• Journal of applied mathematics & informatics
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• v.6 no.1
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• pp.15-30
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• 1999

In this paper the second order semi-discrete and full dis-crete generalized difference schemes for one dimensional parabolic equa-tions are constructed and the optimal order $H^1$ , $L^2$ error estimates and superconvergence results in TEX>$H^1$ are obtained. The results in this paper perfect the theory of generalized difference methods.

• Journal of applied mathematics & informatics
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• v.6 no.1
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• pp.143-162
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• 1999

In this paper we consider the second order generalized difference scheme for the two-point boundary value problem and ob-tain optimal order error estimates in $L^\infty$ and $W^{1,\infty}$ The results in this paper perfect the theory of the second order generalized difference method.

• Kyungpook Mathematical Journal
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• v.45 no.4
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• pp.579-594
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• 2005

In this paper, we will establish some new oscillation criteria for the second-order half-linear delay difference equation $${\Delta}(Pn ({\Delta}Xn)^{\gamma})+q_nx_\array{{\gamma}\\n-{\sigma}}=0,\;n{\geq}n_0$$, where ${\gamma}>0$ is a quotient of odd positive integers. Our results in this paper are sharp and improve some of the well known oscillation results in the literature. Some examples are considered to illustrate our main results.

• Korea-Australia Rheology Journal
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• v.17 no.4
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• pp.149-156
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• 2005

A simple constitutive model for viscoelastic suspensions is discussed in this paper. The model can be used to predict the rheological properties (relative viscosity and all stresses) for viscoelastic suspensions in shear and elongational flow, and the constitutive equations combine a 'viscoelastic' behaviour component and a 'Newtonian' behaviour component. As expected, the model gives a prediction of positive first normal stress difference and negative second normal stress difference; the dimensionless first normal stress difference strongly depends on the shear rate and decreases with the volume fraction of solid phase, but the dimensionless second normal stress difference (in magnitude) is nearly independent of the shear rate and increases with the volume fraction. The relative viscosities and all the stresses have been tested against available experimental measurements.

• Journal of Periodontal and Implant Science
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• v.36 no.2
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• pp.489-502
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• 2006

The purpose of this study was to determine the relationship between the third molar and periodontal status of the adjacent second molar. Fifty patients who had four maxillary and mandibular second molars were consecutively selected for the study subjects. The subjects provided a total of 200 molars, i. e., 100 maxillary and 100 mandibular molars, and classified the groups as follows; third molars that are normally erupted are control group, that are impacted are test 1 group, that are simply extracted are test 2 group, that are surgically extracted are test 3 group. Probing depth, plaque index, gingival index and mobility were measured. The results were as follows. 1. In mesial probing depth, there was no significantly difference. In distal probing depth, there was a significantly difference between control group and test 1 & 3 group in maxilla and between control & test 2 group and test 1& 3 group in mandible(p<0.05). 2. In buccal probing depth, there was a significantly difference between test 2 group and test 3 group in mandible. In lingual probing depth, there was a significantly difference between control group and test 1 & 3 group in mandible(p<0.05). 3. In plaque index, there was a significantly difference between test 1 group and test 2 group in maxilla, between test 1 group and control & test 2 group in mandible(p<0.05). 4. In gingival index, there was a significantly difference between control group and test 1 & 3 group in mandible. In mobility, there was no significantly difference(p<0.05). As a result of this study, the second molars adjacent to the third molars that are impacted or surgically extracted had poor prognosis, so impacted third molars should be extracted in early time and the second molars are actively treated for periodontal health.

• Journal of applied mathematics & informatics
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• v.8 no.1
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• pp.111-128
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• 2001

In this paper, we consider the oscillation of the second-order neutral difference equation Δ²(x/sub n/ - px/sub n-r/) + q/sub n/f(x/sub n/ - σ/sub n/) = 0 as well as the oscillatory behavior of the corresponding ordinary difference equation Δ²z/sub n/ + q/sub n/f(R(n,λ)z/sub n/) = 0

• Journal of applied mathematics & informatics
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• v.13 no.1_2
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• pp.125-138
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• 2003

Some Riccati type difference inequalities are established for the second-order nonlinear difference equations with negative neutral term $\Delta$(a(n)$\Delta$(x(n) - px(n-$\tau$))) + f(n, x($\sigma$(n))) = 0 using these inequalities we obtain some oscillation criteria for the above equation.

• Journal of Ocean Engineering and Technology
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• v.12 no.2 s.28
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• pp.33-42
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• 1998

In the presence of incident waves with different frequencies, the second order sum and difference frequency waves due to the nonlinearity of the incident waves come into existence. Although the magnitudes of the forces produced on a Tension Leg Platform(TLP) by these nonlinear waves are small, they act on the TLP at sum and difference frequencies away from those of the incident waves. So, the second order sum and difference frequency wave loads produced close to the natural frequencies of TLPs often give greater contributions to high and low frequency resonant responses. The second order wave exciting forces and moments have been obtained by the method based on direct integration of pressure acting on the submerged surface of a TLP. The components of the second order forces which depend on first order quantities have been evaluated using the three dimensional source distribution method. The numerical results of time domain analysis for the nonlinear wave exciting forces in regular waves are compared with the numerical ones of frequency domain analysis. The results of comparison confirmed the validity of the proposed approach.

• Journal of the Korean Mathematical Society
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• v.36 no.2
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• pp.381-402
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• 1999

Let {Rn($\chi$)}{{{{ { } atop {n=0} }}}} be a discrete Sobolev orthogonal polynomials (DSOPS) relative to a symmetric bilinear form (p,q)={{{{ INT _{ } }}}} pqd$\mu$0 +{{{{ INT _{ } }}}} p qd$\mu$1, where d$\mu$0 and d$\mu$1 are signed Borel measures on . We find necessary and sufficient conditions for {Rn($\chi$)}{{{{ { } atop {n=0} }}}} to satisfy a second order difference equation 2($\chi$) y($\chi$)+ 1($\chi$) y($\chi$)= ny($\chi$) and classify all such {Rn($\chi$)}{{{{ { } atop {n=0} }}}}. Here, and are forward and backward difference operators defined by f($\chi$) = f($\chi$+1) - f($\chi$) and f($\chi$) = f($\chi$) - f($\chi$-1).

• The Journal of Korean Academy of Sensory Integration
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• v.3 no.1
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• pp.1-11
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• 2005

Objective : The purpose of this study was to get the mean of duration of post-rotatory nystagmus test in normal children and to differentiate the duration of post-rotatory nystagmus test between normal children and children with pervasive developmental disorder. Method : 84 subjects were between 3 and 5 years of age and consisted of 64 normal children and 20 children with the pervasive developmental disorder. Analysis of the data was done by using t-test and ANOVA. Results : The results were as follows: 1. Range of duration of post-rotatory nyatagmus test in normal children was $5{\sim}22$second on left and $7{\sim}21$ second on right and the mean was 12.63 second on left and 12.59 second on right. 2. Range of duration of post-rotatory nystagmus test in children with the pervasive developmental disorder was $3{\sim}11$ second on both and the mean was 5.65 second on left and 5.60 second on right. 3. There was no significant difference between males and females with normal children in duration of post-rotatory nystagmus test. However, there was a significant difference of the mean duration between 3 and 5 years old normal group. 4. Children with pervasive developmental disorder significantly have relatively lower duration than the duration of post-rotatory nystagmus test of normal children. Conclusions : The results of the study showed significant difference between normal children and children with pervasive developmental disorder in duration of post-rotatory nystagmus test and suggest that they could be applied to the baseline of clinical therapy.