Approximation of differentiable and not differentiable signals by the first derivative of sampling Kantorovich operators

2021 ◽  
pp. 125913
Author(s):  
Marco Cantarini ◽  
Danilo Costarelli ◽  
Gianluca Vinti
Keyword(s):  
First Derivative ◽  
Kantorovich Operators

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 On New Classes of Stancu-Kantorovich-Type Operators

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1235
Author(s):  
Bianca Ioana Vasian ◽  
Ștefan Lucian Garoiu ◽  
Cristina Maria Păcurar
Keyword(s):  
Test Functions ◽  
New Class ◽  
Convergence Results ◽  
Error Estimations ◽  
Kantorovich Operators

The present paper introduces new classes of Stancu–Kantorovich operators constructed in the King sense. For these classes of operators, we establish some convergence results, error estimations theorems and graphical properties of approximation for the classes considered, namely, operators that preserve the test functions e0(x)=1 and e1(x)=x, e0(x)=1 and e2(x)=x2, as well as e1(x)=x and e2(x)=x2. The class of operators that preserve the test functions e1(x)=x and e2(x)=x2 is a genuine generalization of the class introduced by Indrea et al. in their paper “A New Class of Kantorovich-Type Operators”, published in Constr. Math. Anal.

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.

scholarly journals Cancer Discrimination Using Fourier Transform Near-Infrared Spectroscopy with Chemometric Models

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Hui Chen ◽  
Zan Lin ◽  
Chao Tan
Keyword(s):  
Cancer Diagnosis ◽  
Near Infrared ◽  
Nir Spectroscopy ◽  
Principal Component ◽  
Classification Model ◽  
Support Vector ◽  
Biomedical Analysis ◽  
First Derivative ◽  
Svm Model ◽  
High Prediction

Near-infrared (NIR) spectroscopy technique offers many potential advantages as tool for biomedical analysis since it enables the subtle biochemical signatures related to pathology to be detected and extracted. In conjunction with advanced chemometrics, NIR spectroscopy opens the possibility of their use in cancer diagnosis. The study focuses on the application of near-infrared (NIR) spectroscopy and classification models for discriminating colorectal cancer. A total of 107 surgical specimens and a corresponding NIR diffuse reflection spectral dataset were prepared. Three preprocessing methods were attempted and least-squares support vector machine (LS-SVM) was used to build a classification model. The hybrid preprocessing of first derivative and principal component analysis (PCA) resulted in the best LS-SVM model with the sensitivity and specificity of 0.96 and 0.96 for the training and 0.94 and 0.96 for test sets, respectively. The similarity performance on both subsets indicated that overfitting did not occur, assuring the robustness and reliability of the developed LS-SVM model. The area of receiver operating characteristic (ROC) curve was 0.99, demonstrating once again the high prediction power of the model. The result confirms the applicability of the combination of NIR spectroscopy, LS-SVM, PCA, and first derivative preprocessing for cancer diagnosis.

HermitianRmatrix in the presence of first-derivative couplings

1984 ◽  
Vol 30 (3) ◽  
pp. 1277-1278 ◽  
Author(s):  
Joseph Macek
Keyword(s):  
First Derivative
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