• Bulletin of the Korean Mathematical Society
• /
• v.60 no.1
• /
• pp.257-279
• /
• 2023

Applying the Lyapunov-Schmidt reduction, we consider spectral stability of small amplitude stationary periodic solutions bifurcating from an equilibrium of the generalized Swift-Hohenberg equation. We follow the mathematical framework developed in [15, 16, 19, 23] to construct such periodic solutions and to determine regions in the parameter space for which they are stable by investigating the movement of the spectrum near zero as parameters vary.

• Bulletin of the Korean Mathematical Society
• /
• v.60 no.2
• /
• pp.425-441
• /
• 2023

This paper is concerned with the value distribution for meromorphic solutions f of a class of nonlinear partial differential-difference equation of first order with small coefficients. We show that such solutions f are uniquely determined by the poles of f and the zeros of f - c, f - d (counting multiplicities) for two distinct small functions c, d.

• Bulletin of the Korean Mathematical Society
• /
• v.61 no.3
• /
• pp.699-715
• /
• 2024

We study the Riemann problem for the pressureless Euler system with the source term depending on the time. By means of the variable substitution, two kinds of Riemann solutions including deltashock and vacuum are constructed. The generalized Rankine-Hugoniot relation and entropy condition of the delta-shock are clarified. Because of the source term, the Riemann solutions are non-self-similar. Moreover, we propose a time-dependent viscous system to show all of the existence, uniqueness and stability of solutions involving the delta-shock by the vanishing viscosity method.

• Bulletin of the Korean Mathematical Society
• /
• v.61 no.1
• /
• pp.29-44
• /
• 2024

In this paper we consider the existence of rotationally symmetric entire solutions for the prescribed higher mean curvature spacelike equations in Minkowski spacetime. As a first step, we study the associated 0-Dirichlet problems on a ball, and then we prove that all possible solutions can be extended to + ∞. The proof of our main results are based upon the topological degree methods and the standard prolongability theorem of ordinary differential equations.

• Journal of Korean Academy of Nursing
• /
• v.16 no.1
• /
• pp.67-80
• /
• 1986

The use of intravenous solutions for fluid replacement has become an integral part of patient care, This widespread use of intravenous solutions has increased the risk of contamination that can lead to septicemia and phlebitis. The literature regarding contamination of in use intravenous solutions recommends a standard 24-hour time limit on the use of these fluids. But the desings of these studies did not incorporate a time variable related to contamination. In other studies, however, time was a manipulated variable: but data regarding the onset of contamination were conflicting. Because published reports conflict with regard to a time standard related to the use of intravenous therapy, additional empirical data are needed upon which to base the standards of care regulating use of intravenous therapy. This study investigated rate of contamination in simulated in-use intravenous solutions to obtain data from which to recomend a standard time period for the administration of intravenous solutions. In this study samples were drawn from 60 bottles of 5% D/W solution at predetermined time intervals over 48 hours and samples were inoculated to Thio-glychollate Broth. After 10 days' culturing in that Broth, samples were cultured on blood agar plates for 18∼48 hours to determine the rate of contamination. was found at all time Period, regardless of the presence or absence of nurse's gloving in the preparation of fluids, the location in which the experimentations were performed, the contamination level of surrounding air, or the length of time during which solutions were opened. Data from this study support the use of a 48-hour time period on which to base the standard involved in ready-to-use simple intravenous solutions without additives. In emergency departments and critical care areas where intravenous solutions are prepared in advance, the suggested time standard supported by the data generated from this study is 48 hours, not 24 hour. Data from this study support a 24-hour time standard for changing in-use intravenous solutions when the contamination results from the manipulation of intravenous infusion system by hospital personnel, or from some other exogenous sources during administration. Because contamination that does occur within 48 hours in intravenous solutions must be introduced from some exogenous sources, further empirical studies based on the identification of sources of contamination and factors that affect the rate of contamination, are needed to investigate the currently employed standard of intravenous therapy and to provide the patient with more efficient and safer intravenous thereapy.

• Restorative Dentistry and Endodontics
• /
• v.37 no.1
• /
• pp.16-23
• /
• 2012

Objectives: Present study was undertaken to investigate the crystal growth onto synthetic hydroxyapatite (HA) seeds in pH 4.3 and pH 7.0 supersaturated solutions with different fluoride concentrations. Materials and Methods: 8 groups of pH 4.3 and 7.0 calcium phosphate supersaturated solutions were prepared with different fluoride concentrations (0, 1, 2 and 4 ppm). Calcium phosphate precipitates yield crystal growth onto the HA seed surface while solutions flow. For evaluation of crystallizing process, the changes of $Ca^{2+}$, $PO{_4}^{3-}$, $F^-$ concentrations of the inlet and outlet solutions were determined. The recovered solid samples were weighed to assess the amount of minerals precipitated, and finally determined their composition to deduce characteristics of crystals. Results: During the seeded crystal growth, there were significantly more consumption of $Ca^{2+}$, $PO{_4}^{3-}$, $F^-$ in pH 4.3 solutions than pH 7.0 (p < 0.05). As fluoride concentration increased in pH 4.3 solution, $Ca^{2+}$, $PO{_4}^{3-}$, $F^-$ consumption in experimental solutions, weight increment of HA seed, and fluoride ratio in crystallized samples were increased. There were significant differences among the groups (p < 0.05). But in pH 7.0 solution, these phenomena were not significant. In pH 7.0 solutions, analyses of crystallized samples showed higher Ca/P ratio in higher fluoride concentration. There were significant differences among the groups (p < 0.05). But in pH 4.3 solution, there were not significant differences in Ca/P ratio. Conclusions: Crystal growth in pH 4.3 solutions was superior to that in pH 7.0 solutions. In pH 4.3 solutions, crystal growth increased with showed in higher fluoride concentration up to 4 ppm.

• Journal of the Korean Association of Geographic Information Studies
• /
• v.12 no.1
• /
• pp.36-43
• /
• 2009

In this study, the impact of the covariance between the baselines on the network-based GPS positioning is analyzed. For the analysis, the multi-baseline solutions with properly modeled covariance between the baselines and the combined solutions from the single-baseline solutions are obtained, respectively. Then, the accuracies of both solutions are evaluated in terms of coordinate residuals, i.e., the differences between the positioning solutions and the published stations' coordinates. The results indicate that the positioning accuracy in static mode depends much on the geometry of GPS satellites rather than the proper modeling of covariance between the baselines. Also, slight but negligible improvement in positioning accuracy is observed in static solutions. Therefore, one may use combined solutions as an alternative to multi-baseline solutions for the network-based GPS positioning. However, multi-baseline solution with properly modeled covariance between the baselines is recommended to use especially for the applications to detect very small displacement, i.e., deformation of the building or bridge.

• Journal of Oral Medicine and Pain
• /
• v.21 no.1
• /
• pp.115-122
• /
• 1996

This study was performed to compare the anticarious effect of the different fluoride adsorbed(Naf, $NH_4F, Na_2PO_3F, SnF_2, TiF_4$) on synthetic hydroxyapatite and enamel. The amount of fluoride adsorbed in synthetic hydroxyapatite under various concentrations and pH of these fluoride solutions was measured by specific electrode. Enamel samples treated with 5 kinds of 1,000ppm fluoride solutions for 10 minutes were evaluated for fluoride uptake and enamel soubility. The results were as follows. 1. The adsorption of fluoride on synthetic hydroxyapatite increased gradually by the concentration of the fluoride solution, In 1,000ppm fluoride solution, the adsorption of fluoride on synthetic hydroxyapatite treated with NH4F and NaF solutions at pH 4.0 was relatively higher than that of other fluoride solutions. In NH4F and NaF solutions, the adsorption of fluoride on powdered enamel was higher at pH 4.0 solution than at pH 7.0 solution. 2. Fluoride uptake from NH4F solution was relatively high. But that from $Na_2PO_3F$ solution was lower than those from other fluoride solutions. 3. Fluoride solutions were significantly effective on enhancing acid resistance. $NH_4F$ solution was relatively more effective than others on enhancing acid resistance. 4. $SnF_2 and TiF_4$ solutions had the same effect on fluoride adsorption, fluoride uptake, and enamel solubility.

• Journal of Astronomy and Space Sciences
• /
• v.22 no.2
• /
• pp.139-146
• /
• 2005

A model of advection-dominated accretion flows has been highlighted in the last decade. Most of calculations are based on self-similar solutions of equations governing the accreting flows. We revisit self-similar solutions of the simplest form of advection-dominated accretion flows. We explore the parameter space thoroughly and seek another category of self-similar solutions. In this study we allow the parameter f less than zero, which denotes the fraction of energy transported through advection. We have found followings: 1. For f > 0, in real ADAF solutions the ratio of specific heats ${\gamma}$ satisfies 1 < ${\gamma}$ < 5/3 for O ${\leq}$ f ${\leq}$ 1. On the other hands, in wind solutions a rotating disk does not exist. 2. For f < 0, in real ADAF solutions with ${\epsilon}$ greater than zero ${\gamma}$ requires rather exotic range, that is, ${\gamma}$ < 1 or ${\gamma}$ > 5/3. When -5/2 < ${\epsilon}$' < 0, however, allowable ${\gamma}$ can be found in ${\gamma}$ < 5/3, in which case 4{\Omega}_0$,_ is imaginary. 3. For a negative $u_0$,+ with f > 0, solutions are only allowed with exotic ${\gamma}$, that is, 1 < ${\gamma}$ or ${\gamma}$ > (5f/2-5/3)/(5f/2-1)when O < f < 2/5, (5f/2-5/3)/(5f/2-1) < ${\gamma}$ < 1 when f > 2/5. Since ${\epsilon}$' is negative, 4{\Omega}_0$,+ is again an imaginary quantity. For a negative $u_0$,+ with f < 0, ${\gamma}$ is allowed in 1 < 7 < (5|f|/2 + 5/3)/(5|f|/2 + 1). We briefly discuss physical implications of what we have found.

• Wind and Structures
• /
• v.5 no.2_3_4
• /
• pp.177-192
• /
• 2002

Computation solutions for the flow around a cube, which were generated as part of the Computational Wind Engineering 2000 Conference Competition, are compared with full-scale measurements. The three solutions shown all use the RANS approach to predict mean flow fields. The major differences appear to be related to the use of the standard $k-{\varepsilon}$, the MMK $k-{\varepsilon}$ and the RNG $k-{\varepsilon}$ turbulence models. The inlet conditions chosen by the three modellers illustrate one of the dilemmas faced in computational wind engineering. While all modeller matched the inlet velocity profile to the full-scale profile, only one of the modellers chose to match the full-scale turbulence data. This approach led to a boundary layer that was not in equilibrium. The approach taken by the other modeller was to specify lower inlet turbulent kinetic energy level, which are more consistent with the turbulence models chosen and lead to a homogeneous boundary layer. For the $0^{\circ}$ case, wind normal to one face of the cube, it is shown that the RNG solution is closest to the full-scale data. This result appears to be associated with the RNG solution showing the correct flow separation and reattachment on the roof. The other solutions show either excessive separation (MMK) or no separation at all (K-E). For the $45^{\circ}$ case the three solutions are fairly similar. None of them correctly predicting the high suctions along the windward edges of the roof. In general the velocity components are more accurately predicted than the pressures. However in all cases the turbulence levels are poorly matched, with all of the solutions failing to match the high turbulence levels measured around the edges of separated flows. Although all of the computational solutions have deficiencies, the variability of results is shown to be similar to that which has been obtained with a similar comparative wind tunnel study. This suggests that the computational solutions are only slightly less reliable than the wind tunnel.