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result(s) for
"Faber "
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Symmetrization for Mixed Operators
In this paper, we prove Talenti's comparison theorem for mixed local/nonlocal elliptic operators and derive the Faber–Krahn inequality for the first eigenvalue of the Dirichlet mixed local/nonlocal problem. Our findings are relevant to the fractional
–Laplacian operator.
Journal Article
The Making of a Renowned Doctor: The Early Experiences of Edmund Dipper (1871-1919)
Dr.Edmund Dipper, a distinguished German doctor practicing in China during the tumultuous decades of the 1920s and 1930s, rose to near-legendary status during the Republican era.Yet, the historical trajectory leading to his acclaim remains shrouded in conflicting narratives.Dipper's formative years demonstrate that his success in China stemmed from a multifaceted background encompassing education, religion, and military service.This was coupled with an unwavering commitment to excellence in medical practice and adaptability and resourcefulness in navigating cross-cultural settings.These factors allowed him to successfully avoid strife between church factions when managing the Faber Hospital.Furthermore, Dipper's remarkable intercultural acumen enabled him to seize a crucial historical opportunity.By adeptly navigating the German Hospital through the repatriation of German citizens after China declared war on Germany in 1917, he not only preserved his own standing but also safeguarded the hospital's key personnel.This strategic maneuvering laid the groundwork for his illustrious career trajectory.Dipper epitomizes a subset of Western doctors in China during this era, underscoring the imperative to further explore their nuanced historical contributions.
Journal Article
Faber Polynomial Coefficient Estimates for Bi-Univalent Functions Defined by Using Differential Subordination and a Certain Fractional Derivative Operator
In this article, we introduce a general family of analytic and bi-univalent functions in the open unit disk, which is defined by applying the principle of differential subordination between analytic functions and the Tremblay fractional derivative operator. The upper bounds for the general coefficients | a n | of functions in this subclass are found by using the Faber polynomial expansion. We have thereby generalized and improved some of the previously published results.
Journal Article
An Extremal Problem for the Bergman Kernel of Orthogonal Polynomials
Let
Γ
⊂
C
be a curve of class
C
(
1
,
α
)
. For
z
0
in the unbounded component of
C
\\
Γ
, and for
n
=
1
,
2
,
.
.
.
, let
ν
n
be a probability measure with
supp
(
ν
n
)
⊂
Γ
which minimizes the Bergman function
B
n
(
ν
,
z
)
:
=
∑
k
=
0
n
|
q
k
ν
(
z
)
|
2
at
z
0
among all probability measures
ν
on
Γ
(here,
{
q
0
ν
,
…
,
q
n
ν
}
are an orthonormal basis in
L
2
(
ν
)
for the holomorphic polynomials of degree at most
n
). We show that
{
ν
n
}
n
tends weak-* to
δ
^
z
0
, the balayage of the point mass at
z
0
onto
Γ
, by relating this to an optimization problem for probability measures on the unit circle. Our proof makes use of estimates for Faber polynomials associated to
Γ
.
Journal Article
ON THE SECOND EIGENVALUE OF COMBINATION BETWEEN LOCAL AND NONLOCAL p-LAPLACIAN
In this paper, we study the mountain pass characterization of the second eigenvalue of the operator − Δ p u − Δ J , p u - _p u - _J,pu and study shape optimization problems related to these eigenvalues.
Journal Article
Faber polynomial coefficient inequalities for bi-Bazilevič functions associated with the Fibonacci-number series and the square-root functions
Two new subclasses of the class of bi-Bazilevič functions, which are related to the Fibonacci-number series and the square-root functions, are introduced and studied in this article. Under a special choice of the parameter involved, these two classes of Bazilevič functions reduce to two new subclasses of star-like biunivalent functions related with the Fibonacci-number series and the square-root functions. Using the Faber polynomial expansion (FPE) technique, we find the general coefficient bounds for the functions belonging to each of these classes. We also find bounds for the initial coefficients for bi-Bazilevič functions and demonstrate how unexpectedly these initial coefficients behave in relation to the square-root functions and the Fibonacci-number series.
Journal Article
