• Kyungpook Mathematical Journal
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• 제48권3호
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• pp.457-463
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• 2008

In this paper, by introducing a new function with two parameters, we give another generalizations of the Hilbert's integral inequality with a mixed kernel $k(x, y) = \frac {1}{A(x+y)+B{\mid}x-y{\mid}}$ and a best constant factors. As applications, some particular results with the best constant factors are considered.

• 대한수학회논문집
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• 제10권2호
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• pp.401-407
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• 1995

The best constants for two distinct weak-type inequalities for martingales and their differential subordinates with values in some spaces isomorphic to a Hilbert space are shown to be the same. This extends the result of Burkholder shown in the Hilbert space setting.

• 대한수학회지
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• 제55권6호
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• pp.1359-1380
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• 2018

In this paper, we prove that if a metric measure space satisfies the volume doubling condition and the Hardy type inequality with the same exponent n ($n{\geq}3$), then it has exactly the n-dimensional volume growth. Besides, three interesting applications of this fact have also been given. The first one is that we prove that complete noncompact smooth metric measure space with non-negative weighted Ricci curvature on which the Hardy type inequality holds with the best constant are isometric to the Euclidean space with the same dimension. The second one is that we show that if a complete n-dimensional Finsler manifold of nonnegative n-Ricci curvature satisfies the Hardy type inequality with the best constant, then its flag curvature is identically zero. The last one is an interesting rigidity result, that is, we prove that if a complete n-dimensional Berwald space of non-negative n-Ricci curvature satisfies the Hardy type inequality with the best constant, then it is isometric to the Minkowski space of dimension n.

• KSBB Journal
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• 제6권2호
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• pp.147-156
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• 1991

Diazotized chitin (CHITN) was synthesized reacting with NaN3 and HCl to alkaline hydrolyzed chitin for the support of immobilized enzyme. Immobilized $\beta$-glucosidase on diazotized chitin(CHITN-Gase) was produced reacting with glutaraldehyds as bifunctional reagent. CHITN-Gase activities were determined reacting with p-nitrophenol-$\beta$-D-glucopyranoside in plug flow reactor as a reference. Optimum temperature, optimum pH, reaction constant and deactivation rate were determined with variation of flow rate and H/D. The particle size of immobilized enzyme in the best was, 35 mesh (CHITN35-Gase). The optimum conditions of immobilized enzyme were $70^{\circ}C$ in temperature and 5.0 in pH. Diameter and flow rate of plug flow reactor in the best was 8.5mm in diameter and 0.8ml/min in flow rate. Reaction constant was mainly influenced by electrostatic force. The best glucose hydrolizing activities of CHITN3 5-Gase was 3.34$\times$10-5 M/1. while that of native-$\beta$-glucosidase was 2.44$\times$10-5 M/1.

• Tribology and Lubricants
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• 제22권2호
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• pp.99-104
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• 2006

The dielectric constants of fresh engine oils were obtained according to various types of oil, temperatures and frequencies. Through analyzing the characteristics of dielectric constant, the related correlation between the changes in dielectric constant of oil and the degree of oil deterioration is going to be found. The dielectric constant was calculated by cross capacitances measured by a sensor tube. Before finding the correlation, as a prerequisites study, the best condition measuring the dielectric constant was found. In general, it was found that the value of dielectric constant became stable below $60^{\circ}C$ regardless frequency variation. Further, above 6kHz, the dielectric constant became stable even if temperature had been above $100^{\circ}C$.

• 한국통신학회논문지
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• 제31권7C호
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• pp.725-734
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• 2006

이 논문의 1부에 이어, 수신안테나 다양성을 쓰는 직접수열 부호분할 다중접속(direct-sequence code division multiple access: DS/CDMA) 시스템에서 의사잡음(pseudonoise: PN) 부호를 획득할 때 평균값(cell average: CA), 큰값(greatest of: GO), 작은값(smallest of: SO) 일정 오경보 확률(constant false alarm rate: CFAR) 처리기의 성능 특성을 비균질 (nonhomogeneous) 잡음 환경에서 얻고 견주어 본다. 균질 잡음 환경에서와는 다르게, 비균질 잡음 환경에서는 큰값 일정 오경보 확률 처리기가 가장 성능이 좋고, 평균값 일정 오경보 확률 처리기가 그 다음으로 성능이 좋다는 것을 볼 수 있다.

• 한국정보디스플레이학회:학술대회논문집
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• 한국정보디스플레이학회 2005년도 International Meeting on Information Displayvol.II
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• pp.1092-1095
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• 2005

The effect of the dielectric constant (${\varepsilon}$) of bonding materials in screen-printed carbon nanotube cathode on field enhancement factor was investigated using the ANSYS software for high-efficient CNT-cathodes. The field enhancement factor increased with decreasing the dielectric constant and reaching a maximum value when the dielectric constant is 1, the value for a vacuum. This indicates that the best bonding materials for screen-printing CNT cathodes should have a low dielectric constant and this can be used as criteria for selecting bonding materials for use in CNT pastes for high-efficient CNT-cathodes

• Kyungpook Mathematical Journal
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• 제49권3호
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• pp.493-506
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• 2009

By using the improved Euler-Maclaurin summation formula and estimating the weight coefficients in this paper, a new dual Hardy-Hilbert's inequality and its reverse form are obtained, which are all with two pairs of conjugate exponents (p, q); (r, s) and a independent parameter ${\lambda}$. In addition, some equivalent forms of the inequalities are considered. We also prove that the constant factors in the new inequalities are all the best possible. As a particular case of our results, we obtain the reverse form of a famous Hardy-Hilbert's inequality.

• 대한수학회지
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• 제49권3호
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• pp.659-670
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• 2012

For any $K$ > $2/{\pi}$ we determine the optimal constant $L(K)$ for which the following holds. If $u$, $tilde{u}$ are conjugate harmonic functions on the unit disc with $\tilde{u}(0)=0$, then $$ {\int}_{-\pi}^{\pi}{\mid}\tilde{u}(e^{i\phi}){\mid}\frac{d{\phi}}{2{\pi}}{\leq}K{\int}_{-\pi}^{\pi}{\mid}u(e^{i{\phi}}){\mid}{\log}^+{\mid}u(e^{i{\phi}}){\mid}\frac{d{\phi}}{2{\pi}}+L(K).$$ We also establish a related estimate for orthogonal harmonic functions given on Euclidean domains as well as an extension concerning orthogonal martingales under differential subordination.

• ETRI Journal
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• 제34권1호
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• pp.142-145
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• 2012

The main challenge at present in constructing hierarchical identity-based encryption (HIBE) is to solve the trade-off between private-key size and ciphertext size. At least one private-key size or ciphertext size in the existing schemes must rely on the hierarchy depth. In this letter, a new hierarchical computing technique is introduced to HIBE. Unlike others, the proposed scheme, which consists of only two group elements, achieves constant-size private keys. In addition, the ciphertext consists of just three group elements, regardless of the hierarchy depth. To the best of our knowledge, it is the first efficient scheme where both ciphertexts and private keys achieve O(1)-size, which is the best trade-off between private-key size and ciphertext size at present. We also give the security proof in the selective-identity model.