum principles to study two examples, an infinite-dimensional linear-quadratic control problem with delay and an optimal control of a Dirichlet problem for a stochastic partial differential equation with delay. Further applications of the two examples to a Cauchy problem for a controlled linear stochastic partial differential equation and an optimal harvesting problem are also considered.

General particle transport equation. Final report

International Nuclear Information System (INIS)

Lafi, A.Y.; Reyes, J.N. Jr.

1994-12-01

The general objectives of this research are as follows: (1) To develop fundamental models for fluid particle coalescence and breakage rates for incorporation into statistically based (Population Balance Approach or Monte Carlo Approach) two-phase thermal hydraulics codes. (2) To develop fundamental models for flow structure transitions based on stability theory and fluid particle interaction rates. This report details the derivation of the mass, momentum and energy conservation equations for a distribution of spherical, chemically non-reacting fluid particles of variable size and velocity. To study the effects of fluid particle interactions on interfacial transfer and flow structure requires detailed particulate flow conservation equations. The equations are derived using a particle continuity equation analogous to Boltzmann's transport equation. When coupled with the appropriate closure equations, the conservation equations can be used to model nonequilibrium, two-phase, dispersed, fluid flow behavior. Unlike the Eulerian volume and time averaged conservation equations, the statistically averaged conservation equations contain additional terms that take into account the change due to fluid particle interfacial acceleration and fluid particle dynamics. Two types of particle dynamics are considered; coalescence and breakage. Therefore, the rate of change due to particle dynamics will consider the gain and loss involved in these processes and implement phenomenological models for fluid particle breakage and coalescence

Differential equations a dynamical systems approach ordinary differential equations

CERN Document Server

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.

The generalized good cut equation

International Nuclear Information System (INIS)

Adamo, T M; Newman, E T

2010-01-01

The properties of null geodesic congruences (NGCs) in Lorentzian manifolds are a topic of considerable importance. More specifically NGCs with the special property of being shear-free or asymptotically shear-free (as either infinity or a horizon is approached) have received a great deal of recent attention for a variety of reasons. Such congruences are most easily studied via solutions to what has been referred to as the 'good cut equation' or the 'generalization good cut equation'. It is the purpose of this paper to study these equations and show their relationship to each other. In particular we show how they all have a four-complex-dimensional manifold (known as H-space, or in a special case as complex Minkowski space) as a solution space.

Differential equations

CERN Document Server

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.

Study of liquid-vapor equilibrium with the help of interpolation equation of state

International Nuclear Information System (INIS)

Vorob'ev, V.S.

1995-01-01

The paper proposes an interpolation equation of state for the ideal gas, in a majority of cases in the Mie-Grueneisen equation. Its interpolation properties are defined by the dependence of the Grueneisen coefficient on density in the rarefaction region which contains two arbitrary constants. Density, Debye temperature, Grueneisen coefficient, heat capacity in the solid phase, static atomic sum in the gaseous phase, critical density, pressure and temperature are assigned as the initial data of the equation. This equation was used to describe set of experimental data by the coexistance curves and saturation pressure for Cs and Hg. 19 refs.; 8 figs.; 2 tabs

Pseudodifferential equations over non-Archimedean spaces

CERN Document Server

Zúñiga-Galindo, W A

2016-01-01

Focusing on p-adic and adelic analogues of pseudodifferential equations, this monograph presents a very general theory of parabolic-type equations and their Markov processes motivated by their connection with models of complex hierarchic systems. The Gelfand-Shilov method for constructing fundamental solutions using local zeta functions is developed in a p-adic setting and several particular equations are studied, such as the p-adic analogues of the Klein-Gordon equation. Pseudodifferential equations for complex-valued functions on non-Archimedean local fields are central to contemporary harmonic analysis and mathematical physics and their theory reveals a deep connection with probability and number theory. The results of this book extend and complement the material presented by Vladimirov, Volovich and Zelenov (1994) and Kochubei (2001), which emphasize spectral theory and evolution equations in a single variable, and Albeverio, Khrennikov and Shelkovich (2010), which deals mainly with the theory and applica...

New Equating Methods and Their Relationships with Levine Observed Score Linear Equating under the Kernel Equating Framework

Science.gov (United States)

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…

Study of equation-of-state of dense helium

International Nuclear Information System (INIS)

Cai Lingcang; Zhang Lin; Xiang Shikai; Jing Fuqian

2001-01-01

Hugoniot EOS, shock temperature of gas helium plasma (the initial pressure is 1.2 MPa and the initial temperature is 293 K) are measured with the help of shock compression technique and transient radiation pyrometer. The experimental Hugoniot data are good agreement with the theoretical prediction by Saha equation pus Debye-Huckel correction

Relations between nonlinear Riccati equations and other equations in fundamental physics

International Nuclear Information System (INIS)

Schuch, Dieter

2014-01-01

Many phenomena in the observable macroscopic world obey nonlinear evolution equations while the microscopic world is governed by quantum mechanics, a fundamental theory that is supposedly linear. In order to combine these two worlds in a common formalism, at least one of them must sacrifice one of its dogmas. Linearizing nonlinear dynamics would destroy the fundamental property of this theory, however, it can be shown that quantum mechanics can be reformulated in terms of nonlinear Riccati equations. In a first step, it will be shown that the information about the dynamics of quantum systems with analytical solutions can not only be obtainable from the time-dependent Schrödinger equation but equally-well from a complex Riccati equation. Comparison with supersymmetric quantum mechanics shows that even additional information can be obtained from the nonlinear formulation. Furthermore, the time-independent Schrödinger equation can also be rewritten as a complex Riccati equation for any potential. Extension of the Riccati formulation to include irreversible dissipative effects is straightforward. Via (real and complex) Riccati equations, other fields of physics can also be treated within the same formalism, e.g., statistical thermodynamics, nonlinear dynamical systems like those obeying a logistic equation as well as wave equations in classical optics, Bose- Einstein condensates and cosmological models. Finally, the link to abstract ''quantizations'' such as the Pythagorean triples and Riccati equations connected with trigonometric and hyperbolic functions will be shown

Developments in functional equations and related topics

CERN Document Server

Ciepliński, Krzysztof; Rassias, Themistocles

2017-01-01

This book presents current research on Ulam stability for functional equations and inequalities. Contributions from renowned scientists emphasize fundamental and new results, methods and techniques. Detailed examples are given to theories to further understanding at the graduate level for students in mathematics, physics, and engineering. Key topics covered in this book include: Quasi means Approximate isometries Functional equations in hypergroups Stability of functional equations Fischer-Muszély equation Haar meager sets and Haar null sets Dynamical systems Functional equations in probability theory Stochastic convex ordering Dhombres functional equation Nonstandard analysis and Ulam stability This book is dedicated in memory of Staniłsaw Marcin Ulam, who posed the fundamental problem concerning approximate homomorphisms of groups in 1940; which has provided the stimulus for studies in the stability of functional equations and inequalities.

Bridging the Knowledge Gaps between Richards' Equation and Budyko Equation

Science.gov (United States)

Wang, D.

2017-12-01

The empirical Budyko equation represents the partitioning of mean annual precipitation into evaporation and runoff. Richards' equation, based on Darcy's law, represents the movement of water in unsaturated soils. The linkage between Richards' equation and Budyko equation is presented by invoking the empirical Soil Conservation Service curve number (SCS-CN) model for computing surface runoff at the event-scale. The basis of the SCS-CN method is the proportionality relationship, i.e., the ratio of continuing abstraction to its potential is equal to the ratio of surface runoff to its potential value. The proportionality relationship can be derived from the Richards' equation for computing infiltration excess and saturation excess models at the catchment scale. Meanwhile, the generalized proportionality relationship is demonstrated as the common basis of SCS-CN method, monthly "abcd" model, and Budyko equation. Therefore, the linkage between Darcy's law and the emergent pattern of mean annual water balance at the catchment scale is presented through the proportionality relationship.

Estimated Glomerular Filtration Rate Correlates Poorly with Four-Hour Creatinine Clearance in Critically Ill Patients with Acute Kidney Injury

Directory of Open Access Journals (Sweden)

Christopher J. Kirwan

2013-01-01

Full Text Available Introduction. RIFLE and AKIN provide a standardised classification of acute kidney injury (AKI, but their categorical rather than continuous nature restricts their use to a research tool. A more accurate real-time description of renal function in AKI is needed, and some published data suggest that equations based on serum creatinine that estimate glomerular filtration rate (eGFR can provide this. In addition, incorporating serum cystatin C concentration into estimates of GFR may improve their accuracy, but no eGFR equations are validated in critically ill patients with AKI. Aim. This study tests whether creatinine or cystatin-C-based eGFR equations, used in patients with CKD, offer an accurate representation of 4-hour creatinine clearance (4CrCl in critically ill patients with AKI. Methods. Fifty-one critically ill patients with AKI were recruited. Thirty-seven met inclusion criteria, and the performance of eGFR equations was compared to 4CrCl. Results. eGFR equations were better than creatinine alone at predicting 4CrCl. Adding cystatin C to estimates did not improve the bias or add accuracy. The MDRD 7 eGFR had the best combination of correlation, bias, percentage error and accuracy. None were near acceptable standards quoted in patients with chronic kidney disease (CKD. Conclusions. eGFR equations are not sufficiently accurate for use in critically ill patients with AKI. Incorporating serum cystatin C does not improve estimates. eGFR should not be used to describe renal function in patients with AKI. Standards of accuracy for validating eGFR need to be set.

The matrix nonlinear Schrodinger equation in dimension 2

DEFF Research Database (Denmark)

Zuhan, L; Pedersen, Michael

2001-01-01

In this paper we study the existence of global solutions to the Cauchy problem for the matrix nonlinear Schrodinger equation (MNLS) in 2 space dimensions. A sharp condition for the global existence is obtained for this equation. This condition is in terms of an exact stationary solution...... of a semilinear elliptic equation. In the scalar case, the MNLS reduces to the well-known cubic nonlinear Schrodinger equation for which existence of solutions has been studied by many authors. (C) 2001 Academic Press....

Parametrically Excited Oscillations of Second-Order Functional Differential Equations and Application to Duffing Equations with Time Delay Feedback

Directory of Open Access Journals (Sweden)

Mervan Pašić

2014-01-01

Full Text Available We study oscillatory behaviour of a large class of second-order functional differential equations with three freedom real nonnegative parameters. According to a new oscillation criterion, we show that if at least one of these three parameters is large enough, then the main equation must be oscillatory. As an application, we study a class of Duffing type quasilinear equations with nonlinear time delayed feedback and their oscillations excited by the control gain parameter or amplitude of forcing term. Finally, some open questions and comments are given for the purpose of further study on this topic.

Quantum adiabatic Markovian master equations

International Nuclear Information System (INIS)

Albash, Tameem; Zanardi, Paolo; Boixo, Sergio; Lidar, Daniel A

2012-01-01

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. (paper)

Rigorous study of the gap equation for an inhomogeneous superconducting state near T/sub c/

International Nuclear Information System (INIS)

Hu, C.R.

1975-01-01

An analytical study of the gap equation in the Bogoliubov formulation is presented. The normal-superconducting phase boundary is simulated by the expression Δ (R/sup =/) = Δ/sub infinity/ tanh / α Δ/sub infinity/z/v/sub f/) theta(z) where Δ/sub infinity/(t) is the equilibrium gap, theta (z) a unit step function and v/sub f/ the Fermi velocity. The Bogoliubov-de Gennes equations are solved in a nonperturbative WKBJ approximation. The gap equation is expanded near T/sub c/ in powers of Δ/sub infinity/ and the major term is of the same order as that given by the Ginzburg-Landau-Gor'kov approximation. Discrepancies in the two values are discussed in detail. It is concluded that the present technique reproduces the Ginzburg-Landau-Gor'kov results except within a BCS coherence length. 25 references

ODE/IM correspondence and modified affine Toda field equations

Energy Technology Data Exchange (ETDEWEB)

Ito, Katsushi; Locke, Christopher

2014-08-15

We study the two-dimensional affine Toda field equations for affine Lie algebra g{sup ^} modified by a conformal transformation and the associated linear equations. In the conformal limit, the associated linear problem reduces to a (pseudo-)differential equation. For classical affine Lie algebra g{sup ^}, we obtain a (pseudo-)differential equation corresponding to the Bethe equations for the Langlands dual of the Lie algebra g, which were found by Dorey et al. in study of the ODE/IM correspondence.

Contact Geometry of Hyperbolic Equations of Generic Type

Directory of Open Access Journals (Sweden)

Dennis The

2008-08-01

Full Text Available We study the contact geometry of scalar second order hyperbolic equations in the plane of generic type. Following a derivation of parametrized contact-invariants to distinguish Monge-Ampère (class 6-6, Goursat (class 6-7 and generic (class 7-7 hyperbolic equations, we use Cartan's equivalence method to study the generic case. An intriguing feature of this class of equations is that every generic hyperbolic equation admits at most a nine-dimensional contact symmetry algebra. The nine-dimensional bound is sharp: normal forms for the contact-equivalence classes of these maximally symmetric generic hyperbolic equations are derived and explicit symmetry algebras are presented. Moreover, these maximally symmetric equations are Darboux integrable. An enumeration of several submaximally symmetric (eight and seven-dimensional generic hyperbolic structures is also given.

Trajectory attractors of equations of mathematical physics

International Nuclear Information System (INIS)

Vishik, Marko I; Chepyzhov, Vladimir V

2011-01-01

In this survey the method of trajectory dynamical systems and trajectory attractors is described, and is applied in the study of the limiting asymptotic behaviour of solutions of non-linear evolution equations. This method is especially useful in the study of dissipative equations of mathematical physics for which the corresponding Cauchy initial-value problem has a global (weak) solution with respect to the time but the uniqueness of this solution either has not been established or does not hold. An important example of such an equation is the 3D Navier-Stokes system in a bounded domain. In such a situation one cannot use directly the classical scheme of construction of a dynamical system in the phase space of initial conditions of the Cauchy problem of a given equation and find a global attractor of this dynamical system. Nevertheless, for such equations it is possible to construct a trajectory dynamical system and investigate a trajectory attractor of the corresponding translation semigroup. This universal method is applied for various types of equations arising in mathematical physics: for general dissipative reaction-diffusion systems, for the 3D Navier-Stokes system, for dissipative wave equations, for non-linear elliptic equations in cylindrical domains, and for other equations and systems. Special attention is given to using the method of trajectory attractors in approximation and perturbation problems arising in complicated models of mathematical physics. Bibliography: 96 titles.

Functional equations with causal operators

CERN Document Server

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.

Solutions manual to accompany Ordinary differential equations

CERN Document Server

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

Semigroup methods for evolution equations on networks

CERN Document Server

Mugnolo, Delio

2014-01-01

This concise text is based on a series of lectures held only a few years ago and originally intended as an introduction to known results on linear hyperbolic and parabolic equations.  Yet the topic of differential equations on graphs, ramified spaces, and more general network-like objects has recently gained significant momentum and, well beyond the confines of mathematics, there is a lively interdisciplinary discourse on all aspects of so-called complex networks. Such network-like structures can be found in virtually all branches of science, engineering and the humanities, and future research thus calls for solid theoretical foundations.      This book is specifically devoted to the study of evolution equations – i.e., of time-dependent differential equations such as the heat equation, the wave equation, or the Schrödinger equation (quantum graphs) – bearing in mind that the majority of the literature in the last ten years on the subject of differential equations of graphs has been devoted to ellip...

Advanced functional evolution equations and inclusions

CERN Document Server

Benchohra, Mouffak

2015-01-01

This book presents up-to-date results on abstract evolution equations and differential inclusions in infinite dimensional spaces. It covers equations with time delay and with impulses, and complements the existing literature in functional differential equations and inclusions. The exposition is devoted to both local and global mild solutions for some classes of functional differential evolution equations and inclusions, and other densely and non-densely defined functional differential equations and inclusions in separable Banach spaces or in Fréchet spaces. The tools used include classical fixed points theorems and the measure-of non-compactness, and each chapter concludes with a section devoted to notes and bibliographical remarks. This monograph is particularly useful for researchers and graduate students studying pure and applied mathematics, engineering, biology and all other applied sciences.

Evaluating Equating Results: Percent Relative Error for Chained Kernel Equating

Science.gov (United States)

Jiang, Yanlin; von Davier, Alina A.; Chen, Haiwen

2012-01-01

This article presents a method for evaluating equating results. Within the kernel equating framework, the percent relative error (PRE) for chained equipercentile equating was computed under the nonequivalent groups with anchor test (NEAT) design. The method was applied to two data sets to obtain the PRE, which can be used to measure equating…

on the properties of solutions and some applications on the TOV differential equation with a model of nuclear equation of state

International Nuclear Information System (INIS)

Esmail, S.F.H.

2006-01-01

the mathematical formulation of numerous physical problems results in differential equations actually non-linear differential equations . in our study we are interested in solutions of differential equations which describe the structure of neutron star in non-relativistic and relativistic cases. the aim of this work is to determine the mass and the radius of a neutron star, by solving the tolmann-oppenheimer-volkoff (TOV) differential equation using different models of the nuclear equation of state (EOS). analytically solutions are obtained for a simple form of the nuclear equation of state of Clayton model and poly trope model. for a more realistic equation of state the TOV differential equation is solved numerically using rung -Kutta method

Handbook of integral equations

CERN Document Server

Polyanin, Andrei D

2008-01-01

This handbook contains over 2,500 integral equations with solutions as well as analytical and numerical methods for solving linear and nonlinear equations. It explores Volterra, Fredholm, WienerHopf, Hammerstein, Uryson, and other equations that arise in mathematics, physics, engineering, the sciences, and economics. This second edition includes new chapters on mixed multidimensional equations and methods of integral equations for ODEs and PDEs, along with over 400 new equations with exact solutions. With many examples added for illustrative purposes, it presents new material on Volterra, Fredholm, singular, hypersingular, dual, and nonlinear integral equations, integral transforms, and special functions.

Monge-Ampere equations and characteristic connection functors

International Nuclear Information System (INIS)

Tunitskii, D V

2001-01-01

We investigate contact equivalence of Monge-Ampere equations. We define a category of Monge-Ampere equations and introduce the notion of a characteristic connection functor. This functor maps the category of Monge-Ampere equations to the category of affine connections. We give a constructive description of the characteristic connection functors corresponding to three subcategories, which include a large class of Monge-Ampere equations of elliptic and hyperbolic type. This essentially reduces the contact equivalence problem for Monge-Ampere equations in the cases under study to the equivalence problem for affine connections. Using E. Cartan's familiar theory, we are thus able to state and prove several criteria of contact equivalence for a large class of elliptic and hyperbolic Monge-Ampere equations

A Study of Schrödinger–Type Equations Appearing in Bohmian Mechanics and in the Theory of Bose–Einstein Condensates

KAUST Repository

Sierra Nunez, Jesus Alfredo

2018-05-16

The Schrödinger equations have had a profound impact on a wide range of fields of modern science, including quantum mechanics, superfluidity, geometrical optics, Bose-Einstein condensates, and the analysis of dispersive phenomena in the theory of PDE. The main purpose of this thesis is to explore two Schrödinger-type equations appearing in the so-called Bohmian formulation of quantum mechanics and in the study of exciton-polariton condensates. For the first topic, the linear Schrödinger equation is the starting point in the formulation of a phase-space model proposed in [1] for the Bohmian interpretation of quantum mechanics. We analyze this model, a nonlinear Vlasov-type equation, as a Hamiltonian system defined on an appropriate Poisson manifold built on Wasserstein spaces, the aim being to establish its existence theory. For this purpose, we employ results from the theory of PDE, optimal transportation, differential geometry and algebraic topology. The second topic of the thesis is the study of a nonlinear Schrödinger equation, called the complex Gross-Pitaevskii equation, appearing in the context of Bose-Einstein condensation of exciton-polaritons. This model can be roughly described as a driven-damped Gross-Pitaevskii equation which shares some similarities with the complex Ginzburg-Landau equation. The difficulties in the analysis of this equation stem from the fact that, unlike the complex Ginzburg-Landau equation, the complex Gross-Pitaevskii equation does not include a viscous dissipation term. Our approach to this equation will be in the framework of numerical computations, using two main tools: collocation methods and numerical continuation for the stationary solutions and a time-splitting spectral method for the dynamics. After performing a linear stability analysis on the computed stationary solutions, we are led to postulate the existence of radially symmetric stationary ground state solutions only for certain values of the parameters in the

Solution and study of nodal neutron transport equation applying the LTSN-DiagExp method

International Nuclear Information System (INIS)

Hauser, Eliete Biasotto; Pazos, Ruben Panta; Vilhena, Marco Tullio de; Barros, Ricardo Carvalho de

2003-01-01

In this paper we report advances about the three-dimensional nodal discrete-ordinates approximations of neutron transport equation for Cartesian geometry. We use the combined collocation method of the angular variables and nodal approach for the spatial variables. By nodal approach we mean the iterated transverse integration of the S N equations. This procedure leads to the set of one-dimensional averages angular fluxes in each spatial variable. The resulting system of equations is solved with the LTS N method, first applying the Laplace transform to the set of the nodal S N equations and then obtained the solution by symbolic computation. We include the LTS N method by diagonalization to solve the nodal neutron transport equation and then we outline the convergence of these nodal-LTS N approximations with the help of a norm associated to the quadrature formula used to approximate the integral term of the neutron transport equation. (author)

Five-equation and robust three-equation methods for solution verification of large eddy simulation

Science.gov (United States)

Dutta, Rabijit; Xing, Tao

2018-02-01

This study evaluates the recently developed general framework for solution verification methods for large eddy simulation (LES) using implicitly filtered LES of periodic channel flows at friction Reynolds number of 395 on eight systematically refined grids. The seven-equation method shows that the coupling error based on Hypothesis I is much smaller as compared with the numerical and modeling errors and therefore can be neglected. The authors recommend five-equation method based on Hypothesis II, which shows a monotonic convergence behavior of the predicted numerical benchmark ( S C ), and provides realistic error estimates without the need of fixing the orders of accuracy for either numerical or modeling errors. Based on the results from seven-equation and five-equation methods, less expensive three and four-equation methods for practical LES applications were derived. It was found that the new three-equation method is robust as it can be applied to any convergence types and reasonably predict the error trends. It was also observed that the numerical and modeling errors usually have opposite signs, which suggests error cancellation play an essential role in LES. When Reynolds averaged Navier-Stokes (RANS) based error estimation method is applied, it shows significant error in the prediction of S C on coarse meshes. However, it predicts reasonable S C when the grids resolve at least 80% of the total turbulent kinetic energy.

Spurious solutions in few-body equations. II. Numerical investigations

International Nuclear Information System (INIS)

Adhikari, S.K.

1979-01-01

A recent analytic study of spurious solutions in few-body equations by Adhikari and Gloeckle is here complemented by numerical investigations. As proposed by Adhikari and Gloeckle we study numerically the spurious solutions in the three-body Weinberg type equations and draw some general conclusions about the existence of spurious solutions in three-body equations with the Weinberg kernel and in other few-body formulations. In particular we conclude that for most of the potentials we encounter in problems of nuclear physics the three-body Weinberg type equation will not have a spurious solution which may interfere with the bound state or scattering calculation. Hence, if proven convenient, the three-body Weinberg type equation can be used in practical calculations. The same conclusion is true for the three-body channel coupling array scheme of Kouri, Levin, and Tobocman. In the case of the set of six coupled four-body equations proposed by Rosenberg et al. and the set of the Bencze-Redish-Sloan equations a careful study of the possible spurious solutions is needed before using these equations in practical calculations

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......This paper studies the equational theories of various exotic semirings presented in the literature. Exotic semirings are semirings whose underlying carrier set is some subset of the set of real numbers equipped with binary operations of minimum or maximum as sum, and addition as product. Two prime...... of these commutative idempotent weak semirings, the paper offers characterizations of the equations that hold in them, decidability results for their equational theories, explicit descriptions of the free algebras in the varieties they generate, and relative axiomatization results. Udgivelsesdato: APR 11...

Lie symmetries for systems of evolution equations

Science.gov (United States)

Paliathanasis, Andronikos; Tsamparlis, Michael

2018-01-01

The Lie symmetries for a class of systems of evolution equations are studied. The evolution equations are defined in a bimetric space with two Riemannian metrics corresponding to the space of the independent and dependent variables of the differential equations. The exact relation of the Lie symmetries with the collineations of the bimetric space is determined.

Linear measure functional differential equations with infinite delay

OpenAIRE

Monteiro, G. (Giselle Antunes); Slavík, A.

2014-01-01

We use the theory of generalized linear ordinary differential equations in Banach spaces to study linear measure functional differential equations with infinite delay. We obtain new results concerning the existence, uniqueness, and continuous dependence of solutions. Even for equations with a finite delay, our results are stronger than the existing ones. Finally, we present an application to functional differential equations with impulses.

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...

Introduction to differential equations

CERN Document Server

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

BRST, generalized Maurer-Cartan equations and CFT

Energy Technology Data Exchange (ETDEWEB)

Zeitlin, Anton M. [Department of Mathematics, Yale University, 442 Dunham Lab, 10 Hillhouse Ave., New Haven, CT 06511 (United States); St. Petersburg Department of Steklov Mathematical Institute, Fontanka, 27, St. Petersburg 191023 (Russian Federation)]. E-mail: zam@math.ipme.ru

2006-12-25

The paper is devoted to the study of BRST charge in perturbed two-dimensional conformal field theory. The main goal is to write the operator equation expressing the conservation law of BRST charge in perturbed theory in terms of purely algebraic operations on the corresponding operator algebra, which are defined via the OPE. The corresponding equations are constructed and their symmetries are studied up to the second order in formal coupling constant. It appears that the obtained equations can be interpreted as generalized Maurer-Cartan ones. We study two concrete examples in detail: the bosonic nonlinear sigma model and perturbed first order theory. In particular, we show that the Einstein equations, which are the conformal invariance conditions for both these perturbed theories, expanded up to the second order, can be rewritten in such generalized Maurer-Cartan form.

Analytical Solution of Pantograph Equation with Incommensurate Delay

Science.gov (United States)

Patade, Jayvant; Bhalekar, Sachin

2017-08-01

Pantograph equation is a delay differential equation (DDE) arising in electrodynamics. This paper studies the pantograph equation with two delays. The existence, uniqueness, stability and convergence results for DDEs are presented. The series solution of the proposed equation is obtained by using Daftardar-Gejji and Jafari method and given in terms of a special function. This new special function has several properties and relations with other functions. Further, we generalize the proposed equation to fractional-order case and obtain its solution.

Stochastic optimal control, forward-backward stochastic differential equations and the Schroedinger equation

Energy Technology Data Exchange (ETDEWEB)

Paul, Wolfgang; Koeppe, Jeanette [Institut fuer Physik, Martin Luther Universitaet, 06099 Halle (Germany); Grecksch, Wilfried [Institut fuer Mathematik, Martin Luther Universitaet, 06099 Halle (Germany)

2016-07-01

The standard approach to solve a non-relativistic quantum problem is through analytical or numerical solution of the Schroedinger equation. We show a way to go around it. This way is based on the derivation of the Schroedinger equation from conservative diffusion processes and the establishment of (several) stochastic variational principles leading to the Schroedinger equation under the assumption of a kinematics described by Nelson's diffusion processes. Mathematically, the variational principle can be considered as a stochastic optimal control problem linked to the forward-backward stochastic differential equations of Nelson's stochastic mechanics. The Hamilton-Jacobi-Bellmann equation of this control problem is the Schroedinger equation. We present the mathematical background and how to turn it into a numerical scheme for analyzing a quantum system without using the Schroedinger equation and exemplify the approach for a simple 1d problem.

Averaged RMHD equations

International Nuclear Information System (INIS)

Ichiguchi, Katsuji

1998-01-01

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)

Electron transfer dynamics: Zusman equation versus exact theory

International Nuclear Information System (INIS)

Shi Qiang; Chen Liping; Nan Guangjun; Xu Ruixue; Yan Yijing

2009-01-01

The Zusman equation has been widely used to study the effect of solvent dynamics on electron transfer reactions. However, application of this equation is limited by the classical treatment of the nuclear degrees of freedom. In this paper, we revisit the Zusman equation in the framework of the exact hierarchical equations of motion formalism, and show that a high temperature approximation of the hierarchical theory is equivalent to the Zusman equation in describing electron transfer dynamics. Thus the exact hierarchical formalism naturally extends the Zusman equation to include quantum nuclear dynamics at low temperatures. This new finding has also inspired us to rescale the original hierarchical equations and incorporate a filtering algorithm to efficiently propagate the hierarchical equations. Numerical exact results are also presented for the electron transfer reaction dynamics and rate constant calculations.

Differential equations

CERN Document Server

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

A Study of Enhanced, Higher Order Boussinesq-Type Equations and Their Numerical Modelling

DEFF Research Database (Denmark)

Banijamali, Babak

model is designated for the solution of higher-order Boussinesq-type equations, formulated in terms of the horizontal velocity at an arbitrary depth vector. Various discretisation techniques and grid definitions have been considered in this endeavour, undertaking a detailed analysis of the selected......This project has encompassed efforts in two separate veins: on the one hand, the acquiring of highly accurate model equations of the Boussinesq-type, and on the other hand, the theoretical and practical work in implementing such equations in the form of conventional numerical models, with obvious...... potential for applications to the realm of numerical modelling in coastal engineering. The derivation and analysis of several forms of higher-order in dispersion and non-linearity Boussinesq-type equations have been undertaken, obtaining and investigating the properties of a new and generalised class...

The GUP and quantum Raychaudhuri equation

Science.gov (United States)

Vagenas, Elias C.; Alasfar, Lina; Alsaleh, Salwa M.; Ali, Ahmed Farag

2018-06-01

In this paper, we compare the quantum corrections to the Schwarzschild black hole temperature due to quadratic and linear-quadratic generalised uncertainty principle, with the corrections from the quantum Raychaudhuri equation. The reason for this comparison is to connect the deformation parameters β0 and α0 with η which is the parameter that characterises the quantum Raychaudhuri equation. The derived relation between the parameters appears to depend on the relative scale of the system (black hole), which could be read as a beta function equation for the quadratic deformation parameter β0. This study shows a correspondence between the two phenomenological approaches and indicates that quantum Raychaudhuri equation implies the existence of a crystal-like structure of spacetime.

Lectures on nonlinear evolution equations initial value problems

CERN Document Server

Racke, Reinhard

2015-01-01

This book mainly serves as an elementary, self-contained introduction to several important aspects of the theory of global solutions to initial value problems for nonlinear evolution equations. The book employs the classical method of continuation of local solutions with the help of a priori estimates obtained for small data. The existence and uniqueness of small, smooth solutions that are defined for all values of the time parameter are investigated. Moreover, the asymptotic behavior of the solutions is described as time tends to infinity. The methods for nonlinear wave equations are discussed in detail. Other examples include the equations of elasticity, heat equations, the equations of thermoelasticity, Schrödinger equations, Klein-Gordon equations, Maxwell equations and plate equations. To emphasize the importance of studying the conditions under which small data problems offer global solutions, some blow-up results are briefly described. Moreover, the prospects for corresponding initial-boundary value p...

Tabular equation of state of lithium for laser-fusion reactor studies

International Nuclear Information System (INIS)

Young, D.A.; Ross, M.; Rogers, F.J.

1979-01-01

A tabular lithium equation of state was formulated from three separate equation-of-state models to carry out hydrodynamic simulations of a lithium-waterfall laser-fusion reactor. The models we used are: ACTEX for the ionized fluid, soft-sphere for the liquid and vapor, and pseudopotential for the hot, dense liquid. The models are smoothly joined over the range of density and temperature conditions appropriate for a laser-fusion reactor. We also fitted the models into two forms suitable for hydrodynamic calculations

Tabular equation of state of lithium for laser-fusion reactor studies

Energy Technology Data Exchange (ETDEWEB)

Young, D.A.; Ross, M.; Rogers, F.J.

1979-01-19

A tabular lithium equation of state was formulated from three separate equation-of-state models to carry out hydrodynamic simulations of a lithium-waterfall laser-fusion reactor. The models we used are: ACTEX for the ionized fluid, soft-sphere for the liquid and vapor, and pseudopotential for the hot, dense liquid. The models are smoothly joined over the range of density and temperature conditions appropriate for a laser-fusion reactor. We also fitted the models into two forms suitable for hydrodynamic calculations.

Oscillation results for certain fractional difference equations

Directory of Open Access Journals (Sweden)

Zhiyun WANG

2017-08-01

Full Text Available Fractional calculus is a theory that studies the properties and application of arbitrary order differentiation and integration. It can describe the physical properties of some systems more accurately, and better adapt to changes in the system, playing an important role in many fields. For example, it can describe the process of tumor growth (growth stimulation and growth inhibition in biomedical science. The oscillation of solutions of two kinds of fractional difference equations is studied, mainly using the proof by contradiction, that is, assuming the equation has a nonstationary solution. For the first kind of equation, the function symbol is firstly determined, and by constructing the Riccati function, the difference is calculated. Then the condition of the function is used to satisfy the contradiction, that is, the assumption is false, which verifies the oscillation of the solution. For the second kind of equation with initial condition, the equivalent fractional sum form of the fractional difference equation are firstly proved. With considering 0<α≤1 and α>1, respectively, by using the properties of Stirling formula and factorial function, the contradictory is got through enhanced processing, namely the assuming is not established, and the sufficient condition for the bounded solutions of the fractional difference equation is obtained. The above results will optimize the relevant conclusions and enrich the relevant results. The results are applied to the specific equations, and the oscillation of the solutions of equations is proved.

How to obtain the covariant form of Maxwell's equations from the continuity equation

International Nuclear Information System (INIS)

Heras, Jose A

2009-01-01

The covariant Maxwell equations are derived from the continuity equation for the electric charge. This result provides an axiomatic approach to Maxwell's equations in which charge conservation is emphasized as the fundamental axiom underlying these equations

Properties of the DKP [Duffin-Kemmer-Petiau] equation

International Nuclear Information System (INIS)

Nieto, M.M.

1988-01-01

After recalling the development of relativistic quantum mechanics, I elucidating the properties of the Duffin-Kemmer-Petiau first-order wave equation for spin-0 and -1 mesons. The DKP equation is formally compared to the Dirac equation, and physically compared to the Klein-Gordon second-order equation for mesons. I point out where the DKP and KG equations predict the same results, and where their predictions are different. I conclude with an example of where these differences might interest people studying quark models of nuclei. 9 refs

Equations of mathematical physics

CERN Document Server

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

Asymptotic behavior of the plasma equation

International Nuclear Information System (INIS)

Kwong, Y.C.

1984-01-01

This paper is concerned with the plasma equation on a bounded smooth domain the N-dimensional Euclidean Space, with non-negative initial data and a homogenous Dirichlet boundary condition. It is known that there exists a finite extinction time T such that the solution decays to zero at T. Berryman and Holland investigated the stability of the profile of the solution as t is approaching T. However, they obtained their results at the expense of some very strong regularity assumptions. By invoking both the nonlinear semi-group theory and a standard regularizing scheme for the equation, the same results are proved without those assumptions by measuring the rate of decay of the solution and estimates are obtained on the time derivative as t is approaching T. As motivated by the regularity assumptions, both the interior and boundary regularities of the solution are studied. Finally, the nonlinearity of the plasma equation is perturbed and the same aspects for the perturbed equation are studied

Model reduction of multiscale chemical langevin equations: a numerical case study.

Science.gov (United States)

Sotiropoulos, Vassilios; Contou-Carrere, Marie-Nathalie; Daoutidis, Prodromos; Kaznessis, Yiannis N

2009-01-01

Two very important characteristics of biological reaction networks need to be considered carefully when modeling these systems. First, models must account for the inherent probabilistic nature of systems far from the thermodynamic limit. Often, biological systems cannot be modeled with traditional continuous-deterministic models. Second, models must take into consideration the disparate spectrum of time scales observed in biological phenomena, such as slow transcription events and fast dimerization reactions. In the last decade, significant efforts have been expended on the development of stochastic chemical kinetics models to capture the dynamics of biomolecular systems, and on the development of robust multiscale algorithms, able to handle stiffness. In this paper, the focus is on the dynamics of reaction sets governed by stiff chemical Langevin equations, i.e., stiff stochastic differential equations. These are particularly challenging systems to model, requiring prohibitively small integration step sizes. We describe and illustrate the application of a semianalytical reduction framework for chemical Langevin equations that results in significant gains in computational cost.

FDTD for Hydrodynamic Electron Fluid Maxwell Equations

Directory of Open Access Journals (Sweden)

Yingxue Zhao

2015-05-01

Full Text Available In this work, we develop a numerical method for solving the three dimensional hydrodynamic electron fluid Maxwell equations that describe the electron gas dynamics driven by an external electromagnetic wave excitation. Our numerical approach is based on the Finite-Difference Time-Domain (FDTD method for solving the Maxwell’s equations and an explicit central finite difference method for solving the hydrodynamic electron fluid equations containing both electron density and current equations. Numerical results show good agreement with the experiment of studying the second-harmonic generation (SHG from metallic split-ring resonator (SRR.

On Degenerate Partial Differential Equations

OpenAIRE

Chen, Gui-Qiang G.

2010-01-01

Some of recent developments, including recent results, ideas, techniques, and approaches, in the study of degenerate partial differential equations are surveyed and analyzed. Several examples of nonlinear degenerate, even mixed, partial differential equations, are presented, which arise naturally in some longstanding, fundamental problems in fluid mechanics and differential geometry. The solution to these fundamental problems greatly requires a deep understanding of nonlinear degenerate parti...

A numerical study of the integral equations for the laser fields in free-electron lasers

International Nuclear Information System (INIS)

Yoo, J. G.; Park, S. H.; Jeong, Y. U.; Lee, B. C.; Rhee, Y. J.; Cho, S. O.

2004-01-01

The dynamics of the radiation fields in free-electron lasers is investigated on the basis of the integro-differential equations in the one-dimensional formulation. For simple cases we solved the integro-differential equations analytically and numerically to test our numerical procedures developed on the basis of the Filon method. The numerical results showed good agreement with the analytical solutions. To confirm the legitimacy of the numerical package, we carried out numerical studies on the inhomogeneous broadening effects, where no analytic solutions are available, due to the energy spread and the emittance of the electron beam.

Mass and energy-capital conservation equations to study the price evolution of non-renewable energy resources

International Nuclear Information System (INIS)

Gori, F.

2006-01-01

Mass conservation equation of non-renewable resources is employed to study the resources remaining in the reservoir according to the extraction policy. The energy conservation equation is transformed into an energy-capital conservation equation. The Hotelling rule is shown to be a special case of the general energy-capital conservation equation when the mass flow rate of extracted resources is equal to unity. Mass and energy-capital conservation equations are then coupled and solved together. It is investigated the price evolution of extracted resources. The conclusion of the Hotelling rule for non-extracted resources, i.e. an exponential increase of the price of non-renewable resources at the rate of current interest, is then generalized. A new parameter, called 'Price Increase Factor', PIF, is introduced as the difference between the current interest rate of capital and the mass flow rate of extraction of non-renewable resources. The price of extracted resources can increase exponentially only if PIF is greater than zero or if the mass flow rate of extraction is lower than the current interest rate of capital. The price is constant if PIF is zero or if the mass flow rate of extraction is equal to the current interest rate. The price is decreasing with time if PIF is smaller than zero or if the mass flow rate of extraction is higher than the current interest rate. (author)

A generalized simplest equation method and its application to the Boussinesq-Burgers equation.

Science.gov (United States)

Sudao, Bilige; Wang, Xiaomin

2015-01-01

In this paper, a generalized simplest equation method is proposed to seek exact solutions of nonlinear evolution equations (NLEEs). In the method, we chose a solution expression with a variable coefficient and a variable coefficient ordinary differential auxiliary equation. This method can yield a Bäcklund transformation between NLEEs and a related constraint equation. By dealing with the constraint equation, we can derive infinite number of exact solutions for NLEEs. These solutions include the traveling wave solutions, non-traveling wave solutions, multi-soliton solutions, rational solutions, and other types of solutions. As applications, we obtained wide classes of exact solutions for the Boussinesq-Burgers equation by using the generalized simplest equation method.

On separable Pauli equations

International Nuclear Information System (INIS)

Zhalij, Alexander

2002-01-01

We classify (1+3)-dimensional Pauli equations for a spin-(1/2) particle interacting with the electro-magnetic field, that are solvable by the method of separation of variables. As a result, we obtain the 11 classes of vector-potentials of the electro-magnetic field A(t,x(vector sign))=(A 0 (t,x(vector sign)), A(vector sign)(t,x(vector sign))) providing separability of the corresponding Pauli equations. It is established, in particular, that the necessary condition for the Pauli equation to be separable into second-order matrix ordinary differential equations is its equivalence to the system of two uncoupled Schroedinger equations. In addition, the magnetic field has to be independent of spatial variables. We prove that coordinate systems and the vector-potentials of the electro-magnetic field providing the separability of the corresponding Pauli equations coincide with those for the Schroedinger equations. Furthermore, an efficient algorithm for constructing all coordinate systems providing the separability of Pauli equation with a fixed vector-potential of the electro-magnetic field is developed. Finally, we describe all vector-potentials A(t,x(vector sign)) that (a) provide the separability of Pauli equation, (b) satisfy vacuum Maxwell equations without currents, and (c) describe non-zero magnetic field

Modified Method of Simplest Equation Applied to the Nonlinear Schrödinger Equation

Science.gov (United States)

Vitanov, Nikolay K.; Dimitrova, Zlatinka I.

2018-03-01

We consider an extension of the methodology of the modified method of simplest equation to the case of use of two simplest equations. The extended methodology is applied for obtaining exact solutions of model nonlinear partial differential equations for deep water waves: the nonlinear Schrödinger equation. It is shown that the methodology works also for other equations of the nonlinear Schrödinger kind.

Study of the equations of a particle in Non- Relativistic Quantum Mechanics

International Nuclear Information System (INIS)

Miltao, Milton Souza Ribeiro; Silva, Vanessa Santos Teles da

2011-01-01

Full text: The study of group theory is relevant to the treatment of physical problems, in which concepts of invariance and symmetry are important. In the field of Non-Relativistic Quantum Mechanics, we can do algebraic considerations taking into account the principles of symmetry, considering the framework of the study of Galileo transformations, which have characteristics of group. Therefore, we discuss the Stern-Gerlach experiment that had the historical importance of demonstrating that the electron has an intrinsic angular momentum. Through discussion of this experiment, we found that the spin appears in Non-Relativistic Quantum Mechanics as a feature of the algebraic structure underlying any physical theory represented by a group. From these studies, we have algebraic considerations for physical systems in non-relativistic domain, which are described by the Schroedinger and Pauli equations, describing the dynamics of particles of spin zero and 1/2 respectively, taking into account the structure of the transformations Galileo. Due to the operatorial, we represent Galileo's transformations by matrices by choosing an appropriate basis of space-time. Using these arrays, we saw group characteristics associated with these transformations, which we call the Galileo Group. We note the invariance of the Schroedinger and Pauli equations after these changes, as well as the physical state associated with it, which is represented by a radius vector in Hilbert space. (author)

Elliptic and solitary wave solutions for Bogoyavlenskii equations system, couple Boiti-Leon-Pempinelli equations system and Time-fractional Cahn-Allen equation

Directory of Open Access Journals (Sweden)

Mostafa M.A. Khater

Full Text Available In this article and for the first time, we introduce and describe Khater method which is a new technique for solving nonlinear partial differential equations (PDEs.. We apply this method for each of the following models Bogoyavlenskii equation, couple Boiti-Leon-Pempinelli system and Time-fractional Cahn-Allen equation. Khater method is very powerful, Effective, felicitous and fabulous method to get exact and solitary wave solution of (PDEs.. Not only just like that but it considers too one of the general methods for solving that kind of equations since it involves some methods as we will see in our discuss of the results. We make a comparison between the results of this new method and another method. Keywords: Bogoyavlenskii equations system, Couple Boiti-Leon-Pempinelli equations system, Time-fractional Cahn-Allen equation, Khater method, Traveling wave solutions, Solitary wave solutions

Schwarz maps of algebraic linear ordinary differential equations

Science.gov (United States)

Sanabria Malagón, Camilo

2017-12-01

A linear ordinary differential equation is called algebraic if all its solution are algebraic over its field of definition. In this paper we solve the problem of finding closed form solution to algebraic linear ordinary differential equations in terms of standard equations. Furthermore, we obtain a method to compute all algebraic linear ordinary differential equations with rational coefficients by studying their associated Schwarz map through the Picard-Vessiot Theory.

Scalar evolution equations for shear waves in incompressible solids: a simple derivation of the Z, ZK, KZK and KP equations

OpenAIRE

Destrade, Michel; Goriely, Alain; Saccomandi, Giuseppe

2011-01-01

We study the propagation of two-dimensional finite-amplitude shear waves in a nonlinear pre-strained incompressible solid, and derive several asymptotic amplitude equations in a simple, consistent, and rigorous manner. The scalar Zabolotskaya (Z) equation is shown to be the asymptotic limit of the equations of motion for all elastic generalized neo-Hookean solids (with strain energy depending only on the first principal invariant of Cauchy-Green strain). However, we show that the Z equation c...

New exact solutions of the Dirac equation. 8

International Nuclear Information System (INIS)

Bagrov, V.G.; Gitman, D.M.; Zadorozhnyj, V.N.; Sukhomlin, N.B.; Shapovalov, V.N.

1978-01-01

The paper continues the investigation into the exact solutions of the Dirac, Klein-Gordon, and Lorentz equations for a charge in an external electromagnetic field. The fields studied do not allow for separation of variables in the Dirac equation, but solutions to the Dirac equation are obtained

A novel numerical flux for the 3D Euler equations with general equation of state

KAUST Repository

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.

Group-theoretical interpretation of the Korteweg-de Vries type equations

International Nuclear Information System (INIS)

Berezin, F.A.; Perelomov, A.M.

1978-01-01

The Korteweg-de Vries equation is studied within the group-theoretical framework. Analogous equations are obtained for which the many-dimensional Schroedinger equation (with nonlocal potential) plays the same role as the one-dimensional Schroedinger equation does in the theory of the Korteweg-de Vries equation

Modified Method of Simplest Equation Applied to the Nonlinear Schrödinger Equation

Directory of Open Access Journals (Sweden)

Vitanov Nikolay K.

2018-03-01

Full Text Available We consider an extension of the methodology of the modified method of simplest equation to the case of use of two simplest equations. The extended methodology is applied for obtaining exact solutions of model nonlinear partial differential equations for deep water waves: the nonlinear Schrödinger equation. It is shown that the methodology works also for other equations of the nonlinear Schrödinger kind.

Integrable dissipative nonlinear second order differential equations via factorizations and Abel equations

Energy Technology Data Exchange (ETDEWEB)

Mancas, Stefan C. [Department of Mathematics, Embry–Riddle Aeronautical University, Daytona Beach, FL 32114-3900 (United States); Rosu, Haret C., E-mail: hcr@ipicyt.edu.mx [IPICYT, Instituto Potosino de Investigacion Cientifica y Tecnologica, Apdo Postal 3-74 Tangamanga, 78231 San Luis Potosí, SLP (Mexico)

2013-09-02

We emphasize two connections, one well known and another less known, between the dissipative nonlinear second order differential equations and the Abel equations which in their first-kind form have only cubic and quadratic terms. Then, employing an old integrability criterion due to Chiellini, we introduce the corresponding integrable dissipative equations. For illustration, we present the cases of some integrable dissipative Fisher, nonlinear pendulum, and Burgers–Huxley type equations which are obtained in this way and can be of interest in applications. We also show how to obtain Abel solutions directly from the factorization of second order nonlinear equations.

Deterministic Brownian motion generated from differential delay equations.

Science.gov (United States)

Lei, Jinzhi; Mackey, Michael C

2011-10-01

This paper addresses the question of how Brownian-like motion can arise from the solution of a deterministic differential delay equation. To study this we analytically study the bifurcation properties of an apparently simple differential delay equation and then numerically investigate the probabilistic properties of chaotic solutions of the same equation. Our results show that solutions of the deterministic equation with randomly selected initial conditions display a Gaussian-like density for long time, but the densities are supported on an interval of finite measure. Using these chaotic solutions as velocities, we are able to produce Brownian-like motions, which show statistical properties akin to those of a classical Brownian motion over both short and long time scales. Several conjectures are formulated for the probabilistic properties of the solution of the differential delay equation. Numerical studies suggest that these conjectures could be "universal" for similar types of "chaotic" dynamics, but we have been unable to prove this.

An Auxiliary Equation for the Bellman Equation in a One-Dimensional Ergodic Control

International Nuclear Information System (INIS)

Fujita, Y.

2001-01-01

In this paper we consider the Bellman equation in a one-dimensional ergodic control. Our aim is to show the existence and the uniqueness of its solution under general assumptions. For this purpose we introduce an auxiliary equation whose solution gives the invariant measure of the diffusion corresponding to an optimal control. Using this solution, we construct a solution to the Bellman equation. Our method of using this auxiliary equation has two advantages in the one-dimensional case. First, we can solve the Bellman equation under general assumptions. Second, this auxiliary equation gives an optimal Markov control explicitly in many examples

Transport equation solving methods

International Nuclear Information System (INIS)

Granjean, P.M.

1984-06-01

This work is mainly devoted to Csub(N) and Fsub(N) methods. CN method: starting from a lemma stated by Placzek, an equivalence is established between two problems: the first one is defined in a finite medium bounded by a surface S, the second one is defined in the whole space. In the first problem the angular flux on the surface S is shown to be the solution of an integral equation. This equation is solved by Galerkin's method. The Csub(N) method is applied here to one-velocity problems: in plane geometry, slab albedo and transmission with Rayleigh scattering, calculation of the extrapolation length; in cylindrical geometry, albedo and extrapolation length calculation with linear scattering. Fsub(N) method: the basic integral transport equation of the Csub(N) method is integrated on Case's elementary distributions; another integral transport equation is obtained: this equation is solved by a collocation method. The plane problems solved by the Csub(N) method are also solved by the Fsub(N) method. The Fsub(N) method is extended to any polynomial scattering law. Some simple spherical problems are also studied. Chandrasekhar's method, collision probability method, Case's method are presented for comparison with Csub(N) and Fsub(N) methods. This comparison shows the respective advantages of the two methods: a) fast convergence and possible extension to various geometries for Csub(N) method; b) easy calculations and easy extension to polynomial scattering for Fsub(N) method [fr

Swarm analysis by using transport equations

International Nuclear Information System (INIS)

Dote, Toshihiko.

1985-01-01

As the basis of weak ionization plasma phenomena, the motion, i.e. swarm, of charged particles in the gas is analyzed by use of the transport equations, from which basic nature of the swarm is discussed. The present report is an overview of the studies made in the past several years. Described are principally the most basic aspects concerning behaviors of the electrons and positive ions, that is, the basic equations and their significance, characteristics of the behaviors of the electron and positive ion swarms as revealed by solving the equations, and various characteristics of the swarm parameters. Contents are: Maxwell-Boltzmann's transport equations, behavior of the electron swarm, energy loss of the electrons, and behavior of the positive ion swarm. (Mori, K.)

The GUP and quantum Raychaudhuri equation

Directory of Open Access Journals (Sweden)

Elias C. Vagenas

2018-06-01

Full Text Available In this paper, we compare the quantum corrections to the Schwarzschild black hole temperature due to quadratic and linear-quadratic generalised uncertainty principle, with the corrections from the quantum Raychaudhuri equation. The reason for this comparison is to connect the deformation parameters β0 and α0 with η which is the parameter that characterises the quantum Raychaudhuri equation. The derived relation between the parameters appears to depend on the relative scale of the system (black hole, which could be read as a beta function equation for the quadratic deformation parameter β0. This study shows a correspondence between the two phenomenological approaches and indicates that quantum Raychaudhuri equation implies the existence of a crystal-like structure of spacetime.

Traveling wave behavior for a generalized fisher equation

International Nuclear Information System (INIS)

Feng Zhaosheng

2008-01-01

There is the widespread existence of wave phenomena in physics, chemistry and biology. This clearly necessitates a study of traveling waves in depth and of the modeling and analysis involved. In the present paper, we study a nonlinear reaction-diffusion equation, which can be regarded as a generalized Fisher equation. Applying the Cole-Hopf transformation and the first integral method, we obtain a class of traveling solitary wave solutions for this generalized Fisher equation

Effective evolution equations from quantum mechanics

OpenAIRE

Leopold, Nikolai

2018-01-01

The goal of this thesis is to provide a mathematical rigorous derivation of the Schrödinger-Klein-Gordon equations, the Maxwell-Schrödinger equations and the defocusing cubic nonlinear Schrödinger equation in two dimensions. We study the time evolution of the Nelson model (with ultraviolet cutoff) in a limit where the number N of charged particles gets large while the coupling of each particle to the radiation field is of order N^{−1/2}. At time zero it is assumed that almost all charges a...

Arithmetic differential equations on $GL_n$, I: differential cocycles

OpenAIRE

Buium, Alexandru; Dupuy, Taylor

2013-01-01

The theory of differential equations has an arithmetic analogue in which derivatives are replaced by Fermat quotients. One can then ask what is the arithmetic analogue of a linear differential equation. The study of usual linear differential equations is the same as the study of the differential cocycle from $GL_n$ into its Lie algebra given by the logarithmic derivative. However we prove here that there are no such cocycles in the context of arithmetic differential equations. In sequels of t...

Covariant field equations in supergravity

Energy Technology Data Exchange (ETDEWEB)

Vanhecke, Bram [KU Leuven, Institute for Theoretical Physics, Leuven (Belgium); Ghent University, Faculty of Physics, Gent (Belgium); Proeyen, Antoine van [KU Leuven, Institute for Theoretical Physics, Leuven (Belgium)

2017-12-15

Covariance is a useful property for handling supergravity theories. In this paper, we prove a covariance property of supergravity field equations: under reasonable conditions, field equations of supergravity are covariant modulo other field equations. We prove that for any supergravity there exist such covariant equations of motion, other than the regular equations of motion, that are equivalent to the latter. The relations that we find between field equations and their covariant form can be used to obtain multiplets of field equations. In practice, the covariant field equations are easily found by simply covariantizing the ordinary field equations. (copyright 2017 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

Covariant field equations in supergravity

International Nuclear Information System (INIS)

Vanhecke, Bram; Proeyen, Antoine van

2017-01-01

Covariance is a useful property for handling supergravity theories. In this paper, we prove a covariance property of supergravity field equations: under reasonable conditions, field equations of supergravity are covariant modulo other field equations. We prove that for any supergravity there exist such covariant equations of motion, other than the regular equations of motion, that are equivalent to the latter. The relations that we find between field equations and their covariant form can be used to obtain multiplets of field equations. In practice, the covariant field equations are easily found by simply covariantizing the ordinary field equations. (copyright 2017 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

Reduction of lattice equations to the Painlevé equations: PIV and PV

Science.gov (United States)

Nakazono, Nobutaka

2018-02-01

In this paper, we construct a new relation between Adler-Bobenko-Suris equations and Painlevé equations. Moreover, using this connection we construct the difference-differential Lax representations of the fourth and fifth Painlevé equations.

An Evaluation of Kernel Equating: Parallel Equating with Classical Methods in the SAT Subject Tests[TM] Program. Research Report. ETS RR-09-06

Science.gov (United States)

Grant, Mary C.; Zhang, Lilly; Damiano, Michele

2009-01-01

This study investigated kernel equating methods by comparing these methods to operational equatings for two tests in the SAT Subject Tests[TM] program. GENASYS (ETS, 2007) was used for all equating methods and scaled score kernel equating results were compared to Tucker, Levine observed score, chained linear, and chained equipercentile equating…

A study on linear and nonlinear Schrodinger equations by the variational iteration method

International Nuclear Information System (INIS)

Wazwaz, Abdul-Majid

2008-01-01

In this work, we introduce a framework to obtain exact solutions to linear and nonlinear Schrodinger equations. The He's variational iteration method (VIM) is used for analytic treatment of these equations. Numerical examples are tested to show the pertinent features of this method

Application of wavelets to singular integral scattering equations

International Nuclear Information System (INIS)

Kessler, B.M.; Payne, G.L.; Polyzou, W.N.

2004-01-01

The use of orthonormal wavelet basis functions for solving singular integral scattering equations is investigated. It is shown that these basis functions lead to sparse matrix equations which can be solved by iterative techniques. The scaling properties of wavelets are used to derive an efficient method for evaluating the singular integrals. The accuracy and efficiency of the wavelet transforms are demonstrated by solving the two-body T-matrix equation without partial wave projection. The resulting matrix equation which is characteristic of multiparticle integral scattering equations is found to provide an efficient method for obtaining accurate approximate solutions to the integral equation. These results indicate that wavelet transforms may provide a useful tool for studying few-body systems

Test equating methods and practices

CERN Document Server

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...

On stochastic differential equations with random delay

International Nuclear Information System (INIS)

Krapivsky, P L; Luck, J M; Mallick, K

2011-01-01

We consider stochastic dynamical systems defined by differential equations with a uniform random time delay. The latter equations are shown to be equivalent to deterministic higher-order differential equations: for an nth-order equation with random delay, the corresponding deterministic equation has order n + 1. We analyze various examples of dynamical systems of this kind, and find a number of unusual behaviors. For instance, for the harmonic oscillator with random delay, the energy grows as exp((3/2) t 2/3 ) in reduced units. We then investigate the effect of introducing a discrete time step ε. At variance with the continuous situation, the discrete random recursion relations thus obtained have intrinsic fluctuations. The crossover between the fluctuating discrete problem and the deterministic continuous one as ε goes to zero is studied in detail on the example of a first-order linear differential equation

Navier-Stokes equations an introduction with applications

CERN Document Server

Łukaszewicz, Grzegorz

2016-01-01

This volume is devoted to the study of the Navier–Stokes equations, providing a comprehensive reference for a range of applications: from students to engineers and mathematicians involved in research on fluid mechanics, dynamical systems, and mathematical modeling. Equipped with only a basic knowledge of calculus, functional analysis, and partial differential equations, the reader is introduced to the concept and applications of the Navier–Stokes equations through a series of fully self-contained chapters. Including lively illustrations that complement and elucidate the text, and a collection of exercises at the end of each chapter, this book is an indispensable, accessible, classroom-tested tool for teaching and understanding the Navier–Stokes equations. Incompressible Navier–Stokes equations describe the dynamic motion (flow) of incompressible fluid, the unknowns being the velocity and pressure as functions of location (space) and time variables. A solution to these equations predicts the behavior o...

Non-Archimedean reaction-ultradiffusion equations and complex hierarchic systems

Science.gov (United States)

Zúñiga-Galindo, W. A.

2018-06-01

We initiate the study of non-Archimedean reaction-ultradiffusion equations and their connections with models of complex hierarchic systems. From a mathematical perspective, the equations studied here are the p-adic counterpart of the integro-differential models for phase separation introduced by Bates and Chmaj. Our equations are also generalizations of the ultradiffusion equations on trees studied in the 1980s by Ogielski, Stein, Bachas, Huberman, among others, and also generalizations of the master equations of the Avetisov et al models, which describe certain complex hierarchic systems. From a physical perspective, our equations are gradient flows of non-Archimedean free energy functionals and their solutions describe the macroscopic density profile of a bistable material whose space of states has an ultrametric structure. Some of our results are p-adic analogs of some well-known results in the Archimedean setting, however, the mechanism of diffusion is completely different due to the fact that it occurs in an ultrametric space.

Fluid/Structure Interaction Studies of Aircraft Using High Fidelity Equations on Parallel Computers

Science.gov (United States)

Guruswamy, Guru; VanDalsem, William (Technical Monitor)

1994-01-01

Abstract Aeroelasticity which involves strong coupling of fluids, structures and controls is an important element in designing an aircraft. Computational aeroelasticity using low fidelity methods such as the linear aerodynamic flow equations coupled with the modal structural equations are well advanced. Though these low fidelity approaches are computationally less intensive, they are not adequate for the analysis of modern aircraft such as High Speed Civil Transport (HSCT) and Advanced Subsonic Transport (AST) which can experience complex flow/structure interactions. HSCT can experience vortex induced aeroelastic oscillations whereas AST can experience transonic buffet associated structural oscillations. Both aircraft may experience a dip in the flutter speed at the transonic regime. For accurate aeroelastic computations at these complex fluid/structure interaction situations, high fidelity equations such as the Navier-Stokes for fluids and the finite-elements for structures are needed. Computations using these high fidelity equations require large computational resources both in memory and speed. Current conventional super computers have reached their limitations both in memory and speed. As a result, parallel computers have evolved to overcome the limitations of conventional computers. This paper will address the transition that is taking place in computational aeroelasticity from conventional computers to parallel computers. The paper will address special techniques needed to take advantage of the architecture of new parallel computers. Results will be illustrated from computations made on iPSC/860 and IBM SP2 computer by using ENSAERO code that directly couples the Euler/Navier-Stokes flow equations with high resolution finite-element structural equations.

On generalized fractional vibration equation

International Nuclear Information System (INIS)

Dai, Hongzhe; Zheng, Zhibao; Wang, Wei

2017-01-01

Highlights: • The paper presents a generalized fractional vibration equation for arbitrary viscoelastically damped system. • Some classical vibration equations can be derived from the developed equation. • The analytic solution of developed equation is derived under some special cases. • The generalized equation is particularly useful for developing new fractional equivalent linearization method. - Abstract: In this paper, a generalized fractional vibration equation with multi-terms of fractional dissipation is developed to describe the dynamical response of an arbitrary viscoelastically damped system. It is shown that many classical equations of motion, e.g., the Bagley–Torvik equation, can be derived from the developed equation. The Laplace transform is utilized to solve the generalized equation and the analytic solution under some special cases is derived. Example demonstrates the generalized transfer function of an arbitrary viscoelastic system.

Differential equations for dummies

CERN Document Server

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.

Every Equation Tells a Story: Using Equation Dictionaries in Introductory Geophysics

Science.gov (United States)

Caplan-Auerbach, Jacqueline

2009-01-01

Many students view equations as a series of variables and operators into which numbers should be plugged rather than as representative of a physical process. To solve a problem they may simply look for an equation with the correct variables and assume it meets their needs, rather than selecting an equation that represents the appropriate physical…

Spectral theories for linear differential equations

International Nuclear Information System (INIS)

Sell, G.R.

1976-01-01

The use of spectral analysis in the study of linear differential equations with constant coefficients is not only a fundamental technique but also leads to far-reaching consequences in describing the qualitative behaviour of the solutions. The spectral analysis, via the Jordan canonical form, will not only lead to a representation theorem for a basis of solutions, but will also give a rather precise statement of the (exponential) growth rates of various solutions. Various attempts have been made to extend this analysis to linear differential equations with time-varying coefficients. The most complete such extensions is the Floquet theory for equations with periodic coefficients. For time-varying linear differential equations with aperiodic coefficients several authors have attempted to ''extend'' the Foquet theory. The precise meaning of such an extension is itself a problem, and we present here several attempts in this direction that are related to the general problem of extending the spectral analysis of equations with constant coefficients. The main purpose of this paper is to introduce some problems of current research. The primary problem we shall examine occurs in the context of linear differential equations with almost periodic coefficients. We call it ''the Floquet problem''. (author)

Spurious solutions in few-body equations

International Nuclear Information System (INIS)

Adhikari, S.K.; Gloeckle, W.

1979-01-01

After Faddeev and Yakubovskii showed how to write connected few-body equations which are free from discrete spurious solutions various authors have proposed different connected few-body scattering equations. Federbush first pointed out that Weinberg's formulation admits the existence of discrete spurious solutions. In this paper we investigate the possibility and consequence of the existence of spurious solutions in some of the few-body formulations. Contrary to a proof by Hahn, Kouri, and Levin and by Bencze and Tandy the channel coupling array scheme of Kouri, Levin, and Tobocman which is also the starting point of a formulation by Hahn is shown to admit spurious solutions. We can show that the set of six coupled four-body equations proposed independently by Mitra, Gillespie, Sugar, and Panchapakesan, by Rosenberg, by Alessandrini, and by Takahashi and Mishima and the seven coupled four-body equations proposed by Sloan and related by matrix multipliers to basic sets which correspond uniquely to the Schroedinger equation. These multipliers are likely to give spurious solutions to these equations. In all these cases spuriosities are shown to have no hazardous consequence if one is interested in studying the scattering problem

Numerical solution of distributed order fractional differential equations

Science.gov (United States)

Katsikadelis, John T.

2014-02-01

In this paper a method for the numerical solution of distributed order FDEs (fractional differential equations) of a general form is presented. The method applies to both linear and nonlinear equations. The Caputo type fractional derivative is employed. The distributed order FDE is approximated with a multi-term FDE, which is then solved by adjusting appropriately the numerical method developed for multi-term FDEs by Katsikadelis. Several example equations are solved and the response of mechanical systems described by such equations is studied. The convergence and the accuracy of the method for linear and nonlinear equations are demonstrated through well corroborated numerical results.

Balancing Chemical Equations.

Science.gov (United States)

Savoy, L. G.

1988-01-01

Describes a study of students' ability to balance equations. Answers to a test on this topic were analyzed to determine the level of understanding and processes used by the students. Presented is a method to teach this skill to high school chemistry students. (CW)

Dryson equations, Ward identities, and the infrared behavior of Yang-Mills theories. [Schwinger-Dyson equations, Slavnov-Taylor identities

Energy Technology Data Exchange (ETDEWEB)

Baker, M.

1979-01-01

It was shown using the Schwinger-Dyson equations and the Slavnov-Taylor identities of Yang-Mills theory that no inconsistency arises if the gluon propagator behaves like (1/p/sup 2/)/sup 2/ for small p/sup 2/. To see whether the theory actually contains such singular long range behavior, a nonperturbative closed set of equations was formulated by neglecting the transverse parts of GAMMA and GAMMA/sub 4/ in the Schwinger-Dyson equations. This simplification preserves all the symmetries of the theory and allows the possibility for a singular low-momentum behavior of the gluon propagator. The justification for neglecting GAMMA/sup (T)/ and GAMMA/sub 4//sup (T)/ is not evident but it is expected that the present study of the resulting equations will elucidate this simplification, which leads to a closed set of equations.

A Study on the Consistency of Discretization Equation in Unsteady Heat Transfer Calculations

Directory of Open Access Journals (Sweden)

Wenhua Zhang

2013-01-01

Full Text Available The previous studies on the consistency of discretization equation mainly focused on the finite difference method, but the issue of consistency still remains with several problems far from totally solved in the actual numerical computation. For instance, the consistency problem is involved in the numerical case where the boundary variables are solved explicitly while the variables away from the boundary are solved implicitly. And when the coefficient of discretization equation of nonlinear numerical case is the function of variables, calculating the coefficient explicitly and the variables implicitly might also give rise to consistency problem. Thus the present paper mainly researches the consistency problems involved in the explicit treatment of the second and third boundary conditions and that of thermal conductivity which is the function of temperature. The numerical results indicate that the consistency problem should be paid more attention and not be neglected in the practical computation.

Improving Teaching Quality and Problem Solving Ability through Contextual Teaching and Learning in Differential Equations: A Lesson Study Approach

Science.gov (United States)

Khotimah, Rita Pramujiyanti; Masduki

2016-01-01

Differential equations is a branch of mathematics which is closely related to mathematical modeling that arises in real-world problems. Problem solving ability is an essential component to solve contextual problem of differential equations properly. The purposes of this study are to describe contextual teaching and learning (CTL) model in…

Neutron transport equation - indications on homogenization and neutron diffusion

International Nuclear Information System (INIS)

Argaud, J.P.

1992-06-01

In PWR nuclear reactor, the practical study of the neutrons in the core uses diffusion equation to describe the problem. On the other hand, the most correct method to describe these neutrons is to use the Boltzmann equation, or neutron transport equation. In this paper, we give some theoretical indications to obtain a diffusion equation from the general transport equation, with some simplifying hypothesis. The work is organised as follows: (a) the most general formulations of the transport equation are presented: integro-differential equation and integral equation; (b) the theoretical approximation of this Boltzmann equation by a diffusion equation is introduced, by the way of asymptotic developments; (c) practical homogenization methods of transport equation is then presented. In particular, the relationships with some general and useful methods in neutronic are shown, and some homogenization methods in energy and space are indicated. A lot of other points of view or complements are detailed in the text or the remarks

New Poisson–Boltzmann type equations: one-dimensional solutions

International Nuclear Information System (INIS)

Lee, Chiun-Chang; Lee, Hijin; Hyon, YunKyong; Lin, Tai-Chia; Liu, Chun

2011-01-01

The Poisson–Boltzmann (PB) equation is conventionally used to model the equilibrium of bulk ionic species in different media and solvents. In this paper we study a new Poisson–Boltzmann type (PB n ) equation with a small dielectric parameter ε 2 and non-local nonlinearity which takes into consideration the preservation of the total amount of each individual ion. This equation can be derived from the original Poisson–Nernst–Planck system. Under Robin-type boundary conditions with various coefficient scales, we demonstrate the asymptotic behaviours of one-dimensional solutions of PB n equations as the parameter ε approaches zero. In particular, we show that in case of electroneutrality, i.e. α = β, solutions of 1D PB n equations have a similar asymptotic behaviour as those of 1D PB equations. However, as α ≠ β (non-electroneutrality), solutions of 1D PB n equations may have blow-up behaviour which cannot be found in 1D PB equations. Such a difference between 1D PB and PB n equations can also be verified by numerical simulations

Drift-free kinetic equations for turbulent dispersion

Science.gov (United States)

Bragg, A.; Swailes, D. C.; Skartlien, R.

2012-11-01

The dispersion of passive scalars and inertial particles in a turbulent flow can be described in terms of probability density functions (PDFs) defining the statistical distribution of relevant scalar or particle variables. The construction of transport equations governing the evolution of such PDFs has been the subject of numerous studies, and various authors have presented formulations for this type of equation, usually referred to as a kinetic equation. In the literature it is often stated, and widely assumed, that these PDF kinetic equation formulations are equivalent. In this paper it is shown that this is not the case, and the significance of differences among the various forms is considered. In particular, consideration is given to which form of equation is most appropriate for modeling dispersion in inhomogeneous turbulence and most consistent with the underlying particle equation of motion. In this regard the PDF equations for inertial particles are considered in the limit of zero particle Stokes number and assessed against the fully mixed (zero-drift) condition for fluid points. A long-standing question regarding the validity of kinetic equations in the fluid-point limit is answered; it is demonstrated formally that one version of the kinetic equation (derived using the Furutsu-Novikov method) provides a model that satisfies this zero-drift condition exactly in both homogeneous and inhomogeneous systems. In contrast, other forms of the kinetic equation do not satisfy this limit or apply only in a limited regime.

Calculation of similarity solutions of partial differential equations

International Nuclear Information System (INIS)

Dresner, L.

1980-08-01

When a partial differential equation in two independent variables is invariant to a group G of stretching transformations, it has similarity solutions that can be found by solving an ordinary differential equation. Under broad conditions, this ordinary differential equation is also invariant to another stretching group G', related to G. The invariance of the ordinary differential equation to G' can be used to simplify its solution, particularly if it is of second order. Then a method of Lie's can be used to reduce it to a first-order equation, the study of which is greatly facilitated by analysis of its direction field. The method developed here is applied to three examples: Blasius's equation for boundary layer flow over a flat plate and two nonlinear diffusion equations, cc/sub t/ = c/sub zz/ and c/sub t/ = (cc/sub z/)/sub z/

Applications of Lie-group methods to the equations of magnetohydrodynamics

International Nuclear Information System (INIS)

Mandrekas, J.

1987-01-01

The invariance properties of various sets of magnetohydrodynamic (MHD) equations are studied using techniques from the theory of differential forms. Equations considered include the ideal MHD equations in different geometries and with different magnetic field configurations, the MHD equations in the presence of gravitational forces due to self-attraction or external fields, and the MHD equations including finite thermal conductivity and magnetic viscosity. The knowledge of the group structure of these equations is then used to introduce similarity variables to these equations. For each choice of similarity variables, the original set of partial differential equations is transformed into a set of ordinary differential equations and the most general form of the initial conditions is determined. Three cases are studied in detail and the corresponding sets of ordinary differential equations are solved numerically: the problem of a blast wave in an inhomogeneous atmosphere, the problem of a piston moving according to a power law in time, and the problem of a piston moving according to an exponential law in time

Solving polynomial differential equations by transforming them to linear functional-differential equations

OpenAIRE

Nahay, John Michael

2008-01-01

We present a new approach to solving polynomial ordinary differential equations by transforming them to linear functional equations and then solving the linear functional equations. We will focus most of our attention upon the first-order Abel differential equation with two nonlinear terms in order to demonstrate in as much detail as possible the computations necessary for a complete solution. We mention in our section on further developments that the basic transformation idea can be generali...

Low-mode truncation methods in the sine-Gordon equation

International Nuclear Information System (INIS)

Xiong Chuyu.

1991-01-01

In this dissertation, the author studies the chaotic and coherent motions (i.e., low-dimensional chaotic attractor) in some near integrable partial differential equations, particularly the sine-Gordon equation and the nonlinear Schroedinger equation. In order to study the motions, he uses low mode truncation methods to reduce these partial differential equations to some truncated models (low-dimensional ordinary differential equations). By applying many methods available to low-dimensional ordinary differential equations, he can understand the low-dimensional chaotic attractor of PDE's much better. However, there are two important questions one needs to answer: (1) How many modes is good enough for the low mode truncated models to capture the dynamics uniformly? (2) Is the chaotic attractor in a low mode truncated model close to the chaotic attractor in the original PDE? And how close is? He has developed two groups of powerful methods to help to answer these two questions. They are the computation methods of continuation and local bifurcation, and local Lyapunov exponents and Lyapunov exponents. Using these methods, he concludes that the 2N-nls ODE is a good model for the sine-Gordon equation and the nonlinear Schroedinger equation provided one chooses a 'good' basis and uses 'enough' modes (where 'enough' depends on the parameters of the system but is small for the parameter studied here). Therefore, one can use 2N-nls ODE to study the chaos of PDE's in more depth

Lorentz-force equations as Heisenberg equations for a quantum system in the euclidean space

International Nuclear Information System (INIS)

Rodriguez D, R.

2007-01-01

In an earlier work, the dynamic equations for a relativistic charged particle under the action of electromagnetic fields were formulated by R. Yamaleev in terms of external, as well as internal momenta. Evolution equations for external momenta, the Lorentz-force equations, were derived from the evolution equations for internal momenta. The mapping between the observables of external and internal momenta are related by Viete formulae for a quadratic polynomial, the characteristic polynomial of the relativistic dynamics. In this paper we show that the system of dynamic equations, can be cast into the Heisenberg scheme for a four-dimensional quantum system. Within this scheme the equations in terms of internal momenta play the role of evolution equations for a state vector, whereas the external momenta obey the Heisenberg equation for an operator evolution. The solutions of the Lorentz-force equation for the motion inside constant electromagnetic fields are presented via pentagonometric functions. (Author)

Differential Equation over Banach Algebra

OpenAIRE

Kleyn, Aleks

2018-01-01

In the book, I considered differential equations of order $1$ over Banach $D$-algebra: differential equation solved with respect to the derivative; exact differential equation; linear homogeneous equation. In noncommutative Banach algebra, initial value problem for linear homogeneous equation has infinitely many solutions.

Iterative solution of the semiconductor device equations

Energy Technology Data Exchange (ETDEWEB)

Bova, S.W.; Carey, G.F. [Univ. of Texas, Austin, TX (United States)

1996-12-31

Most semiconductor device models can be described by a nonlinear Poisson equation for the electrostatic potential coupled to a system of convection-reaction-diffusion equations for the transport of charge and energy. These equations are typically solved in a decoupled fashion and e.g. Newton`s method is used to obtain the resulting sequences of linear systems. The Poisson problem leads to a symmetric, positive definite system which we solve iteratively using conjugate gradient. The transport equations lead to nonsymmetric, indefinite systems, thereby complicating the selection of an appropriate iterative method. Moreover, their solutions exhibit steep layers and are subject to numerical oscillations and instabilities if standard Galerkin-type discretization strategies are used. In the present study, we use an upwind finite element technique for the transport equations. We also evaluate the performance of different iterative methods for the transport equations and investigate various preconditioners for a few generalized gradient methods. Numerical examples are given for a representative two-dimensional depletion MOSFET.

Elements of partial differential equations

CERN Document Server

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

New exact solutions to MKDV-Burgers equation and (2 + 1)-dimensional dispersive long wave equation via extended Riccati equation method

International Nuclear Information System (INIS)

Kong Cuicui; Wang Dan; Song Lina; Zhang Hongqing

2009-01-01

In this paper, with the aid of symbolic computation and a general ansaetz, we presented a new extended rational expansion method to construct new rational formal exact solutions to nonlinear partial differential equations. In order to illustrate the effectiveness of this method, we apply it to the MKDV-Burgers equation and the (2 + 1)-dimensional dispersive long wave equation, then several new kinds of exact solutions are successfully obtained by using the new ansaetz. The method can also be applied to other nonlinear partial differential equations.

Introduction to partial differential equations

CERN Document Server

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.

Backlund transformations and three-dimensional lattice equations

NARCIS (Netherlands)

Nijhoff, F.W.; Capel, H.W.; Wiersma, G.L.; Quispel, G.R.W.

1984-01-01

A (nonlocal) linear integral equation is studied, which allows for Bäcklund transformations in the measure. The compatibility of three of these transformations leads to an integrable nonlinear three-dimensional lattice equation. In appropriate continuum limits the two-dimensional Toda-lattice

A New Fractional Projective Riccati Equation Method for Solving Fractional Partial Differential Equations

International Nuclear Information System (INIS)

Feng Qing-Hua

2014-01-01

In this paper, a new fractional projective Riccati equation method is proposed to establish exact solutions for fractional partial differential equations in the sense of modified Riemann—Liouville derivative. This method can be seen as the fractional version of the known projective Riccati equation method. For illustrating the validity of this method, we apply this method to solve the space-time fractional Whitham—Broer—Kaup (WBK) equations and the nonlinear fractional Sharma—Tasso—Olever (STO) equation, and as a result, some new exact solutions for them are obtained. (general)

A new sine-Gordon equation expansion algorithm to investigate some special nonlinear differential equations

International Nuclear Information System (INIS)

Yan Zhenya

2005-01-01

A new transformation method is developed using the general sine-Gordon travelling wave reduction equation and a generalized transformation. With the aid of symbolic computation, this method can be used to seek more types of solutions of nonlinear differential equations, which include not only the known solutions derived by some known methods but new solutions. Here we choose the double sine-Gordon equation, the Magma equation and the generalized Pochhammer-Chree (PC) equation to illustrate the method. As a result, many types of new doubly periodic solutions are obtained. Moreover when using the method to these special nonlinear differential equations, some transformations are firstly needed. The method can be also extended to other nonlinear differential equations

Asymptotic problems for stochastic partial differential equations

Science.gov (United States)

Salins, Michael

Stochastic partial differential equations (SPDEs) can be used to model systems in a wide variety of fields including physics, chemistry, and engineering. The main SPDEs of interest in this dissertation are the semilinear stochastic wave equations which model the movement of a material with constant mass density that is exposed to both determinstic and random forcing. Cerrai and Freidlin have shown that on fixed time intervals, as the mass density of the material approaches zero, the solutions of the stochastic wave equation converge uniformly to the solutions of a stochastic heat equation, in probability. This is called the Smoluchowski-Kramers approximation. In Chapter 2, we investigate some of the multi-scale behaviors that these wave equations exhibit. In particular, we show that the Freidlin-Wentzell exit place and exit time asymptotics for the stochastic wave equation in the small noise regime can be approximated by the exit place and exit time asymptotics for the stochastic heat equation. We prove that the exit time and exit place asymptotics are characterized by quantities called quasipotentials and we prove that the quasipotentials converge. We then investigate the special case where the equation has a gradient structure and show that we can explicitly solve for the quasipotentials, and that the quasipotentials for the heat equation and wave equation are equal. In Chapter 3, we study the Smoluchowski-Kramers approximation in the case where the material is electrically charged and exposed to a magnetic field. Interestingly, if the system is frictionless, then the Smoluchowski-Kramers approximation does not hold. We prove that the Smoluchowski-Kramers approximation is valid for systems exposed to both a magnetic field and friction. Notably, we prove that the solutions to the second-order equations converge to the solutions of the first-order equation in an Lp sense. This strengthens previous results where convergence was proved in probability.

Scalar evolution equations for shear waves in incompressible solids: a simple derivation of the Z, ZK, KZK and KP equations

KAUST Repository

Destrade, M.

2010-12-08

We study the propagation of two-dimensional finite-amplitude shear waves in a nonlinear pre-strained incompressible solid, and derive several asymptotic amplitude equations in a simple, consistent and rigorous manner. The scalar Zabolotskaya (Z) equation is shown to be the asymptotic limit of the equations of motion for all elastic generalized neo-Hookean solids (with strain energy depending only on the first principal invariant of Cauchy-Green strain). However, we show that the Z equation cannot be a scalar equation for the propagation of two-dimensional shear waves in general elastic materials (with strain energy depending on the first and second principal invariants of strain). Then, we introduce dispersive and dissipative terms to deduce the scalar Kadomtsev-Petviashvili (KP), Zabolotskaya-Khokhlov (ZK) and Khokhlov- Zabolotskaya-Kuznetsov (KZK) equations of incompressible solid mechanics. © 2010 The Royal Society.

Scalar evolution equations for shear waves in incompressible solids: a simple derivation of the Z, ZK, KZK and KP equations

KAUST Repository

Destrade, M.; Goriely, A.; Saccomandi, G.

2010-01-01

We study the propagation of two-dimensional finite-amplitude shear waves in a nonlinear pre-strained incompressible solid, and derive several asymptotic amplitude equations in a simple, consistent and rigorous manner. The scalar Zabolotskaya (Z) equation is shown to be the asymptotic limit of the equations of motion for all elastic generalized neo-Hookean solids (with strain energy depending only on the first principal invariant of Cauchy-Green strain). However, we show that the Z equation cannot be a scalar equation for the propagation of two-dimensional shear waves in general elastic materials (with strain energy depending on the first and second principal invariants of strain). Then, we introduce dispersive and dissipative terms to deduce the scalar Kadomtsev-Petviashvili (KP), Zabolotskaya-Khokhlov (ZK) and Khokhlov- Zabolotskaya-Kuznetsov (KZK) equations of incompressible solid mechanics. © 2010 The Royal Society.

Numerical solutions of the aerosol general dynamic equation for nuclear reactor safety studies

International Nuclear Information System (INIS)

Park, J.W.

1988-01-01

Methods and approximations inherent in modeling of aerosol dynamics and evolution for nuclear reactor source term estimation have been investigated. Several aerosol evolution problems are considered to assess numerical methods of solving the aerosol dynamic equation. A new condensational growth model is constructed by generalizing Mason's formula to arbitrary particle sizes, and arbitrary accommodation of the condensing vapor and background gas at particle surface. Analytical solution is developed for the aerosol growth equation employing the new condensation model. The space-dependent aerosol dynamic equation is solved to assess implications of spatial homogenization of aerosol distributions. The results of our findings are as follows. The sectional method solving the aerosol dynamic equation is quite efficient in modeling of coagulation problems, but should be improved for simulation of strong condensation problems. The J-space transform method is accurate in modeling of condensation problems, but is very slow. For the situation considered, the new condensation model predicts slower aerosol growth than the corresponding isothermal model as well as Mason's model, the effect of partial accommodation is considerable on the particle evolution, and the effect of the energy accommodation coefficient is more pronounced than that of the mass accommodation coefficient. For the initial conditions considered, the space-dependent aerosol dynamics leads to results that are substantially different from those based on the spatially homogeneous aerosol dynamic equation

Dynamics with infinitely many derivatives: variable coefficient equations

International Nuclear Information System (INIS)

Barnaby, Neil; Kamran, Niky

2008-01-01

Infinite order differential equations have come to play an increasingly significant role in theoretical physics. Field theories with infinitely many derivatives are ubiquitous in string field theory and have attracted interest recently also from cosmologists. Crucial to any application is a firm understanding of the mathematical structure of infinite order partial differential equations. In our previous work we developed a formalism to study the initial value problem for linear infinite order equations with constant coefficients. Our approach relied on the use of a contour integral representation for the functions under consideration. In many applications, including the study of cosmological perturbations in nonlocal inflation, one must solve linearized partial differential equations about some time-dependent background. This typically leads to variable coefficient equations, in which case the contour integral methods employed previously become inappropriate. In this paper we develop the theory of a particular class of linear infinite order partial differential equations with variable coefficients. Our formalism is particularly well suited to the types of equations that arise in nonlocal cosmological perturbation theory. As an example to illustrate our formalism we compute the leading corrections to the scalar field perturbations in p-adic inflation and show explicitly that these are small on large scales.

A study on the boundary condition for analysis of bio-heat equation according to light irradiation

Energy Technology Data Exchange (ETDEWEB)

Ko, Dong Guk; Bae, Sung Woo; Im, Ik Tae [Chunbuk Natinal University, Junju (Korea, Republic of)

2015-11-15

In this study, the temperature change in an imitational biological tissue, when its surface is irradiated with bio-light, was measured by experiments. Using the experimental data, an equation for temperature as a function of time was developed in order to use it as a boundary condition in numerical studies for the model. The temperature profile was measured along the depth for several wavelengths and distances of the light source from the tissue. It was found that the temperature of the tissue increased with increasing wavelength and irradiation time; however, the difference in the temperatures with red light and near infrared light was not large. The numerical analysis results obtained by using the developed equation as boundary condition show good agreement with the measured temperatures.

Reactimeter dispersion equation

OpenAIRE

A.G. Yuferov

2016-01-01

The aim of this work is to derive and analyze a reactimeter metrological model in the form of the dispersion equation which connects reactimeter input/output signal dispersions with superimposed random noise at the inlet. It is proposed to standardize the reactimeter equation form, presenting the main reactimeter computing unit by a convolution equation. Hence, the reactimeter metrological characteristics are completely determined by this unit hardware function which represents a transient re...

Squeezing corrections to the Bloch equations

International Nuclear Information System (INIS)

Abundo, M.; Accardi, L.

1991-01-01

The general analysis of quantum noise shows that a squeezing noise can produce quadratic nonlinearities in the Langevin equations leading to the Bloch equations. These quadratic nonlinearities are governed by the imaginary part of the off-diagonal terms of the covariance of the noise (the squeezing terms) and imply a correction to the usual form of the Bloch equations. Here the case of spin-one nuclei subjected to squeezing noises of particular type is studied numerically. It is shown that the corrections to the Bloch equations, suggested by the theory, to the behaviour of the macroscopic nuclear polarization in a scale of times of the order of the relaxation time can be quite substantial. In the equilibrium regime, even if the qualitative behaviour of the system is the same (exponential decay), the numerical equilibrium values predicted by the theory are consistently different from those predicted by the usual Bloch equation. It is suggested that this difference might be used to test experimentally the observable effects of squeezing noises

Semilinear Kolmogorov Equations and Applications to Stochastic Optimal Control

International Nuclear Information System (INIS)

Masiero, Federica

2005-01-01

Semilinear parabolic differential equations are solved in a mild sense in an infinite-dimensional Hilbert space. Applications to stochastic optimal control problems are studied by solving the associated Hamilton-Jacobi-Bellman equation. These results are applied to some controlled stochastic partial differential equations

From the continuous PV to discrete Painleve equations

International Nuclear Information System (INIS)

Tokihiro, T.; Grammaticos, B.; Ramani, A.

2002-01-01

We study the discrete transformations that are associated with the auto-Baecklund of the (continuous) P V equation. We show that several two-parameter discrete Painleve equations can be obtained as contiguity relations of P V . Among them we find the asymmetric d-P II equation which is a well-known form of discrete P III . The relation between the ternary P I (previously obtained through the discrete dressing approach) and P V is also established. A new discrete Painleve equation is also derived. (author)

Symmetries and Invariants of the Time-dependent Oscillator Equation and the Envelope Equation

CERN Document Server

Qin, Hong

2005-01-01

Single-particle dynamics in a time-dependent focusing field is examined. The existence of the Courant-Snyder invariant* is fundamentally the result of the corresponding symmetry admitted by the oscillator equation with time-dependent frequency.** A careful analysis of the admitted symmetries reveals a deeper connection between the nonlinear envelope equation and the oscillator equation. A general theorem regarding the symmetries and invariants of the envelope equation, which includes the existence of the Courant-Snyder invariant as a special case, is demonstrated. The symmetries of the envelope equation enable a fast algorithm for finding matched solutions without using the conventional iterative shooting method.

Einstein-Friedmann equation, nonlinear dynamics and chaotic behaviours

International Nuclear Information System (INIS)

Tanaka, Yosuke; Nakano, Shingo; Ohta, Shigetoshi; Mori, Keisuke; Horiuchi, Tanji

2009-01-01

We have studied the Einstein-Friedmann equation [Case 1] on the basis of the bifurcation theory and shown that the chaotic behaviours in the Einstein-Friedmann equation [Case 1] are reduced to the pitchfork bifurcation and the homoclinic bifurcation. We have obtained the following results: (i) 'The chaos region diagram' (the p-λ plane) in the Einstein-Friedmann equation [Case 1]. (ii) 'The chaos inducing chart' of the homoclinic orbital systems in the unforced differential equations. We have discussed the non-integrable conditions in the Einstein-Friedmann equation and proposed the chaotic model: p=p 0 ρ n (n≥0). In case n≠0,1, the Einstein-Friedmann equation is not integrable and there may occur chaotic behaviours. The cosmological constant (λ) turns out to play important roles for the non-integrable condition in the Einstein-Friedmann equation and also for the pitchfork bifurcation and the homoclinic bifurcation in the relativistic field equation. With the use of the E-infinity theory, we have also discussed the physical quantities in the gravitational field equations, and obtained the formula logκ=-10(1/φ) 2 [1+(φ) 8 ]=-26.737, which is in nice agreement with the experiment (-26.730).

Exact solution of some linear matrix equations using algebraic methods

Science.gov (United States)

Djaferis, T. E.; Mitter, S. K.

1977-01-01

A study is done of solution methods for Linear Matrix Equations including Lyapunov's equation, using methods of modern algebra. The emphasis is on the use of finite algebraic procedures which are easily implemented on a digital computer and which lead to an explicit solution to the problem. The action f sub BA is introduced a Basic Lemma is proven. The equation PA + BP = -C as well as the Lyapunov equation are analyzed. Algorithms are given for the solution of the Lyapunov and comment is given on its arithmetic complexity. The equation P - A'PA = Q is studied and numerical examples are given.

True amplitude wave equation migration arising from true amplitude one-way wave equations

Science.gov (United States)

Zhang, Yu; Zhang, Guanquan; Bleistein, Norman

2003-10-01

One-way wave operators are powerful tools for use in forward modelling and inversion. Their implementation, however, involves introduction of the square root of an operator as a pseudo-differential operator. Furthermore, a simple factoring of the wave operator produces one-way wave equations that yield the same travel times as the full wave equation, but do not yield accurate amplitudes except for homogeneous media and for almost all points in heterogeneous media. Here, we present augmented one-way wave equations. We show that these equations yield solutions for which the leading order asymptotic amplitude as well as the travel time satisfy the same differential equations as the corresponding functions for the full wave equation. Exact representations of the square-root operator appearing in these differential equations are elusive, except in cases in which the heterogeneity of the medium is independent of the transverse spatial variables. Here, we address the fully heterogeneous case. Singling out depth as the preferred direction of propagation, we introduce a representation of the square-root operator as an integral in which a rational function of the transverse Laplacian appears in the integrand. This allows us to carry out explicit asymptotic analysis of the resulting one-way wave equations. To do this, we introduce an auxiliary function that satisfies a lower dimensional wave equation in transverse spatial variables only. We prove that ray theory for these one-way wave equations leads to one-way eikonal equations and the correct leading order transport equation for the full wave equation. We then introduce appropriate boundary conditions at z = 0 to generate waves at depth whose quotient leads to a reflector map and an estimate of the ray theoretical reflection coefficient on the reflector. Thus, these true amplitude one-way wave equations lead to a 'true amplitude wave equation migration' (WEM) method. In fact, we prove that applying the WEM imaging condition

Partial differential equations and boundary-value problems with applications

CERN Document Server

Pinsky, Mark A

2011-01-01

Building on the basic techniques of separation of variables and Fourier series, the book presents the solution of boundary-value problems for basic partial differential equations: the heat equation, wave equation, and Laplace equation, considered in various standard coordinate systems-rectangular, cylindrical, and spherical. Each of the equations is derived in the three-dimensional context; the solutions are organized according to the geometry of the coordinate system, which makes the mathematics especially transparent. Bessel and Legendre functions are studied and used whenever appropriate th

High creatinine clearance in critically ill patients with community-acquired acute infectious meningitis.

Science.gov (United States)

Lautrette, Alexandre; Phan, Thuy-Nga; Ouchchane, Lemlih; Aithssain, Ali; Tixier, Vincent; Heng, Anne-Elisabeth; Souweine, Bertrand

2012-09-27

A high dose of anti-infective agents is recommended when treating infectious meningitis. High creatinine clearance (CrCl) may affect the pharmacokinetic / pharmacodynamic relationships of anti-infective drugs eliminated by the kidneys. We recorded the incidence of high CrCl in intensive care unit (ICU) patients admitted with meningitis and assessed the diagnostic accuracy of two common methods used to identify high CrCl. Observational study performed in consecutive patients admitted with community-acquired acute infectious meningitis (defined by >7 white blood cells/mm3 in cerebral spinal fluid) between January 2006 and December 2009 to one medical ICU. During the first 7 days following ICU admission, CrCl was measured from 24-hr urine samples (24-hr-UV/P creatinine) and estimated according to Cockcroft-Gault formula and the simplified Modification of Diet in Renal Disease (MDRD) equation. High CrCl was defined as CrCl >140 ml/min/1.73 m2 by 24-hr-UV/P creatinine. Diagnostic accuracy was performed with ROC curves analysis. Thirty two patients were included. High CrCl was present in 8 patients (25%) on ICU admission and in 15 patients (47%) during the first 7 ICU days for a median duration of 3 (1-4) days. For the Cockcroft-Gault formula, the best threshold to predict high CrCl was 101 ml/min/1.73 m2 (sensitivity: 0.96, specificity: 0.75, AUC = 0.90 ± 0.03) with a negative likelihood ratio of 0.06. For the simplified MDRD equation, the best threshold to predict high CrCl was 108 ml/min/1.73 m2 (sensitivity: 0.91, specificity: 0.80, AUC = 0.88 ± 0.03) with a negative likelihood ratio of 0.11. There was no difference between the estimated methods in the diagnostic accuracy of identifying high CrCl (p = 0.30). High CrCl is frequently observed in ICU patients admitted with community-acquired acute infectious meningitis. The estimated methods of CrCl could be used as a screening tool to identify high CrCl.

Minimal length, Friedmann equations and maximum density

Energy Technology Data Exchange (ETDEWEB)

Awad, Adel [Center for Theoretical Physics, British University of Egypt,Sherouk City 11837, P.O. Box 43 (Egypt); Department of Physics, Faculty of Science, Ain Shams University,Cairo, 11566 (Egypt); Ali, Ahmed Farag [Centre for Fundamental Physics, Zewail City of Science and Technology,Sheikh Zayed, 12588, Giza (Egypt); Department of Physics, Faculty of Science, Benha University,Benha, 13518 (Egypt)

2014-06-16

Inspired by Jacobson’s thermodynamic approach, Cai et al. have shown the emergence of Friedmann equations from the first law of thermodynamics. We extend Akbar-Cai derivation http://dx.doi.org/10.1103/PhysRevD.75.084003 of Friedmann equations to accommodate a general entropy-area law. Studying the resulted Friedmann equations using a specific entropy-area law, which is motivated by the generalized uncertainty principle (GUP), reveals the existence of a maximum energy density closed to Planck density. Allowing for a general continuous pressure p(ρ,a) leads to bounded curvature invariants and a general nonsingular evolution. In this case, the maximum energy density is reached in a finite time and there is no cosmological evolution beyond this point which leaves the big bang singularity inaccessible from a spacetime prospective. The existence of maximum energy density and a general nonsingular evolution is independent of the equation of state and the spacial curvature k. As an example we study the evolution of the equation of state p=ωρ through its phase-space diagram to show the existence of a maximum energy which is reachable in a finite time.

Numerical search for a Phi4 breather mode and study of the Phi4, sine-Gordon, and Kdv equations with adibatic coefficients

International Nuclear Information System (INIS)

Wingate, C.A.

1978-01-01

Two major problems are studied in this thesis. The first is a numerical search for a stable oscillating mode in the Phi4 equation similar to the one that is known for the sine-Gordon equation. Starting with a widely separated soliton and anti-soliton traveling toward each other, it is observed, after a long period of time (t = 2800), that the solitons form a quasistable oscillating state. An interesting, previously unknown structure in the interaction depending on the initial velocity and initial separation is found and studied in detail. The second topic covered here is a study of the phi4, KdV and sine-Gordon equations when the coefficients vary slowly with time. A general first order solution is found for the wave equation with a non-linear potential and is applied to the phi4 and sine-Gordon potentials. In doing this it is found that the conservation of momentum is equivalent order by order to the secular conditions. Deficiencies in existing calculations for the KdV equation are pointed out through the use of adiabatic invariants and numerical calculations

An Investigation of the Sampling Distributions of Equating Coefficients.

Science.gov (United States)

Baker, Frank B.

1996-01-01

Using the characteristic curve method for dichotomously scored test items, the sampling distributions of equating coefficients were examined. Simulations indicate that for the equating conditions studied, the sampling distributions of the equating coefficients appear to have acceptable characteristics, suggesting confidence in the values obtained…

Error characterization for asynchronous computations: Proxy equation approach

Science.gov (United States)

Sallai, Gabriella; Mittal, Ankita; Girimaji, Sharath

2017-11-01

Numerical techniques for asynchronous fluid flow simulations are currently under development to enable efficient utilization of massively parallel computers. These numerical approaches attempt to accurately solve time evolution of transport equations using spatial information at different time levels. The truncation error of asynchronous methods can be divided into two parts: delay dependent (EA) or asynchronous error and delay independent (ES) or synchronous error. The focus of this study is a specific asynchronous error mitigation technique called proxy-equation approach. The aim of this study is to examine these errors as a function of the characteristic wavelength of the solution. Mitigation of asynchronous effects requires that the asynchronous error be smaller than synchronous truncation error. For a simple convection-diffusion equation, proxy-equation error analysis identifies critical initial wave-number, λc. At smaller wave numbers, synchronous error are larger than asynchronous errors. We examine various approaches to increase the value of λc in order to improve the range of applicability of proxy-equation approach.

Theoretical Study on Equation of State of Porous Mo and Sn

International Nuclear Information System (INIS)

Song Hai-Feng; Tian Ming-Feng; Liu Hai-Feng; Song Hong-Zhou; Zhang Gong-Mu

2014-01-01

We present a first-principles scheme to investigate the equation of state (EOS) of porous materials, based on our recently developed modified mean-field potential approach. By taking the effect of the structural parameters on the free energy into account, we calculate the total energy of materials with initial different densities and then study the EOS of porous Mo and Sn as a prototype. The calculated results are in good agreement with the experimental data available, which demonstrates that our scheme is suitable for investigating EOS of porous materials over a wide range of porosities and pressures

First-order partial differential equations

CERN Document Server

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

Equating Multidimensional Tests under a Random Groups Design: A Comparison of Various Equating Procedures

Science.gov (United States)

Lee, Eunjung

2013-01-01

The purpose of this research was to compare the equating performance of various equating procedures for the multidimensional tests. To examine the various equating procedures, simulated data sets were used that were generated based on a multidimensional item response theory (MIRT) framework. Various equating procedures were examined, including…

Dynamical TAP equations for non-equilibrium Ising spin glasses

DEFF Research Database (Denmark)

Roudi, Yasser; Hertz, John

2011-01-01

We derive and study dynamical TAP equations for Ising spin glasses obeying both synchronous and asynchronous dynamics using a generating functional approach. The system can have an asymmetric coupling matrix, and the external fields can be time-dependent. In the synchronously updated model, the TAP...... equations take the form of self consistent equations for magnetizations at time t+1, given the magnetizations at time t. In the asynchronously updated model, the TAP equations determine the time derivatives of the magnetizations at each time, again via self consistent equations, given the current values...... of the magnetizations. Numerical simulations suggest that the TAP equations become exact for large systems....

A Simple Stochastic Differential Equation with Discontinuous Drift

DEFF Research Database (Denmark)

Simonsen, Maria; Leth, John-Josef; Schiøler, Henrik

2013-01-01

In this paper we study solutions to stochastic differential equations (SDEs) with discontinuous drift. We apply two approaches: The Euler-Maruyama method and the Fokker-Planck equation and show that a candidate density function based on the Euler-Maruyama method approximates a candidate density...... function based on the stationary Fokker-Planck equation. Furthermore, we introduce a smooth function which approximates the discontinuous drift and apply the Euler-Maruyama method and the Fokker-Planck equation with this input. The point of departure for this work is a particular SDE with discontinuous...

Equations of multiparticle dynamics

International Nuclear Information System (INIS)

Chao, A.W.

1987-01-01

The description of the motion of charged-particle beams in an accelerator proceeds in steps of increasing complexity. The first step is to consider a single-particle picture in which the beam is represented as a collection on non-interacting test particles moving in a prescribed external electromagnetic field. Knowing the external field, it is then possible to calculate the beam motion to a high accuracy. The real beam consists of a large number of particles, typically 10 11 per beam bunch. It is sometimes inconvenient, or even impossible, to treat the real beam behavior using the single particle approach. One way to approach this problem is to supplement the single particle by another qualitatively different picture. The commonly used tools in accelerator physics for this purpose are the Vlasov and the Fokker-Planck equations. These equations assume smooth beam distributions and are therefore strictly valid in the limit of infinite number of micro-particles, each carrying an infinitesimal charge. The hope is that by studying the two extremes -- the single particle picture and the picture of smooth beam distributions -- we will be able to describe the behavior of our 10 11 -particle system. As mentioned, the most notable use of the smooth distribution picture is the study of collective beam instabilities. However, the purpose of this lecture is not to address this more advanced subject. Rather, it has the limited goal to familiarize the reader with the analytical tools, namely the Vlasov and the Fokker-Planck equations, as a preparation for dealing with the more advanced problems at later times. We will first derive these equations and then illustrate their applications by several examples which allow exact solutions

Solving the Richardson equations close to the critical points

Energy Technology Data Exchange (ETDEWEB)

DomInguez, F [Departamento de Matematicas, Universidad de Alcala, 28871 Alcala de Henares (Spain); Esebbag, C [Departamento de Matematicas, Universidad de Alcala, 28871 Alcala de Henares (Spain); Dukelsky, J [Instituto de Estructura de la Materia, CSIC, Serrano 123, 28006 Madrid (Spain)

2006-09-15

We study the Richardson equations close to the critical values of the pairing strength g{sub c}, where the occurrence of divergences precludes numerical solutions. We derive a set of equations for determining the critical g values and the non-collapsing pair energies. Studying the behaviour of the solutions close to the critical points, we develop a procedure to solve numerically the Richardson equations for arbitrary coupling strength.

Beginning partial differential equations

CERN Document Server

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

A new formulation of equations of compressible fluids by analogy with Maxwell's equations

International Nuclear Information System (INIS)

Kambe, Tsutomu

2010-01-01

A compressible ideal fluid is governed by Euler's equation of motion and equations of continuity, entropy and vorticity. This system can be reformulated in a form analogous to that of electromagnetism governed by Maxwell's equations with source terms. The vorticity plays the role of magnetic field, while the velocity field plays the part of a vector potential and the enthalpy (of isentropic flows) plays the part of a scalar potential in electromagnetism. The evolution of source terms of fluid Maxwell equations is determined by solving the equations of motion and continuity. The equation of sound waves can be derived from this formulation, where time evolution of the sound source is determined by the equation of motion. The theory of vortex sound of aeroacoustics is included in this formulation. It is remarkable that the forces acting on a point mass moving in a velocity field of an inviscid fluid are analogous in their form to the electric force and Lorentz force in electromagnetism. The significance of the reformulation is interpreted by examples taken from fluid mechanics. This formulation can be extended to viscous fluids without difficulty. The Maxwell-type equations are unchanged by the viscosity effect, although the source terms have additional terms due to viscosities.

Students’ difficulties in solving linear equation problems

Science.gov (United States)

Wati, S.; Fitriana, L.; Mardiyana

2018-03-01

A linear equation is an algebra material that exists in junior high school to university. It is a very important material for students in order to learn more advanced mathematics topics. Therefore, linear equation material is essential to be mastered. However, the result of 2016 national examination in Indonesia showed that students’ achievement in solving linear equation problem was low. This fact became a background to investigate students’ difficulties in solving linear equation problems. This study used qualitative descriptive method. An individual written test on linear equation tasks was administered, followed by interviews. Twenty-one sample students of grade VIII of SMPIT Insan Kamil Karanganyar did the written test, and 6 of them were interviewed afterward. The result showed that students with high mathematics achievement donot have difficulties, students with medium mathematics achievement have factual difficulties, and students with low mathematics achievement have factual, conceptual, operational, and principle difficulties. Based on the result there is a need of meaningfulness teaching strategy to help students to overcome difficulties in solving linear equation problems.

The modified simple equation method for solving some fractional ...

Indian Academy of Sciences (India)

... and processes in various areas of natural science. Thus, many effective and powerful methods have been established and improved. In this study, we establish exact solutions of the time fractional biological population model equation and nonlinearfractional Klein–Gordon equation by using the modified simple equation ...

Partial differential equations in several complex variables

CERN Document Server

Chen, So-Chin

2001-01-01

This book is intended both as an introductory text and as a reference book for those interested in studying several complex variables in the context of partial differential equations. In the last few decades, significant progress has been made in the fields of Cauchy-Riemann and tangential Cauchy-Riemann operators. This book gives an up-to-date account of the theories for these equations and their applications. The background material in several complex variables is developed in the first three chapters, leading to the Levi problem. The next three chapters are devoted to the solvability and regularity of the Cauchy-Riemann equations using Hilbert space techniques. The authors provide a systematic study of the Cauchy-Riemann equations and the \\bar\\partial-Neumann problem, including L^2 existence theorems on pseudoconvex domains, \\frac 12-subelliptic estimates for the \\bar\\partial-Neumann problems on strongly pseudoconvex domains, global regularity of \\bar\\partial on more general pseudoconvex domains, boundary ...

Computational partial differential equations using Matlab

CERN Document Server

Li, Jichun

2008-01-01

Brief Overview of Partial Differential Equations The parabolic equations The wave equations The elliptic equations Differential equations in broader areasA quick review of numerical methods for PDEsFinite Difference Methods for Parabolic Equations Introduction Theoretical issues: stability, consistence, and convergence 1-D parabolic equations2-D and 3-D parabolic equationsNumerical examples with MATLAB codesFinite Difference Methods for Hyperbolic Equations IntroductionSome basic difference schemes Dissipation and dispersion errors Extensions to conservation lawsThe second-order hyperbolic PDE

Integrable systems of partial differential equations determined by structure equations and Lax pair

International Nuclear Information System (INIS)

Bracken, Paul

2010-01-01

It is shown how a system of evolution equations can be developed both from the structure equations of a submanifold embedded in three-space as well as from a matrix SO(6) Lax pair. The two systems obtained this way correspond exactly when a constraint equation is selected and imposed on the system of equations. This allows for the possibility of selecting the coefficients in the second fundamental form in a general way.

Flavored quantum Boltzmann equations

International Nuclear Information System (INIS)

Cirigliano, Vincenzo; Lee, Christopher; Ramsey-Musolf, Michael J.; Tulin, Sean

2010-01-01

We derive from first principles, using nonequilibrium field theory, the quantum Boltzmann equations that describe the dynamics of flavor oscillations, collisions, and a time-dependent mass matrix in the early universe. Working to leading nontrivial order in ratios of relevant time scales, we study in detail a toy model for weak-scale baryogenesis: two scalar species that mix through a slowly varying time-dependent and CP-violating mass matrix, and interact with a thermal bath. This model clearly illustrates how the CP asymmetry arises through coherent flavor oscillations in a nontrivial background. We solve the Boltzmann equations numerically for the density matrices, investigating the impact of collisions in various regimes.

Drift-Diffusion Equation

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 equation for local accumulation time.

Science.gov (United States)

Berezhkovskii, Alexander M

2011-08-21

Cell differentiation in a developing tissue is controlled by the concentration fields of signaling molecules called morphogens. Formation of these concentration fields can be described by the reaction-diffusion mechanism in which locally produced molecules diffuse through the patterned tissue and are degraded. The formation kinetics at a given point of the patterned tissue can be characterized by the local accumulation time, defined in terms of the local relaxation function. Here, we show that this time satisfies an ordinary differential equation. Using this equation one can straightforwardly determine the local accumulation time, i.e., without preliminary calculation of the relaxation function by solving the partial differential equation, as was done in previous studies. We derive this ordinary differential equation together with the accompanying boundary conditions and demonstrate that the earlier obtained results for the local accumulation time can be recovered by solving this equation. © 2011 American Institute of Physics

Asymptotic integration of differential and difference equations

CERN Document Server

Bodine, Sigrun

2015-01-01

This book presents the theory of asymptotic integration for both linear differential and difference equations. This type of asymptotic analysis is based on some fundamental principles by Norman Levinson. While he applied them to a special class of differential equations, subsequent work has shown that the same principles lead to asymptotic results for much wider classes of differential and also difference equations. After discussing asymptotic integration in a unified approach, this book studies how the application of these methods provides several new insights and frequent improvements to results found in earlier literature. It then continues with a brief introduction to the relatively new field of asymptotic integration for dynamic equations on time scales. Asymptotic Integration of Differential and Difference Equations is a self-contained and clearly structured presentation of some of the most important results in asymptotic integration and the techniques used in this field. It will appeal to researchers i...

Symmetries of the Euler compressible flow equations for general equation of state

Energy Technology Data Exchange (ETDEWEB)

Boyd, Zachary M. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Ramsey, Scott D. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Baty, Roy S. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

2015-10-15

The Euler compressible flow equations exhibit different Lie symmetries depending on the equation of state (EOS) of the medium in which the flow occurs. This means that, in general, different types of similarity solution will be available in different flow media. We present a comprehensive classification of all EOS’s to which the Euler equations apply, based on the Lie symmetries admitted by the corresponding flow equations, restricting to the case of 1-D planar, cylindrical, or spherical geometry. The results are conveniently summarized in tables. This analysis also clarifies past work by Axford and Ovsiannikov on symmetry classification.

Alternatives to the Dirac equation

International Nuclear Information System (INIS)

Girvin, S.M.; Brownstein, K.R.

1975-01-01

Recent work by Biedenharn, Han, and van Dam (BHvD) has questioned the uniqueness of the Dirac equation. BHvD have obtained a two-component equation as an alternate to the Dirac equation. Although they later show their alternative to be unitarily equivalent to the Dirac equation, certain physical differences were claimed. BHvD attribute the existence of this alternate equation to the fact that their factorizing matrices were position-dependent. To investigate this, we factor the Klein-Gordon equation in spherical coordinates allowing the factorizing matrices to depend arbitrarily upon theta and phi. It is shown that despite this additional freedom, and without involving any relativistic covariance, the conventional four-component Dirac equation is the only possibility

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.

Nonlinear differential equations

International Nuclear Information System (INIS)

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

Exact RG flow equations and quantum gravity

Science.gov (United States)

de Alwis, S. P.

2018-03-01

We discuss the different forms of the functional RG equation and their relation to each other. In particular we suggest a generalized background field version that is close in spirit to the Polchinski equation as an alternative to the Wetterich equation to study Weinberg's asymptotic safety program for defining quantum gravity, and argue that the former is better suited for this purpose. Using the heat kernel expansion and proper time regularization we find evidence in support of this program in agreement with previous work.

Detecting breast microcalcifications using super-resolution and wave-equation ultrasound imaging: a numerical phantom study

Energy Technology Data Exchange (ETDEWEB)

Huang, Lianjie [Los Alamos National Laboratory; Simonetti, Francesco [IMPERIAL COLLEGE LONDON; Huthwaite, Peter [IMPERIAL COLLEGE LONDON; Rosenberg, Robert [UNM; Williamson, Michael [UNM

2010-01-01

Ultrasound image resolution and quality need to be significantly improved for breast microcalcification detection. Super-resolution imaging with the factorization method has recently been developed as a promising tool to break through the resolution limit of conventional imaging. In addition, wave-equation reflection imaging has become an effective method to reduce image speckles by properly handling ultrasound scattering/diffraction from breast heterogeneities during image reconstruction. We explore the capabilities of a novel super-resolution ultrasound imaging method and a wave-equation reflection imaging scheme for detecting breast microcalcifications. Super-resolution imaging uses the singular value decomposition and a factorization scheme to achieve an image resolution that is not possible for conventional ultrasound imaging. Wave-equation reflection imaging employs a solution to the acoustic-wave equation in heterogeneous media to backpropagate ultrasound scattering/diffraction waves to scatters and form images of heterogeneities. We construct numerical breast phantoms using in vivo breast images, and use a finite-difference wave-equation scheme to generate ultrasound data scattered from inclusions that mimic microcalcifications. We demonstrate that microcalcifications can be detected at full spatial resolution using the super-resolution ultrasound imaging and wave-equation reflection imaging methods.

Distributed Approximating Functional Approach to Burgers' Equation ...

African Journals Online (AJOL)

This equation is similar to, but simpler than, the Navier-Stokes equation in fluid dynamics. To verify this advantage through some comparison studies, an exact series solution are also obtained. In addition, the presented scheme has numerically stable behavior. After demonstrating the convergence and accuracy of the ...

Heat conduction in multifunctional nanotrusses studied using Boltzmann transport equation

International Nuclear Information System (INIS)

Dou, Nicholas G.; Minnich, Austin J.

2016-01-01

Materials that possess low density, low thermal conductivity, and high stiffness are desirable for engineering applications, but most materials cannot realize these properties simultaneously due to the coupling between them. Nanotrusses, which consist of hollow nanoscale beams architected into a periodic truss structure, can potentially break these couplings due to their lattice architecture and nanoscale features. In this work, we study heat conduction in the exact nanotruss geometry by solving the frequency-dependent Boltzmann transport equation using a variance-reduced Monte Carlo algorithm. We show that their thermal conductivity can be described with only two parameters, solid fraction and wall thickness. Our simulations predict that nanotrusses can realize unique combinations of mechanical and thermal properties that are challenging to achieve in typical materials

Quantum linear Boltzmann equation

International Nuclear Information System (INIS)

Vacchini, Bassano; Hornberger, Klaus

2009-01-01

We review the quantum version of the linear Boltzmann equation, which describes in a non-perturbative fashion, by means of scattering theory, how the quantum motion of a single test particle is affected by collisions with an ideal background gas. A heuristic derivation of this Lindblad master equation is presented, based on the requirement of translation-covariance and on the relation to the classical linear Boltzmann equation. After analyzing its general symmetry properties and the associated relaxation dynamics, we discuss a quantum Monte Carlo method for its numerical solution. We then review important limiting forms of the quantum linear Boltzmann equation, such as the case of quantum Brownian motion and pure collisional decoherence, as well as the application to matter wave optics. Finally, we point to the incorporation of quantum degeneracies and self-interactions in the gas by relating the equation to the dynamic structure factor of the ambient medium, and we provide an extension of the equation to include internal degrees of freedom.

Partial differential equations an introduction

CERN Document Server

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 F-equation

International Nuclear Information System (INIS)

Kalinowski, M.W.; Szymanowski, L.

1982-03-01

A generalization of the Truesdell F-equations is proposed and some solutions to them - generalized Fox F-functions - are found. It is also shown that a non-linear difference-differential equation, which does not belong to the Truesdell class, nevertheless may be transformed into the standard F-equation. (author)

How to obtain the covariant form of Maxwell's equations from the continuity equation

Energy Technology Data Exchange (ETDEWEB)

Heras, Jose A [Departamento de Ciencias Basicas, Universidad Autonoma Metropolitana, Unidad Azcapotzalco, Av. San Pablo No. 180, Col. Reynosa, 02200, Mexico D. F. (Mexico); Departamento de Fisica y Matematicas, Universidad Iberoamericana, Prolongacion Paseo de la Reforma 880, Mexico D. F. 01210 (Mexico)

2009-07-15

The covariant Maxwell equations are derived from the continuity equation for the electric charge. This result provides an axiomatic approach to Maxwell's equations in which charge conservation is emphasized as the fundamental axiom underlying these equations.

Study on the Accuracy Improvement of the Second-Kind Fredholm Integral Equations by Using the Buffa-Christiansen Functions with MLFMA

Directory of Open Access Journals (Sweden)

Yue-Qian Wu

2016-01-01

Full Text Available Former works show that the accuracy of the second-kind integral equations can be improved dramatically by using the rotated Buffa-Christiansen (BC functions as the testing functions, and sometimes their accuracy can be even better than the first-kind integral equations. When the rotated BC functions are used as the testing functions, the discretization error of the identity operators involved in the second-kind integral equations can be suppressed significantly. However, the sizes of spherical objects which were analyzed are relatively small. Numerical capability of the method of moments (MoM for solving integral equations with the rotated BC functions is severely limited. Hence, the performance of BC functions for accuracy improvement of electrically large objects is not studied. In this paper, the multilevel fast multipole algorithm (MLFMA is employed to accelerate iterative solution of the magnetic-field integral equation (MFIE. Then a series of numerical experiments are performed to study accuracy improvement of MFIE in perfect electric conductor (PEC cases with the rotated BC as testing functions. Numerical results show that the effect of accuracy improvement by using the rotated BC as the testing functions is greatly different with curvilinear or plane triangular elements but falls off when the size of the object is large.

Study of some properties of partial differential equations by Lie algebra method

International Nuclear Information System (INIS)

Chongdar, A.K.; Ludu, A.

1990-05-01

In this note we present a system of optimal subalgebras of the Lie algebra obtained in course of investigating hypergeometric polynomial. In addition to this we have obtained some reduced equation and invariants of the P.D.E. obtained under certain transformation while studying hypergeometric polynomial by Weisner's method. Some topological properties of the solutions of P.D.E. are pointed out by using the extended jet bundle formalism. Some applications of our work on plasma physics and hydrodynamics are also cited. (author). 8 refs

An introduction to stochastic differential equations

CERN Document Server

Evans, Lawrence C

2014-01-01

These notes provide a concise introduction to stochastic differential equations and their application to the study of financial markets and as a basis for modeling diverse physical phenomena. They are accessible to non-specialists and make a valuable addition to the collection of texts on the topic. -Srinivasa Varadhan, New York University This is a handy and very useful text for studying stochastic differential equations. There is enough mathematical detail so that the reader can benefit from this introduction with only a basic background in mathematical analysis and probability. -George Papa

Orbital stability of solitary waves for Kundu equation

Science.gov (United States)

Zhang, Weiguo; Qin, Yinghao; Zhao, Yan; Guo, Boling

In this paper, we consider the Kundu equation which is not a standard Hamiltonian system. The abstract orbital stability theory proposed by Grillakis et al. (1987, 1990) cannot be applied directly to study orbital stability of solitary waves for this equation. Motivated by the idea of Guo and Wu (1995), we construct three invariants of motion and use detailed spectral analysis to obtain orbital stability of solitary waves for Kundu equation. Since Kundu equation is more complex than the derivative Schrödinger equation, we utilize some techniques to overcome some difficulties in this paper. It should be pointed out that the results obtained in this paper are more general than those obtained by Guo and Wu (1995). We present a sufficient condition under which solitary waves are orbitally stable for 2c+sυ1995) only considered the case 2c+sυ>0. We obtain the results on orbital stability of solitary waves for the derivative Schrödinger equation given by Colin and Ohta (2006) as a corollary in this paper. Furthermore, we obtain orbital stability of solitary waves for Chen-Lee-Lin equation and Gerdjikov-Ivanov equation, respectively.

Lectures on partial differential equations

CERN Document Server

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.

Reduction operators of Burgers equation.

Science.gov (United States)

Pocheketa, Oleksandr A; Popovych, Roman O

2013-02-01

The solution of the problem on reduction operators and nonclassical reductions of the Burgers equation is systematically treated and completed. A new proof of the theorem on the special "no-go" case of regular reduction operators is presented, and the representation of the coefficients of operators in terms of solutions of the initial equation is constructed for this case. All possible nonclassical reductions of the Burgers equation to single ordinary differential equations are exhaustively described. Any Lie reduction of the Burgers equation proves to be equivalent via the Hopf-Cole transformation to a parameterized family of Lie reductions of the linear heat equation.

Thermodynamic quantities for the Klein–Gordon equation

Indian Academy of Sciences (India)

We study some thermodynamic quantities for the Klein–Gordon equation with a linear plus inverselinear, scalar potential. We obtain the energy eigenvalues with the help of the quantization rule from the biconfluent Heun's equation.We use a method based on the Euler–MacLaurin formula to analytically compute thethermal ...

The magnetic field experiment onboard Equator-S and its scientific possibilities

Directory of Open Access Journals (Sweden)

K.-H. Fornacon

1999-12-01

Full Text Available The special feature of the ringcore fluxgate magnetometer on Equator-S is the high time and field resolution. The scientific aim of the experiment is the investigation of waves in the 10–100 picotesla range with a time resolution up to 64 Hz. The instrument characteristics and the influence of the spacecraft on the magnetic field measurement will be discussed. The work shows that the applied pre- and inflight calibration techniques are sufficient to suppress spacecraft interferences. The offset in spin axis direction was determined for the first time with an independent field measurement by the Equator-S Electron Drift Instrument. The data presented gives an impression of the accuracy of the measurement.Key words. Magnetospheric physics (instruments and techniques · Space plasma physics (instruments and techniques

The magnetic field experiment onboard Equator-S and its scientific possibilities

Directory of Open Access Journals (Sweden)

K.-H. Fornacon

Full Text Available The special feature of the ringcore fluxgate magnetometer on Equator-S is the high time and field resolution. The scientific aim of the experiment is the investigation of waves in the 10–100 picotesla range with a time resolution up to 64 Hz. The instrument characteristics and the influence of the spacecraft on the magnetic field measurement will be discussed. The work shows that the applied pre- and inflight calibration techniques are sufficient to suppress spacecraft interferences. The offset in spin axis direction was determined for the first time with an independent field measurement by the Equator-S Electron Drift Instrument. The data presented gives an impression of the accuracy of the measurement.

Key words. Magnetospheric physics (instruments and techniques · Space plasma physics (instruments and techniques

Linear and quasi-linear equations of parabolic type

CERN Document Server

Ladyženskaja, O A; Ural′ceva, N N; Uralceva, N N

1968-01-01

Equations of parabolic type are encountered in many areas of mathematics and mathematical physics, and those encountered most frequently are linear and quasi-linear parabolic equations of the second order. In this volume, boundary value problems for such equations are studied from two points of view: solvability, unique or otherwise, and the effect of smoothness properties of the functions entering the initial and boundary conditions on the smoothness of the solutions.

Michaelis - Menten equation for degradation of insoluble substrate

DEFF Research Database (Denmark)

Andersen, Morten; Kari, Jeppe; Borch, Kim

2017-01-01

substrate it is difficult to assess whether the requirement of the MM equation is met. In this paper we study a simple kinetic model, where removal of attack sites expose new ones which preserve the total accessible substrate, and denote this approach the substrate conserving model. The kinetic equations...... are solved in closed form, both steady states and progress curves, for any admissible values of initial conditions and rate constants. The model is shown to merge with the MM equation and the reverse MM equation when these are valid. The relation between available molar concentration of attack sites and mass...

Relativistic equations of state at finite temperature

International Nuclear Information System (INIS)

Santos, A.M.S.; Menezes, D.P.

2004-01-01

In this work we study the effects of temperature on the equations of state obtained within a relativistic model with and without β equilibrium, over a wide range of densities. We integrate the TOV equations. We also compare the results of the equation of state, effective mass and strangeness fraction from the TM1, NL3 and GL sets of parameters, as well as investigating the importance of antiparticles in the treatment. The have checked that TM1 and NL3 are not appropriate for the description of neutron and protoneutron stars. (author)

Nonlinear dynamics in the Einstein-Friedmann equation

International Nuclear Information System (INIS)

Tanaka, Yosuke; Mizuno, Yuji; Ohta, Shigetoshi; Mori, Keisuke; Horiuchi, Tanji

2009-01-01

We have studied the gravitational field equations on the basis of general relativity and nonlinear dynamics. The space component of the Einstein-Friedmann equation shows the chaotic behaviours in case the following conditions are satisfied: (i)the expanding ratio: h=x . /x max = +0.14) for the occurrence of the chaotic behaviours in the Einstein-Friedmann equation (0 ≤ λ ≤ +0.14). The numerical calculations are performed with the use of the Microsoft EXCEL(2003), and the results are shown in the following cases; λ = 2b = +0.06 and +0.14.

An alternative form of the Darcy equation

Directory of Open Access Journals (Sweden)

Awad Mohamed M.

2014-01-01

Full Text Available This study presents an alternative form of the Darcy equation. This alternative form will be presented with the use of Bejan number (Be in the Left Hand Side (LHS of the equation. The main advantage in this alternative form of the Darcy equation is presenting both the Left Hand Side (LHS and the Right Hand Side (RHS as dimensionless quantities. For instance, this is similar to the relation of Fanning friction factor with Reynolds number for Hagen-Poiseuille flow (fully developed laminar flow in a circular pipe.

Supersymmetric quasipotential equations

International Nuclear Information System (INIS)

Zaikov, R.P.

1981-01-01

A supersymmetric extension of the Logunov-Tavkhelidze quasipotential approach is suggested. The supersymmetric Bethe- Salpeter equation is an initial equation. The transition from the four-time to the two-time Green function is made in the super- center-of-mass system. The two-time Green function has no inverse function in the whole spinor space. The resolvent operator if found using the Majorana character of the spinor wave function. The supersymmetric quasipotential equation is written. The consideration is carried out in the framework of the theory of chiral scalar superfields [ru

Ordinary differential equations

CERN Document Server

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,

Uncertain differential equations

CERN Document Server

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.

Introduction to nonlinear dispersive equations

CERN Document Server

Linares, Felipe

2015-01-01

This textbook introduces the well-posedness theory for initial-value problems of nonlinear, dispersive partial differential equations, with special focus on two key models, the Korteweg–de Vries equation and the nonlinear Schrödinger equation. A concise and self-contained treatment of background material (the Fourier transform, interpolation theory, Sobolev spaces, and the linear Schrödinger equation) prepares the reader to understand the main topics covered: the initial-value problem for the nonlinear Schrödinger equation and the generalized Korteweg–de Vries equation, properties of their solutions, and a survey of general classes of nonlinear dispersive equations of physical and mathematical significance. Each chapter ends with an expert account of recent developments and open problems, as well as exercises. The final chapter gives a detailed exposition of local well-posedness for the nonlinear Schrödinger equation, taking the reader to the forefront of recent research. The second edition of Introdu...

State Equation Determination of Cow Dung Biogas