• 제목/요약/키워드: s-limit shadowing

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VARIOUS SHADOWING PROPERTIES FOR TIME VARYING MAPS

  • Sarkooh, Javad Nazarian
    • 대한수학회보
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    • 제59권2호
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    • pp.481-506
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    • 2022
  • This paper is concerned with the study of various notions of shadowing of dynamical systems induced by a sequence of maps, so-called time varying maps, on a metric space. We define and study the shadowing, h-shadowing, limit shadowing, s-limit shadowing and exponential limit shadowing properties of these dynamical systems. We show that h-shadowing, limit shadowing and s-limit shadowing properties are conjugacy invariant. Also, we investigate the relationships between these notions of shadowing for time varying maps and examine the role that expansivity plays in shadowing properties of such dynamical systems. Specially, we prove some results linking s-limit shadowing property to limit shadowing property, and h-shadowing property to s-limit shadowing and limit shadowing properties. Moreover, under the assumption of expansivity, we show that the shadowing property implies the h-shadowing, s-limit shadowing and limit shadowing properties. Finally, it is proved that the uniformly contracting and uniformly expanding time varying maps exhibit the shadowing, limit shadowing, s-limit shadowing and exponential limit shadowing properties.

TRANSITIVITY, TWO-SIDED LIMIT SHADOWING PROPERTY AND DENSE ω-CHAOS

  • Oprocha, Piotr
    • 대한수학회지
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    • 제51권4호
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    • pp.837-851
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    • 2014
  • We consider ${\omega}$-chaos as defined by S. H. Li in 1993. We show that c-dense ${\omega}$-scrambled sets are present in every transitive system with two-sided limit shadowing property (TSLmSP) and that every transitive map on topological graph has a dense Mycielski ${\omega}$-scrambled set. As a preliminary step, we provide a characterization of dynamical properties of maps with TSLmSP.

신질환(腎疾患) 132례(例)의 초음파진단(超音波診斷) (Ultrasonographic Findings in 132 Cases of Renal Disease)

  • 한혜진;김강석
    • 보험의학회지
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    • 제3권1호
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    • pp.187-208
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    • 1986
  • The conclusions which was acquired one renal cell carcinoma and renal disease 132 cases that was tested renal echogram among 4,499 cases for recent 16 months at medical department, Dae Han Kyoyuk Insurance company from August, 1984 to November, 1985 are as follows: 1. On bur ultrasonography, the echo of tumor was demonstrated with echogenicity as compared with renal parenchyme. 2. The case was stage I by Robson's modification method for pathologic histology. 3. There is no fever, typical triad of renal cell carcinoma and the result of serum biochemical test was within normal limit. 4. The frequency with disease was renal cell carcinoma(0.76%), ureteral stone(1.5%), multicystic kidney(2.27%), hydroureter(2.27%), Bilateral poly cystic kidney(4.55%), hydronephrosis(4.55%), renal agenesis(6.06%) renal calculi(18.18%), simple cyst(60.61%). 5. The frequency with age was 55/1200 case(4.58%) in $41{\sim}50$ years, 13/296 cases(4.39%) in $51{\sim}60$ years, 43/2144 cases(2.01%) in $31{\sim}40$ years, 14/791 cases(1.77%) in $21{\sim}30$ years, 7/53 cases(1.32%) more than 61 years and 0/15(0%) under 20 years. 6. The affected site of renal agenesis 8 cases was right side all. 7. In total renal disease 132 cases, the affected site of 126 cases except bilateral polycystic kidney 6 cases was right kidney 72 cases, left kidney the proportion of right to left 1.6:1 8. In total renal disease 132 cases except bilateral polycystic kidneys 6 cases, the patients affected with both side kidneys were 14 cases. 9. The affection rate with sex in total renal disease 132 cases was 98/2860 cases in male, 34/1819 cases in female and the former was about 2 times than the latter. 10. Classifying the stone with part, nephrolithiasis 24 cases were appeared high frequency, on the contray, ureteral stone 2 cases. 11. 2 cases of ureteral stone developed complication, hydronephrosis and hydroureter. 12. The linear array type transducer was not helpful for the diagnosis of lower ureteral calculi but for the lower ureteral calculi, we could see the stone with high echo in accompanying with acoustic shadowing. 13. In 24 cases of renal calculi, both side nephrolithiasis was 3 cases(12.5%). 14. In renal calculi, solitary stone could be seen extremely much and the number of stone was so much variable from 2 to 10. 15. In 26 cases with renal calculi and ureteral stone, the common clinical manifestation was a intermittent and slight pain. 16. In 80 cases of renal cyst, as one's get older, the affection rate of cyst extremely rised. 17. In bilateral polycystic kidney, large cyst had septum on the whole. 18. The patients with complication were 14 cases(10.6%) of total patients.

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