• Journal of applied mathematics & informatics
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• v.41 no.5
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• pp.923-935
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• 2023

In this paper, we will discuss existence of solution of square-mean pseudo almost automorphic solution for fractional stochastic evolution equations driven by G-Brownian motion which is given as ^c₀D^𝛼_𝜌 Ψ_𝜌 = 𝒜(𝜌)Ψ_𝜌d𝜌 + 𝚽(𝜌, Ψ_𝜌)d𝜌 + ϒ(𝜌, Ψ_𝜌)d ⟨ℵ⟩_𝜌 + χ(𝜌, Ψ_𝜌)dℵ_𝜌, 𝜌 ∈ R. Furthermore, we also prove that solution of the above equation is unique by using Lipschitz conditions and Cauchy-Schwartz inequality. Moreover, examples demonstrate the validity of the obtained main result and we obtain the solution for an equation, and proved that this solution is unique.

• Proceedings of the IEEK Conference
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• 2001.10a
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• pp.84-87
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• 2001

A demand for the aggregates is increasing in the field of civil and architectural industry and so on. In these industries, the particle size and shape of aggregates are important factors and especially spherical or rounded particles are desired. In Japan, waste glass is used as one of the aggregate materials for the pavement or the construction. In this study based on the frictional action of material on each other, an autogenous grinding of silica glass with a stirred mill were carried out in order to eliminate flakelike or squarish particles and get spherical or rounded ones for aggregate materials. The autogenous grinding experiments were conducted by applying loads to the particle layer of silica glass. The particle shape was evaluated by the shape index, N/T and the degree of circularity, Ψ$_{ci}$ . The unfractured particles (20~13mm) were evaluated by N/T and Ψ$_{ci}$ , and the products (finer than 10${\mu}{\textrm}{m}$) by Ψ$_{ci}$ . As a result, N/T of the unfractured particles decreased with an increase of grinding time. Ψ$_{ci}$ of the unfractured particles and the products increased with an increase of grinding time (; progress of grinding), and became almost constant in the long time grinding. These tendencies were not changed by the applied load on the particle layer, but the limit value of Ψ$_{ci}$ at the products were varied with the applied load.plied load.

• Communications of the Korean Mathematical Society
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• v.39 no.2
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• pp.331-343
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• 2024

Let ℜ be a *-algebra with unity I and a nontrivial projection P₁. In this paper, we show that under certain restrictions if a map ψ : ℜ → ℜ satisfies $$\Psi(S_1{\diamond}S_2{\cdot}{\cdot}{\cdot}{\diamond}S_{n-1}{\bullet}S_n)=\sum_{k=1}^nS_1{\diamond}S_2{\diamond}{\cdot}{\cdot}{\cdot}{\diamond}S_{k-1}{\diamond}{\Psi}(S_k){\diamond}S_{k+1}{\diamond}{\cdot}{\cdot}{\cdot}{\diamond}S_{n-1}{\bullet}S_n$$ for all S_n-2, S_n-1, S_n ∈ ℜ and S_i = I for all i ∈ {1, 2, . . . , n - 3}, where n ≥ 3, then ψ is an additive *-derivation.

• Bulletin of the Korean Chemical Society
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• v.18 no.4
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• pp.415-424
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• 1997

Conformational flexibilities of the GlcNAc(β1,3)Gal(β)OMe are investigated through NMR spectroscopy and molecular modeling. Adiabatic energy map generated with a dielectric constant of 50 contains three local minima. All of the molecular dynamics simulations on three local minimum energy structures show fluctuations between two low energy structures, N2 at φ=80° and ψ=60° and N3 at φ=60° and ψ=-40°. We have presented adequate evidences to state that GlcNAc(β1,3)Gal(β)OMe exists in two conformationally discrete forms. Two state model of N2 and N3 conformers with a population ratio of 40:60 is used to calculate the effective cross relaxation rate and reproduces the experimental NOEs very well. Molecular dynamics simulation in conjunction with two state model proves successfully the dynamic equilibrium existed in GlcNAc(β1,3)Gal(β)OMe and can be considered as a powerful method to analyze the motional properties in the structure of carbohydrate. This observation also cautions against the indiscriminate use of a rigid model to analyze NMR data.

• The Transactions of the Korean Institute of Electrical Engineers C
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• v.52 no.10
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• pp.431-435
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• 2003

It is very difficult and dangerous to measure PD(Partial Discharges) from high voltage equipments in outdoor situation. But that is very important thing for preventing them from more serious accident by defects made by insulating degradation. This paper provides useful method to detect PD signals easily without any dangerous situation. Electric field sensor by the principle of capacitor can detect PD signals without direct connection between sensor and high voltage equipment and has very wide frequency range suitable for noise rejection. Electric field sensor and related circuit for processing PD signal show good performance as a PD sensor when it is applied to simulated high power equipment generating PD pulses.

• Bulletin of the Korean Mathematical Society
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• v.60 no.3
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• pp.575-591
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• 2023

Motivated by several generalizations of the Pochhammer symbol and their associated families of hypergeometric functions and hypergeometric polynomials, by choosing to use a very generalized Pochhammer symbol, we aim to introduce certain extensions of the generalized Lauricella function F⁽ⁿ⁾_A and the Humbert's confluent hypergeometric function Ψ⁽ⁿ⁾ of n variables with, as their respective particular cases, the second Appell hypergeometric function F₂ and the generalized Humbert's confluent hypergeometric functions Ψ₂ and investigate their several properties including, for example, various integral representations, finite summation formulas with an s-fold sum and integral representations involving the Laguerre polynomials, the incomplete gamma functions, and the Bessel and modified Bessel functions. Also, pertinent links between the major identities discussed in this article and different (existing or novel) findings are revealed.

• Composites Research
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• v.34 no.2
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• pp.77-81
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• 2021

Due to the high specific strength and stiffness of the composite materials, the composite materials have been extensively used in various industries. In particular, carbon fiber reinforced composites are widely used in many mechanical structures. In addition, since carbon fiber reinforced composites have anisotropic properties, to understand the fatigue behavior of composites with different fiber orientation is very important for the efficient structural design. Therefore, in this paper, the effect fiber orientation on the fatigue life of composite materials was experimentally evaluated. For this purpose, tensile and fatigue tests were performed on the off-axis specimens (0°, 10°, 30°, 45°, 60°, 90°) of the composite materials. As a result of the fatigue tests, the fatigue strength of the composites decreased significantly as the fatigue strength slightly deviated from 0 degrees. On the other hand, the more deviated, the less decreased. This is because the role of supporting the load of fibers decreased as the stacking angle increased. In addition, the fatigue behavior was analyzed by introducing a fatigue strength ratio (Ψ) that eliminates the fiber orientation dependence of the off-axis fatigue behaviors on the unidirectional composites. The off-axis fatigue S-N lines can be reduced to a single line regardless of the fiber orientation by using the fatigue strength ratio (Ψ). Using the fatigue Ψ-N line, it is possible to extract back to any off-axis fatigue S-N lines of the composites with different fiber orientations.

• Kyungpook Mathematical Journal
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• v.51 no.4
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• pp.419-427
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• 2011

In this paper, making use of transformation due to S. N. Singh [21], an at-tempt has been made to establish certain results involving basic bilateral hypergeometric series and continued fractions.

• Kyungpook Mathematical Journal
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• v.60 no.3
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• pp.477-484
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• 2020

For a non-zero complex number b and for m and n in 𝒩₀ = {0, 1, 2, …} let Ψ_n,m(b) denote the class of normalized univalent functions f satisfying the condition ${\Re}\;\[1+{\frac{1}{b}}\(\frac{D^{n+m}f(z)}{D^nf(z)}-1\)\]\;>\;0$ in the unit disk U, where Dⁿ f(z) denotes the Salagean operator of f. Sharp bounds for the Fekete-Szegö functional |a₃ - 𝜇a²₂| are obtained.

• Bulletin of the Korean Mathematical Society
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• v.50 no.2
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• pp.417-430
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• 2013

Let X be a Banach space and ${\psi}$ a continuous convex function on ${\Delta}_{K+1}$ satisfying certain conditions. Let $(X{\bigoplus}X{\bigoplus}{\cdots}{\bigoplus}X)_{\psi}$ be the ${\psi}$-direct sum of X. In this paper, we characterize the K strict convexity, K uniform convexity and uniform non-$l^N_1$-ness of Banach spaces using ${\psi}$-direct sums.