• Nonlinear Functional Analysis and Applications
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• v.26 no.2
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• pp.289-301
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• 2021

In this research, we interpret the notion of a b-cyclic (𝚽, C, D)-contraction for the pair (g, S) of self-mappings on the set Y. We employ our definition to introduce some common fixed point theorems for the two mappings g and S under a set of conditions. Also we introduce an example to support our results.

• Journal of Food Hygiene and Safety
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• v.6 no.1
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• pp.1-12
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• 1991

Fischer 344 rats aged six weeks were diYided into four groups and group 1, 2, and 3 of rats were given an intraperitoneal injection of diethylnitrosamine at 200 mg/kg body weight and group 4 was given saline alone. Two weeks after beginning of the experiment, group 1 and 2 of rats were begun to feed on diets containing 0.02% 2-acetylaminofluorene as a promoter for four weeks. Three weeks after beginning of the experiment, all groups were performed partial hepatectomy. During the last two weeks, group 1 and 3 of rats were received subcutaneously 3 consecutive weekly doses of iron dextran at 0.125 ml/100 g body weight. Subcutaneous injection of iron dextran resulted in hepatic siderosis in group 1 and 3 of rats. Pre neoplastic nodules were identified histopathologically by two markers, resistance to exogenous iron accumulation and glutathione S-transeferase placental form (GST-P) activity, while early carcinogen induced foci were hardly resistant to iron accumulation and though a few lesions were identified, it could hardly be distincted from normal hepatocytes of surroundings. However, GST-P positive nodules as well as foci were clearly distincted from normal hepatic cells of surroundings. In the quantitative analysis of carcinogen-induced nodules and foci, more lesions were detected by immunohistochemical method for GST-P than by prussian blue staining for resistant to iron accumulation. It is concluded that immunohistochemical marker for GST-P is more sensitive and reliable than iron-resistance marker, and that iron-resistance is not useful marker for early detection of carcinogen-induced hepatic lesions.

• Journal of applied mathematics & informatics
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• v.5 no.3
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• pp.717-734
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• 1998

In the present paper is presented a new matrix pencil-based numerical approach achieving the computation of the elemen-tary divisors of a given matrix $A \in C^{n\timesn}$ This computation is at-tained without performing similarity transformations and the whole procedure is based on the construction of the Piecewise Arithmetic Progression Sequence(PAPS) of the associated pencil $\lambda I_n$ -A of matrix A for all the appropriate values of $\lambda$ belonging to the set of eigenvalues of A. This technique produces a stable and accurate numerical algorithm working satisfactorily for matrices with a well defined eigenstructure. The whole technique can be applied for the computation of the first second and Jordan canonical form of a given matrix $A \in C^{n\timesn}$. The results are accurate for matrices possessing a well defined canonical form. In case of defective matrices indications of the most appropriately computed canonical form. In case of defective matrices indication of the most appropriately computed canonical form are given.

• Journal of applied mathematics & informatics
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• v.4 no.1
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• pp.63-82
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• 1997

In experimental situations where n two or three level fac-tors are involoved and n observations are taken then the D-optimal first order saturated design is an $n{\times}n$ matrix with elements $\pm$1 or 0, $\pm$1, with the maximum determinant. Cononical forms are useful for the specification of the non-isomorphic D-optimal designs. In this paper we study canonical forms such as the Smith normal form the first sec-ond and the jordan canonical form of D-optimal designs. Numerical algorithms for the computation of these forms are described and some numerical examples are also given.

• Communications of the Korean Mathematical Society
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• v.34 no.2
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• pp.401-414
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• 2019

Let ${\mathcal{F}}$ denote an algebraically closed field with characteristic not two. Fix an integer $d{\geq}3$, let $Mat_{d+1}({\mathcal{F}})$ denote the ${\mathcal{F}}$-algebra of $(d+1){\times}(d+1)$ matrices with entries in ${\mathcal{F}}$. An ordered pair of matrices A, $A^*$ in $Mat_{d+1}({\mathcal{F}})$ is said to be LB-TD form whenever A is lower bidiagonal with subdiagonal entries all 1 and $A^*$ is irreducible tridiagonal. Let A, $A^*$ be a Leonard pair in $Mat_{d+1}({\mathcal{F}})$ with fundamental parameter ${\beta}=2$, with this assumption there are four families of Leonard pairs, Racah, Hahn, dual Hahn, Krawtchouk type. In this paper we show from these four families only Racah and Krawtchouk have LB-TD form.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.2
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• pp.309-313
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• 2013

In this paper, we show that for a linear dynamical system $f(x)=Ax$ of $\mathbb{C}^n$, $f$ has the limit shadowing property if and only if the matrix A is hyperbolic.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.4
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• pp.609-615
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• 2012

In the current paper, we establish the relationship between the powers of an invertible matrix and the powers of its inverse. More precisely, we prove that if A is an invertible matrix and, if $A^n\;=\;(A_{i,j}(n))$ for all positive integer n, then $A^{-n}\;=\;(A_{i,j}{(-n))$.

• Bulletin of the Korean Mathematical Society
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• v.50 no.5
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• pp.1481-1494
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• 2013

The paper is devoted to the study of finite dimensional complex evolution algebras. The class of evolution algebras isomorphic to evolution algebras with Jordan form matrices is described. For finite dimensional complex evolution algebras the criterium of nilpotency is established in terms of the properties of corresponding matrices. Moreover, it is proved that for nilpotent $n$-dimensional complex evolution algebras the possible maximal nilpotency index is $1+2^{n-1}$.

• Korea Trade Review
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• v.42 no.3
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• pp.123-142
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• 2017

This study is to investigate Right to Chinese Name for Foreigners under Trademark Law of the People's Republic of China. The basketball star Michael Jordan sued Qiaodan Sports in 2012, saying the company had built its business around his Chinese name read as Qiaodan in Chinese without his permission. The Chinese supreme court ruled that the trademark for Jordan's Chinese name should be returned to China's State Administration for Industry and Commerce to be re-awarded, and it means Qiaodan Sports Co. must stop using the Chinese characters for Qiaodan on its merchandise. However, the court rejected Jordan's claim to the romanized or pinyin form of the name "Qiaodan," saying in its judgment that this version may not be closely linked with him. People who want to claim the right to Chinese name, he/she must prove the specific name has linked with him/her. Furthermore, he/she must prove the Chinese firm's actions had displayed "malicious intent" by registering trademarks for his/her Chinese name. The courts approve infringement by Chinese firm and stop to use his/her name in the country.

• Korean Journal of Fisheries and Aquatic Sciences
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• v.9 no.4
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• pp.273-280
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• 1976

Morphological changes of early larval stages of Lophius litulon (Jordan) are described based on 861 individuals collected at the intertidal zone at Haeundae, Busan, on the 20th of June, 1976. Particular emphasis is paid on the development of dorsal spinous rays, ventral fin rays, chromatophore patterns, alimentary canal, gills, branchiostegal rays and teeth. The premordial spinous fin ray of the first dorsal fin appears at the newly hatched larva of around 2.70mm in total length, the second spinous ray at around 5.82mm, and the third spinous ray at around 6.45 nm. Premordial fin rays which develope as a semicircle to cudgel form of the ventral fin appear posterior to the pectoral fin at the larva of around 2.70mm in total length. When the larvae grow up to 6.35mm in total length, the length of the ventral fin is more or less half of the total length of the body. In the early stages$(2.70\~3.75mm)$ melanophores are scattered irregularly on the tail . In the later stages(4.25mm) melanophores are aggregated to form three black spots on medio-lateral part of the tail. The newly hatched larvae have the premordial alimentary canal with mouth and intestine. With decreasing yolk mass the intestine appears more distinctly with curvature, and mouth seems to open. Gills appear at the larvae of 6.35mm in total length; branchiostegal rays appear at the larvae of 6.45mm. Teeth appear at the larvae of 6.25mm.