• 한국수학교육학회지시리즈B:순수및응용수학
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• 제14권2호
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• pp.127-137
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• 2007

The classical Bohr's inequality states that $|z+w|^2{\leq}p|z|^2+q|w|^2$ for all $z,\;w{\in}\mathbb{C}$ and all p, q>1 with $\frac{1}{p}+\frac{1}{q}=1$. In this paper, Bohr's inequality is generalized to the setting of n-inner product spaces for all positive conjugate exponents $p,\;q{\in}\mathbb{R}$. In. In particular, the parallelogram law is recovered and an interesting operator inequality is obtained.

• 대한수학회지
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• 제56권6호
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• pp.1529-1560
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• 2019

We are concerned with the following elliptic equations: $$(-{\Delta})^s_pu+V (x){\mid}u{\mid}^{p-2}u={\lambda}g(x,u){\text{ in }}{\mathbb{R}}^N$$, where $(-{\Delta})_p^s$ is the fractional p-Laplacian operator with 0 < s < 1 < p < $+{\infty}$, sp < N, the potential function $V:{\mathbb{R}}^N{\rightarrow}(0,{\infty})$ is a continuous potential function, and $g:{\mathbb{R}}^N{\times}{\mathbb{R}}{\rightarrow}{\mathbb{R}}$ satisfies a $Carath{\acute{e}}odory$ condition. We show the existence of at least one weak solution for the problem above without the Ambrosetti and Rabinowitz condition. Moreover, we give a positive interval of the parameter ${\lambda}$ for which the problem admits at least one nontrivial weak solution when the nonlinearity g has the subcritical growth condition.

• 대한수학회지
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• 제58권3호
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• pp.703-722
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• 2021

Let G = (V, E) be a connected locally finite and weighted graph, ∆_p be the p-th graph Laplacian. Consider the p-th nonlinear equation -∆_pu + h|u|^p-2u = f(x, u) on G, where p > 2, h, f satisfy certain assumptions. Grigor'yan-Lin-Yang [24] proved the existence of the solution to the above nonlinear equation in a bounded domain Ω ⊂ V. In this paper, we show that there exists a strictly positive solution on the infinite set V to the above nonlinear equation by modifying some conditions in [24]. To the m-order differential operator 𝓛_m,p, we also prove the existence of the nontrivial solution to the analogous nonlinear equation.

• 로봇학회논문지
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• 제13권4호
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• pp.248-255
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• 2018

In this paper, a design for a vehicle body of an armored robot for complex disasters is described. The proposed design considers various requirements in complex disaster situations. Fire, explosion, and poisonous gas may occur simultaneously under those sites. Therefore, the armored robot needs a vehicle body that can protect people from falling objects, high temperature, and poisonous gas. In addition, it should provide intuitive control devices and realistic surrounding views to help the operator respond to emergent situations. To fulfill these requirements of the vehicle body, firstly, the frame was designed to withstand the impact of falling objects. Secondly, the positive pressure device and the cooling device were applied. Thirdly, a panoramic view was implemented that enables real-time observation of surroundings through a number of image sensors. Finally, the cockpit in the vehicle body was designed focused on the manipulability of the armored robot in disaster sites.

• 대한수학회보
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• 제58권6호
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• pp.1315-1325
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• 2021

In this paper, we firstly prove some general inequalities for the Neumann eigenvalues for domains contained in a Euclidean n-space ℝⁿ. Using the general inequalities, we can derive some new Neumann eigenvalues estimates which include an upper bound for the (k + 1)^th eigenvalue and a new estimate for the gap of the consecutive eigenvalues. Moreover, we give sharp lower bound for the first eigenvalue of two kinds of eigenvalue problems of the biharmonic operator with Navier boundary condition on compact Riemannian manifolds with boundary and positive Ricci curvature.

• 대한수학회논문집
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• 제38권3호
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• pp.741-754
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• 2023

In this paper, we study the existence and nonexistence of solutions for a class of Hamiltonian strongly degenerate elliptic system with subcritical growth $$\left{\array{-{\Delta}_{\lambda}u-{\mu}v={\mid}v{\mid}^{p-1}v&&\text{in }{\Omega},\\-{\Delta}_{\lambda}v-{\mu}u={\mid}u{\mid}^{q-1}u&&\text{in }{\Omega},\\u=v=0&&\text{ on }{\partial}{\Omega},}$$ where p, q > 1 and Ω is a smooth bounded domain in ℝ^N, N ≥ 3. Here Δ_λ is the strongly degenerate elliptic operator. The existence of at least a nontrivial solution is obtained by variational methods while the nonexistence of positive solutions are proven by a contradiction argument.

• Journal of applied mathematics & informatics
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• 제41권6호
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• pp.1181-1191
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• 2023

This paper investigates Young inequalities for matrices, a problem closely linked to operator theory, mathematical physics, and the arithmetic-geometric mean inequality. By obtaining new inequalities for unitarily invariant norms, we aim to derive a fresh Young inequality specifically designed for matrices.To lay the foundation for our study, we provide an overview of basic notation related to matrices. Additionally, we review previous advancements made by researchers in the field, focusing on Young improvements.Building upon this existing knowledge, we present several new enhancements of the classical Young inequality for nonnegative real numbers. Furthermore, we establish a matrix version of these improvements, tailored to the specific characteristics of matrices. Through our research, we contribute to a deeper understanding of Young inequalities in the context of matrices.

• 대한수학회논문집
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• 제39권1호
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• pp.149-160
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• 2024

In this paper, we give sufficient conditions for the generalized Ornstein-Uhlenbeck operators perturbed by regular potentials and inverse square potentials A_Φ,G,V,c=∆-∇Φ·∇+G·∇-V+c|x|^-2 with a suitable domain generates a quasi-contractive, positive and analytic C₀-semigroup in L^p(ℝ^N , e^-Φ(x)dx), 1 < p < ∞. The proofs are based on an L^p-weighted Hardy inequality and perturbation techniques. The results extend and improve the generation theorems established by Metoui [7] and Metoui-Mourou [8].

• 한국전자통신학회논문지
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• 제11권2호
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• pp.165-170
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• 2016

본 논문은 $NCV-{\mid}v_1$ > 라이브러리의 새로운 쌍대 구조의 특성과 그 응용에 대한 연구이다. 상태벡터가 고유벡터인 임의 n개 qudit 상의 모든 유니터리 연산은 1개와 2개의 $NCV-{\mid}v_1$ > 라이브러리 들의 합성으로 표현할 수 있다. 본 연구는 입력 상태벡터가 PP로 제한적인 Barenco의 n비트 U(2n) 연산자를 전역 극성의 입력 상태벡터로 확장 실현하는 것이다. 이와 같이 보강된 확장 실현은 유니터리 연산자의 제어게이트 합성 시에 $NCV-{\mid}v_1$ > 과 이의 쌍대인 $NCV^{\dag}-{\mid}v_1$ > 라이브러리 모두를 사용할 경우에 이들이 대칭적 쌍대 성질을 갖고 있어 모든 극성의 상태벡터 입력에 대해 AND 지배적 종속 합성이 가능하기 때문이다.

• Journal of Biosystems Engineering
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• 제29권3호
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• pp.207-216
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• 2004

This study was intended to investigate the characteristics of ride vibrations transmitted to tractor operator during rotary tillage and plowing operations. Seat accelerations of a 41 ps diesel tractor in rotary tillage and plowing were measured and evaluated as specified in the ISO 2631-1. Effects of working speed and tilling depth on ride vibration were investigated. The level of ride vibration was also evaluated in terms of health guidance caution zones. Some of the results of the study are as follows: 1. The level of ride vibration in plowing was about 4.3 times greater than in rotary tillage. 2. The effect of working speed in rotary tillage differs depending upon the tillage depth. The level of ride vibration was increased with the speed, but it decreased over a certain tillage depth. Fore and aft vibration was 2.2-2.7 times severer than horizontal and vertical vibrations. Dominant frequency band was 1-3.15 ㎐ in fore and aft, 1-3.15㎐ and 16-25㎐ in horizontal, and 16-25㎐ in vertical directions. 3. Plowing reduced the ride vibration by 42.8-50.2%. But its positive effect decreased as the plowing speed increased. In plowing operation, ride vibration was similar degrees in fore and aft, horizontal and vertical directions. The dominant frequency band in plowing operation was 1-2.5㎐ in fore and aft, 1-2.5㎐ in horizontal, and 1-8㎐ in vertical directions. 4. On a basis of daily work hours of 4, total level of ride vibrations in plowing operation is likely to be harmful to operator's health.