scholarly journals Some remarks on multivalent functions of higher-order derivatives

2022 ◽  
Vol 40 ◽  
pp. 1-7
Author(s):  
M.K. Aouf ◽  
Abdel Moneim Lashin
Keyword(s):  
Starlike Functions ◽  
Higher Order

Two subclasses G_{p,q}(β) and J_{p,q}(α,β,f(z)) of p-valently starlike functions of higher-order derivatives are introduced. The object of the present paper is to derive some properties for the classes G_{p,q}(β) and J_{p,q}(α,β,f(z)). The results obtained generalize the related works of some authors and some other new results are obtained.

Applications of higher-order q-derivatives to the subclass of q-starlike functions associated with the Janowski functions

2021 ◽  
Vol 6 (2) ◽  
pp. 1110-1125
Author(s):  
Muhammad Sabil Ur Rehman ◽  
◽  
Qazi Zahoor Ahmad ◽  
H. M. Srivastava ◽  
Nazar Khan ◽  
...  
Keyword(s):  
Starlike Functions ◽  
Higher Order ◽  
Janowski Functions

Sharp coefficient bounds for starlike functions associated with the Bell numbers

2019 ◽  
Vol 69 (5) ◽  
pp. 1053-1064 ◽  
Author(s):  
Virendra Kumar ◽  
Nak Eun Cho ◽  
V. Ravichandran ◽  
H. M. Srivastava
Keyword(s):  
Starlike Functions ◽  
Higher Order ◽  
Positive Real Part ◽  
Bell Numbers ◽  
Positive Real ◽  
Sharp Bounds ◽  
Hankel Determinants ◽  
Coefficient Bounds ◽  
The Family ◽  
Schwarzian Derivatives

Abstract Let $\begin{array}{} \mathcal{S}^*_B \end{array}$ be the class of normalized starlike functions associated with a function related to the Bell numbers. By establishing bounds on some coefficient functionals for the family of functions with positive real part, we derive for functions in the class $\begin{array}{} \mathcal{S}^*_B \end{array}$ several sharp coefficient bounds on the first six coefficients and also further sharp bounds on the corresponding Hankel determinants. Bounds on the first three consecutive higher-order Schwarzian derivatives for functions in the class $\begin{array}{} \mathcal{S}^*_B \end{array}$ are investigated.

scholarly journals Higher-order q-derivatives and their applications to subclasses of multivalent Janowski type q-starlike functions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Bilal Khan ◽  
Zhi-Guo Liu ◽  
H. M. Srivastava ◽  
Serkan Araci ◽  
Nazar Khan ◽  
...  
Keyword(s):  
Starlike Functions ◽  
Higher Order ◽  
Sufficient Condition ◽  
Function Classes ◽  
Janowski Functions ◽  
Radius Problems ◽  
Coefficient Inequalities

AbstractIn the present investigation, with the help of certain higher-order q-derivatives, some new subclasses of multivalent q-starlike functions which are associated with the Janowski functions are defined. Then, certain interesting results, for example, radius problems and the results related to distortion, are derived. We also derive a sufficient condition and certain coefficient inequalities for our defined function classes. Some known consequences related to this subject are also highlighted. Finally, the well-demonstrated fact about the $(p,q)$ ( p , q ) -variations is also given in the concluding section.

scholarly journals A Study of Some Families of Multivalent q-Starlike Functions Involving Higher-Order q-Derivatives

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1470
Author(s):  
Bilal Khan ◽  
Zhi-Guo Liu ◽  
Hari M. Srivastava ◽  
Nazar Khan ◽  
Maslina Darus ◽  
...  
Keyword(s):  
Starlike Functions ◽  
Higher Order ◽  
Open Unit ◽  
Sufficient Condition ◽  
Open Unit Disk ◽  
Function Classes ◽  
The Family ◽  
Radius Problems ◽  
Coefficient Inequalities ◽  
Distortion Theorems

In the present investigation, by using certain higher-order q-derivatives, the authors introduce and investigate several new subclasses of the family of multivalent q-starlike functions in the open unit disk. For each of these newly-defined function classes, several interesting properties and characteristics are systematically derived. These properties and characteristics include (for example) distortion theorems and radius problems. A number of coefficient inequalities and a sufficient condition for functions belonging to the subclasses studied here are also discussed. Relevant connections of the various results presented in this investigation with those in earlier works on this subject are also pointed out.

Dual systems for all: Higher-order, role-based relational reasoning as a uniquely derived feature of human cognition

2019 ◽  
Vol 42 ◽  
Author(s):  
Daniel J. Povinelli ◽  
Gabrielle C. Glorioso ◽  
Shannon L. Kuznar ◽  
Mateja Pavlic
Keyword(s):  
Temporal Reasoning ◽  
Higher Order ◽  
Important Case ◽  
Human Cognition ◽  
Relational Reasoning ◽  
Dual Systems ◽  
First Order ◽  
Reasoning System ◽  
Role Based

Abstract Hoerl and McCormack demonstrate that although animals possess a sophisticated temporal updating system, there is no evidence that they also possess a temporal reasoning system. This important case study is directly related to the broader claim that although animals are manifestly capable of first-order (perceptually-based) relational reasoning, they lack the capacity for higher-order, role-based relational reasoning. We argue this distinction applies to all domains of cognition.

Quantitative EPMA of nitrogen : A tricky element in the electron-probe microanalyzer

1992 ◽  
Vol 50 (2) ◽  
pp. 1622-1623
Author(s):  
G.F. Bastin ◽  
H.J.M. Heijligers
Keyword(s):  
Background Subtraction ◽  
Electron Probe ◽  
Detection System ◽  
Higher Order ◽  
Light Elements ◽  
Strong Suppression ◽  
Electron Probe Microanalyzer ◽  
Quantitative Epma ◽  
Peak Count ◽  
Lead Stearate

Among the ultra-light elements B, C, N, and O nitrogen is the most difficult element to deal with in the electron probe microanalyzer. This is mainly caused by the severe absorption that N-Kα radiation suffers in carbon which is abundantly present in the detection system (lead-stearate crystal, carbonaceous counter window). As a result the peak-to-background ratios for N-Kα measured with a conventional lead-stearate crystal can attain values well below unity in many binary nitrides . An additional complication can be caused by the presence of interfering higher-order reflections from the metal partner in the nitride specimen; notorious examples are elements such as Zr and Nb. In nitrides containing these elements is is virtually impossible to carry out an accurate background subtraction which becomes increasingly important with lower and lower peak-to-background ratios. The use of a synthetic multilayer crystal such as W/Si (2d-spacing 59.8 Å) can bring significant improvements in terms of both higher peak count rates as well as a strong suppression of higher-order reflections.

Effects of Higher-Order Laue Zone reflections on structure images

1993 ◽  
Vol 51 ◽  
pp. 450-451
Author(s):  
H. S. Kim ◽  
S. S. Sheinin
Keyword(s):  
Wave Vector ◽  
Theoretical Calculations ◽  
Reciprocal Lattice ◽  
Image Plane ◽  
Bloch Wave ◽  
Dynamical Theory ◽  
Higher Order ◽  
Lattice Image ◽  
Lattice Vector ◽  
Image Position

The importance of image simulation in interpreting experimental lattice images is well established. Normally, in carrying out the required theoretical calculations, only zero order Laue zone reflections are taken into account. In this paper we assess the conditions for which this procedure is valid and indicate circumstances in which higher order Laue zone reflections may be important. Our work is based on an analysis of the requirements for obtaining structure images i.e. images directly related to the projected potential. In the considerations to follow, the Bloch wave formulation of the dynamical theory has been used.The intensity in a lattice image can be obtained from the total wave function at the image plane is given by: where ϕg(z) is the diffracted beam amplitide given by In these equations,the z direction is perpendicular to the entrance surface, g is a reciprocal lattice vector, the Cg(i) are Fourier coefficients in the expression for a Bloch wave, b(i), X(i) is the Bloch wave excitation coefficient, ϒ(i)=k(i)-K, k(i) is a Bloch wave vector, K is the electron wave vector after correction for the mean inner potential of the crystal, T(q) and D(q) are the transfer function and damping function respectively, q is a scattering vector and the summation is over i=l,N where N is the number of beams taken into account.

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