• 한국수학교육학회지시리즈B:순수및응용수학
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• 제29권1호
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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.

• Korean Journal of Mathematics
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• 제32권3호
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• pp.439-451
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• 2024

In the present paper, using the notion of difference sequence spaces, we introduce new kind of Cesàro summable difference sequence spaces of vector valued sequences with the aid of paranorm and modulus function. In addition, we extend the notion of statistical convergence to introduce a new sequence space SC₁(∆, q) which coincides with C¹₁(X, ∆, φ, λ, q) (one of the above defined Cesàro summable difference sequence spaces) under the restriction of bounded modulus function.

• 전기학회논문지P
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• 제52권1호
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• pp.9-13
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• 2003

Energy Distribution Function in pure $CH_4$, $CF_4$ and mixtures of $CF_4$ and Ar, have been analyzed over a range of the reduced electric field strength between 0.1 and 350[Td] by the two-term approximation of the Boltzmann equation (BEq.) method and the Monte Carlo simulation (MCS). The results of the Boltzmann equation and the Monte Carlo simulation have been compared with the data presented by several workers. The deduced transport coefficients for electrons agree reasonably well with the experimental and simulation data obtained by Nakamura and Hayashi. The energy distribution function of electrons in $CF_4-Ar$ mixtures shows the Maxwellian distribution for energy. That is, $f(\varepsilon)$ has the symmetrical shape whose axis of symmetry is a most probably energy. The measured results and the calculated results have been compared each other.

• 호남수학학술지
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• 제28권2호
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• pp.221-224
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• 2006

A Kummer-type transformation formula for the generalized hypergeometric function $_2F_2$ deduced by Exton, rederived in two simple and transparent ways by Miller and generalized by Paris, is again derived by another method.

• 충청수학회지
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• 제36권4호
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• pp.215-221
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• 2023

We characterize a rational period function q(z) for Γ⁺₀ (3) which has a pole only at 0.

• Korean Journal of Mathematics
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• 제32권3호
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• pp.545-560
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• 2024

In the present study, we have constructed a new Banach series space |𝛶^r|^u_p by using concept of absolute Jordan totient summability |𝛶^r, u_n|_p which is derived by the infinite regular matrix of the Jordan's totient function. Also, we prove that the series space |𝛶^r|^u_p is linearly isomorphic to the space of all p-absolutely summable sequences ℓ_p for p ≥ 1. Moreover, we compute the α-, β- and γ- duals of this space and construct Schauder basis for the series space |𝛶^r|^u_p. Finally, we characterize the classes of infinite matrices (|𝛶^r|^u_p, X) and (X, |𝛶^r|^u_p), where X is any given classical sequence spaces ℓ_∞, c, c₀ and ℓ₁.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제16권9호
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• pp.2882-2903
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• 2022

Image super-resolution (SR) processing is of great value in the fields of digital image processing, intelligent security, film and television production and so on. This paper proposed a densely connected deep learning network based on cascade architecture, which can be used to solve the problem of super-resolution in the field of image quality enhancement. We proposed a more efficient residual scaling dense block (RSDB) and the multi-channel cascade architecture to realize more efficient feature reuse. Also we proposed a hybrid loss function based on L₁ error and L_∞ error to achieve better L_∞ error performance. The experimental results show that the overall performance of the network is effectively improved on cascade architecture and residual scaling. Compared with the residual dense net (RDN), the PSNR / SSIM of the new method is improved by 2.24% / 1.44% respectively, and the L_∞ performance is improved by 3.64%. It shows that the cascade connection and residual scaling method can effectively realize feature reuse, improving the residual convergence speed and learning efficiency of our network. The L_∞ performance is improved by 11.09% with only a minimal loses of 1.14% / 0.60% on PSNR / SSIM performance after adopting the new loss function. That is to say, the L_∞ performance can be improved greatly on the new loss function with a minor loss of PSNR / SSIM performance, which is of great value in L_∞ error sensitive tasks.

• 대한수학회보
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• 제57권2호
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• pp.331-343
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• 2020

This paper is concerned with the global behavior of components of radial nodal solutions of semilinear elliptic problems -Δv = λh(x, v) in Ω, v = 0 on ∂Ω, where Ω = {x ∈ R^N : r₁ < |x| < r₂} with 0 < r₁ < r₂, N ≥ 2. The nonlinear term is continuous and satisfies h(x, 0) = h(x, s₁(x)) = h(x, s₂(x)) = 0 for suitable positive, concave function s₁ and negative, convex function s₂, as well as sh(x, s) > 0 for s ∈ ℝ \ {0, s₁(x), s₂(x)}. Moreover, we give the intervals for the parameter λ which ensure the existence and multiplicity of radial nodal solutions for the above problem. For this, we use global bifurcation techniques to prove our main results.

• 대한수학회보
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• 제57권6호
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• pp.1541-1565
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• 2020

Let f be a meromorphic function of finite order ρ with few poles in the sense S_λ(r, f) := O(r^λ+ε) + S(r, f), where λ < ρ and ε ∈ (0, ρ - λ), and let g(f) := Σ^k_j=1b_j(z)f^(k_j)(z + c_j) be a linear delay-differential polynomial of f with small meromorphic coefficients b_j in the sense S_λ(r, f). The zero distribution of fⁿ(g(f))^s - b₀ is considered in this paper, where b₀ is a small function in the sense S_λ(r, f).

• Journal of applied mathematics & informatics
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• 제40권5_6호
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• pp.813-830
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• 2022

The generating functions of the divisor function σ_s(n) = Σ_0<d|n d^s are quasimodular forms. In this paper, we find the basis of the space of quasimodular forms of weight 6 on Γ₀(10) consisting of Eisenstein series and η-quotients. Then we evaluate the convolution sum Σ_ak+bl+cm=n σ(k)σ(l)σ(m) with lcm(a, b, c) = 10 and Σ_al+bm=n lσ(l)σ(m) and Σ_al+bm=n σ₃(l)σ(m) with lcm(a, b) = 10.