• Honam Mathematical Journal
• /
• v.30 no.2
• /
• pp.399-409
• /
• 2008

We consider the most generalized quadratic matrix equation, Q(X) = $A_7XA_6XA_5+A_4XA_3+A_2XA_1+A_0=0$, where X is m ${\times}$ n, $A_7$, $A_4$ and $A_2$ are p ${\times}$ m, $A_6$ is n ${\times}$ m, $A_5$, $A_3$ and $A_l$ are n ${\times}$ q and $A_0$ is p ${\times}$ q matrices with complex elements. The convergence of Newton's method for solving some different types of quadratic matrix equations are considered and we show that the elementwise minimal positive solvents can be found by Newton's method with the zero starting matrices. We finally give numerical results.

• The Korean Journal of Nuclear Medicine Technology
• /
• v.14 no.1
• /
• pp.94-100
• /
• 2010

Purpose: We can evaluate function of kidney by Glomerular Filtration Rate (GFR) test using $^{99m}Tc$-DTPA which is simple. This test is influenced by several parameter such as net syringe count, kidney depth, corrected kidney count, acquisition time and characters of gamma camera. In this study, we evaluated predose count according to matrix size in the GFR test using $^{99m}Tc$-DTPA. Materials and Methods: Gamma camera of Infinia in GE was used, and LEGP collimator, three types of matrix size ($64{\times}64$, $128{\times}128$, $256{\times}256$) and 1.0 of zoom factor were applied. We increased radioactivity concentration from 222 (6), 296 (8), 370 (10), 444 (12) up to 518 MBq (14 mCi) respectively and acquired images according to matrix size at 30 cm distance from detector. Lastly, we evaluated these values and then substituted them for GFR formula. Results: In $64{\times}64$, $128{\times}128$ and $256{\times}256$ of matrix size, counts per second was 26.8, 34.5, 41.5, 49.1 and 55.3 kcps, 25.3, 33.4, 41.0, 48.4 and 54.3 kcps and 25.5, 33.7, 40.8, 48.1 and 54.7 kcps respectively. Total counts for 5 second were 134, 172, 208, 245 and 276 kcounts from $64{\times}64$, 127, 172, 205, 242, 271 kcounts from $128{\times}128$, and 137, 168, 204, 240 and 273 kcounts from $256{\times}256$, and total counts for 60 seconds were 1,503, 1,866, 2,093, 2,280, 2,321 kcounts, 1,511, 1,994, 2,453, 2,890 and 3,244 kcounts, and 1,524, 2,011, 2,439, 2,869 and 3,268 kcounts respectively. It is different from 0 to 30.02 % of percentage difference in $64{\times}64$ of matrix size. But in $128{\times}128$ and $256{\times}256$, it is showed 0.60 and 0.69 % of maximum value each. GFR of percentage difference in $64{\times}64$ represented 6.77% of 222 MBq (6 mCi), 42.89 % of 518 MBq (14 mCi) at 60 seconds respectively. However it is represented 0.60 and 0.63 % each in $128{\times}128$ and $256{\times}256$. Conclusion: There was no big difference in total counts of percentage difference and GFR values acquiring from $128{\times}128$ and $256{\times}256$ of matrix size. But in $64{\times}64$ of matrix size when the total count exceeded 1,500 kcounts, the overflow phenomenon was appeared differently according to predose radioactivity of concentration and acquisition time. Therefore, we must optimize matrix size and net syringe count considering the total count of predose to get accurate GFR results.

• Biomolecules & Therapeutics
• /
• v.18 no.1
• /
• pp.106-110
• /
• 2010

The pharmacokinetics and bioavailability of ambroxol, an expectoration improver and mucolytic agent, were studied to determine the feasibility of enhanced transdermal delivery of ambroxol from the ethylene-vinyl acetate (EVA) matrix system containing polyoxyethylene-2-oleyl ether as an enhancer in rats. The ambroxol-010 matrix system (15 mg/kg) was applied to abdominal skin of rats. Blood samples were collected via the femoral artery for 28 hrs and the plasma concentrations of ambroxol were determined by HPLC. Pharmacokinetic parameters were calculated using Lagran method computer program. The area under the curve (AUC) was significantly higher in the enhancer group ($1,678{\pm}1,413.3\;ng/ml{\cdot}hr$) than that in the control group $1,112{\pm}279\;ng/ml{\cdot}hr$), that is treated transdermally without enhancer, showing about 151% increased bioavailability (p<0.05). The average $C_{max}$ was increased in the enhancer group ($86.0{\pm}21.5\;ng$/ml) compared with the control group ($59.0{\pm}14.8\;ng$/ml). The absolute bioavailability was 13.9% in the transdermal control group, 21.1% in the transdermal enhancer group and 18.1% in the oral administration group compared with the IV group. The $T_{max}$, $K_a$, MRT and $t_{1/2}$ of ambroxol in transdermal enhancer group were increased significantly (p<0.01) compared to those of oral administration. As the ambroxol-EVA matrix containing polyoxyethylene-2-oleyl ether and tributyl citrate was administered to rats via the transdermal routes, the relative bioavailability increased about 1.51-fold compared to the control group, showing a relatively constant, sustained blood concentration. The results of this study show that ambroxol-EVA matrix could be developed as a transdermal delivery system providing sustained plasma concentration.

• Communications of the Korean Mathematical Society
• /
• v.33 no.3
• /
• pp.695-704
• /
• 2018

In this paper, firstly we compute the spectral norm of g-circulant matrices $C_{n,g}=g-Circ(c_0,c_1,{\cdots},c{_{n-1}})$, where $c_i{\geq}0$ or $c_i{\leq}0$ (equivalently $c_i{\cdot}c_j{\geq}0$). After, we compute the spectral norms, determinants and inverses of the g-circulant matrices with the Fibonacci and Lucas numbers.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
• /
• 2012.05a
• /
• pp.95-98
• /
• 2012

This paper describes a multiphase delay-locked loop (DLL) that generates a 32-phase output clock over the operating frequency range of 40 MHz to 280 MHz. The matrix-based delay line is used for high resolution of 1-bit delay. A calibration scheme, which improves the linearity of a delay line, is achieved by calibrating the nonlinearity of the input stage of the matrix. The multi-phase DLL is fabricated by using 0.11-${\mu}m$ CMOS process with a 1.2 V supply. At the operating frequency of 125MHz, the measurement results shows that the DNL is less than +0.51/-0.12 LSB, and the measured peak-to-peak jitter of the multi-phase DLL is 30 ps with input peak-to-peak jitter of 12.9 ps. The area and power consumption of the implemented DLL are $480{\times}550{\mu}m^2$ and 9.6 mW at the supply voltage of 1.2 V, respectively.

• Bulletin of the Korean Mathematical Society
• /
• v.32 no.2
• /
• pp.337-342
• /
• 1995

A semiring is a binary system $(S, +, \times)$ such that (S, +) is an Abelian monoid (identity 0), (S,x) is a monoid (identity 1), $\times$ distributes over +, 0 $\times s s \times 0 = 0$ for all s in S, and $1 \neq 0$. Usually S denotes the system and $\times$ is denoted by juxtaposition. If $(S,\times)$ is Abelian, then S is commutative. Thus all rings are semirings. Some examples of semirings which occur in combinatorics are Boolean algebra of subsets of a finite set (with addition being union and multiplication being intersection) and the nonnegative integers (with usual arithmetic). The concepts of matrix theory are defined over a semiring as over a field. Recently a number of authors have studied various problems of semiring matrix theory. In particular, Minc [4] has written an encyclopedic work on nonnegative matrices.

• The Mathematical Education
• /
• v.49 no.2
• /
• pp.161-174
• /
• 2010

The purpose of the study is to analyze various types of errors appeared in true-false proof problems of matrix and to find out correction method. In order to achieve this purpose, error test was conducted to the subject of 87 second grade students who were chosen from D high schoool. It was shown from this test that the most frequent error type was caused by the lack of understanding about concepts and essential facts of matrix(35.3%), and then caused by the invalid logically reasoning (27.4%), and then caused by the misusing conditions(18.7%). Through three hours of correction lessons with 5 students, the following correction teaching method was proposed. First, it is stressed that the operation rules and properties satisfied in real number system can not be applied in matrix. Second, it is taught that the analytical proof method and the reductio ad absurdum method are useful in the proof problem of matrix. Third, it is explained that the counter example of E=$\begin{pmatrix}1\;0\\0\;1 \end{pmatrix}$, -E should be found in proof of the false statement. Fourth, it is taught that the determinant condition should be checked for the existence of the inverse matrix.

• Journal of the Korean Ceramic Society
• /
• v.28 no.12
• /
• pp.1012-1018
• /
• 1991

SiC whisker-reinforced LAS matrix composites were developed by a mixed colloidal processing route. An optimization of processing conditions was made using the zeta potential data of silica, boehmite, and SiC whisker dispersions. Similarly, the SiC whisker-reinforced composites were also fabricated by the conventional sol-gel process using the hydrolysis-condensation reaction of relevant metal alkoxides. The composites fabricated by the mixed colloidal processing route were characterized by a uniform spatial distribution of SiC whisker throughout the matrix. The fracture toughness increased from 1.3 MPa.m1/2 for the LAS specimen to 5.0 Mpa.m1/2 for the hot-pressed composite (95$0^{\circ}C$ and 20 MPa for 20 min) containing 20 wt% SiC whisker. The increase in fracture toughness appears to result mainly from the crack deflection and the crack bridging by whiskers with some additional toughenings from the whisker pullout and the matrix prestressing mechanisms.

• Journal of Korea Water Resources Association
• /
• v.47 no.2
• /
• pp.95-106
• /
• 2014

This paper analyses the economic effects of the water industry on the Korean economy by using Social Accounting Matrix (SAM). The SAM is constructed based on the Input-Output table, National account and Family income and expenditure survey for Korea in 2009. Through the SAM multiplier analysis, I estimate the effects of water investment. As the results, this study has found the followings. i) output multiplier effects of water sector are 5.300~7.741, ii) value added multiplier effects of water sector are 0.685~1.158, iii) income multiplier effects of water sector are 0.511~0.984, iv) redistributed income multiplier effects of water sector are -0.096~0.247. The results indicate that a significant influence on the industrial production and the household income in Korea.

• Kyungpook Mathematical Journal
• /
• v.59 no.2
• /
• pp.335-340
• /
• 2019

The energy of a graph G is the sum of the absolute values of the eigenvalues of the adjacency matrix of G. Some variants of energy can also be found in the literature, in which the energy is defined for the Laplacian matrix, Distance matrix, Commonneighbourhood matrix or Seidel matrix. The Seidel matrix of the graph G is the square matrix in which $ij^{th}$ entry is -1 or 1, if the vertices $v_i$ and $v_j$ are adjacent or non-adjacent respectively, and is 0, if $v_i=v_j$. The Seidel energy of G is the sum of the absolute values of the eigenvalues of its Seidel matrix. We present here some families of pairs of graphs whose Seidel matrices have different eigenvalues, but who have the same Seidel energies.