Gilbert Ames Bliss, $1876-1951$
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- Bull. Amer. Math. Soc. 58 (1952), 251-264
References
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1. G. A. Bliss, Fundamental existence theorems, The Princeton Colloquium, American Mathematical Society, 1913, Part I (reprinted from 1913 edition, 1934), 2 + 107 pp.
2. G. A. Bliss, Calculus of variations, Carus Mathematical Monograph, no. 1, Chicago, Open Court, 1925 (second impression February 1927), 13 + 189 pp.
3. G. A. Bliss, Variationsrechnung, a translation into German by F. Schwank of Bliss, The calculus of variations (above), Leipzig, Teubner, 1932, 8 + 127 pp.
- Gilbert Ames Bliss, Algebraic functions, Dover Publications, Inc., New York, 1966. MR 0203007
- Gilbert Ames Bliss, Mathematics for Exterior Ballistics, John Wiley & Sons, Inc., New York, 1944. MR 0010480
- Gilbert A. Bliss, Lectures on the Calculus of Variations, University of Chicago Press, Chicago, Ill., 1946. MR 0017881 7. G. A. Bliss, The function concept and the fundamental notions of the calculus, Chapter VI, pp. 263-304, of Monographs on topics of modern mathematics, ed. by J. W. A. Young, Longmans Green, 1911. 1. G. A. Bliss, The problem of Lagrange in the calculus of variations, University of Chicago, Summer 1925 (prepared by O. E. Brown), 2+75 pp. 2. G. A. Bliss, Topics of the calculus of variations, University of Chicago, Spring 1932 (ed. by G. A. Bliss), 5+67 pp. (principally report of lectures by E. J. McShane, and by Richard Courant). 3. G. A. Bliss, The calculus of variations, multiple integrals, University of Chicago, Summer 1933, 3 + 108 pp., Spring 1939, 3+88 pp. 4. G. A. Bliss, The calculus of variations in three-space, University of Chicago, Autumn 1934, 3 + 123 pp., Autumn 1938, 4+320 pp. 5. G. A. Bliss, The problem of Bolza in the calculus of variations, University of Chicago, Winter 1935, 7 + 140 pp. 1. G. A. Bliss, ed. Contributions to the calculus of variations, 1930 (ed. with L. M. Graves), University of Chicago Press, 1931, 7+349 pp. 2. G. A. Bliss, ed. Contributions to the calculus of variations, 1931-32 (ed. with L. M. Graves), University of Chicago Press, 1933, 7+523 pp. 3. G. A. Bliss, ed. Contributions to the calculus of variations, 1933-37 (ed. with L. M. Graves and W. T. Reid), University of Chicago Press, 1937, 7+566 pp. 4. G. A. Bliss, ed. Contributions to the calculus of variations, 1938-41 (ed. with L. M. Graves, M. R. Hestenes, and W. T. Reid), University of Chicago Press, 1942, 7+527 pp. 1. G. A. Bliss, The geodesic lines on the anchor ring (Master’s thesis), University of Chicago, Typewritten. 2. G. A. Bliss, The motion of a heavenly body in a resisting medium, Popular Astronomy vol. 6 (1898) pp. 20-29.
- Gilbert Ames Bliss, The geodesic lines on the anchor ring, Ann. of Math. (2) 4 (1902), no. 1, 1–21. MR 1502291, DOI 10.2307/1967147
- Gilbert Ames Bliss, The second variation of a definite integral when one end-point is variable, Trans. Amer. Math. Soc. 3 (1902), no. 1, 132–141. MR 1500591, DOI 10.1090/S0002-9947-1902-1500591-6 5. G. A. Bliss, Jacobi’s criterion when both end points are variable, Math. Ann. vol. 58 (1904) pp. 70-80.
- Gilbert Ames Bliss, An existence theorem for a differential equation of the second order, with an application to the calculus of variations, Trans. Amer. Math. Soc. 5 (1904), no. 2, 113–125. MR 1500665, DOI 10.1090/S0002-9947-1904-1500665-1
- Gilbert Ames Bliss, Sufficient condition for a minimum with respect to one-sided variations, Trans. Amer. Math. Soc. 5 (1904), no. 4, 477–492. MR 1500686, DOI 10.1090/S0002-9947-1904-1500686-9 8. G. A. Bliss, The exterior and interior of a plane curve, Bull. Amer. Math. Soc. vol. 10 (1904) pp. 398-401.
- G. A. Bliss, The solutions of differential equations of the first order as functions of their initial values, Ann. of Math. (2) 6 (1905), no. 2, 49–68. MR 1503546, DOI 10.2307/2007139 10. G. A. Bliss, A proof of the fundamental theorem of analysis situs, Bull. Amer. Math. Soc. vol. 12 (1906) pp. 336-341.
- Gilbert Ames Bliss, A generalization of the notion of angle, Trans. Amer. Math. Soc. 7 (1906), no. 2, 184–196. MR 1500741, DOI 10.1090/S0002-9947-1906-1500741-5
- Gilbert Ames Bliss and Max Mason, A problem of the calculus of variations in which the integrand is discontinuous, Trans. Amer. Math. Soc. 7 (1906), no. 2, 325–336. MR 1500752, DOI 10.1090/S0002-9947-1906-1500752-X 13. G. A. Bliss, The construction of a field of extremals about a given point, Bull. Amer. Math. Soc. vol. 13 (1907) pp. 321-324.
- Gilbert Ames Bliss, A new form of the simplest problem of the calculus of variations, Trans. Amer. Math. Soc. 8 (1907), no. 3, 405–414. MR 1500795, DOI 10.1090/S0002-9947-1907-1500795-7
- G. A. Bliss, On the inverse problem of the calculus of variations, Ann. of Math. (2) 9 (1908), no. 3, 127–140. MR 1502361, DOI 10.2307/1967456
- Gilbert Ames Bliss, A Method of Deriving Euler’s Equation in the Calculus of Variations, Amer. Math. Monthly 15 (1908), no. 3, 47–54. MR 1516998, DOI 10.2307/2971267
- Max Mason and Gilbert Ames Bliss, The properties of curves in space which minimize a definite integral, Trans. Amer. Math. Soc. 9 (1908), no. 4, 440–466. MR 1500821, DOI 10.1090/S0002-9947-1908-1500821-6 18. G. A. Bliss, A new proof of Weierstrass theorem concerning the factorization of a power series, Bull. Amer. Math. Soc. vol. 16 (1910) pp. 356-359.
- Gilbert Ames Bliss and Max Mason, Fields of extremals in space, Trans. Amer. Math. Soc. 11 (1910), no. 3, 325–340. MR 1500866, DOI 10.1090/S0002-9947-1910-1500866-5 20. G. A. Bliss, A new proof of the existence theorem for implicit functions, Bull. Amer. Math. Soc. vol. 18 (1912) pp. 175-179.
- Gilbert Ames Bliss, A generalization of Weierstrass’ preparation theorem for a power series in several variables, Trans. Amer. Math. Soc. 13 (1912), no. 2, 133–145. MR 1500910, DOI 10.1090/S0002-9947-1912-1500910-7
- Gilbert Ames Bliss, A note on symmetric matrices, Ann. of Math. (2) 16 (1914/15), no. 1-4, 43–44. MR 1502486, DOI 10.2307/1968040
- Gilbert Ames Bliss, A substitute for Duhamel’s theorem, Ann. of Math. (2) 16 (1914/15), no. 1-4, 45–49. MR 1502487, DOI 10.2307/1968041 24. G. A. Bliss, (With F. B. Wiley) A method of subdividing the interior of a simply closed rectifiable curve with an application to Cauchy’s theorem, Bulletin of the Scientific Laboratories of Denison University vol. 17 (1914) pp. 375-389.
- G. A. Bliss and A. L. Underhill, The minimum of a definite integral for unilateral variations in space, Trans. Amer. Math. Soc. 15 (1914), no. 3, 291–310. MR 1500981, DOI 10.1090/S0002-9947-1914-1500981-X
- Gilbert Ames Bliss, The Weierstrass $F$-function for problems of the calculus of variations in space, Trans. Amer. Math. Soc. 15 (1914), no. 4, 369–378. MR 1500985, DOI 10.1090/S0002-9947-1914-1500985-7
- Gilbert Ames Bliss, Generalizations of Geodesic Curvature and a Theorem of Gauss Concerning Geodesic Triangles, Amer. J. Math. 37 (1915), no. 1, 1–18. MR 1507894, DOI 10.2307/2370251 28. G. A. Bliss, A note on functions of lines, Proc. Nat. Acad. Sci. U.S.A. vol. 1 (1915) pp. 173-177. 29. G. A. Bliss, A note on the problem of Lagrange in the calculus of variations, Bull. Amer. Math. Soc. vol. 22 (1916) pp. 220-225.
- Gilbert Ames Bliss, Jacobi’s condition for problems of the calculus of variations in parametric form, Trans. Amer. Math. Soc. 17 (1916), no. 2, 195–206. MR 1501037, DOI 10.1090/S0002-9947-1916-1501037-4 31. G. A. Bliss, Integrals of Lebesgue, Bull. Amer. Math. Soc. vol. 24 (1917) pp. 1-47. 32. G. A. Bliss, A necessary and sufficient condition for the existence of a Stieltjes integral, Proc. Nat. Acad. Sci. U.S.A. vol. 3 (1917) pp. 633-637. 33. G. A. Bliss, Solutions of differential equations as functions of the constants of integration, Bull. Amer. Math. Soc. vol. 25 (1918) pp. 15-26.
- Gilbert Ames Bliss, The problem of Mayer with variable end points, Trans. Amer. Math. Soc. 19 (1918), no. 3, 305–314. MR 1501104, DOI 10.1090/S0002-9947-1918-1501104-7 35. G. A. Bliss, A method of computing differential corrections for a trajectory, Journal of the United States Artillery vol. 51 (1919) pp. 445-449, corrected reprint of earlier article in vol. 50 (1919) pp. 455-460. 36. G. A. Bliss, The use of adjoint systems in the problem of differential corrections for a trajectory, Journal of the United States Artillery vol. 51 (1919) pp. 296-311. 37. G. A. Bliss, Differential corrections for anti-aircraft guns, Blueprint in files at Aberdeen Proving Grounds (1919). 38. G. A. Bliss, Some recent developments in the calculus of variations, Bull. Amer. Math. Soc. vol. 26 (1920) pp. 343-361.
- Gilbert Ames Bliss, Differential equations containing arbitrary functions, Trans. Amer. Math. Soc. 21 (1920), no. 2, 79–92. MR 1501137, DOI 10.1090/S0002-9947-1920-1501137-X
- Gilbert Ames Bliss, Functions of lines in ballistics, Trans. Amer. Math. Soc. 21 (1920), no. 2, 93–106. MR 1501138, DOI 10.1090/S0002-9947-1920-1501138-1
- Gilbert Ames Bliss, Birational transformations simplifying singularities of algebraic curves, Trans. Amer. Math. Soc. 24 (1922), no. 4, 274–285. MR 1501226, DOI 10.1090/S0002-9947-1922-1501226-1 42. G. A. Bliss, The reduction of singularities of plane curves by birational transformation, Bull. Amer. Math. Soc. vol. 29 (1923) pp. 161-183.
- Gilbert Ames Bliss, Algebraic functions and their divisors, Ann. of Math. (2) 26 (1924), no. 1-2, 95–124. MR 1502680, DOI 10.2307/1967747 44. G. A. Bliss, The transformation of Clebsch in the calculus of variations, Proceedings of the International Congress (of 1924) at Toronto, vol. I, 1928, pp. 589-603. 45. G. A. Bliss, A boundary value problem in the calculus of variations, Bull. Amer. Math. Soc. vol. 32 (1926) pp. 317-331.
- Gilbert Ames Bliss, A boundary value problem for a system of ordinary linear differential equations of the first order, Trans. Amer. Math. Soc. 28 (1926), no. 4, 561–584. MR 1501366, DOI 10.1090/S0002-9947-1926-1501366-0 47. G. A. Bliss, Contributions that have been made by pure science to the advancement of engineering and industry. Mathematics, The Scientific Monthly vol. 24 (1927) pp. 308-319. 48. G. A. Bliss, An integral inequality, J. London Math. Soc. vol. 5 (1930) pp. 40-46.
- Gilbert Ames Bliss, The Problem of Lagrange in the Calculus of Variations, Amer. J. Math. 52 (1930), no. 4, 673–744. MR 1506783, DOI 10.2307/2370714
- G. A. Bliss and I. J. Schoenberg, On Separation, Comparison and Oscillation Theorems for Self-Adjoint Systems of Linear Second Order Differential Equations, Amer. J. Math. 53 (1931), no. 4, 781–800. MR 1506854, DOI 10.2307/2371226
- Gilbert Ames Bliss, The problem of Bolza in the calculus of variations, Ann. of Math. (2) 33 (1932), no. 2, 261–274. MR 1503050, DOI 10.2307/1968328 52. G. A. Bliss, The calculus of variations and the quantum theory, Bull. Amer. Math. Soc. vol. 38 (1932) pp. 201-224. 53. G. A. Bliss, (With I. J. Schoenberg) On the derivation of necessary conditions for the problem of Bolza, Bull. Amer. Math. Soc. vol. 38 (1932) pp. 858-864.
- G. A. Bliss, Mathematical Interpretations of Geometrical and Physical Phenomena, Amer. Math. Monthly 40 (1933), no. 8, 472–480. MR 1522896, DOI 10.2307/2302071
- G. A. Bliss and M. R. Hestenes, Sufficient conditions for a problem of Mayer in the calculus of variations, Trans. Amer. Math. Soc. 35 (1933), no. 1, 305–326. MR 1501685, DOI 10.1090/S0002-9947-1933-1501685-1
- G. A. Bliss, The Evolution of Problems of the Calculus of Variations, Amer. Math. Monthly 43 (1936), no. 10, 598–609. MR 1523791, DOI 10.2307/2300531
- G. A. Bliss, Normality and abnormality in the calculus of variations, Trans. Amer. Math. Soc. 43 (1938), no. 3, 365–376. MR 1501950, DOI 10.1090/S0002-9947-1938-1501950-2
- Gilbert A. Bliss, Definitely self-adjoint boundary value problems, Trans. Amer. Math. Soc. 44 (1938), no. 3, 413–428. MR 1501974, DOI 10.1090/S0002-9947-1938-1501974-5
- G. A. Bliss, The calculus of variations for multiple integrals, Amer. Math. Monthly 49 (1942), 77–89. MR 6022, DOI 10.2307/2302660 1. G. A. Bliss, Review of J. Pierpont, Theory of functions, Bull. Amer. Math. Soc. vol. 13 (1906) pp. 119-130. 2. G. A. Bliss, Review of M. Bôcher, Integral equations (Cambridge Tract), Bull. Amer. Math. Soc. vol. 16 (1910) pp. 207-213. 3. G. A. Bliss, Review of L. P. Eisenhart, Differential geometry. Bull. Amer. Math. Soc. vol. 17 (1911) pp. 470-478. 4. G. A. Bliss, Review of V. Volterra, Fonctions des lignes, Bull. Amer. Math. Soc. vol. 21 (1915) pp. 345-355. 5. G. A. Bliss, Review of W. F. Osgood, Topics in the theory of functions of several complex variables (Part II of the Madison Colloquium Lectures), Bull. Amer. Math. Soc. vol. 23 (1916) pp. 35-44. 6. G. A. Bliss, Review of W. Blaschke, Elementare Differentialgeometrie, Bull. Amer. Math. Soc. vol. 29 (1923) pp. 322-325. 7. G. A. Bliss, Review of G. Vivanti, Elementi del calcolo delle variazioni, Bull. Amer. Math. Soc. vol. 32 (1926) pp. 392-393. Trans. in Bolletino di Matematica vol. 22 (1926) pp. lxxxiv-lxxxvi. 8. G. A. Bliss, Review of A. R. Forsyth, Calculus of variations, Bull. Amer. Math. Soc. vol. 34 (1928) pp. 512-514. 9. G. A. Bliss, Review of G. H. Hardy, J. E. Littlewood, and G. Pólya, Inequalities, Science vol. 81 (1935) pp. 565-566. 1. G. A. Bliss, Ernest Julius Wilczynski, Science vol. 76 (1932) pp. 316-317. 2. G. A. Bliss, Eliakim Hastings Moore, Bull. Amer. Math. Soc. vol. 39 (1933) pp. 831-838. 3. G. A. Bliss, Eliakim Hastings Moore, The University Record vol. 19 (1933) pp. 130-134. 4. G. A. Bliss, The scientific work of Eliakim Hastings Moore, Bull. Amer. Math. Soc. vol. 40 (1934) pp. 501-514. 5. G. A. Bliss, Biographical memoir of Eliakim Hastings Moore, 1862-1932, National Academy of Sciences vol. 17 (1936) pp. 83-102, Fifth Memoir (with L. E. Dickson). 6. G. A. Bliss, Herbert Ellsworth Slaught, Science vol. 86 (1937) pp. 72-73 (with L. E. Dickson). 7. G. A. Bliss, Herbert Ellsworth Slaught, University of Chicago Magazine, Midsummer 1937, pp. 22-24. Reprinted in Bulletin of the Kansas Association for Mathematics Teachers vol. 12 (1937) p. 3 and pp. 9-12. 8. G. A. Bliss, Herbert Ellsworth Slaught–In Memoriam, Bull. Amer. Math. Soc. vol. 43 (1937) pp. 595-597.
- G. A. Bliss, Herbert Ellsworth Slaught–Teacher and Friend, Amer. Math. Monthly 45 (1938), no. 1, 5–10. MR 1524156, DOI 10.2307/2303466
- Obituary: Oskar Bolza, Science (N.S.) 97 (1943), 108–109. MR 0007721, DOI 10.1126/science.97.2509.108 11. G. A. Bliss, Oskar Bolza–In Memoriam, Bull. Amer. Math. Soc. vol. 50 (1944) pp. 478-489.
Additional Information
- Journal: Bull. Amer. Math. Soc. 58 (1952), 251-264
- DOI: https://doi.org/10.1090/S0002-9904-1952-09597-5
- MathSciNet review: 0046969