• Bulletin of the Korean Mathematical Society
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• v.48 no.2
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• pp.261-275
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• 2011

We give characterizations of the differentiability points and the non-differentiability points of the Riesz-N$\'{a}$gy-Tak$\'{a}$cs(RNT) singulr function using the distribution sets in the unit interval. Using characterizations, we show that the Hausdorff dimension of the non-differentiability points of the RNT singular function is greater than 0 and the packing dimension of the infinite derivative points of the RNT singular function is less than 1. Further the RNT singular function is nowhere differentiable in the sense of topological magnitude, which leads to that the packing dimension of the non-differentiability points of the RNT singular function is 1. Finally we show that our characterizations generalize a recent result from the ($\tau$, $\tau$ - 1)-expansion associated with the RNT singular function adding a new result for a sufficient condition for the non-differentiability points.

• 한국연소학회:학술대회논문집
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• 2007.05a
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• pp.7-12
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• 2007

To reveal the newly found liftoff height behavior of hydrogen jet, we have experimentally studied the stabilization mechanism of turbulent, lifted jet flames in a non-premixed condition. The objectives of the present research are to report the phenomenon of a liftoff height decreasing as increasing fuel velocity, to analyse the flame structure and behavior of the lifted jet, and to explain the mechanisms of flame stability in hydrogen turbulent non-premixed jet flames. The velocity of hydrogen was varied from 100 to 300m/s and a coaxial air velocity was fixed at 16m/s with a coflow air less than 0.1m/s. For the simultaneous measurement of velocity field and reaction zone. PIV and OH PLIF technique was used with two Nd:Yag lasers and CCD cameras. As results, it has been found that the stabilization of lifted hydrogen diffusion flames is related with a turbulent intensity, which means that combustion occurs where the local flow velocity is valanced with the turbulent flame propagation velocity.

• Proceedings of the Korean Society of Soil and Groundwater Environment Conference
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• 2001.09a
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• pp.27-30
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• 2001

Flow and transport at fracture intersections, and their effects on network scale transport, are investigated in three-dimensional random fracture networks. Fracture intersection mixing rules complete mixing and streamline routing are defined in terms of fluxes normal to the intersection line between two fractures. By analyzing flow statistics and particle transfer probabilities distributed along fracture intersections, it is shown that for various network structures with power law size distributions of fractures, the choice of intersection mixing rule makes comparatively little difference in the overall simulated solute migration patterns. The occurrence and effects of local flows around an intersection (local flow cells) are emphasized. Transport simulations at fracture intersections indicate that local flow circulations can arise from variability within the hydraulic head distribution along intersections, and from the internal no flow condition along fracture boundaries. These local flow cells act as an effective mechanism to enhance the nondiffusive breakthrough tailing often observed in discrete fracture networks. It is shown that such non-Fickian (anomalous) solute transport can be accounted for by considering only advective transport, in the framework of a continuous time random walk model. To clarify the effect of forest environmental changes (forest type difference and clearcut) on water storage capacity in soil and stream flow, watershed had been investigated.

• 한국가시화정보학회:학술대회논문집
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• 2006.12a
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• pp.135-140
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• 2006

The stabilization mechanism of turbulent, lifted jet flames in a non-premixed condition has been studied experimentally. The objectives are to explain the phenomenon of a liftoff height decreasing as increasing fuel velocity and to reveal the mechanisms of flame stability Hydrogen was varied from 100 to 300 m/s and a coaxial air was fixed at 16 m/s with a coflow air less than 0.1 m/s. The technique of PIV and OH PLIF was used simultaneously with CCD and ICCD cameras. It was found that the liftoff height of the jet decreased with an increased fuel jet exit velocity. The leading edge at the flame base was moving along the stoichiometric line. Finally we confirmed that the stabilization of lifted hydrogen diffusion flames is related with a turbulent intensity, which means combustion is occurred where the local flow velocity is equal to the turbulent flame propagation velocity.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.1
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• pp.89-97
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• 2014

We study the existence of mild solutions for neutral differential equations with nonlocal conditions in the ${\alpha}$-norm.

• Journal of the Korean Mathematical Society
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• v.40 no.6
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• pp.951-962
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• 2003

In this paper we address focal points and treat manifolds (M, g) whose Lorentzian metric tensors g have a spacelike $C^{0}$-hypersurface $\Sigma$ [10]. We apply Jacobi fields for such manifolds, and check the local length maximizing properties of $C^1$-geodesics. The condition of maximality of timelike curves(geodesics) passing $C^{0}$-hypersurface is studied.ied.

• Journal of the Chungcheong Mathematical Society
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• v.7 no.1
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• pp.153-164
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• 1994

Let A be a commutative ring with identity and M an A-module. When $U_n$ is a triangular subset of $A_n$, Sharp and Zakeri defined a module of generalized fractions $U_n^{-n}M$. In [SZ3], they described a relation of the Monomial Conjecture and a module of generalized fractions under the condition of a Noetherian local ring. In this paper, we investigate some properties of non-zero generalized fractions and give a generalization of results of Sharp and Zakeri for an arbitrary ring.

• Journal of the Korean Mathematical Society
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• v.42 no.3
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• pp.471-484
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• 2005

We study Riemannian or pseudo-Riemannian manifolds which carry the space of closed conformal vector fields of at least 2-dimension. Subject to the condition that at each point the set of closed conformal vector fields spans a non-degenerate subspace of the tangent space at the point, we prove a global and a local classification theorems for such manifolds.

• The Pure and Applied Mathematics
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• v.15 no.3
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• pp.245-257
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• 2008

In this paper, we find the sufficient conditions of controllability of semi-linear neutral functional differential evolution equations with non local conditions using by fractional power of operators and Sadovskii's fixed point theorem.

• Communications of the Korean Mathematical Society
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• v.38 no.1
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• pp.281-298
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• 2023

A class of systems of Caputo fractional differential equations with integral boundary conditions is considered. A numerical method based on a finite difference scheme on a uniform mesh is proposed. Supremum norm is used to derive an error estimate which is of order κ − 1, 1 < κ < 2. Numerical examples are given which validate our theoretical results.