• Korean Journal of Mathematics
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• 제16권4호
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• pp.565-571
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• 2008

In this paper we present some trace inequalities for positive definite matrices in statistical mechanics. In order to prove the method of the uniform bound on the generating functional for the semi-classical model, we use some trace inequalities and matrix norms and properties of trace for positive definite matrices.

• Journal of applied mathematics & informatics
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• 제8권1호
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• pp.97-109
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• 2001

This article is devoted to “forgotten” and rarely used technique of matrix analysis, introduced in 60-70th and enhanced by authors. We will study the matrix trace operator and it’s differentiability. This idea generalizes the notion of scalar derivative for matrix computations. The list of the most common derivatives is given at the end of the article. Additionally we point out a close connection of this technique with a least square problem in it’s classical and generalized case.

• 충청수학회지
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• 제30권1호
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• pp.21-29
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• 2017

We review a partial trace alternatively defined by the composition of positive linear maps, and see how the partial trace acts on the matrix geometric means. We also study the quantum Tsallis relative entropy under partial trace related with the fidelity.

• Kyungpook Mathematical Journal
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• 제61권3호
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• pp.583-590
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• 2021

In this work we give new upper and lower bounds for the numerical radius of a complex square matrix A using the entries and the trace of A.

• 대한화학회지
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• 제52권6호
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• pp.637-648
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• 2008

• Journal of applied mathematics & informatics
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• 제32권1_2호
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• pp.61-74
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• 2014

This paper describes an iterative method for orthogonal projections $AA^+$ and $A^+A$ of an arbitrary matrix A, where $A^+$ represents the Moore-Penrose inverse. Convergence analysis along with the first and second order error estimates of the method are investigated. Three numerical examples are worked out to show the efficacy of our work. The first example is on a full rank matrix, whereas the other two are on full rank and rank deficient randomly generated matrices. The results obtained by the method are compared with those obtained by another iterative method. The performance measures in terms of mean CPU time (MCT) and the error bounds for computing orthogonal projections are listed in tables. If $Z_k$, k = 0,1,2,... represents the k-th iterate obtained by our method then the sequence of the traces {trace($Z_k$)} is a monotonically increasing sequence converging to the rank of (A). Also, the sequence of traces {trace($I-Z_k$)} is a monotonically decreasing sequence converging to the nullity of $A^*$.

• 분석과학
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• 제7권4호
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• pp.555-561
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• 1994

A method was described for the graphite furnace atomic absorption spectrophotometric determination of trace cadmium, copper, chromium and lead in urine samples. The elements were directly determined without any other treatments. The ash temperature was intensively optimized to improve the large background by the removal of organic materials and alkali and alkali earth metals in urine samples. Two kinds of standard solutions were used to plot calibration curves. From the recovery data, it could be confirmed that the analytical results with the synthetic urine matrix similar to real urine were more accurate than with a deionized water matrix.

• 분석과학
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• 제8권4호
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• pp.435-442
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• 1995

A matrix modification was studied for the determination of trace bismuth in water samples by graphite furnace atomic absorption spectrophotometry. The type and quantity of modifiers as well as the use of auxiliary modifiers were investigated to realize the efficient modification. Palladium was chosen as a single modifier. By the addition of palladium($5{\mu}g/mL$) to 100 ng/mL bismuth solution, the temperatures could be raised from $500^{\circ}C$ to $1,300^{\circ}C$ for the charring and from $2,000^{\circ}C$ to $2,200^{\circ}C$ for the atomization as well as the sensitivity and reproducibility were improved. The absorbance of bismuth was maximum and not changed in the range of Pd $3-25{\mu}g/mL$. And several materials were examined as an auxiliary modifier. The mixed solution of $1{\mu}g/mL$ palladium and $200{\mu}g/mL$ nickel have raised the temperatures as with $5{\mu}g/mL$ palladium only. The maximum absorbance of bismuth was shown in the nickel concentration range of $100-300{\mu}g/mL$ in $1{\mu}g/mL$ palladium modified system. With such optimum conditions, the trace amount of bismuth in several water samples could be determined by a calibration curve method, and good recoveries were also obtained.

• 한국환경보건학회지
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• 제26권4호
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• pp.75-81
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• 2000

A matrix modification was studied for the determination of trace manganese in several seaweeds by electrothermal atomic absorption spectrophotometry(ETAAS). The type and quantity of modifiers were investigated to realize the efficient modification. Palladium was chosen as a single modifier. By the addition of palladium(5$\mu\textrm{g}$/$m\ell$) to 2ng/$m\ell$ manganese solution, the temperatures were raised from 1,00$0^{\circ}C$ to 1,20$0^{\circ}C$ for the charring and from 2,10$0^{\circ}C$ to 2,20$0^{\circ}C$ for the atomization as well as the sensitivity and reproducibility were improved. With such optimum conditions, the trace amount of manganese in several seaweeds(laver, tangle and brown seaweed) could be determined by a calibration curve method, and good recoveries of more than 965 were also obtained in the samples in which a given amount of manganese was spiked. The detection limit of this method was about 0.048ng/$m\ell$.

• 자원리싸이클링
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• 제26권4호
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• pp.50-55
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• 2017

복잡한 모체를 갖는 시료에 존재하는 미량의 원소들은 모체방해효과로 인하여 분석이 어렵다. 따라서 시료모체로부터 미량의 원소들을 분리해서 분석할 수 있다면 그 방해 요인을 줄일 수 있어 분석에 많은 도움이 된다. 시료모체와 미량의 원소들을 분리하기 위하여 인듐 수산화물($In(OH)_3$)을 이용하여 시료 내에 존재하는 미량의 원소들을 공동침전시킴으로서 분석물질을 분리시킨 후에 유도 결합 플라즈마-원자 방출 분광법을 이용하여 분석하는 방법에 대한 연구를 하였다. 이 연구에서는 공동침전의 발생과 회수율을 높일 수 있는 최적의 조건을 실험을 통해 설정하였다. 공동침전물을 석영섬유필터를 사용하여 걸러내고, 공침이 발생하는 시료의 pH를 9.5로 조정하였다. 또한 필터의 침전물을 ICP-AES로 측정하기 위해 질산 30% 용액에 1분 동안 담궈 침전물을 녹였고, 침전물이 녹은 질산용액은 온도변화 없이 농축을 진행하는 최적의 조건을 설정하였다. 이 최적조건을 소금시료에 적용하여 분석한 결과, 신안 증도에서의 소금에서는 중금속이 거의 검출 되지 않았지만 전남 영광 소금의 경우 카드뮴을 제외하고 여러개의 중금속이 미량 검출되었다.