• Geomechanics and Engineering
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• v.3 no.1
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• pp.61-81
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• 2011

In this paper, a complement to the Hoek-Brown criterion is proposed in order to derive the strength of anisotropic rock from strength of the corresponding truly intact rock. The complement is a decay function, which unlike other modifications or suggestions made in the past, is multiplied to the function of the original Hoek-Brown failure criterion for intact rock. This results in a combined and extended form of the criterion which describes the strength of anisotropic rock as a varying fraction of the corresponding truly intact rock strength. Statistical procedures and in particular regression analyses were conducted into data obtained in experiments conducted in the current research program and those collected from the literature in order to define the Hoek-Brown's criterion complement. The complement function was best described by a simple polynomial including only three constants to be empirically evaluated. Further investigations also showed that these constants can be related to the other readily available parameters of rock material which further facilitate determining the constants. A great and prime advantage of the proposed complement is that it is mathematically simple including the least possible number of empirical constants which are easily estimated with minimum experimental effort. Moreover, proposed concept does not suggests any change to the original Hoek-Brown criterion itself or its constants and serves whenever anisotropy does exist in the rock. This further implies on the possibility of using any other failure criterion for intact rock in conjunction with the compliment to reach the strength of anisotropic rock.

• Applied Biological Chemistry
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• v.50 no.2
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• pp.127-131
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• 2007

The molecular design and holographic (H) quantitative structure-activity relationships (HQSARs) on the binding affinity constants between new 3-benzylidenemyosmine analogues and nicotin acetylcholine receptors (nAChRs) of American cockroach (Periplaneta. americana L.) were studied quantitatively. The optimized HQSAR model (IV-2) for the binding affinity constants was derived from fragment distinction of hydrogene atoms in fragment size, 5${\sim}$8 bin. The statistical results of the HQSAR model (IVI-2) exhibited the best predictability and fitness for the binding affinity constants based on the cross-validated value (q$^2$=0.507) and non cross-validated value (r$^2_{nev.}$=0.944). From the graphical analyses of atomic contribution maps, it was revealed that the binding affinity constants depends upon the anabaseine ring in molecule and the most active compounds were designed by optimized HQSAR model (VI-2).

• Nonlinear Functional Analysis and Applications
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• v.29 no.2
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• pp.581-596
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• 2024

A new variety of non-self generalized proximal contraction, called Hardy-Rogers α⁺F-proximal contraction, is shown in this work. Also, with an example, we prove that such contractions satisfying some conditions must have a unique best proximity point. For some particular values of the constants, that we have used to generalize the proximal contraction, we conclude different α⁺F-proximal contraction results of the types Ćirić, Chatterjea, Reich, Kannan, and Banach with proof, that all such type of contractions must have unique best proximity point. We also apply our result to solve a functional equation.

• Environmental Engineering Research
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• v.12 no.1
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• pp.30-35
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• 2007

Fenton system using homogeneous iron catalyst is very powerful in the degradation of organic compounds, but has a disadvantage to remove Fe ions from water after wastewater treatment. Thus, iron catalyst was bounded to support such as inorganic and polymer materials. The PVP supporting iron catalyst showed a good catalytic performance in degradation of phenol contained in waste water and iron catalyst supported on ${SO_4}^{2-}$ type PVP (KEX 511) showed the best catalytic performance. Also, reaction kinetic study was carried out in this system. Reaction constants on various catalysts was obtained from the pseudo first order equation. Reaction rate constants with the heterogenized $FeCl_2/PVP$ catalyst is a three-fold smaller than that of $FeCl_2$ catalyst.

• Bulletin of the Korean Mathematical Society
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• v.55 no.4
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• pp.1209-1219
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• 2018

We provide a direct proof of the following theorem of Kalton, Hollenbeck, and Verbitsky [7]: let H be the Hilbert transform and let a, b be real constants. Then for 1 < p < ${\infty}$ the norm of the operator aI + bH from $L^p(\mathbb{R})$ to $L^p(\mathbb{R})$ is equal to $$\({\max_{x{\in}{\mathbb{R}}}}{\frac{{\mid}ax-b+(bx+a){\tan}{\frac{\pi}{2p}}{\mid}^p+{\mid}ax-b-(bx+a){\tan}{\frac{\pi}{2p}}{\mid}^p}{{\mid}x+{\tan}{\frac{\pi}{2p}}{\mid}^p+{\mid}x-{\tan}{\frac{\pi}{2p}}{\mid}^p}}\)^{\frac{1}{p}}$$. Our proof avoids passing through the analogous result for the conjugate function on the circle, as in [7], and is given directly on the line. We also provide new approximate extremals for aI + bH in the case p > 2.

• Journal of the Korean Mathematical Society
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• v.41 no.1
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• pp.157-174
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• 2004

In this work we discuss "plank problems" for complex Banach spaces and in particular for the classical $L^{p}(\mu)$ spaces. In the case $1\;{\leq}\;p\;{\leq}\;2$ we obtain optimal results and for finite dimensional complex Banach spaces, in a special case, we have improved an early result by K. Ball [3]. By using these results, in some cases we are able to find best possible lower bounds for the norms of homogeneous polynomials which are products of linear forms. In particular, we give an estimate in the case of a real Hilbert space which seems to be a difficult problem. We have also obtained some results on the so-called n-th (linear) polarization constant of a Banach space which is an isometric property of the space. Finally, known polynomial inequalities have been derived as simple consequences of various results related to plank problems.

• Nuclear Engineering and Technology
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• v.36 no.6
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• pp.528-539
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• 2004

It is essential in commercial reactors that the safety limits imposed on the fuel pellets and fuel clad barriers, such as the linear power density (LPD) and the departure from nucleate boiling ratio (DNBR), are not violated during reactor operations. In order to accurately monitor the safety limits of current reactor states, a detailed three-dimensional (3D) core power distribution should be estimated from the in-core detector signals. In this paper, we propose a calculation methodology for detailed 3D core power distribution, using in-core detector signals and core monitoring constants such as the 3D Coupling Coefficients (3DCC), node power fraction, and pin-to-node factors. Also, the calculation method for several core safety parameters is introduced. The core monitoring constants for the real core state are promptly provided by the core design code and on-line MASTER (Multi-purpose Analyzer for Static and Transient Effects of Reactors), coupled with the core monitoring program. through the plant computer, core state variables, which include reactor thermal power, control rod bank position, boron concentration, inlet moderator temperature, and flow rate, are supplied as input data for MASTER. MASTER performs the core calculation based on the neutron balance equation and generates several core monitoring constants corresponding to the real core state in addition to the expected core power distribution. The accuracy of the developed method is verified through a comparison with the current CECOR method. Because in all the verification calculation cases the proposed method shows a more conservative value than the best estimated value and a less conservative one than the current CECOR and COLSS methods, it is also confirmed that this method secures a greater operating margin through the simulation of the YGN-3 Cycle-1 core from the viewpoint of the power peaking factor for the LPD and the pseudo hot pin axial power distribution for the DNBR calculation.

• Journal of the Korean Statistical Society
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• v.11 no.1
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• pp.12-24
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• 1982

Selection procedures are proposed for selecting the 'best' industrial process with the smallest fraction defective. For normally distributed industrial processes, this is equivalent to selecting in terms of coefficients of variation. For the case of known vairances, selection procedures by Bechhofer (1954), and Bechhofer and Turnball (1978) are appropriate. We treat this problem for the case of uknown variances with or without reference to a standard. The large sample solutions of design constants are tabulated and the performance of these approximate solutions are investigated.

• Bulletin of the Korean Chemical Society
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• v.10 no.4
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• pp.377-381
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• 1989

The spectroscopic properties of $FO^+$ and FO were investigated by ab initio calculation. Several different levels of theory, $MP3/6-31G^*,\;MP4/6-311G^*\;and\;CISD/6-31G^*$, were tried and compared with experimental results of FO. In the overall performance the CISD showed the best agreement. Based on these results the spectroscopic constants of $FO^+$ are predicted.

• 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.