scholarly journals On Turan-type inequalities for trigonometric polynomials of half-integer order

2020 ◽  
Vol 27 (2) ◽  
pp. 32
Author(s):  
O.V. Polyakov
Keyword(s):  
Trigonometric Polynomials ◽  
Second Derivative ◽  
Integer Order ◽  
First Derivative ◽  
Half Integer ◽  
Turán Type Inequalities

Some exact inequalities of the Turan type are obtained in the paper for trigonometric polynomials $h(x)$ of half-interger order $n+\frac {1}{2}$, $n=1, 2, ...$, such that all $2n+1$ their zeros are real and located on a segment $[0;2\pi )$. Namely, the inequality that relates the norms in the space $C$ of the  trigonometric polynomials $h(x)$ of half-integer order $n+\frac {1}{2}$, $n=1, 2, ...$, and its second derivative $h''(x)$, $\|h''\|_c\ge \frac {2n+1}{4}\|h\|_c$, that is the inequalities that connect the norms in the space $L_2$ of the  trigonometric polynomials $h(x)$ of half-interger order $n+\frac {1}{2}$, $n=1, 2, ...$, and its first derivative $h'(x)$, that is $\|h'\|_{L_2}\ge \sqrt {\frac {2n+1}{8}}\|h\|_{L_2}$. The resulting inequalities cannot be improved. In proving the theorems, we use the method that was developed by V.F. Babenko and S.A. Pichugov for trigonometric polynomials, all of whose roots are real.

Chebyshev functions of half-integer order

2007 ◽  
Vol 18 (10) ◽  
pp. 743-749
Author(s):  
J. García Ravelo ◽  
R. Cuevas ◽  
A. Queijeiro ◽  
J. J. Peña ◽  
J. Morales
Keyword(s):  
Integer Order ◽  
Half Integer ◽  
Chebyshev Functions

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.

scholarly journals Exact solution of time-fractional partial differential equations using Laplace transform

2016 ◽  
Vol 5 (1) ◽  
pp. 86
Author(s):  
Naser Al-Qutaifi
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Laplace Transform ◽  
Fractional Partial Differential Equations ◽  
Laplace Transform Method ◽  
Partial Differential ◽  
Transform Method ◽  
Integer Order ◽  
First Derivative ◽  
The Laplace Transform

<p>The idea of replacing the first derivative in time by a fractional derivative of order , where , leads to a fractional generalization of any partial differential equations of integer order. In this paper, we obtain a relationship between the solution of the integer order equation and the solution of its fractional extension by using the Laplace transform method.</p>

scholarly journals Superfield approach to interacting N = 2 massive and massless supermultiplets in 3d flat space

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
R. R. Metsaev
Keyword(s):  
Light Cone ◽  
Three Dimensional ◽  
Flat Space ◽  
Arbitrary Spin ◽  
Massless Scalar ◽  
Light Cone Gauge ◽  
First Derivative ◽  
Integer Spin ◽  
Half Integer

Abstract Massive arbitrary spin supermultiplets and massless (scalar and spin one-half) supermultiplets of the N = 2 Poincaré superalgebra in three-dimensional flat space are considered. Both the integer spin and half-integer spin supermultiplets are studied. For such massive and massless supermultiplets, a formulation in terms of light-cone gauge unconstrained superfields defined in a momentum superspace is developed. For the supermultiplets under consideration a superspace first derivative representation for all cubic interaction vertices is obtained. A superspace representation for dynamical generators of the N = 2 Poincaré superalgebra is also found.

scholarly journals Approximating Real-Life BVPs via Chebyshev Polynomials’ First Derivative Pseudo-Galerkin Method

2021 ◽  
Vol 5 (4) ◽  
pp. 165
Author(s):  
Mohamed Abdelhakem ◽  
Toqa Alaa-Eldeen ◽  
Dumitru Baleanu ◽  
Maryam G. Alshehri ◽  
Mamdouh El-Kady
Keyword(s):  
Error Analysis ◽  
Galerkin Method ◽  
Chebyshev Polynomials ◽  
Real Life ◽  
Operational Matrices ◽  
Integer Order ◽  
First Derivative ◽  
The Core ◽  
Life Problems ◽  
Derivatives Of

An efficient technique, called pseudo-Galerkin, is performed to approximate some types of linear/nonlinear BVPs. The core of the performance process is the two well-known weighted residual methods, collocation and Galerkin. A novel basis of functions, consisting of first derivatives of Chebyshev polynomials, has been used. Consequently, new operational matrices for derivatives of any integer order have been introduced. An error analysis is performed to ensure the convergence of the presented method. In addition, the accuracy and the efficiency are verified by solving BVPs examples, including real-life problems.

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.

Sign in / Sign up

Export Citation Format

Share Document