• The Pure and Applied Mathematics
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• v.2 no.1
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• pp.17-24
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• 1995

We begin with a brief survey of some of the known results dealing with Bloch constants. Bloch's theorem asserts that there is a constant B$\_$1.C/(1, 0) such that if f is holomorphic in the open unit disk D and normalized by │f'(0)│$\geq$1, then the Riemann surface of f contains an unramified disk of radius at least B$\_$1.C/(1, 0) (see[7,p.14]).(omitted)

• Proceedings of the Korean Statistical Society Conference
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• 2005.05a
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• pp.179-184
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• 2005

Empirical findings on interet rate dynamics imply that short rates show some long memories and non-Markovin. It is well-known that fractional Brownian motion(fBm) is a proper candidate for modelling this empirical phenomena. fBm, however, is not a semimartingale process. For this reason, it is very hard to apply such processes for asset price modelling. With some modifications, this paper investigate the fBm interest rate theory, and obtain a pure discount bond price and Greeks.

• The Pure and Applied Mathematics
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• v.2 no.2
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• pp.141-148
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• 1995

In this paper we shall consider function p(z) analytic in the open unit circle D and the solutions y(z) of the differential equation y"(Z) ＋ p(z)y(z) = 0. (1.1) The ratio f(z) = u(z)/v(z) of any two independent solutions u(z) and v(z) of (1.1) will be function f(z), meromorphic in D with only simple poles, and such that f'(z) (equation omitted) 0. We shall say that a meromorphic function which satisfies these two condition belongs to the restricted class.(omitted)

• Communications of the Korean Mathematical Society
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• v.36 no.1
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• pp.165-171
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• 2021

The purpose of this paper is to investigate the geometry of complete gradient Yamabe soliton (Mn, g, f, λ) with constant scalar curvature admitting a non-homothetic conformal vector field V leaving the potential vector field invariant. We show that in such manifolds the potential function f is constant and the scalar curvature of g is determined by its soliton scalar. Considering the locally conformally flat case and conformal vector field V, without constant scalar curvature assumption, we show that g has constant curvature and determines the potential function f explicitly.

• The Pure and Applied Mathematics
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• v.29 no.1
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• pp.113-124
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• 2022

In this paper, we plan to introduce the class of the analytic functions called 𝒫 (b) and to investigate the various properties of the functions belonging this class. The modulus of the second coefficient c₂ in the expansion of f(z) = z+c₂z²+… belonging to the given class will be estimated from above. Also, we estimate a modulus of the second angular derivative of f(z) function at the boundary point 𝛼 with f'(𝛼) = 1 - b, b ∈ ℂ, by taking into account their first nonzero two Maclaurin coefficients.

• Communications of the Korean Mathematical Society
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• v.38 no.3
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• pp.837-846
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• 2023

In this paper, we firstly construct a Hsu-B manifold and give some basic results related to it. Then, we address a semi-symmetric metric F-connection on the Hsu-B manifold and obtain the curvature tensor fields of such connection, and study properties of its curvature tensor and torsion tensor fields.

• The Pure and Applied Mathematics
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• v.31 no.1
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• pp.103-117
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• 2024

In this article, we utilize the concepts of hybrid rational Geraghty type generalized F-contraction and to prove some fixed point results for such mappings are in the perspective of partially ordered b-metric like space. Some innovative examples are also presented which substantiate the validity of obtained results. The example is also authenticated with the help of graphical representations.

• The Pure and Applied Mathematics
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• v.19 no.1
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• pp.43-57
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• 2012

By simply splitting the hypergeometric Saran function $F_E$ into eight parts, we show how some useful and generalized relations between $F_E$ and Srivas- tava's hypergeometric function $F^{(3)}$ can be obtained. These main results are shown to be specialized to yield certain relations between functions $_0F_1$, $_1F_1$, $_0F_3$, ${\Psi}_2$, and their products including different combinations with different values of parameters and signs of variables.

• The Pure and Applied Mathematics
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• v.17 no.1
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• pp.65-80
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• 2010

In [17, 18], the fuzzy stability problems for the Cauchy additive functional equation and the Jensen additive functional equation in fuzzy Banach spaces have been investigated. In this paper, we prove the generalized Hyers-Ulam stability of the following quadratic functional equations in fuzzy Banach spaces: (0.1) f(x + y) + f(x - y) = 2f(x) + 2f(y), (0.2) f(ax + by) + f(ax - by) = $2a^2 f(x)\;+\;2b^2f(y)$ for nonzero real numbers a, b with $a\;{\neq}\;{\pm}1$.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.9
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• pp.1897-1904
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• 2002

Monotonic torsional and pure torsional low cycle fatigue(LCF) test with artificial degradation were performed on duplex stainless steel(CF8M). CF8M is used in pipes and valves in nuclear reactor coolant system. It was aged at 430$^{\circ}C$ for 3600hrs. Through the monotonic and LCF test, it is found that mechanical properties(i.e., yield strength, strain hardening exponent, strength coefficient etc.) increase and fatigue life(N$\sub$f/) decreases with degradation of material. The relationship between shear strain amplitude(${\gamma}$$\sub$a/)and N$\sub$f/ was proposed.