Hacettepe Journal of Mathematics and Statistics

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ISSN : 1303-5010
Total articles ≅ 921
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Behrooz Mashayekhy, Ameneh Babaee, Hanieh Mirebrahimi, Hamid Torabi, Mahdi Abdullahi Rashid, Seyyed Zeynal Pashaei
Hacettepe Journal of Mathematics and Statistics pp 1-13; https://doi.org/10.15672/hujms.565367

, Jacqueline Galpin
Hacettepe Journal of Mathematics and Statistics pp 1-19; https://doi.org/10.15672/hujms.516601

Abstract:
Small area estimates have received much attention from both private and public sectors due to the growing demand for effective planning of health services, apportioning of government funds and policy and decision making. The uncertainty of empirical best linear unbiased predictor (EBLUP) estimates is widely assessed by mean squared error (MSE). MSEs are criticized as they are not area specific since they do not depend on the direct estimators from the survey. In this paper, we compare the performances of different MSE estimators with respect to the relative bias and relative risk using a Monte Carlo simulation study. Simulation results suggest the superiority of the proposed MSEs over the existing methods in some situations. As a case study, the 2010/11 household consumption expenditure survey (HCES) and the 2007 housing and population census of Ethiopia have been used to study the performances of the MSE estimators.
Li Guo, Honglin Zou, Jianlong Chen
Hacettepe Journal of Mathematics and Statistics pp 1-16; https://doi.org/10.15672/hujms.731518

Abstract:
Representations for the generalized Drazin inverse of an operator matrix $\begin{pmatrix} A & B\\C& D \end{pmatrix}$ are presented in terms of $A,B,C,D$ and the generalized Drazin inverses of $A,D,$ under the condition that $BD^d = 0$, and $BD_iC = 0$, for any nonnegative integer i. Using the representation, we give a new additive result of the generalized Drazin inverse for two bounded linear operators $P,Q \in B(X)$ with $PQ^d = 0$ and $PQ_iP = 0$, for any integer $ i \geqslant 1$. As corollaries, several well-known results are generalized
R. Ramesh, Julio G. Dix, S. Harikrishnan,
Hacettepe Journal of Mathematics and Statistics pp 1-10; https://doi.org/10.15672/hujms.554157

Abstract:
We consider the oscillatory behavior of solutions to partial dynamic equation on time scales. We establish several oscillation criteria by applying a Ricatti transformation. Examples are provided to justify our results.
Chillumuntala Jayaram, Ünsal Tekir, Suat Koç
Hacettepe Journal of Mathematics and Statistics pp 1-15; https://doi.org/10.15672/hujms.613404

Abstract:
Recall that a ring R is said to be a quasi regular ring if its total quotient ring q(R) is von Neumann regular. It is well known that a ring R is quasi regular iff it is a reduced ring satisfying the property: for each a \in R, ann(ann(a)) = ann(b) for some b \in R. Here, in this study, we extend the notion of quasi regular rings and rings which satisfy the aforementioned property to modules. We give many characterizations and properties of these two classes of modules. Moreover, we investigate the (weak) quasi regular property of trivial extension.
Sedef TAŞKIN, Hikmet Burak Özcan
Hacettepe Journal of Mathematics and Statistics pp 1-3; https://doi.org/10.15672/hujms.649706

Abstract:
In this short note, our aim is to provide novel proofs for the infinitude of primes in an algebraic way. It’s thought that the first proof for the infinitude of primes was given by the Ancient Greek mathematician Euclid. To date, most of the proofs have been based on the fact that every positive integer greater than 1 can be written as a product of prime numbers. However, first we are going to prove a ring theoretic fact that if R is an infinite commutative ring with unity and the cardinality of the set of invertible elements is strictly less than the cardinality of the ring, then there are infinitely many maximal ideals. This fact leads to an elegant proof for the infinitude of primes. In addition, under the same cardinality assumption, we consider the special case in which R is a unique factorization domain (for short UFD) and establish another ring theoretic result. Thanks to it, we give a second proof of the infinitude of primes.
Hacettepe Journal of Mathematics and Statistics pp 1-13; https://doi.org/10.15672/hujms.644665

Abstract:
In this paper, a new version of mean value theorem for interval-valued functions on time scales is established. Meantime, some basic concepts and results associated with semigroups of operators for interval-valued functions on time scales are presented. As an application of semigroups of operators, under certain conditions, we consider the initial value problem for interval-valued differential equations on time scales. Finally, two issues worthy of further discussion are presented.
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