• Bulletin of the Korean Mathematical Society
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• v.37 no.4
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• pp.729-741
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• 2000

In this paper, we study in Banach spaces the existence of fixed points of asymptotically regular mapping T satisfying: for each x, y in the domain and for n=1, 2,…, $$\parallelT^nx-T^ny\parallel\leq$\leq$a_n\parallelx-y\parallel+b_n (\parallelx-T^nx\parallel+\parallely-T^ny\parallely)$$ where $a_n,\; b_n,\; C_n$ are nonnegative constants satisfying certain conditions. We also establish some fixed point theorems for these mappings in a Hibert space, in L(sup)p spaces, in Hardy space H(sup)p, and in Soboleve space $H^{k,p} for 1<\rho<\infty \; and \; k\geq0$. We extend results from papers [10], [11], and others.

• Communications for Statistical Applications and Methods
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• v.16 no.3
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• pp.529-540
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• 2009

In this paper, we present some results on weak laws of large numbers for weighted sums of fuzzy random variables taking values in the space of fuzzy numbers of the real line R. We first give improvements of WLLN for weighted sums of convex-compactly uniformly integrable fuzzy random variables obtained by Joo and Hyun (2005). And then, we consider the case that the averages of expectations of fuzzy random variables converges. As results, WLLN for weighted sums of convexly tight or identically distributed case is obtained.

• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.87-102
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• 2011

The purpose of this paper is to prove strong convergence theorems for finding a common element of the set of fixed points of a weak relatively nonexpansive mapping and the set of solutions of the variational inequality for an inverse-strongly-monotone mapping by a new hybrid method in a Banach space. We shall give an example which is weak relatively nonexpansive mapping but not relatively nonexpansive mapping in Banach space $l^2$. Our results improve and extend the corresponding results announced by Ying Liu[Ying Liu, Strong convergence theorem for relatively nonexpansive mapping and inverse-strongly-monotone mapping in a Banach space, Appl. Math. Mech. -Engl. Ed. 30(7)(2009), 925-932] and some others.

• Communications of the Korean Mathematical Society
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• v.26 no.1
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• pp.23-35
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• 2011

In the present work we construct a composite implicit random iterative process with errors for a finite family of asymptotically nonexpansive random operators and discuss a necessary and sufficient condition for the convergence of this process in an arbitrary real Banach space. It is also proved that this process converges to the common random fixed point of the finite family of asymptotically nonexpansive random operators in the setting of uniformly convex Banach spaces. The present work also generalizes a recently established result in Banach spaces.

• Honam Mathematical Journal
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• v.44 no.1
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• pp.135-145
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• 2022

This paper aims to investigate characterizations on parameters k₁, k₂, k₃, k₄, k₅, l₁, l₂, l₃, and l₄ to find relation between the class of 𝓗(k, l, m, n, o) hypergeometric functions defined by $$5_F_4\[{\array{k_1,\;k_2,\;k_3,\;k_4,\;k_5\\l_1,\;l_2,\;l_3,\;l_4}}\;:\;z\]=\sum\limits_{n=2}^{\infty}\frac{(k_1)_n(k_2)_n(k_3)_n(k_4)_n(k_5)_n}{(l_1)_n(l_2)_n(l_3)_n(l_4)_n(1)_n}z^n$$. We need to find k, l, m and n that lead to the necessary and sufficient condition for the function zF([W]), G = z(2 - F([W])) and $H_1[W]=z^2{\frac{d}{dz}}(ln(z)-h(z))$ to be in 𝓢^*(2^-r), r is a positive integer in the open unit disc 𝒟 = {z : |z| < 1, z ∈ ℂ} with $$h(z)=\sum\limits_{n=0}^{\infty}\frac{(k)_n(l)_n(m)_n(n)_n(1+\frac{k}{2})_n}{(\frac{k}{2})_n(1+k-l)_n(1+k-m)_n(1+k-n)_nn(1)_n}z^n$$ and $$[W]=\[{\array{k,\;1+{\frac{k}{2}},\;l,\;m,\;n\\{\frac{k}{2}},\;1+k-l,\;1+k-m,\;1+k-n}}\;:\;z\]$$.

• Bulletin of the Korean Mathematical Society
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• v.36 no.1
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• pp.147-159
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• 1999

Tabanov investigated the global symmetric perturbation of the integrable billiard mapping in the ellipse [3]. He showed the nonintegrability of the Birkhoff billiard in the perturbed domain by proving that the principal separatrices splitting angle is not zero.In this paper, using the exact separatrix map of an one-degree-of freedom Hamiltoniam system with time periodic perturbation, we show the existence the stochastic layer including the uniformly hyperbolic invariant set which implies the nonintegrability near the separatrices of a Birkhoff's billiard in the domain bounded by $C^2$ convex simple curve constructed by the generic global perturbation of the ellipse.

• East Asian mathematical journal
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• v.26 no.5
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• pp.627-639
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• 2010

In this paper, we introduce a new iterative sequence finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality for an inverse-strongly-monotone mapping in a Banach space. Then we show that the sequence converges strongly to a common element of two sets. Using this result, we consider the problem of finding a common element of the set of fixed points of a nonexpansive mapping and the set of zeros of an inverse-strongly-monotone mapping, the fixed point problem and the classical variational inequality problem. Our results improve and extend the corresponding results announced by many others.

• Journal of radiological science and technology
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• v.29 no.2
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• pp.63-69
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• 2006

In diagnostic ultrasound, the quality of image affect to diagnose. To maintain suboptimal imaging uniformly, Quality Assurance of Ultrasound equipment should take periodically. This is article about examination the quality of image in diagnostic ultrasound to understand conditions of probes in hospitals. There is comparative study of convex and linear probes on ultrasound using tissue-mimicking phantom included simulated cysts, echogenic structures. The ultrasonic attenuation coefficient versus frequency of 0.5 dB is representative of normal liver and 0.7 dB is representative of fatty liver condition in ultrasound phantom. There are results of convex probe, 0.5 dB, vertical group, cystic masses, high contrast masses are mostly shown but 0.7 dB, mid level in vertical group, cystic masses and high contrast masses are nearly visible. In linear probe, 0.5 dB, mid level in vertical group, two or four of them are shown in cystic masses and high contrast masses but there are not visible in 11 of cases. 0.7 dB, there are mostly appear under 6 in vertical group, two or four of them show in cystic masses and high contrast masses and there are not shown in 40 of cases, besides. Linear probes in fatty liver condition of ultrasound instrument are not good in the quality of image practically. So there needs to be replace and fix of probes. Actually management of ultrasound probes is inadequate in hospitals. So if there are program of evaluation to check probes periodically in hospitals from establishment of the ultrasound equipment, there will get better image and have a suitable condition of instruments further more.

• Journal of Korean Tunnelling and Underground Space Association
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• v.19 no.5
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• pp.733-747
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• 2017

In the shallow tunnel, the surrounding ground could be loosened and deformed, which could be the cause of stress change in the ground. Terzaghi has clarified the development of a ground arching induced by the deformation of a tunnel crown in the trap door tests. However, he considered only the case in which that the tunnel crown deformed uniformly. He did not consider the effect of deformation shapes. Therefore, the relation between the shape of the ground relaxation above the tunnel crown and the deformation shape of the tunnel crown is not clear yet. In this study, model tests were performed for the three types of the tunnel crown, such as uniform, concave and convex shapes. As results, it was found that the vertical load would be transferred in various types depending on the deformation shapes of the tunnel crown.

• The Journal of Korean Academy of Prosthodontics
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• v.45 no.1
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• pp.85-97
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• 2007

Statement of problem: Recently, anodic oxidation of cp-titanium is a popular method for treatment of titanium implant surfaces. It is a relatively easy process, and the thickness, structure, composition, and the microstructure of the oxide layer can be variably modified. Moreover the biological properties of the oxide layer can be controlled. Purpose: In this study, the roughness, microstructure, crystal structure of the variously treated groups (current, voltage, frequency, electrolyte, thermal treatment) were evaluated. And the specimens were soaked in simulated body fluid (SBF) to evaluate the effects of the surface characteristics and the oxide layers on the bioactivity of the specimens which were directly related to bone formation and integration. Materials and methods: Surface treatments consisted of either anodization or anodization followed thermal treatment. Specimens were divided into seven groups, depending on their anodizing treatment conditions: constant current mode (350V for group 2), constant voltage mode (155V for group 3), 60 Hz pulse series (230V for group 4, 300V for group 5), and 1000 Hz pulse series (400V for group 6, 460V for group 7). Non-treated native surfaces were used as controls (group 1). In addition, for the purpose of evaluating the effects of thermal treatment, each group was heat treated by elevating the temperature by $5^{\circ}C$ per minute until $600^{\circ}C$ for 1 hour, and then bench cured. Using scanning electron microscope (SEM), porous oxide layers were observed on treated surfaces. The crystal structures and phases of titania were identified by thin-film x-ray diffractmeter (TF-XRD). Atomic force microscope (AFM) was used for roughness measurement (Sa, Sq). To evaluate bioactivity of modified titanium surfaces, each group was soaked in SBF for 168 hours (1 week), and then changed surface characteristics were analyzed by SEM and TF-XRD. Results: On basis of our findings, we concluded the following results. 1. Most groups showed morphologically porous structures. Except group 2, all groups showed fine to coarse convex structures, and the groups with superior quantity of oxide products showed superior morphology. 2. As a result of combined anodization and thermal treatment, there were no effects on composition of crystalline structure. But, heat treatment influenced the quantity of formation of the oxide products (rutile / anatase). 3. Roughness decreased in the order of groups 7,5,2,3,6,4,1 and there was statistical difference between group 7 and the others (p<0.05), but group 7 did not show any bioactivity within a week. 4. In groups that implanted ions (Ca/P) on the oxide layer through current and voltage control, showed superior morphology, and oxide products, but did not express any bioactivity within a week. 5. In group 3, the oxide layer was uniformly organized with rutile, with almost no titanium peak. And there were abnormally more [101] orientations of rutile crystalline structure, and bonelike apatite formation could be seen around these crystalline structures. Conclusion: As a result of control of various factors in anodization (current, voltage, frequency, electrolytes, thermal treatment), the surface morphology, micro-porosity, the 2nd phase formation, crystalline structure, thickness of the oxide layer could be modified. And even more, the bioactivity of the specimens in vitro could be induced. Thus anodic oxidation can be considered as an excellent surface treatment method that will able to not only control the physical properties but enhance the biological characteristics of the oxide layer. Furthermore, it is recommended in near future animal research to prove these results.