• Kyungpook Mathematical Journal
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• v.48 no.3
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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.

• Communications of the Korean Mathematical Society
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• v.10 no.2
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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.

• Journal of the Korean Mathematical Society
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• v.55 no.6
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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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• v.6 no.2
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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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• v.22 no.2
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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 $100^{\circ}C$.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.31 no.7C
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• pp.725-734
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• 2006

As a sequel to Part 1, the performance characteristics of the cell averaging (CA), greatest of (GO), and smallest of (SO) constant false alarm rate (CFAR) processors in nonhomogeneous environment are obtained and compared when receiving antenna diversity is employed in the pseudonoise (PN) code acquisition of direct-sequence code division multiple access (DS/CDMA) systems. Unlike in homogeneous environment, the GO CFAR processor is observed to exhibit the best performance in nonhomogeneous environment, with the CA CFAR processor performing the second best.

• 한국정보디스플레이학회:학술대회논문집
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• 2005.07b
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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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• v.49 no.3
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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.

• Journal of the Korean Mathematical Society
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• v.49 no.3
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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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• v.34 no.1
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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.