• Communications of the Korean Mathematical Society
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• v.35 no.2
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• pp.565-570
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• 2020

We investigate the best equivalence constants for the 𝑙_p-norms and the 𝑙_q-symmetric multilinear operator norms of vectors in ℂⁿ which are induced by symmetric n-linear forms. In this paper, we provides estimates which are either best possible or close to best possible.

• 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.

• International Journal of Aeronautical and Space Sciences
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• v.17 no.4
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• pp.455-466
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• 2016

Chemical-kinetic parameters of the equilibrium constants to evaluate the reverse rate coefficients in the shock layer of a blunt body and the expanding flows are derived for the temperature range from 300 K to 20,000 K. The expanded equilibrium constants for the chemical reactions of the dissociation, ionization, associative ionization, and neutral and charge exchange reactions of the atmospheric species and carbon materials are proposed in the present work. In evaluating the equilibrium constants, the inter-nuclear potential energies of the molecular species are calculated by the analytical potential function of the Hulburt-Hirschfelder model, and the parameters of the analytical model are determined from the semi-classically calculated RKR potentials. The electronic states and energies of the atoms are calculated by the electronic energy grouping model, and the rovibrational states and energies of each electronic states of the molecules are evaluated by the WKB method. The expanded equilibrium constants for 31 types of the reactions are provided for the best curve-fit functions, and the recombination reaction rate coefficients evaluated from the present equilibrium constants are compared with existing measured values.

• Journal of applied mathematics & informatics
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• v.1 no.1
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• pp.13-20
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• 1994

The goal of this paper is to obtain some information on the best con-stants in some weak-type inequalities an X-valued martingale and its transform by a real predictable sequence uniformly bounded in absolute value by one.

• 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.

• Journal of the Korean Mathematical Society
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• v.57 no.3
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• pp.603-616
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• 2020

In the paper, we establish the validity of the weighted discrete and integral Hardy inequalities with periodic weights and find the best possible constants in these inequalities. In addition, by applying the established discrete Hardy inequality to a certain second-order difference equation, we discuss some oscillation and nonoscillation results.

• Journal of the Korea Society for Simulation
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• v.2 no.1
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• pp.125-133
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• 1993

A statistical method is described for estimation of the unknown constants in a theory using both of the computer simulation data and the real experimental data, The best linear unbiased predictor based on a spatial linear model is fitted from the computer simulation data alone. Then nonlinear least squares estimation method is applied to the real experimental data using the fitted prediction model as if it were the true simulation model. An application to the computational nuclear fusion devices is presented, where the nonlinear least squares estimates of four transport coefficients of the theoretical nuclear fusion model are obtained.

• Proceedings of the Korea Society for Simulation Conference
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• 1992.10a
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• pp.6-6
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• 1992

This work deals with nonlinear least squares method for estimating unknown universial constants C in a computer simulation code real experimental data(or database) and computer simulation data. The best linear unbiased predictor based on a spatial statistical model is fitted from the computer simulation data. Then nonlinear least squares estimation method is applied to the real data using the fitted prediction model(or simulation predictor) as if it were the true simulation model. An application to the computational nuclear fusion device is presented.

• Bulletin of the Korean Chemical Society
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• v.20 no.3
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• pp.297-300
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• 1999

The protonation constants of the macrocyclic ligands, 1,4-dioxa-7,10,13,16-tetraaza-cyclooctadecane-N,N',N",N"'-tetra(acetic acid) [N-ac4[18]aneN402] and 1,4-dioxa-7,10,13,16-tetraazacyclooctadecane-1,4-dioxa-7,10,13,16-N,N',N",N"'-tetra(methylacetic acid) [N-meac4[18]aneN4O2] have been determined by using potentiometric method. The protonation constants of the N-ac4[18]aneN4O2 were 9.31 for logK1H, 8.94 for logK2H, 7.82 for logK3H, 4.48 for logK4H and 2.94 for logK5H. And the protonation constants of the N-meac4[18]aneN4O2 were 9.34 for logK1H, 9.13 for logK2H, 8.05 for logK3H, 5.86 for logK4H, and 3.55 for logK5H. The stability constants of complexes on the divalent transition ions (Co2+, Ni2+, Cu2+, and Zn2+) and tiivalent metal ions (Ce3+, Eu3+, Gd3+, and Yb3+) with ligands N-ac4[18]-aneN4O2 and N-meac4[18]aneN4O2 have been obtained from the potentiometric data with the aid of the BEST program. The three higher values of the protonation constants for synthesized macrocyclic ligands correspond to the protonation of nitrogen atoms, and the fourth and fifth values correspond to the protonation of the carboxylate groups for the N-ac4[18]aneN4O2 and N-meac4[18]aneN4O2. The meatal ion affinities of the two tetra-azamacrocyclic ligands with four pendant acetate donor groups or methylacetate donor groups are compared. The effects of the metal ions on the stabilities are discussed, and the trends in stability constants resulting from changing the macrocyclic ring with pendant donor groups and acidity of the metal ions.

• Proceedings of the Korean Institute of Surface Engineering Conference
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• 2003.05a
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• pp.53-53
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• 2003

Plasma polymerized organic thin films were deposited on Si(100) glass and metal substrates using thiophene and ethylcyclohexane precursors by PECVD method. In order to compare electrochemical properties of the as-grown thin films, the effects of the RF plasma power in the range of 30~100 W. AFM showed that the polymer films with smooth surface and sharp interface could be grown under various deposition conditions. Impedance analyzer was utilized for the determination of I-V curve for leakage current density and C-V for dielectric constants, respectively. To obtain C-V curve, we used a MIM structure of metal(Al)-insulator(plasma polymerized thin film)-metal(Pt) structure. Al as the electrode was evaporated on the thiophene films that grew on Pt coated silicon substrates, and the dielectric constants of the as-grown films were then calculated from C- V data measured at 1MHz. From the electrical property measurements such as I-V and C-V characteristics, the minimum dielectric constant and the best leakage current of thiophene thin films were obtained to be about 3.22 and $1{\;}{\times}10^{-11}{\;}A/cm^2$. However, in case of ethylcyclohexane thin films, the minimum dielectric constant and the best leakage current were obtained to be about 3.11 and $5{\;}{\times}10^{-12}{\;}A/cm^2$.