• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.4 no.2
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• pp.41-57
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• 2000

In this paper, we consider first order generalized difference scheme for the two-point boundary value problem and one-dimensional second order parabolic type problem. The optimal error estimates in $L_p$ and $W^{1,p}$ ($2{\leq}p{\leq}{\infty}$) as well as some superconvergence estimates in $W^{1,p}$ ($2{\leq}p{\leq}{\infty}$) are obtained. The main results in this paper perfect the theory of GDM.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.4 no.1
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• pp.67-77
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• 2000

In this paper we consider finite element mathods for nonlinear parabolic problems defined in ${\Omega}{\subset}R^d$ ($d{\leq}4$). A new initial approximation is taken. Optimal order error estimates in $L_p$ for $2{\leq}p{\leq}{\infty}$ are established for arbitrary order finite element. One order superconvergence in $W^{1,p}$ for $2{\leq}q{\leq}{\infty}$ are demonstrated as well.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.9 no.1
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• pp.17-29
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• 2005

In this paper we consider finite element methods for nonlinear hyperbolic integro-differential problems defined in ${\Omega}\;{\subset}\;R^d(d\;{\leq}\;4)$. A new initial approximation of $u_t(0)$ is taken. Optimal order error estimates in $L_p$ for $2\;{\leq}\;p\;{\leq}\;{\infty}$ are established for arbitrary order finite element. One order superconvergence in $W^{1,p}$ for $2\;{\leq}\;p\;{\leq}\;{\infty}$ are demonstrated as well.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.9 no.2
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• pp.55-64
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• 2005

In this paper, generalized difference methods(GDM) for one-dimensional viscoelastic problems are proposed and analyzed. The new initial values are given in the generalized difference scheme, so we obtain optimal error estimates in $L^p$ and $W^{1,p}(2\;{\leq}\;p\;{\leq}\;{\infty})$ as well as some superconvergence estimates in $W^{1,p}(2\;{\leq}\;p\;{\leq}\;{\infty})$ between the GDM solution and the generalized Ritz-Volterra projection of the exact solution.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.7 no.2
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• pp.35-49
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• 2003

In this paper, finite volume element methods for nonlinear parabolic integrodifferential problems are proposed and analyzed. The optimal error estimates in $L^p\;and\;W^{1,p}\;(2\;{\leq}\;p\;{\leq}\;{\infty})$ as well as some superconvergence estimates in $W^{1,p}\;(2\;{\leq}\;p\;{\leq}\;{\infty})$ are obtained. The main results in this paper perfect the theory of FVE methods.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.6 no.2
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• pp.85-97
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• 2002

In this paper, finite volume element methods for nonlinear parabolic problems are proposed and analyzed. Optimal order error estimates in $W^{1,p}$ and $L_p$ are derived for $2{\leq}p{\leq}{\infty}$. In addition, superconvergence for the error between the approximation solution and the generalized elliptic projection of the exact solution (or and the finite element solution) is also obtained.

• Korean Journal of Clinical Pharmacy
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• v.26 no.4
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• pp.312-317
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• 2016

Objective: Midazolam is mainly metabolized by cytochrome P450 (CYP) 3A. Inhibition or induction of CYP3A can affect the pharmacological activity of midazolam. The aims of this study were to develop a population pharmacokinetic (PK) model and evaluate the effect of CYP3A-mediated interactions among ketoconazole, rifampicin, and midazolam. Methods: Three-treatment, three-period, crossover study was conducted in 24 healthy male subjects. Each subject received 1 mg midazolam (control), 1 mg midazolam after pretreatment with 400 mg ketoconazole once daily for 4 days (CYP3A inhibition phase), and 2.5 mg midazolam after pretreatment with 600 mg rifampicin once daily for 10 days (CYP3A induction phase). The population PK analysis was performed using a nonlinear mixed effect model ($NONMEM^{(R)}$ 7.2) based on plasma midazolam concentrations. The PK model was developed, and the first-order conditional estimation with interaction was applied for the model run. A three-compartment model with first-order elimination described the PK. The influence of ketoconazole and rifampicin, CYP3A5 genotype, and demographic characteristics on PK parameters was examined. Goodness-of-fit (GOF) diagnostics and visual predictive checks, as well as bootstrap were used to evaluate the adequacy of the model fit and predictions. Results: Twenty-four subjects contributed to 900 midazolam concentrations. The final parameter estimates (% relative standard error, RSE) were as follows; clearance (CL), 31.8 L/h (6.0%); inter-compartmental clearance (Q) 2, 36.4 L/h (9.7%); Q3, 7.37 L/h (12.0%), volume of distribution (V) 1, 70.7 L (3.6%), V2, 32.9 L (8.8%); and V3, 44.4 L (6.7%). The midazolam CL decreased and increased to 32.5 and 199.9% in the inhibition and induction phases, respectively, compared to that in control phase. Conclusion: A PK model for midazolam co-treatment with ketoconazole and rifampicin was developed using data of healthy volunteers, and the subject's CYP3A status influenced the midazolam PK parameters. Therefore, a population PK model with enzyme-mediated drug interactions may be useful for quantitatively predicting PK alterations.

• Asian Spine Journal
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• v.12 no.6
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• pp.1060-1068
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• 2018

Study Design: Retrospective study. Purpose: Lumbar intervertebral disc degeneration is an important cause of low back pain. Overview of Literature: Spinal fusion is often reported to have a good course for adolescent idiopathic scoliosis (AIS). However, many studies have reported that adjacent segment degeneration is accelerated after lumbar spinal fusion. Radiography is a simple method used to evaluate the orientation of the vertebral column. magnetic resonance imaging (MRI) is the method most often used to specifically evaluate intervertebral disc degeneration. The Pfirrmann classification is a well-known method used to evaluate degenerative lumbar disease. After spinal fusion, an increase in stress, excess mobility, increased intra-disc pressure, and posterior displacement of the axis of motion have been observed in the adjacent segments. Methods: we retrospectively secured and analyzed the data of 15 patients (four boys and 11 girls) with AIS who underwent a spinal fusion surgery. We studied the full-length view of the spine (anterior-posterior and lateral) from the X-ray and MRI obtained from all patients before surgery. Postoperatively, another full-length spine X-ray and lumbosacral MRI were obtained from all participants. Then, pelvic tilt, sacral slope, curve correction, and fused and free segments before and after surgery were calculated based on X-ray studies. MRI images were used to estimate the degree to which intervertebral discs were degenerated using Pfirrmann grading system. Pfirrmann grade before and after surgery were compared with Wilcoxon signed rank test. While analyzing the contribution of potential risk factors for the post-spinal fusion Pfirrmann grade of disc degeneration, we used generalized linear models with robust standard error estimates to account for intraclass correlation that may have been present between discs of the same patient. Results: The mean age of the participant was 14 years, and the mean curvature before and after surgery were 67.8 and 23.8, respectively (p<0.05). During the median follow-up of 5 years, the mean degree of the disc degeneration significantly increased in all patients after surgery (p<0.05) with a Pfirrmann grade of 1 and 2.8 in the L2-L3 before and after surgery, respectively. The corresponding figures at L3-L4, L4-L5, and L5-S1 levels were 1.28 and 2.43, 1.07 and 2.35, and 1 and 2.33, respectively. The lower was the number of free discs below the fusion level, the higher was the Pfirrmann grade of degeneration (p<0.001). Conversely, the higher was the number of the discs fused together, the higher was the Pfirrmann grade. Conclusions: we observed that the disc degeneration aggravated after spinal fusion for scoliosis. While the degree of degeneration as measured by Pfirrmann grade was directly correlated by the number of fused segments, it was negatively correlated with the number of discs that remained free below the lowermost level of the fusion.

• Asian-Australasian Journal of Animal Sciences
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• v.16 no.5
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• pp.639-643
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• 2003

The data on 283 Sahiwal cows, sired by 16 bulls, maintained at Cattle Breeding Farm of Nagpur Veterinary College and Dairy Farm of Agricultural College, Nagpur, were considered for the estimation of genetic parameters. Variance and covariance estimates of first lactation traits were obtained using restricted maximum likelihood technique (REML). When first lactation milk yield (FLMY), first lactation length (FLL) and average daily yield (ADY) traits were considered for REML analysis, the heritabilities were $0.184{\pm}0.146$, $0.132{\pm}0.131$ and $0.141{\pm}0.133$, respectively. While, genetic and phenotypic correlations between them were medium to high except phenotypic correlations between FLL and ADY (-0.025). REML procedure considering FLMY, age at first calving (AFC) and first service period (FSP) combination exhibits heritabilities as $0.274{\pm}0.173$, $0.506{\pm}0.233$ and $0.274{\pm}0.172$, respectively. Genetic correlations were $-0.120{\pm}0.376$, $0.225{\pm}0.423$ and $0.365{\pm}0.331$ between FLMY and AFC, FLMY and FSP, AFC and FSP, respectively. Phenotypic correlations were 0.057, 0.289 and 0.123, respectively. Considering all five traits REML combination heritabilities estimated were $0.238{\pm}0.162$, $0.160{\pm}0.139$, $0.136{\pm}0.132$, $0.409{\pm}0.209$ and $0.259{\pm}0.168$ for FLMY, FLL, ADY, AFC and FSP, respectively. The genetic correlations were positive except FLMY and AFC. The phenotypic correlations were also positive except FLL and ADY, ADY and FSP. Almost all estimates were associated with high standard error.

• Journal of Sericultural and Entomological Science
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• v.8
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• pp.11-25
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• 1968

Various formulae for estimation of leaf production in mulberry trees were investigated and obtained. Four varieties of mulberry trees were used as the materials, and seven characters namely branch length. branch diameter, node number per branch, total branch weight, branch weight except leaves, leaf weight and leaf area, were studied. The formulae to estimate the leaf yield of mulberry trees are as follows: 1. Varietal differences were appeared in means, variances, standard devitations and standard errors of seven characters studied as shown in table 1. 2. Y$_1$=a$_1$X$_1$${\times}$P$_1$......(l) where Y$_1$ means yield per l0a by branch number and leaf weight determination. a$_1$.........leaf weight per branch. X$_1$.......branch number per plant. P$_1$........plant number per l0a. 3. Y$_2$=(a$_2$${\pm}$S. E.${\times}$X$_2$)+P$_1$.......(2) where Y$_2$ means leaf yield per l0a by branch length and leaf weight determination. a$_2$......leaf weight per meter of branch length. S. E. ......standard error. X$_2$....total branch length per plant. P$_1$........plant number per l0a as written above. 4. Y$_3$=(a$_3$${\pm}$S. E${\times}$X$_3$)${\times}$P$_1$.....(3) where Y$_3$ means of yield per l0a by branch diameter measurement. a$_3$.......leaf weight per 1cm of branch diameter. X$_3$......total branch diameter per plant. 5. Y$_4$=(a$_4$${\pm}$S. E.${\times}$X$_4$)P$_1$......(4) where Y$_4$ means leaf yield per 10a by node number determination. a$_4$.......leaf weight per node X$_4$.....total node number per plant. 6. Y$\sub$5/= {(a$\sub$5/${\pm}$S. E.${\times}$X$_2$)Kv}${\times}$P$_1$.......(5) where Y$\sub$5/ means leaf yield per l0a by branch length and leaf area measurement. a$\sub$5/......leaf area per 1 meter of branch length. K$\sub$v/......leaf weight per 100$\textrm{cm}^2$ of leaf area. 7. Y$\sub$6/={(X$_2$$\div$a$\sub$6/${\pm}$S. E.)}${\times}$K$\sub$v/${\times}$P$_1$......(6) where Y$\sub$6/ means leaf yield estimated by leaf area and branch length measurement. a$\sub$6/......branch length per l00$\textrm{cm}^2$ of leaf area. X$_2$, K$\sub$v/ and P$_1$ are written above. 8. Y$\sub$7/= {(a$\sub$7/${\pm}$S. E. ${\times}$X$_3$)}${\times}$K$\sub$v/${\times}$P$_1$.......(7) where Y$\sub$7/ means leaf yield estimates by branch diameter and leaf area measurement. a$\sub$7/......leaf area per lcm of branch diameter. X$_3$, K$\sub$v/ and P$_1$ are written above. 9. Y$\sub$8/= {(X$_3$$\div$a$\sub$8/${\pm}$S. E.)}${\times}$K$\sub$v/${\times}$P$_1$.......(8) where Y$\sub$8/ means leaf yield estimates by leaf area branch diameter. a$\sub$8/......branch diameter per l00$\textrm{cm}^2$ of leaf area. X$_3$, K$\sub$v/, P$_1$ are written above. 10. Y$\sub$9/= {(a$\sub$9/${\pm}$S. E.${\times}$X$_4$)${\times}$K$\sub$v/}${\times}$P$_1$......(9) where Y$\sub$7/ means leaf yield estimates by node number and leaf measurement. a$\sub$9/......leaf area per node of branch. X$_4$, K$\sub$v/, P$_1$ are written above. 11. Y$\sub$10/= {(X$_4$$\div$a$\sub$10/$\div$S. E.)${\times}$K$\sub$v/}${\times}$P$_1$.......(10) where Y$\sub$10/ means leaf yield estimates by leaf area and node number determination. a$\sub$10/.....node number per l00$\textrm{cm}^2$ of leaf area. X$_4$, K$\sub$v/, P$_1$ are written above. Among many estimation methods. estimation method by the branch is the better than the methods by the measurement of node number and branch diameter. Estimation method, by branch length and leaf area determination, by formulae (6), could be the best method to determine the leaf yield of mulberry trees without destroying the leaves and without weighting the leaves of mulberry trees.