• Journal of the Korean Society of Combustion
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• v.12 no.1
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• pp.21-27
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• 2007

The supersonic combustion experiments are carried out using T3 free-piston shock tunnel. Different shock tube fill pressures have various inflow conditions. $15^{\circ}$ inclined hydrogen fuel injection is located before the cavity. Oblique shock is generated at the trailing edge of the cavity and reflects off the top and bottom wall. For non-reacting flow, static pressures in low equivalence ratio are similar to those in no fuel injection. As equivalence ratio is increased, static pressures are increased in the duct. In the similar equivalence ratio, static pressures are increased when total enthalpy is decreased. For reacting flow, the flame is occurred near the cavity. The combustion is weak locally in the middle of the duct. The up and down pressure distribution in the duct means that the supersonic combustion is generated.

• Journal of the Korean Mathematical Society
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• v.58 no.3
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• pp.741-760
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• 2021

In this paper, we exhibit the equivalence between different notions of unique range sets, namely, unique range sets, weighted unique range sets and weak-weighted unique range sets under certain conditions. Also, we present some uniqueness theorems which show how two meromorphic functions are uniquely determined by their two finite shared sets. Moreover, in the last section, we make some observations that help us to construct other new classes of unique range sets.

• East Asian mathematical journal
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• v.33 no.1
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• pp.83-102
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• 2017

The main purpose of this paper is to introduce a pair new class of primal and dual problem associated with an operator. We prove the sufficient optimality theorem, weak duality theorem and strong duality theorem for these problems. The equivalence between the generalized optimization problems and the generalized variational inequality problems is studied in ordered topological vector space modeled in Hilbert spaces. We introduce the concept of partial differential associated (PDA)-operator, PDA-vector function and PDA-antisymmetric function to show the existence of a new class of function called, ($T_{\eta};{\xi}_{\theta}$)-invex functions. We discuss first and second kind of ($T_{\eta};{\xi}_{\theta}$)-invex functions and establish their existence theorems in ordered topological vector spaces.

• The Journal of the Korea Contents Association
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• v.6 no.5
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• pp.29-34
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• 2006

For the almost certainly convergent series $S_n=\sum_{i=1}^nV-i$ of independent random elements in Banach spaces, by investigating tail series laws of large numbers, the rate of convergence of the series $S_n$ to a random variable s is studied in this paper. More specifically, by studying the duality between the limiting behavior of the tail series $T_n=S-S_{n-1}=\sum_{i=n}^{\infty}V-i$ of random variables and that of Banach space valued random elements, an alternative way of proving a result of the previous work, which establishes the equivalence between the tail series weak law of large numbers and a limit law, is provided in a Banach space setting.

• The Pure and Applied Mathematics
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• v.28 no.4
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• pp.355-376
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• 2021

In this paper we wish to establish the integral representations of generalized relative order (𝛼, 𝛽) and generalized relative type (𝛼, 𝛽) of entire and meromorphic functions where 𝛼 and 𝛽 are continuous non-negative functions defined on (-∞, +∞). We also investigate their equivalence relation under some certain condition.

• Journal of the Korean Mathematical Society
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• v.61 no.1
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• pp.29-40
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• 2024

Let S and R be rings and _SC_R a semidualizing bimodule. We introduce the notion of G_C-FP_n-injective modules, which generalizes G_C-FP-injective modules and G_C-weak injective modules. The homological properties and the stability of G_C-FP_n-injective modules are investigated. When S is a left n-coherent ring, several nice properties and new Foxby equivalences relative to G_C-FP_n-injective modules are given.

• Proceedings of the KSME Conference
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• 2007.05b
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• pp.1900-1905
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• 2007

A micro cyclone combustor was developed to be used as a heat source of thermoelectric power generator (TPG). The cyclone combustor was designed so that fuel and air were supplied to the combustion chamber separately. The mixing and flow characteristics in the combustor were investigated numerically. The global equivalence ratio (${\Phi}$), defined using the fuel and air flow rates, was introduced to examine the flow features of the combustor. The mixing of fuel and air inside the combustor could be well understood using the fuel concentration distribution. It was found that the weak recirculating zone was formed upper the fuel-supplying tube in case of ${\Phi}$ < 1.0. In addition, it was found that small regions that have a negative axial velocity exist near the fuel injection ports. It is assumed that these negative axial velocity regions can stabilize a flame inside the micro cyclone combustor.

• The Journal of the Korea Contents Association
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• v.6 no.4
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• pp.63-68
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• 2006

For the almost co티am convergent series $S_n$ of independent random variables, by investigating the limiting behavior of the tail series, $T_n=S-S_{n-1}=\sum_{i=n}^{\infty}X_i$, the rate of convergence of the series $S_n$ to a random variable S is studied in this paper. More specifically, the equivalence between the tail series weak law of large numbers and a limit law is established for a quasi-monotone decreasing sequence, thereby extending a result of Previous work to the wider class of the norming constants.

• 한국연소학회:학술대회논문집
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• 2007.05a
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• pp.139-144
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• 2007

A micro cyclone combustor was developed to be used as a component of mobile power generator (MPG). The cyclone combustor was designed so that fuel and air were supplied to the combustion chamber separately to prevent a flash-back. The flame shape stabilized inside the micro cyclone combustor was visualized experimentally and the flow field and the combustion characteristics of the combustor were investigated numerically. The global equivalence ratio (${\Phi}$), defined using the fuel and air flow rates, was introduced to examine the overall flow and flame features of the combustor. The flame stabilization mechanism could be well understood using the velocity distribution inside the combustor. For only non-reacting case, it was found that a weak recirculating zone was formed upper the fuel-supplying tube in case of ${\Phi}$ < 1.0. It was also found that small regions that have a negative axial velocity exist near the fuel injection ports for both of non-reacting and reacting case. It was identify that a flame front was stabilized at the negative axial velocity regions near the fuel injection ports.

• Journal of the Korean Society of Combustion
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• v.15 no.3
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• pp.1-7
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• 2010

Edge flames have been interested as a basic structure that is concerned to flame stabilization and re-ignition of non-premixed flames. The edge flame consists of a lean premixed flame, a rich premixed flame, and a diffusion flame. In order to investigate fundamental structures of the edge flames at the conditions near the flammability limits, edge flames were stabilized within a heated narrow channel. Highly diluted partially premixed methane was used, and the flow rates of air and the partially premixed mixture were controlled. Various flame behaviors, including a transition between ordinary edge flames and premixed flames, were observed. Flame stabilization characteristics were examined as well. All flame stabilization conditions in this study showed a similar trend: characteristic time scales were inversely proportional to the equivalence ratio defined at the burner inlet. Finally, an interesting flame structure having a weak diffusion branch enveloped by a closed premixed branch was found near the flammability limits even in a fuel-air mixing layer. This structure was named as a "flame-drop" and the importance of this structure was first suggested.