On the variation of Teichmüller's metric

1980 ◽  
Vol 85 (1-2) ◽  
pp. 143-152 ◽  
Author(s):  
Frederick P. Gardiner
Keyword(s):  
Second Derivative ◽  
Difference Quotient ◽  
First Derivative ◽  
The Difference

SynopsisThe main result of this article is the calculation of the first derivative of Teichmüller's metric from an inequality of Reich and Strebel. Furthermore, from the same inequality one is able to calculate information about the difference quotient for the second derivative. From the techniques used here it does not seem possible to determine whether the metric isC2.

Weibull distribution function for cardiac contraction: integrative analysis

1999 ◽  
Vol 277 (5) ◽  
pp. H1940-H1945 ◽  
Author(s):  
Junichi Araki ◽  
Hiromi Matsubara ◽  
Juichiro Shimizu ◽  
Takeshi Mikane ◽  
Satoshi Mohri ◽  
...  
Keyword(s):  
Weibull Distribution ◽  
Systems Engineering ◽  
Pressure Rise ◽  
Left Ventricular ◽  
Cardiac Contraction ◽  
Weibull Function ◽  
Difference Curve ◽  
First Derivative ◽  
The Difference ◽  
Gradual Pressure

The Weibull distribution is widely used to analyze the cumulative loss of performance, i.e., breakdown, of a complex system in systems engineering. We found for the first time that the difference curve of two Weibull distribution functions almost identically fitted the isovolumically contracting left ventricular (LV) pressure-time curve [P( t)] in all 345 beats (3 beats at each of 5 volumes in 23 canine hearts; r = 0.999953 ± 0.000027; mean ± SD). The first derivative of the difference curve also closely fitted the first derivative of the P( t) curve. These results suggest the possibility that the LV isovolumic P( t) curve may be characterized by two counteracting cumulative breakdown systems. Of these, the first breakdown system causes a gradual pressure rise and the second breakdown system causes a gradual pressure fall. This Weibull-function model of the heart seems to give a new systems engineering or integrative physiological view of the logic underlying LV isovolumic pressure generation.

Rapidly convergent Steffensen-based methods for unconstrained optimization

2019 ◽  
Vol 53 (2) ◽  
pp. 657-666
Author(s):  
Mohammad Afzalinejad
Keyword(s):  
Unconstrained Optimization ◽  
Newton's Method ◽  
Optimization Problems ◽  
Quadratic Model ◽  
Second Derivative ◽  
Rapid Convergence ◽  
First Derivative ◽  
Unconstrained Optimization Problems ◽  
Derivative Free ◽  
Steffensen Method

A problem with rapidly convergent methods for unconstrained optimization like the Newton’s method is the computational difficulties arising specially from the second derivative. In this paper, a class of methods for solving unconstrained optimization problems is proposed which implicitly applies approximations to derivatives. This class of methods is based on a modified Steffensen method for finding roots of a function and attempts to make a quadratic model for the function without using the second derivative. Two methods of this kind with non-expensive computations are proposed which just use first derivative of the function. Derivative-free versions of these methods are also suggested for the cases where the gradient formulas are not available or difficult to evaluate. The theory as well as numerical examinations confirm the rapid convergence of this class of methods.

scholarly journals Analysis of the Acid Detergent Fibre Content in Turnip Greens and Turnip Tops (Brassica rapa L. Subsp. rapa) by Means of Near-Infrared Reflectance

Foods ◽  
2019 ◽  
Vol 8 (9) ◽  
pp. 364 ◽  
Author(s):  
Sara Obregón-Cano ◽  
Rafael Moreno-Rojas ◽  
Ana María Jurado-Millán ◽  
María Elena Cartea-González ◽  
Antonio De Haro-Bailón
Keyword(s):  
Standard Error ◽  
Near Infrared ◽  
Mathematical Treatment ◽  
Second Derivative ◽  
Infrared Reflectance ◽  
Near Infrared Reflectance ◽  
First Derivative ◽  
Acid Detergent Fibre ◽  
Turnip Greens ◽  
Turnip Tops

Standard wet chemistry analytical techniques currently used to determine plant fibre constituents are costly, time-consuming and destructive. In this paper the potential of near-infrared reflectance spectroscopy (NIRS) to analyse the contents of acid detergent fibre (ADF) in turnip greens and turnip tops has been assessed. Three calibration equations were developed: in the equation without mathematical treatment the coefficient of determination (R2) was 0.91, in the first-derivative treatment equation R2 = 0.95 and in the second-derivative treatment R2 = 0.96. The estimation accuracy was based on RPD (the ratio between the standard deviation and the standard error of validation) and RER (the ratio between the range of ADF of the validation as a whole and the standard error of prediction) of the external validation. RPD and RER values were of 2.75 and 9.00 for the treatment without derivative, 3.41 and 11.79 with first-derivative, and 3.10 and 11.03 with second-derivative. With the acid detergent residue spectrum the wavelengths were identified and associated with the ADF contained in the sample. The results showed a great potential of NIRS for predicting ADF content in turnip greens and turnip tops.

A theoretical evaluation of linearity

1993 ◽  
Vol 39 (3) ◽  
pp. 405-413 ◽  
Author(s):  
M H Kroll ◽  
K Emancipator
Keyword(s):  
Higher Order ◽  
Visual Evaluation ◽  
Theoretical Evaluation ◽  
First Order ◽  
First Derivative ◽  
Lack Of Fit ◽  
Linear Polynomial ◽  
Straight Line ◽  
The Difference ◽  
Major Property

Abstract The measure of linearity is an important part of the evaluation of a method. According to the NCCLS guidelines (Document EP6-P), results of a linearity experiment are fit to a straight line and judged linear either by visual evaluation, which is subjective, or by the lack-of-fit test. This approach depends on the precision of the method, is not necessarily conclusive, and fails to be quantitative. We define linearity as a measure of how well a first-order (linear) polynomial fits the data compared with a higher-order (nonlinear) polynomial. The major property of a linear polynomial is that the first derivative is a constant. The nonlinearity of a method can be measured by the difference between these two polynomials (first-order and higher-order) at specific values or, as an average, the root-mean difference. This approach is independent of the precision of the assay and is conclusive, quantitative, and objective.

scholarly journals Estimating leaf nitrogen concentration based on the combination with fluorescence spectrum and first-derivative

2020 ◽  
Vol 7 (2) ◽  
pp. 191941
Author(s):  
Jian Yang ◽  
Lin Du ◽  
Wei Gong ◽  
Shuo Shi ◽  
Jia Sun
Keyword(s):  
Fluorescence Spectrum ◽  
Nitrogen Concentration ◽  
Principal Component ◽  
Laser Induced Fluorescence ◽  
Leaf Nitrogen ◽  
Leaf Nitrogen Concentration ◽  
Growth Status ◽  
First Derivative ◽  
Fluorescence Characteristics ◽  
The Difference

Leaf nitrogen concentration (LNC) is a major indicator in the estimation of the crop growth status which has been diffusely applied in remote sensing. Thus, it is important to accurately obtain LNC by using passive or active technology. Laser-induced fluorescence can be applied to monitor LNC in crops through analysing the changing of fluorescence spectral information. Thus, the performance of fluorescence spectrum (FS) and first-derivative fluorescence spectrum (FDFS) for paddy rice (Yangliangyou 6 and Manly Indica) LNC estimation was discussed, and then the proposed FS + FDFS was used to monitor LNC by multivariate analysis. The results showed that the difference between FS ( R 2 = 0.781, s.d. = 0.078) and FDFS ( R 2 = 0.779, s.d. = 0.097) for LNC estimation by using the artificial neural network is not obvious. The proposed FS + FDFS can improved the accuracy of LNC estimation to some extent ( R 2 = 0.813, s.d. = 0.051). Then, principal component analysis was used in FS and FDFS, and extracted the main fluorescence characteristics. The results indicated that the proposed FS + FDFS exhibited higher robustness and stability for LNC estimation ( R 2 = 0.851, s.d. = 0.032) than that only using FS ( R 2 = 0.815, s.d. = 0.059) or FDFS ( R 2 = 0.801, s.d. = 0.065).

scholarly journals Clot Waveform of APTT Has Abnormal Patterns in Subjects with COVID-19

2020 ◽  
Author(s):  
Takuya Shimura ◽  
Makoto Kurano ◽  
Yoshiaki Kanno ◽  
Mahoko Ikeda ◽  
Koh Okamoto ◽  
...  
Keyword(s):  
Disseminated Intravascular Coagulation ◽  
Lupus Anticoagulant ◽  
Peak Level ◽  
Factor Ix ◽  
Second Derivative ◽  
High Frequencies ◽  
First Derivative ◽  
Coagulation Abnormalities ◽  
High Maximum ◽  
Factor Ix Deficiency

Abstract In Coronavirus disease 2019 (COVID-19) subjects, recent evidence suggests the presence of unique coagulation abnormalities. In this study, we performed clot waveform analyses to investigate whether specific modulations are observed in COVID-19 subjects. We analyzed the second derivative of the absorbance in routine APTT tests performed using an ACL-TOP system. We observed high frequencies of abnormal patterns in APTT second-derivative curves that could be classified into an early shoulder type, a late shoulder type, or a biphasic type, high maximum first-derivative and second-derivative peak levels, and a low minimum second-derivative peak level in COVID-19 subjects. These modulations were not observed in subjects with disseminated intravascular coagulation. These abnormal patterns are also observed in patients with lupus anticoagulant, hemophilia, or factor IX deficiency. The plasma fibrinogen levels might also be involved in the abnormal APTT waveforms, especially the high maximum first-derivative and second-derivative peak levels. The abnormal patterns in the APTT second-derivative curves appear with highest frequency at around 2 weeks after the onset of COVID-19 and were not associated with the severity of COVID-19. These results suggest the possible presence of a specific abnormal coagulopathy in COVID-19.

A more conclusive and more inclusive second derivative test

2020 ◽  
Vol 104 (560) ◽  
pp. 247-254
Author(s):  
Ronald Skurnick ◽  
Christopher Roethel
Keyword(s):  
Critical Point ◽  
Critical Points ◽  
Local Minimum ◽  
Local Maximum ◽  
Number Line ◽  
Second Derivative ◽  
First Derivative ◽  
Line Test ◽  
First Derivative Test ◽  
Derivative Test

Given a differentiable function f with argument x, its critical points are those values of x, if any, in its domain for which either f′ (x) = 0 or f′ (x) is undefined. The first derivative test is a number line test that tells us, definitively, whether a given critical point, x = c, of f(x) is a local maximum, a local minimum, or neither. The second derivative test is not a number line test, but can also be applied to classify the critical points of f(x). Unfortunately, the second derivative test is, under certain conditions, inconclusive.

scholarly journals Determination of Metformin Hydrochloride and Glyburide in an Antihyperglycemic Binary Mixture Using High-Performance Liquid Chromatographic-UV and Spectrometric Methods

2010 ◽  
Vol 93 (1) ◽  
pp. 133-140 ◽  
Author(s):  
Hesham Salem
Keyword(s):  
Binary Mixture ◽  
High Performance ◽  
Pharmaceutical Formulations ◽  
High Performance Liquid Chromatographic ◽  
Reversed Phase ◽  
Metformin Hydrochloride ◽  
Second Derivative ◽  
Zero Crossing ◽  
First Derivative

Abstract Three methods were developed for simultaneous determination of metformin hydrochloride and glyburide in an antihyperglycemic binary mixture without previous separation. In the first method, a reversed-phase HPLC column with acetonitrilewater (60 + 40, v/v) mobile phase at 0.9 mL/min flow rate was used to separate both compounds, with UV detection at 254 nm. Linearity was obtained in the concentration range of 0.060.24 µg/mL for glyburide and 1.56.0 µg/mL for metformin hydrochloride. The second method depended on first- and second-derivative UV spectrometry with zero-crossing measurements. The first-derivative amplitude at 261 nm was selected for the assay of glyburide, and the second-derivative amplitude at 235 nm was selected for the assay of metformin hydrochloride. The third method depended on measuring the first derivative of the ratio-spectra at 241 nm for glyburide and 227 nm for metformin hydrochloride. For the second and third methods, Beer's law was obeyed in the range of 1055 µg/mL for glyburide and 20200 µg/mL for metformin. The proposed methods were extensively validated and applied for the analysis of some pharmaceutical formulations containing binary mixtures of the mentioned drugs.

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