ゼミ発表 (2019年10月)

Seminar Presentation (October 2019)

Transcript

1. θϛൃද ۚઘେհ (ؙ໺ݚڀࣨ, ਫ਼౓อূ෇͖਺஋ܭࢉάϧʔϓ OB) 2019 ೥ 10 ݄, ˏദ໦ݚڀࣨ, ਺ֶԠ༻਺ཧઐ߈ ۚઘେհ (ؙ໺ݚڀࣨ OB) θϛൃද 2019 ೥ 10 ݄, ˏദ໦ݚڀࣨ 1 / 18
2. ຊൃදͷྲྀΕ 1 ࣗݾղܾ࣭ͨ͠໰ 2 IPSJ-HPC171 ౔࢈࿩ 3 UTNAS ͓౔࢈࿩ 4 ॳาతͳ࣭໰ 5 Journal ʹ͍ͭͯ 6 ޙظͷ༧ఆ म࿦ରࡦ ദ໦ݚڀࣨ B4 ޲͚ϨΫνϟʔ (ദ໦ݚڀࣨͷօ͞Μͱͷ૬ஊࣄ߲) B3 ޲͚ק༠/આ໌ձ Travel Schedule ࠓޙͷଧͪ߹Θͤ೔ఔ ۚઘେհ (ؙ໺ݚڀࣨ OB) θϛൃද 2019 ೥ 10 ݄, ˏദ໦ݚڀࣨ 2 / 18
3. ࣗݾղܾ࣭ͨ͠໰ ࣗݾղܾ࣭ͨ͠໰ JSIAM ೥ձͷϙελʔൃදͰ dLV (ݻ༗஋໰୊ʹର͢ΔՄੵ෼ΞϧΰϦζϜ) ͷ ࿩͕͋ͬͨͷͰ, ৭ʑڭ͑ͯ΋Β͍·ͨ͠. dLV Ͱݻ༗ϕΫτϧ·Ͱ͸ٻ·Βͳ͍ ݻ༗ϕΫτϧΛٻΊΔʹ͸ Wielandt ͷٯ൓෮͔ Jacobi ๏Λ࢖͏͔͠ͳ͍ Α͏Ͱ͢. ݻ༗஋ɾݻ༗ϕΫτϧ͕͢΂ͯಉ࣌ʹٻ·Δ఺Ͱ, ͜ͷํ๏ (Jacobi ๏) ͸ࣺ͕͍ͯͨ (by ࢁຊઌੜͷ਺஋ղੳೖ໳, 2003, p105) ࠃ֎Ͱ Jacobi ๏ͷ҆ఆੑ͕࠶ධՁ͞Ε͍ͯΔ (by ࢁຊઌੜͷ਺஋ղੳ ೖ໳, 2003, p105) ࠓͰ΋ Jacobi ๏ϒʔϜͬͯ͋Γ·͔͢ ? → ࠓͰ͸ SVD ʹ࢖ΘΕ͍ͯΔΑ͏Ͱ͢ (cf: ӳޠ൛ Wikipedia). ࠷ۙ SVD ͕٭ޫΛཋͼ͍ͯΔΒ͍͠Ͱ͢ 1. 1Netflix Prize and SVD, Stephen Gower, April 18th 2014 ۚઘେհ (ؙ໺ݚڀࣨ OB) θϛൃද 2019 ೥ 10 ݄, ˏദ໦ݚڀࣨ 3 / 18
4. IPSJ-HPC171 ౔࢈࿩ IPSJ-HPC171 ౔࢈࿩ Έͳ͞ΜվΊ·ͯ͠߹͓॓ർΕ͞·Ͱͨ͠ Έͳ͞Μ͕߹॓ߦͬͯΔؒʹ IPSJ-HPC171 ˏ NII ʹߦ͖ͬͯ·ͨ͠ ಺༰: 9 ׂ HPC, 1 ׂ: ਺஋ઢܗ୅਺ ৘ใॲཧֶձݚڀใࠂ (IPSJ SIG Technical Report, ༗ྉ) ΋ೖख͠·ͨ͠ LAPACK ؔ࿈ͷ࿩୊ LAPACK ؔ࿈ͷ࿩୊͕ଟ͔ͬͨͱײͨ͡ͷͰ, LAPACK ౳ͰͲΜͳ͜ͱ͕ Ͱ͖Δͷ͔ௐ΂ͯΈ·ͨ͠ (cf: ӳޠ൛ Wikipedia). LINPACK/EISPACK Λड͚ܧ͍Ͱ͍ΔͷͰ࿈ཱҰ࣍ํఔࣜ΍ݻ༗஋໰୊͸ ΋ͪΖΜ, SVD/GSVD ʹ΋ରԠ͍ͯ͠ΔΑ͏Ͱ͢. ͔͠͠࢒೦ͳ͕Β INTLAB Ͱ͸ SVD/GSVD ʹରԠ͍ͯ͠ͳ͍Α͏Ͱ͢. → ࠷ޙͷ frontier Ͱ͸? (େੴઌੜͷຊʹ SVD ͕গ͚ͩ͋͠Δ) ۚઘେհ (ؙ໺ݚڀࣨ OB) θϛൃද 2019 ೥ 10 ݄, ˏദ໦ݚڀࣨ 4 / 18
5. IPSJ-HPC171 ౔࢈࿩ IPSJ-HPC171 ౔࢈࿩ ଜ্߂ઌੜ͕ʮϑΟϧλΛ࢖͏ GEVP ͷղ๏ʯʹ͍ͭͯߨԋ͠·ͨ͠. ʮ਺஋ղੳ × ճ࿏ཧ࿦ʯͱ͍͏ݚڀ͕૿͍͑ͯΔؾ͕͢Δ ۠ؒԋࢉɾaffine arithmetic→ ճ࿏ཧ࿦ʹԠ༻ (࿦จଟ਺) ճ࿏ཧ࿦ʹग़ͯ͘ΔϑΟϧλΛݻ༗஋໰୊ʹ࢖͏ 2,3,4,5 Α͘ߟ͑ͨΒେੴઌੜ΋ճ࿏ཧ࿦ͷઐ໳Ո ͜͏͍͏࿩୊ʹؔ৺͕͋ͬͨΓ͢Δͷ͔΋ ? 2Tsutomu Ikegami, Tetsuya Sakurai and Umpei Nagashima: A Filter Diagonalization for Generalized Eigenvalue Problems Based on the Sakurai-Sugiura Projection Method, J. Compu. Appl. Math., Vol.233, No.8, pp.1927-1936 (2010). 3Anthony P. Austin and Lloyd N. Trefethen: Computing Eigenvalues of Real Symmetric Matrices with Rational Filters in Real Arithmetic, SIAM J. Sci. Comput, Vol.37, No.3, pp.A1365-A1387 (2015). 4Hiroshi Murakami: Filter Diagonalization Method by Using a Polynomial of a Resolvent as the Filter for a Real Symmetric-Definite Generalized Eigenproblem, in proceedings of EPASA2015, Springer, LNCSE-117, pp.205-232 (2018). 5Hiroshi Murakami: Filters Consist of a Few Resolvents to Solve Real Symmetric-Definite Generalized Eigenproblems, Japan J. Indust. Appl. Math., Vol.36, No.2, pp.579-618 (July 2019). ۚઘେհ (ؙ໺ݚڀࣨ OB) θϛൃද 2019 ೥ 10 ݄, ˏദ໦ݚڀࣨ 5 / 18
6. IPSJ-HPC171 ౔࢈࿩ IPSJ-HPC171 ౔࢈࿩ ஫ҙ ଜ্ઌੜ͕࢖͏ϑΟϧλ ̸= ුಈখ਺఺ϑΟϧλ (cf: Ohta-Ozaki) Ohta, Y., & Ozaki, K. (2019, May). Extension of floating-point filters to absolute and relative errors for numerical computation. In Journal of Physics: Conference Series (Vol. 1218, No. 1, p. 012011). IOP Publishing. ଠా༔ᏻ, & ඌ࡚ࠀٱ. (2018). ܭࢉ஋ͷେখؔ܎Λอূ͢Δුಈখ਺఺ϑΟϧλ. ೔ ຊԠ༻਺ཧֶձ࿦จࢽ, 28(1), 1-17. ଠా༔ᏻ, & ඌ࡚ࠀٱ. (2014). ఺ͱ༗޲௚ઢͷҐஔؔ܎ʹର͢Δුಈখ਺఺ϑΟϧλ ͷ࣮਺ೖྗ΁ͷ֦ுͱತแ΁ͷԠ༻ (࣮༻). ೔ຊԠ༻਺ཧֶձ࿦จࢽ, 24(4), 373-395. ۚઘେհ (ؙ໺ݚڀࣨ OB) θϛൃද 2019 ೥ 10 ݄, ˏദ໦ݚڀࣨ 6 / 18
7. UTNAS ͓౔࢈࿩ UTNAS ͓౔࢈࿩ ࠷ۙ͸ߏ଄อଘܕ਺஋ղ๏͕ྲྀߦ͍ͬͯΔ → ࢄҳଇ, อଘଇʹண໨ ͍ͭʹߏ଄อଘܕ FVM ͕Ͱ͖ͨΒ͍͠ → ਖ਼஋ੑอଘ ਖ਼஋ղେ޷͖ T ઌੜ͕تͿͷ͸ؒҧ͍ͳ͠ ࢀߟ: ߏ଄อଘܕ FEM=DG ๏ ߏ଄อଘܕ FVM Ͱ͸཭ࢄؔ਺ղੳ (཭ࢄ Lp norm, ཭ࢄ Laplacian etc.) Λ࢖͏. → ਫ਼౓อূͱͷ૬ੑ͸ ? (ީิऀू߹͸࡞Γ΍͍͢ ?) ߏ଄อଘܕ FVM Ͱ͸ Voronoi mesh ͷ୅ΘΓʹ dual mesh Λ࢖͏ dual mesh Λ࢖͏ํ͕ (ߏ੒త͔Ͳ͏͔͸ͱ΋͔͘) ޡࠩධՁ͠΍͍͢Β͍͠ Ͱ΋ Voronoi mesh ͕ࠓͰ΋͋Δͱ͍͏͜ͱ͸Կ͔͠Βͷར఺͕͋Δ͸ͣ → ͲΜͳར఺ ? ۚઘେհ (ؙ໺ݚڀࣨ OB) θϛൃද 2019 ೥ 10 ݄, ˏദ໦ݚڀࣨ 7 / 18
8. ॳาతͳ࣭໰ ॳาతͳ࣭໰ ۠ؒԋࢉͷ༻ޠʹ͍࣭ͭͯ໰Ͱ͢. ۠ؒ෯ͷ૿େ: over-estimation ODE/ྗֶܥͷਫ਼౓อূʹ͓͚Δ۠ؒ෯ͷ૿େ: wrapping effect ͜ͷࠩͬͯԿͰ͔͢ ? (ݴ༿Λ࢖͍෼͚Δඞཁ͋Γ·͔͢ ?) ۚઘେհ (ؙ໺ݚڀࣨ OB) θϛൃද 2019 ೥ 10 ݄, ˏദ໦ݚڀࣨ 8 / 18
9. ॳาతͳ࣭໰ ॳาతͳ࣭໰ Rump ͷྫ୊͕·ͨ٭ޫΛཋͼ͍ͯΔΒ͍͠Ͱ͢ (ܦҢෆ໌)6,7,8,9. float ͔Β binary128 ·ͰɺԿͷ໰୊΋ͳ͘ܭࢉͰ͖͍ͯΔΑ͏ʹݟ͑ ͯɺ࣮͸σλϥϝͰɺmpfr150 Ͱ΍ͬͱຊ౰ͷ஋͕ݟ͑Δɻ ༗໊ͳʮ਺஋ܭࢉͷৗࣝʯ10 ͷୈ 4 ষʮͨͬͨҰճ͚ͩͷܭࢉͳΜͯʯ Ͱ͸ɺ ʮܻ਺ n1 Ͱܭࢉͨ݁͠Ռ͕ X1ɺܻ਺ n2 Ͱܭࢉͨ݁͠Ռ͕ X2 ͰɺX1 ͱ X2 ͷҰக͍ͯ͠Δܻ਺͕ m Ͱ͋Ε͹ɺX1 ͸ m ܻਖ਼͘͠ɺ X2 ͸ m+(n2-n1) ܻਖ਼͍͠ʯͱେࡶ೺ʹݴ͑Δͱड़΂͍ͯΔ͕ɺRump ͷྫ୊͸ͦͷྑ͍൓ྫʹͳ͍ͬͯΔɻ(by ദ໦ઌੜ) 6https://discourse.julialang.org/t/reproducing-rump-s-example/6473 7https://gist.github.com/Terminus-IMRC/dc1e12d5b274f830346a3af16ccfda5c 8Loh, E., & Walster, G. W. (2002). Rump’s example revisited. Reliable Computing, 8(3), 245-248. 9Siegfried M. Rump (1988), ”Algorithms for Verified Inclusions: Theory and Practice”, in R. E. Moore, Reliability in Computing: The Role of Interval Methods in Scientific Computing, Boston: Academic Press, pp. 109-126., 10ҏཧਖ਼෉, & ౻໺࿨ݐ. (1985). ਺஋ܭࢉͷৗࣝ. ۚઘେհ (ؙ໺ݚڀࣨ OB) θϛൃද 2019 ೥ 10 ݄, ˏദ໦ݚڀࣨ 9 / 18
10. ॳาతͳ࣭໰ ॳาతͳ࣭໰ Rump ͷྫ୊ΑΓ΋؆୯ͳؔ਺Ͱ΋ಉ͡ݱ৅͕ى͖Δ (by ദ໦ઌੜ). ҏཧઌੜ΋ࣗྗͰ൓ྫʹؾ͚ͮͨͷͰ͸ ? ͦ΋ͦ΋ Rump ઌੜ͕ྫ୊Λ࡞Ζ͏ͱ͖͔͚ͨͬ͠ͱ͸ ? → ࣌ؒ͋Δͱ͖ʹຊਓʹฉ͖·͢ ۚઘେհ (ؙ໺ݚڀࣨ OB) θϛൃද 2019 ೥ 10 ݄, ˏദ໦ݚڀࣨ 10 / 18
11. Journal ʹ͍ͭͯ Journal ʹ͍ͭͯ ࠷ऴతʹ͸࿦จΛ Acta Numerica (Cambridge Univ. Press) BIT Numerical Mathematics Journal of Computational and Applied Mathematics Mathematics of Computation (AMS) Numerische Mathematik SIAM Journal of Numerical Analysis SIAM Journal on Scientific Computing ͋ͨΓʹग़͍ͨ͠ͱࢥ͍ͬͯ·͕͕͢͢͞ʹࠓ͸ݫ͍͠ͱࢥ͏ͷͰ·ͣ͸, JJIAM Reliable Computing International Journal of Mathematics for Industry (Pacific Journal of Mathematics for Industry ͷޙܧͰ World Scientific ͔Βץߦ, open access) ͋ͨΓΛૂ͓͏ͱࢥ͍·͢. ΄͔ʹԿ͔Ҋ͸͋Γ·͔͢ ? ۚઘେհ (ؙ໺ݚڀࣨ OB) θϛൃද 2019 ೥ 10 ݄, ˏദ໦ݚڀࣨ 11 / 18
12. ޙظͷ༧ఆ ޙظͷ༧ఆ Έͳ͞ΜվΊ·ͯ͠લظ & ՆٳΈ͓ർΕ͞·Ͱͨ͠ ޙظ΋Α͍ start ͕੾ΕΔΑ͏ʹ༧ఆΛ࿩͠߹͍͍ͨͱࢥ͍·͢ Agenda म࿦ରࡦ ദ໦ݚڀࣨ B4 ޲͚ϨΫνϟʔ (ദ໦ݚڀࣨͷօ͞Μͱͷ૬ஊࣄ߲) B3 ޲͚ק༠/આ໌ձ (ࢀߟ) Travel Schedule ࠓޙͷଧͪ߹Θͤ೔ఔ ۚઘେհ (ؙ໺ݚڀࣨ OB) θϛൃද 2019 ೥ 10 ݄, ˏദ໦ݚڀࣨ 12 / 18
13. ޙظͷ༧ఆ म࿦ରࡦ म࿦ରࡦ M ઌੜ: म࿦ͷ໘౗Λݟͳ͍ͳΒത࢜՝ఔਐֶΛೝΊͳ͍ (ࢲ͕ M1 ͷࠒ͔ΒΈΜͳݴΘΕͯΔ, ૊৫ථ͕͋ΔͷͰແࢹͰ͖ͳ͍) T ઌੜ: म࿦͸࠷௿ 5 ਓݟͯ΄͍͠ ࣗ෼ʹݚڀςʔϚ͕͍ۙਓ΍ത࢜՝ఔߦ͘ਓͷम࿦ͳΒؒҧ͍ͳ͘ݟΒΕ·͢. ۩ମత׆ಈ introduction ͷߍਖ਼ → ࿦จ͸ introduction Ͱམͱ͞ΕΔ citation ٴͼॻࣜͷ֬ೝ ݁Ռʹର͢Δ comment (ՄೳͳݶΓ) slide ֬ೝ ͝༻໋͓଴ͪͯ͠·͢ !!! ཁ֬ೝࣄ߲ ദ໦ઌੜ΁ͷୈ 1 ߘఏग़೔͸͍ͭͰ͠ΐ͏͔ ? ۚઘେհ (ؙ໺ݚڀࣨ OB) θϛൃද 2019 ೥ 10 ݄, ˏദ໦ݚڀࣨ 13 / 18
14. ޙظͷ༧ఆ ദ໦ݚڀࣨ B4 ޲͚ϨΫνϟʔ (ദ໦ݚڀࣨͷօ͞Μͱͷ૬ஊࣄ߲) ദ໦ݚڀࣨ B4 ޲͚ϨΫνϟʔ (ദ໦ݚڀࣨͷօ͞Μͱͷ૬ஊࣄ߲) M ઌੜ: B4 ͷ໘౗Λݟͳ͍ͳΒത࢜՝ఔਐֶΛೝΊͳ͍ (૊৫ථʹΑΓແࢹͰ͖ͳ͍) ʮB4 ͷ໘౗ΛݟΔʯ(ࢲ͕ M1 ͷࠒ͔ΒΈΜͳݴΘΕͯΔ) ଔ࿦ࢦಋ (ਓ਺͕ଟ͍ͷͰദ໦ݚڀࣨͷ B4 ͚ͩͱ͍ͤͯͩ͘͞͞) ࿦จͷ୳͠ํɾಡΈํΛڭ͑Δ म࿦Ͱ๩͘͠ͳΔ →M2 Ͱ͸ B4 ͷ໘౗͸ݟΒΕͳ͘ͳΔ Ͳ͏ͤ M1 ͸དྷͳ͍ & ͜͏͍͏࣌ʹݶͬͯദ໦ઌੜ΋͍ͳ͍ खۭ͖ͷਓ͕ͨͪؤுΒͳ͍ͱ͍͚ͳ͍ → ਙͩၟӽ͕ͩࢲͷग़൪ͳͷͰ͸ ??? ݚڀωλҰཡΛݟͯࢲ͕ؾ෇͍ͨ͜ͱ (ࢲʹ͍ۙ࿩୊ݶఆ) ৘ใܥ͕஌͓ͬͯ͘ͱ͍͍ͱࢥΘΕΔ࠷৽ LabTech (จݙ୳ࡧɾ؅ཧͳͲ) ʹ͍ͭͯͩͬͨΒൃදͰ͖ͦ͏Ͱ͢. म࢜ଔͰ͋ͬͯ΋ݚڀ৬Λ໨ࢦ͢ͳΒ஌͓ͬͯ͘Ձ஋͸͋Δͱࢥ͍·͢. ۚઘେհ (ؙ໺ݚڀࣨ OB) θϛൃද 2019 ೥ 10 ݄, ˏദ໦ݚڀࣨ 14 / 18
15. ޙظͷ༧ఆ B3 ޲͚ק༠/આ໌ձ B3 ޲͚ק༠/આ໌ձ ΋͏ޙظͳͷͰ B3 ޲͚ק༠/આ໌ձ΁ͷଶ੎Λ੔͑Δ࣌ظͩͱࢥ͏. ͜͏͍͏͜ͱ͸ݪଇͱͯ͠ࡏ੶ϝϯόʔ͕΍Δ΂͖ͩͱࢥ͏ B4/M2 ͸ଔम࿦Ͱ๩͍͠ Ͳ͏ͤ M1 ͸དྷͳ͍ ͜͏͍͏࣌ʹݶͬͯദ໦ઌੜ΋͍ͳ͍ खۭ͖ͷਓ͕ͨͪؤுΔ΂͖ → ਙͩၟӽ͕ͩࢲͷग़൪ͳͷͰ͸ ??? ࢲҊ (͜ΕΛ΍ͬͯΔͱ͜Ζ͸গͳ͔Βͣ͋Δͱࢥ͏) ঁࢠΛલӴʹ͢Δ → ੲ͸ Y ઌੜ͕લӴͩͬͨ खۭ͖ͷஉࢠ͕ཪํɾޙӴʹճΔ ۚઘେհ (ؙ໺ݚڀࣨ OB) θϛൃද 2019 ೥ 10 ݄, ˏദ໦ݚڀࣨ 15 / 18
16. ޙظͷ༧ఆ Travel Schedule Travel Schedule ࢀߟ: ޙظͷ Travel Schedule ਺ֶɾ਺ཧՊֶઐ߈एखݚڀऀͷͨΊͷҟ෼໺ɾҟۀछݚڀަྲྀձ by ೔ຊ ਺ֶձ ˏ౦େ਺ཧ, 10 ݄ 26 ೔ → ത࢜՝ఔߦ͘ਓ͸ߦͬͨํ͕͍͍͔΋ ୈ 28 ճ୯ಠݚڀձɿ2019 ೥ 12 ݄ 2 ೔ (݄) (೔ຊԠ༻਺ཧֶձʮߦྻɾݻ༗ ஋໰୊ͷղ๏ͱͦͷԠ༻ʯݚڀ෦ձ) ࡾ෦ձ࿈ܞʮԠ༻਺ཧηϛφʔʯ ɿ2019 ೥ 12 ݄ࠒ େੴݚڀࣨम࿦ൃදձ & ദ໦ݚڀࣨଔम࿦ൃදձ, 2020 ೥ 2 ্݄० → Կͱ͔৐Γ੾Ζ͏ !!! ೔ຊԠ༻਺ཧֶձ 2020 ೥ݚڀ෦ձ࿈߹ൃදձ, 2020 ೥ 3 ݄ 4 ೔ʢਫʣʙ5 ೔ʢ໦ʣ. தԝେֶޙָԂΩϟϯύε. (& ֶੜݚڀൃදձ → ޙड़) → ͜͜Λ໨ࢦͯ͠ؤுΖ͏ !!! ೔ຊ਺ֶձ 2020 ೥౓೥ձ, 2020 ೥ 3 ݄ 16 ೔ʢ݄ʣʙ19 ೔ʢ໦ʣ, ೔ຊେֶ ཧ޻ֶ෦.→ গͳ͘ͱ΋Ԡ༻਺ֶ෼Պձ͸ฉ͖ʹߦ͘ ۚઘେհ (ؙ໺ݚڀࣨ OB) θϛൃද 2019 ೥ 10 ݄, ˏദ໦ݚڀࣨ 16 / 18
17. ޙظͷ༧ఆ Travel Schedule Travel Schedule JSIAM ֶੜݚڀൃදձ (ࢲ͸աڈ 2 ճࢀՃ) JSIAM एखͷձ͕ओ࠵, poster ൃදܗࣜ ྫ೥͸ 3 ݄ͷ JSIAM લ೔ʹ։͔ΕΔ ৔ॴ͸ JSIAM ͱ΄΅ಉ͡ short presentation ΋͋ΔͷͰ͚ͩ͜͜஫ҙ ೥ձͱҧͬͯ৆͸ͳ͍ → ؾָʹൃදͰ͖Δ poster ͸ଔम࿦ൃදͰͷ slide Λ࢖͍·ΘͤΔ slide ͕షΓ੾Εͳ͘ͳͬͨΒࢴࣳډ͢Δ (ࢲ͕΍Γ·ͨ͠) ۀ੷ʹ count ͞ΕΔ ۚઘେհ (ؙ໺ݚڀࣨ OB) θϛൃද 2019 ೥ 10 ݄, ˏദ໦ݚڀࣨ 17 / 18
18. ޙظͷ༧ఆ ࠓޙͷଧͪ߹Θͤ೔ఔ ࠓޙͷଧͪ߹Θͤ೔ఔ ॏཁݕ౼ࣄ߲ Έͳ͞ΜͦΖͦΖଔम࿦Ͱ๩͘͠ͳΔ͜Ζͩͱࢥ͍·͢. ଧͪ߹ΘͤΛͲͷλΠϛϯάͰଧͪ੾Δ͔ݕ౼͠·͠ΐ͏. ۚઘେհ (ؙ໺ݚڀࣨ OB) θϛൃද 2019 ೥ 10 ݄, ˏദ໦ݚڀࣨ 18 / 18