The sharp bounds of the second and third Hankel determinants for the class 𝓢𝓛*

2020 ◽  
Vol 70 (4) ◽  
pp. 849-862
Author(s):  
Shagun Banga ◽  
S. Sivaprasad Kumar
Keyword(s):  
Triangle Inequality ◽  
Starlike Functions ◽  
Sharp Bound ◽  
The Novel ◽  
Sharp Bounds ◽  
Hankel Determinants ◽  
Lemniscate Of Bernoulli ◽  
Carathéodory Functions ◽  
The Right

AbstractIn this paper, we use the novel idea of incorporating the recently derived formula for the fourth coefficient of Carathéodory functions, in place of the routine triangle inequality to achieve the sharp bounds of the Hankel determinants H3(1) and H2(3) for the well known class 𝓢𝓛* of starlike functions associated with the right lemniscate of Bernoulli. Apart from that the sharp bound of the Zalcman functional: $\begin{array}{} |a_3^2-a_5| \end{array}$ for the class 𝓢𝓛* is also estimated. Further, a couple of interesting results of 𝓢𝓛* are also discussed.

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.

Starlike functions associated with a lune

2017 ◽  
Vol 10 (04) ◽  
pp. 1750064 ◽  
Author(s):  
Shweta Gandhi ◽  
V. Ravichandran
Keyword(s):  
Analytic Function ◽  
Unit Disk ◽  
Half Plane ◽  
Complex Plane ◽  
Starlike Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Lemniscate Of Bernoulli ◽  
The Right

Several subclasses of starlike functions are associated with regions in the right half plane of the complex plane, like half-plane, disks, sectors, parabolas and lemniscate of Bernoulli. For a normalized analytic function [Formula: see text] defined on the open unit disk [Formula: see text] belonging to certain well-known classes of functions associated with the above regions, we investigate the radius [Formula: see text] such that, for the function [Formula: see text], [Formula: see text] lies in the lune defined by [Formula: see text] for all [Formula: see text].

Analytical Study of Violence Theme in Victoria Schwab’s This Savage Song

2019 ◽  
Keyword(s):  
Analytical Study ◽  
Research Paper ◽  
The Novel ◽  
Vicious Cycle ◽  
Aggressive Approach ◽  
Research Article ◽  
The People ◽  
The Social ◽  
Different Dimensions ◽  
The Right

This research article focuses on the theme of violence and its representation by the characters of the novel “This Savage Song” by Victoria Schwab. How violence is transmitted through genes to next generations and to what extent socio- psycho factors are involved in it, has also been discussed. Similarly, in what manner violent events and deeds by the parents affect the psychology of children and how it inculcates aggressive behaviour in their minds has been studied. What role is played by the parents in grooming the personality of children and ultimately their decisions to choose the right or wrong way has been argued. In the light of the theory of Judith Harris, this research paper highlights all the phenomena involved: How the social hierarchy controls the behaviour. In addition, the aggressive approach of the people in their lives has been analyzed in the light of the study of second theorist Thomas W Blume. As the novel is a unique representation of supernatural characters, the monsters, which are the products of some cruel deeds, this research paper brings out different dimensions of human sufferings with respect to these supernatural beings. Moreover, the researcher also discusses that, in what manner the curse of violence creates an inevitable vicious cycle of cruel monsters that makes the life of the characters turbulent and miserable.

The Right to Dream: Gender, Modernity, and the Problem of Class in Kate O'Brien's Bourgeois Bildungsromane

2019 ◽  
Vol 49 (2) ◽  
pp. 276-289
Author(s):  
Naoise Murphy
Keyword(s):  
Middle Class ◽  
Identity Formation ◽  
Coming Of Age ◽  
Female Identity ◽  
Gender And Sexuality ◽  
The Novel ◽  
Class Status ◽  
The Right ◽  
Aristocratic Culture ◽  
Modern Form

Feminist critics have celebrated Kate O'Brien's pioneering approach to gender and sexuality, yet there has been little exploration of her innovations of the coming-of-age narrative. Creating a modern Irish reworking of the Bildungsroman, O'Brien's heroines represent an idealized model of female identity-formation which stands in sharp contrast to the nationalist state's vision of Irish womanhood. Using Franco Moretti's theory of the Bildungsroman, a framing of the genre as a thoroughly ‘modern’ form of the novel, this article applies a critical Marxist lens to O'Brien's output. This reading brings to light the ways in which the limitations of the Bildungsroman work to constrain O'Brien's subversive politics. Their middle-class status remains an integral part of the identity of her heroines, informing the forms of liberation they seek. Fundamentally, O'Brien's idealization of aristocratic culture, elitist exceptionalism and ‘detachment of spirit’ restricts the emancipatory potential of her vision of Irish womanhood.

Homosexuality in K. Sello Duiker’s The Quiet Violence of Dreams: Demythologising the Imaginings and Universalising the Reality

Imbizo ◽  
2020 ◽  
Vol 11 (2) ◽  
Author(s):  
Adetunji Kazeem Adebiyi-Adelabu
Keyword(s):  
Coming Out ◽  
The Novel ◽  
Same Sex ◽  
Black African ◽  
Sex Preference ◽  
National Allegory ◽  
Critical Attention ◽  
Sex Orientation ◽  
The Right

Sello Duiker’s The Quiet Violence of Dreams offers an extensive treatment of homosexuality, a preoccupation which, until recently, is rare in black African fiction. On this account, as well as its depth and openness, the work has attracted some critical attention. It has been read from a masculinity perspective, as a coming-out novel, as a national allegory, as a work that challenges the notion of fixed sexuality, as a work that normalises same-sex sexuality, and so forth. Unlike these studies, this article examines the representation and disquisition around same-sex preference in the novel, with a view to demonstrating how some myths about homosexuality are exploded in the groundbreaking work, and showing that the narrative could also be apprehended as intellectual advocacy for the right to same-sex orientation.

Measuring Earwax Cortisol Concentration Using a Non-Stressful Method (Preprint)

2020 ◽  
Author(s):  
Andrés Herane-Vives
Keyword(s):  
Cortisol Level ◽  
Local Stress ◽  
Extraction Methods ◽  
Cortisol Concentration ◽  
The Novel ◽  
Sampling Device ◽  
Related Factors ◽  
Novel Device ◽  
Cortisol Levels ◽  
The Right

BACKGROUND “Short-term” samples are not the most appropriate for reflecting Chronic Cortisol Concentration (CCC). Although hair is used for reflecting the systemic cortisol level over “long-term”, its use appears clinically problematic. Local stress and non-stress related factors may release a circumscribed cortisol secretion that is accumulated in hair. Non-stressful earwax extraction methods may provide a more accurate specimen to measure CCC. OBJECTIVE Correlate cortisol levels using hair, serum and earwax samples METHODS Earwax from both ears of 37 controls were extracted using a clinical procedure commonly associated with local pain. One month later, earwax from the left ear side was extracted using the same procedure, and earwax from the right ear side was comfortably extracted, using an earwax self-sampling device. Participants also provided one centimetre of hair that represented the retrospective month of cortisol output, and one serum sample that reflected the effect of systemic stressors on cortisol levels. Earwax (ECC), Hair (HCC) and Serum (SCC) Cortisol Concentration were correlated and compared. Confounders´ effect on cortisol levels were studied. RESULTS Serum showed the largest and hair the lowest cortisol concentration (p<0.01). Left-ECC was larger than Right-ECC (p=0.03). Right-ECC was the only sample unaffected by confounders (all p>0.05). Right-ECC and HCC showed the only significant association (r=0.39; p=0.03). CONCLUSIONS The self-sampling device did not represent a local stressor for the ceruminous glands. It provided the cortisol level with the least likely to be affected by confounding factors over the previous month. ECC using the novel device may constitute another accurate, but more suitable and affordable specimen for measuring CCC.

scholarly journals The Sharp Bound of the Hankel Determinant of the Third Kind for Starlike Functions with Real Coefficients

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 721 ◽  
Author(s):  
Oh Sang Kwon ◽  
Young Jae Sim
Keyword(s):  
Analytic Functions ◽  
Starlike Functions ◽  
Sharp Bound ◽  
Hankel Determinant ◽  
The Third

Let SR * be the class of starlike functions with real coefficients, i.e., the class of analytic functions f which satisfy the condition f ( 0 ) = 0 = f ′ ( 0 ) − 1 , Re { z f ′ ( z ) / f ( z ) } > 0 , for z ∈ D : = { z ∈ C : | z | < 1 } and a n : = f ( n ) ( 0 ) / n ! is real for all n ∈ N . In the present paper, it is obtained that the sharp inequalities − 4 / 9 ≤ H 3 , 1 ( f ) ≤ 3 / 9 hold for f ∈ SR * , where H 3 , 1 ( f ) is the third Hankel determinant of order 3 defined by H 3 , 1 ( f ) = a 3 ( a 2 a 4 − a 3 2 ) − a 4 ( a 4 − a 2 a 3 ) + a 5 ( a 3 − a 2 2 ) .

scholarly journals Coefficient inequalities for a class of analytic functions associated with the lemniscate of Bernoulli

2018 ◽  
Vol 37 (4) ◽  
pp. 83-95
Author(s):  
Trailokya Panigrahi ◽  
Janusz Sokól
Keyword(s):  
Upper Bound ◽  
Analytic Functions ◽  
Hankel Determinant ◽  
Lemniscate Of Bernoulli ◽  
Toeplitz Determinant ◽  
Second Hankel Determinant ◽  
Coefficient Inequalities ◽  
The Right

In this paper, a new subclass of analytic functions ML_{\lambda}^{*}  associated with the right half of the lemniscate of Bernoulli is introduced. The sharp upper bound for the Fekete-Szego functional |a_{3}-\mu a_{2}^{2}|  for both real and complex \mu are considered. Further, the sharp upper bound to the second Hankel determinant |H_{2}(1)| for the function f in the class ML_{\lambda}^{*} using Toeplitz determinant is studied. Relevances of the main results are also briefly indicated.

scholarly journals Mother Behavior to Their Daughters As Seen in ''Pride and Prejudice" and "Little Women"

2019 ◽  
Vol 2 (4) ◽  
pp. 620-625
Author(s):  
Fitri Arniati ◽  
Muhammad Darwis ◽  
Nurhayati Rahman ◽  
Fathu Rahman
Keyword(s):  
19Th Century ◽  
Major Theme ◽  
The Novel ◽  
Pride And Prejudice ◽  
Late 19Th Century ◽  
Early 19Th Century ◽  
Little Women ◽  
Women's Role ◽  
The Right

This research is to study about the mother behavior to their daughters as seen in "Pride and Prejudice" and "Little Women". The mother behavior to their daughters show the different way of women as a mother in bringing up their children according to their social and condition at the time. The data were taken from two novels entitled "pride and prejudice" and "little women" is the topic of the study. The  women held in the early 19th century and the late 19th century was described as one that belonged in the home as a wife and mother, and that should marry a man who can support their family. Also throughout the novel women's role in society was described as one that is to be accomplished in household  chore and those of entertainment, such as singing  and playing music. The role of women in society was a major theme throughout the novel "Pride and Prejudice" and "Little Women" The method used in this research  is a study of comparative literature to analyze mother behavior especially for Mrs. Bennet, Lady Catherine de Bourgh, These women have similarities and different behavior in find the right mate for their daughters. This study shows that every woman has characteristics in caring for their children and paying attention to the survival of their children.

scholarly journals Maïssa Bey : romancière de l’agentivité de femmes Entre réécriture de l’Histoire et invention de soi

Il Tolomeo ◽  
2020 ◽  
Author(s):  
Lila Lamrous
Keyword(s):  
Literary Tradition ◽  
Point Of View ◽  
The Novel ◽  
Female Characters ◽  
Patriarchal Society ◽  
The Feminine ◽  
The Right

The study of Maïssa Bey’s novel Surtout ne te retourne pas allows to examine how the Francophone novel represents an earthquake as a poetic, metaphorical and political shockwave. The novel is part of a literary tradition but also shows the singularity of the writing and the engagement of the Algerian novelist Maïssa Bey. It allows to examine the feminine agentivity in the context of the disaster camps in Algeria: from the ravaged space/country emerge the voices of women who enter into resistance to improvise, invent their lives and their identities. The earthquake allows them to free themselves, to take a subversive point of view at society and their status as women in an oppressive patriarchal society. The staged female characters arrogate to themselves the right to reread history and take their destiny back.

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