• Korean Journal of Mathematics
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• v.16 no.4
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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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• v.8 no.1
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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.

• Journal of the Chungcheong Mathematical Society
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• v.30 no.1
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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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• v.61 no.3
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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.

• Journal of the Korean Chemical Society
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• v.52 no.6
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• pp.637-648
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• 2008

• Journal of applied mathematics & informatics
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• v.32 no.1_2
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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 $A^*$.

• Analytical Science and Technology
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• v.7 no.4
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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.

• Analytical Science and Technology
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• v.8 no.4
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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.

• Journal of Environmental Health Sciences
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• v.26 no.4
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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/$m\ell$.

• Resources Recycling
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• v.26 no.4
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• pp.50-55
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• 2017

Determination of trace elements in a sample including complicated matrix is very difficult due to the interference by the matrix. Therefore, if the trace elements can be separated from the complex sample matrix and determined, the interference effects can be reduced, and it is very helpful for the overall analysis. In this study, the analytes of trace elements were separated from the sample matrix by co-precipitation with trace elements using indium hydroxide ($In(OH)_3$), then detected by inductively coupled plasma-atomic emission spectrometer (ICP-AES). Above all, the optimal conditions for the co-precipitation of elements with indium hydroxide were experimentally established. At last, salt was analyzed by the developed analytical method. No heavy metals were not found in Shinan Jeungdo salt, but trace amounts of several heavy metals except for cadmium were found in Cheonnam Yongkwang salt.