• Bulletin of the Korean Mathematical Society
• /
• v.46 no.3
• /
• pp.511-519
• /
• 2009

A matrix $P{\in}\mathbb{C}^{n{\times}n}$ is called a generalized reflection matrix if $P^*$ = P and $P^2$ = I. An $n{\times}n$ complex matrix A is said to be a reflexive (anti-reflexive) matrix with respect to the generalized reflection matrix P if A = PAP (A = -PAP). It is well-known that the reflexive and anti-reflexive matrices with respect to the generalized reflection matrix P have many special properties and widely used in engineering and scientific computations. In this paper, we give new necessary and sufficient conditions for the existence of the reflexive (anti-reflexive) solutions to the linear matrix equation AXB + CY D = E and derive representation of the general reflexive (anti-reflexive) solutions to this matrix equation. By using the obtained results, we investigate the reflexive (anti-reflexive) solutions of some special cases of this matrix equation.

• East Asian mathematical journal
• /
• v.40 no.3
• /
• pp.329-339
• /
• 2024

In the work we generate arithmetic matrix P^(c,b,a) of (cx² + bx+a)ⁿ from a Pascal matrix P^(1,1). We extend an identity P^(1,1))O^(1,1) = P^(1,1,1) with an obtuse matrix O^(1,1) to k degree polynomials. For the purpose we study P^(1,1)kO^(1,1) and find generating polynomials of O^(1,1)k.

• Bulletin of the Korean Mathematical Society
• /
• v.48 no.5
• /
• pp.1093-1103
• /
• 2011

We give the characterizations of the classes of matrix trans-formations ($m(\phi),{\ell}_p$), ($n(\phi),{\ell}_p$) ([5, Theorem 2]), (${\ell}_p,m(\phi)$) ([5, Theorem 1]) and (${\ell}_p,n(\phi)$) for $1{\leq}p{\leq}{\infty}$, establish estimates for the norms of the bounded linear operators defined by those matrix transformations and characterize the corresponding subclasses of compact matrix operators.

• Proceedings of the IEEK Conference
• /
• 1999.06a
• /
• pp.745-748
• /
• 1999

This paper propose the method to derive RM(Reed-Muller) expansion coefficients for Multiple-Valued function. The general method to obtain RM expansion coefficient for p valued n variable is derivation of single variable transform matrix and expand it n times using Kronecker product. The transform matrix used is p$^{n}$ $\times$ p$^{n}$ matrix. In this case the size of matrix increases depending on the augmentation of variables and the operation is complicated. Thus, to solving the problem, we propose derivation of RM expansion coefficients using p$\times$p transform matrix and Karnaugh-map.

• Transactions of Materials Processing
• /
• v.3 no.4
• /
• pp.427-439
• /
• 1994

The high temperature deformation behavior of $SiC_p/Al-Si$ composites and Al-Si matrix was studied by hot torsion test in a range of temperature from $270^{\circ}C$ to $520^{\circ}C$ and at strain rate range of $1.2{\times}10_{-3}~2.16{\times}10_{-1}/sec$. The hot restoration mechanisms for both matrix and composites were found to be dynamic recrystallization(DRX) from the investigation of flow curves and microstructural evolutions. The Si precipitates and SiC particles promoted DRX, and the peak strain$({\varepsilon}_p)$ of the composites was smaller than that of the matrix. Flow stresses of $SiC_p/Al-Si$ composites were found to be generally higher than the matrix, but the difference was quite small at higher temperature due to the decrease of capability of load transfer by SiC particles. With increasing temperature, failure strain of matrix and composites are inclined to increase, the increasing value of failure strain for the $SiC_p/Al-Si$ composites was small compared to that of matrix. The stress dependence of both materials on strain rate() and temperature(T) was examined by hyperbolic sine law, $\.{\varepsilon}=A_1[sinh({\alpha}{\cdot}{\sigma})]_n$exp(-Q/RT)

• Korean Journal of Mathematics
• /
• v.27 no.4
• /
• pp.949-968
• /
• 2019

In this work, we characterize some matrix classes concerning the Binomial sequence spaces b^r,s_∞ and b^r,s_p, where 1 ≤ p < ∞. Moreover, by using the notion of Hausdorff measure of noncompactness, we characterize the class of compact matrix operators from b^r,s₀, b^r,s_c and b^r,s_∞ into c₀, c and ℓ_∞, respectively.

• Bulletin of the Korean Mathematical Society
• /
• v.41 no.2
• /
• pp.199-211
• /
• 2004

For positive integers $\kappa$ and p$\geq$3, let(equation omitted) where $J_{p}$ is the p${\times}$p matrix whose entries are all 1. Then, we determine the minimum permanents and minimizing matrices over (1) the face of $\Omega$(D) and (2) the face of $\Omega$($D^{*}$), where (equation omitted).

• Journal of the Korean Society for Precision Engineering
• /
• v.5 no.1
• /
• pp.50-62
• /
• 1988

An experimental investigation of the machining characteristics of compact vermicular cast iron whose matrix were formulated under two kinds of annealing conditions has been conducted. The various characteristics of the machinability of CA cast iron depending upon its matrix and cutting condition have been obtained from the experiment. The results are as follow. As depth of cut increases, the shear stress slightly decreases in order $P_1, \P_2, \P_3$ which are classified by ferrite matrix of CV cast iron. As depth of cut increases, the normal stress increases, and annealing effect in heavy cutting is smaller than that in light cutting. The cutting energy slightly decreases, as depth of cut increases and the effect of annealing on cutting energy in light cutting is higher than that in heavy cutting. The cutting equation in this study are as follow. $P_1\:\2{\phi}\ + \1.49({\beta} - {\alpha} )=84^{\circ}$ $P_2\:\2{\phi}\ + \1.36({\beta} - {\alpha} )=82^{\circ}$ $P_3\:\2{\phi}\ + \1.34({\beta} - {\alpha} )=79^{\circ}$ Machining constants in this study for $P_1, P_2, P_3$give $74^{\circ} , 66^{\circ}, 61^{\circ}$ Tool wear increases as depth of cut increases, and decreases as ferrit matrix increases.

• Journal of Pharmaceutical Investigation
• /
• v.35 no.6
• /
• pp.453-460
• /
• 2005

4-Aminopyridine (AP) is a potassium channel blocker used in the treatment of neurological disorders such as multiple sclerosis and Alzheimer disease. AP‘s window of therapeutic effect appears to correlate with its plasma halflife (3.5 hours). It demonstrates pH-dependent solubility because of a weakly basic drug. In addition, the resulting release from conventional matrix tablets decreases with increasing pH-milieu of the gastrointestinal tract. The aim of this study is to design sustained release matrix tablet containing AP, overcoming this problem. $Eudragit^{\circledR}$ L 100 (EuL) and sodium alginate were used in an effort to achieve pH independent drug release. The effect of sodium alginate and EuL on drug release from matrix tablet was investigated. The drug release behavior from the different tablets was analyzed by $t_{20%},\;t_{40%},\;t_{60%}$, The exponential diffusion coefficient n, kinetic constant K were calculated according to the Korsmeyer-Peppas equation. The drug release from matrix tablets prepared with sodium alginate was decreased with increasing the content of sodium alginate in pH 7.4 while there is no significant difference in pH 1.2. The exponent n values were determined to be approximately 0.5 and 0.8 respectively, in both pH 1.2 and 7.4. These values indicate diffusion-based anomalous mechanism and erosion-based anomalous mechanism, respectively. The drug release from sodium alginate matrix tablets prepared with solid dispersion of EuL containing drug showed a slow drug release in an acidic medium and a more fast drug release in phosphate medium, compared with sodium alginate matrix tablets prepared with physical mixture. These results may be attributed to the gel forming ability of sodium alginate and pH dependent solubility of EuL. Therefore, sustained-release AP matrix tablets using sodium alginate and EuL were successfully prepared.

• Journal of environmental and Sanitary engineering
• /
• v.16 no.3
• /
• pp.80-86
• /
• 2001

This research was carried out to investigate the effect of microscopic silica matrix coagulation on heavy metals and anion removal in mining wastewater. pH and alkalinity played an important role to coagulate heavy metals such as Al, and Fe and an anion such as ${SO_4}^{2-}$ with silica matrix as well as NaOH. However, the efficiency to form coagulates was much greater in silica matrix-treated wastewater than NaOH-treated one. Fe in wastewater formed coagulation with both silica matrix and NaOH treatments resulting in lowering Fe content in wastewater at above pH 9. For Al removal in wastewater, silica matrix-treated wastewater at above pH 12.3 formed stable coagulate with Al, while NaOH-treated one did not. Alkalinities of 89 and 220 mg/L were required to stabilize silica matrix treated coagulate with Fe and Al, respectively. Reaction time of ten minute was required to provide enough reaction for coagulation between heavy metals and silica matrix. Heavy metals and anion leachates were much lower in coagulate with silica matrix than that with NaOH, which indicates that silica matrix could be used to remove heavy metals efficiently.