• Journal of the Korean Mathematical Society
• /
• v.47 no.3
• /
• pp.455-466
• /
• 2010

For an endomorphism $\alpha$ of a ring R, we introduce the weak $\alpha$-skew Armendariz rings which are a generalization of the $\alpha$-skew Armendariz rings and the weak Armendariz rings, and investigate their properties. Moreover, we prove that a ring R is weak $\alpha$-skew Armendariz if and only if for any n, the $n\;{\times}\;n$ upper triangular matrix ring $T_n(R)$ is weak $\bar{\alpha}$-skew Armendariz, where $\bar{\alpha}\;:\;T_n(R)\;{\rightarrow}\;T_n(R)$ is an extension of $\alpha$ If R is reversible and $\alpha$ satisfies the condition that ab = 0 implies $a{\alpha}(b)=0$ for any a, b $\in$ R, then the ring R[x]/($x^n$) is weak $\bar{\alpha}$-skew Armendariz, where ($x^n$) is an ideal generated by $x^n$, n is a positive integer and $\bar{\alpha}\;:\;R[x]/(x^n)\;{\rightarrow}\;R[x]/(x^n)$ is an extension of $\alpha$. If $\alpha$ also satisfies the condition that ${\alpha}^t\;=\;1$ for some positive integer t, the ring R[x] (resp, R[x; $\alpha$) is weak $\bar{\alpha}$-skew (resp, weak) Armendariz, where $\bar{\alpha}\;:\;R[x]\;{\rightarrow}\;R[x]$ is an extension of $\alpha$.

• Journal of the Korean Mathematical Society
• /
• v.42 no.4
• /
• pp.723-747
• /
• 2005

In this paper, we consider the quartic moment problem suggested by Curto-Fialkow[6]. Given complex numbers $\gamma{\equiv}{\gamma}^{(4)}\;:\;{\gamma00},\;{\gamma01},\;{\gamma10},\;{\gamma01},\;{\gamma11},\;{\gamma20},\;{\gamma03},\;{\gamma12},\;{\gamma21},\;{\gamma30},\;{\gamma04},\;{\gamma13},\;{\gamma22},\;{\gamma31},\;{\gamma40}$, with ${\gamma00},\;>0\;and\;{\gamma}_{ji}={\gamma}_{ij}$ we discuss the conditions for the existence of a positive Borel measure ${\mu}$, supported in the complex plane C such that ${\gamma}_{ij}=\int\;\={z}^i\;z^j\;d{\mu}(0{\leq}i+j{\leq}4)$. We obtain sufficient conditions for flat extension of the quartic moment matrix M(2). Moreover, we examine the existence of flat extensions for nonsingular positive quartic moment matrices M(2).

• Research in Mathematical Education
• /
• v.9 no.3 s.23
• /
• pp.257-267
• /
• 2005

When notions of numbers are expanded from natural number to complex number, a similar mathematical phenomenon can be observed in each number. As a case study, to complex number, the phenomenon is investigated carefully and teaching materials are created. Then complex number is expressed with matrices and is geometrically treated, so a new number which is an extension of complex number is discovered. Thus, teaching material regarding to complex number and matrices is made for students of ordinary level. Moreover, for talented students, material about an extension of complex number can be added to the previous one.

• Journal of the Korean Mathematical Society
• /
• v.52 no.4
• /
• pp.797-819
• /
• 2015

A trapdoor discrete logarithm group is a cryptographic primitive with many applications, and an algorithm that allows discrete logarithm problems to be solved faster using a pre-computed table increases the practicality of using this primitive. Currently, the distinguished point method and one extension to this algorithm are the only pre-computation aided discrete logarithm problem solving algorithms appearing in the related literature. This work investigates the possibility of adopting other pre-computation matrix structures that were originally designed for used with cryptanalytic time memory tradeoff algorithms to work as pre-computation aided discrete logarithm problem solving algorithms. We find that the classical Hellman matrix structure leads to an algorithm that has performance advantages over the two existing algorithms.

• Communications for Statistical Applications and Methods
• /
• v.23 no.4
• /
• pp.321-334
• /
• 2016

In this paper, we propose power t distribution based on t distribution. We also study the properties of and inferences for power t model in order to solve the problem of real data showing both skewness and heavy tails. The comparison of skew t and power t distributions is based on density plots, skewness and kurtosis. Note that, at the given degree of freedom, the kurtosis's range of the power t model surpasses that of the skew t model at all times. We draw inferences for two parameters of the power t distribution and four parameters of the location-scale extension of power t distribution via maximum likelihood. The Fisher information matrix derived is nonsingular on the whole parametric space; in addition we obtain the profile log-likelihood functions on two parameters. The response plots for different sample sizes provide strong evidence for the estimators' existence and unicity. An application of the power t distribution suggests that the model can be very useful for real data.

• Bulletin of the Korean Mathematical Society
• /
• v.53 no.5
• /
• pp.1309-1325
• /
• 2016

This note focuses on a ring property in which upper and lower nilradicals coincide, as a generalizations of symmetric rings. The concept of symmetric ideal and ring in the noncommutative ring theory was initially introduced by Lambek, as an extension of the usual commutative ideal theory. The investigation of symmetric rings provided many useful results to the study in the noncommutative ring theory. So the results obtained from this study may be applicable to observing the structure of zero divisors in various kinds of algebraic systems containing matrix rings and polynomial rings.

• Kyungpook Mathematical Journal
• /
• v.58 no.2
• /
• pp.203-219
• /
• 2018

This paper is devoted to the study of strongly ${\alpha}-semicommutative$ rings, a generalization of strongly semicommutative and ${\alpha}-rigid$ rings. Although the n-by-n upper triangular matrix ring over any ring with identity is not strongly ${\bar{\alpha}}-semicommutative$ for $n{\geq}2$, we show that a special subring of the upper triangular matrix ring over a reduced ring is strongly ${\bar{\alpha}}-semicommutative$ under some additional conditions. Moreover, it is shown that if R is strongly ${\alpha}-semicommutative$ with ${\alpha}(1)=1$ and S is a domain, then the Dorroh extension D of R by S is strongly ${\bar{\alpha}}-semicommutative$.

• Journal of KIISE:Computing Practices and Letters
• /
• v.14 no.3
• /
• pp.296-300
• /
• 2008

Nonnegative tensor factorization(NTF) is a recent multiway(multilineal) extension of nonnegative matrix factorization(NMF), where nonnegativity constraints are imposed on the CANDECOMP/PARAFAC model. In this paper we consider the Tucker model with nonnegativity constraints and develop a new tensor factorization method, referred to as nonnegative Tucker decomposition (NTD). We derive multiplicative updating algorithms for various discrepancy measures: least square error function, I-divergence, and $\alpha$-divergence.

• The Journal of the Acoustical Society of Korea
• /
• v.36 no.6
• /
• pp.394-400
• /
• 2017

This paper shows the extension of SpSF (Sparse Spectrum Fitting) algorithm, which is one of covariance matrix fitting-based DOA (Direction-of-Arrival) estimation algorithms, from the time domain to the frequency domain, and presents that SpSF can be implemented in the frequency domain. The superiority of the SpSF algorithm has been demonstrated by comparing DOA estimation performance with the performance of Conventional DOA estimation algorithm in the frequency domain for sinusoidal incident signals.

• Carbon letters
• /
• v.3 no.3
• /
• pp.127-132
• /
• 2002

Unidirectional polymer composites were prepared using high-strength carbon fibers as reinforcement and phenolic resin as matrix precursor with keeping fiber volume fraction at 30, 40, 50 and 60% respectively. These composites were carbonized at $1000^{\circ}C$ and graphitised at $2600^{\circ}C$ in the inert atmosphere. The carbonized and graphitised composites were characterized for mechanical properties as well as microstructure. Microscopic studies were carried out of the polished surface of carbonized and graphitised composites after etching by chromic acid, to understand the effect of fiber volume fraction on oxidation at fiber-matrix interface. It is found that the flexural strength in polymer composites increases with fiber volume fraction and so does for the carbonised composites. However, the trend was found to be reversed in graphitised composites. In all the carbonized composites anisotropic region has been observed at fiber-matrix interface which transforms into columnar type microstructure upon graphitisation. The extension of strong and weak columnar type microstructure is function of fiber volume fraction. SEM microscopy of the etched surface of the sample reveal that composites containing 40% fiber volume has minimum oxidation at the interface, revealing a strong interfacial bonding.