Comparison of risk prediction using the CKD-EPI equation and the MDRD study equation for estimated glomerular filtration rate.

PubMed

Matsushita, Kunihiro; Mahmoodi, Bakhtawar K; Woodward, Mark; Emberson, Jonathan R; Jafar, Tazeen H; Jee, Sun Ha; Polkinghorne, Kevan R; Shankar, Anoop; Smith, David H; Tonelli, Marcello; Warnock, David G; Wen, Chi-Pang; Coresh, Josef; Gansevoort, Ron T; Hemmelgarn, Brenda R; Levey, Andrew S

2012-05-09

The Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) equation more accurately estimates glomerular filtration rate (GFR) than the Modification of Diet in Renal Disease (MDRD) Study equation using the same variables, especially at higher GFR, but definitive evidence of its risk implications in diverse settings is lacking. To evaluate risk implications of estimated GFR using the CKD-EPI equation compared with the MDRD Study equation in populations with a broad range of demographic and clinical characteristics. A meta-analysis of data from 1.1 million adults (aged ≥ 18 years) from 25 general population cohorts, 7 high-risk cohorts (of vascular disease), and 13 CKD cohorts. Data transfer and analyses were conducted between March 2011 and March 2012. All-cause mortality (84,482 deaths from 40 cohorts), cardiovascular mortality (22,176 events from 28 cohorts), and end-stage renal disease (ESRD) (7644 events from 21 cohorts) during 9.4 million person-years of follow-up; the median of mean follow-up time across cohorts was 7.4 years (interquartile range, 4.2-10.5 years). Estimated GFR was classified into 6 categories (≥90, 60-89, 45-59, 30-44, 15-29, and <15 mL/min/1.73 m(2)) by both equations. Compared with the MDRD Study equation, 24.4% and 0.6% of participants from general population cohorts were reclassified to a higher and lower estimated GFR category, respectively, by the CKD-EPI equation, and the prevalence of CKD stages 3 to 5 (estimated GFR <60 mL/min/1.73 m(2)) was reduced from 8.7% to 6.3%. In estimated GFR of 45 to 59 mL/min/1.73 m(2) by the MDRD Study equation, 34.7% of participants were reclassified to estimated GFR of 60 to 89 mL/min/1.73 m(2) by the CKD-EPI equation and had lower incidence rates (per 1000 person-years) for the outcomes of interest (9.9 vs 34.5 for all-cause mortality, 2.7 vs 13.0 for cardiovascular mortality, and 0.5 vs 0.8 for ESRD) compared with those not reclassified. The corresponding adjusted hazard ratios were 0.80 (95

Cardiovascular risk assessment: addition of CKD and race to the Framingham equation

PubMed Central

Drawz, Paul E.; Baraniuk, Sarah; Davis, Barry R.; Brown, Clinton D.; Colon, Pedro J.; Cujyet, Aloysius B.; Dart, Richard A.; Graumlich, James F.; Henriquez, Mario A.; Moloo, Jamaluddin; Sakalayen, Mohammed G.; Simmons, Debra L.; Stanford, Carol; Sweeney, Mary Ellen; Wong, Nathan D.; Rahman, Mahboob

2012-01-01

Background/Aims The value of the Framingham equation in predicting cardiovascular risk in African Americans and patients with chronic kidney disease (CKD) is unclear. The purpose of the study was to evaluate whether the addition of CKD and race to the Framingham equation improves risk stratification in hypertensive patients. Methods Participants in the Antihypertensive and Lipid-Lowering Treatment to Prevent Heart Attack Trial (ALLHAT) were studied. Those randomized to doxazosin, age greater than 74 years, and those with a history of coronary heart disease (CHD) were excluded. Two risk stratification models were developed using Cox proportional hazards models in a two-thirds developmental sample. The first model included the traditional Framingham risk factors. The second model included the traditional risk factors plus CKD, defined by eGFR categories, and stratification by race (Black vs. Non-Black). The primary outcome was a composite of fatal CHD, nonfatal MI, coronary revascularization, and hospitalized angina. Results There were a total of 19,811 eligible subjects. In the validation cohort, there was no difference in C-statistics between the Framingham equation and the ALLHAT model including CKD and race. This was consistent across subgroups by race and gender and among those with CKD. One exception was among Non-Black women where the C-statistic was higher for the Framingham equation (0.68 vs 0.65, P=0.02). Additionally, net reclassification improvement was not significant for any subgroup based on race and gender, ranging from −5.5% to 4.4%. Conclusion The addition of CKD status and stratification by race does not improve risk prediction in high-risk hypertensive patients. PMID:23194494

Estimation of the Long-term Cardiovascular Events Using UKPDS Risk Engine in Metabolic Syndrome Patients.

PubMed

Shivakumar, V; Kandhare, A D; Rajmane, A R; Adil, M; Ghosh, P; Badgujar, L B; Saraf, M N; Bodhankar, S L

2014-03-01

Long-term cardiovascular complications in metabolic syndrome are a major cause of mortality and morbidity in India and forecasted estimates in this domain of research are scarcely reported in the literature. The aim of present investigation is to estimate the cardiovascular events associated with a representative Indian population of patients suffering from metabolic syndrome using United Kingdom Prospective Diabetes Study risk engine. Patient level data was collated from 567 patients suffering from metabolic syndrome through structured interviews and physician records regarding the input variables, which were entered into the United Kingdom Prospective Diabetes Study risk engine. The patients of metabolic syndrome were selected according to guidelines of National Cholesterol Education Program - Adult Treatment Panel III, modified National Cholesterol Education Program - Adult Treatment Panel III and International Diabetes Federation criteria. A projection for 10 simulated years was run on the engine and output was determined. The data for each patient was processed using the United Kingdom Prospective Diabetes Study risk engine to calculate an estimate of the forecasted value for the cardiovascular complications after a period of 10 years. The absolute risk (95% confidence interval) for coronary heart disease, fatal coronary heart disease, stroke and fatal stroke for 10 years was 3.79 (1.5-3.2), 9.6 (6.8-10.7), 7.91 (6.5-9.9) and 3.57 (2.3-4.5), respectively. The relative risk (95% confidence interval) for coronary heart disease, fatal coronary heart disease, stroke and fatal stroke was 17.8 (12.98-19.99), 7 (6.7-7.2), 5.9 (4.0-6.6) and 4.7 (3.2-5.7), respectively. Simulated projections of metabolic syndrome patients predict serious life-threatening cardiovascular consequences in the representative cohort of patients in western India.

Assessment of the agreement between the Framingham and DAD risk equations for estimating cardiovascular risk in adult Africans living with HIV infection: a cross-sectional study.

PubMed

Noumegni, Steve Raoul; Ama, Vicky Jocelyne Moor; Assah, Felix K; Bigna, Jean Joel; Nansseu, Jobert Richie; Kameni, Jenny Arielle M; Katte, Jean-Claude; Dehayem, Mesmin Y; Kengne, Andre Pascal; Sobngwi, Eugene

2017-01-01

The Absolute cardiovascular disease (CVD) risk evaluation using multivariable CVD risk models is increasingly advocated in people with HIV, in whom existing models remain largely untested. We assessed the agreement between the general population derived Framingham CVD risk equation and the HIV-specific Data collection on Adverse effects of anti-HIV Drugs (DAD) CVD risk equation in HIV-infected adult Cameroonians. This cross-sectional study involved 452 HIV infected adults recruited at the HIV day-care unit of the Yaoundé Central Hospital, Cameroon. The 5-year projected CVD risk was estimated for each participant using the DAD and Framingham CVD risk equations. Agreement between estimates from these equations was assessed using the spearman correlation and Cohen's kappa coefficient. The mean age of participants (80% females) was 44.4 ± 9.8 years. Most participants (88.5%) were on antiretroviral treatment with 93.3% of them receiving first-line regimen. The most frequent cardiovascular risk factors were abdominal obesity (43.1%) and dyslipidemia (33.8%). The median estimated 5-year CVD risk was 0.6% (25th-75th percentiles: 0.3-1.3) using the DAD equation and 0.7% (0.2-2.0) with the Framingham equation. The Spearman correlation between the two estimates was 0.93 ( p  < 0.001). The kappa statistic was 0.61 (95% confident interval: 0.54-0.67) for the agreement between the two equations in classifying participants across risk categories defined as low, moderate, high and very high. Most participants had a low-to-moderate estimated CVD risk, with acceptable level of agreement between the general and HIV-specific equations in ranking CVD risk.

Developing prediction equations and a mobile phone application to identify infants at risk of obesity.

PubMed

Santorelli, Gillian; Petherick, Emily S; Wright, John; Wilson, Brad; Samiei, Haider; Cameron, Noël; Johnson, William

2013-01-01

Advancements in knowledge of obesity aetiology and mobile phone technology have created the opportunity to develop an electronic tool to predict an infant's risk of childhood obesity. The study aims were to develop and validate equations for the prediction of childhood obesity and integrate them into a mobile phone application (App). Anthropometry and childhood obesity risk data were obtained for 1868 UK-born White or South Asian infants in the Born in Bradford cohort. Logistic regression was used to develop prediction equations (at 6 ± 1.5, 9 ± 1.5 and 12 ± 1.5 months) for risk of childhood obesity (BMI at 2 years >91(st) centile and weight gain from 0-2 years >1 centile band) incorporating sex, birth weight, and weight gain as predictors. The discrimination accuracy of the equations was assessed by the area under the curve (AUC); internal validity by comparing area under the curve to those obtained in bootstrapped samples; and external validity by applying the equations to an external sample. An App was built to incorporate six final equations (two at each age, one of which included maternal BMI). The equations had good discrimination (AUCs 86-91%), with the addition of maternal BMI marginally improving prediction. The AUCs in the bootstrapped and external validation samples were similar to those obtained in the development sample. The App is user-friendly, requires a minimum amount of information, and provides a risk assessment of low, medium, or high accompanied by advice and website links to government recommendations. Prediction equations for risk of childhood obesity have been developed and incorporated into a novel App, thereby providing proof of concept that childhood obesity prediction research can be integrated with advancements in technology.

New equations for predicting postoperative risk in patients with hip fracture.

PubMed

Hirose, Jun; Ide, Junji; Irie, Hiroki; Kikukawa, Kenshi; Mizuta, Hiroshi

2009-12-01

Predicting the postoperative course of patients with hip fractures would be helpful for surgical planning and risk management. We therefore established equations to predict the morbidity and mortality rates in candidates for hip fracture surgery using the Estimation of Physiologic Ability and Surgical Stress (E-PASS) risk-scoring system. First we evaluated the correlation between the E-PASS scores and postoperative morbidity and mortality rates in all 722 patients surgically treated for hip fractures during the study period (Group A). Next we established equations to predict morbidity and mortality rates. We then applied these equations to all 633 patients with hip fractures treated at seven other hospitals (Group B) and compared the predicted and actual morbidity and mortality rates to assess the predictive ability of the E-PASS and Physiological and Operative Severity Score for the enUmeration of Mortality and Morbidity (POSSUM) systems. The ratio of actual to predicted morbidity and mortality rates was closer to 1.0 with the E-PASS than the POSSUM system. Our data suggest the E-PASS scoring system is useful for defining postoperative risk and its underlying algorithm accurately predicts morbidity and mortality rates in patients with hip fractures before surgery. This information then can be used to manage their condition and potentially improve treatment outcomes. Level II, prognostic study. See the Guidelines for Authors for a complete description of levels of evidence.

Health risk equations and risk assessment of airborne benzene homologues exposure to drivers and passengers in taxi cabins.

PubMed

Chen, Xiaokai; Feng, Lili; Luo, Huilong; Cheng, Heming

2016-03-01

Interior air environment and health problems of vehicles have attracted increasing attention, and benzene homologues (BHs) including benzene, toluene, ethylbenzene, xylenes, and styrene are primary hazardous gases in vehicular cabins. The BHs impact on the health of passengers and drivers in 38 taxis is assessed, and health risk equations of in-car BHs to different drivers and passengers are induced. The health risk of in-car BHs for male drivers is the highest among all different receptors and is 1.04, 6.67, and 6.94 times more than ones for female drivers, male passengers, and female passengers, respectively. In-car BHs could not lead to the non-cancer health risk to all passengers and drivers as for the maximal value of non-cancer indices is 0.41 and is less than the unacceptable value (1.00) of non-cancer health risk from USEPA. However, in-car BHs lead to cancer health risk to drivers as for the average value of cancer indices is 1.21E-04 which is 1.21 times more than the unacceptable value (1.00E-04) of cancer health risk from USEPA. Finally, for in-car airborne benzene concentration (X, μg/m(3)) to male drivers, female drivers, male passengers, and female passengers, the cancer health risk equations are Y = 1.48E-06X, Y = 1.42E-06X, Y = 2.22E-07X, and Y = 2.13E-07X, respectively, and the non-cancer health risk equations are Y = 1.70E-03X, Y = 1.63E-03X, Y = 2.55E-04X, and Y = 2.45E-04X, respectively.

Sleep apnoea syndrome and 10-year cardiovascular risk in females with type 2 diabetes: relationship with insulin secretion and insulin resistance.

PubMed

Hermans, Michel P; Ahn, Sylvie A; Mahadeb, Yovan P; Rousseau, Michel F

2013-03-01

Obstructive sleep apnoea syndrome (OSAS) is a risk factor for type 2 diabetes mellitus (T2DM) and promotes cardiovascular events, especially in men. The prevalence of sleep apnoea and its association with microvascular and macrovascular diseases and glycaemic control are poorly documented in T2DM women. A total of 305 T2DM women were sleep apnoea diagnosed through (hetero)anamnesis, Epworth's score, oximetry and polysomnography. Sleep apnoea[+] (n = 25) were compared with sleep apnoea[-] (n = 280) regarding cardiovascular risk factors, glucose homeostasis, micro/macrovascular complications and the United Kingdom Prospective Diabetes Study (UKPDS) 10-year risk. Mean (1 SD) age was 66 (12) years, diabetes duration 15 (9) years, sleep apnoea prevalence 8.2% and metabolic syndrome 86%. There were no differences in age, diabetes duration, education, smoking and blood pressure between groups. Sleep apnoea[+] had significantly higher values of body mass index, waist, relative/absolute fat, conicity, visceral fat (all p < 0.0001) and lower skeletal muscle (p = 0.0008). The sleep apnoea[+] group was more insulin resistant [homeostasis model assessment (HOMA S): 37 (20)% versus 59 (44)%; p < 0.0001] and had lesser residual insulin secretion (HOMA B × S: 20 (12)% versus 30 (19)%; p = 0.0006), increased hyperbolic product loss (p = 0.0442) and poorer glycaemic control (HbA1c 69 (12) versus 62 (13) mmol mol(-1) ; p = 0.0099). All atherogenic dyslipidaemia components and inflammatory markers were worsened in sleep apnoea[+]. Women with sleep apnoea had higher UKPDS risk of CAD: 18 (11)% versus 12 (10)% (p = 0.0136). Prevalent micro/macrovascular complications were not different between groups. Sleep apnoea, a frequent comorbidity of T2DM women, is associated with central fat, atherogenic dyslipidaemia, inflammation, worsening β-cell function, poorer glycaemic control and coronary artery disease risk. Sleep apnoea may increase residual vascular risk for microvascular and

Development and validation of risk prediction equations to estimate future risk of blindness and lower limb amputation in patients with diabetes: cohort study

PubMed Central

Coupland, Carol

2015-01-01

Study question Is it possible to develop and externally validate risk prediction equations to estimate the 10 year risk of blindness and lower limb amputation in patients with diabetes aged 25-84 years? Methods This was a prospective cohort study using routinely collected data from general practices in England contributing to the QResearch and Clinical Practice Research Datalink (CPRD) databases during the study period 1998-2014. The equations were developed using 763 QResearch practices (n=454 575 patients with diabetes) and validated in 254 different QResearch practices (n=142 419) and 357 CPRD practices (n=206 050). Cox proportional hazards models were used to derive separate risk equations for blindness and amputation in men and women that could be evaluated at 10 years. Measures of calibration and discrimination were calculated in the two validation cohorts. Study answer and limitations Risk prediction equations to quantify absolute risk of blindness and amputation in men and women with diabetes have been developed and externally validated. In the QResearch derivation cohort, 4822 new cases of lower limb amputation and 8063 new cases of blindness occurred during follow-up. The risk equations were well calibrated in both validation cohorts. Discrimination was good in men in the external CPRD cohort for amputation (D statistic 1.69, Harrell’s C statistic 0.77) and blindness (D statistic 1.40, Harrell’s C statistic 0.73), with similar results in women and in the QResearch validation cohort. The algorithms are based on variables that patients are likely to know or that are routinely recorded in general practice computer systems. They can be used to identify patients at high risk for prevention or further assessment. Limitations include lack of formally adjudicated outcomes, information bias, and missing data. What this study adds Patients with type 1 or type 2 diabetes are at increased risk of blindness and amputation but generally do not have accurate

Development and validation of risk prediction equations to estimate future risk of blindness and lower limb amputation in patients with diabetes: cohort study.

PubMed

Hippisley-Cox, Julia; Coupland, Carol

2015-11-11

Is it possible to develop and externally validate risk prediction equations to estimate the 10 year risk of blindness and lower limb amputation in patients with diabetes aged 25-84 years? This was a prospective cohort study using routinely collected data from general practices in England contributing to the QResearch and Clinical Practice Research Datalink (CPRD) databases during the study period 1998-2014. The equations were developed using 763 QResearch practices (n=454,575 patients with diabetes) and validated in 254 different QResearch practices (n=142,419) and 357 CPRD practices (n=206,050). Cox proportional hazards models were used to derive separate risk equations for blindness and amputation in men and women that could be evaluated at 10 years. Measures of calibration and discrimination were calculated in the two validation cohorts. Risk prediction equations to quantify absolute risk of blindness and amputation in men and women with diabetes have been developed and externally validated. In the QResearch derivation cohort, 4822 new cases of lower limb amputation and 8063 new cases of blindness occurred during follow-up. The risk equations were well calibrated in both validation cohorts. Discrimination was good in men in the external CPRD cohort for amputation (D statistic 1.69, Harrell's C statistic 0.77) and blindness (D statistic 1.40, Harrell's C statistic 0.73), with similar results in women and in the QResearch validation cohort. The algorithms are based on variables that patients are likely to know or that are routinely recorded in general practice computer systems. They can be used to identify patients at high risk for prevention or further assessment. Limitations include lack of formally adjudicated outcomes, information bias, and missing data. Patients with type 1 or type 2 diabetes are at increased risk of blindness and amputation but generally do not have accurate assessments of the magnitude of their individual risks. The new algorithms calculate

The ACC/AHA 2013 pooled cohort equations compared to a Korean Risk Prediction Model for atherosclerotic cardiovascular disease.

PubMed

Jung, Keum Ji; Jang, Yangsoo; Oh, Dong Joo; Oh, Byung-Hee; Lee, Sang Hoon; Park, Seong-Wook; Seung, Ki-Bae; Kim, Hong-Kyu; Yun, Young Duk; Choi, Sung Hee; Sung, Jidong; Lee, Tae-Yong; Kim, Sung Hi; Koh, Sang Baek; Kim, Moon Chan; Chang Kim, Hyeon; Kimm, Heejin; Nam, Chungmo; Park, Sungha; Jee, Sun Ha

2015-09-01

To evaluate the performance of the American College of Cardiology/American Heart Association (ACC/AHA) 2013 Pooled Cohort Equations in the Korean Heart Study (KHS) population and to develop a Korean Risk Prediction Model (KRPM) for atherosclerotic cardiovascular disease (ASCVD) events. The KHS cohort included 200,010 Korean adults aged 40-79 years who were free from ASCVD at baseline. Discrimination, calibration, and recalibration of the ACC/AHA Equations in predicting 10-year ASCVD risk in the KHS cohort were evaluated. The KRPM was derived using Cox model coefficients, mean risk factor values, and mean incidences from the KHS cohort. In the discriminatory analysis, the ACC/AHA Equations' White and African-American (AA) models moderately distinguished cases from non-cases, and were similar to the KRPM: For men, the area under the receiver operating characteristic curve (AUROCs) were 0.727 (White model), 0.725 (AA model), and 0.741 (KRPM); for women, the corresponding AUROCs were 0.738, 0.739, and 0.745. Absolute 10-year ASCVD risk for men in the KHS cohort was overestimated by 56.5% (White model) and 74.1% (AA model), while the risk for women was underestimated by 27.9% (White model) and overestimated by 29.1% (AA model). Recalibration of the ACC/AHA Equations did not affect discriminatory ability but improved calibration substantially, especially in men in the White model. Of the three ASCVD risk prediction models, the KRPM showed best calibration. The ACC/AHA Equations should not be directly applied for ASCVD risk prediction in a Korean population. The KRPM showed best predictive ability for ASCVD risk. Copyright © 2015 Elsevier Ireland Ltd. All rights reserved.

Preventable coronary heart disease events from control of cardiovascular risk factors in US adults with diabetes (projections from utilizing the UKPDS risk engine).

PubMed

Wong, Nathan D; Patao, Christopher; Malik, Shaista; Iloeje, Uchenna

2014-04-15

Type 2 diabetes mellitus (T2DM) carries significant risks for coronary heart disease (CHD). We examined the potential US population impact of single and composite risk factor control. Among US adults with diagnosed T2DM aged≥30 years in the National Health and Nutrition Examination Survey 2007 to 2012, we assessed CHD events preventable using the United Kingdom Prospective Diabetes Study CHD risk engine. We examined in all those not at goal the impact of statistical control of smoking, glycated hemoglobin, systolic blood pressure, and total and high-density lipoprotein cholesterol, according to the predefined criteria setting risk factors at different levels of control representing (1) "All to Goal," (2) at "Nominal Control," or (3) at "Aggressive Control." Preventable CHD events represented the difference between the number of events estimated from the control of these risk factors versus current levels of the risk factors. Of 606 men (representing 6.2 million) and 603 women (6.3 million) with DM and no previous CHD, 1.3 million men and 0.7 million women would develop a CHD event within 10 years if left uncontrolled. Controlling all risk factors to goal was projected to prevent 35% and 45% of CHD events in men and women, respectively. Nominal risk factor control was projected to prevent 36% and 38% and aggressive control 51% and 61% of CHD events, respectively. In conclusion, a significant proportion of CHD events in adults with T2DM could be prevented from composite control of risk factors often not at goal. Copyright © 2014 Elsevier Inc. All rights reserved.

Cardiovascular disease risk prediction equations in 400 000 primary care patients in New Zealand: a derivation and validation study.

PubMed

Pylypchuk, Romana; Wells, Sue; Kerr, Andrew; Poppe, Katrina; Riddell, Tania; Harwood, Matire; Exeter, Dan; Mehta, Suneela; Grey, Corina; Wu, Billy P; Metcalf, Patricia; Warren, Jim; Harrison, Jeff; Marshall, Roger; Jackson, Rod

2018-05-12

Most cardiovascular disease risk prediction equations in use today were derived from cohorts established last century and with participants at higher risk but less socioeconomically and ethnically diverse than patients they are now applied to. We recruited a nationally representative cohort in New Zealand to develop equations relevant to patients in contemporary primary care and compared the performance of these new equations to equations that are recommended in the USA. The PREDICT study automatically recruits participants in routine primary care when general practitioners in New Zealand use PREDICT software to assess their patients' risk profiles for cardiovascular disease, which are prospectively linked to national ICD-coded hospitalisation and mortality databases. The study population included male and female patients in primary care who had no prior cardiovascular disease, renal disease, or congestive heart failure. New equations predicting total cardiovascular disease risk were developed using Cox regression models, which included clinical predictors plus an area-based deprivation index and self-identified ethnicity. Calibration and discrimination performance of the equations were assessed and compared with 2013 American College of Cardiology/American Heart Association Pooled Cohort Equations (PCEs). The additional predictors included in new PREDICT equations were also appended to the PCEs to determine whether they were independent predictors in the equations from the USA. Outcome events were derived for 401 752 people aged 30-74 years at the time of their first PREDICT risk assessment between Aug 27, 2002, and Oct 12, 2015, representing about 90% of the eligible population. The mean follow-up was 4·2 years, and a third of participants were followed for 5 years or more. 15 386 (4%) people had cardiovascular disease events (1507 [10%] were fatal, and 8549 [56%] met the PCEs definition of hard atherosclerotic cardiovascular disease) during 1 685 521

Body Fat Equations and Electrical Bioimpedance Values in Prediction of Cardiovascular Risk Factors in Eutrophic and Overweight Adolescents

PubMed Central

Faria, Franciane Rocha; Faria, Eliane Rodrigues; Cecon, Roberta Stofeles; Barbosa Júnior, Djalma Adão; Franceschini, Sylvia do Carmo Castro; Peluzio, Maria do Carmo Gouveia; Ribeiro, Andréia Queiroz; Lira, Pedro Israel Cabral; Cecon, Paulo Roberto; Priore, Silvia Eloiza

2013-01-01

The aim of this study was to analyze body fat anthropometric equations and electrical bioimpedance analysis (BIA) in the prediction of cardiovascular risk factors in eutrophic and overweight adolescents. 210 adolescents were divided into eutrophic group (G1) and overweight group (G2). The percentage of body fat (% BF) was estimated using 10 body fat anthropometric equations and 2 BIA. We measured lipid profiles, uric acid, insulin, fasting glucose, homeostasis model assessment-insulin resistance (HOMA-IR), and blood pressure. We found that 76.7% of the adolescents exhibited inadequacy of at least one biochemical parameter or clinical cardiovascular risk. Higher values of triglycerides (TG) (P = 0.001), insulin, and HOMA-IR (P < 0.001) were observed in the G2 adolescents. In multivariate linear regression analysis, the % BF from equation (5) was associated with TG, diastolic blood pressure, and insulin in G1. Among the G2 adolescents, the % BF estimated by (5) and (9) was associated with LDL, TG, insulin, and the HOMA-IR. Body fat anthropometric equations were associated with cardiovascular risk factors and should be used to assess the nutritional status of adolescents. In this study, equation (5) was associated with a higher number of cardiovascular risk factors independent of the nutritional status of adolescents. PMID:23762051

Methods applied in cost-effectiveness models for treatment strategies in type 2 diabetes mellitus and their use in Health Technology Assessments: a systematic review of the literature from 2008 to 2013.

PubMed

Charokopou, M; Sabater, F J; Townsend, R; Roudaut, M; McEwan, P; Verheggen, B G

2016-01-01

To identify and compare health-economic models that were developed to evaluate the cost-effectiveness of treatments for type 2 diabetes mellitus (T2DM), and their use within Health Technology Assessments (HTAs). In total, six commonly used databases were searched for articles published between October 2008 and January 2013, using a protocolized search strategy and inclusion criteria. The websites of HTA organizations in nine countries, and proceedings from five relevant conferences, were also reviewed. The identified new health-economic models were qualitatively assessed using six criteria that were developed based on technical components, and characteristics related to the disease or the treatments being assessed. Finally, the number of times the models were applied within HTA reports, published literature, and/or major conferences was determined. Thirteen new models were identified and reviewed in depth. Most of these were based on identical key data sources, and applied a similar model structure, either using Markov modeling or microsimulation techniques. The UKPDS equations and panel regressions were frequently used to estimate the occurrence of diabetes-related complications and the probability of developing risk factors in the long term. The qualitative assessment demonstrated that the CARDIFF, Sheffield T2DM and ECHO T2DM models seem technically equipped to appropriately assess the long-term health-economic consequences of chronic treatments for patients with T2DM. It was observed that the CORE model is the most widely described in literature and conferences, and the most often applied model within HTA submissions, followed by the CARDIFF and UKPDS models. This research provides an overview of T2DM models that were developed between 2008 and January 2013. The outcomes of the qualitative assessments, combined with frequent use in local reimbursement decisions, prove the applicability of the CORE, CARDIFF and UKPDS models to address decision problems related

Accuracy of the Atherosclerotic Cardiovascular Risk Equation in a Large Contemporary, Multiethnic Real-World Population

PubMed Central

Rana, Jamal S.; Tabada, Grace H.; Solomon, Matthew D.; Lo, Joan C.; Jaffe, Marc G.; Sung, Sue Hee; Ballantyne, Christie M.; Go, Alan S.

2016-01-01

Background The accuracy of the 2013 American College of Cardiology/American Heart Association (ACC/AHA) risk equation for atherosclerotic cardiovascular disease (ASCVD) events in contemporary and ethnically diverse populations is not well understood. Objectives We sought to evaluate the accuracy of the 2013 ACC/AHA risk equation within a large, multiethnic population in clinical care. Methods The target population for consideration of cholesterol-lowering therapy in a large, integrated health care delivery system population was identified in 2008 and followed through 2013. The main analyses excluded those with known ASCVD, diabetes mellitus, low-density lipoprotein cholesterol levels <70 or ≥190 mg/dl, prior statin use, or incomplete 5-year follow-up. Patient characteristics were obtained from electronic medical records and ASCVD events were ascertained using validated algorithms for hospitalization databases and death certificates. We compared predicted versus observed 5-year ASCVD risk, overall and by sex and race/ethnicity. We additionally examined predicted versus observed risk in patients with diabetes mellitus. Results Among 307,591 eligible adults without diabetes between 40 and 75 years of age, 22,283 were black, 52,917 Asian/Pacific Islander, and 18,745 Hispanic. We observed 2,061 ASCVD events during 1,515,142 person-years. In each 5-year predicted ASCVD risk category, observed 5-year ASCVD risk was substantially lower: 0.20% for predicted risk <2.50%; 0.65% for predicted risk 2.50 to 3.74%; 0.90% for predicted risk 3.75 to 4.99%; and 1.85% for predicted risk ≥5.00%, with C: 0.74. Similar ASCVD risk overestimation and poor calibration with moderate discrimination (C: 0.68 to 0.74) was observed in sex, racial/ethnic, and socioeconomic status subgroups, and in sensitivity analyses among patients receiving statins for primary prevention. Calibration among 4,242 eligible adults with diabetes was improved, but discrimination was worse (C: 0.64). Conclusions

Regional Screening Levels (RSLs) - Equations

EPA Pesticide Factsheets

Regional Screening Level RSL equations page provides quick access to the equations used in the Chemical Risk Assessment preliminary remediation goal PRG risk based concentration RBC and risk calculator for the assessment of human Health.

Accuracy of the Atherosclerotic Cardiovascular Risk Equation in a Large Contemporary, Multiethnic Population.

PubMed

Rana, Jamal S; Tabada, Grace H; Solomon, Matthew D; Lo, Joan C; Jaffe, Marc G; Sung, Sue Hee; Ballantyne, Christie M; Go, Alan S

2016-05-10

The accuracy of the 2013 American College of Cardiology/American Heart Association (ACC/AHA) Pooled Cohort Risk Equation for atherosclerotic cardiovascular disease (ASCVD) events in contemporary and ethnically diverse populations is not well understood. The goal of this study was to evaluate the accuracy of the 2013 ACC/AHA Pooled Cohort Risk Equation within a large, multiethnic population in clinical care. The target population for consideration of cholesterol-lowering therapy in a large, integrated health care delivery system population was identified in 2008 and followed up through 2013. The main analyses excluded those with known ASCVD, diabetes mellitus, low-density lipoprotein cholesterol levels <70 or ≥190 mg/dl, prior lipid-lowering therapy use, or incomplete 5-year follow-up. Patient characteristics were obtained from electronic medical records, and ASCVD events were ascertained by using validated algorithms for hospitalization databases and death certificates. We compared predicted versus observed 5-year ASCVD risk, overall and according to sex and race/ethnicity. We additionally examined predicted versus observed risk in patients with diabetes mellitus. Among 307,591 eligible adults without diabetes between 40 and 75 years of age, 22,283 were black, 52,917 were Asian/Pacific Islander, and 18,745 were Hispanic. We observed 2,061 ASCVD events during 1,515,142 person-years. In each 5-year predicted ASCVD risk category, observed 5-year ASCVD risk was substantially lower: 0.20% for predicted risk <2.50%; 0.65% for predicted risk 2.50% to <3.75%; 0.90% for predicted risk 3.75% to <5.00%; and 1.85% for predicted risk ≥5.00% (C statistic: 0.74). Similar ASCVD risk overestimation and poor calibration with moderate discrimination (C statistic: 0.68 to 0.74) were observed in sex, racial/ethnic, and socioeconomic status subgroups, and in sensitivity analyses among patients receiving statins for primary prevention. Calibration among 4,242 eligible adults

Regional Screening Levels (RSLs) - Equations (November 2017 )

EPA Pesticide Factsheets

Regional Screening Level RSL equations page provides quick access to the equations used in the Chemical Risk Assessment preliminary remediation goal PRG risk based concentration RBC and risk calculator for the assessment of human Health.

Structural equation model of interactions between risk factors and work-related musculoskeletal complaints among Iranian hospital nurses.

PubMed

Mehralizadeh, Semira; Dehdashti, Alireza; Motalebi Kashani, Masoud

2017-01-01

Statistics indicate a high risk of developing work-related musculoskeletal disorders among hospital nurses. The challenge is to understand the associations between musculoskeletal symptoms and various individual and occupational risk factors. This study examined the direct and indirect interactions of various risk factors with musculoskeletal complaints in hospital nurses. In a cross-sectional design, Iranian hospital nurses from Semnan University of Medical Sciences participated in a questionnaire survey reporting their perceived perceptions of various work-related risk factors and musculoskeletal symptoms. We tested our proposed structural equation model to evaluate the relations between latent and observed concepts and the relative importance and strength of exogenous variables in explaining endogenous musculoskeletal complaints. Measurement model fits the data relatively acceptable. Our findings showed direct effects of psychological, role-related and work posture stressors on musculoskeletal complaints. Fatigue mediated the adverse indirect relations of psychological, role-related, work posture and individual factors with musculoskeletal complaints. Structural equation modeling may provide methodological opportunities in occupational health research with a potential to explain the complexity of interactions among risk factors. Prevention of work-related musculoskeletal disorders among nurses must account for physical and psychosocial conditions.

Structural equation models to estimate risk of infection and tolerance to bovine mastitis.

PubMed

Detilleux, Johann; Theron, Léonard; Duprez, Jean-Noël; Reding, Edouard; Humblet, Marie-France; Planchon, Viviane; Delfosse, Camille; Bertozzi, Carlo; Mainil, Jacques; Hanzen, Christian

2013-03-06

One method to improve durably animal welfare is to select, as reproducers, animals with the highest ability to resist or tolerate infection. To do so, it is necessary to distinguish direct and indirect mechanisms of resistance and tolerance because selection on these traits is believed to have different epidemiological and evolutionary consequences. We propose structural equation models with latent variables (1) to quantify the latent risk of infection and to identify, among the many potential mediators of infection, the few ones that influence it significantly and (2) to estimate direct and indirect levels of tolerance of animals infected naturally with pathogens. We applied the method to two surveys of bovine mastitis in the Walloon region of Belgium, in which we recorded herd management practices, mastitis frequency, and results of bacteriological analyses of milk samples. Structural equation models suggested that, among more than 35 surveyed herd characteristics, only nine (age, addition of urea in the rations, treatment of subclinical mastitis, presence of dirty liner, cows with hyperkeratotic teats, machine stripping, pre- and post-milking teat disinfection, and housing of milking cows in cubicles) were directly and significantly related to a latent measure of bovine mastitis, and that treatment of subclinical mastitis was involved in the pathway between post-milking teat disinfection and latent mastitis. These models also allowed the separation of direct and indirect effects of bacterial infection on milk productivity. Results suggested that infected cows were tolerant but not resistant to mastitis pathogens. We revealed the advantages of structural equation models, compared to classical models, for dissecting measurements of resistance and tolerance to infectious diseases, here bovine mastitis. Using our method, we identified nine major risk factors that were directly associated with an increased risk of mastitis and suggested that cows were tolerant but

[Current role of metformin in treatment of diabetes mellitus type 2].

PubMed

Janssen, J A

2000-09-30

Metformin-associated lactic acidosis is not necessarily due to metformin accumulation. It appears that mortality in patients receiving metformin who develop lactic acidosis is mostly linked to underlying disease. It has been suggested that metformin should be the first-line agent for the treatment of obese type 2 diabetic patients since metformin was associated with a significant decrease in macrovascular events and a reduction of all-cause mortality in the United Kingdom Prospective Diabetes Study (UKPDS) in a substudy. However, in this substudy no significant decrease in microvascular complications was observed in obese subjects with intensive metformin therapy. In addition, the use of metformin in combination with sulfonylurea seemed to be associated with excess risk of diabetes-related and all-cause mortality in obese subjects. Due to the discrepant and contradictory nature of the results in the obese patients and a lack of power the UKPDS offered no decision for any drug for initial therapy of type 2 diabetes. The main message of the UKPDS is that lowering of the blood glucose to the normal range is beneficial irrespective of the hypoglycaemic agent used. A rational approach to therapy in a type 2 diabetes patient who fails to sufficiently lower blood sugar with diet and weight loss is to begin therapy with a sulfonylurea or metformin and to add another oral agent if the desired glycaemic control is not achieved.

Multinational assessment of accuracy of equations for predicting risk of kidney failure: a meta-analysis

PubMed Central

Tangri, Navdeep; Grams, Morgan E.; Levey, Andrew S.; Coresh, Josef; Appel, Lawrence; Astor, Brad C.; Chodick, Gabriel; Collins, Allan J.; Djurdjev, Ognjenka; Elley, C. Raina; Evans, Marie; Garg, Amit X.; Hallan, Stein I.; Inker, Lesley; Ito, Sadayoshi; Jee, Sun Ha; Kovesdy, Csaba P.; Kronenberg, Florian; Lambers Heerspink, Hiddo J.; Marks, Angharad; Nadkarni, Girish N.; Navaneethan, Sankar D.; Nelson, Robert G.; Titze, Stephanie; Sarnak, Mark J.; Stengel, Benedicte; Woodward, Mark; Iseki, Kunitoshi

2016-01-01

Importance Identifying patients at risk of chronic kidney disease (CKD) progression may facilitate more optimal nephrology care. Kidney failure risk equations (KFREs) were previously developed and validated in two Canadian cohorts. Validation in other regions and in CKD populations not under the care of a nephrologist is needed. Objective To evaluate the accuracy of the KFREs across different geographic regions and patient populations through individual-participant data meta-analysis. Data Sources Thirty-one cohorts, including 721,357 participants with CKD Stages 3–5 in over 30 countries spanning 4 continents, were studied. These cohorts collected data from 1982 through 2014. Study Selection Cohorts participating in the CKD Prognosis Consortium with data on end-stage renal disease. Data Extraction and Synthesis Data were obtained and statistical analyses were performed between July 2012 and June 2015. Using the risk factors from the original KFREs, cohort-specific hazard ratios were estimated, and combined in meta-analysis to form new “pooled” KFREs. Original and pooled equation performance was compared, and the need for regional calibration factors was assessed. Main Outcome and Measure Kidney failure (treatment by dialysis or kidney transplantation). Results During a median follow-up of 4 years, 23,829 cases of kidney failure were observed. The original KFREs achieved excellent discrimination (ability to differentiate those who developed kidney failure from those who did not) across all cohorts (overall C statistic, 0.90 (95% CI 0.89–0.92) at 2 years and 0.88 (95% CI 0.86–0.90) at 5 years); discrimination in subgroups by age, race, and diabetes status was similar. There was no improvement with the pooled equations. Calibration (the difference between observed and predicted risk) was adequate in North American cohorts, but the original KFREs overestimated risk in some non-North American cohorts. Addition of a calibration factor that lowered the baseline

Sport Participation and Metabolic Risk During Adolescent Years: A Structured Equation Model.

PubMed

Werneck, AndréOliveira; da Silva, Danilo Rodrigues Pereira; Fernandes, Rômulo Araújo; Ronque, EnioRicardoVaz; Coelho-E-Silva, Manuel J; Cyrino, Edilson Serpeloni

2018-06-21

Sports practice during childhood can influence health indicators in later ages through direct and indirect pathways. Thus, this study aimed to test direct and indirect pathways to the association between sports practice in childhood and metabolic risk in adolescence, adopting physical activity, adiposity, and cardiorespiratory fitness at adolescence as potential mediators. This cross-sectional study with retrospective information was conducted with 991 adolescents (579 girls, 412 boys) aged 10 to 16 y. Sports activity was self-reported in childhood (retrospective data) and physical activity evaluated in adolescence through questionnaires. Somatic maturation (Mirwald method), cardiorespiratory fitness (20-m shuttle-run test), body fat (skinfolds), waist circumference, blood pressure (automatic instrument) and blood variables (fasting glucose, HDL cholesterol, and triglycerides) were measured at adolescence. Waist circumference, blood pressure and blood variables composed the metabolic risk score. Structured equation modeling was adopted. In both sexes, the relationship between sports practice at childhood and metabolic risk was fully mediated by habitual physical activity, which is related to the obesity construct and cardiorespiratory fitness. Obesity was associated with metabolic risk in boys (β=0.062; p<0.001) and girls (β=0.047; p<0.001). The relationship between sports practice in childhood and metabolic risk in adolescence was mediated by physical activity, obesity, and cardiorespiratory fitness. © Georg Thieme Verlag KG Stuttgart · New York.

Time of Concentration equations: the role of morphometric uncertainties in flood risk analysis and management

NASA Astrophysics Data System (ADS)

Martins, Luciano; Díez-Herrero, Andrés; Bodoque, Jose M.; Bateira, Carlos

2016-04-01

The perception of flood risk by the responsible authorities on the flood management disasters and mitigation strategies should be based on an overall evaluation of the uncertainties associated with the procedures for risk assessment and mapping production. This contribution presents the results of the development of mapping evaluation of the time of concentration (tc). This parameter reflects the time-space at which a watershed responds to rainfall events and is the most frequently utilized time parameter, and is of great importance in many hydrologic analysis. Accurate estimates of the tc are very important, for instance, if tc is under-estimated, the result is an over-estimated peak discharge and vice versa, resulting significant variations on the flooded areas, and could have important consequences in terms of the land use and occupation of territory, as management's own flood risk. The methology used evaluate 20 different empirical, semi-empirical and kinematics equations of tc calculation, due to different cartographic scales (1:200000; 1:100000; 1:25000; LIDAR 5x5m &1x1m) in in two hydrographic basins with distinct dimensions and geomorphological characteristics, located in the Gredos Mountain range (Spain). The results suggest that the changes in the cartographic scale, has not influence as significant as one might expect. The most important variations occur in the characteristics of the fequations, use different morphometricparameters in the calculations. Some just are based on geomorphological criteria and other magnify the hydraulic characteristics of the channels, resulting in very different tc values. However, we highlighting the role of cartographic scale particularly in the application of semi-empirical equations that take into account changes in land use and occupation. In this case, the determination of parameters, such as flow coefficient, curve number and roughness coefficient are very sensitive to cartographic scale. Sensitivity analysis

Impact of clinical input variable uncertainties on ten-year atherosclerotic cardiovascular disease risk using new pooled cohort equations.

PubMed

Gupta, Himanshu; Schiros, Chun G; Sharifov, Oleg F; Jain, Apurva; Denney, Thomas S

2016-08-31

Recently released American College of Cardiology/American Heart Association (ACC/AHA) guideline recommends the Pooled Cohort equations for evaluating atherosclerotic cardiovascular risk of individuals. The impact of the clinical input variable uncertainties on the estimates of ten-year cardiovascular risk based on ACC/AHA guidelines is not known. Using a publicly available the National Health and Nutrition Examination Survey dataset (2005-2010), we computed maximum and minimum ten-year cardiovascular risks by assuming clinically relevant variations/uncertainties in input of age (0-1 year) and ±10 % variation in total-cholesterol, high density lipoprotein- cholesterol, and systolic blood pressure and by assuming uniform distribution of the variance of each variable. We analyzed the changes in risk category compared to the actual inputs at 5 % and 7.5 % risk limits as these limits define the thresholds for consideration of drug therapy in the new guidelines. The new-pooled cohort equations for risk estimation were implemented in a custom software package. Based on our input variances, changes in risk category were possible in up to 24 % of the population cohort at both 5 % and 7.5 % risk boundary limits. This trend was consistently noted across all subgroups except in African American males where most of the cohort had ≥7.5 % baseline risk regardless of the variation in the variables. The uncertainties in the input variables can alter the risk categorization. The impact of these variances on the ten-year risk needs to be incorporated into the patient/clinician discussion and clinical decision making. Incorporating good clinical practices for the measurement of critical clinical variables and robust standardization of laboratory parameters to more stringent reference standards is extremely important for successful implementation of the new guidelines. Furthermore, ability to customize the risk calculator inputs to better represent unique clinical

Use of Case History Data for the Development of Equations in Predicting High Risk, Reading Disabled Students.

ERIC Educational Resources Information Center

Stratton, Beverly D.; And Others

Demographic data on 92 subjects identified as having reading problems were used to develop equations useful in identifying high risk, reading disabled students. Multiple linear regression analysis of the data indicated that reading disability (1) had a significant positive relationship with birth order and number of siblings; (2) had a positive…

Estimating Time to ESRD Using Kidney Failure Risk Equations: Results From the African American Study of Kidney Disease and Hypertension (AASK)

PubMed Central

Grams, Morgan E.; Li, Liang; Greene, Tom H.; Tin, Adrienne; Sang, Yingying; Kao, W.H. Linda; Lipkowitz, Michael S.; Wright, Jackson T.; Chang, Alex R.; Astor, Brad C.; Appel, Lawrence J.

2014-01-01

Background Planning for renal replacement therapy, such as referral for arteriovenous fistula placement and transplantation, is often guided by level of estimated glomerular filtration rate (eGFR). The use of risk equations might enable more accurate estimation of time to end-stage renal disease (ESRD), thus improving patient care. Study Design Prospective observational study. Setting & Participants 1,094 participants in the African-American Study of Kidney Disease and Hypertension (AASK) cohort. Predictor Age, sex, urine protein-creatinine ratio ≥1 g/g, APOL1 high-risk status, and 3-year antecedent eGFR decline. Outcome Cumulative incidence of ESRD from five different starting points: eGFR values of 30 and 15 ml/min/1.73 m2, and a 5%, 10%, and 20% 1-year ESRD risk, estimated by a published, 4-variable kidney failure risk equation. Results There were 566 participants who developed an eGFR of 30 ml/min/1.73 m2, 244 who developed eGFR of 15 ml/min/1.73 m2, and 437, 336, and 259 who developed a 5%, 10%, and 20% 1-year ESRD risk, respectively. The 1-year cumulative incidence of ESRD was 4.3% from eGFR 30 ml/min/1.73 m2, 49.0% from eGFR 15 ml/min/1.73 m2, 6.7% from 5% ESRD risk, 15.0% from 10% ESRD risk, and 29% from 20% ESRD risk. From eGFR 30 ml/min/1.73 m2, there were several risk factors that predicted ESRD risk. From eGFR 15 ml/min/1.73 m2, only level of proteinuria did; median time to ESRD was 9 and 19 months in those with higher and lower proteinuria, respectively. Median times were less variable from corresponding ESRD risk thresholds. For example, median time to ESRD from 20% ESRD risk was 22 and 25 months among those with higher and lower proteinuria, respectively. Limitations Relatively homogeneous population of African Americans with hypertensive kidney disease. Conclusions The results of the present study suggest the potential benefit of incorporating kidney failure risk equations into clinical care, with selection of a specific threshold guided by its

Habitual sleep duration and predicted 10-year cardiovascular risk using the pooled cohort risk equations among US adults.

PubMed

Ford, Earl S

2014-12-02

The association between sleep duration and predicted cardiovascular risk has been poorly characterized. The objective of this study was to examine the association between self-reported sleep duration and predicted 10-year cardiovascular risk among US adults. Data from 7690 men and nonpregnant women who were aged 40 to 79 years, who were free of self-reported heart disease and stroke, and who participated in a National Health and Nutrition Examination Survey from 2005 to 2012 were analyzed. Sleep duration was self-reported. Predicted 10-year cardiovascular risk was calculated using the pooled cohort equations. Among the included participants, 13.1% reported sleeping ≤5 hours, 24.4% reported sleeping 6 hours, 31.9% reported sleeping 7 hours, 25.2% reported sleeping 8 hours, 4.0% reported sleeping 9 hours, and 1.3% reported sleeping ≥10 hours. After adjustment for covariates, geometric mean-predicted 10-year cardiovascular risk was 4.0%, 3.6%, 3.4%, 3.5%, 3.7%, and 3.7% among participants who reported sleeping ≤5, 6, 7, 8, 9, and ≥10 hours per night, respectively (PWald chi-square<0.001). The age-adjusted percentages of predicted cardiovascular risk ≥20% for the 6 intervals of sleep duration were 14.5%, 11.9%, 11.0%, 11.4%, 11.8%, and 16.3% (PWald chi-square=0.022). After maximal adjustment, however, sleep duration was not significantly associated with cardiovascular risk ≥20% (PWald chi-square=0.698). Mean-predicted 10-year cardiovascular risk was lowest among adults who reported sleeping 7 hours per night and increased as participants reported sleeping fewer and more hours. © 2014 The Authors. Published on behalf of the American Heart Association, Inc., by Wiley Blackwell.

Applying Self-Determination Theory to Adolescent Sexual-Risk Behavior and Knowledge: A Structural Equation Model [Formula: see text].

PubMed

Riley, Bettina H; McDermott, Ryon C

2018-05-01

National health priorities identify adolescent sexual-risk behavior outcomes as research and intervention targets for mental health. Reduce sexual-risk behavioral outcomes by applying self-determination theory to focus on decision-making autonomy. This study examined late adolescents' recollections of parental autonomy support/sexual-risk communication experiences and autonomy motivation as predictors of sexual-risk behaviors/knowledge. A convenience sample ( N = 249) of 19- and 20-year-old university students completed self-report questionnaires. Structural equation modeling with latent variables examined direct/indirect effects in the hypothesized model. Parents contributed uniquely through sexual-risk communication and/or autonomy support to late adolescents' autonomous motivation. The final model evidenced acceptable fit and explained 12% of the variation in adolescent sexual-risk behavior, 7% in adolescent autonomous motivation, and 2% in adolescent sexual-risk knowledge. Psychiatric mental health nurses should conduct further research and design interventions promoting parent autonomy support and adolescent autonomous motivation to reduce sexual risk-behavior and increase sexual-risk knowledge.

Structural equation modeling in environmental risk assessment.

PubMed

Buncher, C R; Succop, P A; Dietrich, K N

1991-01-01

Environmental epidemiology requires effective models that take individual observations of environmental factors and connect them into meaningful patterns. Single-factor relationships have given way to multivariable analyses; simple additive models have been augmented by multiplicative (logistic) models. Each of these steps has produced greater enlightenment and understanding. Models that allow for factors causing outputs that can affect later outputs with putative causation working at several different time points (e.g., linkage) are not commonly used in the environmental literature. Structural equation models are a class of covariance structure models that have been used extensively in economics/business and social science but are still little used in the realm of biostatistics. Path analysis in genetic studies is one simplified form of this class of models. We have been using these models in a study of the health and development of infants who have been exposed to lead in utero and in the postnatal home environment. These models require as input the directionality of the relationship and then produce fitted models for multiple inputs causing each factor and the opportunity to have outputs serve as input variables into the next phase of the simultaneously fitted model. Some examples of these models from our research are presented to increase familiarity with this class of models. Use of these models can provide insight into the effect of changing an environmental factor when assessing risk. The usual cautions concerning believing a model, believing causation has been proven, and the assumptions that are required for each model are operative.

Uncertainty Considerations for Ballistic Limit Equations

NASA Technical Reports Server (NTRS)

Schonberg, W. P.; Evans, H. J.; Williamsen, J. E.; Boyer, R. L.; Nakayama, G. S.

2005-01-01

The overall risk for any spacecraft system is typically determined using a Probabilistic Risk Assessment (PRA). A PRA attempts to determine the overall risk associated with a particular mission by factoring in all known risks (and their corresponding uncertainties, if known) to the spacecraft during its mission. The threat to mission and human life posed by the mircro-meteoroid & orbital debris (MMOD) environment is one of the risks. NASA uses the BUMPER II program to provide point estimate predictions of MMOD risk for the Space Shuttle and the International Space Station. However, BUMPER II does not provide uncertainty bounds or confidence intervals for its predictions. With so many uncertainties believed to be present in the models used within BUMPER II, providing uncertainty bounds with BUMPER II results would appear to be essential to properly evaluating its predictions of MMOD risk. The uncertainties in BUMPER II come primarily from three areas: damage prediction/ballistic limit equations, environment models, and failure criteria definitions. In order to quantify the overall uncertainty bounds on MMOD risk predictions, the uncertainties in these three areas must be identified. In this paper, possible approaches through which uncertainty bounds can be developed for the various damage prediction and ballistic limit equations encoded within the shuttle and station versions of BUMPER II are presented and discussed. We begin the paper with a review of the current approaches used by NASA to perform a PRA for the Space Shuttle and the International Space Station, followed by a review of the results of a recent sensitivity analysis performed by NASA using the shuttle version of the BUMPER II code. Following a discussion of the various equations that are encoded in BUMPER II, we propose several possible approaches for establishing uncertainty bounds for the equations within BUMPER II. We conclude with an evaluation of these approaches and present a recommendation

Patient reactions to a web-based cardiovascular risk calculator in type 2 diabetes: a qualitative study in primary care.

PubMed

Nolan, Tom; Dack, Charlotte; Pal, Kingshuk; Ross, Jamie; Stevenson, Fiona A; Peacock, Richard; Pearson, Mike; Spiegelhalter, David; Sweeting, Michael; Murray, Elizabeth

2015-03-01

Use of risk calculators for specific diseases is increasing, with an underlying assumption that they promote risk reduction as users become better informed and motivated to take preventive action. Empirical data to support this are, however, sparse and contradictory. To explore user reactions to a cardiovascular risk calculator for people with type 2 diabetes. Objectives were to identify cognitive and emotional reactions to the presentation of risk, with a view to understanding whether and how such a calculator could help motivate users to adopt healthier behaviours and/or improve adherence to medication. Qualitative study combining data from focus groups and individual user experience. Adults with type 2 diabetes were recruited through website advertisements and posters displayed at local GP practices and diabetes groups. Participants used a risk calculator that provided individualised estimates of cardiovascular risk. Estimates were based on UK Prospective Diabetes Study (UKPDS) data, supplemented with data from trials and systematic reviews. Risk information was presented using natural frequencies, visual displays, and a range of formats. Data were recorded and transcribed, then analysed by a multidisciplinary group. Thirty-six participants contributed data. Users demonstrated a range of complex cognitive and emotional responses, which might explain the lack of change in health behaviours demonstrated in the literature. Cardiovascular risk calculators for people with diabetes may best be used in conjunction with health professionals who can guide the user through the calculator and help them use the resulting risk information as a source of motivation and encouragement. © British Journal of General Practice 2015.

Determining rural risk for aneurysmal subarachnoid hemorrhages: A structural equation modeling approach.

PubMed

Nichols, Linda Jayne; Gall, Seana; Stirling, Christine

2016-01-01

An aneurysmal subarachnoid hemorrhage (aSAH) carries a high disability burden. The true impact of rurality as a predictor of outcome severity is unknown. Our aim is to clarify the relationship between the proposed explanations of regional and rural health disparities linked to severity of outcome following an aSAH. An initial literature search identified limited data directly linking geographical location, rurality, rural vulnerability, and aSAH. A further search noting parallels with ischemic stroke and acute myocardial infarct literature presented a number of diverse and interrelated predictors. This a priori knowledge informed the development of a conceptual framework that proposes the relationship between rurality and severity of outcome following an aSAH utilizing structural equation modeling. The presented conceptual framework explores a number of system, environmental, and modifiable risk factors. Socioeconomic characteristics, modifiable risk factors, and timely treatment that were identified as predictors of severity of outcome following an aSAH and within each of these defined predictors a number of contributing specific individual predictors are proposed. There are considerable gaps in the current knowledge pertaining to the impact of rurality on the severity of outcome following an aSAH. Absent from the literature is any investigation of the cumulative impact and multiplicity of risk factors associated with rurality. The proposed conceptual framework hypothesizes a number of relationships between both individual level and system level predictors, acknowledging that intervening predictors may mediate the effect of one variable on another.

Is gravidity 4+ a risk factor for oral clefts? A case-control study in eight South american countries using structural equation modeling.

PubMed

Gili, Juan Antonio; Poletta, Fernando Adrián; Campaña, Hebe; Comas, Belén; Pawluk, Mariela; Rittler, Monica; López-Camelo, Jorge Santiago

2013-09-01

Background : There is disagreement about the association between cleft lip with or without cleft palate and multigravidity, which could be explained by differences of adjusting for maternal age, Amerindian ancestry, and socioeconomic status. Objective : The aim was to evaluate gravidity 4+ (four or more gestations) as a risk factor for cleft lip with or without cleft palate in South America. Design : We used a matched (1:1) case-control study with structural equation modeling for related causes. Data were obtained from 1,371,575 consecutive newborn infants weighing ≥500 g who were born in the hospitals of the Estudio Colaborativo Latinoamericano de Malformaciones Congénitas (ECLAMC) network between 1982 and 1999. There were a total of 1,271 cases with cleft lip with or without cleft palate (excluding midline and atypical cleft lip with or without cleft palate). A total of 1,227 case-control pairs were obtained, matched by maternal age, newborn gender, and year and place of birth. Potential confounders and intermediary variables were analyzed with structural equation modeling. Results : The crude risk of gravidity 4+ was 1.41 and the 95% confidence interval was 1.14 to 1.61. When applying structural equation modeling, the effect of multigravidity on the risk of cleft lip with or without cleft palate was 1.22 and the 95% confidence interval was 0.91 to 1.39. Conclusions : Multigravid mothers (more than four gestations) showed no greater risk of bearing children who had cleft lip with or without cleft palate than mothers with two or three births. Therefore, the often observed and reported association between multigravidity and oral clefts likely reflects the effect of other risk factors related to low socioeconomic status in South American populations.

Applying new Magee equations for predicting the Oncotype Dx recurrence score.

PubMed

Sughayer, Maher; Alaaraj, Rolla; Alsughayer, Ahmad

2018-04-24

Breast cancer is one of the most prevalent cancers in women. Oncotype Dx is a multi-gene assay frequently used to predict the recurrence risk for estrogen receptor-positive early breast cancer, with values < 18 considered low risk; ≥ 18 and ≤ 30, intermediate risk; and > 30, high risk. Patients at a high risk for recurrence are more likely to benefit from chemotherapy treatment. In this study, clinicopathological parameters for 37 cases of early breast cancer with available Oncotype Dx results were used to estimate the recurrence score using the three new Magee equations. Correlation studies with Oncotype Dx results were performed. Applying the same cutoff points as Oncotype Dx, patients were categorized into low-, intermediate- and high-risk groups according to their estimated recurrence scores. Pearson correlation coefficient (R) values between estimated and actual recurrence score were 0.73, 0.66, and 0.70 for Magee equations 1, 2 and 3, respectively. The concordance values between actual and estimated recurrence scores were 57.6%, 52.9%, and 57.6% for Magee equations 1, 2 and 3, respectively. Using standard pathologic measures and immunohistochemistry scores in these three linear Magee equations, most low and high recurrence risk cases can be predicted with a strong positive correlation coefficient, high concordance and negligible two-step discordance. Magee equations are user-friendly and can be used to predict the recurrence score in early breast cancer cases.

SETS. Set Equation Transformation System

DOE Office of Scientific and Technical Information (OSTI.GOV)

Worrell, R.B.

1992-01-13

SETS is used for symbolic manipulation of Boolean equations, particularly the reduction of equations by the application of Boolean identities. It is a flexible and efficient tool for performing probabilistic risk analysis (PRA), vital area analysis, and common cause analysis. The equation manipulation capabilities of SETS can also be used to analyze noncoherent fault trees and determine prime implicants of Boolean functions, to verify circuit design implementation, to determine minimum cost fire protection requirements for nuclear reactor plants, to obtain solutions to combinatorial optimization problems with Boolean constraints, and to determine the susceptibility of a facility to unauthorized access throughmore » nullification of sensors in its protection system.« less

Predicting the risk of Lyme borreliosis after a tick bite, using a structural equation model.

PubMed

Hofhuis, Agnetha; van de Kassteele, Jan; Sprong, Hein; van den Wijngaard, Cees C; Harms, Margriet G; Fonville, Manoj; Docters van Leeuwen, Arieke; Simões, Mariana; van Pelt, Wilfrid

2017-01-01

Understanding and quantification of the risk of Lyme borreliosis after a tick bite can aid development of prevention strategies against Lyme borreliosis. We used 3,525 single tick bite reports from three large prospective studies on the transmission risk of tick-borne pathogens to humans, with 50 reports of Lyme borreliosis during the follow-up period, among 1,973 reports with known outcome. A structural equation model was applied to estimate the risk of Lyme borreliosis after a tick bite, and quantify the influence of: developmental stage of the tick, detection of Borrelia burgdorferi s.l. DNA in the tick by PCR, tick engorgement, patient-estimated duration of tick attachment, and patient age. The overall risk of developing Lyme borreliosis after a tick bite was 2.6% (95%CI 1.4-5.1). The risk increased with: - Tick engorgement: 1.4% (95%CI 0.7%-2.3%) for low engorgement to 5.5% (95%CI 2.8%-9.2%) for substantially engorged ticks;- Rising patient-estimated tick attachment duration: 2.0% (95%CI 1.3%-2.8%) after <12 hours, to 5.2% (95%CI 3.0%-8.9%) after ≥4 days;- Detection of Borrelia burgdorferi s.l. DNA in ticks: 6.7% (95%CI 3.6%-13.5%), versus 1.4% (95%CI 0.7%-2.9%) when ticks tested negative.The highest observed risk of Lyme borreliosis was 14.4% (95%CI 6.8%-24.6%) after one tick bite of a substantially engorged tick that tested positive for Borrelia burgdorferi s.l. DNA, which corresponds to one new case of Lyme borreliosis per 7 (95%CI 4-15) of such tick bites. An individual's risk of Lyme borreliosis after a tick bite can be predicted with tick engorgement, patient-estimated duration of tick attachment, and detection of Borrelia burgdorferi s.l. DNA in the tick.

A 19-SNP coronary heart disease gene score profile in subjects with type 2 diabetes: the coronary heart disease risk in type 2 diabetes (CoRDia study) study baseline characteristics.

PubMed

Beaney, Katherine E; Ward, Claire E; Bappa, Dauda A S; McGale, Nadine; Davies, Anna K; Hirani, Shashivadan P; Li, KaWah; Howard, Philip; Vance, Dwaine R; Crockard, Martin A; Lamont, John V; Newman, Stanton; Humphries, Steve E

2016-10-03

The coronary risk in diabetes (CoRDia) trial (n = 211) compares the effectiveness of usual diabetes care with a self-management intervention (SMI), with and without personalised risk information (including genetics), on clinical and behavioural outcomes. Here we present an assessment of randomisation, the cardiac risk genotyping assay, and the genetic characteristics of the recruits. Ten-year coronary heart disease (CHD) risk was calculated using the UKPDS score. Genetic CHD risk was determined by genotyping 19 single nucleotide polymorphisms (SNPs) using Randox's Cardiac Risk Prediction Array and calculating a gene score (GS). Accuracy of the array was assessed by genotyping a subset of pre-genotyped samples (n = 185). Overall, 10-year CHD risk ranged from 2-72 % but did not differ between the randomisation groups (p = 0.13). The array results were 99.8 % concordant with the pre-determined genotypes. The GS did not differ between the Caucasian participants in the CoRDia SMI plus risk group (n = 66) (p = 0.80) and a sample of UK healthy men (n = 1360). The GS was also associated with LDL-cholesterol (p = 0.05) and family history (p = 0.03) in a sample of UK healthy men (n = 1360). CHD risk is high in this group of T2D subjects. The risk array is an accurate genotyping assay, and is suitable for estimating an individual's genetic CHD risk. Trial registration This study has been registered at ClinicalTrials.gov; registration identifier NCT01891786.

Psychotropic substance abuse among adolescents: a structural equation model on risk and protective factors.

PubMed

Rumpold, Gerhard; Klingseis, Michael; Dornauer, Kurt; Kopp, Martin; Doering, Stephan; Höfer, Stefan; Mumelter, Birgit; Schüssler, Gerhard

2006-01-01

The use of psychotropic substances in adolescents represents a serious public health problem. In this study a representative sample of 485 Austrian students between 14 and 18 years of age were investigated with a semistructured interview about substance-related issues and completed the general health questionnaire. The following rates of regular psychotropic substance use were found: cigarettes 41.4%, alcohol 44.5%, cannabis 10.1%, and other illicit substances 3%. Logistic regression analyses and structural equation modeling revealed the following major risk factors for substance use: peer pressure, negative family atmosphere, school difficulties, and psychopathology. Knowledge about substance use acted as a protective factor. Prevention of adolescent substance use and misuse should aim at these different targets. Information about coping with peer pressure may be a particularly promising route of intervention.

Predicting the risk of Lyme borreliosis after a tick bite, using a structural equation model

PubMed Central

Sprong, Hein; van den Wijngaard, Cees C.; Harms, Margriet G.; Fonville, Manoj; Docters van Leeuwen, Arieke; Simões, Mariana; van Pelt, Wilfrid

2017-01-01

Background Understanding and quantification of the risk of Lyme borreliosis after a tick bite can aid development of prevention strategies against Lyme borreliosis. Methods We used 3,525 single tick bite reports from three large prospective studies on the transmission risk of tick-borne pathogens to humans, with 50 reports of Lyme borreliosis during the follow-up period, among 1,973 reports with known outcome. A structural equation model was applied to estimate the risk of Lyme borreliosis after a tick bite, and quantify the influence of: developmental stage of the tick, detection of Borrelia burgdorferi s.l. DNA in the tick by PCR, tick engorgement, patient-estimated duration of tick attachment, and patient age. Results The overall risk of developing Lyme borreliosis after a tick bite was 2.6% (95%CI 1.4–5.1). The risk increased with: - Tick engorgement: 1.4% (95%CI 0.7%-2.3%) for low engorgement to 5.5% (95%CI 2.8%-9.2%) for substantially engorged ticks; - Rising patient-estimated tick attachment duration: 2.0% (95%CI 1.3%-2.8%) after <12 hours, to 5.2% (95%CI 3.0%-8.9%) after ≥4 days; - Detection of Borrelia burgdorferi s.l. DNA in ticks: 6.7% (95%CI 3.6%-13.5%), versus 1.4% (95%CI 0.7%-2.9%) when ticks tested negative. The highest observed risk of Lyme borreliosis was 14.4% (95%CI 6.8%-24.6%) after one tick bite of a substantially engorged tick that tested positive for Borrelia burgdorferi s.l. DNA, which corresponds to one new case of Lyme borreliosis per 7 (95%CI 4–15) of such tick bites. Conclusions An individual's risk of Lyme borreliosis after a tick bite can be predicted with tick engorgement, patient-estimated duration of tick attachment, and detection of Borrelia burgdorferi s.l. DNA in the tick. PMID:28742149

Prediction of Cardiovascular Disease by the Framingham-REGICOR Equation in the High-Risk PREDIMED Cohort: Impact of the Mediterranean Diet Across Different Risk Strata.

PubMed

Amor, Antonio J; Serra-Mir, Mercè; Martínez-González, Miguel A; Corella, Dolores; Salas-Salvadó, Jordi; Fitó, Montserrat; Estruch, Ramón; Serra-Majem, Lluis; Arós, Fernando; Babio, Nancy; Ros, Emilio; Ortega, Emilio

2017-03-13

The usefulness of cardiovascular disease (CVD) predictive equations in different populations is debatable. We assessed the efficacy of the Framingham-REGICOR scale, validated for the Spanish population, to identify future CVD in participants, who were predefined as being at high-risk in the PREvención con DIeta MEDiterránea (PREDIMED) study-a nutrition-intervention primary prevention trial-and the impact of adherence to the Mediterranean diet on CVD across risk categories. In a post hoc analysis, we assessed the CVD predictive value of baseline estimated risk in 5966 PREDIMED participants (aged 55-74 years, 57% women; 48% with type 2 diabetes mellitus). Major CVD events, the primary PREDIMED end point, were an aggregate of myocardial infarction, stroke, and cardiovascular death. Multivariate-adjusted Cox regression was used to calculate hazard ratios for major CVD events and effect modification from the Mediterranean diet intervention across risk strata (low, moderate, high, very high). The Framingham-REGICOR classification of PREDIMED participants was 25.1% low risk, 44.5% moderate risk, and 30.4% high or very high risk. During 6-year follow-up, 188 major CVD events occurred. Hazard ratios for major CVD events increased in parallel with estimated risk (2.68, 4.24, and 6.60 for moderate, high, and very high risk), particularly in men (7.60, 13.16, and 15.85, respectively, versus 2.16, 2.28, and 3.51, respectively, in women). Yet among those with low or moderate risk, 32.2% and 74.3% of major CVD events occurred in men and women, respectively. Mediterranean diet adherence was associated with CVD risk reduction regardless of risk strata ( P >0.4 for interaction). Incident CVD increased in parallel with estimated risk in the PREDIMED cohort, but most events occurred in non-high-risk categories, particularly in women. Until predictive tools are improved, promotion of the Mediterranean diet might be useful to reduce CVD independent of baseline risk. URL: http

Low cardiorespiratory fitness and coronary artery calcification: Complementary cardiovascular risk predictors in asymptomatic type 2 diabetics.

PubMed

Zafrir, Barak; Azaiza, Mohanad; Gaspar, Tamar; Dobrecky-Mery, Idit; Azencot, Mali; Lewis, Basil S; Rubinshtein, Ronen; Halon, David A

2015-08-01

Despite its well-established prognostic value, cardiorespiratory fitness (CRF) is not incorporated routinely in risk assessment tools. Whether low CRF provides additional predictive information in asymptomatic type 2 diabetics beyond conventional risk scores and coronary artery calcification (CAC) is unclear. We studied 600 type 2 diabetics aged 55-74 years without known coronary heart disease. CRF was quantified in metabolic equivalents (METs) by maximal treadmill testing and categorized as tertiles of percent predicted METs (ppMETs) achieved. CAC was calculated by non-enhanced computed tomography scans. The individual and joint association of both measures with an outcome event of all-cause mortality, myocardial infarction or stroke, was determined over a mean follow-up period of 80 ± 16 months. There were 72 (12%) events during follow-up. Low CRF was independently associated with event risk after adjustment for traditional risk factors and CAC (HR 2.25, 95% CI 1.41-3.57, p = 0.001). CRF (unfit/fit) allowed further outcome discrimination both amongst diabetics with low CAC scores (9.5% versus 2.0% event rate), and amongst diabetics with high CAC scores (23.5% versus 12.4% event rate), p < 0.001. The addition of CRF to a model comprising UKPDS and CAC scores improved the area under the curve for event prediction from 0.66 to 0.71, p = 0.03, with a positive continuous net reclassification improvement (NRI) of 0.451, p = 0.002. CRF, quantified by ppMETs, provided independent prognostic information which was additive to CAC. Low CRF may identify asymptomatic diabetic subjects at higher risk for all-cause mortality, myocardial infarction or stroke, despite low CAC. Copyright © 2015 Elsevier Ireland Ltd. All rights reserved.

Cardiovascular risk prediction tools for populations in Asia.

PubMed

Barzi, F; Patel, A; Gu, D; Sritara, P; Lam, T H; Rodgers, A; Woodward, M

2007-02-01

Cardiovascular risk equations are traditionally derived from the Framingham Study. The accuracy of this approach in Asian populations, where resources for risk factor measurement may be limited, is unclear. To compare "low-information" equations (derived using only age, systolic blood pressure, total cholesterol and smoking status) derived from the Framingham Study with those derived from the Asian cohorts, on the accuracy of cardiovascular risk prediction. Separate equations to predict the 8-year risk of a cardiovascular event were derived from Asian and Framingham cohorts. The performance of these equations, and a subsequently "recalibrated" Framingham equation, were evaluated among participants from independent Chinese cohorts. Six cohort studies from Japan, Korea and Singapore (Asian cohorts); six cohort studies from China; the Framingham Study from the US. 172,077 participants from the Asian cohorts; 25,682 participants from Chinese cohorts and 6053 participants from the Framingham Study. In the Chinese cohorts, 542 cardiovascular events occurred during 8 years of follow-up. Both the Asian cohorts and the Framingham equations discriminated cardiovascular risk well in the Chinese cohorts; the area under the receiver-operator characteristic curve was at least 0.75 for men and women. However, the Framingham risk equation systematically overestimated risk in the Chinese cohorts by an average of 276% among men and 102% among women. The corresponding average overestimation using the Asian cohorts equation was 11% and 10%, respectively. Recalibrating the Framingham risk equation using cardiovascular disease incidence from the non-Chinese Asian cohorts led to an overestimation of risk by an average of 4% in women and underestimation of risk by an average of 2% in men. A low-information Framingham cardiovascular risk prediction tool, which, when recalibrated with contemporary data, is likely to estimate future cardiovascular risk with similar accuracy in Asian

Novel Equations for Estimating Lean Body Mass in Peritoneal Dialysis Patients

PubMed Central

Dong, Jie; Li, Yan-Jun; Xu, Rong; Yang, Zhi-Kai; Zheng, Ying-Dong

2015-01-01

♦ Objectives: To develop and validate equations for estimating lean body mass (LBM) in peritoneal dialysis (PD) patients. ♦ Methods: Two equations for estimating LBM, one based on mid-arm muscle circumference (MAMC) and hand grip strength (HGS), i.e., LBM-M-H, and the other based on HGS, i.e., LBM-H, were developed and validated with LBM obtained by dual-energy X-ray absorptiometry (DEXA). The developed equations were compared to LBM estimated from creatinine kinetics (LBM-CK) and anthropometry (LBM-A) in terms of bias, precision, and accuracy. The prognostic values of LBM estimated from the equations in all-cause mortality risk were assessed. ♦ Results: The developed equations incorporated gender, height, weight, and dialysis duration. Compared to LBM-DEXA, the bias of the developed equations was lower than that of LBM-CK and LBM-A. Additionally, LBM-M-H and LBM-H had better accuracy and precision. The prognostic values of LBM in all-cause mortality risk based on LBM-M-H, LBM-H, LBM-CK, and LBM-A were similar. ♦ Conclusions: Lean body mass estimated by the new equations based on MAMC and HGS was correlated with LBM obtained by DEXA and may serve as practical surrogate markers of LBM in PD patients. PMID:26293839

Novel Equations for Estimating Lean Body Mass in Peritoneal Dialysis Patients.

PubMed

Dong, Jie; Li, Yan-Jun; Xu, Rong; Yang, Zhi-Kai; Zheng, Ying-Dong

2015-12-01

♦ To develop and validate equations for estimating lean body mass (LBM) in peritoneal dialysis (PD) patients. ♦ Two equations for estimating LBM, one based on mid-arm muscle circumference (MAMC) and hand grip strength (HGS), i.e., LBM-M-H, and the other based on HGS, i.e., LBM-H, were developed and validated with LBM obtained by dual-energy X-ray absorptiometry (DEXA). The developed equations were compared to LBM estimated from creatinine kinetics (LBM-CK) and anthropometry (LBM-A) in terms of bias, precision, and accuracy. The prognostic values of LBM estimated from the equations in all-cause mortality risk were assessed. ♦ The developed equations incorporated gender, height, weight, and dialysis duration. Compared to LBM-DEXA, the bias of the developed equations was lower than that of LBM-CK and LBM-A. Additionally, LBM-M-H and LBM-H had better accuracy and precision. The prognostic values of LBM in all-cause mortality risk based on LBM-M-H, LBM-H, LBM-CK, and LBM-A were similar. ♦ Lean body mass estimated by the new equations based on MAMC and HGS was correlated with LBM obtained by DEXA and may serve as practical surrogate markers of LBM in PD patients. Copyright © 2015 International Society for Peritoneal Dialysis.

Uncertainty Considerations for Ballistic Limit Equations

NASA Technical Reports Server (NTRS)

Schonberg, W. P.; Evans, H. J.; Williamsen, J. E; Boyer, R. L.; Nakayama, G. S.

2005-01-01

The overall risk for any spacecraft system is typically determined using a Probabilistic Risk Assessment (PRA). A PRA determines the overall risk associated with a particular mission by factoring in all known risks to the spacecraft during its mission. The threat to mission and human life posed by the micro-meteoroid and orbital debris (MMOD) environment is one of the risks. NASA uses the BUMPER II program to provide point estimate predictions of MMOD risk for the Space Shuttle and the ISS. However, BUMPER II does not provide uncertainty bounds or confidence intervals for its predictions. In this paper, we present possible approaches through which uncertainty bounds can be developed for the various damage prediction and ballistic limit equations encoded within the Shuttle and Station versions of BUMPER II.

Nutrition, Balance and Fear of Falling as Predictors of Risk for Falls among Filipino Elderly in Nursing Homes: A Structural Equation Model (SEM)

ERIC Educational Resources Information Center

de Guzman, Allan B.; Ines, Joanna Louise C.; Inofinada, Nina Josefa A.; Ituralde, Nielson Louie J.; Janolo, John Robert E.; Jerezo, Jnyv L.; Jhun, Hyae Suk J.

2013-01-01

While a number of empirical studies have been conducted regarding risk for falls among the elderly, there is still a paucity of similar studies in a developing country like the Philippines. This study purports to test through Structural Equation Modeling (SEM) a model that shows the interaction between and among nutrition, balance, fear of…

The influence of sensation-seeking and parental and peer influences in early adolescence on risk involvement through middle adolescence: A structural equation modeling analysis.

PubMed

Wang, Bo; Deveaux, Lynette; Lunn, Sonja; Dinaj-Koci, Veronica; Li, Xiaoming; Stanton, Bonita

2016-03-01

This study examined the relationships between youth and parental sensation-seeking, peer influence, parental monitoring and youth risk involvement in adolescence using structural equation modeling. Beginning in grade-six, longitudinal data were collected from 543 students over three years. Youth sensation-seeking in grade six contributed to risk involvement in early adolescence (grades six and seven) indirectly through increased peer risk influence and decreased parental monitoring but did not have a direct contribution. It contributed directly and indirectly to risk involvement in middle adolescence (grades eight and nine). Parent sensation-seeking at baseline was positively associated with peer risk influence and negatively associated with parental monitoring; it had no direct effect on adolescent risk involvement. Parental monitoring buffers negative peer influence on adolescent risk involvement. Results highlight the need for intervention efforts to provide normative feedback about adolescent risky behaviors and to vary among families in which parents and/or youth have high sensation-seeking propensities.

Kinetic energy equations for the average-passage equation system

NASA Technical Reports Server (NTRS)

Johnson, Richard W.; Adamczyk, John J.

1989-01-01

Important kinetic energy equations derived from the average-passage equation sets are documented, with a view to their interrelationships. These kinetic equations may be used for closing the average-passage equations. The turbulent kinetic energy transport equation used is formed by subtracting the mean kinetic energy equation from the averaged total instantaneous kinetic energy equation. The aperiodic kinetic energy equation, averaged steady kinetic energy equation, averaged unsteady kinetic energy equation, and periodic kinetic energy equation, are also treated.

Prediction of morbidity and mortality in patients with type 2 diabetes.

PubMed

Wells, Brian J; Roth, Rachel; Nowacki, Amy S; Arrigain, Susana; Yu, Changhong; Rosenkrans, Wayne A; Kattan, Michael W

2013-01-01

Introduction. The objective of this study was to create a tool that accurately predicts the risk of morbidity and mortality in patients with type 2 diabetes according to an oral hypoglycemic agent. Materials and Methods. The model was based on a cohort of 33,067 patients with type 2 diabetes who were prescribed a single oral hypoglycemic agent at the Cleveland Clinic between 1998 and 2006. Competing risk regression models were created for coronary heart disease (CHD), heart failure, and stroke, while a Cox regression model was created for mortality. Propensity scores were used to account for possible treatment bias. A prediction tool was created and internally validated using tenfold cross-validation. The results were compared to a Framingham model and a model based on the United Kingdom Prospective Diabetes Study (UKPDS) for CHD and stroke, respectively. Results and Discussion. Median follow-up for the mortality outcome was 769 days. The numbers of patients experiencing events were as follows: CHD (3062), heart failure (1408), stroke (1451), and mortality (3661). The prediction tools demonstrated the following concordance indices (c-statistics) for the specific outcomes: CHD (0.730), heart failure (0.753), stroke (0.688), and mortality (0.719). The prediction tool was superior to the Framingham model at predicting CHD and was at least as accurate as the UKPDS model at predicting stroke. Conclusions. We created an accurate tool for predicting the risk of stroke, coronary heart disease, heart failure, and death in patients with type 2 diabetes. The calculator is available online at http://rcalc.ccf.org under the heading "Type 2 Diabetes" and entitled, "Predicting 5-Year Morbidity and Mortality." This may be a valuable tool to aid the clinician's choice of an oral hypoglycemic, to better inform patients, and to motivate dialogue between physician and patient.

p-Euler equations and p-Navier-Stokes equations

NASA Astrophysics Data System (ADS)

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.

Hammett equation and generalized Pauling's electronegativity equation.

PubMed

Liu, Lei; Fu, Yao; Liu, Rui; Li, Rui-Qiong; Guo, Qing-Xiang

2004-01-01

Substituent interaction energy (SIE) was defined as the energy change of the isodesmic reaction X-spacer-Y + H-spacer-H --> X-spacer-H + H-spacer-Y. It was found that this SIE followed a simple equation, SIE(X,Y) = -ksigma(X)sigma(Y), where k was a constant dependent on the system and sigma was a certain scale of electronic substituent constant. It was demonstrated that the equation was applicable to disubstituted bicyclo[2.2.2]octanes, benzenes, ethylenes, butadienes, and hexatrienes. It was also demonstrated that Hammett's equation was a derivative form of the above equation. Furthermore, it was found that when spacer = nil the above equation was mathematically the same as Pauling's electronegativity equation. Thus it was shown that Hammett's equation was a derivative form of the generalized Pauling's electronegativity equation and that a generalized Pauling's electronegativity equation could be utilized for diverse X-spacer-Y systems. In addition, the total electronic substituent effects were successfully separated into field/inductive and resonance effects in the equation SIE(X,Y) = -k(1)F(X)F(Y) - k(2)R(X)R(Y) - k(3)(F(X)R(Y) + R(X)F(Y)). The existence of the cross term (i.e., F(X)R(Y) and R(X)F(Y)) suggested that the field/inductive effect was not orthogonal to the resonance effect because the field/inductive effect from one substituent interacted with the resonance effect from the other. Further studies on multi-substituted systems suggested that the electronic substituent effects should be pairwise and additive. Hence, the SIE in a multi-substituted system could be described using the equation SIE(X1, X2, ..., Xn) = Sigma(n-1)(i=1)Sigma(n)(j=i+1)k(ij)sigma(X)isigma(X)j.

Evaluation of the Pooled Cohort Equations for Prediction of Cardiovascular Risk in a Contemporary Prospective Cohort.

PubMed

Emdin, Connor A; Khera, Amit V; Natarajan, Pradeep; Klarin, Derek; Baber, Usman; Mehran, Roxana; Rader, Daniel J; Fuster, Valentin; Kathiresan, Sekar

2017-03-15

Most guidelines suggest a baseline risk assessment to guide atherosclerotic cardiovascular disease (ASCVD) prevention strategies. The American Heart Association/American College of Cardiology Pooled Cohort Equations (PCEs) is one tool to assess baseline risk; however, the accuracy of this tool has been called into question. We aimed to examine the calibration and discrimination of the PCEs in the BioImage study, a contemporary multiethnic cohort of asymptomatic adults enrolled from 2008 to 2009 in the Humana Health System in Chicago, Illinois, and Fort Lauderdale, Florida. Our primary end point was hard ASCVD, defined as cardiovascular death, myocardial infarction, and stroke. A total of 3,635 adults who were not on lipid-lowering therapy at baseline were followed for a maximum of 4.6 years. The mean age was 68.6 years; 2000 (55%) participants were women and 935 patients reported being of non-white race (26%). Although 74 ASCVD events were observed over a median follow-up of 2.7 years, 198 events were predicted by the PCEs. The observed event rate was 7.9 per 1,000 participant-years (95% confidence interval [CI] 6.1 to 9.8), whereas the predicted rate by the PCEs was 21 per 1,000 participant-years (95% CI 20.7 to 21.8). This represents an overestimation of 167% (Hosmer-Lemeshow chi-square = 173; p <0.001). With regard to discrimination, the C-statistic of the PCEs was 0.65 (CI 0.58 to 0.71). In an analysis restricted to 3,080 participants without diabetes mellitus and with low-density lipoprotein cholesterol between 70 and 189 mg/dl, the PCEs similarly overestimated risk by 181% (152 predicted events vs 54 observed events; p <0.001). The PCEs substantially overestimate ASCVD risk in this middle-aged adult insured population. Refinement of existing risk prediction functions may be warranted. Copyright © 2016 Elsevier Inc. All rights reserved.

Prognostic assessment of estimated glomerular filtration rate by the new Chronic Kidney Disease Epidemiology Collaboration equation in comparison with the Modification of Diet in Renal Disease Study equation.

PubMed

Skali, Hicham; Uno, Hajime; Levey, Andrew S; Inker, Lesley A; Pfeffer, Marc A; Solomon, Scott D

2011-09-01

Systematic reporting of estimated glomerular filtration rate (eGFR) using the Modification of Diet in Renal Disease (MDRD) Study equation is recommended for detection of chronic kidney disease and prediction of cardiovascular (CV) risk. The Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) equation is a newly developed and validated formula for eGFR that is more accurate at normal or near-normal eGFR. We aimed to assess the incremental prognostic accuracy of eGFR(CKD-EPI) versus eGFR(MDRD) in subjects at increased risk for CV disease. We performed a post hoc analysis of the VALIANT trial that enrolled 14,527 patients with acute myocardial infarction with signs and symptoms of heart failure and/or left ventricular systolic dysfunction. The eGFR(MDRD) and eGFR(CKD-EPI) were computed using age, gender, race, and baseline creatinine level. Patients were categorized according to their eGFR using each equation. To assess the incremental prognostic value of eGFR(CKD-EPI), the net reclassification improvement was calculated for the composite end point of CV death, recurrent myocardial infarction, heart failure, or stroke. Twenty-four percent of the subjects were reclassified into a different eGFR category using eGFR(CKD-EPI). The composite end point occurred in 33% of the subjects in this cohort. Based on eGFR(CKD-EPI), subjects reclassified into a higher eGFR experienced fewer events than those reclassified into a lower eGFR (21% vs 43%). In unadjusted analyses, the composite end point risk in subjects with eGFR between 75 and 90 mL/min per 1.73 m(2) was comparable with the referent group (eGFR between 90 and 105) using eGFR(MDRD) (hazard ratio 1.1, 95% CI 0.9-1.2) but was significantly higher using eGFR(CKD-EPI) (hazard ratio 1.2, 95% CI 1.1-1.4). The net reclassification improvement for eGFR(CKD-EPI) over eGFR(MDRD) was 8.7%. The CKD-EPI equation provides more accurate risk stratification than the MDRD Study equation in patients at high risk for CV disease

Impact of Replacing the Pooled Cohort Equation With Other Cardiovascular Disease Risk Scores on Atherosclerotic Cardiovascular Disease Risk Assessment (from the Multi-Ethnic Study of Atherosclerosis [MESA]).

PubMed

Qureshi, Waqas T; Michos, Erin D; Flueckiger, Peter; Blaha, Michael; Sandfort, Veit; Herrington, David M; Burke, Gregory; Yeboah, Joseph

2016-09-01

The increase in statin eligibility by the new cholesterol guidelines is mostly driven by the Pooled Cohort Equation (PCE) criterion (≥7.5% 10-year PCE). The impact of replacing the PCE with either the modified Framingham Risk Score (FRS) or the Systematic Coronary Risk Evaluation (SCORE) on assessment of atherosclerotic cardiovascular disease (ASCVD) risk assessment and statin eligibility remains unknown. We assessed the comparative benefits of using the PCE, FRS, and SCORE for ASCVD risk assessment in the Multi-Ethnic Study of Atherosclerosis. Of 6,815 participants, 654 (mean age 61.4 ± 10.3; 47.1% men; 37.1% whites; 27.2% blacks; 22.3% Hispanics; 12.0% Chinese-Americans) were included in analysis. Area under the curve (AUC) and decision curve analysis were used to compare the 3 risk scores. Decision curve analysis is the plot of net benefit versus probability thresholds; net benefit = true positive rate - (false positive rate × weighting factor). Weighting factor = Threshold probability/1 - threshold probability. After a median of 8.6 years, 342 (6.0%) ASCVD events (myocardial infarction, coronary heart disease death, fatal or nonfatal stroke) occurred. All 4 risk scores had acceptable discriminative ability for incident ASCVD events; (AUC [95% CI] PCE: 0.737 [0.713 to 0.762]; FRS: 0.717 [0.691 to 0.743], SCORE (high risk) 0.722 [0.696 to 0.747], and SCORE (low risk): 0.721 [0.696 to 0.746]. At the ASCVD risk threshold recommended for statin eligibility for primary prevention (≥7.5%), the PCE provides the best net benefit. Replacing the PCE with the SCORE (high), SCORE (low) and FRS results in a 2.9%, 8.9%, and 17.1% further increase in statin eligibility. The PCE has the best discrimination and net benefit for primary ASCVD risk assessment in a US-based multiethnic cohort compared with the SCORE or the FRS. Copyright © 2016 Elsevier Inc. All rights reserved.

The role of burnout syndrome as a mediator for the effect of psychosocial risk factors on the intensity of musculoskeletal disorders: a structural equation modeling approach.

PubMed

Gholami, Tahereh; Pahlavian, Ahmad Heidari; Akbarzadeh, Mahdi; Motamedzade, Majid; Moghaddam, Rashid Heidari

2016-01-01

This study examined the hypothesis that burnout syndrome mediates effects of psychosocial risk factors and intensity of musculoskeletal disorders (MSDs) among hospital nurses. The sample was composed of 415 nurses from various wards across five hospitals of Iran's Hamedan University of Medical Sciences. Data were collected through three questionnaires: job content questionnaire, Maslach burnout inventory and visual analogue scale. Results of structural equation modeling with a mediating effect showed that psychosocial risk factors were significantly related to changes in burnout, which in turn affects intensity of MSDs.

Cardiovascular risk

PubMed Central

Payne, Rupert A

2012-01-01

Cardiovascular disease is a major, growing, worldwide problem. It is important that individuals at risk of developing cardiovascular disease can be effectively identified and appropriately stratified according to risk. This review examines what we understand by the term risk, traditional and novel risk factors, clinical scoring systems, and the use of risk for informing prescribing decisions. Many different cardiovascular risk factors have been identified. Established, traditional factors such as ageing are powerful predictors of adverse outcome, and in the case of hypertension and dyslipidaemia are the major targets for therapeutic intervention. Numerous novel biomarkers have also been described, such as inflammatory and genetic markers. These have yet to be shown to be of value in improving risk prediction, but may represent potential therapeutic targets and facilitate more targeted use of existing therapies. Risk factors have been incorporated into several cardiovascular disease prediction algorithms, such as the Framingham equation, SCORE and QRISK. These have relatively poor predictive power, and uncertainties remain with regards to aspects such as choice of equation, different risk thresholds and the roles of relative risk, lifetime risk and reversible factors in identifying and treating at-risk individuals. Nonetheless, such scores provide objective and transparent means of quantifying risk and their integration into therapeutic guidelines enables equitable and cost-effective distribution of health service resources and improves the consistency and quality of clinical decision making. PMID:22348281

Computing generalized Langevin equations and generalized Fokker-Planck equations.

PubMed

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.

Relationship between Telomere Length, Genetic Traits and Environmental/Occupational Exposures in Bladder Cancer Risk by Structural Equation Modelling.

PubMed

Pavanello, Sofia; Carta, Angela; Mastrangelo, Giuseppe; Campisi, Manuela; Arici, Cecilia; Porru, Stefano

2017-12-21

Background : Telomere length (TL) maintenance plays an important role in bladder cancer (BC) and prognosis. However the manifold influence of everyday life exposures and genetic traits on leucocyte TL (LTL), is not fully elucidated. Methods : Within the framework of a hospital-based case ( n = 96)/control ( n = 94) study (all Caucasian males), we investigated the extent to which LTL and BC risk were modulated by genetic polymorphisms and environmental and occupational exposures. Data on lifetime smoking, alcohol and coffee drinking, dietary habits and occupational exposures, pointing to aromatic amines (AAs) and polycyclic aromatic hydrocarbons (PAHs) were collected. Structural equation modelling (SEM) analysis appraised this complex relationships. Results : The SEM analysis indicates negative direct links ( p < 0.05) between LTL with age, DNA adducts, alcohol and NAT2, and positive ones with coffee, MPO and XRCC3; and between BC risk ( p < 0.01) with cigarettes, cumulative exposure to AAs and coffee, while are negative with LTL and age. There was evidence of indirect effects ( p < 0.05) on BC risk, probably via LTL reduction, by age and NAT2 (positive link), MPO and XRCC3 (negative link). Our study supports evidence that LTL attrition is a critical event in BC. The new finding that LTL erosion depends on some preventable everyday life exposures genetically modulated, opens new perspectives in BC prevention.

Relationship between Telomere Length, Genetic Traits and Environmental/Occupational Exposures in Bladder Cancer Risk by Structural Equation Modelling

PubMed Central

Pavanello, Sofia; Carta, Angela; Mastrangelo, Giuseppe; Campisi, Manuela; Porru, Stefano

2017-01-01

Background: Telomere length (TL) maintenance plays an important role in bladder cancer (BC) and prognosis. However the manifold influence of everyday life exposures and genetic traits on leucocyte TL (LTL), is not fully elucidated. Methods: Within the framework of a hospital-based case (n = 96)/control (n = 94) study (all Caucasian males), we investigated the extent to which LTL and BC risk were modulated by genetic polymorphisms and environmental and occupational exposures. Data on lifetime smoking, alcohol and coffee drinking, dietary habits and occupational exposures, pointing to aromatic amines (AAs) and polycyclic aromatic hydrocarbons (PAHs) were collected. Structural equation modelling (SEM) analysis appraised this complex relationships. Results: The SEM analysis indicates negative direct links (p < 0.05) between LTL with age, DNA adducts, alcohol and NAT2, and positive ones with coffee, MPO and XRCC3; and between BC risk (p < 0.01) with cigarettes, cumulative exposure to AAs and coffee, while are negative with LTL and age. There was evidence of indirect effects (p < 0.05) on BC risk, probably via LTL reduction, by age and NAT2 (positive link), MPO and XRCC3 (negative link). Conclusions: Our study supports evidence that LTL attrition is a critical event in BC. The new finding that LTL erosion depends on some preventable everyday life exposures genetically modulated, opens new perspectives in BC prevention. PMID:29267235

Risk factors and visual fatigue of baggage X-ray security screeners: a structural equation modelling analysis.

PubMed

Yu, Rui-Feng; Yang, Lin-Dong; Wu, Xin

2017-05-01

This study identified the risk factors influencing visual fatigue in baggage X-ray security screeners and estimated the strength of correlations between those factors and visual fatigue using structural equation modelling approach. Two hundred and five X-ray security screeners participated in a questionnaire survey. The result showed that satisfaction with the VDT's physical features and the work environment conditions were negatively correlated with the intensity of visual fatigue, whereas job stress and job burnout had direct positive influences. The path coefficient between the image quality of VDT and visual fatigue was not significant. The total effects of job burnout, job stress, the VDT's physical features and the work environment conditions on visual fatigue were 0.471, 0.469, -0.268 and -0.251 respectively. These findings indicated that both extrinsic factors relating to VDT and workplace environment and psychological factors including job burnout and job stress should be considered in the workplace design and work organisation of security screening tasks to reduce screeners' visual fatigue. Practitioner Summary: This study identified the risk factors influencing visual fatigue in baggage X-ray security screeners and estimated the strength of correlations between those factors and visual fatigue. The findings were of great importance to the workplace design and the work organisation of security screening tasks to reduce screeners' visual fatigue.

A structural equation modelling approach to explore the role of B vitamins and immune markers in lung cancer risk.

PubMed

Baltar, Valéria Troncoso; Xun, Wei W; Johansson, Mattias; Ferrari, Pietro; Chuang, Shu-Chun; Relton, Caroline; Ueland, Per Magne; Midttun, Øivind; Slimani, Nadia; Jenab, Mazda; Clavel-Chapelon, Françoise; Boutron-Ruault, Marie-Christine; Fagherazzi, Guy; Kaaks, Rudolf; Rohrmann, Sabine; Boeing, Heiner; Weikert, Cornelia; Bueno-de-Mesquita, Bas; Boshuizen, Hendriek; van Gils, Carla H; Onland-Moret, N Charlotte; Agudo, Antonio; Barricarte, Aurelio; Navarro, Carmen; Rodríguez, Laudina; Castaño, José Maria Huerta; Larrañaga, Nerea; Khaw, Kay-Tee; Wareham, Nick; Allen, Naomi E; Crowe, Francesca; Gallo, Valentina; Norat, Teresa; Krogh, Vittorio; Masala, Giovanna; Panico, Salvatore; Sacerdote, Carlotta; Tumino, Rosario; Trichopoulou, Antonia; Lagiou, Pagona; Trichopoulos, Dimitrios; Rasmuson, Torgny; Hallmans, Göran; Roswall, Nina; Tjønneland, Anne; Riboli, Elio; Brennan, Paul; Vineis, Paolo

2013-08-01

The one-carbon metabolism (OCM) is considered key in maintaining DNA integrity and regulating gene expression, and may be involved in the process of carcinogenesis. Several B-vitamins and amino acids have been implicated in lung cancer risk, via the OCM directly as well as immune system activation. However it is unclear whether these factors act independently or through complex mechanisms. The current study applies structural equations modelling (SEM) to further disentangle the mechanisms involved in lung carcinogenesis. SEM allows simultaneous estimation of linear relations where a variable can be the outcome in one equation and the predictor in another, as well as allowing estimation using latent variables (factors estimated by correlation matrix). A large number of biomarkers have been analysed from 891 lung cancer cases and 1,747 controls nested within the European Prospective Investigation into Cancer and Nutrition (EPIC) cohort. Four putative mechanisms in the OCM and immunity were investigated in relation to lung cancer risk: methionine-homocysteine metabolism, folate cycle, transsulfuration, and mechanisms involved in inflammation and immune activation, all adjusted for tobacco exposure. The hypothesized SEM model confirmed a direct and protective effect for factors representing methionine-homocysteine metabolism (p = 0.020) and immune activation (p = 0.021), and an indirect protective effect of folate cycle (p = 0.019), after adjustment for tobacco smoking. In conclusion, our results show that in the investigation of the involvement of the OCM, the folate cycle and immune system in lung carcinogenesis, it is important to consider complex pathways (by applying SEM) rather than the effects of single vitamins or nutrients (e.g. using traditional multiple regression). In our study SEM were able to suggest a greater role of the methionine-homocysteine metabolism and immune activation over other potential mechanisms.

The Long and Winding Road to Optimal HbA1c Measurement

PubMed Central

Little, Randie R.; Rohlfing, Curt

2016-01-01

The importance of hemoglobin A1c (HbA1c) as an indicator of mean glycemia and risks for complications in patients with diabetes mellitus was established by the results of long-term clinical trials, most notably the Diabetes Control and Complications Trial (DCCT) and United Kingdom Prospective Diabetes Study (UKPDS), published in 1993 and 1998 respectively. However, clinical application of recommended HbA1c targets that were based on these studies was difficult due to lack of comparability of HbA1c results among assay methods and laboratories. Thus, the National Glycohemoglobin Standardization Program (NGSP) was initiated in 1996 with the goal of standardizing HbA1c results to those of the DCCT/UKPDS. HbA1c standardization efforts have been highly successful; however, a number of issues have emerged on the “long and winding road” to better HbA1c, including the development of a higher-order HbA1c reference method by the International Federation of Clinical Chemistry (IFCC), recommendations to use HbA1c to diagnose as well as monitor diabetes, and point-of-care (POC) HbA1c testing. Here, we review the past, present and future of HbA1c standardization and describe the current status of HbA1c testing, including limitations that healthcare providers need to be aware of when interpreting HbA1c results. PMID:23318564

Basic lubrication equations

NASA Technical Reports Server (NTRS)

Hamrock, B. J.; Dowson, D.

1981-01-01

Lubricants, usually Newtonian fluids, are assumed to experience laminar flow. The basic equations used to describe the flow are the Navier-Stokes equation of motion. The study of hydrodynamic lubrication is, from a mathematical standpoint, the application of a reduced form of these Navier-Stokes equations in association with the continuity equation. The Reynolds equation can also be derived from first principles, provided of course that the same basic assumptions are adopted in each case. Both methods are used in deriving the Reynolds equation, and the assumptions inherent in reducing the Navier-Stokes equations are specified. Because the Reynolds equation contains viscosity and density terms and these properties depend on temperature and pressure, it is often necessary to couple the Reynolds with energy equation. The lubricant properties and the energy equation are presented. Film thickness, a parameter of the Reynolds equation, is a function of the elastic behavior of the bearing surface. The governing elasticity equation is therefore presented.

Comparison of the prevalence and mortality risk of CKD in Australia using the CKD Epidemiology Collaboration (CKD-EPI) and Modification of Diet in Renal Disease (MDRD) Study GFR estimating equations: the AusDiab (Australian Diabetes, Obesity and Lifestyle) Study.

PubMed

White, Sarah L; Polkinghorne, Kevan R; Atkins, Robert C; Chadban, Steven J

2010-04-01

The Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) is more accurate than the Modification of Diet in Renal Disease (MDRD) Study equation. We applied both equations in a cohort representative of the Australian adult population. Population-based cohort study. 11,247 randomly selected noninstitutionalized Australians aged >or= 25 years who attended a physical examination during the baseline AusDiab (Australian Diabetes, Obesity and Lifestyle) Study survey. Glomerular filtration rate (GFR) was estimated using the MDRD Study and CKD-EPI equations. Kidney damage was defined as urine albumin-creatinine ratio >or= 2.5 mg/mmol in men and >or= 3.5 mg/mmol in women or urine protein-creatinine ratio >or= 0.20 mg/mg. Chronic kidney disease (CKD) was defined as estimated GFR (eGFR) >or= 60 mL/min/1.73 m(2) or kidney damage. Participants were classified into 3 mutually exclusive subgroups: CKD according to both equations; CKD according to the MDRD Study equation, but no CKD according to the CKD-EPI equation; and no CKD according to both equations. All-cause mortality was examined in subgroups with and without CKD. Serum creatinine and urinary albumin, protein, and creatinine measured on a random spot morning urine sample. 266 participants identified as having CKD according to the MDRD Study equation were reclassified to no CKD according to the CKD-EPI equation (estimated prevalence, 1.9%; 95% CI, 1.4-2.6). All had an eGFR >or= 45 mL/min/1.73 m(2) using the MDRD Study equation. Reclassified individuals were predominantly women with a favorable cardiovascular risk profile. The proportion of reclassified individuals with a Framingham-predicted 10-year cardiovascular risk >or= 30% was 7.2% compared with 7.9% of the group with no CKD according to both equations and 45.3% of individuals retained in stage 3a using both equations. There was no evidence of increased all-cause mortality in the reclassified group (age- and sex-adjusted hazard ratio vs no CKD, 1.01; 95% CI, 0

Normative equations for central augmentation index: assessment of inter-population applicability and how it could be improved

PubMed Central

Jeroncic, Ana; Gunjaca, Grgo; Mrsic, Danijela Budimir; Mudnic, Ivana; Brizic, Ivica; Polasek, Ozren; Boban, Mladen

2016-01-01

Common reference values of arterial stiffness indices could be effective screening tool in detecting vascular phenotypes at risk. However, populations of the same ethnicity may differ in vascular phenotype due to different environmental pressure. We examined applicability of normative equations for central augmentation index (cAIx) derived from Danish population with low cardiovascular risk on the corresponding Croatian population from the Mediterranean area. Disagreement between measured and predicted cAIx was assessed by Bland-Altman analysis. Both, cAIx-age distribution and normative equation fitted on Croatian data were highly comparable to Danish low-risk sample. Contrarily, Bland-Altman analysis of cAIx disagreement revealed a curvilinear deviation from the line of full agreement indicating that the equations were not equally applicable across age ranges. Stratification of individual data into age decades eliminated curvilinearity in all but the 30–39 (men) and 40–49 (women) decades. In other decades, linear disagreement independent of age persisted indicating that cAIx determinants other than age were not envisaged/compensated for by proposed equations. Therefore, established normative equations are equally applicable to both Nordic and Mediterranean populations but are of limited use. If designed for narrower age ranges, the equations’ sensitivity in detecting vascular phenotypes at risk and applicability to different populations could be improved. PMID:27230110

Cost-effectiveness of sitagliptin-based treatment regimens in European patients with type 2 diabetes and haemoglobin A1c above target on metformin monotherapy.

PubMed

Schwarz, B; Gouveia, M; Chen, J; Nocea, G; Jameson, K; Cook, J; Krishnarajah, G; Alemao, E; Yin, D; Sintonen, H

2008-06-01

Sitagliptin is a novel oral incretin enhancer that acts by inhibiting the dipeptidyl peptidase 4 enzyme and is indicated in Europe as a treatment adjunct to metformin (MF), sulphonylurea (SU), MF plus SU and diet and exercise, in the management of type 2 diabetes mellitus. The objective of the current analysis was to evaluate the cost-effectiveness of adding sitagliptin to the regimens of patients with haemoglobin A1c (HbA1C) above the International Diabetes Federation goal (6.5%) while on MF in six European countries: Austria, Finland, Portugal, Scotland (United Kingdom), Spain and Sweden. A discrete event simulation model, which employed the United Kingdom Prospective Diabetes Study (UKPDS) Outcomes Model risk equations for predicting risks of diabetes-related complication, was used. Lifetime costs and benefits were projected for alternative treatment strategies of adding sitagliptin, compared with adding rosiglitazone or a SU to MF in patients not at HbA1C goal on MF monotherapy. Changes in HbA1C as well as side effects associated with these different treatment strategies were based on clinical trial data. Mean baseline values from local epidemiologic studies involving patients with type 2 diabetes not at HbA1C goal on MF monotherapy were included in the current analysis. Costs of medications, side effects and direct costs of diabetes-related complications were based on country-specific data. UKPDS-based disutility weights associated with diabetes complications were incorporated. Disutilities associated with medication side effects were based on published data. All future costs and benefits were discounted according to local guidelines on cost-effectiveness analysis. One-way sensitivity analyses were conducted by varying key input parameters. The discounted incremental cost-effectiveness ratios (ICER) associated with the addition of sitagliptin to MF, compared with adding rosiglitazone, in the different countries analysed ranged from treatment with sitagliptin

Predicting the impact of population level risk reduction in cardio-vascular disease and stroke on acute hospital admission rates over a 5 year period--a pilot study.

PubMed

Whitfield, Malcolm D; Gillett, Michael; Holmes, Michael; Ogden, Elaine

2006-12-01

The brief for this study was to produce a practical, evidence based, financial planning tool, which could be used to present an economic argument for funding a public health-based prevention programme in coronary heart disease (CHD) related illness on the same basis as treatment interventions. To explore the possibility of using multivariate risk prediction equations, derived from the Framingham and other studies, to estimate how many people in a population are likely to be admitted to hospital in the next 5-10 years with cardio vascular disease (CVD) related events such as heart attacks, strokes, heart failure and kidney disease. To estimate the potential financial impact of reductions in hospital admissions, on an 'invest to save' basis, if primary care trusts (PCTs) were to invest in public health based interventions to reduce cardiovascular risk at a population level. The populations of five UK PCTs were entered into a spreadsheet based decision tree model, in terms of age and sex (this equated to around 620,000 adults). An estimation was made to determine how many people, in each age group, were likely to be diabetic. Population risk factors such as smoking rates, mean body mass index (BMI), mean total cholesterol and mean systolic blood pressure were entered by age group. The spreadsheet then used a variant of the Framingham equation to calculate how many non-diabetic people in each age group were likely to have a heart attack or stroke in the next 5 years. In addition heart failure and dialysis admission rates were estimated based upon risk factors for incidence. The United Kingdom Prospective Diabetes Study (UKPDS) risk engines 56 and 60 were used to calculate the risk of CHD and stroke, respectively, in people with type 2 diabetes. The spreadsheet deducted the number of people likely to die before reaching hospital and produced a predicted number of hospital admissions for each category over a 5-year period. The final part of the calculation attached a

Comparison of Kernel Equating and Item Response Theory Equating Methods

ERIC Educational Resources Information Center

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…

[New topics regarding equations for GFR estimation based on serum creatinine and cystatin C].

PubMed

Horio, Masaru

2014-02-01

Japanese GFR equations and CKD-EPI equations based on standardized serum creatinine and standardized cystatin C are recommended in recent Japanese CKD guides and KDIGO guidelines for CKD management, respectively. CKD-EPIcreat overestimates GFR in Japanese subjects, probably due to the difference in muscle mass between Japanese and Caucasians. Unlike CKD-EPIcreat, CKD-EPIcys performs well in Japanese subjects, indicating the advantages of using cystatin C as a GFR marker. KDIGO guidelines suggest measuring eGFRcys in adults with eGFRcreat of 45-59 ml/min/1.73 m2 who do not have markers of kidney damage if confirmation of CKD is required. Creatinine is excreted by glomerular filtration, but also secreted by the tubules. Alteration of the tubular secretion of creatinine may influence the performance of GFR equations based on serum creatinine. Multivariate analysis showed that GFR and serum albumin levels were independent parameters affecting the fractional excretion of creatinine (FE-Cr). Alteration of FE-Cr according to the serum albumin levels may be one of the reasons for the bias of GFR equations based on serum creatinine. Low GFR is a risk factor for all-cause and cardiovascular mortality in a general population. However, the relationship between eGFR and the hazard risk of events is different depending on whether cystatin C or creatinine is used to calculate eGFR. The association between eGFRcys and the hazard risk is much stronger compared with eGFRcreat. Cystatin C may be a useful alternative to creatinine for detecting a high risk of complications in a general population and subjects with CKD.

Evaluation of the HbA1c Reduction Cut Point for a Nonglycemic Effect on Cardiovascular Benefit of Hypoglycemic Agents in Patients with Type 2 Diabetes Based on Endpoint Events.

PubMed

Wu, Yuchao; Tang, Lizhi; Zhang, Fang; Yan, Zhe; Li, Jing; Tong, Nanwei

2018-01-01

Atherosclerotic cardiovascular disease (ASCVD) is a major cause of death among patients with diabetes but can be improved by certain hypoglycemic agents. However, adjudicating criteria on whether improvements are a glycemic or nonglycemic effect of these agents remain unclear. Hypoglycemic agents that produce a cardiovascular benefit in nondiabetic patients are considered to do so via a nonglycemic effect. We performed a subgroup analysis for primary and secondary prevention or very high risk of ASCVD in patients with type 2 diabetes (T2DM). Where glycosylated hemoglobin (HbA1c) was reduced to the same extent in a head-to-head comparison, cardiovascular benefits were judged as a nonglycemic effect. Furthermore, by analyzing the endpoints of four important randomized controlled intensive glucose control studies, UKPDS33, ADVANCE, ACCORD, and VADT, we calculated the cut point of HbA1c reduction for a nonglycemic effect on cardiovascular benefit by hypoglycemic agents in ASCVD groups of different severities. For the ASCVD primary prevention group of T2DM, UKPDS33 indicated a reduction in HbA1c < 0.9%, and a cardiovascular benefit within 10 years was considered a nonglycemic effect. For ASCVD secondary prevention or in the very high-risk group, pioglitazone exerted a nonglycemic effect on cardiovascular benefit in nondiabetic patients with insulin resistance; metformin may exert a similar effect in T2DM patients in a head-to-head study. Analysis of T2DM intensive glucose control studies showed a reduction in HbA1c of <1.0%, and a cardiovascular benefit after approximately 5 years was deemed a nonglycemic effect. For ASCVD primary prevention in T2DM, a reduction in HbA1c < 0.9% and a cardiovascular benefit within 10 years were considered a nonglycemic effect. For ASCVD secondary prevention or in a very high-risk population, a reduction in HbA1c < 1.0% and a cardiovascular benefit within about 5 years were also considered a nonglycemic effect.

A stochastic differential equation analysis of cerebrospinal fluid dynamics.

PubMed

Raman, Kalyan

2011-01-18

Clinical measurements of intracranial pressure (ICP) over time show fluctuations around the deterministic time path predicted by a classic mathematical model in hydrocephalus research. Thus an important issue in mathematical research on hydrocephalus remains unaddressed--modeling the effect of noise on CSF dynamics. Our objective is to mathematically model the noise in the data. The classic model relating the temporal evolution of ICP in pressure-volume studies to infusions is a nonlinear differential equation based on natural physical analogies between CSF dynamics and an electrical circuit. Brownian motion was incorporated into the differential equation describing CSF dynamics to obtain a nonlinear stochastic differential equation (SDE) that accommodates the fluctuations in ICP. The SDE is explicitly solved and the dynamic probabilities of exceeding critical levels of ICP under different clinical conditions are computed. A key finding is that the probabilities display strong threshold effects with respect to noise. Above the noise threshold, the probabilities are significantly influenced by the resistance to CSF outflow and the intensity of the noise. Fluctuations in the CSF formation rate increase fluctuations in the ICP and they should be minimized to lower the patient's risk. The nonlinear SDE provides a scientific methodology for dynamic risk management of patients. The dynamic output of the SDE matches the noisy ICP data generated by the actual intracranial dynamics of patients better than the classic model used in prior research.

Chemical Equation Balancing.

ERIC Educational Resources Information Center

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)

Development of prediction equations for estimating appendicular skeletal muscle mass in Japanese men and women.

PubMed

Furushima, Taishi; Miyachi, Motohiko; Iemitsu, Motoyuki; Murakami, Haruka; Kawano, Hiroshi; Gando, Yuko; Kawakami, Ryoko; Sanada, Kiyoshi

2017-08-29

This study aimed to develop and cross-validate prediction equations for estimating appendicular skeletal muscle mass (ASM) and to examine the relationship between sarcopenia defined by the prediction equations and risk factors for cardiovascular diseases (CVD) or osteoporosis in Japanese men and women. Subjects were healthy men and women aged 20-90 years, who were randomly allocated to the following two groups: the development group (D group; 257 men, 913 women) and the cross-validation group (V group; 119 men, 112 women). To develop prediction equations, stepwise multiple regression analyses were performed on data obtained from the D group, using ASM measured by dual-energy X-ray absorptiometry (DXA) as a dependent variable and five easily obtainable measures (age, height, weight, waist circumference, and handgrip strength) as independent variables. When the prediction equations for ASM estimation were applied to the V group, a significant correlation was found between DXA-measured ASM and predicted ASM in both men and women (R 2  = 0.81 and R 2  = 0.72). Our prediction equations had higher R 2 values compared to previously developed equations (R 2  = 0.75-0.59 and R 2  = 0.69-0.40) in both men and women. Moreover, sarcopenia defined by predicted ASM was related to risk factors for osteoporosis and CVD, as well as sarcopenia defined by DXA-measured ASM. In this study, novel prediction equations were developed and cross-validated in Japanese men and women. Our analyses validated the clinical significance of these prediction equations and showed that previously reported equations were not applicable in a Japanese population.

Cystatin C-based glomerular filtration rate associates more closely with mortality than creatinine-based or combined glomerular filtration rate equations in unselected patients.

PubMed

Helmersson-Karlqvist, Johanna; Ärnlöv, Johan; Larsson, Anders

2016-10-01

Decreased glomerular filtration rate (GFR) is an important cardiovascular risk factor, but estimated GFR (eGFR) may differ depending on whether it is based on creatinine or cystatin C. A combined creatinine/cystatin C equation has recently been shown to best estimate GFR; however, the benefits of using the combined equation for risk prediction in routine clinical care have been less studied. This study compares mortality risk prediction by eGFR using the combined creatinine/cystatin C equation (CKD-EPI), a sole creatinine equation (CKD-EPI) and a sole cystatin C equation (CAPA), respectively, using assays that are traceable to international calibrators. All patients analysed for both creatinine and cystatin C from the same blood sample tube (n = 13,054) during 2005-2007 in Uppsala University Hospital Laboratory were divided into eGFR risk categories>60, 30-60 and <30 mL/min/1.73 m(2) by each eGFR equation. During follow-up (median 4.6 years), 4398 participants died, of which 1396 deaths were due to cardiovascular causes. Reduced eGFR was significantly associated with death as assessed by all eGFR equations. The net reclassification improvement (NRI) for the combination equation compared with the sole creatinine equation was 0.10 (p < 0.001) for all-cause mortality and 0.08 (p < 0.001) for cardiovascular mortality, indicating improved reclassification. In contrast, NRI for the combination equation, compared with the sole cystatin C equation, was -0.06 (p < 0.001) for all-cause mortality and -0.02 (p = 0.032) for cardiovascular mortality, indicating a worsened reclassification. In routine clinical care, cystatin C-based eGFR was more closely associated with mortality compared with both creatinine-based eGFR and creatinine/cystatin C-based eGFR. © The European Society of Cardiology 2016.

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

ERIC Educational Resources Information Center

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…

[Cardiorespiratory fitness and cardiometabolic risk in young adults].

PubMed

Secchi, Jeremías D; García, Gastón C

2013-01-01

The assessment of VO₂max allow classify subjects according to the health risk. However the factors that may affect the classifications have been little studied. The main purpose was to determine whether the type of VO₂max prediction equation and the Fitnessgram criterion-referenced standards modified the proportion of young adults classified with a level of aerobic capacity cardiometabolic risk indicative. The study design was observational, cross-sectional and relational. Young adults (n= 240) participated voluntarily. The VO₂max was estimated by 20-m shuttle run test applying 9 predictive equations. The differences in the classifications were analyzed with the Cochran Q and McNemar tests. The level of aerobic capacity indicative of cardiometabolic risk ranged between 7.1% and 70.4% depending on the criterion-referenced standards and predictive equation used (p<0.001). A higher percentage of women were classified with an unhealthy level in all equations (women: 29.4% to 85.3% vs 4.8% to 51% in men), regardless of the criterion-referenced standards (p<0.001). Both sexes and irrespective of the equation applied the old criterion-referenced standards classified a lower proportion of subjects (men: 4.8% to 48.1% and women: 39.4% a 68.4%) with unhealthy aerobic capacity (p ≤ 0.004). The type of VO₂max prediction equation and Fitnessgram criterion-referenced standards changed classifications young adults with a level of aerobic capacity of cardiometabolic risk indicative.

Assessing Equating Results on Different Equating Criteria

ERIC Educational Resources Information Center

Tong, Ye; Kolen, Michael

2005-01-01

The performance of three equating methods--the presmoothed equipercentile method, the item response theory (IRT) true score method, and the IRT observed score method--were examined based on three equating criteria: the same distributions property, the first-order equity property, and the second-order equity property. The magnitude of the…

Predicting the 10-Year Risks of Atherosclerotic Cardiovascular Disease in Chinese Population: The China-PAR Project (Prediction for ASCVD Risk in China).

PubMed

Yang, Xueli; Li, Jianxin; Hu, Dongsheng; Chen, Jichun; Li, Ying; Huang, Jianfeng; Liu, Xiaoqing; Liu, Fangchao; Cao, Jie; Shen, Chong; Yu, Ling; Lu, Fanghong; Wu, Xianping; Zhao, Liancheng; Wu, Xigui; Gu, Dongfeng

2016-11-08

The accurate assessment of individual risk can be of great value to guiding and facilitating the prevention of atherosclerotic cardiovascular disease (ASCVD). However, prediction models in common use were formulated primarily in white populations. The China-PAR project (Prediction for ASCVD Risk in China) is aimed at developing and validating 10-year risk prediction equations for ASCVD from 4 contemporary Chinese cohorts. Two prospective studies followed up together with a unified protocol were used as the derivation cohort to develop 10-year ASCVD risk equations in 21 320 Chinese participants. The external validation was evaluated in 2 independent Chinese cohorts with 14 123 and 70 838 participants. Furthermore, model performance was compared with the Pooled Cohort Equations reported in the American College of Cardiology/American Heart Association guideline. Over 12 years of follow-up in the derivation cohort with 21 320 Chinese participants, 1048 subjects developed a first ASCVD event. Sex-specific equations had C statistics of 0.794 (95% confidence interval, 0.775-0.814) for men and 0.811 (95% confidence interval, 0.787-0.835) for women. The predicted rates were similar to the observed rates, as indicated by a calibration χ 2 of 13.1 for men (P=0.16) and 12.8 for women (P=0.17). Good internal and external validations of our equations were achieved in subsequent analyses. Compared with the Chinese equations, the Pooled Cohort Equations had lower C statistics and much higher calibration χ 2 values in men. Our project developed effective tools with good performance for 10-year ASCVD risk prediction among a Chinese population that will help to improve the primary prevention and management of cardiovascular disease. © 2016 American Heart Association, Inc.

A comparison of the Slaughter skinfold-thickness equations and BMI in predicting body fatness and cardiovascular disease risk factor levels in children1234

PubMed Central

Horlick, Mary; Berenson, Gerald S

2013-01-01

Background: Although estimation of percentage body fat with the Slaughter skinfold-thickness equations (PBFSlaughter) is widely used, the accuracy of this method has not been well studied. Objective: The objective was to determine the accuracy of the Slaughter skinfold-thickness equations. Design: We compared agreement between PBFSlaughter and estimations derived from dual-energy X-ray absorptiometry (PBFDXA) in 1169 children in the Pediatric Rosetta Body Composition Project and the relation to cardiovascular disease risk factors, as compared with body mass index (BMI), in 6725 children in the Bogalusa Heart Study. Results: PBFSlaughter was highly correlated (r = 0.90) with PBFDXA, but it markedly overestimated levels of PBFDXA in children with large skinfold thicknesses. In the 65 boys with a sum of skinfold thicknesses (subscapular- plus triceps-skinfold thicknesses) ≥50 mm, PBFSlaughter overestimated PBFDXA by 12 percentage points. The comparable overestimation in girls with a high skinfold sum was 6 percentage points. We also found that, after adjustment for sex and age, BMI showed slightly stronger associations with lipid, lipoprotein, insulin, and blood pressure values than did PBFSlaughter. Conclusions: These results indicate that PBFSlaughter, which was developed among a group of much thinner children and adolescents, is fairly accurate among nonobese children, but markedly overestimates the body fatness of children who have thick skinfold thicknesses. Furthermore, PBFSlaughter has no advantage over sex- and age-adjusted BMIs at identifying children who are at increased risk of cardiovascular disease based on lipid, lipoprotein, insulin, and blood pressure values. PMID:24153344

The Cumulative Lifting Index (CULI) for the Revised NIOSH Lifting Equation: Quantifying Risk for Workers With Job Rotation.

PubMed

Garg, Arun; Kapellusch, Jay M

2016-08-01

The objectives were to: (a) develop a continuous frequency multiplier (FM) for the Revised NIOSH Lifting Equation (RNLE) as a function of lifting frequency and duration of a lifting task, and (b) describe the Cumulative Lifting Index (CULI), a methodology for estimating physical exposure to workers with job rotation. The existing FM for the RNLE (FME) does not differentiate between task duration >2 hr and <8 hr, which makes quantifying physical exposure to workers with job rotation difficult and presents challenges to job designers. Using the existing FMs for 1, 2, and 8 hr of task durations, we developed a continuous FM (FMP) that extends to 12 hr per day. We simulated 157,500 jobs consisting of two tasks each and, using different combinations of Frequency Independent Lifting Index, lifting frequency and duration of lifting. Biomechanical stresses were estimated using the CULI, time-weighted average (TWA), and peak exposure. The median difference between FME and FMP was ±1% (range: 0%-15%). Compared to CULI, TWA underestimated risk of low-back pain (LBP) for 18% to 30% of jobs, and peak exposure for an assumed 8-hr work shift overestimated risk of LBP for 20% to 25% of jobs. Peak task exposure showed 90% agreement with CULI but ignored one of two tasks. The CULI partially addressed the underestimation of physical exposure using the TWA approach and overestimation of exposure using the peak-exposure approach. The proposed FM and CULI may provide more accurate physical exposure estimates, and therefore estimated risk of LBP, for workers with job rotation. © 2016, Human Factors and Ergonomics Society.

Double-Plate Penetration Equations

NASA Technical Reports Server (NTRS)

Hayashida, K. B.; Robinson, J. H.

2000-01-01

This report compares seven double-plate penetration predictor equations for accuracy and effectiveness of a shield design. Three of the seven are the Johnson Space Center original, modified, and new Cour-Palais equations. The other four are the Nysmith, Lundeberg-Stern-Bristow, Burch, and Wilkinson equations. These equations, except the Wilkinson equation, were derived from test results, with the velocities ranging up to 8 km/sec. Spreadsheet software calculated the projectile diameters for various velocities for the different equations. The results were plotted on projectile diameter versus velocity graphs for the expected orbital debris impact velocities ranging from 2 to 15 km/sec. The new Cour-Palais double-plate penetration equation was compared to the modified Cour-Palais single-plate penetration equation. Then the predictions from each of the seven double-plate penetration equations were compared to each other for a chosen shield design. Finally, these results from the equations were compared with test results performed at the NASA Marshall Space Flight Center. Because the different equations predict a wide range of projectile diameters at any given velocity, it is very difficult to choose the "right" prediction equation for shield configurations other than those exactly used in the equations' development. Although developed for various materials, the penetration equations alone cannot be relied upon to accurately predict the effectiveness of a shield without using hypervelocity impact tests to verify the design.

The Effectiveness of Circular Equating as a Criterion for Evaluating Equating.

ERIC Educational Resources Information Center

Wang, Tianyou; Hanson, Bradley A.; Harris, Deborah J.

Equating a test form to itself through a chain of equatings, commonly referred to as circular equating, has been widely used as a criterion to evaluate the adequacy of equating. This paper uses both analytical methods and simulation methods to show that this criterion is in general invalid in serving this purpose. For the random groups design done…

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

ERIC Educational Resources Information Center

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…

Relations between nonlinear Riccati equations and other equations in fundamental physics

NASA Astrophysics Data System (ADS)

Schuch, Dieter

2014-10-01

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.

Bridging the Knowledge Gaps between Richards' Equation and Budyko Equation

NASA Astrophysics Data System (ADS)

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.

Synthesizing Risk from Summary Evidence Across Multiple Risk Factors.

PubMed

Shrier, Ian; Colditz, Graham A; Steele, Russell J

2018-07-01

Although meta-analyses provide summary effect estimates that help advise patient care, patients often want to compare their overall health to the general population. The Harvard Cancer Risk Index was published in 2004 and uses risk ratio estimates and prevalence estimates from original studies across many risk factors to provide an answer to this question. However, the published version of the formula only uses dichotomous risk factors and its derivation was not provided. The objective of this brief report was to provide the derivation of a more general form of the equation that allows the incorporation of risk factors with three or more levels.

Turning Equations Into Stories: Using "Equation Dictionaries" in an Introductory Geophysics Class

NASA Astrophysics Data System (ADS)

Caplan-Auerbach, J.

2008-12-01

To students with math fear, equations can be intimidating and overwhelming. This discomfort is reflected in some of the frequent questions heard in introductory geophysics: "which equation should I use?" and "does T stand for travel time or period?" Questions such as these indicate that many students view equations as a series of variables and operators rather than as a representation of a physical process. To solve a problem they may simply look for an equation with the correct variables and assume that it meets their needs, rather than selecting an equation that represents the appropriate physical process. These issues can be addressed by encouraging students to think of equations as stories, and to describe them in prose. This is the goal of the Equation Dictionary project, used in Western Washington University's introductory geophysics course. Throughout the course, students create personal equation dictionaries, adding an entry each time an equation is introduced. Entries consist of (a) the equation itself, (b) a brief description of equation variables, (c) a prose description of the physical process described by the equation, and (d) any additional notes that help them understand the equation. Thus, rather than simply writing down the equations for the velocity of body waves, a student might write "The speed of a seismic body wave is controlled by the material properties of the medium through which it passes." In a study of gravity a student might note that the International Gravity Formula describes "the expected value of g at a given latitude, correcting for Earth's shape and rotation." In writing these definitions students learn that equations are simplified descriptions of physical processes, and that understanding the process is more useful than memorizing a sequence of variables. Dictionaries also serve as formula sheets for exams, which encourages students to write definitions that are meaningful to them, and to organize their thoughts clearly. Finally

Progression to Uncontrolled Severe Asthma: A Novel Risk Equation.

PubMed

Casciano, Julian; Krishnan, Jerry; Small, Mary Buatti; Li, Chenghui; Dotiwala, Zenobia; Martin, Bradley C

2017-01-01

Recently published asthma guidelines by the European Respiratory Society and the American Thoracic Society (ERS-ATS) define severe disease based on medication use and control level. These guidelines also emphasize that asthma severity involves certain biomarker phenotypes, one of them being eosinophilic phenotype. The quantification of the influence of eosinophil level toward predicting disease severity can help decision makers manage therapy better earlier. To develop a risk-scoring algorithm to identify patients at greater risk of developing uncontrolled severe asthma as defined by ERS-ATS guidelines. Data on asthma patients were extracted from the EMRClaims + database from January 2004 to July 2011. Patients with continuous enrollment 12 months before and after the date of the first encounter with a diagnosis of asthma (index date) with at least 1 blood eosinophil test result in the 12 months after the index date, but before the development of uncontrolled severe asthma or the study end date, were included. Uncontrolled severe asthma was defined as the first date on which all criteria of the ERS-ATS definition were first satisfied in the 12 months after the index date. Age (≥ 50 years vs. < 50 years), race, and sex were measured at index, and the Charlson Comorbidity Index (CCI) score (> 0 vs. 0) was measured in the pre-index period. Elevated eosinophil level was defined as a test result with ≥ 400 cells/µL. The study cohort was randomly split 50-50 into derivation and validation samples. Cox proportional hazards regression was used to develop the risk score for uncontrolled severe asthma using the derivation cohort with independent variables of eosinophil level, age, sex, race, and CCI. A bootstrapping procedure was used to generate 1,000 samples from the derivation cohort. Variables significant in ≥ 50% of the samples were retained in the final regression model. A risk score was then calculated based on the coefficient estimates of the final model. C

Evaluating Equating Results: Percent Relative Error for Chained Kernel Equating

ERIC Educational Resources Information Center

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…

Generalized Thomas-Fermi equations as the Lampariello class of Emden-Fowler equations

NASA Astrophysics Data System (ADS)

Rosu, Haret C.; Mancas, Stefan C.

2017-04-01

A one-parameter family of Emden-Fowler equations defined by Lampariello's parameter p which, upon using Thomas-Fermi boundary conditions, turns into a set of generalized Thomas-Fermi equations comprising the standard Thomas-Fermi equation for p = 1 is studied in this paper. The entire family is shown to be non integrable by reduction to the corresponding Abel equations whose invariants do not satisfy a known integrability condition. We also discuss the equivalent dynamical system of equations for the standard Thomas-Fermi equation and perform its phase-plane analysis. The results of the latter analysis are similar for the whole class.

Single wall penetration equations

NASA Technical Reports Server (NTRS)

Hayashida, K. B.; Robinson, J. H.

1991-01-01

Five single plate penetration equations are compared for accuracy and effectiveness. These five equations are two well-known equations (Fish-Summers and Schmidt-Holsapple), two equations developed by the Apollo project (Rockwell and Johnson Space Center (JSC), and one recently revised from JSC (Cour-Palais). They were derived from test results, with velocities ranging up to 8 km/s. Microsoft Excel software was used to construct a spreadsheet to calculate the diameters and masses of projectiles for various velocities, varying the material properties of both projectile and target for the five single plate penetration equations. The results were plotted on diameter versus velocity graphs for ballistic and spallation limits using Cricket Graph software, for velocities ranging from 2 to 15 km/s defined for the orbital debris. First, these equations were compared to each other, then each equation was compared with various aluminum projectile densities. Finally, these equations were compared with test results performed at JSC for the Marshall Space Flight Center. These equations predict a wide variety of projectile diameters at a given velocity. Thus, it is very difficult to choose the 'right' prediction equation. The thickness of a single plate could have a large variation by choosing a different penetration equation. Even though all five equations are empirically developed with various materials, especially for aluminum alloys, one cannot be confident in the shield design with the predictions obtained by the penetration equations without verifying by tests.

Development and validation of QMortality risk prediction algorithm to estimate short term risk of death and assess frailty: cohort study.

PubMed

Hippisley-Cox, Julia; Coupland, Carol

2017-09-20

Objectives  To derive and validate a risk prediction equation to estimate the short term risk of death, and to develop a classification method for frailty based on risk of death and risk of unplanned hospital admission. Design  Prospective open cohort study. Participants  Routinely collected data from 1436 general practices contributing data to QResearch in England between 2012 and 2016. 1079 practices were used to develop the scores and a separate set of 357 practices to validate the scores. 1.47 million patients aged 65-100 years were in the derivation cohort and 0.50 million patients in the validation cohort. Methods  Cox proportional hazards models in the derivation cohort were used to derive separate risk equations in men and women for evaluation of the risk of death at one year. Risk factors considered were age, sex, ethnicity, deprivation, smoking status, alcohol intake, body mass index, medical conditions, specific drugs, social factors, and results of recent investigations. Measures of calibration and discrimination were determined in the validation cohort for men and women separately and for each age and ethnic group. The new mortality equation was used in conjunction with the existing QAdmissions equation (which predicts risk of unplanned hospital admission) to classify patients into frailty groups. Main outcome measure  The primary outcome was all cause mortality. Results  During follow-up 180 132 deaths were identified in the derivation cohort arising from 4.39 million person years of observation. The final model included terms for age, body mass index, Townsend score, ethnic group, smoking status, alcohol intake, unplanned hospital admissions in the past 12 months, atrial fibrillation, antipsychotics, cancer, asthma or chronic obstructive pulmonary disease, living in a care home, congestive heart failure, corticosteroids, cardiovascular disease, dementia, epilepsy, learning disability, leg ulcer, chronic liver disease or pancreatitis

Decreased GFR estimated by MDRD or Cockcroft-Gault equation predicts incident CVD: the strong heart study.

PubMed

Shara, Nawar M; Resnick, Helaine E; Lu, Li; Xu, Jiaqiong; Vupputuri, Suma; Howard, Barbara V; Umans, Jason G

2009-01-01

Kidney function, expressed as glomerular filtration rate (GFR), is commonly estimated from serum creatinine (Scr) and, when decreased, may serve as a nonclassical risk factor for incident cardiovascular disease (CVD). The ability of estimated GFR (eGFR) to predict CVD events during 5-10 years of follow-up is assessed using data from the Strong Heart Study (SHS), a large cohort with a high prevalence of diabetes. eGFRs were calculated with the abbreviated Modification of Diet in Renal Disease study (MDRD) and the Cockcroft-Gault (CG) equations. These estimates were compared in participants with normal and abnormal Scr. The association between eGFR and incident CVD was assessed. More subjects were labeled as having low eGFR (<60 ml/min per 1.73 m2) by the MDRD or CG equation, than by Scr alone. When Scr was in the normal range, both equations labeled similar numbers of participants as having low eGFRs, although concordance between the equations was poor. However, when Scr was elevated, the MDRD equation labeled more subjects as having low eGFR. Persons with low eGFR had increased risk of CVD. The MDRD and CG equations labeled more participants as having decreased GFR than did Scr alone. Decreased eGFR was predictive of CVD in this American Indian population with a high prevalence of obesity and type 2 diabetes mellitus.

The Fourier transforms for the spatially homogeneous Boltzmann equation and Landau equation

NASA Astrophysics Data System (ADS)

Meng, Fei; Liu, Fang

2018-03-01

In this paper, we study the Fourier transforms for two equations arising in the kinetic theory. The first equation is the spatially homogeneous Boltzmann equation. The Fourier transform of the spatially homogeneous Boltzmann equation has been first addressed by Bobylev (Sov Sci Rev C Math Phys 7:111-233, 1988) in the Maxwellian case. Alexandre et al. (Arch Ration Mech Anal 152(4):327-355, 2000) investigated the Fourier transform of the gain operator for the Boltzmann operator in the cut-off case. Recently, the Fourier transform of the Boltzmann equation is extended to hard or soft potential with cut-off by Kirsch and Rjasanow (J Stat Phys 129:483-492, 2007). We shall first establish the relation between the results in Alexandre et al. (2000) and Kirsch and Rjasanow (2007) for the Fourier transform of the Boltzmann operator in the cut-off case. Then we give the Fourier transform of the spatially homogeneous Boltzmann equation in the non cut-off case. It is shown that our results cover previous works (Bobylev 1988; Kirsch and Rjasanow 2007). The second equation is the spatially homogeneous Landau equation, which can be obtained as a limit of the Boltzmann equation when grazing collisions prevail. Following the method in Kirsch and Rjasanow (2007), we can also derive the Fourier transform for Landau equation.

How to Obtain the Covariant Form of Maxwell's Equations from the Continuity Equation

ERIC Educational Resources Information Center

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.

Some Properties of the Fractional Equation of Continuity and the Fractional Diffusion Equation

NASA Astrophysics Data System (ADS)

Fukunaga, Masataka

2006-05-01

The fractional equation of continuity (FEC) and the fractional diffusion equation (FDE) show peculiar behaviors that are in the opposite sense to those expected from the equation of continuity and the diffusion equation, respectively. The behaviors are interpreted in terms of the memory effect of the fractional time derivatives included in the equations. Some examples are given by solutions of the FDE.

Prognostic value of chronic kidney disease in patients with coronary heart disease: role of estimating equations.

PubMed

Zhang, Qiu-Li; Brenner, Hermann; Koenig, Wolfgang; Rothenbacher, Dietrich

2010-07-01

Chronic kidney disease (CKD) increases risk of coronary heart disease (CHD), but the impact of using different equations for estimating kidney function on CHD is not clear yet. This study described the prognostic value of CKD as defined by various creatinine- (Cr-eGFR) and cystatin C-based estimating (Cys-eGFR) equations and their combinations on subsequent cardiovascular disease (CVD) events in patients with CHD. Cohort study. Patients with coronary heart disease in in-patient rehabilitation and long-term follow-up (mean 63.4 months). 1050 patients with coronary heart disease aged 30-70 years at baseline. CKD was defined as eGFR<60 mL/min/1.73 m2 (CKD stages 3-5) estimated by three Cr-eGFR equations (Cockroft-Gault equation adjusted for body surface area (CG/BSA), Modification of Diet in Renal Disease Study (MDRD) equation, CKD-EPIcrea) and by two Cys-eGFR equations (Arnal-Dade equation, CKD-EPIcys) and a combination. The primary endpoint of our study was subsequent CVD events. During follow-up 118 patients (11.2%) experienced the outcome of our study. CKD assessed by the CG/BSA, MDRD, and CKD-EPIcrea equations showed no statistically significant association with subsequent CVD events after adjustment for multiple covariates (hazard ratio (HR) 1.45 [95% CI, 0.81-2.59], HR 1.47 [95% CI, 0.84-2.60], and HR 1.31 [95% CI, 0.72-2.83], respectively). By contrast, the Cys-eGFR equations were much stronger associated with subsequent CVD endpoints (Arnal-Dade: HR, 2.01 [95% CI, 1.34-3.04]; CKD-EPIcys HR, 2.22 [95% CI, 1.46-3.37]). The CKD-EPIcys also provided the highest area under the curve value. Our study shows that prevalent CKD is an independent risk factor for subsequent CVD in patients with prevalent CHD and implies that Cys-eGFR equations show a better clinical utility compared to the Cr-eGFR equations. Copyright (c) 2010 Elsevier Ireland Ltd. All rights reserved.

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

PubMed

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.

A Generalized Simplest Equation Method and Its Application to the Boussinesq-Burgers Equation

PubMed Central

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. PMID:25973605

Modified Method of Simplest Equation Applied to the Nonlinear Schrödinger Equation

NASA Astrophysics Data System (ADS)

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.

The Pendulum Equation

ERIC Educational Resources Information Center

Fay, Temple H.

2002-01-01

We investigate the pendulum equation [theta] + [lambda][squared] sin [theta] = 0 and two approximations for it. On the one hand, we suggest that the third and fifth-order Taylor series approximations for sin [theta] do not yield very good differential equations to approximate the solution of the pendulum equation unless the initial conditions are…

Nonlinear and dissipative constitutive equations for coupled first-order acoustic field equations that are consistent with the generalized Westervelt equation

NASA Astrophysics Data System (ADS)

Verweij, Martin D.; Huijssen, Jacob

2006-05-01

In diagnostic medical ultrasound, it has become increasingly important to evaluate the nonlinear field of an acoustic beam that propagates in a weakly nonlinear, dissipative medium and that is steered off-axis up to very wide angles. In this case, computations cannot be based on the widely used KZK equation since it applies only to small angles. To benefit from successful computational schemes from elastodynamics and electromagnetics, we propose to use two first-order acoustic field equations, accompanied by two constitutive equations, as an alternative basis. This formulation quite naturally results in the contrast source formalism, makes a clear distinction between fundamental conservation laws and medium behavior, and allows for a straightforward inclusion of any medium inhomogenities. This paper is concerned with the derivation of relevant constitutive equations. We take a pragmatic approach and aim to find those constitutive equations that represent the same medium as implicitly described by the recognized, full wave, nonlinear equations such as the generalized Westervelt equation. We will show how this is achieved by considering the nonlinear case without attenuation, the linear case with attenuation, and the nonlinear case with attenuation. As a result we will obtain surprisingly simple constitutive equations for the full wave case.

Family-oriented cardiac risk estimator: a Java web-based applet.

PubMed

Crouch, Michael A; Jadhav, Ashwin

2003-01-01

We developed a Java applet that calculates four different estimates of a person's 10-year risk for heart attack: (1) Estimate based on Framingham equation (2) Framingham equation estimate modified by C-reactive protein (CRP) level (3) Framingham estimate modified by family history of heart disease in parents or siblings (4) Framingham estimate modified by both CRP and family heart disease history. This web-based, family-oriented cardiac risk estimator uniquely considers family history and CRP while estimating risk.

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

NASA Astrophysics Data System (ADS)

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.

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

ERIC Educational Resources Information Center

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…

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

ERIC Educational Resources Information Center

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…

Generalized Spencer-Lewis equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Filippone, W.L.

The Spencer-Lewis equation, which describes electron transport in homogeneous media when continuous slowing down theory is valid, is derived from the Boltzmann equation. Also derived is a time-dependent generalized Spencer-Lewis equation valid for inhomogeneous media. An independent verification of this last equation is obtained for the one-dimensional case using particle balance considerations.

Value of adding the renal pathological score to the kidney failure risk equation in advanced diabetic nephropathy.

PubMed

Yamanouchi, Masayuki; Hoshino, Junichi; Ubara, Yoshifumi; Takaichi, Kenmei; Kinowaki, Keiichi; Fujii, Takeshi; Ohashi, Kenichi; Mise, Koki; Toyama, Tadashi; Hara, Akinori; Kitagawa, Kiyoki; Shimizu, Miho; Furuichi, Kengo; Wada, Takashi

2018-01-01

There have been a limited number of biopsy-based studies on diabetic nephropathy, and therefore the clinical importance of renal biopsy in patients with diabetes in late-stage chronic kidney disease (CKD) is still debated. We aimed to clarify the renal prognostic value of pathological information to clinical information in patients with diabetes and advanced CKD. We retrospectively assessed 493 type 2 diabetics with biopsy-proven diabetic nephropathy in four centers in Japan. 296 patients with stage 3-5 CKD at the time of biopsy were identified and assigned two risk prediction scores for end-stage renal disease (ESRD): the Kidney Failure Risk Equation (KFRE, a score composed of clinical parameters) and the Diabetic Nephropathy Score (D-score, a score integrated pathological parameters of the Diabetic Nephropathy Classification by the Renal Pathology Society (RPS DN Classification)). They were randomized 2:1 to development and validation cohort. Hazard Ratios (HR) of incident ESRD were reported with 95% confidence interval (CI) of the KFRE, D-score and KFRE+D-score in Cox regression model. Improvement of risk prediction with the addition of D-score to the KFRE was assessed using c-statistics, continuous net reclassification improvement (NRI), and integrated discrimination improvement (IDI). During median follow-up of 1.9 years, 194 patients developed ESRD. The cox regression analysis showed that the KFRE,D-score and KFRE+D-score were significant predictors of ESRD both in the development cohort and in the validation cohort. The c-statistics of the D-score was 0.67. The c-statistics of the KFRE was good, but its predictive value was weaker than that in the miscellaneous CKD cohort originally reported (c-statistics, 0.78 vs. 0.90) and was not significantly improved by adding the D-score (0.78 vs. 0.79, p = 0.83). Only continuous NRI was positive after adding the D-score to the KFRE (0.4%; CI: 0.0-0.8%). We found that the predict values of the KFRE and the D-score were

Cardiovascular Risk Assessment in Elderly Living Kidney Donors: Risk Comparison Before and After Donation Using QRISK Equation.

PubMed

Kadhum, Murtaza; Abbas, Madiha; Ghazanfar, Abbas

2017-04-01

This study aimed to assess whether donor age would increase the risk of cardiovascular comorbidities during the first few years after donation. Cardiovascular risk was calculated using the QRISK tool (University of Nottingham and EMIS, Nottingham, UK). Data were collected from 221 living renal transplant donors at St. George's University Hospital NHS Foundation Trust between 2008 and 2012 before and after donation (at 6, 12, and 24 mo). QRISK scores were calculated for each patient at these time points before stratifying our patients into 2 cohorts: cohort A (age ≤ 59 y) and cohort B (age ≥ 60 y). QRISK scores were then compared using unpaired t tests. Before donation, mean QRISK scores were 3.4% in cohort A and 12.4% in cohort B (P < .001). At 6, 12, and 24 months after kidney donation, the risks were 3.3% and 12.2% (P < .001), 3.8% and 13.6% (P < .001), and 5% and 15.4% (P < .001) in cohort A versus cohort B. When we analyzed risk before donation, both age groups showed a significant increase in cardiovascular risk at 24 months. This subtle increase in cardiovascular risk in the 2 groups may be attributed to changing patient demographics, such as the increasing age of patients, rather than the donation itself. Elderly kidney donors, therefore, are a key source of donation after satisfactory cardiovascular work-up. However, elderly kidney donors will require long-term postoperative follow-up care and specific counseling aimed at reducing modifiable cardiovascular risk factors.

The eight tetrahedron equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hietarinta, J.; Nijhoff, F.

1997-07-01

In this paper we derive from arguments of string scattering a set of eight tetrahedron equations, with different index orderings. It is argued that this system of equations is the proper system that represents integrable structures in three dimensions generalizing the Yang{endash}Baxter equation. Under additional restrictions this system reduces to the usual tetrahedron equation in the vertex form. Most known solutions fall under this class, but it is by no means necessary. Comparison is made with the work on braided monoidal 2-categories also leading to eight tetrahedron equations. {copyright} {ital 1997 American Institute of Physics.}

Revised Framingham Stroke Risk Score, Nontraditional Risk Markers, and Incident Stroke in a Multiethnic Cohort.

PubMed

Flueckiger, Peter; Longstreth, Will; Herrington, David; Yeboah, Joseph

2018-02-01

Limited data exist on the performance of the revised Framingham Stroke Risk Score (R-FSRS) and the R-FSRS in conjunction with nontraditional risk markers. We compared the R-FSRS, original FSRS, and the Pooled Cohort Equation for stroke prediction and assessed the improvement in discrimination by nontraditional risk markers. Six thousand seven hundred twelve of 6814 participants of the MESA (Multi-Ethnic Study of Atherosclerosis) were included. Cox proportional hazard, area under the curve, net reclassification improvement, and integrated discrimination increment analysis were used to assess and compare each stroke prediction risk score. Stroke was defined as fatal/nonfatal strokes (hemorrhagic or ischemic). After mean follow-up of 10.7 years, 231 of 6712 (3.4%) strokes were adjudicated (2.7% ischemic strokes). Mean stroke risks using the R-FSRS, original FSRS, and Pooled Cohort Equation were 4.7%, 5.9%, and 13.5%. The R-FSRS had the best calibration (Hosmer-Lemeshow goodness-of-fit, χ 2 =6.55; P =0.59). All risk scores were predictive of incident stroke. C statistics of R-FSRS (0.716) was similar to Pooled Cohort Equation (0.716), but significantly higher than the original FSRS (0.653; P =0.01 for comparison with R-FSRS). Adding nontraditional risk markers individually to the R-FSRS did not improve discrimination of the R-FSRS in the area under the curve analysis, but did improve category-less net reclassification improvement and integrated discrimination increment for incident stroke. The addition of coronary artery calcium to R-FSRS produced the highest category-less net reclassification improvement (0.36) and integrated discrimination increment (0.0027). Similar results were obtained when ischemic strokes were used as the outcome. The R-FSRS downgraded stroke risk but had better calibration and discriminative ability for incident stroke compared with the original FSRS. Nontraditional risk markers modestly improved the discriminative ability of the R-FSRS, with

Conservational PDF Equations of Turbulence

NASA Technical Reports Server (NTRS)

Shih, Tsan-Hsing; Liu, Nan-Suey

2010-01-01

Recently we have revisited the traditional probability density function (PDF) equations for the velocity and species in turbulent incompressible flows. They are all unclosed due to the appearance of various conditional means which are modeled empirically. However, we have observed that it is possible to establish a closed velocity PDF equation and a closed joint velocity and species PDF equation through conditions derived from the integral form of the Navier-Stokes equations. Although, in theory, the resulted PDF equations are neither general nor unique, they nevertheless lead to the exact transport equations for the first moment as well as all higher order moments. We refer these PDF equations as the conservational PDF equations. This observation is worth further exploration for its validity and CFD application

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

NASA Astrophysics Data System (ADS)

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

Derivation of kinetic equations from non-Wiener stochastic differential equations

NASA Astrophysics Data System (ADS)

Basharov, A. M.

2013-12-01

Kinetic differential-difference equations containing terms with fractional derivatives and describing α -stable Levy processes with 0 < α < 1 have been derived in a unified manner in terms of one-dimensional stochastic differential equations controlled merely by the Poisson processes.

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

ERIC Educational Resources Information Center

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…

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

ERIC Educational Resources Information Center

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…

Brownian motion from Boltzmann's equation.

NASA Technical Reports Server (NTRS)

Montgomery, D.

1971-01-01

Two apparently disparate lines of inquiry in kinetic theory are shown to be equivalent: (1) Brownian motion as treated by the (stochastic) Langevin equation and Fokker-Planck equation; and (2) Boltzmann's equation. The method is to derive the kinetic equation for Brownian motion from the Boltzmann equation for a two-component neutral gas by a simultaneous expansion in the density and mass ratios.

The Kadomtsev{endash}Petviashvili equation as a source of integrable model equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Maccari, A.

1996-12-01

A new integrable and nonlinear partial differential equation (PDE) in 2+1 dimensions is obtained, by an asymptotically exact reduction method based on Fourier expansion and spatiotemporal rescaling, from the Kadomtsev{endash}Petviashvili equation. The integrability property is explicitly demonstrated, by exhibiting the corresponding Lax pair, that is obtained by applying the reduction technique to the Lax pair of the Kadomtsev{endash}Petviashvili equation. This model equation is likely to be of applicative relevance, because it may be considered a consistent approximation of a large class of nonlinear evolution PDEs. {copyright} {ital 1996 American Institute of Physics.}

Nonlinear differential equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

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 ismore » 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.« less

Wave equations in conformal gravity

NASA Astrophysics Data System (ADS)

Du, Juan-Juan; Wang, Xue-Jing; He, You-Biao; Yang, Si-Jiang; Li, Zhong-Heng

2018-05-01

We study the wave equation governing massless fields of all spins (s = 0, 1 2, 1, 3 2 and 2) in the most general spherical symmetric metric of conformal gravity. The equation is separable, the solution of the angular part is a spin-weighted spherical harmonic, and the radial wave function may be expressed in terms of solutions of the Heun equation which has four regular singular points. We also consider various special cases of the metric and find that the angular wave functions are the same for all cases, the actual shape of the metric functions affects only the radial wave function. It is interesting to note that each radial equation can be transformed into a known ordinary differential equation (i.e. Heun equation, or confluent Heun equation, or hypergeometric equation). The results show that there are analytic solutions for all the wave equations of massless spin fields in the spacetimes of conformal gravity. This is amazing because exact solutions are few and far between for other spacetimes.

Convergence of Galerkin approximations for operator Riccati equations: A nonlinear evolution equation approach

NASA Technical Reports Server (NTRS)

Rosen, I. G.

1988-01-01

An approximation and convergence theory was developed for Galerkin approximations to infinite dimensional operator Riccati differential equations formulated in the space of Hilbert-Schmidt operators on a separable Hilbert space. The Riccati equation was treated as a nonlinear evolution equation with dynamics described by a nonlinear monotone perturbation of a strongly coercive linear operator. A generic approximation result was proven for quasi-autonomous nonlinear evolution system involving accretive operators which was then used to demonstrate the Hilbert-Schmidt norm convergence of Galerkin approximations to the solution of the Riccati equation. The application of the results was illustrated in the context of a linear quadratic optimal control problem for a one dimensional heat equation.

Reduction operators of Burgers equation.

PubMed

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.

Methods for Equating Mental Tests.

DTIC Science & Technology

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

Reduction operators of Burgers equation

PubMed Central

Pocheketa, Oleksandr A.; Popovych, Roman O.

2013-01-01

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. PMID:23576819

A spectral boundary integral equation method for the 2-D Helmholtz equation

NASA Technical Reports Server (NTRS)

Hu, Fang Q.

1994-01-01

In this paper, we present a new numerical formulation of solving the boundary integral equations reformulated from the Helmholtz equation. The boundaries of the problems are assumed to be smooth closed contours. The solution on the boundary is treated as a periodic function, which is in turn approximated by a truncated Fourier series. A Fourier collocation method is followed in which the boundary integral equation is transformed into a system of algebraic equations. It is shown that in order to achieve spectral accuracy for the numerical formulation, the nonsmoothness of the integral kernels, associated with the Helmholtz equation, must be carefully removed. The emphasis of the paper is on investigating the essential elements of removing the nonsmoothness of the integral kernels in the spectral implementation. The present method is robust for a general boundary contour. Aspects of efficient implementation of the method using FFT are also discussed. A numerical example of wave scattering is given in which the exponential accuracy of the present numerical method is demonstrated.

The numerical solution of linear multi-term fractional differential equations: systems of equations

NASA Astrophysics Data System (ADS)

Edwards, John T.; Ford, Neville J.; Simpson, A. Charles

2002-11-01

In this paper, we show how the numerical approximation of the solution of a linear multi-term fractional differential equation can be calculated by reduction of the problem to a system of ordinary and fractional differential equations each of order at most unity. We begin by showing how our method applies to a simple class of problems and we give a convergence result. We solve the Bagley Torvik equation as an example. We show how the method can be applied to a general linear multi-term equation and give two further examples.

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

ERIC Educational Resources Information Center

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…

Cost effectiveness of self-monitoring of blood glucose (SMBG) for patients with type 2 diabetes and not on insulin: impact of modelling assumptions on recent Canadian findings.

PubMed

Tunis, Sandra L

2011-11-01

the COMPUS base-case ICER. SMBG was associated with modest risk reductions (0.10-0.70%) for six of seven complications. Assuming an SMBG advantage of -0.30% decreased the current base-case ICER by over $Can10 000 per QALY gained. With adherence of 66% and 87%, ICERs were (respectively) $Can39 231 and $Can54 349 per QALY gained. Incorporating a more representative complication history and 15% complication cost increase resulted in an ICER of $Can49 743 per QALY gained. These results underscore the importance of modelling assumptions regarding the duration of HbA(1c) effect. The current study shares several COMPUS limitations relating to the UKPDS model being designed for newly diagnosed patients, and to randomized controlled trial monitoring rates. Neither study explicitly examined the impact of varying the duration of initial HbA(1c) effects, or of medication or other treatment changes. Because the COMPUS research will potentially influence clinical practice and reimbursement policy in Canada, understanding the impact of assumptions on cost-effectiveness results seems especially important. Demonstrating that COMPUS ICERs were greatly reduced through variations in a small number of inputs may encourage additional clinical research designed to measure SMBG effects within the context of optimal disease management. It may also encourage additional economic evaluations that incorporate lessons learned and best practices for assessing the overall value of SMBG for type 2 diabetes in insulin-naive patients.

Standard Errors of Equating for the Percentile Rank-Based Equipercentile Equating with Log-Linear Presmoothing

ERIC Educational Resources Information Center

Wang, Tianyou

2009-01-01

Holland and colleagues derived a formula for analytical standard error of equating using the delta-method for the kernel equating method. Extending their derivation, this article derives an analytical standard error of equating procedure for the conventional percentile rank-based equipercentile equating with log-linear smoothing. This procedure is…

A new integrable equation combining the modified KdV equation with the negative-order modified KdV equation: multiple soliton solutions and a variety of solitonic solutions

NASA Astrophysics Data System (ADS)

Wazwaz, Abdul-Majid

2018-07-01

A new third-order integrable equation is constructed via combining the recursion operator of the modified KdV equation (MKdV) and its inverse recursion operator. The developed equation will be termed the modified KdV-negative order modified KdV equation (MKdV-nMKdV). The complete integrability of this equation is confirmed by showing that it nicely possesses the Painlevé property. We obtain multiple soliton solutions for the newly developed integrable equation. Moreover, this equation enjoys a variety of solutions which include solitons, peakons, cuspons, negaton, positon, complexiton and other solutions.

Local Linear Observed-Score Equating

ERIC Educational Resources Information Center

Wiberg, Marie; van der Linden, Wim J.

2011-01-01

Two methods of local linear observed-score equating for use with anchor-test and single-group designs are introduced. In an empirical study, the two methods were compared with the current traditional linear methods for observed-score equating. As a criterion, the bias in the equated scores relative to true equating based on Lord's (1980)…

A Comparative Analysis of Pre-Equating and Post-Equating in a Large-Scale Assessment, High Stakes Examination

ERIC Educational Resources Information Center

Ojerinde, Dibu; Popoola, Omokunmi; Onyeneho, Patrick; Egberongbe, Aminat

2016-01-01

Statistical procedure used in adjusting test score difficulties on test forms is known as "equating". Equating makes it possible for various test forms to be used interchangeably. In terms of where the equating method fits in the assessment cycle, there are pre-equating and post-equating methods. The major benefits of pre-equating, when…

Mapping Erosion Risk in California's Rangelands Using the Universal Soil Loss Equation (USLE)

NASA Astrophysics Data System (ADS)

Salls, W. B.; O'Geen, T. T.

2015-12-01

Soil loss constitutes a multi-faceted problem for agriculture: in addition to reducing soil fertility and crop yield, it compromises downstream water quality. Sediment itself is a major issue for aquatic ecosystems, but also serves as a vector for transporting nutrients, pesticides, and pathogens. Rangelands are thought to be a contributor to water quality degradation in California, particularly in the northern Coast Range. Though total maximum daily loads (TMDLs) have been imposed in some watersheds, and countless rangeland water quality outreach activities have been conducted, the connection between grazing intensity recommendations and changes in water quality is poorly understood at the state level. This disconnect gives rise to poorly informed regulations and discourages adoption of best management practices by ranchers. By applying the Universal Soil Loss Equation (USLE) at a statewide scale, we highlighted areas most prone to erosion. We also investigated how two different grazing intensity scenarios affect modeled soil loss. Geospatial data layers representing the USLE parameters—rainfall erosivity, soil erodibility, slope length and steepness, and cover—were overlaid to model annual soil loss. Monitored suspended sediment data from a small North Coast watershed with grazing as the predominant land use was used to validate the model. Modeled soil loss values were nearly one order of magnitude higher than monitored values; average soil loss feeding the downstream-most site was modeled at 0.329 t ha-1 yr-1, whereas storm-derived sediment passing the site over two years was calculated to be 0.037 t ha-1 yr-1. This discrepancy may stem from the fact that the USLE models detached sediment, whereas stream monitoring reflects sediment detached and subsequently transported to the waterway. Preliminary findings from the statewide map support the concern that the North Coast is particularly at risk given its combination of intense rain, erodible soils, and

A Comparison of the Kernel Equating Method with Traditional Equating Methods Using SAT[R] Data

ERIC Educational Resources Information Center

Liu, Jinghua; Low, Albert C.

2008-01-01

This study applied kernel equating (KE) in two scenarios: equating to a very similar population and equating to a very different population, referred to as a distant population, using SAT[R] data. The KE results were compared to the results obtained from analogous traditional equating methods in both scenarios. The results indicate that KE results…

Existing creatinine-based equations overestimate glomerular filtration rate in Indians.

PubMed

Kumar, Vivek; Yadav, Ashok Kumar; Yasuda, Yoshinari; Horio, Masaru; Kumar, Vinod; Sahni, Nancy; Gupta, Krishan L; Matsuo, Seiichi; Kohli, Harbir Singh; Jha, Vivekanand

2018-02-01

Accurate estimation of glomerular filtration rate (GFR) is important for diagnosis and risk stratification in chronic kidney disease and for selection of living donors. Ethnic differences have required correction factors in the originally developed creatinine-based GFR estimation equations for populations around the world. Existing equations have not been validated in the vegetarian Indian population. We examined the performance of creatinine and cystatin-based GFR estimating equations in Indians. GFR was measured by urinary clearance of inulin. Serum creatinine was measured using IDMS-traceable Jaffe's and enzymatic assays, and cystatin C by colloidal gold immunoassay. Dietary protein intake was calculated by measuring urinary nitrogen appearance. Bias, precision and accuracy were calculated for the eGFR equations. A total of 130 participants (63 healthy kidney donors and 67 with CKD) were studied. About 50% were vegetarians, and the remainder ate meat 3.8 times every month. The average creatinine excretion were 14.7 mg/kg/day (95% CI: 13.5 to 15.9 mg/kg/day) and 12.4 mg/kg/day (95% CI: 11.2 to 13.6 mg/kg/day) in males and females, respectively. The average daily protein intake was 46.1 g/day (95% CI: 43.2 to 48.8 g/day). The mean mGFR in the study population was 51.66 ± 31.68 ml/min/1.73m 2 . All creatinine-based eGFR equations overestimated GFR (p < 0.01 for each creatinine based eGFR equation). However, eGFR by CKD-EPI Cys was not significantly different from mGFR (p = 0.38). The CKD-EPI Cys exhibited lowest bias [mean bias: -3.53 ± 14.70 ml/min/1.73m 2 (95% CI: -0.608 to -0.98)] and highest accuracy (P 30 : 74.6%). The GFR in the healthy population was 79.44 ± 20.19 (range: 41.90-134.50) ml/min/1.73m 2 . Existing creatinine-based GFR estimating equations overestimate GFR in Indians. An appropriately powered study is needed to develop either a correction factor or a new equation for accurate assessment of kidney function in the

A Hybrid Method of Moment Equations and Rate Equations to Modeling Gas-Grain Chemistry

NASA Astrophysics Data System (ADS)

Pei, Y.; Herbst, E.

2011-05-01

Grain surfaces play a crucial role in catalyzing many important chemical reactions in the interstellar medium (ISM). The deterministic rate equation (RE) method has often been used to simulate the surface chemistry. But this method becomes inaccurate when the number of reacting particles per grain is typically less than one, which can occur in the ISM. In this condition, stochastic approaches such as the master equations are adopted. However, these methods have mostly been constrained to small chemical networks due to the large amounts of processor time and computer power required. In this study, we present a hybrid method consisting of the moment equation approximation to the stochastic master equation approach and deterministic rate equations to treat a gas-grain model of homogeneous cold cloud cores with time-independent physical conditions. In this model, we use the standard OSU gas phase network (version OSU2006V3) which involves 458 gas phase species and more than 4000 reactions, and treat it by deterministic rate equations. A medium-sized surface reaction network which consists of 21 species and 19 reactions accounts for the productions of stable molecules such as H_2O, CO, CO_2, H_2CO, CH_3OH, NH_3 and CH_4. These surface reactions are treated by a hybrid method of moment equations (Barzel & Biham 2007) and rate equations: when the abundance of a surface species is lower than a specific threshold, say one per grain, we use the ``stochastic" moment equations to simulate the evolution; when its abundance goes above this threshold, we use the rate equations. A continuity technique is utilized to secure a smooth transition between these two methods. We have run chemical simulations for a time up to 10^8 yr at three temperatures: 10 K, 15 K, and 20 K. The results will be compared with those generated from (1) a completely deterministic model that uses rate equations for both gas phase and grain surface chemistry, (2) the method of modified rate equations (Garrod

Field equations from Killing spinors

NASA Astrophysics Data System (ADS)

Açık, Özgür

2018-02-01

From the Killing spinor equation and the equations satisfied by their bilinears, we deduce some well-known bosonic and fermionic field equations of mathematical physics. Aside from the trivially satisfied Dirac equation, these relativistic wave equations in curved spacetimes, respectively, are Klein-Gordon, Maxwell, Proca, Duffin-Kemmer-Petiau, Kähler, twistor, and Rarita-Schwinger equations. This result shows that, besides being special kinds of Dirac fermions, Killing fermions can be regarded as physically fundamental. For the Maxwell case, the problem of motion is analysed in a reverse manner with respect to the studies of Einstein-Groemer-Infeld-Hoffmann and Jean Marie Souriau. In the analysis of the gravitino field, a generalised 3-ψ rule is found which is termed the vanishing trace constraint.

Construction of Chained True Score Equipercentile Equatings under the Kernel Equating (KE) Framework and Their Relationship to Levine True Score Equating. Research Report. ETS RR-09-24

ERIC Educational Resources Information Center

Chen, Haiwen; Holland, Paul

2009-01-01

In this paper, we develop a new chained equipercentile equating procedure for the nonequivalent groups with anchor test (NEAT) design under the assumptions of the classical test theory model. This new equating is named chained true score equipercentile equating. We also apply the kernel equating framework to this equating design, resulting in a…

A Probabilistic Risk Assessment of Groundwater-Related Risks at Excavation Sites

NASA Astrophysics Data System (ADS)

Jurado, A.; de Gaspari, F.; Vilarrasa, V.; Sanchez-Vila, X.; Fernandez-Garcia, D.; Tartakovsky, D. M.; Bolster, D.

2010-12-01

Excavation sites such as those associated with the construction of subway lines, railways and highway tunnels are hazardous places, posing risks to workers, machinery and surrounding buildings. Many of these risks can be groundwater related. In this work we develop a general framework based on a probabilistic risk assessment (PRA) to quantify such risks. This approach is compatible with standard PRA practices and it employs many well-developed risk analysis tools, such as fault trees. The novelty and computational challenges of the proposed approach stem from the reliance on stochastic differential equations, rather than reliability databases, to compute the probabilities of basic events. The general framework is applied to a specific case study in Spain. It is used to estimate and minimize risks for a potential construction site of an underground station for the new subway line in the Barcelona metropolitan area.

Modified equations, rational solutions, and the Painleve property for the Kadomtsev--Petviashvili and Hirota--Satsuma equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Weiss, J.

1985-09-01

We propose a method for finding the Lax pairs and rational solutions of integrable partial differential equations. That is, when an equation possesses the Painleve property, a Baecklund transformation is defined in terms of an expansion about the singular manifold. This Baecklund transformation obtains (1) a type of modified equation that is formulated in terms of Schwarzian derivatives and (2) a Miura transformation from the modified to the original equation. By linearizing the (Ricati-type) Miura transformation the Lax pair is found. On the other hand, consideration of the (distinct) Baecklund transformations of the modified equations provides a method for themore » iterative construction of rational solutions. This also obtains the Lax pairs for the modified equations. In this paper we apply this method to the Kadomtsev--Petviashvili equation and the Hirota--Satsuma equations.« less

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

NASA Technical Reports Server (NTRS)

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.

The non-autonomous YdKN equation and generalized symmetries of Boll equations

NASA Astrophysics Data System (ADS)

Gubbiotti, G.; Scimiterna, C.; Levi, D.

2017-05-01

In this paper, we study the integrability of a class of nonlinear non-autonomous quad graph equations compatible around the cube introduced by Boll in the framework of the generalized Adler, Bobenko, and Suris (ABS) classification. We show that all these equations possess three-point generalized symmetries which are subcases of either the Yamilov discretization of the Krichever-Novikov equation or of its non-autonomous extension. We also prove that all those symmetries are integrable as they pass the algebraic entropy test.

Flight assessment in patients with respiratory disease: hypoxic challenge testing vs. predictive equations.

PubMed

Martin, S E; Bradley, J M; Buick, J B; Bradbury, I; Elborn, J S

2007-06-01

Predictive equations have been proposed as a simpler alternative to hypoxic challenge testing (HCT) for determining the risk of in-flight hypoxia. To assess agreement between hypoxic challenge testing (HCT) and predictive equations for assessment of in-flight hypoxia. Retrospective study. Patients with chronic obstructive pulmonary disease (COPD) (n = 15), interstitial lung disease (ILD) (n = 15) and cystic fibrosis (CF) (n = 15) were studied. Spirometry was recorded prior to hypoxic inhalation and oxygen saturations (SpO2) were recorded before, after and during hypoxic inhalation. Blood gases were analysed before and after hypoxic inhalation and when SpO2 = 85%. An HCT was performed using the Ventimask method. The PaO2 at altitude was estimated for each group using four published predictive equations, which use values of PaO2 (ground) and lung function measurements to predict altitude PaO2. Results were interpreted using the BTS recommendations for prescription of in-flight oxygen post HCT. The Stuart Maxwell test of overall homogeneity was used to assess agreement between HCT results and each of the predictive equations. Ground PaO2 was significantly greater in patients with CF than either ILD or COPD (p < 0.05). PaO2 in all three groups significantly decreased following HCT. With the exception of equation 3, significantly fewer patients in each group would require in-flight O2 if prescription was based on HCT, compared to predictive equations (p < 0.05). Predictive equations considerably overestimate the need for in-flight O2, compared to HCT.

Solving Ordinary Differential Equations

NASA Technical Reports Server (NTRS)

Krogh, F. T.

1987-01-01

Initial-value ordinary differential equation solution via variable order Adams method (SIVA/DIVA) package is collection of subroutines for solution of nonstiff ordinary differential equations. There are versions for single-precision and double-precision arithmetic. Requires fewer evaluations of derivatives than other variable-order Adams predictor/ corrector methods. Option for direct integration of second-order equations makes integration of trajectory problems significantly more efficient. Written in FORTRAN 77.

Investigations of Sayre's Equation.

NASA Astrophysics Data System (ADS)

Shiono, Masaaki

Available from UMI in association with The British Library. Since the discovery of X-ray diffraction, various methods of using it to solve crystal structures have been developed. The major methods used can be divided into two categories: (1) Patterson function based methods; (2) Direct phase-determination methods. In the early days of structure determination from X-ray diffraction, Patterson methods played the leading role. Direct phase-determining methods ('direct methods' for short) were introduced by D. Harker and J. S. Kasper in the form of inequality relationships in 1948. A significant development of direct methods was produced by Sayre (1952). The equation he introduced, generally called Sayre's equation, gives exact relationships between structure factors for equal atoms. Later Cochran (1955) derived the so-called triple phase relationship, the main means by which it has become possible to find the structure factor phases automatically by computer. Although the background theory of direct methods is very mathematical, the user of direct-methods computer programs needs no detailed knowledge of these automatic processes in order to solve structures. Recently introduced direct methods are based on Sayre's equation, so it is important to investigate its properties thoroughly. One such new method involves the Sayre equation tangent formula (SETF) which attempts to minimise the least square residual for the Sayre's equations (Debaerdemaeker, Tate and Woolfson; 1985). In chapters I-III the principles and developments of direct methods will be described and in chapters IV -VI the properties of Sayre's equation and its modification will be discussed. Finally, in chapter VII, there will be described the investigation of the possible use of an equation, similar in type to Sayre's equation, derived from the characteristics of the Patterson function.

Improving multilevel Monte Carlo for stochastic differential equations with application to the Langevin equation.

PubMed

Müller, Eike H; Scheichl, Rob; Shardlow, Tony

2015-04-08

This paper applies several well-known tricks from the numerical treatment of deterministic differential equations to improve the efficiency of the multilevel Monte Carlo (MLMC) method for stochastic differential equations (SDEs) and especially the Langevin equation. We use modified equations analysis as an alternative to strong-approximation theory for the integrator, and we apply this to introduce MLMC for Langevin-type equations with integrators based on operator splitting. We combine this with extrapolation and investigate the use of discrete random variables in place of the Gaussian increments, which is a well-known technique for the weak approximation of SDEs. We show that, for small-noise problems, discrete random variables can lead to an increase in efficiency of almost two orders of magnitude for practical levels of accuracy.

Construction and accuracy of partial differential equation approximations to the chemical master equation.

PubMed

Grima, Ramon

2011-11-01

The mesoscopic description of chemical kinetics, the chemical master equation, can be exactly solved in only a few simple cases. The analytical intractability stems from the discrete character of the equation, and hence considerable effort has been invested in the development of Fokker-Planck equations, second-order partial differential equation approximations to the master equation. We here consider two different types of higher-order partial differential approximations, one derived from the system-size expansion and the other from the Kramers-Moyal expansion, and derive the accuracy of their predictions for chemical reactive networks composed of arbitrary numbers of unimolecular and bimolecular reactions. In particular, we show that the partial differential equation approximation of order Q from the Kramers-Moyal expansion leads to estimates of the mean number of molecules accurate to order Ω(-(2Q-3)/2), of the variance of the fluctuations in the number of molecules accurate to order Ω(-(2Q-5)/2), and of skewness accurate to order Ω(-(Q-2)). We also show that for large Q, the accuracy in the estimates can be matched only by a partial differential equation approximation from the system-size expansion of approximate order 2Q. Hence, we conclude that partial differential approximations based on the Kramers-Moyal expansion generally lead to considerably more accurate estimates in the mean, variance, and skewness than approximations of the same order derived from the system-size expansion.

Optimization of one-way wave equations.

USGS Publications Warehouse

Lee, M.W.; Suh, S.Y.

1985-01-01

The theory of wave extrapolation is based on the square-root equation or one-way equation. The full wave equation represents waves which propagate in both directions. On the contrary, the square-root equation represents waves propagating in one direction only. A new optimization method presented here improves the dispersion relation of the one-way wave equation. -from Authors

Introducing Chemical Formulae and Equations.

ERIC Educational Resources Information Center

Dawson, Chris; Rowell, Jack

1979-01-01

Discusses when the writing of chemical formula and equations can be introduced in the school science curriculum. Also presents ways in which formulae and equations learning can be aided and some examples for balancing and interpreting equations. (HM)

The statistical theory of the fracture of fragile bodies. Part 2: The integral equation method

NASA Technical Reports Server (NTRS)

Kittl, P.

1984-01-01

It is demonstrated how with the aid of a bending test, the Weibull fracture risk function can be determined - without postulating its analytical form - by resolving an integral equation. The respective solutions for rectangular and circular section beams are given. In the first case the function is expressed as an algorithm and in the second, in the form of series. Taking into account that the cumulative fracture probability appearing in the solution to the integral equation must be continuous and monotonically increasing, any case of fabrication or selection of samples can be treated.

Gauge-invariant flow equation

NASA Astrophysics Data System (ADS)

Wetterich, C.

2018-06-01

We propose a closed gauge-invariant functional flow equation for Yang-Mills theories and quantum gravity that only involves one macroscopic gauge field or metric. It is based on a projection on physical and gauge fluctuations. Deriving this equation from a functional integral we employ the freedom in the precise choice of the macroscopic field and the effective average action in order to realize a closed and simple form of the flow equation.

Algebraic Construction of Exact Difference Equations from Symmetry of Equations

NASA Astrophysics Data System (ADS)

Itoh, Toshiaki

2009-09-01

Difference equations or exact numerical integrations, which have general solutions, are treated algebraically. Eliminating the symmetries of the equation, we can construct difference equations (DCE) or numerical integrations equivalent to some ODEs or PDEs that means both have the same solution functions. When arbitrary functions are given, whether we can construct numerical integrations that have solution functions equal to given function or not are treated in this work. Nowadays, Lie's symmetries solver for ODE and PDE has been implemented in many symbolic software. Using this solver we can construct algebraic DCEs or numerical integrations which are correspond to some ODEs or PDEs. In this work, we treated exact correspondence between ODE or PDE and DCE or numerical integration with Gröbner base and Janet base from the view of Lie's symmetries.

Generalization of the lightning electromagnetic equations of Uman, McLain, and Krider based on Jefimenko equations

DOE PAGES

Shao, Xuan-Min

2016-04-12

The fundamental electromagnetic equations used by lightning researchers were introduced in a seminal paper by Uman, McLain, and Krider in 1975. However, these equations were derived for an infinitely thin, one-dimensional source current, and not for a general three-dimensional current distribution. In this paper, we introduce a corresponding pair of generalized equations that are determined from a three-dimensional, time-dependent current density distribution based on Jefimenko's original electric and magnetic equations. To do this, we derive the Jefimenko electric field equation into a new form that depends only on the time-dependent current density similar to that of Uman, McLain, and Krider,more » rather than on both the charge and current densities in its original form. The original Jefimenko magnetic field equation depends only on current, so no further derivation is needed. We show that the equations of Uman, McLain, and Krider can be readily obtained from the generalized equations if a one-dimensional source current is considered. For the purpose of practical applications, we discuss computational implementation of the new equations and present electric field calculations for a three-dimensional, conical-shape discharge.« less

Comparison between results of solution of Burgers' equation and Laplace's equation by Galerkin and least-square finite element methods

NASA Astrophysics Data System (ADS)

Adib, Arash; Poorveis, Davood; Mehraban, Farid

2018-03-01

In this research, two equations are considered as examples of hyperbolic and elliptic equations. In addition, two finite element methods are applied for solving of these equations. The purpose of this research is the selection of suitable method for solving each of two equations. Burgers' equation is a hyperbolic equation. This equation is a pure advection (without diffusion) equation. This equation is one-dimensional and unsteady. A sudden shock wave is introduced to the model. This wave moves without deformation. In addition, Laplace's equation is an elliptical equation. This equation is steady and two-dimensional. The solution of Laplace's equation in an earth dam is considered. By solution of Laplace's equation, head pressure and the value of seepage in the directions X and Y are calculated in different points of earth dam. At the end, water table is shown in the earth dam. For Burgers' equation, least-square method can show movement of wave with oscillation but Galerkin method can not show it correctly (the best method for solving of the Burgers' equation is discrete space by least-square finite element method and discrete time by forward difference.). For Laplace's equation, Galerkin and least square methods can show water table correctly in earth dam.

Improving multilevel Monte Carlo for stochastic differential equations with application to the Langevin equation

PubMed Central

Müller, Eike H.; Scheichl, Rob; Shardlow, Tony

2015-01-01

This paper applies several well-known tricks from the numerical treatment of deterministic differential equations to improve the efficiency of the multilevel Monte Carlo (MLMC) method for stochastic differential equations (SDEs) and especially the Langevin equation. We use modified equations analysis as an alternative to strong-approximation theory for the integrator, and we apply this to introduce MLMC for Langevin-type equations with integrators based on operator splitting. We combine this with extrapolation and investigate the use of discrete random variables in place of the Gaussian increments, which is a well-known technique for the weak approximation of SDEs. We show that, for small-noise problems, discrete random variables can lead to an increase in efficiency of almost two orders of magnitude for practical levels of accuracy. PMID:27547075

Quantum integrability and functional equations

NASA Astrophysics Data System (ADS)

Volin, Dmytro

2010-03-01

In this thesis a general procedure to represent the integral Bethe Ansatz equations in the form of the Reimann-Hilbert problem is given. This allows us to study in simple way integrable spin chains in the thermodynamic limit. Based on the functional equations we give the procedure that allows finding the subleading orders in the solution of various integral equations solved to the leading order by the Wiener-Hopf technics. The integral equations are studied in the context of the AdS/CFT correspondence, where their solution allows verification of the integrability conjecture up to two loops of the strong coupling expansion. In the context of the two-dimensional sigma models we analyze the large-order behavior of the asymptotic perturbative expansion. Obtained experience with the functional representation of the integral equations allowed us also to solve explicitly the crossing equations that appear in the AdS/CFT spectral problem.

Reflections on Chemical Equations.

ERIC Educational Resources Information Center

Gorman, Mel

1981-01-01

The issue of how much emphasis balancing chemical equations should have in an introductory chemistry course is discussed. The current heavy emphasis on finishing such equations is viewed as misplaced. (MP)

Development and progression of nephropathy in type 2 diabetes: the United Kingdom Prospective Diabetes Study (UKPDS 64).

PubMed

Adler, Amanda I; Stevens, Richard J; Manley, Sue E; Bilous, Rudy W; Cull, Carole A; Holman, Rury R

2003-01-01

The progression of nephropathy from diagnosis of type 2 diabetes has not been well described from a single population. This study sought to describe the development and progression through the stages of microalbuminuria, macroalbuminuria, persistently elevated plasma creatinine or renal replacement therapy (RRT), and death. Using observed and modeled data from 5097 subjects in the UK Prospective Diabetes Study, we measured the annual probability of transition from stage to stage (incidence), prevalence, cumulative incidence, ten-year survival, median duration per stage, and risk of death from all-causes or cardiovascular disease. From diagnosis of diabetes, progression to microalbuminuria occurred at 2.0% per year, from microalbuminuria to macroalbuminuria at 2.8% per year, and from macroalbuminuria to elevated plasma creatinine (>or=175 micromol/L) or renal replacement therapy at 2.3% per year. Ten years following diagnosis of diabetes, the prevalence of microalbuminuria was 24.9%, of macroalbuminuria was 5.3%, and of elevated plasma creatinine or RRT was 0.8%. Patients with elevated plasma creatinine or RRT had an annual death rate of 19.2% (95% confidence interval, CI, 14.0 to 24.4%). There was a trend for increasing risk of cardiovascular death with increasing nephropathy (P < 0.0001), with an annual rate of 0.7% for subjects in the stage of no nephropathy, 2.0% for those with microalbuminuria, 3.5% for those with macroalbuminuria, and 12.1% with elevated plasma creatinine or RRT. Individuals with macroalbuminuria were more likely to die in any year than to develop renal failure. The proportion of patients with type 2 diabetes who develop microalbuminuria is substantial with one quarter affected by 10 years from diagnosis. Relatively fewer patients develop macroalbuminuria, but in those who do, the death rate exceeds the rate of progression to worse nephropathy.

Algorithm and code development for unsteady three-dimensional Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Obayashi, Shigeru

1994-01-01

Aeroelastic tests require extensive cost and risk. An aeroelastic wind-tunnel experiment is an order of magnitude more expensive than a parallel experiment involving only aerodynamics. By complementing the wind-tunnel experiments with numerical simulations, the overall cost of the development of aircraft can be considerably reduced. In order to accurately compute aeroelastic phenomenon it is necessary to solve the unsteady Euler/Navier-Stokes equations simultaneously with the structural equations of motion. These equations accurately describe the flow phenomena for aeroelastic applications. At ARC a code, ENSAERO, is being developed for computing the unsteady aerodynamics and aeroelasticity of aircraft, and it solves the Euler/Navier-Stokes equations. The purpose of this cooperative agreement was to enhance ENSAERO in both algorithm and geometric capabilities. During the last five years, the algorithms of the code have been enhanced extensively by using high-resolution upwind algorithms and efficient implicit solvers. The zonal capability of the code has been extended from a one-to-one grid interface to a mismatching unsteady zonal interface. The geometric capability of the code has been extended from a single oscillating wing case to a full-span wing-body configuration with oscillating control surfaces. Each time a new capability was added, a proper validation case was simulated, and the capability of the code was demonstrated.

Extension of the Schrodinger equation

NASA Astrophysics Data System (ADS)

Somsikov, Vyacheslav

2017-03-01

Extension of the Schrodinger equation is submitted by removing its limitations appearing due to the limitations of the formalism of Hamilton, based on which this equation was obtained. For this purpose the problems of quantum mechanics arising from the limitations of classical mechanics are discussed. These limitations, in particular, preclude the use of the Schrodinger equation to describe the time symmetry violation. The extension of the Schrodinger equation is realized based on the principle of duality symmetry. According to this principle the dynamics of the systems is determined by the symmetry of the system and by the symmetry of the space. The extension of the Schrodinger equation was obtained from the dual expression of energy, represented in operator form. For this purpose the independent micro - and macro-variables that determine respectively the dynamics of quantum particle system relative to its center of mass and the movement of the center of mass in space are used. The solution of the extended Schrodinger equation for the system near equilibrium is submitted. The main advantage of the extended Schrodinger equation is that it is applicable to describe the interaction and evolution of quantum systems in inhomogeneous field of external forces.

Metrisability of Painlevé equations

NASA Astrophysics Data System (ADS)

Contatto, Felipe; Dunajski, Maciej

2018-02-01

We solve the metrisability problem for the six Painlevé equations, and more generally for all 2nd order ordinary differential equations with the Painlevé property, and determine for which of these equations their integral curves are geodesics of a (pseudo) Riemannian metric on a surface.

The Forced Hard Spring Equation

ERIC Educational Resources Information Center

Fay, Temple H.

2006-01-01

Through numerical investigations, various examples of the Duffing type forced spring equation with epsilon positive, are studied. Since [epsilon] is positive, all solutions to the associated homogeneous equation are periodic and the same is true with the forcing applied. The damped equation exhibits steady state trajectories with the interesting…

Interpretation of Bernoulli's Equation.

ERIC Educational Resources Information Center

Bauman, Robert P.; Schwaneberg, Rolf

1994-01-01

Discusses Bernoulli's equation with regards to: horizontal flow of incompressible fluids, change of height of incompressible fluids, gases, liquids and gases, and viscous fluids. Provides an interpretation, properties, terminology, and applications of Bernoulli's equation. (MVL)

An Illustration of a Longitudinal Cross-Lagged Design for Larger Structural Equation Models. Teacher's Corner.

ERIC Educational Resources Information Center

Burkholder, Gary J.; Harlow, Lisa L.

2003-01-01

Tested a model of HIV behavior risk, using a fully cross-lagged, longitudinal design to illustrate the analysis of larger structural equation models. Data from 527 women who completed a survey at three time points show excellent fit of the model to the data. (SLD)

On integrability of the Killing equation

NASA Astrophysics Data System (ADS)

Houri, Tsuyoshi; Tomoda, Kentaro; Yasui, Yukinori

2018-04-01

Killing tensor fields have been thought of as describing the hidden symmetry of space(-time) since they are in one-to-one correspondence with polynomial first integrals of geodesic equations. Since many problems in classical mechanics can be formulated as geodesic problems in curved space and spacetime, solving the defining equation for Killing tensor fields (the Killing equation) is a powerful way to integrate equations of motion. Thus it has been desirable to formulate the integrability conditions of the Killing equation, which serve to determine the number of linearly independent solutions and also to restrict the possible forms of solutions tightly. In this paper, we show the prolongation for the Killing equation in a manner that uses Young symmetrizers. Using the prolonged equations, we provide the integrability conditions explicitly.

Adaptive Osher-type scheme for the Euler equations with highly nonlinear equations of state

NASA Astrophysics Data System (ADS)

Lee, Bok Jik; Toro, Eleuterio F.; Castro, Cristóbal E.; Nikiforakis, Nikolaos

2013-08-01

For the numerical simulation of detonation of condensed phase explosives, a complex equation of state (EOS), such as the Jones-Wilkins-Lee (JWL) EOS or the Cochran-Chan (C-C) EOS, are widely used. However, when a conservative scheme is used for solving the Euler equations with such equations of state, a spurious solution across the contact discontinuity, a well known phenomenon in multi-fluid systems, arises even for single materials. In this work, we develop a generalised Osher-type scheme in an adaptive primitive-conservative framework to overcome the aforementioned difficulties. Resulting numerical solutions are compared with the exact solutions and with the numerical solutions from the Godunov method in conjunction with the exact Riemann solver for the Euler equations with Mie-Grüneisen form of equations of state, such as the JWL and the C-C equations of state. The adaptive scheme is extended to second order and its empirical convergence rates are presented, verifying second order accuracy for smooth solutions. Through a suite of several tests problems in one and two space dimensions we illustrate the failure of conservative schemes and the capability of the methods of this paper to overcome the difficulties.

Group foliation of finite difference equations

NASA Astrophysics Data System (ADS)

Thompson, Robert; Valiquette, Francis

2018-06-01

Using the theory of equivariant moving frames, a group foliation method for invariant finite difference equations is developed. This method is analogous to the group foliation of differential equations and uses the symmetry group of the equation to decompose the solution process into two steps, called resolving and reconstruction. Our constructions are performed algorithmically and symbolically by making use of discrete recurrence relations among joint invariants. Applications to invariant finite difference equations that approximate differential equations are given.

Derivation and Validation of a New Cardiovascular Risk Score for People With Type 2 Diabetes

PubMed Central

Elley, C. Raina; Robinson, Elizabeth; Kenealy, Tim; Bramley, Dale; Drury, Paul L.

2010-01-01

OBJECTIVE To derive a 5-year cardiovascular disease (CVD) risk equation from usual-care data that is appropriate for people with type 2 diabetes from a wide range of ethnic groups, variable glycemic control, and high rates of albuminuria in New Zealand. RESEARCH DESIGN AND METHODS This prospective open-cohort study used primary-care data from 36,127 people with type 2 diabetes without previous CVD to derive a CVD equation using Cox proportional hazards regression models. Data from 12,626 people from a geographically different area were used for validation. Outcome measure was time to first fatal or nonfatal cardiovascular event, derived from national hospitalization and mortality records. Risk factors were age at diagnosis, diabetes duration, sex, systolic blood pressure, smoking status, total cholesterol–to–HDL ratio, ethnicity, glycated hemoglobin (A1C), and urine albumin-to-creatinine ratio. RESULTS Baseline median age was 59 years, 51% were women, 55% were of non-European ethnicity, and 33% had micro- or macroalbuminuria. Median follow-up was 3.9 years (141,169 person-years), including 10,030 individuals followed for at least 5 years. At total of 6,479 first cardiovascular events occurred during follow-up. The 5-year observed risk was 20.8% (95% CI 20.3–21.3). Risk increased with each 1% A1C (adjusted hazard ratio 1.06 [95% CI 1.05–1.08]), when macroalbuminuria was present (2.04 [1.89–2.21]), and in Indo-Asians (1.29 [1.14–1.46]) and Maori (1.23 [1.14–1.32]) compared with Europeans. The derived risk equations performed well on the validation cohort compared with other risk equations. CONCLUSIONS Renal function, ethnicity, and glycemic control contribute significantly to cardiovascular risk prediction. Population-appropriate risk equations can be derived from routinely collected data. PMID:20299482

Equating with Miditests Using IRT

ERIC Educational Resources Information Center

Fitzpatrick, Joseph; Skorupski, William P.

2016-01-01

The equating performance of two internal anchor test structures--miditests and minitests--is studied for four IRT equating methods using simulated data. Originally proposed by Sinharay and Holland, miditests are anchors that have the same mean difficulty as the overall test but less variance in item difficulties. Four popular IRT equating methods…

Solving Nonlinear Coupled Differential Equations

NASA Technical Reports Server (NTRS)

Mitchell, L.; David, J.

1986-01-01

Harmonic balance method developed to obtain approximate steady-state solutions for nonlinear coupled ordinary differential equations. Method usable with transfer matrices commonly used to analyze shaft systems. Solution to nonlinear equation, with periodic forcing function represented as sum of series similar to Fourier series but with form of terms suggested by equation itself.

Updated hazard rate equations for dual safeguard systems.

PubMed

Rothschild, Marc

2007-04-11

A previous paper by this author [M.J. Rothschild, Updated hazard rate equation for single safeguards, J. Hazard. Mater. 130 (1-2) (2006) 15-20] showed that commonly used analytical methods for quantifying failure rates overestimates the risk in some circumstances. This can lead the analyst to mistakenly believe that a given operation presents an unacceptable risk. For a single safeguard system, a formula was presented in that paper that accurately evaluates the risk over a wide range of conditions. This paper expands on that analysis by evaluating the failure rate for dual safeguard systems. The safeguards can be activated at the same time or at staggered times, and the safeguard may provide an indication whether it was successful upon a challenge, or its status may go undetected. These combinations were evaluated using a Monte Carlo simulation. Empirical formulas for evaluating the hazard rate were developed from this analysis. It is shown that having the safeguards activate at the same time while providing positive feedback of their individual actions is the most effective arrangement in reducing the hazard rate. The hazard rate can also be reduced by staggering the testing schedules of the safeguards.

Is the Wheeler-DeWitt equation more fundamental than the Schrödinger equation?

NASA Astrophysics Data System (ADS)

Shestakova, Tatyana P.

The Wheeler-DeWitt equation was proposed 50 years ago and until now it is the cornerstone of most approaches to quantization of gravity. One can find in the literature, the opinion that the Wheeler-DeWitt equation is even more fundamental than the basic equation of quantum theory, the Schrödinger equation. We still should remember that we are in the situation when no observational data can confirm or reject the fundamental status of the Wheeler-DeWitt equation, so we can give just indirect arguments in favor of or against it, grounded on mathematical consistency and physical relevance. I shall present the analysis of the situation and comparison of the standard Wheeler-DeWitt approach with the extended phase space approach to quantization of gravity. In my analysis, I suppose, first, that a future quantum theory of gravity must be applicable to all phenomena from the early universe to quantum effects in strong gravitational fields, in the latter case, the state of the observer (the choice of a reference frame) may appear to be significant. Second, I suppose that the equation for the wave function of the universe must not be postulated but derived by means of a mathematically consistent procedure, which exists in path integral quantization. When applying this procedure to any gravitating system, one should take into account features of gravity, namely, nontrivial spacetime topology and possible absence of asymptotic states. The Schrödinger equation has been derived early for cosmological models with a finite number of degrees of freedom, and just recently it has been found for the spherically symmetric model which is a simplest model with an infinite number of degrees of freedom. The structure of the Schrödinger equation and its general solution appears to be very similar in these cases. The obtained results give grounds to say that the Schrödinger equation retains its fundamental meaning in constructing quantum theory of gravity.

Reduction of the equation for lower hybrid waves in a plasma to a nonlinear Schroedinger equation

NASA Technical Reports Server (NTRS)

Karney, C. F. F.

1977-01-01

Equations describing the nonlinear propagation of waves in an anisotropic plasma are rarely exactly soluble. However it is often possible to make approximations that reduce the exact equations into a simpler equation. The use of MACSYMA to make such approximations, and so reduce the equation describing lower hybrid waves into the nonlinear Schrodinger equation which is soluble by the inverse scattering method is demonstrated. MACSYMA is used at several stages in the calculation only because there is a natural division between calculations that are easiest done by hand, and those that are easiest done by machine.

The Complexity of One-Step Equations

ERIC Educational Resources Information Center

Ngu, Bing

2014-01-01

An analysis of one-step equations from a cognitive load theory perspective uncovers variation within one-step equations. The complexity of one-step equations arises from the element interactivity across the operational and relational lines. The higher the number of operational and relational lines, the greater the complexity of the equations.…

Simple Derivation of the Lindblad Equation

ERIC Educational Resources Information Center

Pearle, Philip

2012-01-01

The Lindblad equation is an evolution equation for the density matrix in quantum theory. It is the general linear, Markovian, form which ensures that the density matrix is Hermitian, trace 1, positive and completely positive. Some elementary examples of the Lindblad equation are given. The derivation of the Lindblad equation presented here is…

Symbolic computation of recurrence equations for the Chebyshev series solution of linear ODE's. [ordinary differential equations

NASA Technical Reports Server (NTRS)

Geddes, K. O.

1977-01-01

If a linear ordinary differential equation with polynomial coefficients is converted into integrated form then the formal substitution of a Chebyshev series leads to recurrence equations defining the Chebyshev coefficients of the solution function. An explicit formula is presented for the polynomial coefficients of the integrated form in terms of the polynomial coefficients of the differential form. The symmetries arising from multiplication and integration of Chebyshev polynomials are exploited in deriving a general recurrence equation from which can be derived all of the linear equations defining the Chebyshev coefficients. Procedures for deriving the general recurrence equation are specified in a precise algorithmic notation suitable for translation into any of the languages for symbolic computation. The method is algebraic and it can therefore be applied to differential equations containing indeterminates.

Systematic derivation of reaction-diffusion equations with distributed delays and relations to fractional reaction-diffusion equations and hyperbolic transport equations: application to the theory of Neolithic transition.

PubMed

Vlad, Marcel Ovidiu; Ross, John

2002-12-01

We introduce a general method for the systematic derivation of nonlinear reaction-diffusion equations with distributed delays. We study the interactions among different types of moving individuals (atoms, molecules, quasiparticles, biological organisms, etc). The motion of each species is described by the continuous time random walk theory, analyzed in the literature for transport problems, whereas the interactions among the species are described by a set of transformation rates, which are nonlinear functions of the local concentrations of the different types of individuals. We use the time interval between two jumps (the transition time) as an additional state variable and obtain a set of evolution equations, which are local in time. In order to make a connection with the transport models used in the literature, we make transformations which eliminate the transition time and derive a set of nonlocal equations which are nonlinear generalizations of the so-called generalized master equations. The method leads under different specified conditions to various types of nonlocal transport equations including a nonlinear generalization of fractional diffusion equations, hyperbolic reaction-diffusion equations, and delay-differential reaction-diffusion equations. Thus in the analysis of a given problem we can fit to the data the type of reaction-diffusion equation and the corresponding physical and kinetic parameters. The method is illustrated, as a test case, by the study of the neolithic transition. We introduce a set of assumptions which makes it possible to describe the transition from hunting and gathering to agriculture economics by a differential delay reaction-diffusion equation for the population density. We derive a delay evolution equation for the rate of advance of agriculture, which illustrates an application of our analysis.

PREFACE: Symmetries and integrability of difference equations Symmetries and integrability of difference equations

NASA Astrophysics Data System (ADS)

Levi, Decio; Olver, Peter; Thomova, Zora; Winternitz, Pavel

2009-11-01

The concept of integrability was introduced in classical mechanics in the 19th century for finite dimensional continuous Hamiltonian systems. It was extended to certain classes of nonlinear differential equations in the second half of the 20th century with the discovery of the inverse scattering transform and the birth of soliton theory. Also at the end of the 19th century Lie group theory was invented as a powerful tool for obtaining exact analytical solutions of large classes of differential equations. Together, Lie group theory and integrability theory in its most general sense provide the main tools for solving nonlinear differential equations. Like differential equations, difference equations play an important role in physics and other sciences. They occur very naturally in the description of phenomena that are genuinely discrete. Indeed, they may actually be more fundamental than differential equations if space-time is actually discrete at very short distances. On the other hand, even when treating continuous phenomena described by differential equations it is very often necessary to resort to numerical methods. This involves a discretization of the differential equation, i.e. a replacement of the differential equation by a difference one. Given the well developed and understood techniques of symmetry and integrability for differential equations a natural question to ask is whether it is possible to develop similar techniques for difference equations. The aim is, on one hand, to obtain powerful methods for solving `integrable' difference equations and to establish practical integrability criteria, telling us when the methods are applicable. On the other hand, Lie group methods can be adapted to solve difference equations analytically. Finally, integrability and symmetry methods can be combined with numerical methods to obtain improved numerical solutions of differential equations. The origin of the SIDE meetings goes back to the early 1990s and the first

On the transition from the Ginzburg-Landau equation to the extended Fisher-Kolmogorov equation

NASA Astrophysics Data System (ADS)

Rottschäfer, Vivi; Doelman, Arjen

1998-07-01

The Ginzburg-Landau (GL) equation ‘generically’ describes the behaviour of small perturbations of a marginally unstable basic state in systems on unbounded domains. In this paper we consider the transition from this generic situation to a degenerate (co-dimension 2) case in which the GL approach is no longer valid. Instead of studying a general underlying model problem, we consider a two-dimensional system of coupled reaction-diffusion equations in one spatial dimension. We show that near the degeneration the behaviour of small perturbations is governed by the extended Fisher-Kolmogorov (eFK) equation (at leading order). The relation between the GL-equation and the eFK-equation is quite subtle, but can be analysed in detail. The main goal of this paper is to study this relation, which we do asymptotically. The asymptotic analysis is compared to numerical simulations of the full reaction-diffusion system. As one approaches the co-dimension 2 point, we observe that the stable stationary periodic patterns predicted by the GL-equation evolve towards various different families of stable, stationary (but not necessarily periodic) so-called ‘multi-bump’ solutions. In the literature, these multi-bump patterns are shown to exist as solutions of the eFK-equation, but there is no proof of the asymptotic stability of these solutions. Our results suggest that these multi-bump patterns can also be asymptotically stable in large classes of model problems.

Local Observed-Score Kernel Equating

ERIC Educational Resources Information Center

Wiberg, Marie; van der Linden, Wim J.; von Davier, Alina A.

2014-01-01

Three local observed-score kernel equating methods that integrate methods from the local equating and kernel equating frameworks are proposed. The new methods were compared with their earlier counterparts with respect to such measures as bias--as defined by Lord's criterion of equity--and percent relative error. The local kernel item response…

Nonlinear Gyro-Landau-Fluid Equations

NASA Astrophysics Data System (ADS)

Raskolnikov, I.; Mattor, Nathan; Parker, Scott E.

1996-11-01

We present fluid equations which describe the effects of both linear and nonlinear Landau damping (wave-particle-wave effects). These are derived using a recently developed analytical method similar to renormalization group theory. (Scott E. Parker and Daniele Carati, Phys. Rev. Lett. 75), 441 (1995). In this technique, the phase space structure inherent in Landau damping is treated analytically by building a ``renormalized collisionality'' onto a bare collisionality (which may be taken as vanishingly small). Here we apply this technique to the nonlinear ion gyrokinetic equation in slab geometry, obtaining nonlinear fluid equations for density, parallel momentum and heat. Wave-particle resonances are described by two functions appearing in the heat equation: a renormalized ``collisionality'' and a renormalized nonlinear coupling coeffient. It will be shown that these new equations may correct a deficiency in existing gyrofluid equations, (G. W. Hammett and F. W. Perkins, Phys. Rev. Lett. 64,) 3019 (1990). which can severely underestimate the strength of nonlinear interaction in regimes where linear resonance is strong. (N. Mattor, Phys. Fluids B 4,) 3952 (1992).

Equation Discovery for Model Identification in Respiratory Mechanics of the Mechanically Ventilated Human Lung

NASA Astrophysics Data System (ADS)

Ganzert, Steven; Guttmann, Josef; Steinmann, Daniel; Kramer, Stefan

Lung protective ventilation strategies reduce the risk of ventilator associated lung injury. To develop such strategies, knowledge about mechanical properties of the mechanically ventilated human lung is essential. This study was designed to develop an equation discovery system to identify mathematical models of the respiratory system in time-series data obtained from mechanically ventilated patients. Two techniques were combined: (i) the usage of declarative bias to reduce search space complexity and inherently providing the processing of background knowledge. (ii) A newly developed heuristic for traversing the hypothesis space with a greedy, randomized strategy analogical to the GSAT algorithm. In 96.8% of all runs the applied equation discovery system was capable to detect the well-established equation of motion model of the respiratory system in the provided data. We see the potential of this semi-automatic approach to detect more complex mathematical descriptions of the respiratory system from respiratory data.

Bianchi transformation between the real hyperbolic Monge-Ampère equation and the Born-Infeld equation

NASA Astrophysics Data System (ADS)

Mokhov, O. I.; Nutku, Y.

1994-10-01

By casting the Born-Infeld equation and the real hyperbolic Monge-Ampère equation into the form of equations of hydrodynamic type, we find that there exists an explicit transformation between them. This is Bianchi transformation.

Successfully Transitioning to Linear Equations

ERIC Educational Resources Information Center

Colton, Connie; Smith, Wendy M.

2014-01-01

The Common Core State Standards for Mathematics (CCSSI 2010) asks students in as early as fourth grade to solve word problems using equations with variables. Equations studied at this level generate a single solution, such as the equation x + 10 = 25. For students in fifth grade, the Common Core standard for algebraic thinking expects them to…

Algorithmic framework for group analysis of differential equations and its application to generalized Zakharov-Kuznetsov equations

NASA Astrophysics Data System (ADS)

Huang, Ding-jiang; Ivanova, Nataliya M.

2016-02-01

In this paper, we explain in more details the modern treatment of the problem of group classification of (systems of) partial differential equations (PDEs) from the algorithmic point of view. More precisely, we revise the classical Lie algorithm of construction of symmetries of differential equations, describe the group classification algorithm and discuss the process of reduction of (systems of) PDEs to (systems of) equations with smaller number of independent variables in order to construct invariant solutions. The group classification algorithm and reduction process are illustrated by the example of the generalized Zakharov-Kuznetsov (GZK) equations of form ut +(F (u)) xxx +(G (u)) xyy +(H (u)) x = 0. As a result, a complete group classification of the GZK equations is performed and a number of new interesting nonlinear invariant models which have non-trivial invariance algebras are obtained. Lie symmetry reductions and exact solutions for two important invariant models, i.e., the classical and modified Zakharov-Kuznetsov equations, are constructed. The algorithmic framework for group analysis of differential equations presented in this paper can also be applied to other nonlinear PDEs.

A note on improved F-expansion method combined with Riccati equation applied to nonlinear evolution equations.

PubMed

Islam, Md Shafiqul; Khan, Kamruzzaman; Akbar, M Ali; Mastroberardino, Antonio

2014-10-01

The purpose of this article is to present an analytical method, namely the improved F-expansion method combined with the Riccati equation, for finding exact solutions of nonlinear evolution equations. The present method is capable of calculating all branches of solutions simultaneously, even if multiple solutions are very close and thus difficult to distinguish with numerical techniques. To verify the computational efficiency, we consider the modified Benjamin-Bona-Mahony equation and the modified Korteweg-de Vries equation. Our results reveal that the method is a very effective and straightforward way of formulating the exact travelling wave solutions of nonlinear wave equations arising in mathematical physics and engineering.

A note on improved F-expansion method combined with Riccati equation applied to nonlinear evolution equations

PubMed Central

Islam, Md. Shafiqul; Khan, Kamruzzaman; Akbar, M. Ali; Mastroberardino, Antonio

2014-01-01

The purpose of this article is to present an analytical method, namely the improved F-expansion method combined with the Riccati equation, for finding exact solutions of nonlinear evolution equations. The present method is capable of calculating all branches of solutions simultaneously, even if multiple solutions are very close and thus difficult to distinguish with numerical techniques. To verify the computational efficiency, we consider the modified Benjamin–Bona–Mahony equation and the modified Korteweg-de Vries equation. Our results reveal that the method is a very effective and straightforward way of formulating the exact travelling wave solutions of nonlinear wave equations arising in mathematical physics and engineering. PMID:26064530

Unsplit complex frequency shifted perfectly matched layer for second-order wave equation using auxiliary differential equations.

PubMed

Gao, Yingjie; Zhang, Jinhai; Yao, Zhenxing

2015-12-01

The complex frequency shifted perfectly matched layer (CFS-PML) can improve the absorbing performance of PML for nearly grazing incident waves. However, traditional PML and CFS-PML are based on first-order wave equations; thus, they are not suitable for second-order wave equation. In this paper, an implementation of CFS-PML for second-order wave equation is presented using auxiliary differential equations. This method is free of both convolution calculations and third-order temporal derivatives. As an unsplit CFS-PML, it can reduce the nearly grazing incidence. Numerical experiments show that it has better absorption than typical PML implementations based on second-order wave equation.

Turbulent fluid motion 3: Basic continuum equations

NASA Technical Reports Server (NTRS)

Deissler, Robert G.

1991-01-01

A derivation of the continuum equations used for the analysis of turbulence is given. These equations include the continuity equation, the Navier-Stokes equations, and the heat transfer or energy equation. An experimental justification for using a continuum approach for the study of turbulence is given.

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.

PubMed

Ji, Hongwei; Zhang, Han; Xiong, Jing; Yu, Shikai; Chi, Chen; Bai, Bin; Li, Jue; Blacher, Jacques; Zhang, Yi; Xu, Yawei

2017-01-01

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. 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. In multivariate regression analysis, only eGFRs from aCKD-EPI were significantly and inversely associated with carotid IMT ( P =0.005). In multivariate logistic models, decreased eGFR from all the equations were significantly associated with lower ABI ( P <0.001), microalbuminuria ( P =0.02 to P <0.001) and increased cf-PWV ( P <0.001). Only decreased eGFRs from aCKD-EPI and cCKD-EPI equations were significantly associated with increased IMT (both crude P <0.05). In the receiver operator characteristic

On the Inclusion of Difference Equation Problems and Z Transform Methods in Sophomore Differential Equation Classes

ERIC Educational Resources Information Center

Savoye, Philippe

2009-01-01

In recent years, I started covering difference equations and z transform methods in my introductory differential equations course. This allowed my students to extend the "classical" methods for (ordinary differential equation) ODE's to discrete time problems arising in many applications.

Fractional Diffusion Equations and Anomalous Diffusion

NASA Astrophysics Data System (ADS)

Evangelista, Luiz Roberto; Kaminski Lenzi, Ervin

2018-01-01

Preface; 1. Mathematical preliminaries; 2. A survey of the fractional calculus; 3. From normal to anomalous diffusion; 4. Fractional diffusion equations: elementary applications; 5. Fractional diffusion equations: surface effects; 6. Fractional nonlinear diffusion equation; 7. Anomalous diffusion: anisotropic case; 8. Fractional Schrödinger equations; 9. Anomalous diffusion and impedance spectroscopy; 10. The Poisson–Nernst–Planck anomalous (PNPA) models; References; Index.

Ordinary differential equations.

PubMed

Lebl, Jiří

2013-01-01

In this chapter we provide an overview of the basic theory of ordinary differential equations (ODE). We give the basics of analytical methods for their solutions and also review numerical methods. The chapter should serve as a primer for the basic application of ODEs and systems of ODEs in practice. As an example, we work out the equations arising in Michaelis-Menten kinetics and give a short introduction to using Matlab for their numerical solution.

Generalization of Einstein's gravitational field equations

NASA Astrophysics Data System (ADS)

Moulin, Frédéric

2017-12-01

The Riemann tensor is the cornerstone of general relativity, but as is well known it does not appear explicitly in Einstein's equation of gravitation. This suggests that the latter may not be the most general equation. We propose here for the first time, following a rigorous mathematical treatment based on the variational principle, that there exists a generalized 4-index gravitational field equation containing the Riemann curvature tensor linearly, and thus the Weyl tensor as well. We show that this equation, written in n dimensions, contains the energy-momentum tensor for matter and that of the gravitational field itself. This new 4-index equation remains completely within the framework of general relativity and emerges as a natural generalization of the familiar 2-index Einstein equation. Due to the presence of the Weyl tensor, we show that this equation contains much more information, which fully justifies the use of a fourth-order theory.

Agent-Based vs. Equation-based Epidemiological Models:A Model Selection Case Study

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sukumar, Sreenivas R; Nutaro, James J

This paper is motivated by the need to design model validation strategies for epidemiological disease-spread models. We consider both agent-based and equation-based models of pandemic disease spread and study the nuances and complexities one has to consider from the perspective of model validation. For this purpose, we instantiate an equation based model and an agent based model of the 1918 Spanish flu and we leverage data published in the literature for our case- study. We present our observations from the perspective of each implementation and discuss the application of model-selection criteria to compare the risk in choosing one modeling paradigmmore » to another. We conclude with a discussion of our experience and document future ideas for a model validation framework.« less

Mortality Prediction in the Oldest Old with Five Different Equations to Estimate Glomerular Filtration Rate: The Health and Anemia Population-based Study

PubMed Central

Mandelli, Sara; Riva, Emma; Tettamanti, Mauro; Detoma, Paolo; Giacomin, Adriano; Lucca, Ugo

2015-01-01

Background Kidney function declines considerably with age, but little is known about its clinical significance in the oldest-old. Objectives To study the association between reduced glomerular filtration rate (GFR) estimated according to five equations with mortality in the oldest-old. Design Prospective population-based study. Setting Municipality of Biella, Piedmont, Italy. Participants 700 subjects aged 85 and older participating in the “Health and Anemia” Study in 2007–2008. Measurements GFR was estimated using five creatinine-based equations: the Cockcroft-Gault (C-G), Modification of Diet in Renal Disease (MDRD), MAYO Clinic, Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) and Berlin Initiative Study-1 (BIS-1). Survival analysis was used to study mortality in subjects with reduced eGFR (<60 mL/min/1.73m2) compared to subjects with eGFR ≥60 mL/min/1.73m2. Results Prevalence of reduced GFR was 90.7% with the C-G, 48.1% with MDRD, 23.3% with MAYO, 53.6% with CKD-EPI and 84.4% with BIS-1. After adjustment for confounders, two-year mortality was significantly increased in subjects with reduced eGFR using BIS-1 and C-G equations (adjusted HRs: 2.88 and 3.30, respectively). Five-year mortality was significantly increased in subjects with eGFR <60 mL/min/1.73m2 using MAYO, CKD-EPI and, in a graduated fashion in reduced eGFR categories, MDRD. After 5 years, oldest old with an eGFR <30 mL/min/1.73m2 showed a significantly higher risk of death whichever equation was used (adjusted HRs between 2.04 and 2.70). Conclusion In the oldest old, prevalence of reduced eGFR varies noticeably depending on the equation used. In this population, risk of mortality was significantly higher for reduced GFR estimated with the BIS-1 and C-G equations over the short term. Though after five years the MDRD appeared on the whole a more consistent predictor, differences in mortality prediction among equations over the long term were less apparent. Noteworthy, subjects with

Mortality Prediction in the Oldest Old with Five Different Equations to Estimate Glomerular Filtration Rate: The Health and Anemia Population-based Study.

PubMed

Mandelli, Sara; Riva, Emma; Tettamanti, Mauro; Detoma, Paolo; Giacomin, Adriano; Lucca, Ugo

2015-01-01

Kidney function declines considerably with age, but little is known about its clinical significance in the oldest-old. To study the association between reduced glomerular filtration rate (GFR) estimated according to five equations with mortality in the oldest-old. Prospective population-based study. Municipality of Biella, Piedmont, Italy. 700 subjects aged 85 and older participating in the "Health and Anemia" Study in 2007-2008. GFR was estimated using five creatinine-based equations: the Cockcroft-Gault (C-G), Modification of Diet in Renal Disease (MDRD), MAYO Clinic, Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) and Berlin Initiative Study-1 (BIS-1). Survival analysis was used to study mortality in subjects with reduced eGFR (<60 mL/min/1.73 m(2)) compared to subjects with eGFR ≥ 60 mL/min/1.73 m(2). Prevalence of reduced GFR was 90.7% with the C-G, 48.1% with MDRD, 23.3% with MAYO, 53.6% with CKD-EPI and 84.4% with BIS-1. After adjustment for confounders, two-year mortality was significantly increased in subjects with reduced eGFR using BIS-1 and C-G equations (adjusted HRs: 2.88 and 3.30, respectively). Five-year mortality was significantly increased in subjects with eGFR <60 mL/min/1.73 m(2) using MAYO, CKD-EPI and, in a graduated fashion in reduced eGFR categories, MDRD. After 5 years, oldest old with an eGFR <30 mL/min/1.73 m(2) showed a significantly higher risk of death whichever equation was used (adjusted HRs between 2.04 and 2.70). In the oldest old, prevalence of reduced eGFR varies noticeably depending on the equation used. In this population, risk of mortality was significantly higher for reduced GFR estimated with the BIS-1 and C-G equations over the short term. Though after five years the MDRD appeared on the whole a more consistent predictor, differences in mortality prediction among equations over the long term were less apparent. Noteworthy, subjects with a severely reduced GFR were consistently at higher risk of death

The Equations of Oceanic Motions

NASA Astrophysics Data System (ADS)

Müller, Peter

2006-10-01

Modeling and prediction of oceanographic phenomena and climate is based on the integration of dynamic equations. The Equations of Oceanic Motions derives and systematically classifies the most common dynamic equations used in physical oceanography, from large scale thermohaline circulations to those governing small scale motions and turbulence. After establishing the basic dynamical equations that describe all oceanic motions, M|ller then derives approximate equations, emphasizing the assumptions made and physical processes eliminated. He distinguishes between geometric, thermodynamic and dynamic approximations and between the acoustic, gravity, vortical and temperature-salinity modes of motion. Basic concepts and formulae of equilibrium thermodynamics, vector and tensor calculus, curvilinear coordinate systems, and the kinematics of fluid motion and wave propagation are covered in appendices. Providing the basic theoretical background for graduate students and researchers of physical oceanography and climate science, this book will serve as both a comprehensive text and an essential reference.

How Fear-Arousing News Messages Affect Risk Perceptions and Intention to Talk About Risk.

PubMed

Paek, Hye-Jin; Oh, Sang-Hwa; Hove, Thomas

2016-09-01

Building on the theoretical arguments of the impersonal-impact and differential-impact hypotheses, this study has a twofold purpose: first, to demonstrate how fear-arousing media messages about risk are associated with personal-level risk perception, as well as, and perhaps more so than, societal-level risk perception; and second, to examine how the resulting risk perceptions can mediate intention to talk about the risk with family and friends. A news message evaluation study was conducted among the general public in South Korea concerning two major risks, carcinogens and bovine spongiform encephalopathy (BSE). Two sets of structural equation models reveal three main findings: (a) Fear-arousing news messages are positively related to personal-level risk perception, as well as to societal-level risk perception; (b) fear-arousing news messages result in intention to talk about the risk directly and indirectly through risk perception; and (c) personal-level risk perception appears more strongly related to intention to talk than does societal-level risk perception, although such relationships may vary across risk topics.

Explicit integration of Friedmann's equation with nonlinear equations of state

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, Shouxin; Gibbons, Gary W.; Yang, Yisong, E-mail: chensx@henu.edu.cn, E-mail: gwg1@damtp.cam.ac.uk, E-mail: yisongyang@nyu.edu

2015-05-01

In this paper we study the integrability of the Friedmann equations, when the equation of state for the perfect-fluid universe is nonlinear, in the light of the Chebyshev theorem. A series of important, yet not previously touched, problems will be worked out which include the generalized Chaplygin gas, two-term energy density, trinomial Friedmann, Born-Infeld, two-fluid models, and Chern-Simons modified gravity theory models. With the explicit integration, we are able to understand exactly the roles of the physical parameters in various models play in the cosmological evolution which may also offer clues to a profound understanding of the problems in generalmore » settings. For example, in the Chaplygin gas universe, a few integrable cases lead us to derive a universal formula for the asymptotic exponential growth rate of the scale factor, of an explicit form, whether the Friedmann equation is integrable or not, which reveals the coupled roles played by various physical sectors and it is seen that, as far as there is a tiny presence of nonlinear matter, conventional linear matter makes contribution to the dark matter, which becomes significant near the phantom divide line. The Friedmann equations also arise in areas of physics not directly related to cosmology. We provide some examples ranging from geometric optics and central orbits to soap films and the shape of glaciated valleys to which our results may be applied.« less

Solution Methods for Certain Evolution Equations

NASA Astrophysics Data System (ADS)

Vega-Guzman, Jose Manuel

Solution methods for certain linear and nonlinear evolution equations are presented in this dissertation. Emphasis is placed mainly on the analytical treatment of nonautonomous differential equations, which are challenging to solve despite the existent numerical and symbolic computational software programs available. Ideas from the transformation theory are adopted allowing one to solve the problems under consideration from a non-traditional perspective. First, the Cauchy initial value problem is considered for a class of nonautonomous and inhomogeneous linear diffusion-type equation on the entire real line. Explicit transformations are used to reduce the equations under study to their corresponding standard forms emphasizing on natural relations with certain Riccati(and/or Ermakov)-type systems. These relations give solvability results for the Cauchy problem of the parabolic equation considered. The superposition principle allows to solve formally this problem from an unconventional point of view. An eigenfunction expansion approach is also considered for this general evolution equation. Examples considered to corroborate the efficacy of the proposed solution methods include the Fokker-Planck equation, the Black-Scholes model and the one-factor Gaussian Hull-White model. The results obtained in the first part are used to solve the Cauchy initial value problem for certain inhomogeneous Burgers-type equation. The connection between linear (the Diffusion-type) and nonlinear (Burgers-type) parabolic equations is stress in order to establish a strong commutative relation. Traveling wave solutions of a nonautonomous Burgers equation are also investigated. Finally, it is constructed explicitly the minimum-uncertainty squeezed states for quantum harmonic oscillators. They are derived by the action of corresponding maximal kinematical invariance group on the standard ground state solution. It is shown that the product of the variances attains the required minimum value

Sparse dynamics for partial differential equations

PubMed Central

Schaeffer, Hayden; Caflisch, Russel; Hauck, Cory D.; Osher, Stanley

2013-01-01

We investigate the approximate dynamics of several differential equations when the solutions are restricted to a sparse subset of a given basis. The restriction is enforced at every time step by simply applying soft thresholding to the coefficients of the basis approximation. By reducing or compressing the information needed to represent the solution at every step, only the essential dynamics are represented. In many cases, there are natural bases derived from the differential equations, which promote sparsity. We find that our method successfully reduces the dynamics of convection equations, diffusion equations, weak shocks, and vorticity equations with high-frequency source terms. PMID:23533273

Sparse dynamics for partial differential equations.

PubMed

Schaeffer, Hayden; Caflisch, Russel; Hauck, Cory D; Osher, Stanley

2013-04-23

We investigate the approximate dynamics of several differential equations when the solutions are restricted to a sparse subset of a given basis. The restriction is enforced at every time step by simply applying soft thresholding to the coefficients of the basis approximation. By reducing or compressing the information needed to represent the solution at every step, only the essential dynamics are represented. In many cases, there are natural bases derived from the differential equations, which promote sparsity. We find that our method successfully reduces the dynamics of convection equations, diffusion equations, weak shocks, and vorticity equations with high-frequency source terms.

Creatinine-Based and Cystatin C-Based GFR Estimating Equations and Their Non-GFR Determinants in Kidney Transplant Recipients.

PubMed

Keddis, Mira T; Amer, Hatem; Voskoboev, Nikolay; Kremers, Walter K; Rule, Andrew D; Lieske, John C

2016-09-07

eGFR equations have been evaluated in kidney transplant recipients with variable performance. We assessed the performance of the Modification of Diet in Renal Disease equation and the Chronic Kidney Disease Epidemiology Collaboration equations on the basis of creatinine, cystatin C, and both (eGFR creatinine-cystatin C) compared with measured GFR by iothalamate clearance and evaluated their non-GFR determinants and associations across 15 cardiovascular risk factors. A cross-sectional cohort of 1139 kidney transplant recipients >1 year after transplant was analyzed. eGFR bias, precision, and accuracy (percentage of estimates within 30% of measured GFR) were assessed. Interaction of each cardiovascular risk factor with eGFR relative to measured GFR was determined. Median measured GFR was 55.0 ml/min per 1.73 m(2). eGFR creatinine overestimated measured GFR by 3.1% (percentage of estimates within 30% of measured GFR of 80.4%), and eGFR Modification of Diet in Renal Disease underestimated measured GFR by 2.2% (percentage of estimates within 30% of measured GFR of 80.4%). eGFR cystatin C underestimated measured GFR by -13.7% (percentage of estimates within 30% of measured GFR of 77.1%), and eGFR creatinine-cystatin C underestimated measured GFR by -8.1% (percentage of estimates within 30% of measured GFR of 86.5%). Lower measured GFR associated with older age, women, obesity, longer time after transplant, lower HDL, lower hemoglobin, lower albumin, higher triglycerides, higher proteinuria, and an elevated cardiac troponin T level but did not associate with diabetes, smoking, cardiovascular events, pretransplant dialysis, or hemoglobin A1c. These risk factor associations differed for five risk factors with eGFR creatinine, six risk factors for eGFR Modification of Diet in Renal Disease, ten risk factors for eGFR cystatin C, and four risk factors for eGFR creatinine-cystatin C. Thus, eGFR creatinine and eGFR creatinine-cystatin C are preferred over eGFR cystatin C in

Coupled radial Schrödinger equations written as Dirac-type equations: application to an amplitude-phase approach

NASA Astrophysics Data System (ADS)

Thylwe, Karl-Erik; McCabe, Patrick

2012-04-01

The classical amplitude-phase method due to Milne, Wilson, Young and Wheeler in the 1930s is known to be a powerful computational tool for determining phase shifts and energy eigenvalues in cases where a sufficiently slowly varying amplitude function can be found. The key for the efficient computations is that the original single-state radial Schrödinger equation is transformed to a nonlinear equation, the Milne equation. Such an equation has solutions that may or may not oscillate, depending on boundary conditions, which then requires a robust recipe for locating the (optimal) ‘almost constant’ solutions for its use in the method. For scattering problems the solutions of the amplitude equations always approach constants as the radial distance r tends to infinity, and there is no problem locating the ‘optimal’ amplitude functions from a low-order semiclassical approximation. In the present work, the amplitude-phase approach is generalized to two coupled Schrödinger equations similar to an earlier generalization to radial Dirac equations. The original scalar amplitude then becomes a vector quantity, and the original Milne equation is generalized accordingly. Numerical applications to resonant electron-atom scattering are illustrated.

The Camassa-Holm equation as an incompressible Euler equation: A geometric point of view

NASA Astrophysics Data System (ADS)

Gallouët, Thomas; Vialard, François-Xavier

2018-04-01

The group of diffeomorphisms of a compact manifold endowed with the L2 metric acting on the space of probability densities gives a unifying framework for the incompressible Euler equation and the theory of optimal mass transport. Recently, several authors have extended optimal transport to the space of positive Radon measures where the Wasserstein-Fisher-Rao distance is a natural extension of the classical L2-Wasserstein distance. In this paper, we show a similar relation between this unbalanced optimal transport problem and the Hdiv right-invariant metric on the group of diffeomorphisms, which corresponds to the Camassa-Holm (CH) equation in one dimension. Geometrically, we present an isometric embedding of the group of diffeomorphisms endowed with this right-invariant metric in the automorphisms group of the fiber bundle of half densities endowed with an L2 type of cone metric. This leads to a new formulation of the (generalized) CH equation as a geodesic equation on an isotropy subgroup of this automorphisms group; On S1, solutions to the standard CH thus give radially 1-homogeneous solutions of the incompressible Euler equation on R2 which preserves a radial density that has a singularity at 0. An other application consists in proving that smooth solutions of the Euler-Arnold equation for the Hdiv right-invariant metric are length minimizing geodesics for sufficiently short times.

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

NASA Astrophysics Data System (ADS)

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.

Lax representations for matrix short pulse equations

NASA Astrophysics Data System (ADS)

Popowicz, Z.

2017-10-01

The Lax representation for different matrix generalizations of Short Pulse Equations (SPEs) is considered. The four-dimensional Lax representations of four-component Matsuno, Feng, and Dimakis-Müller-Hoissen-Matsuno equations are obtained. The four-component Feng system is defined by generalization of the two-dimensional Lax representation to the four-component case. This system reduces to the original Feng equation, to the two-component Matsuno equation, or to the Yao-Zang equation. The three-component version of the Feng equation is presented. The four-component version of the Matsuno equation with its Lax representation is given. This equation reduces the new two-component Feng system. The two-component Dimakis-Müller-Hoissen-Matsuno equations are generalized to the four-parameter family of the four-component SPE. The bi-Hamiltonian structure of this generalization, for special values of parameters, is defined. This four-component SPE in special cases reduces to the new two-component SPE.

Optimal Control for Stochastic Delay Evolution Equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Meng, Qingxin, E-mail: mqx@hutc.zj.cn; Shen, Yang, E-mail: skyshen87@gmail.com

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 applymore » 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.« less

Coronary risk assessment by point-based vs. equation-based Framingham models: significant implications for clinical care.

PubMed

Gordon, William J; Polansky, Jesse M; Boscardin, W John; Fung, Kathy Z; Steinman, Michael A

2010-11-01

US cholesterol guidelines use original and simplified versions of the Framingham model to estimate future coronary risk and thereby classify patients into risk groups with different treatment strategies. We sought to compare risk estimates and risk group classification generated by the original, complex Framingham model and the simplified, point-based version. We assessed 2,543 subjects age 20-79 from the 2001-2006 National Health and Nutrition Examination Surveys (NHANES) for whom Adult Treatment Panel III (ATP-III) guidelines recommend formal risk stratification. For each subject, we calculated the 10-year risk of major coronary events using the original and point-based Framingham models, and then compared differences in these risk estimates and whether these differences would place subjects into different ATP-III risk groups (<10% risk, 10-20% risk, or >20% risk). Using standard procedures, all analyses were adjusted for survey weights, clustering, and stratification to make our results nationally representative. Among 39 million eligible adults, the original Framingham model categorized 71% of subjects as having "moderate" risk (<10% risk of a major coronary event in the next 10 years), 22% as having "moderately high" (10-20%) risk, and 7% as having "high" (>20%) risk. Estimates of coronary risk by the original and point-based models often differed substantially. The point-based system classified 15% of adults (5.7 million) into different risk groups than the original model, with 10% (3.9 million) misclassified into higher risk groups and 5% (1.8 million) into lower risk groups, for a net impact of classifying 2.1 million adults into higher risk groups. These risk group misclassifications would impact guideline-recommended drug treatment strategies for 25-46% of affected subjects. Patterns of misclassifications varied significantly by gender, age, and underlying CHD risk. Compared to the original Framingham model, the point-based version misclassifies millions

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

PubMed

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.

The Statistical Drake Equation

NASA Astrophysics Data System (ADS)

Maccone, Claudio

2010-12-01

We provide the statistical generalization of the Drake equation. From a simple product of seven positive numbers, the Drake equation is now turned into the product of seven positive random variables. We call this "the Statistical Drake Equation". The mathematical consequences of this transformation are then derived. The proof of our results is based on the Central Limit Theorem (CLT) of Statistics. In loose terms, the CLT states that the sum of any number of independent random variables, each of which may be ARBITRARILY distributed, approaches a Gaussian (i.e. normal) random variable. This is called the Lyapunov Form of the CLT, or the Lindeberg Form of the CLT, depending on the mathematical constraints assumed on the third moments of the various probability distributions. In conclusion, we show that: The new random variable N, yielding the number of communicating civilizations in the Galaxy, follows the LOGNORMAL distribution. Then, as a consequence, the mean value of this lognormal distribution is the ordinary N in the Drake equation. The standard deviation, mode, and all the moments of this lognormal N are also found. The seven factors in the ordinary Drake equation now become seven positive random variables. The probability distribution of each random variable may be ARBITRARY. The CLT in the so-called Lyapunov or Lindeberg forms (that both do not assume the factors to be identically distributed) allows for that. In other words, the CLT "translates" into our statistical Drake equation by allowing an arbitrary probability distribution for each factor. This is both physically realistic and practically very useful, of course. An application of our statistical Drake equation then follows. The (average) DISTANCE between any two neighboring and communicating civilizations in the Galaxy may be shown to be inversely proportional to the cubic root of N. Then, in our approach, this distance becomes a new random variable. We derive the relevant probability density

Are cystatin C-based equations superior to creatinine-based equations for estimating GFR in Chinese elderly population?

PubMed

Pei, Xiaohua; Liu, Qiao; He, Juan; Bao, Lihua; Yan, Chengjing; Wu, Jianqing; Zhao, Weihong

2012-12-01

Cystatin C has been proposed as a surrogate marker of kidney function. The elderly population accounts for the largest proportion of chronic kidney disease (CKD) patients. The aim of this study was to assess the diagnostic value of serum cystatin C and compare the applicability of cystatin C-based equations with serum creatinine (Scr)-based equations for estimating glomerular filtration rate (GFR). The estimated GFR (eGFR) values from six cystatin C-based equations (Tan, MacIsaac, Ma, Stevens1-3) and three Scr-based equations (CG, MDRD, CKD-EPI) were compared with the reference GFR (rGFR) values from 99mTc-DTPA renal dynamic imaging method. A total of 110 elderly Chinese (60-92 year, 71.05±7.62 year) were enrolled. Cystatin C had better diagnostic value than Scr (relationship coefficient with rGFR: cystatin C -0.847 vs. Scr -0.729, P<0.01; sensitivity: cystatin C 0.90 vs. Scr 0.55, P<0.01; AUCROC: cystatin C 0.857 vs. Scr 0.757, P<0.01). All the equations predicted GFR more accurately for rGFR≥60 ml/min/1.73 m2 than for rGFR<60 ml/min/1.73 m2. Most equations had acceptable accuracy. The cystatin C-based equations deviated from rGFR by -12.78 ml/min/1.73 m2 to -2.12 ml/min/1.73 m2, with accuracy varying from 64.6 to 82.7%. The Scr-based equations deviated from rGFR by -5.37 ml/min/1.73 m2 to -0.68 ml/min/1.73 m2, with accuracy varying from 77.3 to 79.1%. The CKD-EPI, MacIsaac and Ma equations predicted no bias with rGFR (P>0.05), with higher accuracy and lower deviation in the total group. The MacIsaac, CKD-EPI and Stevens3 equations could be optimal for those with normal and mildly impaired kidney function, whereas the Ma equation for those with CKD. Cystatin C is a promising kidney function marker. However, not all cystatin C-based equations could be superior to the Scr-equations.

Nonlinear ordinary difference equations

NASA Technical Reports Server (NTRS)

Caughey, T. K.

1979-01-01

Future space vehicles will be relatively large and flexible, and active control will be necessary to maintain geometrical configuration. While the stresses and strains in these space vehicles are not expected to be excessively large, their cumulative effects will cause significant geometrical nonlinearities to appear in the equations of motion, in addition to the nonlinearities caused by material properties. Since the only effective tool for the analysis of such large complex structures is the digital computer, it will be necessary to gain a better understanding of the nonlinear ordinary difference equations which result from the time discretization of the semidiscrete equations of motion for such structures.

Twisted Quantum Lax Equations

NASA Astrophysics Data System (ADS)

Jurčo, Branislav; Schupp, Peter

We show the construction of twisted quantum Lax equations associated with quantum groups, and solve these equations using factorization properties of the corresponding quantum groups. Our construction generalizes in many respects the AKS construction for Lie groups and the construction of M. A. Semenov-Tian-Shansky for the Lie-Poisson case.

Performance of Predictive Equations Specifically Developed to Estimate Resting Energy Expenditure in Ventilated Critically Ill Children.

PubMed

Jotterand Chaparro, Corinne; Taffé, Patrick; Moullet, Clémence; Laure Depeyre, Jocelyne; Longchamp, David; Perez, Marie-Hélène; Cotting, Jacques

2017-05-01

To determine, based on indirect calorimetry measurements, the biases of predictive equations specifically developed recently for estimating resting energy expenditure (REE) in ventilated critically ill children, or developed for healthy populations but used in critically ill children. A secondary analysis study was performed using our data on REE measured in a previous prospective study on protein and energy needs in pediatric intensive care unit. We included 75 ventilated critically ill children (median age, 21 months) in whom 407 indirect calorimetry measurements were performed. Fifteen predictive equations were used to estimate REE: the equations of White, Meyer, Mehta, Schofield, Henry, the World Health Organization, Fleisch, and Harris-Benedict and the tables of Talbot. Their differential and proportional biases (with 95% CIs) were computed and the bias plotted in graphs. The Bland-Altman method was also used. Most equations underestimated and overestimated REE between 200 and 1000 kcal/day. The equations of Mehta, Schofield, and Henry and the tables of Talbot had a bias ≤10%, but the 95% CI was large and contained values by far beyond ±10% for low REE values. Other specific equations for critically ill children had even wider biases. In ventilated critically ill children, none of the predictive equations tested met the performance criteria for the entire range of REE between 200 and 1000 kcal/day. Even the equations with the smallest bias may entail a risk of underfeeding or overfeeding, especially in the youngest children. Indirect calorimetry measurement must be preferred. Copyright © 2016 Elsevier Inc. All rights reserved.

Relationships between basic soils-engineering equations and basic ground-water flow equations

USGS Publications Warehouse

Jorgensen, Donald G.

1980-01-01

The many varied though related terms developed by ground-water hydrologists and by soils engineers are useful to each discipline, but their differences in terminology hinder the use of related information in interdisciplinary studies. Equations for the Terzaghi theory of consolidation and equations for ground-water flow are identical under specific conditions. A combination of the two sets of equations relates porosity to void ratio and relates the modulus of elasticity to the coefficient of compressibility, coefficient of volume compressibility, compression index, coefficient of consolidation, specific storage, and ultimate compaction. Also, transient ground-water flow is related to coefficient of consolidation, rate of soil compaction, and hydraulic conductivity. Examples show that soils-engineering data and concepts are useful to solution of problems in ground-water hydrology.

Entrainment in the master equation.

PubMed

Margaliot, Michael; Grüne, Lars; Kriecherbauer, Thomas

2018-04-01

The master equation plays an important role in many scientific fields including physics, chemistry, systems biology, physical finance and sociodynamics. We consider the master equation with periodic transition rates. This may represent an external periodic excitation like the 24 h solar day in biological systems or periodic traffic lights in a model of vehicular traffic. Using tools from systems and control theory, we prove that under mild technical conditions every solution of the master equation converges to a periodic solution with the same period as the rates. In other words, the master equation entrains (or phase locks) to periodic excitations. We describe two applications of our theoretical results to important models from statistical mechanics and epidemiology.

Entrainment in the master equation

PubMed Central

Grüne, Lars; Kriecherbauer, Thomas

2018-01-01

The master equation plays an important role in many scientific fields including physics, chemistry, systems biology, physical finance and sociodynamics. We consider the master equation with periodic transition rates. This may represent an external periodic excitation like the 24 h solar day in biological systems or periodic traffic lights in a model of vehicular traffic. Using tools from systems and control theory, we prove that under mild technical conditions every solution of the master equation converges to a periodic solution with the same period as the rates. In other words, the master equation entrains (or phase locks) to periodic excitations. We describe two applications of our theoretical results to important models from statistical mechanics and epidemiology. PMID:29765669

Rogue waves in the two dimensional nonlocal nonlinear Schrödinger equation and nonlocal Klein-Gordon equation.

PubMed

Liu, Wei; Zhang, Jing; Li, Xiliang

2018-01-01

In this paper, we investigate two types of nonlocal soliton equations with the parity-time (PT) symmetry, namely, a two dimensional nonlocal nonlinear Schrödinger (NLS) equation and a coupled nonlocal Klein-Gordon equation. Solitons and periodic line waves as exact solutions of these two nonlocal equations are derived by employing the Hirota's bilinear method. Like the nonlocal NLS equation, these solutions may have singularities. However, by suitable constraints of parameters, nonsingular breather solutions are generated. Besides, by taking a long wave limit of these obtained soliton solutions, rogue wave solutions and semi-rational solutions are derived. For the two dimensional NLS equation, rogue wave solutions are line rogue waves, which arise from a constant background with a line profile and then disappear into the same background. The semi-rational solutions shows intriguing dynamical behaviours: line rogue wave and line breather arise from a constant background together and then disappear into the constant background again uniformly. For the coupled nonlocal Klein-Gordon equation, rogue waves are localized in both space and time, semi-rational solutions are composed of rogue waves, breathers and periodic line waves. These solutions are demonstrated analytically to exist for special classes of nonlocal equations relevant to optical waveguides.

Rogue waves in the two dimensional nonlocal nonlinear Schrödinger equation and nonlocal Klein-Gordon equation

PubMed Central

Zhang, Jing; Li, Xiliang

2018-01-01

In this paper, we investigate two types of nonlocal soliton equations with the parity-time (PT) symmetry, namely, a two dimensional nonlocal nonlinear Schrödinger (NLS) equation and a coupled nonlocal Klein-Gordon equation. Solitons and periodic line waves as exact solutions of these two nonlocal equations are derived by employing the Hirota’s bilinear method. Like the nonlocal NLS equation, these solutions may have singularities. However, by suitable constraints of parameters, nonsingular breather solutions are generated. Besides, by taking a long wave limit of these obtained soliton solutions, rogue wave solutions and semi-rational solutions are derived. For the two dimensional NLS equation, rogue wave solutions are line rogue waves, which arise from a constant background with a line profile and then disappear into the same background. The semi-rational solutions shows intriguing dynamical behaviours: line rogue wave and line breather arise from a constant background together and then disappear into the constant background again uniformly. For the coupled nonlocal Klein-Gordon equation, rogue waves are localized in both space and time, semi-rational solutions are composed of rogue waves, breathers and periodic line waves. These solutions are demonstrated analytically to exist for special classes of nonlocal equations relevant to optical waveguides. PMID:29432495

High-order rogue waves of the Benjamin-Ono equation and the nonlocal nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

Liu, Wei

2017-10-01

High-order rogue wave solutions of the Benjamin-Ono equation and the nonlocal nonlinear Schrödinger equation are derived by employing the bilinear method, which are expressed by simple polynomials. Typical dynamics of these high-order rogue waves are studied by analytical and graphical ways. For the Benjamin-Ono equation, there are two types of rogue waves, namely, bright rogue waves and dark rogue waves. In particular, the fundamental rogue wave pattern is different from the usual fundamental rogue wave patterns in other soliton equations. For the nonlocal nonlinear Schrödinger equation, the exact explicit rogue wave solutions up to the second order are presented. Typical rogue wave patterns such as Peregrine-type, triple and fundamental rogue waves are put forward. These high-order rogue wave patterns have not been shown before in the nonlocal Schrödinger equation.

Dynamical systems theory for nonlinear evolution equations.

PubMed

Choudhuri, Amitava; Talukdar, B; Das, Umapada

2010-09-01

We observe that the fully nonlinear evolution equations of Rosenau and Hymann, often abbreviated as K(n,m) equations, can be reduced to Hamiltonian form only on a zero-energy hypersurface belonging to some potential function associated with the equations. We treat the resulting Hamiltonian equations by the dynamical systems theory and present a phase-space analysis of their stable points. The results of our study demonstrate that the equations can, in general, support both compacton and soliton solutions. For the K(2,2) and K(3,3) cases one type of solutions can be obtained from the other by continuously varying a parameter of the equations. This is not true for the K(3,2) equation for which the parameter can take only negative values. The K(2,3) equation does not have any stable point and, in the language of mechanics, represents a particle moving with constant acceleration.

Scale-dependent behavior of scale equations.

PubMed

Kim, Pilwon

2009-09-01

We propose a new mathematical framework to formulate scale structures of general systems. Stack equations characterize a system in terms of accumulative scales. Their behavior at each scale level is determined independently without referring to other levels. Most standard geometries in mathematics can be reformulated in such stack equations. By involving interaction between scales, we generalize stack equations into scale equations. Scale equations are capable to accommodate various behaviors at different scale levels into one integrated solution. On contrary to standard geometries, such solutions often reveal eccentric scale-dependent figures, providing a clue to understand multiscale nature of the real world. Especially, it is suggested that the Gaussian noise stems from nonlinear scale interactions.

Accuracy of perturbative master equations.

PubMed

Fleming, C H; Cummings, N I

2011-03-01

We consider open quantum systems with dynamics described by master equations that have perturbative expansions in the system-environment interaction. We show that, contrary to intuition, full-time solutions of order-2n accuracy require an order-(2n+2) master equation. We give two examples of such inaccuracies in the solutions to an order-2n master equation: order-2n inaccuracies in the steady state of the system and order-2n positivity violations. We show how these arise in a specific example for which exact solutions are available. This result has a wide-ranging impact on the validity of coupling (or friction) sensitive results derived from second-order convolutionless, Nakajima-Zwanzig, Redfield, and Born-Markov master equations.

Transition between free-space Helmholtz equation solutions with plane sources and parabolic wave equation solutions.

PubMed

Mahillo-Isla, R; Gonźalez-Morales, M J; Dehesa-Martínez, C

2011-06-01

The slowly varying envelope approximation is applied to the radiation problems of the Helmholtz equation with a planar single-layer and dipolar sources. The analyses of such problems provide procedures to recover solutions of the Helmholtz equation based on the evaluation of solutions of the parabolic wave equation at a given plane. Furthermore, the conditions that must be fulfilled to apply each procedure are also discussed. The relations to previous work are given as well.

The Equation, the Whole Equation, and Nothing but the Equation! One Approach to the Teaching of Linear Equations.

ERIC Educational Resources Information Center

Pirie, Susan E. B.; Martin, Lyndon

1997-01-01

Presents the results of a case study which looked at the mathematics classroom of one teacher trying to teach mathematics with meaning to pupils or lower ability at the secondary level. Contrasts methods of teaching linear equations to a variety of ability levels and uses the Pirie-Kieren model to account for the successful growth in understanding…

Dark soliton solution of Sasa-Satsuma equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ohta, Y.

2010-03-08

The Sasa-Satsuma equation is a higher order nonlinear Schroedinger type equation which admits bright soliton solutions with internal freedom. We present the dark soliton solutions for the equation by using Gram type determinant. The dark solitons have no internal freedom and exist for both defocusing and focusing equations.

Squared eigenfunctions for the Sasa-Satsuma equation

NASA Astrophysics Data System (ADS)

Yang, Jianke; Kaup, D. J.

2009-02-01

Squared eigenfunctions are quadratic combinations of Jost functions and adjoint Jost functions which satisfy the linearized equation of an integrable equation. They are needed for various studies related to integrable equations, such as the development of its soliton perturbation theory. In this article, squared eigenfunctions are derived for the Sasa-Satsuma equation whose spectral operator is a 3×3 system, while its linearized operator is a 2×2 system. It is shown that these squared eigenfunctions are sums of two terms, where each term is a product of a Jost function and an adjoint Jost function. The procedure of this derivation consists of two steps: First is to calculate the variations of the potentials via variations of the scattering data by the Riemann-Hilbert method. The second one is to calculate the variations of the scattering data via the variations of the potentials through elementary calculations. While this procedure has been used before on other integrable equations, it is shown here, for the first time, that for a general integrable equation, the functions appearing in these variation relations are precisely the squared eigenfunctions and adjoint squared eigenfunctions satisfying, respectively, the linearized equation and the adjoint linearized equation of the integrable system. This proof clarifies this procedure and provides a unified explanation for previous results of squared eigenfunctions on individual integrable equations. This procedure uses primarily the spectral operator of the Lax pair. Thus two equations in the same integrable hierarchy will share the same squared eigenfunctions (except for a time-dependent factor). In the Appendix, the squared eigenfunctions are presented for the Manakov equations whose spectral operator is closely related to that of the Sasa-Satsuma equation.

Almost periodic solutions to difference equations

NASA Technical Reports Server (NTRS)

Bayliss, A.

1975-01-01

The theory of Massera and Schaeffer relating the existence of unique almost periodic solutions of an inhomogeneous linear equation to an exponential dichotomy for the homogeneous equation was completely extended to discretizations by a strongly stable difference scheme. In addition it is shown that the almost periodic sequence solution will converge to the differential equation solution. The preceding theory was applied to a class of exponentially stable partial differential equations to which one can apply the Hille-Yoshida theorem. It is possible to prove the existence of unique almost periodic solutions of the inhomogeneous equation (which can be approximated by almost periodic sequences) which are the solutions to appropriate discretizations. Two methods of discretizations are discussed: the strongly stable scheme and the Lax-Wendroff scheme.

Semiclassical regularization of Vlasov equations and wavepackets for nonlinear Schrödinger equations

NASA Astrophysics Data System (ADS)

Athanassoulis, Agissilaos

2018-03-01

We consider the semiclassical limit of nonlinear Schrödinger equations with initial data that are well localized in both position and momentum (non-parametric wavepackets). We recover the Wigner measure (WM) of the problem, a macroscopic phase-space density which controls the propagation of the physical observables such as mass, energy and momentum. WMs have been used to create effective models for wave propagation in: random media, quantum molecular dynamics, mean field limits, and the propagation of electrons in graphene. In nonlinear settings, the Vlasov-type equations obtained for the WM are often ill-posed on the physically interesting spaces of initial data. In this paper we are able to select the measure-valued solution of the 1  +  1 dimensional Vlasov-Poisson equation which correctly captures the semiclassical limit, thus finally resolving the non-uniqueness in the seminal result of Zhang et al (2012 Comm. Pure Appl. Math. 55 582-632). The same approach is also applied to the Vlasov-Dirac-Benney equation with small wavepacket initial data, extending several known results.

The physics behind Van der Burgh's empirical equation, providing a new predictive equation for salinity intrusion in estuaries

NASA Astrophysics Data System (ADS)

Zhang, Zhilin; Savenije, Hubert H. G.

2017-07-01

The practical value of the surprisingly simple Van der Burgh equation in predicting saline water intrusion in alluvial estuaries is well documented, but the physical foundation of the equation is still weak. In this paper we provide a connection between the empirical equation and the theoretical literature, leading to a theoretical range of Van der Burgh's coefficient of 1/2 < K < 2/3 for density-driven mixing which falls within the feasible range of 0 < K < 1. In addition, we developed a one-dimensional predictive equation for the dispersion of salinity as a function of local hydraulic parameters that can vary along the estuary axis, including mixing due to tide-driven residual circulation. This type of mixing is relevant in the wider part of alluvial estuaries where preferential ebb and flood channels appear. Subsequently, this dispersion equation is combined with the salt balance equation to obtain a new predictive analytical equation for the longitudinal salinity distribution. Finally, the new equation was tested and applied to a large database of observations in alluvial estuaries, whereby the calibrated K values appeared to correspond well to the theoretical range.

A Bayesian Nonparametric Approach to Test Equating

ERIC Educational Resources Information Center

Karabatsos, George; Walker, Stephen G.

2009-01-01

A Bayesian nonparametric model is introduced for score equating. It is applicable to all major equating designs, and has advantages over previous equating models. Unlike the previous models, the Bayesian model accounts for positive dependence between distributions of scores from two tests. The Bayesian model and the previous equating models are…

The Effect of Repeaters on Equating

ERIC Educational Resources Information Center

Kim, HeeKyoung; Kolen, Michael J.

2010-01-01

Test equating might be affected by including in the equating analyses examinees who have taken the test previously. This study evaluated the effect of including such repeaters on Medical College Admission Test (MCAT) equating using a population invariance approach. Three-parameter logistic (3-PL) item response theory (IRT) true score and…

Evaluation of ergonomic physical risk factors in a truck manufacturing plant: case study in SCANIA Production Angers

PubMed Central

ZARE, Mohsen; MALINGE-OUDENOT, Agnes; HÖGLUND, Robert; BIAU, Sophie; ROQUELAURE, Yves

2015-01-01

The aims of this study were 1) to assess the ergonomic physical risk factors from practitioner’s viewpoint in a truck assembly plant with an in-house observational method and the NIOSH lifting equation, and 2) to compare the results of both methods and their differences. The in-house ergonomic observational method for truck assembly i.e. the SCANIA Ergonomics Standard (SES) and the NIOSH lifting equation were applied to evaluate physical risk factors and lifting of loads by operators. Both risk assessment approaches revealed various levels of risk, ranging from low to high. Two workstations were identified by the SES method as high risk. The NIOSH lifting index (LI) was greater than two for four lifting tasks. The results of the SES method disagreed with the NIOSH lifting equation for lifting tasks. Moreover, meaningful variations in ergonomic risk patterns were found for various truck models at each workstation. These results provide a better understanding of the physical ergonomic exposure from practitioner’s point of view in the automotive assembly plant. PMID:26423331

Evaluation of ergonomic physical risk factors in a truck manufacturing plant: case study in SCANIA Production Angers.

PubMed

Zare, Mohsen; Malinge-Oudenot, Agnes; Höglund, Robert; Biau, Sophie; Roquelaure, Yves

2016-01-01

The aims of this study were 1) to assess the ergonomic physical risk factors from practitioner's viewpoint in a truck assembly plant with an in-house observational method and the NIOSH lifting equation, and 2) to compare the results of both methods and their differences. The in-house ergonomic observational method for truck assembly i.e. the SCANIA Ergonomics Standard (SES) and the NIOSH lifting equation were applied to evaluate physical risk factors and lifting of loads by operators. Both risk assessment approaches revealed various levels of risk, ranging from low to high. Two workstations were identified by the SES method as high risk. The NIOSH lifting index (LI) was greater than two for four lifting tasks. The results of the SES method disagreed with the NIOSH lifting equation for lifting tasks. Moreover, meaningful variations in ergonomic risk patterns were found for various truck models at each workstation. These results provide a better understanding of the physical ergonomic exposure from practitioner's point of view in the automotive assembly plant.

Prolongation structures of nonlinear evolution equations

NASA Technical Reports Server (NTRS)

Wahlquist, H. D.; Estabrook, F. B.

1975-01-01

A technique is developed for systematically deriving a 'prolongation structure' - a set of interrelated potentials and pseudopotentials - for nonlinear partial differential equations in two independent variables. When this is applied to the Korteweg-de Vries equation, a new infinite set of conserved quantities is obtained. Known solution techniques are shown to result from the discovery of such a structure: related partial differential equations for the potential functions, linear 'inverse scattering' equations for auxiliary functions, Backlund transformations. Generalizations of these techniques will result from the use of irreducible matrix representations of the prolongation structure.

Governing equations for electro-conjugate fluid flow

NASA Astrophysics Data System (ADS)

Hosoda, K.; Takemura, K.; Fukagata, K.; Yokota, S.; Edamura, K.

2013-12-01

An electro-conjugation fluid (ECF) is a kind of dielectric liquid, which generates a powerful flow when high DC voltage is applied with tiny electrodes. This study deals with the derivation of the governing equations for electro-conjugate fluid flow based on the Korteweg-Helmholtz (KH) equation which represents the force in dielectric liquid subjected to high DC voltage. The governing equations consist of the Gauss's law, charge conservation with charge recombination, the KH equation, the continuity equation and the incompressible Navier-Stokes equations. The KH equation consists of coulomb force, dielectric constant gradient force and electrostriction force. The governing equation gives the distribution of electric field, charge density and flow velocity. In this study, direct numerical simulation (DNS) is used in order to get these distribution at arbitrary time. Successive over-relaxation (SOR) method is used in analyzing Gauss's law and constrained interpolation pseudo-particle (CIP) method is used in analyzing charge conservation with charge recombination. The third order Runge-Kutta method and conservative second-order-accurate finite difference method is used in analyzing the Navier-Stokes equations with the KH equation. This study also deals with the measurement of ECF ow generated with a symmetrical pole electrodes pair which are made of 0.3 mm diameter piano wire. Working fluid is FF-1EHA2 which is an ECF family. The flow is observed from the both electrodes, i.e., the flow collides in between the electrodes. The governing equation successfully calculates mean flow velocity in between the collector pole electrode and the colliding region by the numerical simulation.

Estimating Glomerular Filtration Rate in Kidney Transplant Recipients: Comparing a Novel Equation With Commonly Used Equations in this Population

PubMed Central

Salvador, Cathrin L.; Hartmann, Anders; Åsberg, Anders; Bergan, Stein; Rowe, Alexander D.; Mørkrid, Lars

2017-01-01

Background Assessment of glomerular filtration rate (GFR) is important in kidney transplantation. The aim was to develop a kidney transplant specific equation for estimating GFR and evaluate against published equations commonly used for GFR estimation in these patients. Methods Adult kidney recipients (n = 594) were included, and blood samples were collected 10 weeks posttransplant. GFR was measured by 51Cr-ethylenediaminetetraacetic acid clearance. Patients were randomized into a reference group (n = 297) to generate a new equation and a test group (n = 297) for comparing it with 7 alternative equations. Results Two thirds of the test group were males. The median (2.5-97.5 percentile) age was 52 (23-75) years, cystatin C, 1.63 (1.00-3.04) mg/L; creatinine, 117 (63-220) μmol/L; and measured GFR, 51 (29-78) mL/min per 1.73 m2. We also performed external evaluation in 133 recipients without the use of trimethoprim, using iohexol clearance for measured GFR. The Modification of Diet in Renal Disease equation was the most accurate of the creatinine-equations. The new equation, estimated GFR (eGFR) = 991.15 × (1.120sex/([age0.097] × [cystatin C0.306] × [creatinine0.527]); where sex is denoted: 0, female; 1, male, demonstrating a better accuracy with a low bias as well as good precision compared with reference equations. Trimethoprim did not influence the performance of the new equation. Conclusions The new equation demonstrated superior accuracy, precision, and low bias. The Modification of Diet in Renal Disease equation was the most accurate of the creatinine-based equations. PMID:29536033

On the evolution of perturbations to solutions of the Kadomtsev-Petviashvilli equation using the Benney-Luke equation

NASA Astrophysics Data System (ADS)

Ablowitz, Mark J.; Curtis, Christopher W.

2011-05-01

The Benney-Luke equation, which arises as a long wave asymptotic approximation of water waves, contains the Kadomtsev-Petviashvilli (KP) equation as a leading-order maximal balanced approximation. The question analyzed is how the Benney-Luke equation modifies the so-called web solutions of the KP equation. It is found that the Benney-Luke equation introduces dispersive radiation which breaks each of the symmetric soliton-like humps well away from the interaction region of the KP web solution into a tail of multi-peaked oscillating profiles behind the main solitary hump. Computation indicates that the wave structure is modified near the center of the interaction region. Both analytical and numerical techniques are employed for working with non-periodic, non-decaying solutions on unbounded domains.

Asymptotic problems for stochastic partial differential equations

NASA Astrophysics Data System (ADS)

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.

Similarity solution of the Boussinesq equation

NASA Astrophysics Data System (ADS)

Lockington, D. A.; Parlange, J.-Y.; Parlange, M. B.; Selker, J.

Similarity transforms of the Boussinesq equation in a semi-infinite medium are available when the boundary conditions are a power of time. The Boussinesq equation is reduced from a partial differential equation to a boundary-value problem. Chen et al. [Trans Porous Media 1995;18:15-36] use a hodograph method to derive an integral equation formulation of the new differential equation which they solve by numerical iteration. In the present paper, the convergence of their scheme is improved such that numerical iteration can be avoided for all practical purposes. However, a simpler analytical approach is also presented which is based on Shampine's transformation of the boundary value problem to an initial value problem. This analytical approximation is remarkably simple and yet more accurate than the analytical hodograph approximations.

Dichotomies for generalized ordinary differential equations and applications

NASA Astrophysics Data System (ADS)

Bonotto, E. M.; Federson, M.; Santos, F. L.

2018-03-01

In this work we establish the theory of dichotomies for generalized ordinary differential equations, introducing the concepts of dichotomies for these equations, investigating their properties and proposing new results. We establish conditions for the existence of exponential dichotomies and bounded solutions. Using the correspondences between generalized ordinary differential equations and other equations, we translate our results to measure differential equations and impulsive differential equations. The fact that we work in the framework of generalized ordinary differential equations allows us to manage functions with many discontinuities and of unbounded variation.

A Versatile Technique for Solving Quintic Equations

ERIC Educational Resources Information Center

Kulkarni, Raghavendra G.

2006-01-01

In this paper we present a versatile technique to solve several types of solvable quintic equations. In the technique described here, the given quintic is first converted to a sextic equation by adding a root, and the resulting sextic equation is decomposed into two cubic polynomials as factors in a novel fashion. The resultant cubic equations are…

On the renewal risk model under a threshold strategy

NASA Astrophysics Data System (ADS)

Dong, Yinghui; Wang, Guojing; Yuen, Kam C.

2009-08-01

In this paper, we consider the renewal risk process under a threshold dividend payment strategy. For this model, the expected discounted dividend payments and the Gerber-Shiu expected discounted penalty function are investigated. Integral equations, integro-differential equations and some closed form expressions for them are derived. When the claims are exponentially distributed, it is verified that the expected penalty of the deficit at ruin is proportional to the ruin probability.

Fast sweeping method for the factored eikonal equation

NASA Astrophysics Data System (ADS)

Fomel, Sergey; Luo, Songting; Zhao, Hongkai

2009-09-01

We develop a fast sweeping method for the factored eikonal equation. By decomposing the solution of a general eikonal equation as the product of two factors: the first factor is the solution to a simple eikonal equation (such as distance) or a previously computed solution to an approximate eikonal equation. The second factor is a necessary modification/correction. Appropriate discretization and a fast sweeping strategy are designed for the equation of the correction part. The key idea is to enforce the causality of the original eikonal equation during the Gauss-Seidel iterations. Using extensive numerical examples we demonstrate that (1) the convergence behavior of the fast sweeping method for the factored eikonal equation is the same as for the original eikonal equation, i.e., the number of iterations for the Gauss-Seidel iterations is independent of the mesh size, (2) the numerical solution from the factored eikonal equation is more accurate than the numerical solution directly computed from the original eikonal equation, especially for point sources.

On inter-tidal transport equation

USGS Publications Warehouse

Cheng, Ralph T.; Feng, Shizuo; Pangen, Xi

1989-01-01

The transports of solutes, sediments, nutrients, and other tracers are fundamental to the interactive physical, chemical, and biological processes in estuaries. The characteristic time scales for most estuarine biological and chemical processes are on the order of several tidal cycles or longer. To address the long-term transport mechanism meaningfully, the formulation of an inter-tidal conservation equation is the main subject of this paper. The commonly used inter-tidal conservation equation takes the form of a convection-dispersion equation in which the convection is represented by the Eulerian residual current, and the dispersion terms are due to the introduction of a Fickian hypothesis, unfortunately, the physical significance of this equation is not clear, and the introduction of a Fickian hypothesis is at best an ad hoc approximation. Some recent research results on the Lagrangian residual current suggest that the long-term transport problem is more closely related to the Lagrangian residual current than to the Eulerian residual current. With the aid of additional insight of residual current, the inter-tidal transport equation has been reformulated in this paper using a small perturbation method for a weakly nonlinear tidal system. When tidal flows can be represented by an M2 system, the new intertidal transport equation also takes the form of a convective-dispersion equation without the introduction of a Fickian hypothesis. The convective velocity turns out to be the first order Lagrangian residual current (the sum of the Eulerian residual current and the Stokes’ drift), and the correlation terms take the form of convection with the Stokes’ drift as the convective velocity. The remaining dispersion terms are perturbations of lower order solution to higher order solutions due to shear effect and turbulent mixing.

Cable equation for general geometry

NASA Astrophysics Data System (ADS)

López-Sánchez, Erick J.; Romero, Juan M.

2017-02-01

The cable equation describes the voltage in a straight cylindrical cable, and this model has been employed to model electrical potential in dendrites and axons. However, sometimes this equation might give incorrect predictions for some realistic geometries, in particular when the radius of the cable changes significantly. Cables with a nonconstant radius are important for some phenomena, for example, discrete swellings along the axons appear in neurodegenerative diseases such as Alzheimers, Parkinsons, human immunodeficiency virus associated dementia, and multiple sclerosis. In this paper, using the Frenet-Serret frame, we propose a generalized cable equation for a general cable geometry. This generalized equation depends on geometric quantities such as the curvature and torsion of the cable. We show that when the cable has a constant circular cross section, the first fundamental form of the cable can be simplified and the generalized cable equation depends on neither the curvature nor the torsion of the cable. Additionally, we find an exact solution for an ideal cable which has a particular variable circular cross section and zero curvature. For this case we show that when the cross section of the cable increases the voltage decreases. Inspired by this ideal case, we rewrite the generalized cable equation as a diffusion equation with a source term generated by the cable geometry. This source term depends on the cable cross-sectional area and its derivates. In addition, we study different cables with swelling and provide their numerical solutions. The numerical solutions show that when the cross section of the cable has abrupt changes, its voltage is smaller than the voltage in the cylindrical cable. Furthermore, these numerical solutions show that the voltage can be affected by geometrical inhomogeneities on the cable.

Drift-free kinetic equations for turbulent dispersion

NASA Astrophysics Data System (ADS)

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.

Drift-free kinetic equations for turbulent dispersion.

PubMed

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.

More Issues in Observed-Score Equating

ERIC Educational Resources Information Center

van der Linden, Wim J.

2013-01-01

This article is a response to the commentaries on the position paper on observed-score equating by van der Linden (this issue). The response focuses on the more general issues in these commentaries, such as the nature of the observed scores that are equated, the importance of test-theory assumptions in equating, the necessity to use multiple…

Managing Element Interactivity in Equation Solving

ERIC Educational Resources Information Center

Ngu, Bing Hiong; Phan, Huy P.; Yeung, Alexander Seeshing; Chung, Siu Fung

2018-01-01

Between two popular teaching methods (i.e., balance method vs. inverse method) for equation solving, the main difference occurs at the operational line (e.g., +2 on both sides vs. -2 becomes +2), whereby it alters the state of the equation and yet maintains its equality. Element interactivity occurs on both sides of the equation in the balance…

Schrödinger equation revisited

PubMed Central

Schleich, Wolfgang P.; Greenberger, Daniel M.; Kobe, Donald H.; Scully, Marlan O.

2013-01-01

The time-dependent Schrödinger equation is a cornerstone of quantum physics and governs all phenomena of the microscopic world. However, despite its importance, its origin is still not widely appreciated and properly understood. We obtain the Schrödinger equation from a mathematical identity by a slight generalization of the formulation of classical statistical mechanics based on the Hamilton–Jacobi equation. This approach brings out most clearly the fact that the linearity of quantum mechanics is intimately connected to the strong coupling between the amplitude and phase of a quantum wave. PMID:23509260

Approximate solutions to Mathieu's equation

NASA Astrophysics Data System (ADS)

Wilkinson, Samuel A.; Vogt, Nicolas; Golubev, Dmitry S.; Cole, Jared H.

2018-06-01

Mathieu's equation has many applications throughout theoretical physics. It is especially important to the theory of Josephson junctions, where it is equivalent to Schrödinger's equation. Mathieu's equation can be easily solved numerically, however there exists no closed-form analytic solution. Here we collect various approximations which appear throughout the physics and mathematics literature and examine their accuracy and regimes of applicability. Particular attention is paid to quantities relevant to the physics of Josephson junctions, but the arguments and notation are kept general so as to be of use to the broader physics community.

New nonlinear evolution equations from surface theory

NASA Astrophysics Data System (ADS)

Gürses, Metin; Nutku, Yavuz

1981-07-01

We point out that the connection between surfaces in three-dimensional flat space and the inverse scattering problem provides a systematic way for constructing new nonlinear evolution equations. In particular we study the imbedding for Guichard surfaces which gives rise to the Calapso-Guichard equations generalizing the sine-Gordon (SG) equation. Further, we investigate the geometry of surfaces and their imbedding which results in the Korteweg-deVries (KdV) equation. Then by constructing a family of applicable surfaces we obtain a generalization of the KdV equation to a compressible fluid.

The cost effectiveness of rapid-acting insulin aspart compared with human insulin in type 2 diabetes patients: an analysis from the Japanese third-party payer perspective.

PubMed

Pollock, R F; Valentine, W J; Pilgaard, T; Nishimura, H

2011-01-01

. 4.684 years) and an increase of 0.023 quality-adjusted life-years (QALYs) (3.800 vs. 3.776 QALYs) when compared with regular human insulin. Insulin aspart also incurred lower costs (JPY 481,586 vs. 594,717, difference -113,131) which resulted from the decreased incidence of cardiovascular events with insulin aspart (0.013 events per patient year vs. 0.030 on regular human insulin). Breakdown of costs indicated that pharmacy costs were higher with insulin aspart (JPY 346,608 vs. 278,468), but these costs were more than offset by the reduced costs associated with cardiovascular complications and hypoglycaemia over 5 years of treatment (JPY 134,978 vs. 316,249). Sensitivity analysis showed that insulin aspart was still cost-effective in the case where only 18% of the within-trial cardiovascular and mortality benefit over regular human insulin was captured in the model (assuming a willingness-to-pay threshold of JPY 5,000,000). The NICE study cohort was relatively small (n = 325), meaning that caution should be exercised when calculating and interpreting the incremental cost-effectiveness ratio. Also, despite the differences in cardiovascular risk profile between the Japanese and UK populations, UKPDS-derived risk equations were used to project MI outcomes and PCI and CABG procedures and UKPDS HRQoL scores were applied to all health states. While these risk formulas and HRQoL utilities may not be directly applicable to the Japanese population, no equivalent Japanese-specific data are currently available. In a Japanese type 2 diabetes population, prescribing rapid-acting insulin aspart significantly reduced cardiovascular complications over 5- and 10-year time horizons, resulting in increased quality of life and decreased costs when compared with human insulin.

A Harmonic Solution for the Hyperbolic Heat Conduction Equation and Its Relationship to the Guyer-Krumhansl Equation

NASA Astrophysics Data System (ADS)

Zhukovsky, K. V.

2018-01-01

A particular solution of the hyperbolic heat-conduction equation was constructed using the method of operators. The evolution of a harmonic solution is studied, which simulates the propagation of electric signals in long wire transmission lines. The structures of the solutions of the telegraph equation and of the Guyer-Krumhansl equation are compared. The influence of the phonon heat-transfer mechanism in the environment is considered from the point of view of heat conductivity. The fulfillment of the maximum principle for the obtained solutions is considered. The frequency dependences of heat conductivity in the telegraph equation and in an equation of the Guyer-Krumhansl type are studied and compared with each other. The influence of the Knudsen number on heat conductivity in the model of thin films is studied.

Simple derivation of the Lindblad equation

NASA Astrophysics Data System (ADS)

Pearle, Philip

2012-07-01

The Lindblad equation is an evolution equation for the density matrix in quantum theory. It is the general linear, Markovian, form which ensures that the density matrix is Hermitian, trace 1, positive and completely positive. Some elementary examples of the Lindblad equation are given. The derivation of the Lindblad equation presented here is ‘simple’ in that all it uses is the expression of a Hermitian matrix in terms of its orthonormal eigenvectors and real eigenvalues. Thus, it is appropriate for students who have learned the algebra of quantum theory. Where helpful, arguments are first given in a two-dimensional Hilbert space.

Does consideration of either psychological or material disadvantage improve coronary risk prediction? Prospective observational study of Scottish men.

PubMed

Macleod, John; Metcalfe, Chris; Smith, George Davey; Hart, Carole

2007-09-01

To assess the value of psychosocial risk factors in discriminating between individuals at higher and lower risk of coronary heart disease, using risk prediction equations. Prospective observational study. Scotland. 5191 employed men aged 35 to 64 years and free of coronary heart disease at study enrollment Area under receiver operating characteristic (ROC) curves for risk prediction equations including different risk factors for coronary heart disease. During the first 10 years of follow up, 203 men died of coronary heart disease and a further 200 were admitted to hospital with this diagnosis. Area under the ROC curve for the standard Framingham coronary risk factors was 74.5%. Addition of "vital exhaustion" and psychological stress led to areas under the ROC curve of 74.5% and 74.6%, respectively. Addition of current social class and lifetime social class to the standard Framingham equation gave areas under the ROC curve of 74.6% and 74.9%, respectively. In no case was there strong evidence for improved discrimination of the model containing the novel risk factor over the standard model. Consideration of psychosocial risk factors, including those that are strong independent predictors of heart disease, does not substantially influence the ability of risk prediction tools to discriminate between individuals at higher and lower risk of coronary heart disease.

On Reductions of the Hirota-Miwa Equation

NASA Astrophysics Data System (ADS)

Hone, Andrew N. W.; Kouloukas, Theodoros E.; Ward, Chloe

2017-07-01

The Hirota-Miwa equation (also known as the discrete KP equation, or the octahedron recurrence) is a bilinear partial difference equation in three independent variables. It is integrable in the sense that it arises as the compatibility condition of a linear system (Lax pair). The Hirota-Miwa equation has infinitely many reductions of plane wave type (including a quadratic exponential gauge transformation), defined by a triple of integers or half-integers, which produce bilinear ordinary difference equations of Somos/Gale-Robinson type. Here it is explained how to obtain Lax pairs and presymplectic structures for these reductions, in order to demonstrate Liouville integrability of some associated maps, certain of which are related to reductions of discrete Toda and discrete KdV equations.

Protein electrostatics: a review of the equations and methods used to model electrostatic equations in biomolecules--applications in biotechnology.

PubMed

Neves-Petersen, Maria Teresa; Petersen, Steffen B

2003-01-01

The molecular understanding of the initial interaction between a protein and, e.g., its substrate, a surface or an inhibitor is essentially an understanding of the role of electrostatics in intermolecular interactions. When studying biomolecules it is becoming increasingly evident that electrostatic interactions play a role in folding, conformational stability, enzyme activity and binding energies as well as in protein-protein interactions. In this chapter we present the key basic equations of electrostatics necessary to derive the equations used to model electrostatic interactions in biomolecules. We will also address how to solve such equations. This chapter is divided into two major sections. In the first part we will review the basic Maxwell equations of electrostatics equations called the Laws of Electrostatics that combined will result in the Poisson equation. This equation is the starting point of the Poisson-Boltzmann (PB) equation used to model electrostatic interactions in biomolecules. Concepts as electric field lines, equipotential surfaces, electrostatic energy and when can electrostatics be applied to study interactions between charges will be addressed. In the second part we will arrive at the electrostatic equations for dielectric media such as a protein. We will address the theory of dielectrics and arrive at the Poisson equation for dielectric media and at the PB equation, the main equation used to model electrostatic interactions in biomolecules (e.g., proteins, DNA). It will be shown how to compute forces and potentials in a dielectric medium. In order to solve the PB equation we will present the continuum electrostatic models, namely the Tanford-Kirkwood and the modified Tandord-Kirkwood methods. Priority will be given to finding the protonation state of proteins prior to solving the PB equation. We also present some methods that can be used to map and study the electrostatic potential distribution on the molecular surface of proteins. The

Nonlocal electrical diffusion equation

NASA Astrophysics Data System (ADS)

Gómez-Aguilar, J. F.; Escobar-Jiménez, R. F.; Olivares-Peregrino, V. H.; Benavides-Cruz, M.; Calderón-Ramón, C.

2016-07-01

In this paper, we present an analysis and modeling of the electrical diffusion equation using the fractional calculus approach. This alternative representation for the current density is expressed in terms of the Caputo derivatives, the order for the space domain is 0<β≤1 and for the time domain is 0<γ≤2. We present solutions for the full fractional equation involving space and time fractional derivatives using numerical methods based on Fourier variable separation. The case with spatial fractional derivatives leads to Levy flight type phenomena, while the time fractional equation is related to sub- or super diffusion. We show that the mathematical concept of fractional derivatives can be useful to understand the behavior of semiconductors, the design of solar panels, electrochemical phenomena and the description of anomalous complex processes.

Multi-Hamiltonian structure of equations of hydrodynamic type

NASA Astrophysics Data System (ADS)

Gümral, H.; Nutku, Y.

1990-11-01

The discussion of the Hamiltonian structure of two-component equations of hydrodynamic type is completed by presenting the Hamiltonian operators for Euler's equation governing the motion of plane sound waves of finite amplitude and another quasilinear second-order wave equation. There exists a doubly infinite family of conserved Hamiltonians for the equations of gas dynamics that degenerate into one, namely, the Benney sequence, for shallow-water waves. Infinite sequences of conserved quantities for these equations are also presented. In the case of multicomponent equations of hydrodynamic type, it is shown, that Kodama's generalization of the shallow-water equations admits bi-Hamiltonian structure.

Canonical equations of Hamilton for the nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

Liang, Guo; Guo, Qi; Ren, Zhanmei

2015-09-01

We define two different systems of mathematical physics: the second order differential system (SODS) and the first order differential system (FODS). The Newton's second law of motion and the nonlinear Schrödinger equation (NLSE) are the exemplary SODS and FODS, respectively. We obtain a new kind of canonical equations of Hamilton (CEH), which exhibit some kind of symmetry in form and are formally different from the conventional CEH without symmetry [H. Goldstein, C. Poole, J. Safko, Classical Mechanics, third ed., Addison- Wesley, 2001]. We also prove that the number of the CEHs is equal to the number of the generalized coordinates for the FODS, but twice the number of the generalized coordinates for the SODS. We show that the FODS can only be expressed by the new CEH, but not introduced by the conventional CEH, while the SODS can be done by both the new and the conventional CEHs. As an example, we prove that the nonlinear Schrödinger equation can be expressed with the new CEH in a consistent way.

THE COSMIC RAY EQUATOR AND THE GEOMAGNETISM

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sakurai, K.

1960-01-01

It was formerly thought that the disagreement of the position of geomagnetic dipole equator with that of the cosmic ray equator was caused by 45 deg westward shifting of the latter. Referring to the theory of geomagnetic effect on cosmic rays, it was determined whether such westward shifting could be existent or not. It was found that the deviation of the cosmic ray equator from the geomagnetic dipole equator is negligible even if the magnetic cavity is present around the earth's outer atmosphere. Taking into account such results, the origin of the cosmic ray equator was investigated. It was foundmore » that this equater could be produced by the higher harmonic components combined with the dipole component of geomagnetism. The relation of the origin of the cosmic ray equater to the eccentric dipoles, near the outer pant of the earth's core, contributing to the secular variation of geomagnetism was considered. (auth)« less

Langevin equation versus kinetic equation: Subdiffusive behavior of charged particles in a stochastic magnetic field

DOE Office of Scientific and Technical Information (OSTI.GOV)

Balescu, R.; Wang, H.; Misguich, J.H.

1994-12-01

The running diffusion coefficient [ital D]([ital t]) is evaluated for a system of charged particles undergoing the effect of a fluctuating magnetic field and of their mutual collisions. The latter coefficient can be expressed either in terms of the mean square displacement (MSD) of a test particle, or in terms of a correlation between a fluctuating distribution function and the magnetic field fluctuation. In the first case a stochastic differential equation of Langevin type for the position of a test particle must be solved; the second problem requires the determination of the distribution function from a kinetic equation. Using suitablemore » simplifications, both problems are amenable to exact analytic solution. The conclusion is that the equivalence of the two approaches is by no means automatically guaranteed. A new type of object, the hybrid kinetic equation'' is constructed: it automatically ensures the equivalence with the Langevin results. The same conclusion holds for the generalized Fokker--Planck equation. The (Bhatnagar--Gross--Krook) (BGK) model for the collisions yields a completely wrong result. A linear approximation to the hybrid kinetic equation yields an inexact behavior, but represents an acceptable approximation in the strongly collisional limit.« less

Consistent three-equation model for thin films

NASA Astrophysics Data System (ADS)

Richard, Gael; Gisclon, Marguerite; Ruyer-Quil, Christian; Vila, Jean-Paul

2017-11-01

Numerical simulations of thin films of newtonian fluids down an inclined plane use reduced models for computational cost reasons. These models are usually derived by averaging over the fluid depth the physical equations of fluid mechanics with an asymptotic method in the long-wave limit. Two-equation models are based on the mass conservation equation and either on the momentum balance equation or on the work-energy theorem. We show that there is no two-equation model that is both consistent and theoretically coherent and that a third variable and a three-equation model are required to solve all theoretical contradictions. The linear and nonlinear properties of two and three-equation models are tested on various practical problems. We present a new consistent three-equation model with a simple mathematical structure which allows an easy and reliable numerical resolution. The numerical calculations agree fairly well with experimental measurements or with direct numerical resolutions for neutral stability curves, speed of kinematic waves and of solitary waves and depth profiles of wavy films. The model can also predict the flow reversal at the first capillary trough ahead of the main wave hump.

Alternate solution to generalized Bernoulli equations via an integrating factor: an exact differential equation approach

NASA Astrophysics Data System (ADS)

Tisdell, C. C.

2017-08-01

Solution methods to exact differential equations via integrating factors have a rich history dating back to Euler (1740) and the ideas enjoy applications to thermodynamics and electromagnetism. Recently, Azevedo and Valentino presented an analysis of the generalized Bernoulli equation, constructing a general solution by linearizing the problem through a substitution. The purpose of this note is to present an alternative approach using 'exact methods', illustrating that a substitution and linearization of the problem is unnecessary. The ideas may be seen as forming a complimentary and arguably simpler approach to Azevedo and Valentino that have the potential to be assimilated and adapted to pedagogical needs of those learning and teaching exact differential equations in schools, colleges, universities and polytechnics. We illustrate how to apply the ideas through an analysis of the Gompertz equation, which is of interest in biomathematical models of tumour growth.

Chandrasekhar equations for infinite dimensional systems

NASA Technical Reports Server (NTRS)

Ito, K.; Powers, R.

1985-01-01

The existence of Chandrasekhar equations for linear time-invariant systems defined on Hilbert spaces is investigated. An important consequence is that the solution to the evolutional Riccati equation is strongly differentiable in time, and that a strong solution of the Riccati differential equation can be defined. A discussion of the linear-quadratic optimal-control problem for hereditary differential systems is also included.

Oscillating solutions for nonlinear Helmholtz equations

NASA Astrophysics Data System (ADS)

Mandel, Rainer; Montefusco, Eugenio; Pellacci, Benedetta

2017-12-01

Existence results for radially symmetric oscillating solutions for a class of nonlinear autonomous Helmholtz equations are given and their exact asymptotic behaviour at infinity is established. Some generalizations to nonautonomous radial equations as well as existence results for nonradial solutions are found. Our theorems prove the existence of standing waves solutions of nonlinear Klein-Gordon or Schrödinger equations with large frequencies.

Simulation of floods caused by overloaded sewer systems: extensions of shallow-water equations

NASA Astrophysics Data System (ADS)

Hilden, Michael

2005-03-01

The outflow of water from a manhole onto a street is a typical flow problem within the simulation of floods in urban areas that are caused by overloaded sewer systems in the event of heavy rains. The reliable assessment of the flood risk for the connected houses requires accurate simulations of the water flow processes in the sewer system and in the street.The Navier-Stokes equations (NSEs) describe the free surface flow of the fluid water accurately, but since their numerical solution requires high CPU times and much memory, their application is not practical. However, their solutions for selected flow problems are applied as reference states to assess the results of other model approaches.The classical shallow-water equations (SWEs) require only fractions (factor 1/100) of the NSEs' computational effort. They assume hydrostatic pressure distribution, depth-averaged horizontal velocities and neglect vertical velocities. These shallow-water assumptions are not fulfilled for the outflow of water from a manhole onto the street. Accordingly, calculations show differences between NSEs and SWEs solutions.The SWEs are extended in order to assess the flood risks in urban areas reliably within applicable computational efforts. Separating vortex regions from the main flow and approximating vertical velocities to involve their contributions into a pressure correction yield suitable results.

SIMULTANEOUS DIFFERENTIAL EQUATION COMPUTER

DOEpatents

Collier, D.M.; Meeks, L.A.; Palmer, J.P.

1960-05-10

A description is given for an electronic simulator for a system of simultaneous differential equations, including nonlinear equations. As a specific example, a homogeneous nuclear reactor system including a reactor fluid, heat exchanger, and a steam boiler may be simulated, with the nonlinearity resulting from a consideration of temperature effects taken into account. The simulator includes three operational amplifiers, a multiplier, appropriate potential sources, and interconnecting R-C networks.

Simple taper: Taper equations for the field forester

Treesearch

David R. Larsen

2017-01-01

"Simple taper" is set of linear equations that are based on stem taper rates; the intent is to provide taper equation functionality to field foresters. The equation parameters are two taper rates based on differences in diameter outside bark at two points on a tree. The simple taper equations are statistically equivalent to more complex equations. The linear...

Predicting one repetition maximum equations accuracy in paralympic rowers with motor disabilities.

PubMed

Schwingel, Paulo A; Porto, Yuri C; Dias, Marcelo C M; Moreira, Mônica M; Zoppi, Cláudio C

2009-05-01

Predicting one repetition maximum equations accuracy in paralympic rowers Resistance training intensity is prescribed using percentiles of the maximum strength, defined as the maximum tension generated for a muscle or muscular group. This value is found through the application of the one maximal repetition (1RM) test. One maximal repetition test demands time and still is not appropriate for some populations because of the risk it offers. In recent years, the prediction of maximal strength, through predicting equations, has been used to prevent the inconveniences of the 1RM test. The purpose of this study was to verify the accuracy of 12 1RM predicting equations for disabled rowers. Nine male paralympic rowers (7 one-leg amputated rowers and 2 cerebral paralyzed rowers; age, 30 +/- 7.9 years; height, 175.1 +/- 5.9 cm; weight, 69 +/- 13.6 kg) performed 1RM test for lying T-bar row and flat barbell bench press exercises to determine upper-body strength and leg press exercise to determine lower-body strength. One maximal repetition test was performed, and based on submaximal repetitions loads, several linear and exponential equations models were tested with regard of their accuracy. We did not find statistical differences for lying T-bar row and bench press exercises between measured and predicted 1RM values (p = 0.84 and 0.23 for lying T-bar row and flat barbell bench press, respectively); however, leg press exercise reached a high significant difference between measured and predicted values (p < 0.01). In conclusion, rowers with motor disabilities tolerate 1RM testing procedures, and predicting 1RM equations are accurate for bench press and lying T-bar row, but not for leg press, in this kind of athlete.

An integrable semi-discrete Degasperis-Procesi equation

NASA Astrophysics Data System (ADS)

Feng, Bao-Feng; Maruno, Ken-ichi; Ohta, Yasuhiro

2017-06-01

Based on our previous work on the Degasperis-Procesi equation (Feng et al J. Phys. A: Math. Theor. 46 045205) and the integrable semi-discrete analogue of its short wave limit (Feng et al J. Phys. A: Math. Theor. 48 135203), we derive an integrable semi-discrete Degasperis-Procesi equation by Hirota’s bilinear method. Furthermore, N-soliton solution to the semi-discrete Degasperis-Procesi equation is constructed. It is shown that both the proposed semi-discrete Degasperis-Procesi equation, and its N-soliton solution converge to ones of the original Degasperis-Procesi equation in the continuum limit.

The new "intermediate risk" group: a comparative analysis of the new 2013 ACC/AHA risk assessment guidelines versus prior guidelines in men.

PubMed

Blaha, Michael J; Dardari, Zeina A; Blumenthal, Roger S; Martin, Seth S; Nasir, Khurram; Al-Mallah, Mouaz H

2014-11-01

The 2013 ACC/AHA Report on the Assessment of Cardiovascular (CVD) Risk redefined "intermediate risk". We sought to critically compare the intermediate risk groups identified by prior guidelines and the new ACC/AHA guidelines. We analyzed data from 30,005 adult men free of known CVD from a large, multi-ethnic study of middle-aged adults. The Framingham Risk Score was calculated using published equations, and CVD risk was calculated using the new ACC/AHA Pooled Cohort Equations Risk Estimator. We first compared the size and characteristics of the intermediate risk group identified by the old (ATP III, 10-20% 10-year CHD risk) and new guidelines (5-7.4% 10-year CVD risk). We then defined time-to-high-risk as the length of time an individual patient resides in the intermediate risk group before progressing to high risk status based on advancing age alone. The mean age of the study population was 53 ± 13 years, and 24% were African-American. Patients identified as intermediate risk by the new ACC/AHA Guidelines were younger and more likely to be African-American and have lower risk factor burden (all p < 0.05). The new intermediate risk group was just 37% the size of the traditional ATP III intermediate risk group, while the new high risk group was 103% larger. Under the new guidelines, men remain intermediate risk for an average of just 3 years, compared to 8 years under the prior guidelines (63% shorter time-to-high-risk, p < 0.05), before progressing to high risk based on advancing age alone. The new 2013 ACC/AHA risk assessment guidelines produce a markedly smaller, lower absolute risk, and more temporary "intermediate risk" group. These findings reshape the modern understanding of "intermediate risk", and have distinct implications for risk assessment, clinical decision making, and pharmacotherapy in primary prevention. Copyright © 2014 Elsevier Ireland Ltd. All rights reserved.

Media Use and Perceived Risk as Predictors of Marijuana Use

ERIC Educational Resources Information Center

Beaudoin, Christopher E.; Hong, Traci

2012-01-01

Objectives: To assess the influence of media use and perceived risk on marijuana use outcomes. Methods: With survey data from 750 US young adults, structural equation modeling tested how attitudes, behaviors, and behavioral intention specific to marijuana use are influenced by perceived personal and societal risk of marijuana use, media campaign…

The Jeffcott equations in nonlinear rotordynamics

NASA Technical Reports Server (NTRS)

Zalik, R. A.

1987-01-01

The Jeffcott equations are a system of coupled differential equations representing the behavior of a rotating shaft. This is a simple model which allows investigation of the basic dynamic behavior of rotating machinery. Nolinearities can be introduced by taking into consideration deadband, side force, and rubbing, among others. The properties of the solutions of the Jeffcott equations with deadband are studied. In particular, it is shown how bounds for the solution of these equations can be obtained from bounds for the solutions of the linearized equations. By studying the behavior of the Fourier transforms of the solutions, we are also able to predict the onset of destructive vibrations. These conclusions are verified by means of numerical solutions of the equations, and of power spectrum density (PSD) plots. This study offers insight into a possible detection method to determine pump stability margins during flight and hot fire tests, and was motivated by the need to explain a phenomenon observed in the development phase of the cryogenic pumps of the Space Shuttle, during hot fire ground testing; namely, the appearance of vibrations at frequencies that could not be accounted for by means of linear models.

Oscillations and Rolling for Duffing's Equation

NASA Astrophysics Data System (ADS)

Aref'eva, I. Ya.; Piskovskiy, E. V.; Volovich, I. V.

2013-01-01

The Duffing equation has been used to model nonlinear dynamics not only in mechanics and electronics but also in biology and in neurology for the brain process modeling. Van der Pol's method is often used in nonlinear dynamics to improve perturbation theory results when describing small oscillations. However, in some other problems of nonlinear dynamics particularly in case of Duffing-Higgs equation in field theory, for the Einsten-Friedmann equations in cosmology and for relaxation processes in neurology not only small oscillations regime is of interest but also the regime of slow rolling. In the present work a method for approximate solution to nonlinear dynamics equations in the rolling regime is developed. It is shown that in order to improve perturbation theory in the rolling regime it turns out to be effective to use an expansion in hyperbolic functions instead of trigonometric functions as it is done in van der Pol's method in case of small oscillations. In particular the Duffing equation in the rolling regime is investigated using solution expressed in terms of elliptic functions. Accuracy of obtained approximation is estimated. The Duffing equation with dissipation is also considered.

Covariant Conformal Decomposition of Einstein Equations

NASA Astrophysics Data System (ADS)

Gourgoulhon, E.; Novak, J.

It has been shown1,2 that the usual 3+1 form of Einstein's equations may be ill-posed. This result has been previously observed in numerical simulations3,4. We present a 3+1 type formalism inspired by these works to decompose Einstein's equations. This decomposition is motivated by the aim of stable numerical implementation and resolution of the equations. We introduce the conformal 3-``metric'' (scaled by the determinant of the usual 3-metric) which is a tensor density of weight -2/3. The Einstein equations are then derived in terms of this ``metric'', of the conformal extrinsic curvature and in terms of the associated derivative. We also introduce a flat 3-metric (the asymptotic metric for isolated systems) and the associated derivative. Finally, the generalized Dirac gauge (introduced by Smarr and York5) is used in this formalism and some examples of formulation of Einstein's equations are shown.

Equation-derived body fat percentage indicates metabolic abnormalities among normal-weight adults in a rural Chinese population.

PubMed

Liu, Xin; Zhao, Yaling; Li, Qiang; Dang, Shaonong; Yan, Hong

2017-07-08

Obesity classification using body mass index (BMI) may miss subjects with elevated body fat percentage (BF%) and related metabolic risk factors. We aimed to evaluate whether BF% calculated by equations could provide more information about metabolic risks, in addition to BMI classification, in a cross-sectional rural Chinese population. A total of 2,990 men and women aged 18-80 years were included in this study. BF% was calculated using previously validated Chinese-specific equations. Metabolic syndrome was defined according to the updated National Cholesterol Education Program Panel III criteria for Asian Americans. In total, 33.6% men and 32.9% women were overweight/obese according to BMI classification. Among those within the normal BMI range, 25.4% men and 54.7% women were indicated as overweight or obese given their elevated BF% (men: BF% ≥ 20%; women: BF% ≥ 30%). In both men and women, compared with those with normal BMI and BF% (NBB), subjects with normal BMI but elevated BF% (NBOB) were more likely to carry abnormal serum lipid profile and to have higher risks of metabolic syndrome. The multivariable adjusted odds ratios (95% confidence intervals) for metabolic syndrome were 5.45 (2.37-9.53, P < 0.001) and 5.65 (3.36-9.52, P < 0.001) for men and women, respectively. Moreover, the women with NBOB also showed higher blood pressure and serum uric acid than women with NBB. Our study suggested that high BF% based on equations may indicate adverse metabolic profiles among rural Chinese adults with a normal BMI. © 2017 Wiley Periodicals, Inc.

Inverse scattering transform for the time dependent Schrödinger equation with applications to the KPI equation

NASA Astrophysics Data System (ADS)

Zhou, Xin

1990-03-01

For the direct-inverse scattering transform of the time dependent Schrödinger equation, rigorous results are obtained based on an opertor-triangular-factorization approach. By viewing the equation as a first order operator equation, similar results as for the first order n x n matrix system are obtained. The nonlocal Riemann-Hilbert problem for inverse scattering is shown to have solution.

Chandrasekhar equations for infinite dimensional systems

NASA Technical Reports Server (NTRS)

Ito, K.; Powers, R. K.

1985-01-01

Chandrasekhar equations are derived for linear time invariant systems defined on Hilbert spaces using a functional analytic technique. An important consequence of this is that the solution to the evolutional Riccati equation is strongly differentiable in time and one can define a strong solution of the Riccati differential equation. A detailed discussion on the linear quadratic optimal control problem for hereditary differential systems is also included.

New Zealand Diabetes Cohort Study cardiovascular risk score for people with Type 2 diabetes: validation in the PREDICT cohort.

PubMed

Robinson, Tom; Elley, C Raina; Wells, Sue; Robinson, Elizabeth; Kenealy, Tim; Pylypchuk, Romana; Bramley, Dale; Arroll, Bruce; Crengle, Sue; Riddell, Tania; Ameratunga, Shanthi; Metcalf, Patricia; Drury, Paul L

2012-09-01

New Zealand (NZ) guidelines recommend treating people for cardiovascular disease (CVD) risk on the basis of five-year absolute risk using a NZ adaptation of the Framingham risk equation. A diabetes-specific Diabetes Cohort Study (DCS) CVD predictive risk model has been developed and validated using NZ Get Checked data. To revalidate the DCS model with an independent cohort of people routinely assessed using PREDICT, a web-based CVD risk assessment and management programme. People with Type 2 diabetes without pre-existing CVD were identified amongst people who had a PREDICT risk assessment between 2002 and 2005. From this group we identified those with sufficient data to allow estimation of CVD risk with the DCS models. We compared the DCS models with the NZ Framingham risk equation in terms of discrimination, calibration, and reclassification implications. Of 3044 people in our study cohort, 1829 people had complete data and therefore had CVD risks calculated. Of this group, 12.8% (235) had a cardiovascular event during the five-year follow-up. The DCS models had better discrimination than the currently used equation, with C-statistics being 0.68 for the two DCS models and 0.65 for the NZ Framingham model. The DCS models were superior to the NZ Framingham equation at discriminating people with diabetes who will have a cardiovascular event. The adoption of a DCS model would lead to a small increase in the number of people with diabetes who are treated with medication, but potentially more CVD events would be avoided.

Technique for handling wave propagation specific effects in biological tissue: mapping of the photon transport equation to Maxwell's equations.

PubMed

Handapangoda, Chintha C; Premaratne, Malin; Paganin, David M; Hendahewa, Priyantha R D S

2008-10-27

A novel algorithm for mapping the photon transport equation (PTE) to Maxwell's equations is presented. Owing to its accuracy, wave propagation through biological tissue is modeled using the PTE. The mapping of the PTE to Maxwell's equations is required to model wave propagation through foreign structures implanted in biological tissue for sensing and characterization of tissue properties. The PTE solves for only the magnitude of the intensity but Maxwell's equations require the phase information as well. However, it is possible to construct the phase information approximately by solving the transport of intensity equation (TIE) using the full multigrid algorithm.

Quadratic equations in Banach space, perturbation techniques and applications to Chandrasekhar's and related equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Argyros, I.K.

1984-01-01

In this dissertation perturbation techniques are developed, based on the contraction mapping principle which can be used to prove existence and uniqueness for the quadratic equation x = y + lambdaB(x,x) (1) in a Banach space X; here B: XxX..-->..X is a bounded, symmetric bilinear operator, lambda is a positive parameter and y as a subset of X is fixed. The following is the main result. Theorem. Suppose F: XxX..-->..X is a bounded, symmetric bilinear operator and that the equation z = y + lambdaF(z,z) has a solution z/sup */ of sufficiently small norm. Then equation (1) has a uniquemore » solution in a certain closed ball centered at z/sup */. Applications. The theorem is applied to the famous Chandrasekhar equation and to the Anselone-Moore system which are of the form (1) above and yields existence and uniqueness for a solution of (1) for larger values of lambda than previously known, as well as more accurate information on the location of solutions.« less

The cost-effectiveness of dapagliflozin versus sulfonylurea as an add-on to metformin in the treatment of Type 2 diabetes mellitus.

PubMed

Charokopou, M; McEwan, P; Lister, S; Callan, L; Bergenheim, K; Tolley, K; Postema, R; Townsend, R; Roudaut, M

2015-07-01

To assess the cost-effectiveness of dapagliflozin, a sodium-glucose co-transporter-2 (SGLT-2) inhibitor, compared with a sulfonylurea, when added to metformin for treatment of UK people with Type 2 diabetes mellitus inadequately controlled on metformin alone. Clinical inputs sourced from a head-to-head randomized controlled trial (RCT) informed the Cardiff diabetes decision model. Risk equations developed from the United Kingdom Prospective Diabetes Study (UKPDS) were used in conjunction with the clinical inputs to predict disease progression and the incidence of micro- and macrovascular complications over a lifetime horizon. Cost and utility data were generated to present the incremental cost-effectiveness ratio (ICER) for both treatment arms, and sensitivity and scenario analyses were conducted to assess the impact of uncertainty on the final model results. The dapagliflozin treatment arm was associated with a mean incremental benefit of 0.467 quality-adjusted life years (QALYs) [95% confidence interval (CI): 0.420; 0.665], with an incremental cost of £1246 (95% CI: £613; £1637). This resulted in an ICER point estimate of £2671 per QALY gained. Incremental costs were shown to be insensitive to parameter variation, with only treatment-related weight change having a significant impact on the incremental QALYs. Probabilistic sensitivity analysis determined that dapagliflozin had a 100% probability of being cost-effective at a willingness-to-pay threshold of £20,000 per QALY. Dapagliflozin in combination with metformin was shown to be a cost-effective treatment option compared with sulfonylurea from a UK healthcare perspective for people with Type 2 diabetes mellitus who are inadequately controlled on metformin monotherapy. © 2015 The Authors. Diabetic Medicine © 2015 Diabetes UK.

Cost effectiveness of atorvastatin in patients with type 2 diabetes mellitus: a pharmacoeconomic analysis of the collaborative atorvastatin diabetes study in the belgian population.

PubMed

Annemans, L; Marbaix, S; Webb, K; Van Gaal, L; Scheen, A

2010-01-01

Patients with type 2 diabetes mellitus have a high risk of developing cardiovascular (CV) disease. The clinical benefit of use of statins in patients with type 2 diabetes has been demonstrated in several randomized, controlled trials, including the CARDS clinical trial. Based on the clinical CARDS data, the favourable cost effectiveness of atorvastatin 10 mg in patients with type 2 diabetes has been demonstrated in countries such as the UK and France. This study aimed to estimate the cost effectiveness in the Belgian setting of atorvastatin 10 mg compared with no treatment for the primary prevention of CV events in type 2 diabetes patients without a history of CV disease. A Markov model with 1-year cycles was developed to simulate the CV event and death risk according to the therapeutic approach initiated. The transition probabilities for CV events in the 'no statin treatment' group were derived from the risk equations reported from the large UKPDS. Risk reductions from the CARDS clinical trial were used to adjust these CV event probabilities in the atorvastatin 10 mg treatment group. The characteristics of type 2 diabetes patients without a CV history were derived from the Belgian OCAPI survey. The public healthcare payers' perspective was taken into account for costing. The direct medical costs of CV events were based on the Public Health Authorities' hospital database for acute care costs and on the literature for the follow-up costs. The impact on the reimbursement system of generic entry to the market was considered in the drug cost. Costs were valued as at year 2009; costs and outcomes were discounted at 3% and 1.5%, respectively. Based on a 5-year time horizon, atorvastatin was demonstrated to be cost effective with an incremental cost/quality-adjusted life-year (QALY) of euro 16,681. Over a lifetime horizon (25 years), atorvastatin was demonstrated to be a cost-saving therapeutic intervention. At a threshold of euro 30,000/QALY, atorvastatin had a 98

Higuchi equation: derivation, applications, use and misuse.

PubMed

Siepmann, Juergen; Peppas, Nicholas A

2011-10-10

Fifty years ago, the legendary Professor Takeru Higuchi published the derivation of an equation that allowed for the quantification of drug release from thin ointment films, containing finely dispersed drug into a perfect sink. This became the famous Higuchi equation whose fiftieth anniversary we celebrate this year. Despite the complexity of the involved mass transport processes, Higuchi derived a very simple equation, which is easy to use. Based on a pseudo-steady-state approach, a direct proportionality between the cumulative amount of drug released and the square root of time can be demonstrated. In contrast to various other "square root of time" release kinetics, the constant of proportionality in the classical Higuchi equation has a specific, physically realistic meaning. The major benefits of this equation include the possibility to: (i) facilitate device optimization, and (ii) to better understand the underlying drug release mechanisms. The equation can also be applied to other types of drug delivery systems than thin ointment films, e.g., controlled release transdermal patches or films for oral controlled drug delivery. Later, the equation was extended to other geometries and related theories have been proposed. The aim of this review is to highlight the assumptions the derivation of the classical Higuchi equation is based on and to give an overview on the use and potential misuse of this equation as well as of related theories. Copyright © 2011 Elsevier B.V. All rights reserved.

Studying relaxation phenomena via effective master equations

NASA Astrophysics Data System (ADS)

Chan, David; Wan, Jones T. K.; Chu, L. L.; Yu, K. W.

2000-04-01

The real-time dynamics of various relaxation phenomena can be conveniently formulated by a master equation with the enumeration of transition rates between given classes of conformations. To study the relaxation time towards equilibrium, it suffices to solve for the second largest eigenvalue of the resulting eigenvalue equation. Generally speaking, there is no analytic solution for the dynamic equation. Mean-field approaches generally yield misleading results while the presumably exact Monte-Carlo methods require prohibitive time steps in most real systems. In this work, we propose an exact decimation procedure for reducing the number of conformations significantly, while there is no loss of information, i.e., the reduced (or effective) equation is an exact transformed version of the original one. However, we have to pay the price: the initial Markovianity of the evolution equation is lost and the reduced equation contains memory terms in the transition rates. Since the transformed equation has significantly reduced number of degrees of freedom, the systems can readily be diagonalized by iterative means, to obtain the exact second largest eigenvalue and hence the relaxation time. The decimation method has been applied to various relaxation equations with generally desirable results. The advantages and limitations of the method will be discussed.

Classifying bilinear differential equations by linear superposition principle

NASA Astrophysics Data System (ADS)

Zhang, Lijun; Khalique, Chaudry Masood; Ma, Wen-Xiu

2016-09-01

In this paper, we investigate the linear superposition principle of exponential traveling waves to construct a sub-class of N-wave solutions of Hirota bilinear equations. A necessary and sufficient condition for Hirota bilinear equations possessing this specific sub-class of N-wave solutions is presented. We apply this result to find N-wave solutions to the (2+1)-dimensional KP equation, a (3+1)-dimensional generalized Kadomtsev-Petviashvili (KP) equation, a (3+1)-dimensional generalized BKP equation and the (2+1)-dimensional BKP equation. The inverse question, i.e., constructing Hirota Bilinear equations possessing N-wave solutions, is considered and a refined 3-step algorithm is proposed. As examples, we construct two very general kinds of Hirota bilinear equations of order 4 possessing N-wave solutions among which one satisfies dispersion relation and another does not satisfy dispersion relation.

Equations for Automotive-Transmission Performance

NASA Technical Reports Server (NTRS)

Chazanoff, S.; Aston, M. B.; Chapman, C. P.

1984-01-01

Curve-fitting procedure ensures high confidence levels. Threedimensional plot represents performance of small automatic transmission coasting in second gear. In equation for plot, PL power loss, S speed and T torque. Equations applicable to manual and automatic transmissions over wide range of speed, torque, and efficiency.

Stratifying empiric risk of schizophrenia among first degree relatives using multiple predictors in two independent Indian samples.

PubMed

Bhatia, Triptish; Gettig, Elizabeth A; Gottesman, Irving I; Berliner, Jonathan; Mishra, N N; Nimgaonkar, Vishwajit L; Deshpande, Smita N

2016-12-01

Schizophrenia (SZ) has an estimated heritability of 64-88%, with the higher values based on twin studies. Conventionally, family history of psychosis is the best individual-level predictor of risk, but reliable risk estimates are unavailable for Indian populations. Genetic, environmental, and epigenetic factors are equally important and should be considered when predicting risk in 'at risk' individuals. To estimate risk based on an Indian schizophrenia participant's family history combined with selected demographic factors. To incorporate variables in addition to family history, and to stratify risk, we constructed a regression equation that included demographic variables in addition to family history. The equation was tested in two independent Indian samples: (i) an initial sample of SZ participants (N=128) with one sibling or offspring; (ii) a second, independent sample consisting of multiply affected families (N=138 families, with two or more sibs/offspring affected with SZ). The overall estimated risk was 4.31±0.27 (mean±standard deviation). There were 19 (14.8%) individuals in the high risk group, 75 (58.6%) in the moderate risk and 34 (26.6%) in the above average risk (in Sample A). In the validation sample, risks were distributed as: high (45%), moderate (38%) and above average (17%). Consistent risk estimates were obtained from both samples using the regression equation. Familial risk can be combined with demographic factors to estimate risk for SZ in India. If replicated, the proposed stratification of risk may be easier and more realistic for family members. Copyright © 2016. Published by Elsevier B.V.

Symmetry classification of time-fractional diffusion equation

NASA Astrophysics Data System (ADS)

Naeem, I.; Khan, M. D.

2017-01-01

In this article, a new approach is proposed to construct the symmetry groups for a class of fractional differential equations which are expressed in the modified Riemann-Liouville fractional derivative. We perform a complete group classification of a nonlinear fractional diffusion equation which arises in fractals, acoustics, control theory, signal processing and many other applications. Introducing the suitable transformations, the fractional derivatives are converted to integer order derivatives and in consequence the nonlinear fractional diffusion equation transforms to a partial differential equation (PDE). Then the Lie symmetries are computed for resulting PDE and using inverse transformations, we derive the symmetries for fractional diffusion equation. All cases are discussed in detail and results for symmetry properties are compared for different values of α. This study provides a new way of computing symmetries for a class of fractional differential equations.

Stochastic differential equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sobczyk, K.

1990-01-01

This book provides a unified treatment of both regular (or random) and Ito stochastic differential equations. It focuses on solution methods, including some developed only recently. Applications are discussed, in particular an insight is given into both the mathematical structure, and the most efficient solution methods (analytical as well as numerical). Starting from basic notions and results of the theory of stochastic processes and stochastic calculus (including Ito's stochastic integral), many principal mathematical problems and results related to stochastic differential equations are expounded here for the first time. Applications treated include those relating to road vehicles, earthquake excitations and offshoremore » structures.« less

The study of nonlinear almost periodic differential equations without recourse to the H-classes of these equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Slyusarchuk, V. E., E-mail: V.E.Slyusarchuk@gmail.com, E-mail: V.Ye.Slyusarchuk@NUWM.rv.ua

2014-06-01

The well-known theorems of Favard and Amerio on the existence of almost periodic solutions to linear and nonlinear almost periodic differential equations depend to a large extent on the H-classes and the requirement that the bounded solutions of these equations be separated. The present paper provides different conditions for the existence of almost periodic solutions. These conditions, which do not depend on the H-classes of the equations, are formulated in terms of a special functional on the set of bounded solutions of the equations under consideration. This functional is used, in particular, to test whether solutions are separated. Bibliography: 24more » titles. (paper)« less

Validating and Improving Interrill Erosion Equations

PubMed Central

Zhang, Feng-Bao; Wang, Zhan-Li; Yang, Ming-Yi

2014-01-01

Existing interrill erosion equations based on mini-plot experiments have largely ignored the effects of slope length and plot size on interrill erosion rate. This paper describes a series of simulated rainfall experiments which were conducted according to a randomized factorial design for five slope lengths (0.4, 0.8, 1.2, 1.6, and 2 m) at a width of 0.4 m, five slope gradients (17%, 27%, 36%, 47%, and 58%), and five rainfall intensities (48, 62.4, 102, 149, and 170 mm h−1) to perform a systematic validation of existing interrill erosion equations based on mini-plots. The results indicated that the existing interrill erosion equations do not adequately describe the relationships between interrill erosion rate and its influencing factors with increasing slope length and rainfall intensity. Univariate analysis of variance showed that runoff rate, rainfall intensity, slope gradient, and slope length had significant effects on interrill erosion rate and that their interactions were significant at p = 0.01. An improved interrill erosion equation was constructed by analyzing the relationships of sediment concentration with rainfall intensity, slope length, and slope gradient. In the improved interrill erosion equation, the runoff rate and slope factor are the same as in the interrill erosion equation in the Water Erosion Prediction Project (WEPP), with the weight of rainfall intensity adjusted by an exponent of 0.22 and a slope length term added with an exponent of −0.25. Using experimental data from WEPP cropland soil field interrill erodibility experiments, it has been shown that the improved interrill erosion equation describes the relationship between interrill erosion rate and runoff rate, rainfall intensity, slope gradient, and slope length reasonably well and better than existing interrill erosion equations. PMID:24516624

Self-Regulated Strategy Development Instruction for Teaching Multi-Step Equations to Middle School Students Struggling in Math

ERIC Educational Resources Information Center

Cuenca-Carlino, Yojanna; Freeman-Green, Shaqwana; Stephenson, Grant W.; Hauth, Clara

2016-01-01

Six middle school students identified as having a specific learning disability or at risk for mathematical difficulties were taught how to solve multi-step equations by using the self-regulated strategy development (SRSD) model of instruction. A multiple-probe-across-pairs design was used to evaluate instructional effects. Instruction was provided…

Rationale and design of the ADDITION-Leicester study, a systematic screening programme and Randomised Controlled Trial of multi-factorial cardiovascular risk intervention in people with Type 2 Diabetes Mellitus detected by screening

PubMed Central

2010-01-01

Background Earlier diagnosis followed by multi-factorial cardiovascular risk intervention may improve outcomes in Type 2 Diabetes Mellitus (T2DM). Latent phase identification through screening requires structured, appropriately targeted population-based approaches. Providers responsible for implementing screening policy await evidence of clinical and cost effectiveness from randomised intervention trials in screen-detected T2DM cases. UK South Asians are at particularly high risk of abnormal glucose tolerance and T2DM. To be effective national screening programmes must achieve good coverage across the population by identifying barriers to the detection of disease and adapting to the delivery of earlier care. Here we describe the rationale and methods of a systematic community screening programme and randomised controlled trial of cardiovascular risk management within a UK multiethnic setting (ADDITION-Leicester). Design A single-blind cluster randomised, parallel group trial among people with screen-detected T2DM comparing a protocol driven intensive multi-factorial treatment with conventional care. Methods ADDITION-Leicester consists of community-based screening and intervention phases within 20 general practices coordinated from a single academic research centre. Screening adopts a universal diagnostic approach via repeated 75g-Oral Glucose Tolerance Tests within an eligible non-diabetic population of 66,320 individuals aged 40-75 years (25-75 years South Asian). Volunteers also provide detailed medical and family histories; complete health questionnaires, undergo anthropometric measures, lipid profiling and a proteinuria assessment. Primary outcome is reduction in modelled Coronary Heart Disease (UKPDS CHD) risk at five years. Seven thousand (30% of South Asian ethnic origin) volunteers over three years will be recruited to identify a screen-detected T2DM cohort (n = 285) powered to detected a 6% relative difference (80% power, alpha 0.05) between treatment

Students' Understanding of Quadratic Equations

ERIC Educational Resources Information Center

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…

The GUP and quantum Raychaudhuri equation

NASA Astrophysics Data System (ADS)

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.

Critical spaces for quasilinear parabolic evolution equations and applications

NASA Astrophysics Data System (ADS)

Prüss, Jan; Simonett, Gieri; Wilke, Mathias

2018-02-01

We present a comprehensive theory of critical spaces for the broad class of quasilinear parabolic evolution equations. The approach is based on maximal Lp-regularity in time-weighted function spaces. It is shown that our notion of critical spaces coincides with the concept of scaling invariant spaces in case that the underlying partial differential equation enjoys a scaling invariance. Applications to the vorticity equations for the Navier-Stokes problem, convection-diffusion equations, the Nernst-Planck-Poisson equations in electro-chemistry, chemotaxis equations, the MHD equations, and some other well-known parabolic equations are given.

High risk sexual behaviors for HIV among the in-school youth in Swaziland: a structural equation modeling approach.

PubMed

Sacolo, Hlengiwe Nokuthula; Chung, Min-Huey; Chu, Hsin; Liao, Yuan-Mei; Chen, Chiung-Hua; Ou, Keng-Liang; Chang, Lu-I; Chou, Kuei-Ru

2013-01-01

Global efforts in response to the increased prevalence of the human immunodeficiency virus (HIV) are mainly aimed at reducing high risk sexual behaviors among young people. However, knowledge regarding intentions of young people to engage in protective sexual behaviors is still lacking in many countries around the world, especially in Sub-Saharan Africa where prevalence of human immunodeficiency virus is the highest. The objective of this study was to test the theory of planned behavior (TPB) for predicting factors associated with protective sexual behaviors, including sexual abstinence and condom use, among in-school youths aged between 15 and 19 years in Swaziland. This cross-sectional survey was conducted using a anonymous questionnaire. A two-stage stratified and cluster random sampling method was used. Approximately one hundred pupils from each of four schools agreed to participate in the study, providing a total sample size of 403 pupils of which 369 were ultimately included for data analysis. The response rate was 98%. Structural equation modeling was used to analyse hypothesized paths. The TPB model used in this study was effective in predicting protective sexual behavior among Swazi in-school youths, as shown by model fit indices. All hypothesized constructs significantly predicted intentions for abstinence and condom use, except perceived abstinence controls. Subjective norms were the strongest predictors of intention for premarital sexual abstinence; however, perceived controls for condom use were the strongest predictors of intention for condom use. Our findings support application of the model in predicting determinants of condom use and abstinence intentions among Swazi in-school youths.

High Risk Sexual Behaviors for HIV among the In-School Youth in Swaziland: A Structural Equation Modeling Approach

PubMed Central

Chu, Hsin; Liao, Yuan-Mei; Chen, Chiung-Hua; Ou, Keng-Liang; Chang, Lu-I; Chou, Kuei-Ru

2013-01-01

Background Global efforts in response to the increased prevalence of the human immunodeficiency virus (HIV) are mainly aimed at reducing high risk sexual behaviors among young people. However, knowledge regarding intentions of young people to engage in protective sexual behaviors is still lacking in many countries around the world, especially in Sub-Saharan Africa where prevalence of human immunodeficiency virus is the highest. The objective of this study was to test the theory of planned behavior (TPB) for predicting factors associated with protective sexual behaviors, including sexual abstinence and condom use, among in-school youths aged between 15 and 19 years in Swaziland. Methods This cross-sectional survey was conducted using a anonymous questionnaire. A two-stage stratified and cluster random sampling method was used. Approximately one hundred pupils from each of four schools agreed to participate in the study, providing a total sample size of 403 pupils of which 369 were ultimately included for data analysis. The response rate was 98%. Structural equation modeling was used to analyse hypothesized paths. Results The TPB model used in this study was effective in predicting protective sexual behavior among Swazi in-school youths, as shown by model fit indices. All hypothesized constructs significantly predicted intentions for abstinence and condom use, except perceived abstinence controls. Subjective norms were the strongest predictors of intention for premarital sexual abstinence; however, perceived controls for condom use were the strongest predictors of intention for condom use. Conclusions Our findings support application of the model in predicting determinants of condom use and abstinence intentions among Swazi in-school youths. PMID:23861756

Alternate Solution to Generalized Bernoulli Equations via an Integrating Factor: An Exact Differential Equation Approach

ERIC Educational Resources Information Center

Tisdell, C. C.

2017-01-01

Solution methods to exact differential equations via integrating factors have a rich history dating back to Euler (1740) and the ideas enjoy applications to thermodynamics and electromagnetism. Recently, Azevedo and Valentino presented an analysis of the generalized Bernoulli equation, constructing a general solution by linearizing the problem…

Relationship between estimated cardiovascular disease risk and insulin resistance in a black African population living with HIV: a cross-sectional study from Cameroon.

PubMed

Noumegni, Steve Raoul; Bigna, Jean Joel; Ama Moor Epse Nkegoum, Vicky Jocelyne; Nansseu, Jobert Richie; Assah, Felix K; Jingi, Ahmadou Musa; Guewo-Fokeng, Magellan; Leumi, Steve; Katte, Jean-Claude; Dehayem, Mesmin Y; Mfeukeu Kuate, Liliane; Kengne, Andre Pascal; Sobngwi, Eugene

2017-08-11

Cardiovascular disease (CVD) and metabolic diseases are growing concerns among patients with HIV infection as a consequence of the improving survival of this population. We aimed to assess the relationship between CVD risk and insulin resistance in a group of black African individuals with HIV infection. This cross-sectional study involved patients with HIV infection aged 30-74 years and followed up at the Yaoundé Central Hospital, Cameroon. Absolute CVD risk was calculated using the Framingham and the DAD CVD risk equations while the HOMA-IR index was used to assess insulin resistance (index ≥2.1). A total of 452 patients (361 women; 80%) were screened. The mean age was 44.4 years and most of the respondents were on antiretroviral therapy (88.5%). The median 5-year cardiovascular risk was 0.7% (25th-75th percentiles: 0.2-2.0) and 0.6% (0.3-1.3) according to the Framingham and DAD equations respectively. Of all participants, 47.3% were insulin resistant. The Framingham equation derived absolute CVD risk was significantly associated with insulin resistance; while no linear association was found using the DAD equation. The relationship between cardiovascular risk and insulin resistance in black African patients with HIV infection seems to depend on the cardiovascular risk equation used. © Article author(s) (or their employer(s) unless otherwise stated in the text of the article) 2017. All rights reserved. No commercial use is permitted unless otherwise expressly granted.

Derivation of the Schrodinger Equation from the Hamilton-Jacobi Equation in Feynman's Path Integral Formulation of Quantum Mechanics

ERIC Educational Resources Information Center

Field, J. H.

2011-01-01

It is shown how the time-dependent Schrodinger equation may be simply derived from the dynamical postulate of Feynman's path integral formulation of quantum mechanics and the Hamilton-Jacobi equation of classical mechanics. Schrodinger's own published derivations of quantum wave equations, the first of which was also based on the Hamilton-Jacobi…

Coupled rotor and fuselage equations of motion

NASA Technical Reports Server (NTRS)

Warmbrodt, W.

1979-01-01

The governing equations of motion of a helicopter rotor coupled to a rigid body fuselage are derived. A consistent formulation is used to derive nonlinear periodic coefficient equations of motion which are used to study coupled rotor/fuselage dynamics in forward flight. Rotor/fuselage coupling is documented and the importance of an ordering scheme in deriving nonlinear equations of motion is reviewed. The nature of the final equations and the use of multiblade coordinates are discussed.

Nonlinear acoustic wave equations with fractional loss operators.

PubMed

Prieur, Fabrice; Holm, Sverre

2011-09-01

Fractional derivatives are well suited to describe wave propagation in complex media. When introduced in classical wave equations, they allow a modeling of attenuation and dispersion that better describes sound propagation in biological tissues. Traditional constitutive equations from solid mechanics and heat conduction are modified using fractional derivatives. They are used to derive a nonlinear wave equation which describes attenuation and dispersion laws that match observations. This wave equation is a generalization of the Westervelt equation, and also leads to a fractional version of the Khokhlov-Zabolotskaya-Kuznetsov and Burgers' equations. © 2011 Acoustical Society of America

Fractional-calculus diffusion equation

PubMed Central

2010-01-01

Background Sequel to the work on the quantization of nonconservative systems using fractional calculus and quantization of a system with Brownian motion, which aims to consider the dissipation effects in quantum-mechanical description of microscale systems. Results The canonical quantization of a system represented classically by one-dimensional Fick's law, and the diffusion equation is carried out according to the Dirac method. A suitable Lagrangian, and Hamiltonian, describing the diffusive system, are constructed and the Hamiltonian is transformed to Schrodinger's equation which is solved. An application regarding implementation of the developed mathematical method to the analysis of diffusion, osmosis, which is a biological application of the diffusion process, is carried out. Schrödinger's equation is solved. Conclusions The plot of the probability function represents clearly the dissipative and drift forces and hence the osmosis, which agrees totally with the macro-scale view, or the classical-version osmosis. PMID:20492677

On the Mo-Papas equation

NASA Astrophysics Data System (ADS)

Aguirregabiria, J. M.; Chamorro, A.; Valle, M. A.

1982-05-01

A new heuristic derivation of the Mo-Papas equation for charged particles is given. It is shown that this equation cannot be derived for a point particle by closely following Dirac's classical treatment of the problem. The Mo-Papas theory and the Bonnor-Rowe-Marx variable mass dynamics are not compatible.

Generalized Multilevel Structural Equation Modeling

ERIC Educational Resources Information Center

Rabe-Hesketh, Sophia; Skrondal, Anders; Pickles, Andrew

2004-01-01

A unifying framework for generalized multilevel structural equation modeling is introduced. The models in the framework, called generalized linear latent and mixed models (GLLAMM), combine features of generalized linear mixed models (GLMM) and structural equation models (SEM) and consist of a response model and a structural model for the latent…

Localization of the eigenvalues of linear integral equations with applications to linear ordinary differential equations.

NASA Technical Reports Server (NTRS)

Sloss, J. M.; Kranzler, S. K.

1972-01-01

The equivalence of a considered integral equation form with an infinite system of linear equations is proved, and the localization of the eigenvalues of the infinite system is expressed. Error estimates are derived, and the problems of finding upper bounds and lower bounds for the eigenvalues are solved simultaneously.

Relationship between Anthropometric Measures and Cardiovascular Risk Factors in Children and Adolescents

PubMed Central

Burgos, Miria Suzana; Burgos, Leandro Tibiriçá; Camargo, Marcelo Dias; Franke, Silvia Isabel Rech; Prá, Daniel; da Silva, Antônio Marcos Vargas; Borges, Tássia Silvana; Todendi, Pâmela Ferreira; Reckziegel, Miriam Beatris; Reuter, Cézane Priscila

2013-01-01

Background Obesity has been identified as an important risk factor in the development of cardiovascular diseases; however, other factors, combined or not with obesity, can influence cardiovascular risk and should be considered in cardiovascular risk stratification in pediatrics. Objective To analyze the association between anthropometry measures and cardiovascular risk factors, to investigate the determinants to changes in blood pressure (BP), and to propose a prediction equation to waist circumference (WC) in children and adolescents. Methods We evaluated 1,950 children and adolescents, aged 7 to 18 years. Visceral fat was assessed by WC and waist hip relationship, BP and body mass index (BMI). In a randomly selected subsample of these volunteers (n = 578), total cholesterol, glucose and triglycerides levels were evaluated. Results WC was positively correlated with BMI (r = 0.85; p < 0.001) and BP (SBP r = 0.45 and DBP = 0.37; p < 0.001). Glycaemia and triglycerides showed a weak correlation with WC (r = 0.110; p = 0.008 e r = 0.201; p < 0.001, respectively). Total cholesterol did not correlate with any of the variables. Age, BMI and WC were significant predictors on the regression models for BP (p < 0.001). We propose a WC prediction equation for children and adolescents: boys: y = 17.243 + 0.316 (height in cm); girls: y = 25.197 + 0.256 (height in cm). Conclusion WC is associated with cardiovascular risk factors and presents itself as a risk factor predictor of hypertension in children and adolescents. The WC prediction equation proposed by us should be tested in future studies. PMID:23979777

Exact solutions for (1 + 1)-dimensional nonlinear dispersive modified Benjamin-Bona-Mahony equation and coupled Klein-Gordon equations.

PubMed

Khan, Kamruzzaman; Akbar, M Ali; Islam, S M Rayhanul

2014-01-01

In this work, recently developed modified simple equation (MSE) method is applied to find exact traveling wave solutions of nonlinear evolution equations (NLEEs). To do so, we consider the (1 + 1)-dimensional nonlinear dispersive modified Benjamin-Bona-Mahony (DMBBM) equation and coupled Klein-Gordon (cKG) equations. Two classes of explicit exact solutions-hyperbolic and trigonometric solutions of the associated equations are characterized with some free parameters. Then these exact solutions correspond to solitary waves for particular values of the parameters. 02.30.Jr; 02.70.Wz; 05.45.Yv; 94.05.Fg.

The Bach equations in spin-coefficient form

NASA Astrophysics Data System (ADS)

Forbes, Hamish

2018-06-01

Conformal gravity theories are defined by field equations that determine only the conformal structure of the spacetime manifold. The Bach equations represent an early example of such a theory, we present them here in component form in terms of spin- and boost-weighted spin-coefficients using the compacted spin-coefficient formalism. These equations can be used as an efficient alternative to the standard tensor form. As a simple application we solve the Bach equations for pp-wave and static spherically symmetric spacetimes.

On implicit abstract neutral nonlinear differential equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hernández, Eduardo, E-mail: lalohm@ffclrp.usp.br; O’Regan, Donal, E-mail: donal.oregan@nuigalway.ie

2016-04-15

In this paper we continue our developments in Hernández and O’Regan (J Funct Anal 261:3457–3481, 2011) on the existence of solutions for abstract neutral differential equations. In particular we extend the results in Hernández and O’Regan (J Funct Anal 261:3457–3481, 2011) for the case of implicit nonlinear neutral equations and we focus on applications to partial “nonlinear” neutral differential equations. Some applications involving partial neutral differential equations are presented.

Simplified Relativistic Force Transformation Equation.

ERIC Educational Resources Information Center

Stewart, Benjamin U.

1979-01-01

A simplified relativistic force transformation equation is derived and then used to obtain the equation for the electromagnetic forces on a charged particle, calculate the electromagnetic fields due to a point charge with constant velocity, transform electromagnetic fields in general, derive the Biot-Savart law, and relate it to Coulomb's law.…

Shock formation in the dispersionless Kadomtsev-Petviashvili equation

NASA Astrophysics Data System (ADS)

Grava, T.; Klein, C.; Eggers, J.

2016-04-01

The dispersionless Kadomtsev-Petviashvili (dKP) equation {{≤ft({{u}t}+u{{u}x}\\right)}x}={{u}yy} is one of the simplest nonlinear wave equations describing two-dimensional shocks. To solve the dKP equation numerically we use a coordinate transformation inspired by the method of characteristics for the one-dimensional Hopf equation {{u}t}+u{{u}x}=0 . We show numerically that the solutions to the transformed equation stays regular for longer times than the solution of the dKP equation. This permits us to extend the dKP solution as the graph of a multivalued function beyond the critical time when the gradients blow up. This overturned solution is multivalued in a lip shape region in the (x, y) plane, where the solution of the dKP equation exists in a weak sense only, and a shock front develops. A local expansion reveals the universal scaling structure of the shock, which after a suitable change of coordinates corresponds to a generic cusp catastrophe. We provide a heuristic derivation of the shock front position near the critical point for the solution of the dKP equation, and study the solution of the dKP equation when a small amount of dissipation is added. Using multiple-scale analysis, we show that in the limit of small dissipation and near the critical point of the dKP solution, the solution of the dissipative dKP equation converges to a Pearcey integral. We test and illustrate our results by detailed comparisons with numerical simulations of both the regularized equation, the dKP equation, and the asymptotic description given in terms of the Pearcey integral.

Boundary-layer equations in generalized curvilinear coordinates

NASA Technical Reports Server (NTRS)

Panaras, Argyris G.

1987-01-01

A set of higher-order boundary-layer equations is derived valid for three-dimensional compressible flows. The equations are written in a generalized curvilinear coordinate system, in which the surface coordinates are nonorthogonal; the third axis is restricted to be normal to the surface. Also, higher-order viscous terms which are retained depend on the surface curvature of the body. Thus, the equations are suitable for the calculation of the boundary layer about arbitrary vehicles. As a starting point, the Navier-Stokes equations are derived in a tensorian notation. Then by means of an order-of-magnitude analysis, the boundary-layer equations are developed. To provide an interface between the analytical partial differentiation notation and the compact tensor notation, a brief review of the most essential theorems of the tensor analysis related to the equations of the fluid dynamics is given. Many useful quantities, such as the contravariant and the covariant metrics and the physical velocity components, are written in both notations.

Equivalent equations of motion for gravity and entropy

DOE Office of Scientific and Technical Information (OSTI.GOV)

Czech, Bartlomiej; Lamprou, Lampros; McCandlish, Samuel

We demonstrate an equivalence between the wave equation obeyed by the entanglement entropy of CFT subregions and the linearized bulk Einstein equation in Anti-de Sitter space. In doing so, we make use of the formalism of kinematic space and fields on this space. We show that the gravitational dynamics are equivalent to a gauge invariant wave-equation on kinematic space and that this equation arises in natural correspondence to the conformal Casimir equation in the CFT.

Equivalent equations of motion for gravity and entropy

DOE PAGES

Czech, Bartlomiej; Lamprou, Lampros; McCandlish, Samuel; ...

2017-02-01

We demonstrate an equivalence between the wave equation obeyed by the entanglement entropy of CFT subregions and the linearized bulk Einstein equation in Anti-de Sitter space. In doing so, we make use of the formalism of kinematic space and fields on this space. We show that the gravitational dynamics are equivalent to a gauge invariant wave-equation on kinematic space and that this equation arises in natural correspondence to the conformal Casimir equation in the CFT.

Applications of Capstone depleted uranium aerosol risk data to military combat risk management.

PubMed

Daxon, Eric G; Parkhurst, Mary Ann; Melanson, Mark A; Roszell, Laurie E

2009-03-01

Risks to personnel engaged in military operations include not only the threat of enemy firepower but also risks from exposure to other hazards such as radiation. Combatant commanders of the U.S. Army carefully weigh risks of casualties before implementing battlefield actions using an established paradigm that takes these risks into consideration. As a result of the inclusion of depleted uranium (DU) anti-armor ammunition in the conventional (non-nuclear) weapons arsenal, the potential for exposure to DU aerosols and its associated chemical and radiological effects becomes an element of the commanders' risk assessment. The Capstone DU Aerosol Study measured the range of likely DU oxide aerosol concentrations created inside a combat vehicle perforated with a DU munition, and the Capstone Human Health Risk Assessment (HHRA) estimated the associated doses and calculated risks. This paper focuses on the development of a scientific approach to adapt the risks from DU's non-uniform dose distribution within the body using the current U.S. Department of Defense radiation risk management approach. The approach developed equates the Radiation Exposure Status categories to the estimated radiological risks of DU and makes use of the Capstone-developed Renal Effects Group as a measure of chemical risk from DU intake. Recommendations are provided for modifying Army guidance and policy in order to better encompass the potential risks from DU aerosol inhalation during military operations.

Marcus equation

DOE R&D Accomplishments Database

1998-09-21

In the late 1950s to early 1960s Rudolph A. Marcus developed a theory for treating the rates of outer-sphere electron-transfer reactions. Outer-sphere reactions are reactions in which an electron is transferred from a donor to an acceptor without any chemical bonds being made or broken. (Electron-transfer reactions in which bonds are made or broken are referred to as inner-sphere reactions.) Marcus derived several very useful expressions, one of which has come to be known as the Marcus cross-relation or, more simply, as the Marcus equation. It is widely used for correlating and predicting electron-transfer rates. For his contributions to the understanding of electron-transfer reactions, Marcus received the 1992 Nobel Prize in Chemistry. This paper discusses the development and use of the Marcus equation. Topics include self-exchange reactions; net electron-transfer reactions; Marcus cross-relation; and proton, hydride, atom and group transfers.

Green function of the double-fractional Fokker-Planck equation: path integral and stochastic differential equations.

PubMed

Kleinert, H; Zatloukal, V

2013-11-01

The statistics of rare events, the so-called black-swan events, is governed by non-Gaussian distributions with heavy power-like tails. We calculate the Green functions of the associated Fokker-Planck equations and solve the related stochastic differential equations. We also discuss the subject in the framework of path integration.

Evaluation of various equations for estimating renal function in elderly Chinese patients with type 2 diabetes mellitus

PubMed Central

Guo, Mei; Niu, Jian-Ying; Ye, Xian-Wu; Han, Xiao-Jie; Zha, Ying; Hong, Yang; Fang, Hong; Gu, Yong

2017-01-01

Background The clinical assessment of kidney function based on the estimated glomerular filtration rate (GFR) in older patients remains controversial. This study evaluated the concordance and feasibility of using various creatinine-based equations for estimating GFR in elderly Chinese patients with type 2 diabetes mellitus (T2DM). Methods A cross-sectional analytical study was conducted in 21,723 older diabetic patients (≥60 years) based on electronic health records (EHR) for Minhang District, Shanghai, China. The concordance of chronic kidney disease (CKD) classification among different creatinine-based equations was assessed based on Kappa values, intraclass correlation coefficient (ICC) statistics, and the eGFR agreement between the equations was tested using Bland–Altman plots. The GFR was estimated using the Cockcroft–Gault (CG), Berlin Initiative Study 1 (BIS1), simplified Modification of Diet in Renal Disease (MDRD), MDRD modified for Chinese populations (mMDRD), chronic kidney disease epidemiology collaboration (CKD-EPI), CKD-EPI in Asians (CKD-EPI-Asia), and Ruijin equations. Results Overall, the proportion of CKD stages 3–5 (eGFR <60 mL/min/1.73 m2) was calculated as 28.9%, 39.1%, 11.8%, 8.4%, 14.3%, 11.5%, and 12.7% by the eGFRCG, eGFRBIS1, eGFRMDRD, eGFRmMDRD, eGFRCKD-EPI, eGFRCKD-EPI-Asia, and eGFRRuijin equations, respectively. The concordance of albuminuria and decreased eGFR based on the different equations was poor by both the Kappa (<0.2) and ICC (<0.4) statistics. The CKD-EPI-Asia equation resulted in excellent concordance with the CKD-EPI (ICC =0.931), MDRD (ICC =0.963), mMDRD (ICC =0.892), and Ruijin (ICC =0.956) equations for the classification of CKD stages, whereas the BIS1 equation exhibited good concordance with the CG equation (ICC =0.809). In addition, significant differences were observed for CKD stage 1 among all these equations. Conclusion Accurate GFR values are difficult to estimate using creatinine-based equations in older

Solving Absolute Value Equations Algebraically and Geometrically

ERIC Educational Resources Information Center

Shiyuan, Wei

2005-01-01

The way in which students can improve their comprehension by understanding the geometrical meaning of algebraic equations or solving algebraic equation geometrically is described. Students can experiment with the conditions of the absolute value equation presented, for an interesting way to form an overall understanding of the concept.

Equational Sentence Structure in Eskimo.

ERIC Educational Resources Information Center

Hofmann, Th. R.

A comparison of the syntactic characteristics of mathematical equations and Eskimo syntax is made, and a proposal that Eskimo has a level of structure similar to that of equations is described. P:t performative contrast is reanalyzed. Questions and speculations on the formal treatment of this type of structure in transformational grammar, and its…

Graphical Solution of Polynomial Equations

ERIC Educational Resources Information Center

Grishin, Anatole

2009-01-01

Graphing utilities, such as the ubiquitous graphing calculator, are often used in finding the approximate real roots of polynomial equations. In this paper the author offers a simple graphing technique that allows one to find all solutions of a polynomial equation (1) of arbitrary degree; (2) with real or complex coefficients; and (3) possessing…

Kinetic Equation for an Unstable Plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Balescu, R.

1963-01-01

A kinetic equation is derived for the description of the evolution in time of the distribution of velocities in a spatially homogeneous ionized gas that, at the initial time, is able to sustain exponentially growing oscillations. This equation is expressed in terms of a functional of the distribution finction that obeys the same integral equation as in the stable case. Although the method of solution used in the stable case breaks down, the equation can still be solved in closed form under unstable conditions, and hence an explicit form of the kinetic equation is obtained. The latter contains the normalmore » collision term and a new additional term describing the stabilization of the plasma. The latter acts through friction and diffusion and brings the plasma into a state of neutral stability. From there on the system evolves toward thermal equilibrium under the action of the normal collision term as well as of an additional Fokker-Planck- like term with timedependent coefficients, which however becomes less and less efficient as the plasma approaches equilibrium.« less

Non-autonomous equations with unpredictable solutions

NASA Astrophysics Data System (ADS)

Akhmet, Marat; Fen, Mehmet Onur

2018-06-01

To make research of chaos more amenable to investigating differential and discrete equations, we introduce the concepts of an unpredictable function and sequence. The topology of uniform convergence on compact sets is applied to define unpredictable functions [1,2]. The unpredictable sequence is defined as a specific unpredictable function on the set of integers. The definitions are convenient to be verified as solutions of differential and discrete equations. The topology is metrizable and easy for applications with integral operators. To demonstrate the effectiveness of the approach, the existence and uniqueness of the unpredictable solution for a delay differential equation are proved as well as for quasilinear discrete systems. As a corollary of the theorem, a similar assertion for a quasilinear ordinary differential equation is formulated. The results are demonstrated numerically, and an application to Hopfield neural networks is provided. In particular, Poincaré chaos near periodic orbits is observed. The completed research contributes to the theory of chaos as well as to the theory of differential and discrete equations, considering unpredictable solutions.

Generalized Landau Equation for a System with a Self-Consistent Mean Field - Derivation from an N-Particle Liouville Equation

NASA Astrophysics Data System (ADS)

Kandrup, H.

1981-02-01

Assume that the evolution of a system is determined by an N-particle Liouville equation. Suppose, moreover, that the particles which compose the system interact via a long range force like gravity so that the system will be spatially inhomogeneous. In this case, the mean force acting upon a test particle does not vanish, so that one wishes to isolate a self-consistent mean field and distinguish its "systematic" effects from the effects of "fluctuations." This is done here. The time-dependent projection operator formalism of Willis and Picard is used to obtain an exact equation for the time evolution of an appropriately defined one-particle probability density. If one implements the assumption that the "fluctuation" time scale is much shorter than both the relaxation and dynamical time scales, this exact equation can be approximated as a closed Markovian equation. In the limiting case of spatial homogeneity, one recovers precisely the standard Landau equation, which is customarily derived by a stochastic binary-encounter argument. This equation is contrasted with the standard heuristic equation for a mean field theory, as formulated for a Newtonian r-1 gravitational potential in stellar dynamics.

Generalized spheroidal wave equation and limiting cases

NASA Astrophysics Data System (ADS)

Figueiredo, B. D. Bonorino

2007-01-01

We find sets of solutions to the generalized spheroidal wave equation (GSWE) or, equivalently, to the confluent Heun equation. Each set is constituted by three solutions, one given by a series of ascending powers of the independent variable, and the others by series of regular and irregular confluent hypergeometric functions. For a fixed set, the solutions converge over different regions of the complex plane but present series coefficients proportional to each other. These solutions for the GSWE afford solutions to a double-confluent Heun equation by a taking-limit process due to Leaver. [E. W. Leaver, J. Math. Phys. 27, 1238 (1986)]. Another procedure, called Whittaker-Ince limit [B. D. Figueiredo, J. Math. Phys. 46, 113503 (2005)], provides solutions in series of powers and Bessel functions for two other equations with a different type of singularity at infinity. In addition, new solutions are obtained for the Whittaker-Hill and Mathieu equations [F. M. Arscott, Proc. R. Soc. Edinburg A67, 265 (1967)] by considering these as special cases of both the confluent and double-confluent Heun equations. In particular, we find that each of the Lindemann-Stieltjes solutions for the Mathieu equation [E. T. Whittaker and G. N. Watson, A Course of Modern Analysis, Cambridge University Press (1945)] is associated with two expansions in series of Bessel functions. We also discuss a set of solutions in series of hypergeometric and confluent hypergeometric functions for the GSWE and use their Leaver limits to obtain infinite-series solutions for the Schrödinger equation with an asymmetric double-Morse potential. Finally, the possibility of extending the solutions of the GSWE to the general Heun equation is briefly discussed.

Transitional Instability, Psychological Health, and Sexual Risk Taking among College Students

ERIC Educational Resources Information Center

Bowers, Jill R.; Segrin, Chris

2017-01-01

This study examined the effects of transitional instability on college students' (n = 402) psychological distress and sexual risk taking at two different time points over one year. Tested through structural equation models, the data revealed transitional instability had significant positive effects on psychological distress and sexual risk taking…

Gravitational closure of matter field equations

NASA Astrophysics Data System (ADS)

Düll, Maximilian; Schuller, Frederic P.; Stritzelberger, Nadine; Wolz, Florian

2018-04-01

The requirement that both the matter and the geometry of a spacetime canonically evolve together, starting and ending on shared Cauchy surfaces and independently of the intermediate foliation, leaves one with little choice for diffeomorphism-invariant gravitational dynamics that can equip the coefficients of a given system of matter field equations with causally compatible canonical dynamics. Concretely, we show how starting from any linear local matter field equations whose principal polynomial satisfies three physicality conditions, one may calculate coefficient functions which then enter an otherwise immutable set of countably many linear homogeneous partial differential equations. Any solution of these so-called gravitational closure equations then provides a Lagrangian density for any type of tensorial geometry that features ultralocally in the initially specified matter Lagrangian density. Thus the given system of matter field equations is indeed closed by the so obtained gravitational equations. In contrast to previous work, we build the theory on a suitable associated bundle encoding the canonical configuration degrees of freedom, which allows one to include necessary constraints on the geometry in practically tractable fashion. By virtue of the presented mechanism, one thus can practically calculate, rather than having to postulate, the gravitational theory that is required by specific matter field dynamics. For the special case of standard model matter one obtains general relativity.

Nonlinear Poisson Equation for Heterogeneous Media

PubMed Central

Hu, Langhua; Wei, Guo-Wei

2012-01-01

The Poisson equation is a widely accepted model for electrostatic analysis. However, the Poisson equation is derived based on electric polarizations in a linear, isotropic, and homogeneous dielectric medium. This article introduces a nonlinear Poisson equation to take into consideration of hyperpolarization effects due to intensive charges and possible nonlinear, anisotropic, and heterogeneous media. Variational principle is utilized to derive the nonlinear Poisson model from an electrostatic energy functional. To apply the proposed nonlinear Poisson equation for the solvation analysis, we also construct a nonpolar solvation energy functional based on the nonlinear Poisson equation by using the geometric measure theory. At a fixed temperature, the proposed nonlinear Poisson theory is extensively validated by the electrostatic analysis of the Kirkwood model and a set of 20 proteins, and the solvation analysis of a set of 17 small molecules whose experimental measurements are also available for a comparison. Moreover, the nonlinear Poisson equation is further applied to the solvation analysis of 21 compounds at different temperatures. Numerical results are compared to theoretical prediction, experimental measurements, and those obtained from other theoretical methods in the literature. A good agreement between our results and experimental data as well as theoretical results suggests that the proposed nonlinear Poisson model is a potentially useful model for electrostatic analysis involving hyperpolarization effects. PMID:22947937

Nonlinear Poisson equation for heterogeneous media.

PubMed

Hu, Langhua; Wei, Guo-Wei

2012-08-22

The Poisson equation is a widely accepted model for electrostatic analysis. However, the Poisson equation is derived based on electric polarizations in a linear, isotropic, and homogeneous dielectric medium. This article introduces a nonlinear Poisson equation to take into consideration of hyperpolarization effects due to intensive charges and possible nonlinear, anisotropic, and heterogeneous media. Variational principle is utilized to derive the nonlinear Poisson model from an electrostatic energy functional. To apply the proposed nonlinear Poisson equation for the solvation analysis, we also construct a nonpolar solvation energy functional based on the nonlinear Poisson equation by using the geometric measure theory. At a fixed temperature, the proposed nonlinear Poisson theory is extensively validated by the electrostatic analysis of the Kirkwood model and a set of 20 proteins, and the solvation analysis of a set of 17 small molecules whose experimental measurements are also available for a comparison. Moreover, the nonlinear Poisson equation is further applied to the solvation analysis of 21 compounds at different temperatures. Numerical results are compared to theoretical prediction, experimental measurements, and those obtained from other theoretical methods in the literature. A good agreement between our results and experimental data as well as theoretical results suggests that the proposed nonlinear Poisson model is a potentially useful model for electrostatic analysis involving hyperpolarization effects. Copyright © 2012 Biophysical Society. Published by Elsevier Inc. All rights reserved.

Students' Equation Understanding and Solving in Iran

ERIC Educational Resources Information Center

Barahmand, Ali; Shahvarani, Ahmad

2014-01-01

The purpose of the present article is to investigate how 15-year-old Iranian students interpret the concept of equation, its solution, and studying the relation between the students' equation understanding and solving. Data from two equation-solving exercises are reported. Data analysis shows that there is a significant relationship between…

Applying Meta-Analysis to Structural Equation Modeling

ERIC Educational Resources Information Center

Hedges, Larry V.

2016-01-01

Structural equation models play an important role in the social sciences. Consequently, there is an increasing use of meta-analytic methods to combine evidence from studies that estimate the parameters of structural equation models. Two approaches are used to combine evidence from structural equation models: A direct approach that combines…

From differential to difference equations for first order ODEs

NASA Technical Reports Server (NTRS)

Freed, Alan D.; Walker, Kevin P.

1991-01-01

When constructing an algorithm for the numerical integration of a differential equation, one should first convert the known ordinary differential equation (ODE) into an ordinary difference equation. Given this difference equation, one can develop an appropriate numerical algorithm. This technical note describes the derivation of two such ordinary difference equations applicable to a first order ODE. The implicit ordinary difference equation has the same asymptotic expansion as the ODE itself, whereas the explicit ordinary difference equation has an asymptotic that is similar in structure but different in value when compared with that of the ODE.

Multi-Hamiltonian structure of the Born-Infeld equation

NASA Astrophysics Data System (ADS)

Arik, Metin; Neyzi, Fahrünisa; Nutku, Yavuz; Olver, Peter J.; Verosky, John M.

1989-06-01

The multi-Hamiltonian structure, conservation laws, and higher order symmetries for the Born-Infeld equation are exhibited. A new transformation of the Born-Infeld equation to the equations of a Chaplygin gas is presented and explored. The Born-Infeld equation is distinguished among two-dimensional hyperbolic systems by its wealth of such multi-Hamiltonian structures.

xRage Equation of State

DOE Office of Scientific and Technical Information (OSTI.GOV)

Grove, John W.

2016-08-16

The xRage code supports a variety of hydrodynamic equation of state (EOS) models. In practice these are generally accessed in the executing code via a pressure-temperature based table look up. This document will describe the various models supported by these codes and provide details on the algorithms used to evaluate the equation of state.

More on a Functional Equation

ERIC Educational Resources Information Center

Deakin, Michael A. B.

2006-01-01

This classroom note presents a final solution for the functional equation: f(xy)=xf(y) + yf(x). The functional equation if formally similar to the familiar product rule of elementary calculus and this similarity prompted its study by Ren et al., who derived some results concerning it. The purpose of this present note is to extend these results and…

The applicability of eGFR equations to different populations.

PubMed

Delanaye, Pierre; Mariat, Christophe

2013-09-01

The Cockcroft-Gault equation for estimating glomerular filtration rate has been learnt by every generation of medical students over the decades. Since the publication of the Modification of Diet in Renal Disease (MDRD) study equation in 1999, however, the supremacy of the Cockcroft-Gault equation has been relentlessly disputed. More recently, the Chronic Kidney Disease Epidemiology (CKD-EPI) consortium has proposed a group of novel equations for estimating glomerular filtration rate (GFR). The MDRD and CKD-EPI equations were developed following a rigorous process, are expressed in a way in which they can be used with standardized biomarkers of GFR (serum creatinine and/or serum cystatin C) and have been evaluated in different populations of patients. Today, the MDRD Study equation and the CKD-EPI equation based on serum creatinine level have supplanted the Cockcroft-Gault equation. In many regards, these equations are superior to the Cockcroft-Gault equation and are now specifically recommended by international guidelines. With their generalized use, however, it has become apparent that those equations are not infallible and that they fail to provide an accurate estimate of GFR in certain situations frequently encountered in clinical practice. After describing the processes that led to the development of the new GFR-estimating equations, this Review discusses the clinical situations in which the applicability of these equations is questioned.

Some problems in fractal differential equations

NASA Astrophysics Data System (ADS)

Su, Weiyi

2016-06-01

Based upon the fractal calculus on local fields, or p-type calculus, or Gibbs-Butzer calculus ([1],[2]), we suggest a constructive idea for "fractal differential equations", beginning from some special examples to a general theory. However, this is just an original idea, it needs lots of later work to support. In [3], we show example "two dimension wave equations with fractal boundaries", and in this note, other examples, as well as an idea to construct fractal differential equations are shown.

Some More Solutions of Burgers' Equation

NASA Astrophysics Data System (ADS)

Kumar, Mukesh; Kumar, Raj

2015-01-01

In this work, similarity solutions of viscous one-dimensional Burgers' equation are attained by using Lie group theory. The symmetry generators are used for constructing Lie symmetries with commuting infinitesimal operators which lead the governing partial differential equation (PDE) to ordinary differential equation (ODE). Most of the constructed solutions are found in terms of Bessel functions which are new as far as authors are aware. Effect of various parameters in the evolutional profile of the solutions are shown graphically and discussed them physically.

Multigrid Techniques for Highly Indefinite Equations

NASA Technical Reports Server (NTRS)

Shapira, Yair

1996-01-01

A multigrid method for the solution of finite difference approximations of elliptic PDE's is introduced. A parallelizable version of it, suitable for two and multi level analysis, is also defined, and serves as a theoretical tool for deriving a suitable implementation for the main version. For indefinite Helmholtz equations, this analysis provides a suitable mesh size for the coarsest grid used. Numerical experiments show that the method is applicable to diffusion equations with discontinuous coefficients and highly indefinite Helmholtz equations.

Legendre-tau approximations for functional differential equations

NASA Technical Reports Server (NTRS)

Ito, K.; Teglas, R.

1986-01-01

The numerical approximation of solutions to linear retarded functional differential equations are considered using the so-called Legendre-tau method. The functional differential equation is first reformulated as a partial differential equation with a nonlocal boundary condition involving time-differentiation. The approximate solution is then represented as a truncated Legendre series with time-varying coefficients which satisfy a certain system of ordinary differential equations. The method is very easy to code and yields very accurate approximations. Convergence is established, various numerical examples are presented, and comparison between the latter and cubic spline approximation is made.

Legendre-Tau approximations for functional differential equations

NASA Technical Reports Server (NTRS)

Ito, K.; Teglas, R.

1983-01-01

The numerical approximation of solutions to linear functional differential equations are considered using the so called Legendre tau method. The functional differential equation is first reformulated as a partial differential equation with a nonlocal boundary condition involving time differentiation. The approximate solution is then represented as a truncated Legendre series with time varying coefficients which satisfy a certain system of ordinary differential equations. The method is very easy to code and yields very accurate approximations. Convergence is established, various numerical examples are presented, and comparison between the latter and cubic spline approximations is made.

Roy-Steiner equations for πN scattering

NASA Astrophysics Data System (ADS)

Ruiz de Elvira, J.; Ditsche, C.; Hoferichter, M.; Kubis, B.; Meißner, U.-G.

2014-06-01

In this talk, we present a coupled system of integral equations for the πN → πN (s-channel) and ππ → N̅N (t-channel) lowest partial waves, derived from Roy-Steiner equations for pion-nucleon scattering. After giving a brief overview of this system of equations, we present the solution of the t-channel sub-problem by means of Muskhelishvili-Omnès techniques, and solve the s-channel sub-problem after finding a set of phase shifts and subthreshold parameters which satisfy the Roy-Steiner equations.

Consistent description of kinetic equation with triangle anomaly

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pu Shi; Gao Jianhua; Wang Qun

2011-05-01

We provide a consistent description of the kinetic equation with a triangle anomaly which is compatible with the entropy principle of the second law of thermodynamics and the charge/energy-momentum conservation equations. In general an anomalous source term is necessary to ensure that the equations for the charge and energy-momentum conservation are satisfied and that the correction terms of distribution functions are compatible to these equations. The constraining equations from the entropy principle are derived for the anomaly-induced leading order corrections to the particle distribution functions. The correction terms can be determined for the minimum number of unknown coefficients in onemore » charge and two charge cases by solving the constraining equations.« less

Liouvillian propagators, Riccati equation and differential Galois theory

NASA Astrophysics Data System (ADS)

Acosta-Humánez, Primitivo; Suazo, Erwin

2013-11-01

In this paper a Galoisian approach to building propagators through Riccati equations is presented. The main result corresponds to the relationship between the Galois integrability of the linear Schrödinger equation and the virtual solvability of the differential Galois group of its associated characteristic equation. As the main application of this approach we solve Ince’s differential equation through the Hamiltonian algebrization procedure and the Kovacic algorithm to find the propagator for a generalized harmonic oscillator. This propagator has applications which describe the process of degenerate parametric amplification in quantum optics and light propagation in a nonlinear anisotropic waveguide. Toy models of propagators inspired by integrable Riccati equations and integrable characteristic equations are also presented.

Data-driven discovery of partial differential equations

PubMed Central

Rudy, Samuel H.; Brunton, Steven L.; Proctor, Joshua L.; Kutz, J. Nathan

2017-01-01

We propose a sparse regression method capable of discovering the governing partial differential equation(s) of a given system by time series measurements in the spatial domain. The regression framework relies on sparsity-promoting techniques to select the nonlinear and partial derivative terms of the governing equations that most accurately represent the data, bypassing a combinatorially large search through all possible candidate models. The method balances model complexity and regression accuracy by selecting a parsimonious model via Pareto analysis. Time series measurements can be made in an Eulerian framework, where the sensors are fixed spatially, or in a Lagrangian framework, where the sensors move with the dynamics. The method is computationally efficient, robust, and demonstrated to work on a variety of canonical problems spanning a number of scientific domains including Navier-Stokes, the quantum harmonic oscillator, and the diffusion equation. Moreover, the method is capable of disambiguating between potentially nonunique dynamical terms by using multiple time series taken with different initial data. Thus, for a traveling wave, the method can distinguish between a linear wave equation and the Korteweg–de Vries equation, for instance. The method provides a promising new technique for discovering governing equations and physical laws in parameterized spatiotemporal systems, where first-principles derivations are intractable. PMID:28508044

Data-driven discovery of partial differential equations.

PubMed

Rudy, Samuel H; Brunton, Steven L; Proctor, Joshua L; Kutz, J Nathan

2017-04-01

We propose a sparse regression method capable of discovering the governing partial differential equation(s) of a given system by time series measurements in the spatial domain. The regression framework relies on sparsity-promoting techniques to select the nonlinear and partial derivative terms of the governing equations that most accurately represent the data, bypassing a combinatorially large search through all possible candidate models. The method balances model complexity and regression accuracy by selecting a parsimonious model via Pareto analysis. Time series measurements can be made in an Eulerian framework, where the sensors are fixed spatially, or in a Lagrangian framework, where the sensors move with the dynamics. The method is computationally efficient, robust, and demonstrated to work on a variety of canonical problems spanning a number of scientific domains including Navier-Stokes, the quantum harmonic oscillator, and the diffusion equation. Moreover, the method is capable of disambiguating between potentially nonunique dynamical terms by using multiple time series taken with different initial data. Thus, for a traveling wave, the method can distinguish between a linear wave equation and the Korteweg-de Vries equation, for instance. The method provides a promising new technique for discovering governing equations and physical laws in parameterized spatiotemporal systems, where first-principles derivations are intractable.

Differential Equations Models to Study Quorum Sensing.

PubMed

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.

Catmull-Rom Curve Fitting and Interpolation Equations

ERIC Educational Resources Information Center

Jerome, Lawrence

2010-01-01

Computer graphics and animation experts have been using the Catmull-Rom smooth curve interpolation equations since 1974, but the vector and matrix equations can be derived and simplified using basic algebra, resulting in a simple set of linear equations with constant coefficients. A variety of uses of Catmull-Rom interpolation are demonstrated,…

Evolution of basic equations for nearshore wave field

PubMed Central

ISOBE, Masahiko

2013-01-01

In this paper, a systematic, overall view of theories for periodic waves of permanent form, such as Stokes and cnoidal waves, is described first with their validity ranges. To deal with random waves, a method for estimating directional spectra is given. Then, various wave equations are introduced according to the assumptions included in their derivations. The mild-slope equation is derived for combined refraction and diffraction of linear periodic waves. Various parabolic approximations and time-dependent forms are proposed to include randomness and nonlinearity of waves as well as to simplify numerical calculation. Boussinesq equations are the equations developed for calculating nonlinear wave transformations in shallow water. Nonlinear mild-slope equations are derived as a set of wave equations to predict transformation of nonlinear random waves in the nearshore region. Finally, wave equations are classified systematically for a clear theoretical understanding and appropriate selection for specific applications. PMID:23318680

Turbulence kinetic energy equation for dilute suspensions

NASA Technical Reports Server (NTRS)

Abou-Arab, T. W.; Roco, M. C.

1989-01-01

A multiphase turbulence closure model is presented which employs one transport equation, namely the turbulence kinetic energy equation. The proposed form of this equation is different from the earlier formulations in some aspects. The power spectrum of the carrier fluid is divided into two regions, which interact in different ways and at different rates with the suspended particles as a function of the particle-eddy size ratio and density ratio. The length scale is described algebraically. A mass/time averaging procedure for the momentum and kinetic energy equations is adopted. The resulting turbulence correlations are modeled under less retrictive assumptions comparative to previous work. The closures for the momentum and kinetic energy equations are given. Comparisons of the predictions with experimental results on liquid-solid jet and gas-solid pipe flow show satisfactory agreement.

FAST TRACK COMMUNICATION Quasi self-adjoint nonlinear wave equations

NASA Astrophysics Data System (ADS)

Ibragimov, N. H.; Torrisi, M.; Tracinà, R.

2010-11-01

In this paper we generalize the classification of self-adjoint second-order linear partial differential equation to a family of nonlinear wave equations with two independent variables. We find a class of quasi self-adjoint nonlinear equations which includes the self-adjoint linear equations as a particular case. The property of a differential equation to be quasi self-adjoint is important, e.g. for constructing conservation laws associated with symmetries of the differential equation.

Dynamic modeling of environmental risk associated with drilling discharges to marine sediments.

PubMed

Durgut, İsmail; Rye, Henrik; Reed, Mark; Smit, Mathijs G D; Ditlevsen, May Kristin

2015-10-15

Drilling discharges are complex mixtures of base-fluids, chemicals and particulates, and may, after discharge to the marine environment, result in adverse effects on benthic communities. A numerical model was developed to estimate the fate of drilling discharges in the marine environment, and associated environmental risks. Environmental risk from deposited drilling waste in marine sediments is generally caused by four types of stressors: oxygen depletion, toxicity, burial and change of grain size. In order to properly model these stressors, natural burial, biodegradation and bioturbation processes were also included. Diagenetic equations provide the basis for quantifying environmental risk. These equations are solved numerically by an implicit-central differencing scheme. The sediment model described here is, together with a fate and risk model focusing on the water column, implemented in the DREAM and OSCAR models, both available within the Marine Environmental Modeling Workbench (MEMW) at SINTEF in Trondheim, Norway. Copyright © 2015 Elsevier Ltd. All rights reserved.

Students’ difficulties in solving linear equation problems

NASA Astrophysics Data System (ADS)

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 Weyl-Lanczos equations and the Lanczos wave equation in four dimensions as systems in involution

NASA Astrophysics Data System (ADS)

Dolan, P.; Gerber, A.

2003-07-01

The Weyl-Lanczos equations in four dimensions form a system in involution. We compute its Cartan characters explicitly and use Janet-Riquier theory to confirm the results in the case of all space-times with a diagonal metric tensor and for the plane wave limit of space-times. We write the Lanczos wave equation as an exterior differential system and, with assistance from Janet-Riquier theory, we compute its Cartan characters and find that it forms a system in involution. We compare these Cartan characters with those of the Weyl-Lanczos equations. All results hold for the real analytic case.

Anomalous Diffusion Approximation of Risk Processes in Operational Risk of Non-Financial Corporations

NASA Astrophysics Data System (ADS)

Magdziarz, M.; Mista, P.; Weron, A.

2007-05-01

We introduce an approximation of the risk processes by anomalous diffusion. In the paper we consider the case, where the waiting times between successive occurrences of the claims belong to the domain of attraction of alpha -stable distribution. The relationship between the obtained approximation and the celebrated fractional diffusion equation is emphasised. We also establish upper bounds for the ruin probability in the considered model and give some numerical examples.

A Method for the Construction of Hereditary Constitutive Equations of Laminates Bases on a Hereditary Constitutive Equation for a Layer

NASA Astrophysics Data System (ADS)

Dumansky, Alexander M.; Tairova, Lyudmila P.

2008-09-01

A method for the construction of hereditary constitutive equation is proposed for the laminate on the basis of hereditary constitutive equations of a layer. The method is developed from the assumption that in the directions of axes of orthotropy the layer follows elastic behavior, and obeys hereditary constitutive equations under shear. The constitutive equations of the laminate are constructed on the basis of classical laminate theory and algebra of resolvent operators. Effective matrix algorithm and relationships of operator algebra are used to derive visco-elastic stiffness and compliance of the laminate. The example of construction of hereditary constitutive equations of cross-ply carbon fiber-reinforced plastic is presented.

Duality Quantum Simulation of the Yang-Baxter Equation

NASA Astrophysics Data System (ADS)

Zheng, Chao; Wei, Shijie

2018-04-01

The Yang-Baxter equation has become a significant theoretical tool in a variety of areas of physics. It is desirable to investigate the quantum simulation of the Yang-Baxter equation itself, exploring the connections between quantum integrability and quantum information processing, in which the unity of both the Yang-Baxter equation system and its quantum entanglement should be kept as a whole. In this work, we propose a duality quantum simulation algorithm of the Yang-Baxter equation, which contains the Yang-Baxter system and an ancillary qubit. Contrasting to conventional methods in which the two hand sides of the equation are simulated separately, they are simulated simultaneously in this proposal. Consequently, it opens up a way to further investigate entanglements in a Yang-Baxter equation.

Duality Quantum Simulation of the Yang-Baxter Equation

NASA Astrophysics Data System (ADS)

Zheng, Chao; Wei, Shijie

2018-07-01

The Yang-Baxter equation has become a significant theoretical tool in a variety of areas of physics. It is desirable to investigate the quantum simulation of the Yang-Baxter equation itself, exploring the connections between quantum integrability and quantum information processing, in which the unity of both the Yang-Baxter equation system and its quantum entanglement should be kept as a whole. In this work, we propose a duality quantum simulation algorithm of the Yang-Baxter equation, which contains the Yang-Baxter system and an ancillary qubit. Contrasting to conventional methods in which the two hand sides of the equation are simulated separately, they are simulated simultaneously in this proposal. Consequently, it opens up a way to further investigate entanglements in a Yang-Baxter equation.

Equating Scores from Adaptive to Linear Tests

ERIC Educational Resources Information Center

van der Linden, Wim J.

2006-01-01

Two local methods for observed-score equating are applied to the problem of equating an adaptive test to a linear test. In an empirical study, the methods were evaluated against a method based on the test characteristic function (TCF) of the linear test and traditional equipercentile equating applied to the ability estimates on the adaptive test…

Lie symmetries for systems of evolution equations

NASA Astrophysics Data System (ADS)

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.

Stability for a class of difference equations

NASA Astrophysics Data System (ADS)

Muroya, Yoshiaki; Ishiwata, Emiko

2009-06-01

We consider the following non-autonomous and nonlinear difference equations with unbounded delays: where 0equation to be globally asymptotically stable. These conditions improve the well known stability conditions for linear and nonlinear difference equations.

Some Conceptual Issues in Observed-Score Equating

ERIC Educational Resources Information Center

van der Linden, Wim J.

2013-01-01

In spite of all of the technical progress in observed-score equating, several of the more conceptual aspects of the process still are not well understood. As a result, the equating literature struggles with rather complex criteria of equating, lack of a test-theoretic foundation, confusing terminology, and ad hoc analyses. A return to Lord's…

Polynomial functors and combinatorial Dyson-Schwinger equations

NASA Astrophysics Data System (ADS)

Kock, Joachim

2017-04-01

We present a general abstract framework for combinatorial Dyson-Schwinger equations, in which combinatorial identities are lifted to explicit bijections of sets, and more generally equivalences of groupoids. Key features of combinatorial Dyson-Schwinger equations are revealed to follow from general categorical constructions and universal properties. Rather than beginning with an equation inside a given Hopf algebra and referring to given Hochschild 1-cocycles, our starting point is an abstract fixpoint equation in groupoids, shown canonically to generate all the algebraic structures. Precisely, for any finitary polynomial endofunctor P defined over groupoids, the system of combinatorial Dyson-Schwinger equations X = 1 + P(X) has a universal solution, namely the groupoid of P-trees. The isoclasses of P-trees generate naturally a Connes-Kreimer-like bialgebra, in which the abstract Dyson-Schwinger equation can be internalised in terms of canonical B+-operators. The solution to this equation is a series (the Green function), which always enjoys a Faà di Bruno formula, and hence generates a sub-bialgebra isomorphic to the Faà di Bruno bialgebra. Varying P yields different bialgebras, and cartesian natural transformations between various P yield bialgebra homomorphisms and sub-bialgebras, corresponding for example to truncation of Dyson-Schwinger equations. Finally, all constructions can be pushed inside the classical Connes-Kreimer Hopf algebra of trees by the operation of taking core of P-trees. A byproduct of the theory is an interpretation of combinatorial Green functions as inductive data types in the sense of Martin-Löf type theory (expounded elsewhere).

Special solutions to Chazy equation

NASA Astrophysics Data System (ADS)

Varin, V. P.

2017-02-01

We consider the classical Chazy equation, which is known to be integrable in hypergeometric functions. But this solution has remained purely existential and was never used numerically. We give explicit formulas for hypergeometric solutions in terms of initial data. A special solution was found in the upper half plane H with the same tessellation of H as that of the modular group. This allowed us to derive some new identities for the Eisenstein series. We constructed a special solution in the unit disk and gave an explicit description of singularities on its natural boundary. A global solution to Chazy equation in elliptic and theta functions was found that allows parametrization of an arbitrary solution to Chazy equation. The results have applications to analytic number theory.

The halo Boltzmann equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Biagetti, Matteo; Desjacques, Vincent; Kehagias, Alex

2016-04-01

Dark matter halos are the building blocks of the universe as they host galaxies and clusters. The knowledge of the clustering properties of halos is therefore essential for the understanding of the galaxy statistical properties. We derive an effective halo Boltzmann equation which can be used to describe the halo clustering statistics. In particular, we show how the halo Boltzmann equation encodes a statistically biased gravitational force which generates a bias in the peculiar velocities of virialized halos with respect to the underlying dark matter, as recently observed in N-body simulations.

Low RMRratio as a Surrogate Marker for Energy Deficiency, the Choice of Predictive Equation Vital for Correctly Identifying Male and Female Ballet Dancers at Risk.

PubMed

Staal, Sarah; Sjödin, Anders; Fahrenholtz, Ida; Bonnesen, Karen; Melin, Anna Katarina

2018-06-22

Ballet dancers are reported to have an increased risk for energy deficiency with or without disordered eating behavior. A low ratio between measured ( m ) and predicted ( p ) resting metabolic rate (RMR ratio  < 0.90) is a recognized surrogate marker for energy deficiency. We aimed to evaluate the prevalence of suppressed RMR using different methods to calculate p RMR and to explore associations with additional markers of energy deficiency. Female (n = 20) and male (n = 20) professional ballet dancers, 19-35 years of age, were enrolled. m RMR was assessed by respiratory calorimetry (ventilated open hood). p RMR was determined using the Cunningham and Harris-Benedict equations, and different tissue compartments derived from whole-body dual-energy X-ray absorptiometry assessment. The protocol further included assessment of body composition and bone mineral density, blood pressure, disordered eating (Eating Disorder Inventory-3), and for females, the Low Energy Availability in Females Questionnaire. The prevalence of suppressed RMR was generally high but also clearly dependent on the method used to calculate p RMR, ranging from 25% to 80% in males and 35% to 100% in females. Five percent had low bone mineral density, whereas 10% had disordered eating and 25% had hypotension. Forty percent of females had elevated Low Energy Availability in Females Questionnaire score and 50% were underweight. Suppressed RMR was associated with elevated Low Energy Availability in Females Questionnaire score in females and with higher training volume in males. In conclusion, professional ballet dancers are at risk for energy deficiency. The number of identified dancers at risk varies greatly depending on the method used to predict RMR when using RMR ratio as a marker for energy deficiency.

Analytical solution of tt¯ dilepton equations

NASA Astrophysics Data System (ADS)

Sonnenschein, Lars

2006-03-01

The top quark antiquark production system in the dilepton decay channel is described by a set of equations which is nonlinear in the unknown neutrino momenta. Its most precise and least time consuming solution is of major importance for measurements of top quark properties like the top quark mass and tt¯ spin correlations. The initial system of equations can be transformed into two polynomial equations with two unknowns by means of elementary algebraic operations. These two polynomials of multidegree two can be reduced to one univariate polynomial of degree four by means of resultants. The obtained quartic equation is solved analytically.

Orbital stability of solitary waves for Kundu equation

NASA Astrophysics Data System (ADS)

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+sυ<0, while Guo and Wu (1995) 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.

A Riemann-Hilbert Approach for the Novikov Equation

NASA Astrophysics Data System (ADS)

Boutet de Monvel, Anne; Shepelsky, Dmitry; Zielinski, Lech

2016-09-01

We develop the inverse scattering transform method for the Novikov equation u_t-u_{txx}+4u^2u_x=3u u_xu_{xx}+u^2u_{xxx} considered on the line xin(-∞,∞) in the case of non-zero constant background. The approach is based on the analysis of an associated Riemann-Hilbert (RH) problem, which in this case is a 3× 3 matrix problem. The structure of this RH problem shares many common features with the case of the Degasperis-Procesi (DP) equation having quadratic nonlinear terms (see [Boutet de Monvel A., Shepelsky D., Nonlinearity 26 (2013), 2081-2107, arXiv:1107.5995]) and thus the Novikov equation can be viewed as a ''modified DP equation'', in analogy with the relationship between the Korteweg-de Vries (KdV) equation and the modified Korteweg-de Vries (mKdV) equation. We present parametric formulas giving the solution of the Cauchy problem for the Novikov equation in terms of the solution of the RH problem and discuss the possibilities to use the developed formalism for further studying of the Novikov equation.

Evaluation of pier-scour equations for coarse-bed streams

USGS Publications Warehouse

Chase, Katherine J.; Holnbeck, Stephen R.

2004-01-01

Streambed scour at bridge piers is among the leading causes of bridge failure in the United States. Several pier-scour equations have been developed to calculate potential scour depths at existing and proposed bridges. Because many pier-scour equations are based on data from laboratory flumes and from cohesionless silt- and sand-bottomed streams, they tend to overestimate scour for piers in coarse-bed materials. Several equations have been developed to incorporate the mitigating effects of large particle sizes on pier scour, but further investigations are needed to evaluate how accurately pier-scour depths calculated by these equations match measured field data. This report, prepared in cooperation with the Montana Department of Transportation, describes the evaluation of five pier-scour equations for coarse-bed streams. Pier-scour and associated bridge-geometry, bed-material, and streamflow-measurement data at bridges over coarse-bed streams in Montana, Alaska, Maryland, Ohio, and Virginia were selected from the Bridge Scour Data Management System. Pier scour calculated using the Simplified Chinese equation, the Froehlich equation, the Froehlich design equation, the HEC-18/Jones equation and the HEC-18/Mueller equation for flood events with approximate recurrence intervals of less than 2 to 100 years were compared to 42 pier-scour measurements. Comparison of results showed that pier-scour depths calculated with the HEC-18/Mueller equation were seldom smaller than measured pier-scour depths. In addition, pier-scour depths calculated using the HEC-18/Mueller equation were closer to measured scour than for the other equations that did not underestimate pier scour. However, more data are needed from coarse-bed streams and from less frequent flood events to further evaluate pier-scour equations.

Modifiable Prostate Cancer Risk Reduction and Early Detection Behaviors in Black Men

ERIC Educational Resources Information Center

Odedina, Folakemi T.; Scrivens, John J., Jr.; Larose-Pierre, Margareth; Emanuel, Frank; Adams, Angela Denise; Dagne, Getachew A.; Pressey, Shannon Alexis; Odedina, Oladapo

2011-01-01

Objective: To explore the personal factors related to modifiable prostate cancer risk-reduction and detection behaviors among black men. Methods: Three thousand four hundred thirty (3430) black men were surveyed and structural equation modeling employed to test study hypotheses. Results: Modifiable prostate cancer risk-reduction behavior was found…

Solution of a modified fractional diffusion equation

NASA Astrophysics Data System (ADS)

Langlands, T. A. M.

2006-07-01

Recently, a modified fractional diffusion equation has been proposed [I. Sokolov, J. Klafter, From diffusion to anomalous diffusion: a century after Einstein's brownian motion, Chaos 15 (2005) 026103; A.V. Chechkin, R. Gorenflo, I.M. Sokolov, V.Yu. Gonchar, Distributed order time fractional diffusion equation, Frac. Calc. Appl. Anal. 6 (3) (2003) 259279; I.M. Sokolov, A.V. Checkin, J. Klafter, Distributed-order fractional kinetics, Acta. Phys. Pol. B 35 (2004) 1323.] for describing processes that become less anomalous as time progresses by the inclusion of a second fractional time derivative acting on the diffusion term. In this letter we give the solution of the modified equation on an infinite domain. In contrast to the solution of the traditional fractional diffusion equation, the solution of the modified equation requires an infinite series of Fox functions instead of a single Fox function.

A Least-Squares Transport Equation Compatible with Voids

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hansen, Jon; Peterson, Jacob; Morel, Jim

Standard second-order self-adjoint forms of the transport equation, such as the even-parity, odd-parity, and self-adjoint angular flux equation, cannot be used in voids. Perhaps more important, they experience numerical convergence difficulties in near-voids. Here we present a new form of a second-order self-adjoint transport equation that has an advantage relative to standard forms in that it can be used in voids or near-voids. Our equation is closely related to the standard least-squares form of the transport equation with both equations being applicable in a void and having a nonconservative analytic form. However, unlike the standard least-squares form of the transportmore » equation, our least-squares equation is compatible with source iteration. It has been found that the standard least-squares form of the transport equation with a linear-continuous finite-element spatial discretization has difficulty in the thick diffusion limit. Here we extensively test the 1D slab-geometry version of our scheme with respect to void solutions, spatial convergence rate, and the intermediate and thick diffusion limits. We also define an effective diffusion synthetic acceleration scheme for our discretization. Our conclusion is that our least-squares S n formulation represents an excellent alternative to existing second-order S n transport formulations« less

Finite-dimensional linear approximations of solutions to general irregular nonlinear operator equations and equations with quadratic operators

NASA Astrophysics Data System (ADS)

Kokurin, M. Yu.

2010-11-01

A general scheme for improving approximate solutions to irregular nonlinear operator equations in Hilbert spaces is proposed and analyzed in the presence of errors. A modification of this scheme designed for equations with quadratic operators is also examined. The technique of universal linear approximations of irregular equations is combined with the projection onto finite-dimensional subspaces of a special form. It is shown that, for finite-dimensional quadratic problems, the proposed scheme provides information about the global geometric properties of the intersections of quadrics.

Loop equations and bootstrap methods in the lattice

DOE PAGES

Anderson, Peter D.; Kruczenski, Martin

2017-06-17

Pure gauge theories can be formulated in terms of Wilson Loops by means of the loop equation. In the large-N limit this equation closes in the expectation value of single loops. In particular, using the lattice as a regulator, it becomes a well defined equation for a discrete set of loops. In this paper we study different numerical approaches to solving this equation.

Sonar equations for planetary exploration.

PubMed

Ainslie, Michael A; Leighton, Timothy G

2016-08-01

The set of formulations commonly known as "the sonar equations" have for many decades been used to quantify the performance of sonar systems in terms of their ability to detect and localize objects submerged in seawater. The efficacy of the sonar equations, with individual terms evaluated in decibels, is well established in Earth's oceans. The sonar equations have been used in the past for missions to other planets and moons in the solar system, for which they are shown to be less suitable. While it would be preferable to undertake high-fidelity acoustical calculations to support planning, execution, and interpretation of acoustic data from planetary probes, to avoid possible errors for planned missions to such extraterrestrial bodies in future, doing so requires awareness of the pitfalls pointed out in this paper. There is a need to reexamine the assumptions, practices, and calibrations that work well for Earth to ensure that the sonar equations can be accurately applied in combination with the decibel to extraterrestrial scenarios. Examples are given for icy oceans such as exist on Europa and Ganymede, Titan's hydrocarbon lakes, and for the gaseous atmospheres of (for example) Jupiter and Venus.

Nonintegrable semidiscrete Hirota equation: gauge-equivalent structures and dynamical properties.

PubMed

Ma, Li-Yuan; Zhu, Zuo-Nong

2014-09-01

In this paper, we investigate nonintegrable semidiscrete Hirota equations, including the nonintegrable semidiscrete Hirota(-) equation and the nonintegrable semidiscrete Hirota(+) equation. We focus on the topics on gauge-equivalent structures and dynamical behaviors for the two nonintegrable semidiscrete equations. By using the concept of the prescribed discrete curvature, we show that, under the discrete gauge transformations, the nonintegrable semidiscrete Hirota(-) equation and the nonintegrable semidiscrete Hirota(+) equation are, respectively, gauge equivalent to the nonintegrable generalized semidiscrete modified Heisenberg ferromagnet equation and the nonintegrable generalized semidiscrete Heisenberg ferromagnet equation. We prove that the two discrete gauge transformations are reversible. We study the dynamical properties for the two nonintegrable semidiscrete Hirota equations. The exact spatial period solutions of the two nonintegrable semidiscrete Hirota equations are obtained through the constructions of period orbits of the stationary discrete Hirota equations. We discuss the topic regarding whether the spatial period property of the solution to the nonintegrable semidiscrete Hirota equation is preserved to that of the corresponding gauge-equivalent nonintegrable semidiscrete equations under the action of discrete gauge transformation. By using the gauge equivalent, we obtain the exact solutions to the nonintegrable generalized semidiscrete modified Heisenberg ferromagnet equation and the nonintegrable generalized semidiscrete Heisenberg ferromagnet equation. We also give the numerical simulations for the stationary discrete Hirota equations. We find that their dynamics are much richer than the ones of stationary discrete nonlinear Schrödinger equations.

Numerical solution of distributed order fractional differential equations

NASA Astrophysics Data System (ADS)

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.

Analytic solutions for Long's equation and its generalization

NASA Astrophysics Data System (ADS)

Humi, Mayer

2017-12-01

Two-dimensional, steady-state, stratified, isothermal atmospheric flow over topography is governed by Long's equation. Numerical solutions of this equation were derived and used by several authors. In particular, these solutions were applied extensively to analyze the experimental observations of gravity waves. In the first part of this paper we derive an extension of this equation to non-isothermal flows. Then we devise a transformation that simplifies this equation. We show that this simplified equation admits solitonic-type solutions in addition to regular gravity waves. These new analytical solutions provide new insights into the propagation and amplitude of gravity waves over topography.

A net volume equation for Indiana.

Treesearch

W. Brad Smith; Carol A. Weist

1982-01-01

Describes a Weibull-type volume equation for Indiana developed as part of the ongoing Resource Evaluation research in the Central States. Equation coefficients are presented by species groupings for both cubic foot and board foot volumes for three tree class categories.

Fifth-order complex Korteweg-de Vries-type equations

NASA Astrophysics Data System (ADS)

Khanal, Netra; Wu, Jiahong; Yuan, Juan-Ming

2012-05-01

This paper studies spatially periodic complex-valued solutions of the fifth-order Korteweg-de Vries (KdV)-type equations. The aim is at several fundamental issues including the existence, uniqueness and finite-time blowup problems. Special attention is paid to the Kawahara equation, a fifth-order KdV-type equation. When a Burgers dissipation is attached to the Kawahara equation, we establish the existence and uniqueness of the Fourier series solution with the Fourier modes decaying algebraically in terms of the wave numbers. We also examine a special series solution to the Kawahara equation and prove the convergence and global regularity of such solutions associated with a single mode initial data. In addition, finite-time blowup results are discussed for the special series solution of the Kawahara equation.

Hamiltonian structure of the Lotka-Volterra equations

NASA Astrophysics Data System (ADS)

Nutku, Y.

1990-03-01

The Lotka-Volterra equations governing predator-prey relations are shown to admit Hamiltonian structure with respect to a generalized Poisson bracket. These equations provide an example of a system for which the naive criterion for the existence of Hamiltonian structure fails. We show further that there is a three-component generalization of the Lotka-Volterra equations which is a bi-Hamiltonian system.

Analytical Solutions of the KDV-KZK Equation

NASA Astrophysics Data System (ADS)

Gan, W. S.

The KdV-KZK equation for fluids developed by me was presented at the ICSV 11 in St. Petersburg in July 2004. In this paper, I made an attempt on the analytical solutions of this equation using the perturbation method. Some physical interpretation of the solutions is given. A brief introduction to KdV-KZK equation for solids is given

Analogy between the Navier-Stokes equations and Maxwell's equations: Application to turbulence

NASA Astrophysics Data System (ADS)

Marmanis, Haralambos

1998-06-01

A new theory of turbulence is initiated, based on the analogy between electromagnetism and turbulent hydrodynamics, for the purpose of describing the dynamical behavior of averaged flow quantities in incompressible fluid flows of high Reynolds numbers. The starting point is the recognition that the vorticity (w=∇×u) and the Lamb vector (l=w×u) should be taken as the kernel of a dynamical theory of turbulence. The governing equations for these fields can be obtained by the Navier-Stokes equations, which underlie the whole evolution. Then whatever parts are not explicitly expressed as a function of w or l only are gathered and treated as source terms. This is done by introducing the concepts of turbulent charge and turbulent current. Thus we are led to a closed set of linear equations for the averaged field quantities. The premise is that the earlier introduced sources will be apt for modeling, in the sense that their distribution will depend only on the geometry and the total energetics of the flow. The dynamics described in the preceding manner is what we call the metafluid dynamics.

Solving Equations Today.

ERIC Educational Resources Information Center

Shumway, Richard J.

1989-01-01

Illustrated is the problem of solving equations and some different strategies students might employ when using available technology. Gives illustrations for: exact solutions, approximate solutions, and approximate solutions which are graphically generated. (RT)

Geometrical Solutions of Quadratic Equations.

ERIC Educational Resources Information Center

Grewal, A. S.; Godloza, L.

1999-01-01

Demonstrates that the equation of a circle (x-h)2 + (y-k)2 = r2 with center (h; k) and radius r reduces to a quadratic equation x2-2xh + (h2 + k2 -r2) = O at the intersection with the x-axis. Illustrates how to determine the center of a circle as well as a point on a circle. (Author/ASK)

Applications of Capstone Depleted Uranium Aerosol Risk Data to Military Combat Risk Management

DOE Office of Scientific and Technical Information (OSTI.GOV)

Daxon, Eric G.; Parkhurst, MaryAnn; Melanson, Mark A.

2009-03-01

Risks to personnel engaged in military operations include not only the threat of enemy firepower but also risks from exposure to other hazards such as radiation. Combatant commanders of the U. S. Army carefully weigh risks of casualties before implementing battlefield actions using an established paradigm that take these risks into consideration. As a result of the inclusion of depleted uranium (DU) anti-armor ammunition in the conventional (non-nuclear) weapons arsenal, the potential for exposure to DU aerosols and its associated chemical and radiological effects becomes an element of the commanders’ risk assessment. The Capstone DU Aerosol Study measured the rangemore » of likely DU oxide aerosol concentrations created inside a combat vehicle perforated with a DU munition, and the Capstone Human Health Risk Assessment (HHRA) estimated the associated doses and calculated risks. This paper focuses on the development of a scientific approach to adapt the risks from DU’s non uniform dose distribution within the body using the current U.S. Department of Defense (DoD) radiation risk management approach. The approach developed equates the Radiation Exposure Status (RES) categories to the estimated radiological risks of DU and makes use of the Capstone-developed Renal Effects Group (REG) as a measure of chemical risk from DU intake. Recommendations are provided for modifying Army guidance and policy in order to better encompass the potential risks from DU aerosol inhalation during military operations.« less

The Drake Equation revisited

NASA Astrophysics Data System (ADS)

Konesky, Gregory

2009-08-01

In the almost half century since the Drake Equation was first conceived, a number of profound discoveries have been made that require each of the seven variables of this equation to be reconsidered. The discovery of hydrothermal vents on the ocean floor, for example, as well as the ever-increasing extreme conditions in which life is found on Earth, suggest a much wider range of possible extraterrestrial habitats. The growing consensus that life originated very early in Earth's history also supports this suggestion. The discovery of exoplanets with a wide range of host star types, and attendant habitable zones, suggests that life may be possible in planetary systems with stars quite unlike our Sun. Stellar evolution also plays an important part in that habitable zones are mobile. The increasing brightness of our Sun over the next few billion years, will place the Earth well outside the present habitable zone, but will then encompass Mars, giving rise to the notion that some Drake Equation variables, such as the fraction of planets on which life emerges, may have multiple values.

An approach to rogue waves through the cnoidal equation

NASA Astrophysics Data System (ADS)

Lechuga, Antonio

2014-05-01

Lately it has been realized the importance of rogue waves in some events happening in open seas. Extreme waves and extreme weather could explain some accidents, but not all of them. Every now and then inflicted damages on ships only can be reported to be caused by anomalous and elusive waves, such as rogue waves. That's one of the reason why they continue attracting considerable interest among researchers. In the frame of the Nonlinear Schrödinger equation(NLS), Witham(1974) and Dingemans and Otta (2001)gave asymptotic solutions in moving coordinates that transformed the NLS equation in a ordinary differential equation that is the Duffing or cnoidal wave equation. Applying the Zakharov equation, Stiassnie and Shemer(2004) and Shemer(2010)got also a similar equation. It's well known that this ordinary equation can be solved in elliptic functions. The main aim of this presentation is to sort out the domains of the solutions of this equation, that, of course, are linked to the corresponding solutions of the partial differential equations(PDEs). That being, Lechuga(2007),a simple way to look for anomalous waves as it's the case with some "chaotic" solutions of the Duffing equation.