Consistent Method for PDF Solutions of Random Oscillators

1999 ◽  
Vol 125 (4) ◽  
pp. 443-447 ◽  
Author(s):  
Guo-Kang Er
Author(s):  
Roger G. Harrison ◽  
Paul W. Todd ◽  
Scott R. Rudge ◽  
Demetri P. Petrides

Designed for undergraduates, graduate students, and industry practitioners, Bioseparations Science and Engineering fills a critical need in the field of bioseparations. Current, comprehensive, and concise, it covers bioseparations unit operations in unprecedented depth. In each of the chapters, the authors use a consistent method of explaining unit operations, starting with a qualitative description noting the significance and general application of the unit operation. They then illustrate the scientific application of the operation, develop the required mathematical theory, and finally, describe the applications of the theory in engineering practice, with an emphasis on design and scaleup. Unique to this text is a chapter dedicated to bioseparations process design and economics, in which a process simular, SuperPro Designer® is used to analyze and evaluate the production of three important biological products. New to this second edition are updated discussions of moment analysis, computer simulation, membrane chromatography, and evaporation, among others, as well as revised problem sets. Unique features include basic information about bioproducts and engineering analysis and a chapter with bioseparations laboratory exercises. Bioseparations Science and Engineering is ideal for students and professionals working in or studying bioseparations, and is the premier text in the field.


1975 ◽  
Vol 58 (5) ◽  
pp. 1051-1061
Author(s):  
William P Cochrane ◽  
James F Lawrence ◽  
Young W Lee ◽  
Ronald B Maybury ◽  
Brian P Wilson

Abstract An interlaboratory investigation of technical chlordane residues in food crops was carried out to determine the most practical and consistent method of reporting results. Using a technical chlordane reference standard, 8 gas chromatographic stationary phases were studied for their resolution capabilities. The best separations were obtained with SE-30 and its OV-1 equivalent. Using these columns and electron capture detection, potatoes and carrots from supervised field experiments were analyzed in duplicate and quantitated by using 4 methods of calculation. The data were statistically treated to determine the precision and bias for each method. Also, 1 sample was analyzed in duplicate on 2 different occasions by 6 laboratories to substantiate the initial conclusions. Based on the criterion of high precision it is suggested that a comparison of total area under the chromatogram of the sample with total area of a standard technical chlordane be the method of quantitation. Only peaks which are common to both standard and sample have any significance in this type of calculation.


2021 ◽  
Vol 17 (1) ◽  
Author(s):  
A. Meier ◽  
J. McGree ◽  
R. Klee ◽  
J. Preuß ◽  
D. Reiche ◽  
...  

Abstract Background Endocrinopathic, or hyperinsulinaemia-associated laminitis (HAL) is a common and debilitating equine foot disease, and although no pharmacological treatments are registered, several are under development. To evaluate the effect of such treatments, an accurate and consistent method is needed to track the clinical signs of laminitis over time, and the natural history of the disease, in terms of a ‘normal’ pattern of improvement, needs to be understood. This study examined the improvement pattern in clinical cases of naturally-occurring HAL subjected to a range of best-practice interventions, using two different scoring methods. Eighty horses and ponies with suspected HAL were enrolled in a study conducted at 16 veterinary practices across Germany. The severity of laminitis was assessed by independent veterinarians using both the traditional Obel method and a modified Obel method developed by Meier and colleagues. Assessments were made on the day of diagnosis (d 0), then on days 4, 9, 14, 25 and 42 during the intervention period. Pain medications were withheld for 24 h prior to clinical examination in all cases. Results Time to marked improvement from laminitis varied between individuals, but was difficult to monitor accurately using the Obel method, with the median grade being 2/4 on days 0 and 4, then 0/4 from d 9 onwards. More subtle changes could be identified using the Meier method, however, and the median scores were seen to follow the form of an exponential decay model in most horses, improving from 8/12 on d 0, to 0/12 on d 25. Within this composite scoring method, considerable variation was observed in the rate of improvement of individual clinical signs, with the average time taken for each sign to reach a median score of 0 ranging from 4 days (foot lift and weight shifting) to 25 days (gait when turned in a circle) across all 80 horses. Conclusions The Meier method provides a reliable and consistent method for monitoring the clinical status of horses with HAL, and despite the variability, the pattern of improvement described here should provide a useful benchmark against which individual cases and new treatments can be assessed.


Atoms ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 50
Author(s):  
Charlotte Froese Fischer

The paper reviews the history of B-spline methods for atomic structure calculations for bound states. It highlights various aspects of the variational method, particularly with regard to the orthogonality requirements, the iterative self-consistent method, the eigenvalue problem, and the related sphf, dbsr-hf, and spmchf programs. B-splines facilitate the mapping of solutions from one grid to another. The following paper describes a two-stage approach where the goal of the first stage is to determine parameters of the problem, such as the range and approximate values of the orbitals, after which the level of accuracy is raised. Once convergence has been achieved the Virial Theorem, which is evaluated as a check for accuracy. For exact solutions, the V/T ratio for a non-relativistic calculation is −2.


2020 ◽  
Vol 10 (10) ◽  
pp. 3647
Author(s):  
Peter Fiener ◽  
Tomáš Dostál ◽  
Josef Krása ◽  
Elmar Schmaltz ◽  
Peter Strauss ◽  
...  

In the European Union, soil erosion is identified as one of the main environmental threats, addressed with a variety of rules and regulations for soil and water conservation. The by far most often officially used tool to determine soil erosion is the Universal Soil Loss Equation (USLE) and its regional adaptions. The aim of this study is to use three different regional USLE-based approaches in three different test catchments in the Czech Republic, Germany, and Austria to determine differences in model results and compare these with the revised USLE-base European soil erosion map. The different regional model adaptations and implementation techniques result in substantial differences in test catchment specific mean erosion (up to 75% difference). Much more pronounced differences were modelled for individual fields. The comparison of the region-specific USLE approaches with the revised USLE-base European erosion map underlines the problems and limitations of harmonization procedures. The EU map limits the range of modelled erosion and overall shows a substantially lower mean erosion compared to all region-specific approaches. In general, the results indicate that even if many EU countries use USLE technology as basis for soil conservation planning, a truly consistent method does not exist, and more efforts are needed to homogenize the different methods without losing the USLE-specific knowledge developed in the different regions over the last decades.


2000 ◽  
Vol 3 (1) ◽  
Author(s):  
Matthew Eichner ◽  
Mark McClellan ◽  
David A. Wise

We are engaged in a long-term project to analyze the determinants of health care cost differences across firms. An important first step is to summarize the nature of expenditure differences across plans. The goal of this article is to develop methods for identifying and quantifying those factors that account for the wide differences in health care expenditures observed across plans.We consider eight plans that vary in average expenditure for individuals filing claims, from a low of $1,645 to a high of $2,484. We present a statistically consistent method for decomposing the cost differences across plans into component parts based on demographic characteristics of plan participants, the mix of diagnoses for which participants are treated, and the cost of treatment for particular diagnoses. The goal is to quantify the contribution of each of these components to the difference between average cost and the cost in a given firm. The demographic mix of plan enrollees accounts for wide differnces in cost ($649). Perhaps the most noticeable feature of the results is that, after adjusting for demographic mix, the difference in expenditures accounted for by the treatment costs given diagnosis ($807) is almost as wide as the unadjusted range in expenditures ($838). Differences in cost due to the different illnesses that are treated, after adjusting for demographic mix, also accounts for large differences in cost ($626). These components of cost do not move together; for example, demographic mix may decrease expenditure under a particular plan while the diagnosis mix may increase costs.Our hope is that understanding the reasons for cost differences across plans will direct more focused attention to controlling costs. Indeed, this work is intended as an important first step toward that goal.


2019 ◽  
Vol 15 (5) ◽  
pp. 339-348
Author(s):  
Z. Akbar ◽  
O.A. Al-Juhaishi ◽  
T.A.O. Olusa ◽  
H.M.S. Davies

The equine tarsus is the most common area of the hind limb associated with lameness. Tarsal function is probably directly related to its conformation. Previous conformational measurement methods and radiological data are either limited or too specific to explain the complex tarsus conformation in different loading conditions. This study aimed to develop a consistent method to evaluate equine tarsal conformation from lateromedial radiographs. Twenty cadaveric hind limbs from 15 adult horses of different breeds were cut at the distal one third of the tibia. Hind limbs mounted in a loading rig and positioned with the metatarsus vertical were digitally radiographed. The zero-degree lateromedial (ZLM) was defined by vertical and horizontal landmarks including overlapping of the lateral and medial trochlea of the talus and a contact point between the dorsal edges of lateral and medial borders of the distal central tarsal bone. Radiographs missing these features were retaken to achieve consistent ZLM views. Specific radiographic features were selected as landmarks to develop tarsal parameters based on their clarity and their being consistently identifiable. The intra-rater repeatability of ten measurable morphometric parameters was evaluated with each radiograph measured twice with an interval of at least one month and Bland-Altman plots developed from this data. Repeat measurements did not differ significantly (Intraclass correlation coefficients (ICC) ranged from 0.731-0.966). This study provides a base for evaluation of the tarsal conformation by radiography.


2011 ◽  
Vol 78 (6) ◽  
Author(s):  
Richard V. Beblo ◽  
Lisa Mauck Weiland

Presented are the experimental results of two light activated shape memory polymer (LASMP) formulations. The optical stimulus used to activate the materials is detailed including a mapping of the spatial optical intensity at the surface of the sample. From this, results of energy calculations are presented including the amount of energy available for transitioning from the glassy state to the rubbery state and from the rubbery state to the glassy state, highlighting one of the major advantages of LASMP as requiring less energy to transition than thermally activated shape memory polymers. The mechano-optical experimental setup and procedure is detailed and provides a consistent method for evaluating this relatively new class of shape memory polymer. A chemical kinetic model is used to predict both the theoretical glassy state modulus, as only the sample averaged modulus is experimentally attainable, as well as the through thickness distribution of Young’s modulus. The experimental and model results for these second generation LASMP formulations are then compared with earlier LASMP generations (detailed previously in Beblo and Mauck Weiland, 2009, “Light Activated Shape Memory Polymer Characterization,” ASME J. Appl. Mech., 76, pp. 8) and typical thermally activated shape memory polymer.


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