• Journal of the Korean Mathematical Society
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• v.55 no.4
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• pp.1005-1018
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• 2018

Let ${\Sigma}_{g,n,b}$ denote the orientable surface obtained from the closed orientable surface ${\Sigma}_g$ of genus $g{\geq}2$ by deleting the interior of $n{\geq}1$ distinct topological disks and $b{\geq}1$ points. Using the notion of symplectic chain complex, the present paper establishes a formula for computing Reidemeister torsion of the surface ${\Sigma}_{g,n,b}$ in terms of Reidemeister torsion of the closed surface ${\Sigma}_g$, Reidemeister torsion of disk, and Reidemeister torsion of punctured disk.

• Kyungpook Mathematical Journal
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• v.59 no.3
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• pp.377-389
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• 2019

We evaluate the convolution sum $W_{a,b}(n):=\sum_{al+bm=n}{\sigma}(l){\sigma}(m)$ for (a, b) = (1, 28),(4, 7),(2, 7) for all positive integers n. We use a modular form approach. We also re-evaluate the known sums $W_{1,14}(n)$ and $W_{1,7}(n)$ with our method. We then use these evaluations to determine the number of representations of n by the octonary quadratic form $x^2_1+x^2_2+x^2_3+x^2_4+7(x^2_5+x^2_6+x^2_7+x^2_8)$. Finally we express the modular forms ${\Delta}_{4,7}(z)$, ${\Delta}_{4,14,1}(z)$ and ${\Delta}_{4,14,2}(z)$ (given in [10, 14]) as linear combinations of eta quotients.

• Bulletin of the Korean Chemical Society
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• v.15 no.5
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• pp.353-356
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• 1994

The $CN(B^2{\Sigma}^+)$ radical was produced in a jet using an electric dc discharge of the precursor $CH_3CN$ with inert carrier gases. The rotationally resolved Fourier transform emission spectra of the 0-0 band of the $(B^2{\Sigma}^+{\to}X^2{\Sigma}^+)$ transition of CN have exhibited different distribution of the intensity for the carrier gases He and Ar, respectively. From the analysis of intensity distribution in the spectra, the mechanism for rotational cooling process of CN radical in a supersonic expansion has been suggested.

• Bulletin of the Korean Chemical Society
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• v.16 no.5
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• pp.449-453
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• 1995

An exact quantum mechanical theory is employed to treat predissociation process of the $A^2{\Sigma}^+$ state of OH. The widths and positions of the lower (v= 2 and v= 3) rovibrational levels are calculated. Energy shifts of the resonances from the zeroth order (pure Hund'scase (b)) positions are shown to be small for N $\leq$ 10, indicating that the $A^2{\Sigma}^+$ state can be described as case (b) very well for low N. Due to the differential interactions of the $A^2{\Sigma}^+_{1/2}$ and $A^2{\Sigma}^+_{-1/2}$ states with $X^2II$and $2^2II$ states, small splittings between the $F_1$ and $F_2$ levels are predicted. Calculated lifetimes of the resonances agree with experimental results reasonably well.

• Journal of the Korean Chemical Society
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• v.7 no.3
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• pp.211-215
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• 1963

Inter-relationship between the Hammett equation and the linear enthalpy-entropy effect has been discussed by deriving a new set of equations; ${\Delta}{\Delata}H^{\neq}=a{\sigma}+b{\Delta}{\Delta}S^{\neq}$ and ${\Delta}{\Delta}F^{\neq}=a{sigma}+(b-T){\Delta}{\Delta}S^{\neq}$ where a = -1.36p. Theoretical analysis show that the Hammett, Leffler and Brown equations are special limited forms of these general equations. A necessary and sufficient test of substituent effect can thus be provided by the plot of $({\Delta}{\Delta}H^{\neq}-a{\sigma)$ versus ${\Delta}{\Delta}S^{\neq}$.

• Journal of Industrial Technology
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• v.4
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• pp.29-35
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• 1984

Buckling is a significant behavior to be considered whenever we design steel structures. In the case of H-shape beams, the lateral buckling occured by bending moment must be considered. Because of the lateral buckling of H-shape beams, the bending strength of the beams are determined by the lateral buckling stress instead of the allowable bending stress. Lateral buckling stress equation, consisting of two terms, i. e. ${\sigma}_{cr}({\nu},{\omega})={\sqrt{[{\sigma}_{cr}({\nu})]^2+[{\sigma}_{cr}({\omega})]^2}}$ has been using, but for the practical purpose of use the following equations are using two, i. e. ${\sigma}_{cr}({\nu})={\frac{0.65E}{{\ell}_h/A_f}}$, ${\sigma}_{cr}({\omega})={\frac{{\pi}^2E}{({\ell}_b/i_b)^2}}$. When we use the above equations, the results are different according to the shape of beam section, and they a re rather complex. In this study lateral buckling stress equation is derived, and the proposed formula$({\sigma}_{cr}(t))$ is compared with above mentioned two basic and practical equations. To verify the proposed formula experimentaly, 16H-shape beams which have different slender ratios arc tested by applying pure bending momet. Through the experiments the buckling behavior of H-shape beams is clarified, and the results shows that the proposed formula$({\sigma}_{cr}(t))$ is accurate enough for practical purpose.

• Geomechanics and Engineering
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• v.11 no.5
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• pp.639-655
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• 2016

The effect of particle breakage and intermediate principal stress ratio on the behaviour of crushable granular assemblies under true triaxial stress conditions is studied using the discrete element method. Numerical results show that the increase of intermediate principal stress ratio $b(b=({\sigma}_2-{\sigma}_3)/({\sigma}_1-{\sigma}_3))$ results in the increase of dilatancy at low confining pressures but the decrease of dilatancy at high confining pressures, which stems from the distinct increasing compaction caused by breakage with b. The influence of b on the evolution of the peak apparent friction angle is also weakened by particle breakage. For low relative breakage, the relationship between the peak apparent friction angle and b is close to the Lade-Duncan failure model, whereas it conforms to the Matsuoka-Nakai failure model for high relative breakage. In addition, the increasing tendency of relative breakage, calculated based on a fractal particle size distribution with the fractal dimension being 2.5, declines with the increasing confining pressure and axial strain, which implies the existence of an ultimate graduation. Finally, the relationship between particle breakage and plastic work is found to conform to a unique hyperbolic correlation regardless of the test conditions.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.1
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• pp.89-99
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• 2009

Let $\mu$ be a finite positive Borel measure on the unit ball $B{\subset}\mathbb{C}^n$ and $\nu$ be the Euclidean volume measure such that ${\nu}(B)=1$. For the unit sphere $S=\{z:{\mid}z{\mid}=1\}$, $\sigma$ is the rotation-invariant measure on S such that ${\sigma}(S)=1$. Let $\mathcal{P}[f]$ be the invariant Poisson integral of f. We will show that there is a constant M > 0 such that $\int_B{\mid}{\mathcal{P}}[f](z){\mid}^{p}d{\mu}(z){\leq}M\;{\int}_B{\mid}{\mathcal{P}}[f](z)^pd{\nu}(z)$ for all $f{\in}L^p({\sigma})$ if and only if ${\parallel}{\mu}{\parallel_r}\;=\;sup_{z{\in}B}\;\frac{\mu(E(z,r))}{\nu(E(z,r))}\;<\;\infty$.

• Korean Journal of Clinical Laboratory Science
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• v.36 no.2
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• pp.121-126
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• 2004

The primary goal of six sigma is to improve patient satisfaction, and thereby profitability, by reducing and eliminating defects. Defects may be related to any aspect of customer satisfaction: high product quality, schedule adherence, cost minimization, process capability indices, defects per unit, and yield. Many six sigma metrics can be mathematically related to the others. Literally, six means six standard deviations from the mean or median value. As applied to quality metrics, the term indicates that failures are at least six standard deviations from the mean or norm. This would mean about 3.4 failures per million opportunities for failure. The objective of six sigma quality is to reduce process output variation so that on a long term basis, which is the customer's aggregate experience with our process over time, this will result in no more than 3.4 defect Parts Per Million(PPM) opportunities (or 3.4 Defects Per Million Opportunities. For a process with only one specification limit (upper or lower), this results in six process standard deviations between the mean of the process and the customer's specification limit (hence, 6 Sigma). The results of applicative six sigma experiment studied on 18 items TP, ALB, T.B, ALP, AST, ALT, CL, CK, LD, K, Na, CRE, BUN, T.C, GLU, AML, CA tests in clinical chemistry were follows. Assessment of process performance fits within six sigma tolerance limits were TP, ALB, T.B, ALP, AST, ALT, CL, CK, LD, K, Na, CRE, BUN, T.C, GLU, AML, CA with 72.2%, items that fit within five sigma limits were total bilirubin, chloride and sodium were 3 sigma. We were sure that the goal of six sigma would reduce test variation in the process.

• Microbiology and Biotechnology Letters
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• v.19 no.6
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• pp.553-560
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• 1991

In the previous paper (10). a new temperate phage, Sigma FA1 had been isolated from B. circulans. Sigma FA1 had an icosahedral head with a diameter of about 70 nm, and a tail about 15 nm long, and beared a circularly permuted, linear duplex DNA. Signla FA1 killed sensitive cells by a single-hit process. Phage DNA injected into the cell immediately after infection was degraded slowly. Our results indicate that the killing action of Sigma FA1 is different from the phenomenon of abortive infection and suggest that the killing might be caused by a proteinaceous component of Sigma FA1.