• Communications of the Korean Mathematical Society
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• v.36 no.4
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• pp.685-704
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• 2021

The purpose of this paper is to establish a very general Cameron-Storvick theorem involving the generalized analytic Feynman integral of functionals on the product function space C²_a,b[0, T]. The function space C_a,b[0, T] can be induced by the generalized Brownian motion process associated with continuous functions a and b. To do this we first introduce the class ${\mathcal{F}}^{a,b}_{A_1,A_2}$ of functionals on C²_a,b[0, T] which is a generalization of the Kallianpur and Bromley Fresnel class ${\mathcal{F}}_{A_1,A_2}$. We then proceed to establish a Cameron-Storvick theorem on the product function space C²_a,b[0, T]. Finally we use our Cameron-Storvick theorem to obtain several meaningful results and examples.

• Korean Journal of Mathematics
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• v.28 no.4
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• pp.699-715
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• 2020

In this paper, we give estimates of the Hankel determinant H₂(1) in a novel class 𝓝 (𝜀) of analytical functions in the unit disc. In addition, the relation between the Fekete-Szegö function H₂(1) and the module of the angular derivative of the analytical function p(z) at a boundary point b of the unit disk will be given. In this association, the coefficients in the Hankel determinant b₂, b₃ and b₄ will be taken into consideration. Moreover, in a class of analytic functions on the unit disc, assuming the existence of angular limit on the boundary point, the estimations below of the modulus of angular derivative have been obtained.

• Korean Journal of Mathematics
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• v.27 no.4
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• pp.1043-1059
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• 2019

In this paper, we use some theta function identities involving two parameters h_n,k and h'_n,k for the theta function φ to establish new evaluations of Ramanujan's cubic continued fraction.

• Bulletin of the Korean Mathematical Society
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• v.57 no.5
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• pp.1241-1249
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• 2020

Let Ω be a domain in ℂⁿ. Suppose that ∂Ω is smooth pseudoconvex of D'Angelo finite type near a boundary point ξ₀ ∈ ∂Ω and the Levi form has corank at most 1 at ξ₀. Our goal is to show that if the squeezing function s_Ω(𝜂_j) tends to 1 or the Fridman invariant h_Ω(𝜂_j) tends to 0 for some sequence {𝜂_j} ⊂ Ω converging to ξ₀, then this point must be strongly pseudoconvex.

• Korean Journal of Mathematics
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• v.31 no.3
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• pp.305-311
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• 2023

We exhibit some properties of the weighted Berezin transform T_αf on L^∞(B_n) and on L¹(B_n). As the main result, we prove that if f ∈ L^∞(B_n) with lim_k→∞ T^k_αf exists, then there exist unique M-harmonic function g and $h{\in}{\bar{(I-T_{\alpha})L^{\infty}(B_n)}}$ such that f = g + h. We also show that of the norm of weighted Berezin operator T_α on L¹(B_n, ν) converges to 1 as α tends to infinity, where ν is an ordinary Lebesgue measure.

• The Pure and Applied Mathematics
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• v.30 no.3
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• pp.337-345
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• 2023

Different versions of the boundary Schwarz lemma for the 𝒩 (𝜌) class are discussed in this study. Also, for the function g(z) = z+b₂z²+b₃z³+... defined in the unit disc D such that g ∈ 𝒩 (𝜌), we estimate a modulus of the angular derivative of g(z) function at the boundary point 1 ∈ 𝜕D with g'(1) = 1 + 𝜎 (1 - 𝜌), where ${\rho}={\frac{1}{n}}{\sum\limits_{i=1}^{n}}g(c_i)={\frac{g^{\prime}(c_1)+g^{\prime}(c_2)+{\ldots}+g^{\prime}(c_n)}{n}}{\in}g^{\prime}(D)$ and 𝜌≠1, 𝜎 > 1 and c₁, c₂, ..., c_n ∈ 𝜕D. That is, we shall give an estimate below |g"(1)| according to the first nonzero Taylor coefficient of about two zeros, namely z = 0 and z ≠ 0. Estimating is made by using the arithmetic average of n different derivatives g'(c₁), g'(c₂), ..., g'(c_n).

• Physical Therapy Korea
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• v.29 no.3
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• pp.200-207
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• 2022

Background: The oxygen uptake efficiency slope (OUES) is the most important index for accurately measuring cardiopulmonary function in patients with acute ischemic heart disease. However, the relationship between the OUES variables and important cardiopulmonary function parameters remain unelucidated for patients with acute ischemic heart disease, which accounts for the largest proportion of heart disease. Objects: The present cross sectional clinical study aimed to determine the multiple relationships among the cardiopulmonary function variables mentioned above in adults with acute ischemic heart disease. Methods: A convenience sample of 110 adult inpatients with ischemic heart disease (age: 57.4 ± 11.3 y; 95 males, 15 females) was enrolled at the hospital cardiac rehabilitation center. The correlation between the important cardiopulmonary function indicators including peak oxygen uptake (VO₂ peak), minute ventilation (VE)/carbon dioxide production (VCO₂) slope, heart rate recovery (HRR), and ejection fraction (EF) and OUES was confirmed. Results: This study showed that OUES was highly correlated with VO₂ peak, VE/VCO₂ slope, and HRR parameters. Conclusion: The OUES can be used as an accurate indicator for cardiopulmonary function. There are other factors that influence aerobic capacity besides EF, so there is no correlation with EF. Effective cardiopulmonary rehabilitation programs can be designed based on OUES during submaximal exercise in patients with acute ischemic heart disease.

• Nonlinear Functional Analysis and Applications
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• v.26 no.2
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• pp.323-329
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• 2021

The main object of the present paper is to investigate some radius results of the functions f(z) = z + Σ^∞_n=2 a_nzⁿ(|z| < 1) with |a_n| ≤ n for all n ∈ ℕ. Some applications for certain operator defined through convolution are also considered.

• Bulletin of the Korean Mathematical Society
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• v.58 no.4
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• pp.915-937
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• 2021

In this paper we deal with the open problem posed by Lü, Li and Yang [10]. In fact, we prove the following result: Let f(z) be a transcendental meromorphic function of finite order having finitely many poles, c₁, c₂, …, c_n ∈ ℂ\{0} and k, n ∈ ℕ. Suppose fⁿ(z), f(z+c₁)f(z+c₂) ⋯ f(z+c_n) share 0 CM and fⁿ(z)-Q₁(z), (f(z+c₁)f(z+c₂) ⋯ f(z+c_n))^(k) - Q₂(z) share (0, 1), where Q₁(z) and Q₂(z) are non-zero polynomials. If n ≥ k+1, then $(f(z+c_1)f(z+c_2)\;{\cdots}\;f(z+c_n))^{(k)}\;{\equiv}\;{\frac{Q_2(z)}{Q_1(z)}}f^n(z)$. Furthermore, if Q₁(z) ≡ Q₂(z), then $f(z)=c\;e^{\frac{\lambda}{n}z}$, where c, λ ∈ ℂ \ {0} such that e^{λ(c₁+c₂+⋯+c_n)} = 1 and λ^k = 1. Also we exhibit some examples to show that the conditions of our result are the best possible.

• The Journal of the Acoustical Society of Korea
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• v.19 no.5
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• pp.79-83
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• 2000

When passband ripple α/sub p/ and stopband attenuation α/sub s/ at the w/sub s/ where the stopband begins are specified in filter design, △α/sub s/ usually exceeds the specification by △α/sub s/ due to the necessity that the order n of the filter function be an integer. In this paper, we apply a trade-off method to remove the excess stopband attenuation △α/sub s/ for reducing the value of pole-Q and improving the characteristics of the Chebyshev filter function. We also apply the trade-off method of pole-Q reduction to the modified Chebyshev function, and then the 4 types of function have been analyzed to compare in frequency and time domain characteristics. The trade-off method reduces the pole-Q which influences the filter characteristics to maximum 49.6% without increase of the order n. Thus implies that they have the improved characteristics such as the reduced passband ripple and flatter delay characteristics as compared Chebyshev filter function before trade-off. And the unit step response shows shorter delay time and settling time in time domain performance.