Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

 

 

Solomon Lefschetz. An appreciation in memoriam


Author: Lawrence Markus
Journal: Bull. Amer. Math. Soc. 79 (1973), 663-680
MathSciNet review: 0316207
Full-text PDF

References | Additional Information

References [Enhancements On Off] (What's this?)

  • S. Lefschetz, Two theorems on conics, Ann. of Math. (2) 14 (1912/13), no. 1-4, 47–50. MR 1502437, 10.2307/1967598
  • [2] Solomon Lefschetz, On the V33with five nodes of the second species in S4, Bull. Amer. Math. Soc. 18: 384-386.
  • Solomon Lefschetz, A page of mathematical autobiography, Bull. Amer. Math. Soc. 74 (1968), 854–879. MR 0240803, 10.1090/S0002-9904-1968-12059-2
  • Solomon Lefschetz, On the existence of loci with given singularities, Trans. Amer. Math. Soc. 14 (1913), no. 1, 23–41. MR 1500934, 10.1090/S0002-9947-1913-1500934-0
  • Solomon Lefschetz, On Some Topological Properties of Plane Curves and a Theorem of Möbius, Amer. J. Math. 35 (1913), no. 2, 189–200. MR 1506181, 10.2307/2370281
  • S. Lefschetz, Geometry on Ruled Surfaces, Amer. J. Math. 36 (1914), no. 4, 392–394. MR 1506231, 10.2307/2370371
  • [7] Solomon Lefschetz, On cubic surfaces and their nodes, Kansas Univ. Science Bull. 9: 69-78.
  • [8] Solomon Lefschetz, The equation of Picard-Fuchs for an algebraic surface with arbitrary singularities, Bull. Amer. Math. Soc. 21: 227-232.
  • [9] Solomon Lefschetz, Note on the n-dimensional cycles of an algebraic n-dimensional variety, Rend. Circ. Mat. Palermo 40: 38-43.
  • S. Lefschetz, The arithmetic genus of an algebraic manifold immersed in another, Ann. of Math. (2) 17 (1916), no. 4, 197–212. MR 1503582, 10.2307/2007207
  • S. Lefschetz, A Direct Proof of De Moivre’s Formula, Amer. Math. Monthly 23 (1916), no. 10, 366–368. MR 1518644, 10.2307/2971824
  • [12] Solomon Lefschetz, On the residues of double integrals belonging to an algebraic surface, Quart. J. Math. 47: 333-343.
  • [13] Solomon Lefschetz, Note on a problem in the theory of algebraic manifolds, Kansas Univ. Science Bull. 10: 3-9.
  • [14] Solomon Lefschetz, Sur certains cycles à deux dimensions des surfaces algébriques, Accad. Lincei. Rend. (5) 26:228-234.
  • [15] Solomon Lefschetz, Sur les intégrales multiples des variétés algébriques, C. R. Acad. Sci. Paris 164: 850-853.
  • [16] Solomon Lefschetz, Sur les intégrales doubles des variétés algébriques, Ann. di Mat. (3) 26: 227-260.
  • [17] Solomon Lefschetz, Sur l' analyse situs des variétés algébriques, C. R. Acad. Sci. Paris 168: 672-674.
  • [18] Solomon Lefschetz, Sur les variétés abéliennes, C. R. Acad. Sci. Paris 168: 758-761.
  • [19] Solomon Lefschetz, On the real folds of Abelian varieties, Proc. Nat. Acad. Sci. U. S. A. 5: 103-106.
  • [20] Solomon Lefschetz, Real hypersurfaces contained in Abelian varieties, Proc. Nat. Acad. Sci. U. S. A. 5: 296-298.
  • S. Lefschetz, Algebraic surfaces, their cycles and integrals, Ann. of Math. (2) 21 (1920), no. 4, 225–258. MR 1503620, 10.2307/2007214
  • [22] Solomon Lefschetz, Quelques remarques sur la multiplication complexe, Comptes Rendus du Congrès International des Mathématiciens (Strasbourg, Sept. 1920), É. Privat, Toulouse, 1921, pp. 300-307.
  • [23] Solomon Lefschetz, Sur le théorème d' existence des fonctions abéliennes, Accad. Lincei. Rend. (5) 30: 48-50.
  • Solomon Lefschetz, On certain numerical invariants of algebraic varieties with application to abelian varieties, Trans. Amer. Math. Soc. 22 (1921), no. 3, 327–406. MR 1501178, 10.1090/S0002-9947-1921-1501178-3
  • [25] Solomon Lefschetz, Continuous transformations of manifolds, Proc. Nat. Acad. Sci. U. S. A. 9: 90-93.
  • Solomon Lefschetz, A page of mathematical autobiography, The Lefschetz centennial conference, Part I (Mexico City, 1984) Contemp. Math., vol. 58, Amer. Math. Soc., Providence, RI, 1986, pp. 1–26. MR 860401, 10.1090/conm/058.1/860401
  • [27] Solomon Lefschetz, Sur les intégrales de seconde espèce des variétés algébriques, C. R. Acad. Sci. Paris 176: 941-943.
  • [28] Solomon Lefschetz, Report on curves traced on algebraic surfaces, Bull. Amer. Math. Soc. 29: 242-258.
  • S. Lefschetz, L’analysis situs et la géométrie algébrique, Gauthier-Villars, Paris, 1950 (French). MR 0033557
  • [30] Solomon Lefschetz, Sur les intégrales multiples des variétés algébriques, J. Math. Pures Appl. (9) 3: 319-343.
  • [31] Solomon Lefschetz, Intersections of complexes on manifolds, Proc. Nat. Acad. Sci. U. S. A. 11: 287-289.
  • [32] Solomon Lefschetz, Continuous transformations of manifolds, Proc. Nat. Acad. Sci. U. S. A. 11: 290-292.
  • Solomon Lefschetz, Intersections and transformations of complexes and manifolds, Trans. Amer. Math. Soc. 28 (1926), no. 1, 1–49. MR 1501331, 10.1090/S0002-9947-1926-1501331-3
  • [34] Solomon Lefschetz, Transformations of manifolds with a boundary, Proc. Nat. Acad. Sci. U. S. A. 12: 737-739.
  • [35] Solomon Lefschetz, Un théorème sur les fonctions abéliennes, In Memoriam N. I. Lobatschevskii, Kazan', Glavnauka, pp. 186-190.
  • Solomon Lefschetz, Manifolds with a boundary and their transformations, Trans. Amer. Math. Soc. 29 (1927), no. 2, 429–462. MR 1501397, 10.1090/S0002-9947-1927-1501397-1
  • S. Lefschetz, Correspondences between algebraic curves, Ann. of Math. (2) 28 (1926/27), no. 1-4, 342–354. MR 1502787, 10.2307/1968379
  • [38] Solomon Lefschetz, The residual set of a complex on a manifold and related questions, Proc. Nat. Acad. Sci. U. S. A. 13: 614-622, 805-807.
  • [39] Solomon Lefschetz, On the functional independence of ratios of theta functions, Proc. Nat. Acad. Sci. U. S. A. 13: 657-659.
  • [40] Solomon Lefschetz, Transcendental theory: Singular correspondences between algebraic curves: Hyperelliptic surfaces and Abelian varieties, Selected Topics in Algebraic Geometry, vol. 1. Chaps. 15-17, pp. 310-395; NRC Bulletin no. 63, Report of the Committee on Rational Transformations of the National Research Council, Washington, D. C.
  • S. Lefschetz, A Theorem on Correspondences on Algebraic Curves, Amer. J. Math. 50 (1928), no. 2, 159–166. MR 1506663, 10.2307/2371753
  • S. Lefschetz, Closed point sets on a manifold, Ann. of Math. (2) 29 (1927/28), no. 1-4, 232–254. MR 1502836, 10.2307/1967998
  • [43] Solomon Lefschetz, Géométrie sur les surfaces et les variétés algébriques, Mém. Sci. Math., fasc. 40, Gauthier-Villars, Paris.
  • [44] Solomon Lefschetz, Duality relations in topology, Proc. Nat. Acad. Sci. U. S. A. 15: 367-369.
  • [45] Solomon Lefschetz, Topology, Amer. Math. Soc. Colloq. Publ., vol. 12, Amer. Math. Soc. Providence, R. I. See [100].
  • [46] Solomon Lefschetz, Les transformations continues des ensembles fermés et leurs points fixes, C. R. Acad. Sci. Paris 190: 99-100.
  • [47] Solomon Lefschetz, (with W. W. Flexner), On the duality theorems for the Betti numbers of topological manifolds, Proc. Nat. Acad. Sci. U. S. A. 16: 530-533.
  • S. Lefschetz, On transformations of closed sets, Ann. of Math. (2) 31 (1930), no. 2, 271–280. MR 1502941, 10.2307/1968097
  • Solomon Lefschetz, On compact spaces, Ann. of Math. (2) 32 (1931), no. 3, 521–538. MR 1503014, 10.2307/1968249
  • [50] Solomon Lefschetz, On certain properties of separable spaces, Proc. Nat. Acad. Sci. U. S. A. 18: 202-203.
  • S. Lefschetz, On separable spaces, Ann. of Math. (2) 33 (1932), no. 3, 525–537. MR 1503074, 10.2307/1968533
  • *[52] Solomon Lefschetz, Invariance absolue et invariance relative en géométrie algébrique, Mat. Sb. 39: 97-102.
  • *[53] Solomon Lefschetz, On singular chains and cycles, Bull. Amer. Math. Soc. 39: 124-129.
  • S. Lefschetz and J. H. C. Whitehead, On analytical complexes, Trans. Amer. Math. Soc. 35 (1933), no. 2, 510–517. MR 1501698, 10.1090/S0002-9947-1933-1501698-X
  • S. Lefschetz, On Generalized Manifolds, Amer. J. Math. 55 (1933), no. 1-4, 469–504. MR 1506980, 10.2307/2371146
  • [56] Solomon Lefschetz, Elementary one- and two-dimensional topology, A course given by Prof. Lefschetz, Spring 1934; notes by H. Wallman, Princeton University, Princeton, N. J. (mimeographed).
  • S. Lefschetz, On locally connected and related sets, Ann. of Math. (2) 35 (1934), no. 1, 118–129. MR 1503148, 10.2307/1968124
  • [58] Solomon Lefschetz, Topology, Lectures 1934/35; notes by N. Steenrod and H. Wallman, Princeton University, Princeton, N. J. (mimeographed).
  • [59] Solomon Lefschetz, Algebraicheskaia geometriia: metody, problemy, tendentsii, Trudy Vtorogo Vsesoiuznogo Matematicheskogo S"ezda, vol. 1, (Leningrad, 24-30 June 1934), Leningrad-Moscow, pp. 337-349. An invited address at the Second All-Union Mathematical Congress.
  • S. Lefschetz, Chain-deformations in topology, Duke Math. J. 1 (1935), no. 1, 1–18. MR 1545859, 10.1215/S0012-7094-35-00101-6
  • [61] Solomon Lefschetz, Application of chain-deformations to critical points and extremals, Proc. Nat. Acad. Sci. U. S. A. 21: 220-222.
  • [62] Solomon Lefschetz, A theorem on extremals. I, II, Proc. Nat. Acad. Sci. U. S. A. 21: 272-274, 362-364.
  • S. Lefschetz, On critical sets, Duke Math. J. 1 (1935), no. 3, 392–412. MR 1545885, 10.1215/S0012-7094-35-00127-2
  • S. Lefschetz, On locally-connected and related sets. (Second paper), Duke Math. J. 2 (1936), no. 3, 435–442. MR 1545934, 10.1215/S0012-7094-36-00234-X
  • *[65] Solomon Lefschetz, Locally connected sets and their applications, Mat. Sb. 1: 715-717; A contribution to the First International Topological Conference, September 1935.
  • [66] Solomon Lefschetz, Sur les transformations des complexes en sphères, Fund. Math. 27: 94-115.
  • Solomon Lefschetz, The early development of algebraic topology, Bol. Soc. Brasil. Mat. 1 (1970), no. 1, 1–48. MR 0326703
  • Solomon Lefschetz, Algebraic geometry, Princeton University Press, Princeton, N. J., 1953. MR 0056950
  • Solomon Lefschetz, Witold Hurewicz, in memoriam, Bull. Amer. Math. Soc. 63 (1957), 77–82. MR 0085992, 10.1090/S0002-9904-1957-10101-3
  • [70] Solomon Lefschetz, The role of algebra in topology, Bull. Amer. Math. Soc. 43: 345-359. Address of retiring president of the American Mathematical Society.
  • S. Lefschetz, On the fixed point formula, Ann. of Math. (2) 38 (1937), no. 4, 819–822. MR 1503373, 10.2307/1968838
  • [72] Solomon Lefschetz, Lectures on algebraic grometry. Part II, 1937/38, Princeton Univ. Press, Princeton, N. J. (planographed).
  • S. Lefschetz, On chains of topological spaces, Ann. of Math. (2) 39 (1938), no. 2, 383–396. MR 1503415, 10.2307/1968794
  • [74] Solomon Lefschetz, On locally connected sets and retracts, Proc. Nat. Acad. Sci. U. S. A. 24: 392-393.
  • [75] Solomon Lefschetz, Sur les transformations des complexes en sphères (note complémentaire), Fund. Math. 31: 4-14.
  • *[76] Solomon Lefschetz, Singular and continuous complexes, chains and cycles, Mat. Sb. 3: 271-285.
  • [77] Solomon Lefschetz, On the mapping of abstract spaces on polytopes, Proc. Nat. Acad. Sci. U. S. A. 25: 49-50.
  • Solomon Lefschetz, Abstract complexes, Lectures in Topology, University of Michigan Press, Ann Arbor, Mich., 1941, pp. 1–28. MR 0005296
  • Solomon Lefschetz, Algebraic Topology, American Mathematical Society Colloquium Publications, v. 27, American Mathematical Society, New York, 1942. MR 0007093
  • Solomon Lefschetz, Topics in Topology, Annals of Mathematics Studies, no. 10, Princeton University Press, Princeton, N. J., 1942. MR 0007094
  • Solomon Lefschetz, Algebraic Topology, American Mathematical Society Colloquium Publications, v. 27, American Mathematical Society, New York, 1942. MR 0007093
  • [82] Solomon Lefschetz, Introduction to non-linear mechanics, by N. M. Krylov and N. N. Bogoljubov; a free translation by S. Lefschetz of excerpts from two Russian monographs; Ann. of Math. Studies, no. 11, Princeton Univ. Press. Princeton, N. J. ; Oxford Univ. Press, London. MR 4, 142.
  • S. Lefschetz, Existence of periodic solutions for certain differential equations, Proc. Nat. Acad. Sci. U. S. A. 29 (1943), 29–32. MR 0007462
  • Solomon Lefschetz, Lectures on Differential Equations, Annals of Mathematics Studies, no.14, Princeton Univeristy Press, Princeton, N. J.; Oxford University Press, London, 1946. MR 0016788
  • Solomon Lefschetz, Introduction to Topology, Princeton Mathematical Series, vol. 11, Princeton University Press, Princeton, N. J., 1949. MR 0031708
  • A. A. Andronow and C. E. Chaikin, Theory of Oscillations, Princeton University Press, Princeton, N. J., 1949. English Language Edition Edited Under the Direction of Solomon Lefschetz. MR 0029027
  • [87] Solomon Lefschetz, Scientific research in the U. S. S. R. : Mathematics, Amer. Acad. Polit. Soc. Sci. Ann. 263: 139-140.
  • [88] Solomon Lefschetz, Contributions to the theory of nonlinear oscillations, edited by S. Lefschetz, Ann. of Math. Studies, no. 20, Princeton Univ. Press, Princeton, N. J.; Oxford Univ. Press, London.
  • S. Lefschetz, The structure of mathematics, American Scientist 38 (1950), 105–111. MR 0032543
  • [90] Solomon Lefschetz, Numerical calculations in nonlinear mechanics, Problems for the Numerical Analysis of the Future, Nat. Bur. Standards Appl. Math. Ser., no. 15, U. S. Government Printing Office, Washington, D. C., pp. 10-12. MR 13, 162.
  • [91] Solomon Lefschetz, Contributions to the theory of nonlinear oscillations. Vol. 2, edited by S. Lefschetz, Ann. of Math. Studies, no. 29, Princeton Univ. Press, Princeton, N. J.; Oxford Univ. Press, London.
  • Solomon Lefschetz, Notes on differential equations, Contributions to the Theory of Nonlinear Oscillations, vol. II, Princeton University Press, Princeton, 1952, pp. 61–73. MR 0051992
  • Solomon Lefschetz, Stability of nonlinear control systems, Mathematics in Science and Engineering, Vol. 13, Academic Press, New York-London, 1965. MR 0175676
  • [94] Solomon Lefschetz, Algunos trabajos recientes sobre ecuaciones diferenciales, Memoria de Congreso Cientifico Mexicano, vol. 1, U. N. A. M., Mexico, pp. 122-123.
  • [95] Solomon Lefschetz, Las grades corrientes en las matemáticas del siglo XX, Memoria de Congreso Cientifico Mexicano, vol. 1, U. N. A. M., Mexico, pp. 206-211.
  • S. Lefschetz, Russian contributions to differential equations, Proceedings of the Symposium on Nonlinear Circuit Analysis, New York, 1953, Polytechnic Institute of Brooklyn, New York, 1953, pp. 68–74. MR 0065446
  • Solomon Lefschetz, Complete families of periodic solutions of differential equations, Comment. Math. Helv. 28 (1954), 341–345. MR 0068061
  • S. Lefschetz, On Liénard’s differential equation, Proceedings of Symposia in Applied Mathematics, Vol. V, Wave motion and vibration theory, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1954, pp. 149–153. MR 0062306
  • Solomon Lefschetz, On a theorem of Bendixson, Bol. Soc. Mat. Mexicana (2) 1 (1956), 13–27. MR 0082003
  • [100] Solomon Lefschetz, Topology, 2nd ed., Chelsea, New York. (Cf. [45]).
  • Solomon Lefschetz, On coincidences of transformations, Bol. Soc. Mat. Mexicana (2) 2 (1957), 16–25. MR 0094808
  • Solomon Lefschetz, The ambiguous case in planar differential systems, Bol. Soc. Mat. Mexicana (2) 2 (1957), 63–74. MR 0104031
  • Solomon Lefschetz, Witold Hurewicz, in memoriam, Bull. Amer. Math. Soc. 63 (1957), 77–82. MR 0085992, 10.1090/S0002-9904-1957-10101-3
  • Solomon Lefschetz, The early development of algebraic topology, Bol. Soc. Brasil. Mat. 1 (1970), no. 1, 1–48. MR 0326703
  • Solomon Lefschetz, Differential equations: Geometric theory, Second edition. Pure and Applied Mathematics, Vol. VI, Interscience Publishers, a division of John Wiley & Sons, New York-Lond on, 1963. MR 0153903
  • Solomon Lefschetz, On the critical points of a class of differential equations, Contributions to the theory of nonlinear oscillations, Vol. IV, Annals of Mathematics Studies, no. 41, Princeton University Press, Princeton, N.J., 1958, pp. 19–28. MR 0104032
  • Solomon Lefschetz, Liapunov and stability in dynamical systems, Bol. Soc. Mat. Mexicana (2) 3 (1958), 25–39. MR 0098223
  • [108] Solomon Lefschetz, The stability theory of Liapunov, Lecture Series, no. 37, University Institute for Fluid Dynamics and Applied Mathematics, College Park, Md.
  • Solomon Lefschetz, Controls: an application of the direct method of Liapunov, Bol. Soc. Mat. Mexicana (2) 5 (1960), 139–143. MR 0132894
  • Solomon Lefschetz, On automatic controls, IRE Trans. CT-7 (1960), 474–475. MR 0120109
  • Solomon Lefschetz, New results on critical cases in differential equations, Rev. Un. Mat. Argentina 20 (1962), 122–124 (Spanish). MR 0149020
  • Solomon Lefschetz, The critical case in differential equations, Bol. Soc. Mat. Mexicana (2) 6 (1961), 5–18. MR 0133523
  • [113] Solomon Lefschetz, Geometricheskaia teoriia differentsial'nykh Uravnenii, IL, Moscow. (Transl. of [105]). MR 22 #12257.
  • [114] Solomon Lefschetz, (with J. P. LaSalle), Stability by Liapunov' s direct method, Math. in Sci. and Engineering, vol. 4, Academic Press, New York. MR 24 #A2712.
  • Joseph P. LaSalle and Solomon Lefschetz, Recent Soviet contributions to ordinary differential equations and nonlinear mechanics, J. Math. Anal. Appl. 2 (1961), 467–499. MR 0124993
  • Solomon Lefschetz, Differential equations: Geometric theory, Second edition. Pure and Applied Mathematics, Vol. VI, Interscience Publishers, a division of John Wiley & Sons, New York-Lond on, 1963. MR 0153903
  • Recent Soviet contributions to mathematics, Edited by J. P. LaSalle and S. Lefschetz, The Macmillan Co., New York, 1962. MR 0167383
  • S. Lefschetz, On indirect automatic controls, Analytic methods in the theory of non-linear vibrations (Proc. Internat. Sympos. Non-linear Vibrations, Vol. I, 1961) Izdat. Akad. Nauk Ukrain. SSR, Kiev, 1963, pp. 23–24 (English, with Russian summary). MR 0158790
  • Solomon Lefschetz, Some mathematical considerations on nonlinear automatic controls, Contributions to Differential Equations 1 (1963), 1–28. MR 0155068
  • [120] Solomon Lefschetz, Elementos de topologia, Universidad Nacional Autónoma de México.
  • International Symposium on Nonlinear Differential Equations and Nonlinear Mechanics, Academic Press, New York-London, 1963. MR 0146430
  • [122] Solomon Lefschetz, Stability of nonlinear automatic control systems, Math, in Sci. and Engineering, vol. 13, Academic Press. MR 30 #5860.
  • Solomon Lefschetz, Liapunov stability and controls, J. Soc. Indust. Appl. Math. Ser. A Control 3 (1965), 1–6. MR 0197198
  • Solomon Lefschetz, Planar graphs and related topics, Proc. Nat. Acad. Sci. U.S.A. 54 (1965), 1763–1765. MR 0189011
  • Solomon Lefschetz, Recent advances in the stability of nonlinear controls, SIAM Rev. 7 (1965), 1-12. MR 0179438
  • Solomon Lefschetz, Some applications of topology to networks, Proc. Third Annual Allerton Conf. on Circuit and System Theory, Univ. Illinois, Urbana, Ill., 1965, pp. 1–6. MR 0247958
  • [127] Solomon Lefschetz, Stability in dynamics, William Pierson Field Engineering Lectures, March 3, 4, 10, 11, 1966, Princeton University School of Engineering and Applied Science.
  • [127a] Solomon Lefschetz, (with J. P. LaSalle), Zarys teorii stabilności Lapunowa i jego metody bezpośredniej (Polish) (Transl. of [114]). MR 33 #6051.
  • S. Lefšec, Ustoichivost nelineinykh sistem avtomaticheskogo upravleniya, Appendix B by Kenneth Meyer. Translated from the English by È. L. Nappel′baum, Izdat. “Mir”, Moscow, 1967, 1967 (Russian). MR 0226133
  • Solomon Lefschetz, Geometric differential equations: Recent past and proximate future, Differential Equations and Dynamical Systems (Proc. Internat. Sympos., Mayaguez, P. R., 1965) Academic Press, New York, 1967, pp. 1–14. MR 0222385
  • Solomon Lefschetz, On a theorem of Bendixson, J. Differential Equations 4 (1968), 66–101. MR 0219800
  • Solomon Lefschetz, A page of mathematical autobiography, Bull. Amer. Math. Soc. 74 (1968), 854–879. MR 0240803, 10.1090/S0002-9904-1968-12059-2
  • Solomon Lefschetz, The Lurie problem on nonlinear controls, Lectures in Differential Equations, Vol. I, Van Nostrand, New York, 1969, pp. 9–19. MR 0242526
  • Solomon Lefschetz, The early development of algebraic geometry, Amer. Math. Monthly 76 (1969), 451–460. MR 0242828
  • [133] Solomon Lefschetz, Luther Pfahler Eisenhart, 1876-1965: A biographical memoir, Nat. Acad. Sci. U. S. A., Biographical Memoirs 40: 69-90.
  • Solomon Lefschetz, Severi’s theory of the base for an algebraic surface, J. Analyse Math. 23 (1970), 215–225. MR 0276234
  • [135] Solomon Lefschetz, Selected topics in algebraic geometry, Chelsea, New York.
  • [136] Solomon Lefschetz, Selected papers, Chelsea, New York (Contains articles identified by *).


Additional Information

DOI: https://doi.org/10.1090/S0002-9904-1973-13256-2