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2019
12
1
ISSN 2008-1898
63
A new alpha power transformed family of distributions: properties and applications to the Weibull model
A new alpha power transformed family of distributions: properties and applications to the Weibull model
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In this article, a new technique of alpha-power transformation is used to propose a new class of lifetime distributions. Four special models of the new family are presented. Some mathematical properties of the proposed model including estimation of the unknown parameters using the method of maximum likelihood are discussed. For the illustrative purposes of the new proposal, a three-parameter special model of this class, namely, new alpha-power transformed Weibull distribution is considered in detail. The proposed distribution offers greater distributional flexibility and is able to model data with increasing, decreasing, and constant or more importantly with bathtub-shaped failure rates. Type-1 and Type-II censoring estimation are discussed. A simulation study based on complete sample of the new model is also carried out. Finally, the usefulness and efficiency of the new proposal is illustrated by analyzing two real data sets.
1
20
I.
Elbatal
Department of Mathematics and Statistics, College of Science
Al Imam Mohammad Ibn Saud Islamic University
Saudi Arabia
iielbatal@imamu.edu.sa
Zubair
Ahmad
Department of Statistics
Quaid-i-Azam University 45320
Pakistan
z.ferry21@gmail.com
M.
Elgarhy
Vice Presidency for Graduate Studies and Scientific Research
University of Jeddah
KSA
m_elgarhy85@yahoo.com
Abdullah M.
Almarashi
Statistics Department, Faculty of Science
King AbdulAziz University
Kingdom of Saudi Arabia
aalmarashi@kau.edu.sa
Alpha- power transformation
Weibull distribution
type-I and type-II censoring
bathtub shape
moment generating function
maximum likelihood estimation
Article.1.pdf
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An efficient iterative algorithm for finding a nontrivial symmetric solution of the Yang-Baxter-like matrix equation
An efficient iterative algorithm for finding a nontrivial symmetric solution of the Yang-Baxter-like matrix equation
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This paper presents an efficient iterative method to obtain a nontrivial symmetric solution of the Yang-Baxter-like matrix equation \(AXA=XAX \). Necessary conditions for the convergence of the propounded iterative method are derived. Finally, three numerical examples to illustrate the efficiency of the proposed method and the preciseness of our theoretical results are provided.
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29
Chacha Stephen
Chacha
Mathematics department
Mkwawa University College of Education
Tanzania
chchstephen@yahoo.com
Hyun-Min
Kim
Mathematics department
Pusan National University
Republic of Korea
hyunmin@pusan.ac.kr
Yang-Baxter matrix equation
iterative method
nontrivial solution
Newton's method
Article.2.pdf
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]
Mathematical model of generalized thermoelastic infinite medium with a spherical cavity and fractional order strain
Mathematical model of generalized thermoelastic infinite medium with a spherical cavity and fractional order strain
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In this paper, a new mathematical model of a thermoelastic isotropic unbounded medium contains a spherical cavity thermally shocked under generalized thermo-elasticity with the fractional order strain model. The governing system of the partial differential equations has been derived in Laplace transform domain, and the inversion was done numerically by using the sum of Riemann approximation techniques. The numerical outputs of the displacement, the temperature, the stress, and the strain have been obtained and presented graphically. The fractional order parameter has an essential consequence on the stress, the strain, and the displacement distributions while its effect on the temperature increment distribution is very limited.
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37
Eman A. N.
Al-Lehaibi
Mathematics Department, College of Science and Arts-Sharoura
Najran University
KSA
dremanallehaibi@gmail.com
Generalized thermo-elasticity
spherical cavity
fractional calculus
fractional strain
Article.3.pdf
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]
Common fixed point theorems for compatible mappings of type (A) satisfying certain contractive conditions in partial metric space
Common fixed point theorems for compatible mappings of type (A) satisfying certain contractive conditions in partial metric space
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The aim of this paper is to prove common fixed point theorems for compatible mappings of type (A) for three self-mappings satisfying certain contractive conditions and its topological properties in partial metric spaces.
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47
Durdana
Lateef
College of Science
Taibah University
Kingdom of Saudi Arabia
drdurdanamaths@gmail.com
Fixed point
self-mappings
compatibility of type (A)
partial metric space
Article.4.pdf
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]
Common fixed point theorems in Menger probabilistic metric spaces using the CLRg property
Common fixed point theorems in Menger probabilistic metric spaces using the CLRg property
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Under some weaker conditions of the \(\varphi\), some common fixed point theorems for weakly compatible mappings are established in Menger probabilistic metric spaces. Using the CLRg property, our results show that the completeness of underlying spaces is not necessary for fixed point theorems. In order to illustrate our results, we provide two examples in which other theorems cannot be applied.
48
55
Shuang
Wang
School of Mathematical Sciences
Yancheng Teachers University
P. R. China
wangshuang19841119@163.com
Dingbian
Qian
School of Mathematical Sciences
Soochow University
China
dbqian@suda.edu.cn
Menger probabilistic metric spaces
weakly compatible mappings
common fixed points
common limit in the range property
Article.5.pdf
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[1]
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J.-X. Fang, Common fixed point theorems of compatible and weakly compatible maps in Menger spaces, Nonlinear Anal., 71 (2009), 1833-1843
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J.-X. Fang, On \(\varphi\)-contractions in probabilistic and fuzzy metric spaces, Fuzzy Sets and Systems, 267 (2015), 86-99
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J. Jachymski, On probabilistic \(\phi\)-contractions on Menger spaces, Nonlinear Anal., 73 (2010), 2199-2203
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M. Jain, K. Tas, S. Kumar, N. Gupta , Coupled fixed point theorems for a pair of weakly compatible maps along with CLRg property in fuzzy metric spaces, J. Appl. Math., 2012 (2012), 1-13
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]
A note on the second kind \(q\)-Apostol Bernoulli numbers, polynomials, and Zeta function
A note on the second kind \(q\)-Apostol Bernoulli numbers, polynomials, and Zeta function
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In this paper we consider a new type of the \(q\)-Apostol Bernoulli numbers and polynomials. Firstly, we define the \(q\)-Apostol Bernoulli numbers and polynomials by making use of their generating function. Also, we observe many properties, i.e., the recurrence formula, the difference equation, the differential relation.
56
64
C. K.
An
Department of Mathematics
Hannam University
Korea
ack7165@gmail.com
H. Y.
Lee
Department of Mathematics
Hannam University
Korea
normaliz@hnu.kr
Y. R.
Kim
Department of Mathematics
Hannam University
Korea
cantor73@naver.com
The second kind \(q\)-Apostol Bernoulli polynomials
the second kind \(q\)-Apostol Bernoulli numbers
zeta function
Article.6.pdf
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]