• Communications for Statistical Applications and Methods
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• v.26 no.2
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• pp.91-102
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• 2019

In this paper, we propose a new estimation method based on a weighted linear regression framework to obtain some estimators for unknown parameters in a two-parameter Rayleigh distribution under a progressive Type-II censoring scheme. We also provide unbiased estimators of the location parameter and scale parameter which have a nuisance parameter, and an estimator based on a pivotal quantity which does not depend on the other parameter. The proposed weighted least square estimator (WLSE) of the location parameter is not dependent on the scale parameter. In addition, the WLSE of the scale parameter is not dependent on the location parameter. The results are compared with the maximum likelihood method and pivot-based estimation method. The assessments and comparisons are done using Monte Carlo simulations and real data analysis. The simulation results show that the estimators ${\hat{\mu}}_u({\hat{\theta}}_p)$ and ${\hat{\theta}}_p({\hat{\mu}}_u)$ are superior to the other estimators in terms of the mean squared error (MSE) and bias.

• The Pure and Applied Mathematics
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• v.29 no.4
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• pp.335-352
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• 2022

In this paper, we give an extended version of fixed point results for 𝜃-contraction and 𝜃-𝜙-contraction and define a new type of contraction, namely, cyclic 𝜃-contraction and cyclic 𝜃-𝜙-contraction in a complete metric space. Moreover, we prove the existence of best proximity point for cyclic 𝜃-contraction and cyclic 𝜃-𝜙-contraction. Also, we establish best proximity result in the setting of uniformly convex Banach space.

• Journal of the Korean Mathematical Society
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• v.60 no.5
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• pp.959-986
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• 2023

Zhai and Lin recently proved that if G is an n-vertex connected 𝜃(1, 2, r + 1)-free graph, then for odd r and n ⩾ 10r, or for even r and n ⩾ 7r, one has ${\rho}(G){\leq}{\sqrt{{\lfloor}{\frac{n^2}{4}}{\rfloor}}}$, and equality holds if and only if G is $K_{{\lceil}{\frac{n}{2}}{\rceil},{\lfloor}{\frac{n}{2}}{\rfloor}}$. In this paper, for large enough n, we prove a sharp upper bound for the spectral radius in an n-vertex H-free non-bipartite graph, where H is 𝜃(1, 2, 3) or 𝜃(1, 2, 4), and we characterize all the extremal graphs. Furthermore, for n ⩾ 137, we determine the maximum number of edges in an n-vertex 𝜃(1, 2, 4)-free non-bipartite graph and characterize the unique extremal graph.

• Journal of the Korean Crystal Growth and Crystal Technology
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• v.10 no.6
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• pp.378-380
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• 2000

The epitaxial $BaTiO_{3}$ thin film was prepared on the MgO substrate by the coating-pyrolysis process using a mixed solution of Ba-naphthenate and Ti-naphthenate. The crystal structure of the epitaxial $BaTiO_{3}$ thin film was characterized by XRD ${\theta}/2{\theta}$ scan and asymmetric {303} rocking curve scan. The epitaxial $BaTiO_{3}$ thin film had the cubic phase with the lattice parameter of a = c = 0.4018 nm.

• Journal of the Korean Statistical Society
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• v.6 no.2
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• pp.167-177
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• 1977

유전적 질환이 있는 가계에서 출생하는 자녀중에서 유전적인 질환을 보유할 수 있는 확률을 예측하는 방법의 하나로서 우도추정치(likelihood estimator)를 사용하는 것은 분리분석(segregation analysis)에서 중요한 역할을 하고 있다. Elston과 Stewart(1971)는 이러한 분석방법의 일반적인 통계모형을 정립하였으며 필자(1974)와 Morton 등 (1974)은 complex segregation이 될 때에 분석되는 4가지의 통계모형을 주장하였다. 본 연구의 목적은 multiple ascertainment $\pi$가 존재하는 경우 분리확률모수(segregation parameter) $\theta$의 우도추정치를 구하고 둘째로 oligogenic case에 대한 이론적인 배경을 구명하고자 한다.

• Journal of the Korean Society for Precision Engineering
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• v.14 no.8
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• pp.146-154
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• 1997

Solenoid-folw control type ABS is used with a 'dump and reapply' pressure control arrangement instead of using 2/2 (normal open/close) solenoid valves in convensional systems(sol. -sol. control type), a flow control valve is used which replaces the (no) inlet valve. The flow control valve controls fluid flow providing a nearly constant reapply rate( .theta. ) after the dump plase of ABS operation. In this study, to investigate a characteristics of brake pressure by PWM control, test rig was consisted of ABS hydraulic modulator, digital controller, pneumatic power supply and brake master cylinder. For comparison with experi- mental results, system modelling and computer simulation were performed. As a result, experiment results showed fairly agreement with the simulation. Also, it is shown that the pressure gradient (tan .theta. ) is affected by pressure, frequency, duty ratio and expressed with an exponential funtion.

• Journal of applied mathematics & informatics
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• v.40 no.1_2
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• pp.327-339
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• 2022

In this paper, we introduce arithmetic ${\mathcal{I}}$-statistically convergent sequence space $A{\mathcal{I}}SC$, ${\mathcal{I}}$-lacunary arithmetic statistically convergent sequence space $A{\mathcal{I}}SC_{\theta}$, strongly ${\mathcal{I}}$-lacunary arithmetic convergent sequence space $AN_{\theta}[{\mathcal{I}}]$ and prove some inclusion relations between these spaces. Futhermore, we give ${\mathcal{I}}$-lacunary arithmetic statistical continuity. Finally, we define ${\mathcal{I}}$-Cesàro arithmetic summability, strongly ${\mathcal{I}}$-Cesàro arithmetic summability. Also, we investigate the relationship between the concepts of strongly ${\mathcal{I}}$-Cesàro arithmetic summability, strongly ${\mathcal{I}}$-lacunary arithmetic summability and arithmetic ${\mathcal{I}}$ -statistically convergence.

• Bulletin of the Korean Mathematical Society
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• v.22 no.1
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• pp.17-22
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• 1985

B.M. Munshi and D.S. Bassan defined and developed the concept of super continuity in [5]. The concept has been investigated further by I. L. Reilly and M. K. Vamanamurthy in [6] where super continuity is characterized in terms of the semi-regularization topology. Super continuity is related to the concepts of .delta.-continuity and strong .theta.-continuity developed by T. Noiri in [7]. The purpose of this note is to derive relationships between super continuity and other strong continuity conditions and to develop additional properties of super continuous functions. Super continuity implies continuity, but the converse implication is false [5]. Super continuity is strictly between strong .theta.-continuity and .delta.-continuity and strictly between complete continuity and .delta.-continuity. The symbols X and Y will denote topological spaces with no separation axioms assumed unless explicity stated. The closure and interior of a subset U of a space X will be denoted by Cl(U) and Int(U) respectively and U is said to be regular open (resp. regular closed) if U=Int[Cl(U) (resp. U=Cl(Int(U)]. If necessary, a subscript will be added to denote the space in which the closure or interior is taken.

• Communications of the Korean Mathematical Society
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• v.39 no.2
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• pp.345-352
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• 2024

We introduce a new class of bi-partition function c_k(n), which counts the number of bi-color partitions of n in which the second color only appears at the parts that are multiples of k. We consider two partitions to be the same if they can be obtained by switching the color of parts that are congruent to zero modulo k. We show that the generating function for c_k(n) involves the partial theta function and obtain the following congruences: c₂(27n + 26) ≡ 0 (mod 3) and c₃(4n + 2) ≡ 0 (mod 2).

• The Pure and Applied Mathematics
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• v.31 no.2
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• pp.189-200
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• 2024

We derive modular equations of degree 3 to find corresponding theta-function identities. We use them to find some new evaluations of $G(e^{-{\pi}{\sqrt{n}}})$ and $G(-e^{-{\pi}{\sqrt{n}}})$ for $n\,=\,\frac{25}{3{\cdot}4^{m-1}}$ and $\frac{4^{1-m}}{3{\cdot}25}$, where m = 0, 1, 2.