• Kyungpook Mathematical Journal
• /
• v.59 no.3
• /
• pp.377-389
• /
• 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
• /
• v.13 no.3
• /
• pp.334-336
• /
• 1992

Through two different techniques TGA and DSC the thermal decomposition processes of salicyaldehyde G-P complexes having the general formula: $$[MCl_2(L)_2]^{2+}$2Cl^-$; where L = salicyaldehyde carbohydrazone pyridinum cation, and M= Fe(III), Co(II), Cu(II) and Zn(II), have been studied. From the obtained thermogravimetric curves the following parameters n, $E_{\alpha}$, A, ${\Delta}S^{\neq}$, ${\Delta}H^{\neq}$ and ${\Delta}G^{\neq}$ were evaluated. The effect of the nature of the metal ions present in the complexes studied upon the calculated thermodynamic parameters was reported. A suitable mechanism for the thermal decomposition process was suggested.

• Journal of the Korean Society of Food Science and Nutrition
• /
• v.32 no.3
• /
• pp.325-337
• /
• 2003

This study was designed to determine the distribution of trans fatty acids (tFAs) isomers of Processed foods commonly consumed in Korea. The tFAs positional isomers were analyzed using GC/MS spectrometer with HP-23 cis/trans FAME, capillary column (50m $\times$ 0.20 mm, id., 0.2 ${\mu}{\textrm}{m}$ film thickness) for 41 food samples. TFAs isomers were identified by comparing retention time with standards and GC/MS spectrum. In margarines, the content of tFAs ranged from 4.0% to 25.16% and the most abundant positional isomer of tFAs was C18:1 $\Delta$9t. In oils and fats, lards contained higher levels of tFAs (5.70~16.54%) than shortenings (6.77~10.55%). Shortenings contained higher levels of C18:1 $\Delta$9t (3.1~5.1%) than lard (1.6~4.3%), but corn oils had no tFAs. In seasonings, mayonnaise had no C16:1 $\Delta$9t, whereas C18:3t was detected. The content of tFAs in confectioneries was wide (16.20~52.16%). Among them, instant popcorns contained the highest amount of tFAs. Milk and dairy products showed even distribution of tFAS such as C18:1t, C18:2t, and C18:3t. Predominant tFAS isomer of condensed milk and ice cream was C16:1 $\Delta$9t. Frozen french fries and fried chicken contained higher levels of C18:1$\Delta$9t (9.4%), whereas grilled pork (jowl) had no C18:1 $\Delta$9t. The amount of tFAs per serving size was the highest in popcorn, followed by frozen pizza, frozen french fries, fried chicken, and bakeries.

• Journal of the Korean Chemical Society
• /
• v.34 no.5
• /
• pp.483-489
• /
• 1990

The rate of hydrolysis of insecticidal 2-chloro-l-(2,4,5-trichlorophenyl)-vinyldimethylphosphate(Gardona) have been investigated in 25${\%}$ aqueous methanol. Studies at varying pH suggest that the hydrolysis of Gardona proceeds through the bimolecular (Ad$_{N-E}$) mechanism involving the transition state and carbanion intermediate as evidenced by solvent effect (m < 0.4, n < 0.7, [m] ${\ll}$ [l](associative SN$_2$ type)), thermodynamic parameters (${\{Delta}S^{\neq}$ = -27∼-32 e.u. & ${\{Delta}H^{\neq}$ = 13∼18 Kcal/mole), hydrolysis rate equation (k = k$_A+_B$ [OH-]), general base catalysis and hydrolysis product analysis, respectively.

• The Bulletin of The Korean Astronomical Society
• /
• v.35 no.2
• /
• pp.51.1-51.1
• /
• 2010

We report an example of Pi2 pulsation exhibiting different frequency between dawn and dusk. This Pi2 pulsation occurred around 1932 UT on February 14, 2008, and was observed at low-latitude Bohyun (BOH, L = 1.35, MLT = 3.8) and Hermanus (HER, L = 1.83, MLT = 20.1) stations. The pulsation starts simultaneously at both stations but the frequency is higher at BOH than at HER. At the time of the Pi2, THEMIS-A (THA) and THEMIS-D (THD) were on dawn (L = 2.9, MLT = 5.3) and dusk (L = 2.8, MLT = 18), respectively, in the inner magnetosphere. We find a nearly identical waveform and period between THA ${\delta}Bz$ and BOH ${\delta}H$ and between THD ${\delta}Bz$ and HER ${\delta}H$ with a near $0^{\circ}$ phase delay. This observation implies that Pi2-associated fastmode wave in the inner magnetosphere is not excited globally as a single frequency at all longitudes. We suggest that the different frequency between dawn and dusk is due to dawn-dusk asymmetry of the plasmasphere.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.16 no.9
• /
• pp.1605-1614
• /
• 1992

The effects of % overload (% O.L), baseline stress intensity factor range (.DELTA. $K_{b}$) and dimension-less crack depth (a/W) are examined for the retardation behaviors after a single overload and high-low block loads in 7075-T73 aluminum alloy. And wheeler model, which is one of the fatigue life prediction models, is modified to predict retardation life using these test results. The retardation cycles( $N_{d}$) increased with a decrease in a/W and an increase in % O.L. and (.DELTA. $K_{b}$) These effects are more severe after high-low block loads than single overload. In the case of single overload, the main mechanisms of the retardation are the crack closure and the relaxation of K due to crack branching. But in the case of high-low block loads, that of the main mechanism is the crack closure caused by the accumulated compressive residual stree at the crack tip, which is related with the contact of fracture surfaces. Test results were multiple regression analyzed and got regressed shaping correction factors, (n)$_{REG}$, as function of %O.L., a/W and (.DELTA. $K_{b}$) Wheeler model is modified by using these (n)$_{REG}$. The number of delay cycles calculated by modified Wheeler model were in good agreement with the test results of this study.y.udy.y.y.y.

• Korean journal of food and cookery science
• /
• v.10 no.1
• /
• pp.24-28
• /
• 1994

The effects of synthetic and carrot carotene on the browning of polyphenolics extracted from potato for eliminating the effects of other components in potato which inhibit the browning of potato juice and the potato polyphenol oxidase (PPO) activity were investigated. Total phenolics content in potato sample was 1.854mg/g D.W. and PPO activity was 100 unit. Delta 'L'value of polyphenolics extracted from potato decreased makedly, but that of potato with carrot decreased little by little. Potato with P-carotene showed a little decrease after 50 min. At the same time, polyphenolics extracted from potato were mixed with carotene extracted from carrot or with syntetic $\beta$-carotene. As the results, the delta 'L'value of the former increased but decreased similarly to the latter after 1 hour. The effects of enzyme and substrate concentration on the browning of PPO extracted from potato were investigated. Optimum enzyme concentration was 10% and optimum substrate concentration was 13.3% $\beta$-carotene concentration did not appear to influence significantly on PPO activity.

• Communications of the Korean Mathematical Society
• /
• v.33 no.3
• /
• pp.1025-1037
• /
• 2018

We consider an ill-posed problem for the heat equation $u_{xx}=u_t$ in the quarter plane {x > 0, t > 0}. We propose a new method to compute the heat flux $h(t)=u_x(1,t)$ from the boundary temperature g(t) = u(1, t). The operator $g{\mapsto}h=Hg$ is unbounded in $L^2({\mathbb{R}})$, so we approximate h(t) by $h_{\delta}(t)=u_x(1+{\delta},\;t)$, ${\delta}{\rightarrow}0$. When noise is present, the data is $g_{\epsilon}$ leading to a corresponding heat $h_{{\delta},{\epsilon}}$. We obtain an estimate of the error ${\parallel}h-h_{{\delta},{\epsilon}}{\parallel}$, as well as the error when $h_{{\delta},{\epsilon}}$ is approximated by the trapezoidal rule. With an a priori choice rule ${\delta}={\delta}({\epsilon})$ and ${\tau}={\tau}({\epsilon})$, the step size of the trapezoidal rule, the main theorem gives the error of the heat flux as a function of noise level ${\epsilon}$. Numerical examples show that the proposed method is effective and stable.

• Journal of the Korean Mathematical Society
• /
• v.44 no.3
• /
• pp.627-645
• /
• 2007

We investigate the eigenvalues of the semi-circulant preconditioned matrix for the finite difference scheme corresponding to the second-order elliptic operator with the variable coefficients given by $L_vu\;:=-{\Delta}u+a(x,\;y)u_x+b(x,\;y)u_y+d(x,\;y)u$, where a and b are continuously differentiable functions and d is a positive bounded function. The semi-circulant preconditioning operator $L_cu$ is constructed by using the leading term of $L_vu$ plus the constant reaction term such that $L_cu\;:=-{\Delta}u+d_cu$. Using the field of values arguments, we show that the eigenvalues of the preconditioned matrix are clustered at some number. Some numerical evidences are also provided.

• Journal of the Korea Academia-Industrial cooperation Society
• /
• v.6 no.1
• /
• pp.12-16
• /
• 2005

We used electrostatic force microscopy to probe carbon nanotubes. There is a linear relationship between the phase shift (${\Delta}{\phi}^{-l/2}$) and the inverse tube length ($L^{-1}$) of carbon nanotubes. When the distance(h) between the tip and the carbon nanotubes increase, the phase shift on EFM image decrease by a factor of $1/h^2$