• Title/Summary/Keyword: critical point equation

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Determining Kimbab Shelf-life with a HACCP System (HACCP을 적용하여 생산한 김밥의 유통기한 설정)

  • Lee, Jin-Hyang;Bae, Hyun-Joo
    • Korean journal of food and cookery science
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    • v.27 no.2
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    • pp.61-71
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    • 2011
  • This study was conducted to estimate the shelf-life of Kimbab manufactured using a Hazard Analysis and Critical Control Point (HACCP). We performed a microbiological verification after applying the HACCP plan to Kimbab. Additionally, the shelf-life of Kimbab at each holding temperature was calculated as a regression equation between the aerobic plate counts and holding time during the storage period. The critical control points of the HACCP plan, that were applied to Kimbab, included: cold-holding of refrigerated foods, checking the endpoint cooking temperature of heated food, and cold-holding of cooked foods. As a result of the microbiological verification of Kimbab, the aerobic plate counts averaged 3.46 log CFU/g. In contrast, the coliforms, E. coli, Staphylococcus aureus, and Salmonella spp. were not detected in any of the samples. The estimated shelf-life of Kimbab was calculated to be 45 hours at $10^{\circ}C$, 29 hours at $15^{\circ}C$, 6 hours at $25^{\circ}C$ and 3 hours at $35^{\circ}C$. In conclusion, manufacturers should apply a prerequisite program and a HACCP system for a safe consumption of ready-to-eat foods and label products with a proper shelf-life. Distributors should control the proper holding time-temperature until sale and consumers should eat immediately after purchasing ready-to-eat foods.

Crack effect on the elastic buckling behavior of axially and eccentrically loaded columns

  • Zhou, L.;Huang, Y.
    • Structural Engineering and Mechanics
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    • v.22 no.2
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    • pp.169-184
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    • 2006
  • A close form solution of the maximum deflection for cracked columns with rectangular cross-sections was developed and thus the elastic buckling behavior and ultimate bearing capacity were studied analytically. First, taking into account the effect of the crack in the potential energy of elastic systems, a trigonometric series solution for the elastic deflection equation of an arbitrary crack position was derived by use of the Rayleigh-Ritz energy method and an analytical expression of the maximum deflection was obtained. By comparison with the rotational spring model (Okamura et al. 1969) and the equivalent stiffness method (Sinha et al. 2002), the advantages of the present solution are that there are few assumed conditions and the effect of axial compression on crack closure was considered. Second, based on the above solutions, the equilibrium paths of the elastic buckling were analytically described for cracked columns subjected to both axial and eccentric compressive load. Finally, as examples, the influence of crack depth, load eccentricity and column slenderness on the elastic buckling behavior was investigated in the case of a rectangular column with a single-edge crack. The relationship of the load capacity of the column with respect to crack depth and eccentricity or slenderness was also illustrated. The analytical and numerical results from the examples show that there are three kinds of collapse mechanisms for the various states of cracking, eccentricity and slenderness. These are the bifurcation for axial compression, the limit point instability for the condition of the deeper crack and lighter eccentricity and the fracture for higher eccentricity. As a result, the conception of critical transition eccentricity $(e/h)_c$, from limit-point buckling to fracture failure, was proposed and the critical values of $(e/h)_c$ were numerically determined for various eccentricities, crack depths and slenderness.

Assessing asymmetric steel angle strength under biaxial eccentric loading

  • Shu-Ti Chung;Wei-Ting Hsu
    • Structural Engineering and Mechanics
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    • v.91 no.5
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    • pp.517-526
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    • 2024
  • Due to the asymmetric cross-section of unequal-angle steel, the application of loads can induce axial rotation, leading to a series of buckling failure behaviors. Special attention must be paid during the design process. The present study aims to analyze the structural behavior of asymmetric steel angle members under various eccentric loading conditions, considering the complex biaxial bending interaction that arises when the angle steel is connected to the panel. Several key factors are investigated in this paper, including the effects of uniaxial and biaxial eccentricity on the structural behavior and the eccentric axial compression strength of long and short legs at different load application points. Potential risks associated with the specified load points, based on the AISC specifications, are also discussed. The study observed that the strength values of the members exhibited significant changes when the eccentric load deviates from the specified point. The relative position of the eccentric load point and the slenderness ratio of the member are critical influencing factors. Overall, this research intends to enhance the accuracy and reliability of strength analysis methods for asymmetric single angle steel members, providing valuable insights and guidance for a safer and more efficient design.

BIFURCATION PROBLEM FOR A CLASS OF QUASILINEAR FRACTIONAL SCHRÖDINGER EQUATIONS

  • Abid, Imed
    • Journal of the Korean Mathematical Society
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    • v.57 no.6
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    • pp.1347-1372
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    • 2020
  • We study bifurcation for the following fractional Schrödinger equation $$\{\left.\begin{eqnarray}(-{\Delta})^su+V(x)u&=&{\lambda}f(u)&&{\text{in}}\;{\Omega}\\u&>&0&&{\text{in}}\;{\Omega}\\u&=&0&&{\hspace{32}}{\text{in}}\;{\mathbb{R}}^n{\backslash}{\Omega}\end{eqnarray}\right$$ where 0 < s < 1, n > 2s, Ω is a bounded smooth domain of ℝn, (-∆)s is the fractional Laplacian of order s, V is the potential energy satisfying suitable assumptions and λ is a positive real parameter. The nonlinear term f is a positive nondecreasing convex function, asymptotically linear that is $\lim_{t{\rightarrow}+{\infty}}\;{\frac{f(t)}{t}}=a{\in}(0,+{\infty})$. We discuss the existence, uniqueness and stability of a positive solution and we also prove the existence of critical value and the uniqueness of extremal solutions. We take into account the types of Bifurcation problem for a class of quasilinear fractional Schrödinger equations, we also establish the asymptotic behavior of the solution around the bifurcation point.

On the critical maps of the dirichlet functional with volume constraint

  • Koh, Young-Mee
    • Bulletin of the Korean Mathematical Society
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    • v.32 no.2
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    • pp.303-308
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    • 1995
  • We consider a torus T, that is, a compact surface with genus 1 and $\Omega = D^2 \times S^1$ topologically with $\partial\Omega = T$, where $D^2$ is the open unit disk and $S^1$ is the unit circle. Let $\omega = (x,y)$ denote the generic point on T. For a smooth immersion $u : T \to R^3$, we define the Dirichlet functional by $$ E(u) = \frac{2}{1} \int_{T} $\mid$\nabla u$\mid$^2 d\omega $$ and the volume functional by $$ V(u) = \frac{3}{1} \int_{T} u \cdot u_x \Lambda u_y d\omege $$.

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A NONEXISTENCE THEOREM FOR STABLE EXPONENTIALLY HARMONIC MAPS

  • Koh, Sung-Eun
    • Bulletin of the Korean Mathematical Society
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    • v.32 no.2
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    • pp.211-214
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    • 1995
  • Let M and N be compact Riemannian manifolds and $f : M \to N$ be a smooth map. Following J. Eells, f is exponentially harmonic if it represents a critical point of the exponential energy integral $$ E(f) = \int_{M} exp(\left\$\mid$ df \right\$\mid$^2) dM $$ where $(\left\ df $\mid$\right\$\mid$^2$ is the energy density defined as $\sum_{i=1}^{m} \left\$\mid$ df(e_i) \right\$\mid$^2$, m = dimM, for orthonormal frame $e_i$ of M. The Euler- Lagrange equation of the exponential energy functional E can be written $$ exp(\left\$\mid$ df \right\$\mid$^2)(\tau(f) + df(\nabla\left\$\mid$ df \right\$\mid$^2)) = 0 $$ where $\tau(f)$ is the tension field along f. Hence, if the energy density is constant, every harmonic map is exponentially harmonic and vice versa.

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A Numerical Analysis Approach for Design of Cable Dome Structures (케이블 돔 구조물 설계를 위한 수치해석 방법)

  • Kim, Jae-Yeol;Jang, Dong-Woo
    • Proceeding of KASS Symposium
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    • 2008.05a
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    • pp.89-94
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    • 2008
  • This paper deals with the method of self-equilibrium stress mode analysis of cable dome structures. From the point of view of analysis, cable dome structure is a kind of unstable truss structure which is stabilized by means of introduction of prestressing. The prestress must be introduced according to a specific proportion among different structural member and it is determined by an analysis called self-equilibrium stress mode analysis. The mathematical equation involved in the self-equilibrium stress mode analysis is a system of linear equations which can be solved numerically by adopting the concept of Moore-Penrose generalized inverse. The calculation of the generalized inverse is carried out by rank factorization method. This method involves a parameter called epsilon which plays a critical role in self-equilibrium stress mode analysis. It is thus of interest to investigate the range of epsilon which produces consistent solution during the analysis of self-equilibrium stress mode.

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A Study on the Heat Transfer Control Characteristics of Benard Flow a Magnetic Fluids in a Rectangular Enclosure (장방형 용기내 자성유체의 Benard유동에 대한 전열 제어 특성에 관한 연구)

  • Ahn, Jong-kug;Seo, Lee-Soo;Park, Gil-Moon
    • The KSFM Journal of Fluid Machinery
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    • v.7 no.4 s.25
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    • pp.32-39
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    • 2004
  • This study deals with the Benard Flow of Magnetic Fluids in a rectangular cavity which the ratio between height and width is 1 : 4 and the base side or left side is a heating face while other sides are to be cooling faces. When Magnetic field was equally impressed, considering the internal rotation of the elementary ferromagnetic particle, we found the following result from the numerical analysis of the GSMAC algorithm applied to the equation of the magnetic fluid. Benard flow is controlled by intensity and direction of magnetic fields, and critical point appears when especially magnetic field with a heating base and side area near H=-7000 and H=-10000 is applied.

Nonlinear Elliptic Equations under Dirichlet boundary Condition (Dirichlet 경계조건하에서의 비선형 타원형 방정식)

  • Han, Chun-Ho;Kim, Zheng-Guo
    • Journal of Industrial Technology
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    • v.18
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    • pp.61-67
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    • 1998
  • 이 논문에서는 Diruchlet 경계 조건을 갖는 비선형 타원형 방정식 $-{\Delta}u+g(u)=f(x)$의 해의 존재에 대한 연구를 하였다. 존재하는 해의 다중성을 증명하기 위하여 임계점 이론과 롤의 정리를 사용하였으며, 대응되는 범함수에 따라서 방정식의 해와 임계점이 동시에 나타난다는 정리를 이용하였다. 이 때 $g(u)=bu^+-au^-$으로 나타날 때 외력항 (방정식의 우변)의 상수로 주어지는 경우 적어도 두 개의 해가 존재한다는 것을 증명하였다. 만약 우변(외력항)의 상수가 음수이거나 0인 경우이 방정식의 해가 존재하지 않거나 자명한 해만 존재하기 때문에 상수는 양수인 것으로 가정하였다.

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Phase Equilibria Measurement of Binary Mixture for the Propoxylated Neopentyl Glycol Diacrylate in Supercritical Carbon Dioxide

  • Byun, Hun-Soo
    • Korean Chemical Engineering Research
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    • v.54 no.2
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    • pp.206-212
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    • 2016
  • Experimental data are reported on the phase equilibrium of propoxylated neopentyl glycol diacrylate in supercritical carbon dioxide. Phase equilibria data were measured in static method at a temperature of (313.2, 333.2, 353.2, 373.2 and 393.2) K and at pressures up to 27.82 MPa. At a constant pressure, the solubility of propoxylated neopentyl glycol diacrylate for the (carbon dioxide + propoxylated neopentyl glycol diacrylate) system increases as temperature increases. The (carbon dioxide + propoxylated neopentyl glycol diacrylate) system exhibits type-I phase behavior. The experimental result for the (carbon dioxide + propoxylated neopentyl glycol diacrylate) system is correlated with Peng-Robinson equation of state using mixing rule. The critical property of propoxylated neopentyl glycol diacrylate is predicted with Joback and Lyderson method.