• 대한수학회보
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• 제50권3호
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• pp.935-949
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• 2013

In this paper, we study surfaces in $\mathb{E}^3$ whose Gauss map G satisfies the equation ${\Box}G=f(G+C)$ for a smooth function $f$ and a constant vector C, where ${\Box}$ stands for the Cheng-Yau operator. We focus on surfaces with constant Gaussian curvature, constant mean curvature and constant principal curvature with such a property. We obtain some classification and characterization theorems for these kinds of surfaces. Finally, we give a characterization of surfaces whose Gauss map G satisfies the equation ${\Box}G={\lambda}(G+C)$ for a constant ${\lambda}$ and a constant vector C.

• 호남수학학술지
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• 제35권4호
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• pp.683-699
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• 2013

In this paper, an improved ($\frac{G^{\prime}}{G}$)-expansion method is proposed for obtaining travelling wave solutions of nonlinear evolution equations. The proposed technique called ($\frac{F}{G}$)-expansion method is more powerful than the method ($\frac{G^{\prime}}{G}$)-expansion method. The efficiency of the method is demonstrated on a variety of nonlinear partial differential equations such as KdV equation, mKd equation and Boussinesq equations. As a result, more travelling wave solutions are obtained including not only all the known solutions but also the computation burden is greatly decreased compared with the existing method. The travelling wave solutions are expressed by the hyperbolic functions and the trigonometric functions. The result reveals that the proposed method is simple and effective, and can be used for many other nonlinear evolutions equations arising in mathematical physics.

• Journal of applied mathematics & informatics
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• 제38권5_6호
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• pp.507-518
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• 2020

In this article, we establish some fixed point results in G-metric spaces using the modified JS-G-contractions and we provide some suitable examples to support the results. Also, we give an application to solve an integral equation.

• Journal of applied mathematics & informatics
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• 제13권1_2호
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• pp.117-123
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• 2003

For an n ${\times}$ n real matrix X, let ${\Phi}$(X) = X o (X$\^$-1/)$\^$T/, where o stands for the Hadamard (entrywise) product. Suppose A, B, G and D are n ${\times}$ n real nonsingular matrices, and among them there are at least one solutions to the equation (equation omitted). An equivalent condition which enable (equation omitted) become a real solution ot the equation (equation omitted), is given. As application, we get new real solutions to the matrix equation (equation omitted) by applying the results of Zhang. Yang and Cao [SIAM.J.Matrix Anal.Appl, 21(1999), pp: 642-645] and Chen [SIAM.J.Matrix Anal.Appl, 22(2001), pp:965-970]. At the same time, all solutions of the matrix equation (equation omitted) are also given.

• 한국연소학회:학술대회논문집
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• 한국연소학회 2000년도 제20회 KOSCO SYMPOSIUM 논문집
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• pp.189-196
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• 2000

A numerical simulation was conducted to analyze the interaction of flame and vortices. The characteristic scales of flame and vortices were limited in the thin laminar flamelet regime. Within this regime, flame is assumed as discontinuity surface and its motion in flow field was described by G-equation instead of full governing equations. Additional approximations include distribution of line volume sources on flame surface to simulate effect of volume expansion. Contrast to previous calculations, current study employed vortex transport equation to evaluate attenuation and smearing of vortices. Two extreme conditions of frozen vortex and frozen flame were considered to validate the current method. Comparison with direct numerical simulation resulted in satisfactory quantitative agreement with higher computational efficiency which warrants the usefulness of the present model in more complex situation.

• 한국수산과학회지
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• 제21권3호
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• pp.169-176
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• 1988

In order to obtain the objective indices which can assess the quality and the shelf-life of dried squid, nonenzymatic browning, carbonyl value, trimethyl amine (TMA) and trimethyl amine oxide (TMAO) decrease and panel test were determined in dried squid at various water activity levels. When the data of nonenzymatic browning fit a zero order equation, $r^2$ value were more than 0.92 except aw 0.52 for 0.8241. Through variance analysis for the data of browning extent and TMAO decrease, the confidence limits of regression equation were $99\%$ and their limit values of shelf-life were shown 0.45390 O. D./g. solid and 190.322 g/g respectively. In case of TMAO, $r^2$ value was calculated more than 0.95. Linear regression equation for the correlation between browning data and average panel score was Y=0.6138-0.053X and its $r^2$ value was 0.9285. Also in TMAO decrease, the equation was InY=2.0314+0.08269x and $r^2$ value was 0.7854. The shelf-life, evaluated by nonenzymatic browning, TMAO decrease and panel test, was 110-170 days at aw 0.45-0.76 except aw 0.15.

• 산업기술연구
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• 제19권
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• pp.253-260
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• 1999

Two thermodynamic models were used to predict the partial molar volumes of solutes in supercritical carbon dioxide at infinite dilution: (1) the Peng-Robinson equation of state with various mixing rules including those based on $EOS/G^E$ (2) the Kirkwood Buff fluctuation integral with the hard sphere expansion (HSE) method. The Kirkwood-Buff fluctuation integral method, in which an equation of state for pure component and molecular parameters are required, produced better results especially near the critical point than the Peng-Robinson equation of state with the several mixing rules based an $EOS/G^E$. When the $EOS/G^E$ mixing rules were used, poorer results were obtained compared with the classical mixing rule and Kirkwood-Buff model.

• 한국작물학회지
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• 제53권1호
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• pp.15-20
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• 2008

검정콩 종피에 함유된 안토시아닌의 색소별 함량을 비파괴적으로 신속하게 분석하기 위하여 NIRS(근적외선 분광분석기)를 이용한 모델을 개발하였다. 재료는 검정콩 유전자원 300 계통을 사용하였으며, HPLC에서 분석된 종피의 안토시아닌 함량치를 NIRS 스펙트럼에 적용시킨 후 검량식을 작성하였다. NIRS의 검량식을 몇 가지 방법에 의하여 비교 분석한 결과 1차미분된 스펙트럼을 MPLS(Modified Partial Least Squares)를 이용한 회귀식에 이용하는 것이 가장 적합하였다. HPLC를 이용한 유전자원들의 성분 함량과 NIRS에서 도출된 검량식과의 상관계수는 C3G, D3G 및 Pt3G가 각각 0.952, 0.936과 0.833을 나타내었다. 이들 검량식은 validation file에서도 C3G와 D3G는 0.897, 0.849의 높은 상관을 보였으며, 이는 NIRS를 이용하여 검정콩의 안토시아닌 함량을 신속하게 분석할 수 있음을 나타내는 것으로 판단되었다.

• KSBB Journal
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• 제6권1호
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• pp.85-90
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• 1991

Experiments of alcohol fermentation of the yeast,K. fragi1is CBS 1555 were performed to obtain the following results. In these experiments, the initial concentrations of sugar which was composed of inulin and fructose as weight ratio of one to one were 30, 50, 75, 100 and 150g/l and the initial densities of the microorganism were less than 0.5g/l, 10g/1 to 15g/1, and 50g/l. The functional relationship among specific growthrates, sugar concentrations, and alcohol concentrations could be expressed by Aiba-shoda equation and the specific growth rate represented the trend that decreased with increase in the initial concentration of the microorganism. Also, $\mu$max and Ks of Monod's equation could be expressed as the function of initial cell concentration like the following equations. $\mu$max=0.8-0.008X Ks=0.54X+8 In the region that sugar, alcohol and cell concentrations were 10g/1 to 120g/l, 0g/l to 60g/l and 0.5g/l to 50g/l respectively, the differences between the experimental values and the calculated ones for specific growth rate approached to 40% with respect to experimental values at the worst cases, but in most cases, those were distributed in the range of less than 20%.

• Food Science and Biotechnology
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• 제14권2호
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• pp.301-303
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• 2005

State diagram of highly concentrated branched oligosaccharides (HBOS) was constructed to better understand phase behavior of mixtures with different size of oligosaccharides. It showed dramatic plasticizing effect on glass transition, which was successfully described based on Couchman-Karasz equation model. $T_g$' estimated from state diagram corresponded well with previous empirical data measured by maximum ice formation through isothermal holding (annealing) process. Estimated $T_g$' and $C_g$' values were $-36.3^{\circ}C$ and 79.99%, respectively. $T_g$' value of HBOS was approximately $10^{\circ}C$ higher than that of sucrose, while $C_g$' value was similar to those of general carbohydrate materials, which could be useful for applications in frozen system.