In defense of the first derivative test

1985 ◽  
Vol 13 (4) ◽  
pp. 75-77
Author(s):  
Wan Fu Chi
Keyword(s):  
First Derivative ◽  
First Derivative Test ◽  
Derivative Test

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.

Novel UV Spectrophotometric Method for the Quantitative Analysis of CefpodoximeProxetil in Pharmaceutical Formulations by First Derivative Technique

2017 ◽  
Vol 8 (03) ◽  
Author(s):  
Potdar S. S. ◽  
Karajgi S. R. ◽  
Simpi C. C. ◽  
Kalyane N. V.
Keyword(s):  
Quantitative Analysis ◽  
Spectrophotometric Method ◽  
Dosage Form ◽  
Pharmaceutical Formulations ◽  
First Derivative ◽  
Good Linearity ◽  
Beer's Law ◽  
Beer’S Law ◽  
Tablet Dosage ◽  
Ich Guideline

The spectrophotometric method for estimation of CefpodoximeProxetil employed first derivative amplitude UV spectrophotometric method for analysis using methanol as solvent for the drug. CefpodoximeProxetil has absorbance maxima at 235nm and obeys Beer’s law in concentration range 10-50µg/ml with good linearity i.e. r2 about 0.999. The recovery studies established accuracy of the proposed method; result validated according to ICH guideline. Results were found satisfactory and reproducible. The method was successfully for evaluation of CefpodoximeProxetil in tablet dosage form without interference of common excipients.

scholarly journals Superpixel Segmentation Based on Anisotropic Edge Strength

2019 ◽  
Vol 5 (6) ◽  
pp. 57 ◽  
Author(s):  
Gang Wang ◽  
Bernard De Baets
Keyword(s):  
Distance Measure ◽  
Saliency Detection ◽  
Experimental Results ◽  
Segmentation Method ◽  
Superpixel Segmentation ◽  
Gaussian Kernels ◽  
First Derivative ◽  
Edge Strength

Superpixel segmentation can benefit from the use of an appropriate method to measure edge strength. In this paper, we present such a method based on the first derivative of anisotropic Gaussian kernels. The kernels can capture the position, direction, prominence, and scale of the edge to be detected. We incorporate the anisotropic edge strength into the distance measure between neighboring superpixels, thereby improving the performance of an existing graph-based superpixel segmentation method. Experimental results validate the superiority of our method in generating superpixels over the competing methods. It is also illustrated that the proposed superpixel segmentation method can facilitate subsequent saliency detection.

scholarly journals Existence results for first derivative dependent ϕ-Laplacian boundary value problems

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Imran Talib ◽  
Thabet Abdeljawad
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Continuous Functions ◽  
Existence Of Solution ◽  
Existence Results ◽  
Main Concern ◽  
First Derivative ◽  
Boundary Functions ◽  
Carathéodory Function

Abstract Our main concern in this article is to investigate the existence of solution for the boundary-value problem $$\begin{aligned}& (\phi \bigl(x'(t)\bigr)'=g_{1} \bigl(t,x(t),x'(t)\bigr),\quad \forall t\in [0,1], \\& \Upsilon _{1}\bigl(x(0),x(1),x'(0)\bigr)=0, \\& \Upsilon _{2}\bigl(x(0),x(1),x'(1)\bigr)=0, \end{aligned}$$ ( ϕ ( x ′ ( t ) ) ′ = g 1 ( t , x ( t ) , x ′ ( t ) ) , ∀ t ∈ [ 0 , 1 ] , ϒ 1 ( x ( 0 ) , x ( 1 ) , x ′ ( 0 ) ) = 0 , ϒ 2 ( x ( 0 ) , x ( 1 ) , x ′ ( 1 ) ) = 0 , where $g_{1}:[0,1]\times \mathbb{R}^{2}\rightarrow \mathbb{R}$ g 1 : [ 0 , 1 ] × R 2 → R is an $L^{1}$ L 1 -Carathéodory function, $\Upsilon _{i}:\mathbb{R}^{3}\rightarrow \mathbb{R} $ ϒ i : R 3 → R are continuous functions, $i=1,2$ i = 1 , 2 , and $\phi :(-a,a)\rightarrow \mathbb{R}$ ϕ : ( − a , a ) → R is an increasing homeomorphism such that $\phi (0)=0$ ϕ ( 0 ) = 0 , for $0< a< \infty $ 0 < a < ∞ . We obtain the solvability results by imposing some new conditions on the boundary functions. The new conditions allow us to ensure the existence of at least one solution in the sector defined by well ordered functions. These ordered functions do not require one to check the definitions of lower and upper solutions. Moreover, the monotonicity assumptions on the arguments of boundary functions are not required in our case. An application is considered to ensure the applicability of our results.

scholarly journals Simulating Heat Stress of Coal Gangue Spontaneous Combustion on Vegetation Using Alfalfa Leaf Water Content Spectral Features as Indicators

2021 ◽  
Vol 13 (13) ◽  
pp. 2634
Author(s):  
Qiyuan Wang ◽  
Yanling Zhao ◽  
Feifei Yang ◽  
Tao Liu ◽  
Wu Xiao ◽  
...  
Keyword(s):  
Heat Stress ◽  
Water Content ◽  
Spontaneous Combustion ◽  
Leaf Water ◽  
Coal Gangue ◽  
Leaf Water Content ◽  
Spectral Features ◽  
Lasso Regression ◽  
Stress Assessment ◽  
First Derivative

Vegetation heat-stress assessment in the reclamation areas of coal gangue dumps is of great significance in controlling spontaneous combustion; through a temperature gradient experiment, we collected leaf spectra and water content data on alfalfa. We then obtained the optimal spectral features of appropriate leaf water content indicators through time series analysis, correlation analysis, and Lasso regression analysis. A spectral feature-based long short-term memory (SF-LSTM) model is proposed to estimate alfalfa’s heat stress level; the live fuel moisture content (LFMC) varies significantly with time and has high regularity. Correlation analysis of the raw spectrum, first-derivative spectrum, spectral reflectance indices, and leaf water content data shows that LFMC and spectral data were the most strongly correlated. Combined with Lasso regression analysis, the optimal spectral features were the first-derivative spectral value at 1661 nm (abbreviated as FDS (1661)), RVI (1525,1771), DVI (1412,740), and NDVI (1447,1803). When the classification strategies were divided into three categories and the time sequence length of the spectral features was set to five consecutive monitoring dates, the SF-LSTM model had the highest accuracy in estimating the heat stress level in alfalfa; the results provide an important theoretical basis and technical support for vegetation heat-stress assessment in coal gangue dump reclamation areas.

scholarly journals Three Different Spectrophotometric Methods for Simultaneous Determination of Pyriproxyfen and Chlorothalonil Residues in Cucumber and Cabbage Samples

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Shilan A. Omer ◽  
Nabil A. Fakhre
Keyword(s):  
Simultaneous Determination ◽  
Simultaneous Estimation ◽  
Zero Crossing ◽  
Spectrophotometric Methods ◽  
First Derivative ◽  
The Third ◽  
Mean Centering ◽  
Relative Standard ◽  
One Way Anova

In this study, three simple and accurate spectrophotometric methods for simultaneous determination of pyriproxyfen and chlorothalonil residues in cucumbers and cabbages grown in experimental greenhouse were studied. The first method was based on the zero-crossing technique measurement for first and second derivative spectrophotometry. The second method was based on the first derivative of the ratio spectra. However, the third method was based on mean centering of ratio spectra. These procedures lack any previous separation steps. The calibration curves for three spectrophotometric methods are linear in the concentration range of 1–30 μg·mL−1 and 0.5–7 μg·mL−1 for pyriproxyfen and chlorothalonil successively. The recoveries ranged from 82.12–97.40% for pyriproxyfen and 81.51–97.04% for chlorothalonil with relative standard deviations less than 4.95% and 5.45% in all instances for pyriproxyfen and chlorothalonil, respectively. The results obtained from the proposed methods were compared statistically by using one-way ANOVA, and the results revealed there were no significant differences between ratio spectra and mean centering methods with the zero-crossing technique. The proposed methods are successfully applied for the simultaneous estimation of the residue of both pesticides in cucumber and cabbage samples.

Sign in / Sign up

Export Citation Format

Share Document