Paper's Title:

Examples of Fractals Satisfying the Quasihyperbolic Boundary Condition

Author(s):

Petteri Harjulehto and Riku Klén

Department of Mathematics and Statistics,
FI-20014 University of Turku,
Finland

E-mail: petteri.harjulehto@utu.fi

E-mail: riku.klen@utu.fi

Abstract:

In this paper we give explicit examples of bounded domains that satisfy the quasihyperbolic boundary condition and calculate the values for the constants. These domains are also John domains and we calculate John constants as well. The authors do not know any other paper where exact values of parameters has been estimated.

Paper's Title:

Hyponormal and K-Quasi-Hyponormal Operators On Semi-Hilbertian Spaces

Author(s):

Ould Ahmed Mahmoud Sid Ahmed and Abdelkader Benali

Mathematics Department,
College of Science,
Aljouf University,
Aljouf 2014,
Saudi Arabia.
E-mail: sididahmed@ju.edu.sa

Mathematics Department, Faculty of Science,
Hassiba Benbouali, University of Chlef,
B.P. 151 Hay Essalem, Chlef 02000,
Algeria.
E-mail: benali4848@gmail.com

Abstract:

Let H be a Hilbert space and let A be a positive bounded operator on H. The semi-inner product < u|v>_A:=<Au|v>, u,v ∈ H induces a semi-norm || .||_A on H. This makes H into a semi-Hilbertian space. In this paper we introduce the notions of hyponormalities and k-quasi-hyponormalities for operators on semi Hilbertian space (H,||.||_A), based on the works that studied normal, isometry, unitary and partial isometries operators in these spaces. Also, we generalize some results which are already known for hyponormal and quasi-hyponormal operators. An operator T ∈ B_A (H) is said to be (A, k)-quasi-hyponormal if

Paper's Title:

Fekete Szegö problem on the Class of Bazilevič functions B₁(α) related to the Lemniscate Bernoulli

Author(s):

N. M. Asih, Marjono, Sa'adatul Fitri, Ratno Bagus Edy Wibowo

Department of Mathematics,
University of Brawijaya,
Malang 65145,
Indonesia.
Department of Mathematics,
University of Udayana,
Bali,
Indonesia.
E-mail: madeasih@unud.ac.id

Department of Mathematics,
University of Brawijaya,
Malang 65145,
Indonesia.
E-mail: marjono@ub.ac.id

Department of Mathematics,
University of Brawijaya,
Malang 65145,
Indonesia.
E-mail: saadatulfitri@ub.ac.id

Department of Mathematics,
University of Brawijaya,
Malang 65145,
Indonesia.
E-mail: rbagus@ub.ac.id

Abstract:

We provide a sharp boundaries inequalities for Fekete Szegö problem |a₃-μ a₂²|, the coefficients of logarithmic function log~ f(z)/z, and the coefficients of the inverse function f(f'(w)) on the Bazilevič functions B₁(α) related to the Lemniscate Bernoulli on the unit disk D={z: |z| < 1}. We obtained the result by using some properties of function with positive real part relates to coefficients problems.

Paper's Title:

Hyperbolic Models Arising in the Theory of Longitudinal Vibration of Elastic Bars

Author(s):

¹I. Fedotov, ¹J. Marais, ^1,2M. Shatalov and ¹H.M. Tenkam

¹Department of Mathematics and Statistics,
Tshwane University of Technology
 Private Bag X6680, Pretoria 0001
South Africa.

fedotovi@tut.ac.za, julian.marais@gmail.com, djouosseutenkamhm@tut.ac.za.

 ²Manufacturing and Materials
Council of Scientific and Industrial Research (CSIR)
P.O. Box 395, Pretoria, 0001
South Africa.
mshatlov@csir.co.za

Abstract:

In this paper a unified approach to the derivation of families of one
dimensional hyperbolic differential equations and boundary conditions describing
the longitudinal vibration of elastic bars is outlined. The longitudinal and
lateral displacements are expressed in the form of a power series expansion in
the lateral coordinate. Equations of motion and boundary conditions are derived
using Hamilton's variational principle. Most of the well known models in this
field fall within the frames of the proposed theory, including the classical
model, and the more elaborated models proposed by by Rayleigh, Love, Bishop,
Mindlin, Herrmann and McNiven. The exact solution is presented for the
Mindlin-Herrmann case in terms of Green functions. Finally, deductions regarding
the accuracy of the models are made by comparison with the exact
Pochhammer-Chree solution for an isotropic cylinder.

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