• Journal of applied mathematics & informatics
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• v.34 no.3_4
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• pp.309-317
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• 2016

Let V be a Euclidean Jordan algebra with a symmetric cone K. We show that for a Z-transformation L with the additional property L(K) ⊆ K (which we will call ’cone-preserving’), GUS ⇔ strictly copositive on K ⇔ monotone + P. Specializing the result to the Stein transformation S_A(X) := X - AXA^T on the space of real symmetric matrices with the property $S_A(S^n_+){\subseteq}S^n_+$, we deduce that S_A GUS ⇔ I ± A positive definite.

• Journal of applied mathematics & informatics
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• v.33 no.1_2
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• pp.229-234
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• 2015

In the setting of semidefinite linear complementarity problems on $S^n$, we focus on the Stein Transformation $S_A(X):=X-AXA^T$ for $A{\in}R^{n{\times}n}$ that is positive semidefinite preserving (i.e., $S_A(S^n_+){\subseteq}S^n_+$) and show that such transformation is strictly monotone if and only if it is nondegenerate. We also show that a positive semidefinite preserving $S_A$ has the Ultra-GUS property if and only if $1{\not\in}{\sigma}(A){\sigma}(A)$.

• Journal of applied mathematics & informatics
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• v.32 no.1_2
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• pp.285-295
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• 2014

In the setting of semidenite linear complementarity problems on $S^n$, we focus on the Stein Transformation $S_A(X)\;:=X-AXA^T$, and show that $S_A$ is (strictly) monotone if and only if ${\nu}_r(UAU^T{\circ}\;UAU^T)$(<)${\leq}1$, for all orthogonal matrices U where ${\circ}$ is the Hadamard product and ${\nu}_r$ is the real numerical radius. In particular, we show that if ${\rho}(A)$ < 1 and ${\nu}_r(UAU^T{\circ}\;UAU^T){\leq}1$, then SDLCP($S_A$, Q) has a unique solution for all $Q{\in}S^n$. In an attempt to characterize the GUS-property of a nonmonotone $S_A$, we give an instance of a nonnormal $2{\times}2$ matrix A such that SDLCP($S_A$, Q) has a unique solution for Q either a diagonal or a symmetric positive or negative semidenite matrix. We show that this particular $S_A$ has the $P^{\prime}_2$-property.

• The Korean Journal of Pesticide Science
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• v.15 no.4
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• pp.441-452
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• 2011

This study was carried out to survey the residual characteristics of endocrine disruptor (ED)-suspected pesticides in greenhouse soils and assess their leachabilites to groundwater. Greenhouse soils were collected from 40 sites of greenhouse in 2008 in Korea. Sixteen ED-suspected pesticides which had been using in Korea, such as alachlor, benomyl, carbaryl, cypermethrin, 2,4-D, dicofol, endosulfan, fenvalerate, malathion, mancozeb, metribuzin, metiram, methomyl, parathion, trifluralin, and vinclozolin, in the soils, were analyzed by chromatographic methods using GLC-ECD and HPLC-DAD/FLD. Limits of detection (LODs) of the test pesticides ranged from 0.0004 to 0.005 mg/kg. Recoveries of the target pesticides from soil ranged from 72.69 to 115.28%. Four pesticides including cypermethrin were detected in the range of from 0.001 to 2.019 mg/kg, representing that their detection rate from greenhouse soils was 37.5%. The highest detection rate was observed from endosulfan which was detected from 16 site soils of the total samples, indicating that endosulfan is persistent in soil because of its very low mobility and high adsorption characteristics in soil. Based on the groundwater ubiquity scores (GUSs) of the pesticides detected from greenhouse soils, most of them have little possibilities of groundwater contamination except the fungicide vinclozolin with some leaching potential because of high water solubility and very low soil adsorption property.