Bohr radius for certain classes of close-to-convex harmonic mappings

We define two new subclasses, $HS(k, \lambda, b, \alpha)$ and \linebreak $\overline{HS}(k, \lambda, b, \alpha)$, of univalent harmonic mappings using multiplier transformation. We obtain a sufficient condition for harmonic univalent functions to be in $HS(k,\lambda,b,\alpha)$ and we prove that this condition is also necessary for the functions in the class $\overline{HS} (k,\lambda,b,\alpha)$. We also obtain extreme points, distortion bounds, convex combination, radius of convexity and Bernandi-Libera-Livingston integral for the functions in the class $\overline{HS}(k,\lambda,b,\alpha)$.

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On a Subclass of Univalent Harmonic Mappings Convex in the Imaginary Direction

Advances in Mathematics: Scientific Journal ◽

10.37418/amsj.9.1.35 ◽

2020 ◽

pp. 445-454

Author(s):

Deepali Khurana ◽

Sushma Gupta ◽

Sukhjit Singh

Keyword(s):

Present Article ◽

Unit Disk ◽

Imaginary Axis ◽

Harmonic Mappings ◽

Open Unit ◽

Open Unit Disk ◽

Distortion Bounds ◽

Univalent Harmonic Mappings

In the present article, we consider a class of univalent harmonic mappings, $\mathcal{C}_{T} = \left\{ T_{c}[f] =\frac{f+czf'}{1+c}+\overline{\frac{f-czf'}{1+c}}; \; c>0\;\right\}$ and $f$ is convex univalent in $\mathbb{D}$, whose functions map the open unit disk $\mathbb{D}$ onto a domain convex in the direction of the imaginary axis. We estimate coefficient, growth and distortion bounds for the functions of the same class.

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Sharp Bohr Radius Constants for Certain Analytic Functions

Bulletin of the Malaysian Mathematical Sciences Society ◽

10.1007/s40840-020-01071-x ◽

2021 ◽

Vol 44 (3) ◽

pp. 1771-1785

Author(s):

Swati Anand ◽

Naveen Kumar Jain ◽

Sushil Kumar

Keyword(s):

Analytic Functions ◽

Bohr Radius

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On subclasses of harmonic mappings involving Frasin operator

Afrika Matematika ◽

10.1007/s13370-021-00889-3 ◽

2021 ◽

Author(s):

Muhammad G. Khan ◽

Bakhtiar Ahmad ◽

Zabidin Salleh ◽

Iing Lukman

Keyword(s):

Harmonic Mappings

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RENORMALIZATION OF FERMI VELOCITY IN A COMPOSITE TWO DIMENSIONAL ELECTRON GAS

International Journal of Modern Physics B ◽

10.1142/s0217979293000214 ◽

1993 ◽

Vol 07 (01n03) ◽

pp. 87-94 ◽

Cited By ~ 1

Author(s):

M. WEGER ◽

L. BURLACHKOV

Keyword(s):

Electron Gas ◽

Fermi Velocity ◽

Bohr Radius ◽

Dimensional Electron ◽

Temperature Dependent ◽

Two Dimensional Electron Gas ◽

Self Energy ◽

2D System ◽

Dimensional Electron Gas ◽

The One

We calculate the self-energy Σ(k, ω) of an electron gas with a Coulomb interaction in a composite 2D system, consisting of metallic layers of thickness d ≳ a 0, where a 0 = ħ2∊1/ me 2 is the Bohr radius, separated by layers with a dielectric constant ∊2 and a lattice constant c perpendicular to the planes. The behavior of the electron gas is determined by the dimensionless parameters k F a 0 and k F c ∊2/∊1. We find that when ∊2/∊1 is large (≈5 or more), the velocity v(k) becomes strongly k-dependent near k F , and v ( k F ) is enhanced by a factor of 5-10. This behavior is similar to the one found by Lindhard in 1954 for an unscreened electron gas; however here we take screening into account. The peak in v(k) is very sharp (δ k/k F is a few percent) and becomes sharper as ∊2/∊1 increases. This velocity renormalization has dramatic effects on the transport properties; the conductivity at low T increases like the square of the velocity renormalization and the resistivity due to elastic scattering becomes temperature dependent, increasing approximately linearly with T. For scattering by phonons, ρ ∝ T 2. Preliminary measurements suggest an increase in v k in YBCO very close to k F .

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On the univalence of certain integral for harmonic mappings

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2017.05.056 ◽

2017 ◽

Vol 455 (1) ◽

pp. 381-388 ◽

Cited By ~ 1

Author(s):

Víctor Bravo ◽

Rodrigo Hernández ◽

Osvaldo Venegas

Keyword(s):

Harmonic Mappings

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Dependence of Mono-Vacancy Formation Energy on the Parameter of Ashcroft's Potential

Defect and Diffusion Forum ◽

10.4028/www.scientific.net/ddf.278.25 ◽

2008 ◽

Vol 278 ◽

pp. 25-32 ◽

Cited By ~ 3

Author(s):

Amitava Ghorai

Keyword(s):

Correlation Functions ◽

Formation Energy ◽

Model Potential ◽

Group Iv ◽

Vacancy Formation Energy ◽

Core Model ◽

Bohr Radius ◽

Fcc Metals ◽

Group I ◽

Pseudopotential Approach

We show the calculation of the monovacancy formation energy ( v FH E1 ) for three different group-I monovalent fcc metals (Cu, Ag and Au) and two group-IV tetravalent fcc metals (Pb and Th) use a pseudopotential approach. Ashcroft's empty core model potential (AECMP) and nine different exchange and correlation functions (ECF) are used. The variation of v FH E1 with the parameter c r of AECMP for different ECF shows variations with the metals, and c r is observed to be greater than Bohr radius.

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