Celebratio Mathematica

Gilbert Ames Bliss

Gilbert Ames Bliss: 1876–1951

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G. A. Bliss: The geodes­ic lines on the an­chor ring. Ph.D. thesis, Uni­versity of Chica­go, 1900. Ad­vised by O. Bolza. MR 2936782

G. A. Bliss: “The second vari­ation of a def­in­ite in­teg­ral when one end-point is vari­able,” Trans. Amer. Math. Soc. 3 : 1 (1902), pp. 132–​141. MR 1500591 JFM 33.​0385.​01

G. A. Bliss: “Jac­obi’s cri­terion when both end-points are vari­able,” Math. Ann. 58 : 1–​2 (1903), pp. 70–​80. MR 1511229 JFM 34.​0402.​01

G. A. 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 : 2 (1904), pp. 113–​125. MR 1500665 JFM 35.​0340.​01

G. A. Bliss: “The solu­tions of dif­fer­en­tial equa­tions of the first or­der as func­tions of their ini­tial val­ues,” Ann. of Math. (2) 6 : 2 (January 1905), pp. 49–​68. MR 1503546 JFM 36.​0389.​01

G. A. Bliss and M. Ma­son: “A prob­lem of the Cal­cu­lus of Vari­ations in which the in­teg­rand is dis­con­tinu­ous,” Trans. Amer. Math. Soc. 7 : 2 (1906), pp. 325–​336. MR 1500752 JFM 37.​0402.​01

G. A. Bliss: “A gen­er­al­iz­a­tion of the no­tion of angle,” Trans. Amer. Math. Soc. 7 : 2 (1906), pp. 184–​196. MR 1500741 JFM 37.​0490.​01

G. A. Bliss: “A new form of the simplest prob­lem of the Cal­cu­lus of Vari­ations,” Trans. Amer. Math. Soc. 8 : 3 (1907), pp. 405–​414. MR 1500795 JFM 38.​0408.​01

M. Ma­son and G. A. Bliss: “The prop­er­ties of curves in space which min­im­ize a def­in­ite in­teg­ral,” Trans. Amer. Math. Soc. 9 : 4 (1908), pp. 440–​466. MR 1500821 JFM 39.​0441.​01

G. A. Bliss: “On the in­verse prob­lem of the Cal­cu­lus of Vari­ations,” Ann. of Math. (2) 9 : 3 (April 1908), pp. 127–​140. MR 1502361 JFM 39.​0445.​01

G. A. Bliss and M. Ma­son: “Fields of ex­tremals in space,” Trans. Amer. Math. Soc. 11 : 3 (1910), pp. 325–​340. MR 1500866 JFM 41.​0437.​01

G. A. Bliss: “A new proof of Wei­er­strass’s the­or­em con­cern­ing the fac­tor­iz­a­tion of a power series,” Bull. Amer. Math. Soc. 16 : 7 (1910), pp. 356–​359. MR 1558920 JFM 41.​0286.​03

G. A. Bliss: “A new proof of the ex­ist­ence the­or­em for im­pli­cit func­tions,” Bull. Amer. Math. Soc. 18 : 4 (1912), pp. 175–​179. MR 1559180 JFM 43.​0483.​04

G. A. Bliss: “A gen­er­al­iz­a­tion of Wei­er­strass’ pre­par­a­tion the­or­em for a power series in sev­er­al vari­ables,” Trans. Amer. Math. Soc. 13 : 2 (April 1912), pp. 133–​145. MR 1500910 JFM 43.​0504.​02

G. A. Bliss: “Fun­da­ment­al ex­ist­ence the­or­ems,” pp. i–​ii,1–​107 in The Prin­ceton Col­loqui­um (Prin­ceton Uni­versity, 15–17 Septem­ber 1909), part 1. Amer­ic­an Math­em­at­ic­al So­ci­ety (New York), 1913. JFM 44.​0365.​01

G. A. Bliss and A. L. Un­der­hill: “The min­im­um of a def­in­ite in­teg­ral for uni­lat­er­al vari­ations in space,” Trans. Amer. Math. Soc. 15 : 3 (1914), pp. 291–​310. MR 1500981 JFM 45.​0605.​03

G. A. Bliss: “Gen­er­al­iz­a­tions of geodes­ic curvature and a the­or­em of Gauss con­cern­ing geodes­ic tri­angles,” Amer. J. Math. 37 : 1 (January 1915), pp. 1–​18. MR 1507894 JFM 45.​0859.​02

G. A. Bliss: “Jac­obi’s con­di­tion for prob­lems of the Cal­cu­lus of Vari­ations in para­met­ric form,” Trans. Amer. Math. Soc. 17 : 2 (April 1916), pp. 195–​206. MR 1501037 JFM 46.​0758.​03

G. A. Bliss: “Solu­tions of dif­fer­en­tial equa­tions as func­tions of the con­stants of in­teg­ra­tion,” Bull. Amer. Math. Soc. 25 : 1 (1918), pp. 15–​26. MR 1560139 JFM 47.​0940.​01

G. A. Bliss: “A meth­od of com­put­ing dif­fer­en­tial cor­rec­tions for a tra­ject­ory,” J. U.S. Ar­til­lery 51 (1919), pp. 445–​449. Cor­rec­ted copy of earli­er print­ing in vol. 50 (pp. 455–460).

G. A. Bliss: “The use of ad­joint sys­tems in the prob­lem of dif­fer­en­tial cor­rec­tions for a tra­ject­ory,” J. U.S. Ar­til­lery 51 (1919), pp. 296–​311.

G. A. Bliss: Dif­fer­en­tial cor­rec­tions for anti-air­craft guns. Technical report, Ab­er­deen Prov­ing Ground, 1919.

G. A. Bliss: “Func­tions of lines in bal­list­ics,” Trans. Amer. Math. Soc. 21 : 2 (1920), pp. 93–​106. MR 1501138 JFM 47.​0382.​02

G. A. Bliss: “Dif­fer­en­tial equa­tions con­tain­ing ar­bit­rary func­tions,” Trans. Amer. Math. Soc. 21 : 2 (1920), pp. 79–​92. MR 1501137

G. A. Bliss: “Bira­tion­al trans­form­a­tions sim­pli­fy­ing sin­gu­lar­it­ies of al­geb­ra­ic curves,” Trans. Amer. Math. Soc. 24 : 4 (1922), pp. 274–​285. MR 1501226 JFM 50.​0266.​02

G. A. Bliss: “The re­duc­tion of sin­gu­lar­it­ies of plane curves by bira­tion­al trans­form­a­tion,” Bull. Amer. Math. Soc. 29 : 4 (1923), pp. 161–​183. Pres­id­en­tial ad­dress de­livered be­fore the Amer­ic­an Math­em­at­ic­al So­ci­ety, Decem­ber 28, 1922. MR 1560693 JFM 49.​0264.​01

G. A. Bliss: “Al­geb­ra­ic func­tions and their di­visors,” Ann. of Math. (2) 26 : 1–​2 (September–October 1924), pp. 95–​124. MR 1502680 JFM 50.​0699.​03

G. A. Bliss: “A bound­ary value prob­lem in the Cal­cu­lus of Vari­ations,” Bull. Amer. Math. Soc. 32 : 4 (1926), pp. 317–​331. MR 1561219 JFM 52.​0509.​02

G. A. Bliss: “A bound­ary value prob­lem for a sys­tem of or­din­ary lin­ear dif­fer­en­tial equa­tions of the first or­der,” Trans. Amer. Math. Soc. 28 : 4 (1926), pp. 561–​584. MR 1501366 JFM 52.​0453.​13

G. Bliss: “The trans­form­a­tion of Cleb­sch in the Cal­cu­lus of Vari­ations,” pp. 589–​603 in Pro­ceed­ings of the In­ter­na­tion­al Math­em­at­ic­al Con­gress (Toronto, 11–16 Au­gust 1924), vol. 1. Edi­ted by J. C. Fields. Uni­versity of Toronto Press, 1928. JFM 54.​0532.​03

G. A. Bliss: “The prob­lem of Lag­range in the Cal­cu­lus of Vari­ations,” Amer. J. Math. 52 : 4 (October 1930), pp. 673–​744. MR 1506783 JFM 56.​0435.​01

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 : 4 (October 1931), pp. 781–​800. MR 1506854 JFM 57.​0528.​01 Zbl 0003.​25702

Top­ics of the Cal­cu­lus of Vari­ations. Edi­ted by G. Bliss. Uni­versity of Chica­go, 1932. Prin­cip­ally a re­port on lec­tures by E. J. Mc­Shane and Richard Cour­ant.

G. A. Bliss: Al­geb­ra­ic func­tions. AMS Col­loqui­um Pub­lic­a­tions 16. Amer­ic­an Math­em­at­ic­al So­ci­ety (New York), 1933. JFM 59.​0384.​03 Zbl 0008.​21004

G. A. Bliss: The Cal­cu­lus of Vari­ations, mul­tiple in­teg­rals. Uni­versity of Chica­go, 1933. MR 2936825

G. A. Bliss: “Def­in­itely self-ad­joint bound­ary value prob­lems,” Trans. Amer. Math. Soc. 44 : 3 (1938), pp. 413–​428. MR 1501974 JFM 64.​0438.​02 Zbl 0020.​03204

G. A. Bliss: “The Cal­cu­lus of Vari­ations for mul­tiple in­teg­rals,” Amer. Math. Monthly 49 : 2 (February 1942), pp. 77–​89. MR 0006022 Zbl 0063.​00455

G. A. Bliss: Lec­tures on the cal­cu­lus of vari­ations. Uni­versity of Chica­go Press (Chica­go, IL), 1946. MR 0017881 Zbl 0063.​00459