scholarly journals Coefficient functionals for a class of bounded turning functions related to modified sigmoid function

2021 ◽  
Vol 7 (2) ◽  
pp. 3133-3149
Author(s):  
Muhammad Ghaffar Khan ◽  
◽  
Nak Eun Cho ◽  
Timilehin Gideon Shaba ◽  
Bakhtiar Ahmad ◽  
...  
Keyword(s):  
Present Article ◽  
Fourth Order ◽  
Symmetric Functions ◽  
Second Order ◽  
Sigmoid Function ◽  
Hankel Determinant ◽  
Hankel Determinants ◽  
The Third ◽  
Bounded Turning

<abstract><p>The main objective of the present article is to define the class of bounded turning functions associated with modified sigmoid function. Also we investigate and determine sharp results for the estimates of four initial coefficients, Fekete-Szegö functional, the second-order Hankel determinant, Zalcman conjucture and Krushkal inequality. Furthermore, we evaluate bounds of the third and fourth-order Hankel determinants for the class and for the 2-fold and 3-fold symmetric functions.</p></abstract>

scholarly journals A Study of Third Hankel Determinant Problem for Certain Subfamilies of Analytic Functions Involving Cardioid Domain

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 418 ◽  
Author(s):  
Lei Shi ◽  
Izaz Ali ◽  
Muhammad Arif ◽  
Nak Eun Cho ◽  
Shehzad Hussain ◽  
...  
Keyword(s):  
Present Article ◽  
Unit Disk ◽  
Analytic Functions ◽  
Symmetric Functions ◽  
Hankel Determinant ◽  
The Third

In the present article, we consider certain subfamilies of analytic functions connected with the cardioid domain in the region of the unit disk. The purpose of this article is to investigate the estimates of the third Hankel determinant for these families. Further, the same bounds have been investigated for two-fold and three-fold symmetric functions.

scholarly journals Coefficient Problems in a Class of Functions with Bounded Turning Associated with Sine Function

2021 ◽  
Vol 14 (1) ◽  
pp. 53-64
Author(s):  
Muhammad Ghaffar Khan ◽  
Bakhtiar Ahmad ◽  
Janusz Sokol ◽  
Zubair Muhammad ◽  
Wali Khan Mashwani ◽  
...  
Keyword(s):  
Power Series ◽  
Univalent Functions ◽  
Upper Bounds ◽  
Sine Function ◽  
Hankel Determinant ◽  
Hankel Determinants ◽  
The Third ◽  
Coefficient Problems ◽  
Bounded Turning ◽  
Class Of Functions

The Hankel determinant for a function having power series was first defined by Pommerenke. The growth of Hankel determinant has been evaluated for different subcollections of univalent functions. Many subclasses with bounded turning are several interesting geometric properties. In this paper, some classes of functions with bounded turning which connect to the sine function are studied in the region of the unit disc in order. Our purpose is to obtain some upper bounds for the third and fourth Hankel determinants related to such classes.

scholarly journals A Study of Third and Fourth Hankel Determinant Problem for a Particular Class of Bounded Turning Functions

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Gaganpreet Kaur ◽  
Gurmeet Singh ◽  
Muhammad Arif ◽  
Ronnason Chinram ◽  
Javed Iqbal
Keyword(s):  
Fourth Order ◽  
Upper Bound ◽  
Symmetric Functions ◽  
Upper Bounds ◽  
Hankel Determinant ◽  
Derivative Operator ◽  
The Family ◽  
Bounded Turning

In this present paper, a new generalized class ℛ p , q from the family of function with bounded turning was introduced by using p , q - derivative operator. Our aim for this class is to find out the upper bound of third- and fourth-order Hankel determinant. Moreover, the upper bounds for two-fold and three-fold symmetric functions for this class are also obtained.

Third Hankel determinants for two classes of analytic functions with real coefficients

2021 ◽  
Vol 33 (4) ◽  
pp. 973-986
Author(s):  
Young Jae Sim ◽  
Paweł Zaprawa
Keyword(s):  
Analytic Functions ◽  
Univalent Functions ◽  
Upper Bounds ◽  
Hankel Determinant ◽  
Lower And Upper Bounds ◽  
Hankel Determinants ◽  
The Third ◽  
Typically Real ◽  
Class Of Functions ◽  
Typically Real Functions

Abstract In recent years, the problem of estimating Hankel determinants has attracted the attention of many mathematicians. Their research have been focused mainly on deriving the bounds of H 2 , 2 {H_{2,2}} or H 3 , 1 {H_{3,1}} over different subclasses of 𝒮 {\mathcal{S}} . Only in a few papers third Hankel determinants for non-univalent functions were considered. In this paper, we consider two classes of analytic functions with real coefficients. The first one is the class 𝒯 {\mathcal{T}} of typically real functions. The second object of our interest is 𝒦 ℝ ⁢ ( i ) {\mathcal{K}_{\mathbb{R}}(i)} , the class of functions with real coefficients which are convex in the direction of the imaginary axis. In both classes, we find lower and upper bounds of the third Hankel determinant. The results are sharp.

scholarly journals A Study of Fourth-Order Hankel Determinants for Starlike Functions Connected with the Sine Function

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Hai-Yan Zhang ◽  
Huo Tang
Keyword(s):  
Fourth Order ◽  
Starlike Functions ◽  
Function Class ◽  
Upper Bounds ◽  
Sine Function ◽  
Hankel Determinant ◽  
Hankel Determinants

In this paper, upper bounds for the fourth-order Hankel determinant H 4 1 for the function class S s ∗ associated with the sine function are given.

Conservative Transport Schemes for Spherical Geodesic Grids: High-Order Flux Operators for ODE-Based Time Integration

2011 ◽  
Vol 139 (9) ◽  
pp. 2962-2975 ◽  
Author(s):  
William C. Skamarock ◽  
Almut Gassmann
Keyword(s):  
Fourth Order ◽  
Time Integration ◽  
Higher Order ◽  
Second Order ◽  
Time Step ◽  
Diffusion Term ◽  
The Third ◽  
Integration Schemes ◽  
Order Scheme ◽  
Runge Kutta

Higher-order finite-volume flux operators for transport algorithms used within Runge–Kutta time integration schemes on irregular Voronoi (hexagonal) meshes are proposed and tested. These operators are generalizations of third- and fourth-order operators currently used in atmospheric models employing regular, orthogonal rectangular meshes. Two-dimensional least squares fit polynomials are used to evaluate the higher-order spatial derivatives needed to cancel the leading-order truncation error terms of the standard second-order centered formulation. Positive definite or monotonic behavior is achieved by applying an appropriate limiter during the final Runge–Kutta stage within a given time step. The third- and fourth-order formulations are evaluated using standard transport tests on the sphere. The new schemes are more accurate and significantly more efficient than the standard second-order scheme and other schemes in the literature examined by the authors. The third-order formulation is equivalent to the fourth-order formulation plus an additional diffusion term that is proportional to the Courant number. An optimal value for the coefficient scaling this diffusion term is chosen based on qualitative evaluation of the test results. Improvements using the higher-order scheme in place of the traditional second-order centered approach are illustrated within 3D unstable baroclinic wave simulations produced using two global nonhydrostatic models employing spherical Voronoi meshes.

Study on Tractor-Semitrailer Shimmy of High Speed

2012 ◽  
Vol 433-440 ◽  
pp. 7420-7424
Author(s):  
Mei Zhi Xie ◽  
Bei Li ◽  
Chao Yi Wei ◽  
Feng Yan Yi
Keyword(s):  
Transfer Function ◽  
Dynamic Model ◽  
Fourth Order ◽  
High Speed ◽  
Damping Ratio ◽  
Second Order ◽  
Original Model ◽  
The Third

Through the establishment of dynamic model of tractor-semitrailer, calculate its transfer function. In the case of the third and fourth state of balanced coefficient is very small in the original model, the model of the tractor-semitrailer of fourth-order drop for second-order using MATLAB-modred () function and balreal () function, seek of relationship between damping ratio and the speed of tractor-semitrailer, The results show that: the tractor-semitrailer shimmy of high-speed is speed inversely proportional to the damping ratio, the higher the speed, the smaller the damping ratio, and thus more likely to shock and shimmy.

Applications of the MBPT in the localized representation the behaviour of the localization terms

1988 ◽  
Vol 53 (9) ◽  
pp. 2073-2081 ◽  
Author(s):  
Ede Kapuy ◽  
Zoltán Csépes ◽  
Ferencz Bartha ◽  
Ferencz Bogár ◽  
Cornelia Kozmutza
Keyword(s):  
Fourth Order ◽  
Correlation Energy ◽  
Computer Time ◽  
Second Order ◽  
Saturated Hydrocarbons ◽  
Local Effects ◽  
The Third ◽  
Non Local ◽  
Cyclic Polyenes

The behaviour of the localization corrections of the MBPT is investigated. It is shown that calculating the third and fourth order localization corrections we obtain sufficiently accurate results to the second order correlation energy both for cyclic polyenes and for saturated hydrocarbons. The evaluation of the localization diagrams does not require significant extra computer time. The extra computer time can be recovered if small non-local effects will be neglected.

scholarly journals The Light Curves of Double-Mode Cepheids: The CO Aur Case

1998 ◽  
Vol 185 ◽  
pp. 389-390
Author(s):  
E. Poretti ◽  
I. Pardo
Keyword(s):  
Frequency Analysis ◽  
Fourth Order ◽  
A Priori ◽  
Cross Coupling ◽  
Second Order ◽  
Light Curves ◽  
Third Order ◽  
The Third ◽  
Coupling Terms ◽  
Phase Differences

In two recent papers (Pardo & Poretti 1997; Poretti & Pardo 1997) we analyzed all the available photometry of galactic double-mode Cepheids (DMCs) with the aim of detecting in each case the importance of the harmonics and of the cross coupling terms. We found that no a priori fit can be reliably applied to the measurements of a DMC, but a careful frequency analysis must be done to evaluate the importance of each term. As a further application of this technique, we obtained very precise indications about the properties of the Fourier parameters. When discussing the generalized phase differences Gi,j we demonstrated that plotting them as a function of the order |i|+|j|, there are well-defined regions where they are confined: the second order terms have π < Gi,j < 3π/2; the third order terms have π/2 < Gi,j < π; the fourth order terms cluster around 2π.

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