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123 124 125 126 </head> 127 <body class="wsite-theme-light tall-header-page wsite-page-analysis"><div class="header-wrap"> 128 <div class="container"> 129 <table id="header"> 130 <tr> 131 <td id="logo"><span class="wsite-logo"> 132 133 <a href="/"> 134 135 <span id="wsite-title"> Neo-classical physics</span> 136 137 </a> 138 139</span></td> 140 <td id="header-right"> 141 <table> 142 <tr> 143 <td class="phone-number"></td> 144 <td class="social"></td> 145 <td class="search"></td> 146 </tr> 147 </table> 148 </td> 149 </tr> 150 </table> 151 </div> 152</div> 153<div class="main-wrap"> 154 <div class="container"> 155 <div id="main"> 156 <div id="banner"> 157 <div class="wsite-header"></div> 158 </div> 159 <div id="navigation"> 160 <ul class="wsite-menu-default"> 161 <li id="pg812096350226685952" class="wsite-menu-item-wrap"> 162 <a 163 href="/" 164 class="wsite-menu-item" 165 > 166 Home 167 </a> 168 169 </li> 170 <li id="pg501922448104792031" class="wsite-menu-item-wrap"> 171 <a 172 href="/algebras.html" 173 class="wsite-menu-item" 174 > 175 Algebras 176 </a> 177 178 </li> 179 <li id="active" class="wsite-menu-item-wrap"> 180 <a 181 href="/analysis.html" 182 class="wsite-menu-item" 183 > 184 Analysis 185 </a> 186 187 </li> 188 <li id="pg223983767423969446" class="wsite-menu-item-wrap"> 189 <a 190 href="/topology.html" 191 class="wsite-menu-item" 192 > 193 Topology 194 </a> 195 196 </li> 197 <li id="pg680296257581584656" class="wsite-menu-item-wrap"> 198 <a 199 href="/geometry.html" 200 class="wsite-menu-item" 201 > 202 Geometry 203 </a> 204 205 </li> 206 <li id="pg479098151185829397" class="wsite-menu-item-wrap"> 207 <a 208 href="/spacetime-structure.html" 209 class="wsite-menu-item" 210 > 211 Spacetime structure 212 </a> 213 214 </li> 215 <li id="pg663406384674618957" class="wsite-menu-item-wrap"> 216 <a 217 href="/theoretical-mechanics.html" 218 class="wsite-menu-item" 219 > 220 Theoretical mechanics 221 </a> 222 223 </li> 224 <li id="pg296305103650549985" class="wsite-menu-item-wrap"> 225 <a 226 href="/electromagnetism.html" 227 class="wsite-menu-item" 228 > 229 Electromagnetism 230 </a> 231 232 </li> 233 <li id="pg773913576856764377" class="wsite-menu-item-wrap"> 234 <a 235 href="/wave-theory.html" 236 class="wsite-menu-item" 237 > 238 Wave theory 239 </a> 240 241 </li> 242 <li id="pg364025069993580806" class="wsite-menu-item-wrap"> 243 <a 244 href="/thermodynamics.html" 245 class="wsite-menu-item" 246 > 247 Thermodynamics 248 </a> 249 250 </li> 251 <li id="pg264921894109145360" class="wsite-menu-item-wrap"> 252 <a 253 href="/general-system-theory.html" 254 class="wsite-menu-item" 255 > 256 General system Theory 257 </a> 258 259 </li> 260 </ul> 261 <div class="clear"></div> 262 </div> 263 <div id="content"> 264 <div id="wsite-content" class="wsite-elements wsite-not-footer"> 265 <h2 class="wsite-content-title" style="text-align:left;"></h2> 266<div class="paragraph" style="text-align:left;display:block;"><br /> <font size="6" style="font-weight:bold"><span>Analysis</span></font><br /><br /><span>_______________________________________________________________________________________________________________________________________________________<br />­­­­­­­­­­­­­­ <br /> <font size="5"> <strong>PERSONAL RESEARCH</strong></font><br />_______________________________________________________________________________________________________________________________________________________<br /><br /> <font size="4"><u>Book</u></font></span><br /><br /><font size="4"><span><em> </em>D. H. Delphenich (ed.),<em> Selected papers on geodesic fields, </em>Neo-classical Press, Spring Valley, OH, 2013.<br /><br />(Download consists of two files: <a href="/uploads/3/4/3/6/34363841/geodesic_fields_-_pt._1.pdf">I</a> and <a href="/uploads/3/4/3/6/34363841/geodesic_fields_-_pt._2.pdf">II</a>, Table of Contents below)</span></font><br /><br /><span> <font size="4"><u>Articles</u></font><br />­­­­­­­­­­­­­­<br /><font size="4"><a href="/uploads/3/4/3/6/34363841/integrability_and_non-holonomic_constraints.pdf">D. H. Delphenich</a>, “On the variational formulation of systems with non-holonomic constraints,” Ann. Phys. (Berlin) <strong>18</strong> (2009), 649-670.<br /><br /><a href="/uploads/3/4/3/6/34363841/integrability_and_non-conservative_systems.pdf">D. H. Delphenich</a>, “Integrability and the variational formulation of non-conservative mechanical systems,” Ann. Phys. (Berlin) <strong>18</strong> (2009), 45-56<br /><br /><a href="/uploads/3/4/3/6/34363841/generalized_noether_theorem.pdf">D. H. Delphenich</a>, “A generalization of Noether's theorem based on the virtual work functional,” <a href="http://arxiv.org/abs/1109.0461">arXiv:1109.0461</a></font></span><br /><br /><font size="4"><font color="#000000">D. H. Delphenich, "On the role of integrability in a large class of physical systems," <a href="http://arxiv.org/abs/1210.4976">arXiv:1210.4976</a>.</font></font><br /><br /><br /><span>_______________________________________________________________________________________________________________________________________________________<br />­­­­­­­­­­­­­­<br /> <font size="5"><strong>TRANSLATIONS</strong></font><br />_______________________________________________________________________________________________________________________________________________________<br />­­­­­­­­­­­­­­</span><br /><font size="4"> <span style="font-weight:bold">Calculus of variations</span><br /><br /><span><span><span><span><a href="/uploads/3/4/3/6/34363841/jacobi_-_calc._var._and_diff._eqs..pdf">C. G. J. Jacobi</a>, "On the theory of the calculus of variations and differential equations," J. f. d. reine u. angew. Math. <strong>17</strong> (1837), 68-82.</span></span></span></span></font><br /><br /><font size="5"><font size="4"><a href="/uploads/3/4/3/6/34363841/beltrami_-_geodesics.pdf">E. Beltrami</a>, "On the theory of geodetic lines," Rendiconti del Reale Istituto Lombardo (2) <strong>1</strong> (1868), 708-718; <em>Opera matematiche</em>, v. I, 366-373.</font></font><br /><br /><font size="5"><font size="4"><a href="/uploads/3/4/3/6/34363841/mayer_-_maxima_and_minima.pdf">A. Mayer</a>, "On the criteria for maxima and minima of simple integrals," J. reine angew. Math. <strong>69</strong> (1868), 238-263.</font></font><br /><br /><font size="4"><a href="/uploads/3/4/3/6/34363841/mayer_-_history_of_least_action.pdf">A. Mayer</a>, "History of the principle of least action," Inaugural lecture, von Veit, Leipzig, 1877.</font><br /><br /><font size="5"><font size="4"><a href="/uploads/3/4/3/6/34363841/mayer_-_isoperimetric_problem.pdf">A. Mayer</a>, "The criteria for the maxima and minima of simple integrals in isoperimetric problems," Math. Ann. <strong>13</strong> (1878), 55-68.</font></font><br /><br /><font size="4"><a href="/uploads/3/4/3/6/34363841/frobenius_-_adjoint_diff_express.pdf">G. Frobenius</a>, "On adjoint linear differential expressions," J. reine angew. Math. <strong>85</strong> (1878), 185-213.</font><br /><br /><font size="4"><a href="/uploads/3/4/3/6/34363841/imchentsky_-_kinetic_potential.pdf">B. Imchenestsky</a>, "On the transformation of a differential equation of even order to the form of an isoperimetric equation," Bull. Acad. imp. Sci. St.-Petersbourg (3) <strong>31</strong> (1887), 283-291.<br /><br /><a href="/uploads/3/4/3/6/34363841/zorawski_-_integral_invariants.pdf">K. Zorawski</a>, "On integral invariants of continuous transformation groups," Bull. int. de l'Aca
266d. des Sci. de Cracovie (1889-1900), 127-130.</font><br /><br /><font size="4"><a href="/uploads/3/4/3/6/34363841/volterra_-_calc_var.pdf">V. Volterra</a>, "On the differential equations that are deduced from questions in the calculus of variations," Rend. Acc. dei Lincei (4) <strong>6</strong> (1890), 43-54; <em>Opere matematiche</em>, v. I, 454-463.</font><br /><br /><font size="5"><font size="4"><a href="/uploads/3/4/3/6/34363841/volterra_-_hj_theory.pdf">V. Volterra</a>, "On an extension of the Jacobi-Hamilton theory in the calculus of variations," Rend. Acc. Lincei (5) <strong>6</strong> (1890), 127-138; <em>Opere matematiche</em>, v. I, 464-476.<br /><br /><a href="/uploads/3/4/3/6/34363841/stackel_-_motion_in_an_n-dim_man.pdf">P. Staeckel</a>, "On the motion of a point in an <em>n</em>-fold manifold," Math. Ann. <strong>42</strong> (1893), 537-563.</font></font><br /><br /><font size="4"><a href="/uploads/3/4/3/6/34363841/stackel_-_a_class_of_probs_in_dyn.pdf">P. Staeckel</a>, "On a class of problems in dynamics," C. R. Acad. Sci. Paris <strong>116</strong> (1893), 485-487.<br /><br /><a href="/uploads/3/4/3/6/34363841/stackel_-_integrating_hj_eq.pdf">P. Staeckel</a>, "On the integration of Hamilton’s differential equation," C. R. Acad. Sci. Paris <strong>121</strong> (1895), 489-492.</font><br /><br /><font size="5"><font size="4"><a href="/uploads/3/4/3/6/34363841/mayer_-_lagrange_multipliers.pdf">A. Mayer</a>, "Lagrange's method of multipliers and the most general problem in the calculus of variations for one independent variable," Ber. Verh. Kon. Sachs. Ges. Wiss. Leipzig <strong>47</strong> (1895), 129-144.</font></font><br /><br /><font size="5"><font size="4"><a href="/uploads/3/4/3/6/34363841/mayer_-_kinetic_potential.pdf">A. Mayer</a>, "The existence condition for a kinetic potential," Ber. Kön. Ges. Wiss. Leipzig <strong>48</strong> (1896), 519-529.</font></font><br /><br /><font size="5"><font size="4"><a href="/uploads/3/4/3/6/34363841/darboux_-_xi._-_auxiliary_equation.pdf">G. Darboux</a>, "On the auxiliary equation," from <em>Leçons sur la théorie générale des surfaces</em>, Gauthier-Villars, Paris, 1896, Partie IV, Note XI, pp. 505-516.</font></font><br /><br /><font size="4"><a href="/uploads/3/4/3/6/34363841/lie_-_integral_invariants_i.pdf">S. Lie</a>, "The theory of integral invariants is a corollary to the theory of differential invariants," Leip. Ber. (1897); Ges. Abh., V. IV, art. XXVII.<br /><br /><a href="/uploads/3/4/3/6/34363841/lie_-_integral_invariants_ii.pdf">S. Lie</a>, "On integral invariants and their use in the theory of differential equations," Leip. Ber. <strong>4</strong> (1897), 369-410; <em>Ges. Abh</em>., v. VI, art. XXVIII, pp. 664-701.</font><br /><br /><font size="5"><font size="4"><a href="/uploads/3/4/3/6/34363841/hirsch_-_characteristic_property.pdf">A. Hirsch</a>, "On the characteristic property of the differential equations of the calculus of variations," Math. Ann. <strong>2</strong> (1897), 49-72.</font></font><br /><br /><font size="4"><a href="/uploads/3/4/3/6/34363841/lie_-_integral_invariants_i.pdf">S. Lie</a>, "The theory of integral invariants is a corollary to the theory of differential invariants," Leipziger. Berichte (1897), Heft III, submitted on 14-7-1897, pp. 342-357. Presented at the session on 3-5-1897; <em>Gesammelte Abhandlungen</em>, v. IV, art. XXVII, pp. 649-663.<br /><br /><a href="/uploads/3/4/3/6/34363841/escherich_-_second_variation_-_i.pdf">G. von Escherich</a>, "The second variation of a simple integral," Sitz. Kaiserliche Akad. Wiss. Wien, Math.-Naturwiss. Klasse <strong>107</strong> (1898), 1191-1250.</font><br /><br /><font size="5"><font size="4"><a href="/uploads/3/4/3/6/34363841/hirsch_-_existence_of_kin_pot.pdf">A. Hirsch</a>, "The existence conditions for the generalized kinetic potential," Math. Ann. <strong>50</strong> (1898), 429-441.</font></font><br /><br /><font size="5"><font size="4"><a href="/uploads/3/4/3/6/34363841/boehm_-_existence_of_a_kinetic_potential.pdf">K. Boehm</a>, "The existence conditions for a kinetic potential that depends upon the first and second differential quotients of the coordinates," J. reine angew. Math. <strong>121</strong> (1900), 124-140.</font></font><br /><br /><font size="5"><font size="4"><a href="/uploads/3/4/3/6/34363841/voss_-_hamilton_and_maupertuis.pdf">A. Voss</a>, "On the principles of Hamilton and Maupertuis," Gottinger Nachrichten (1900), 322-327.</font></font><br /><br /><font size="5"><font size="4">A. Kneser, <em>The Calculus of variations</em>, Vieweg and Sons, Braunschweig, 1900: <a href="/uploads/3/4/3/6/34363841/kneser_-_calc_var_i.pdf">Part I</a>, <a href="/uploads/3/4/3/6/34363841/kneser_-_calc_var_ii.pdf">Part II</a>.</font></font><br /><br /><font size="5"><font size="4"><a href="/uploads/3/4/3/6/34363841/de_donder_-_integral_invariants.pdf">Th. De Donder, </a><em>Study of the Integral Invariants</em>, Gauthier-Villars, Paris, 1901.</font></font><br /><br /><font size="5"><font size="4"><a href="/uploads/3/4/3/6/34363841/koenigsberger_-_princ_of_mech.pdf">L. Koenigsberger</a>, <em>Principles of Mechanics. Mathematical Investigations</em>, B. G. Teubner, Leipzig, 1901.</font></font><br /><br /><font size="4"><a href="/uploads/3/4/3/6/34363841/de_donder_-_integral_invariants_-_2.pdf">Th. De Donder</a>, "Study of integral invariants (Part Two)," Rend. Circ. mat. di Palermo (1) <strong>16</strong> (1902), 155-179.</font><br /><br /><font size="5"><font size="4"><a href="/uploads/3/4/3/6/34363841/morera_-_lagrange_equations.pdf">G. Morera</a>, "On the Lagrange dynamical equations," Atti Reale Accad. sci. Torino <strong>38</strong> (1902-03), 121-134.</font></font><br /><br /><font size="4"><a href="/uploads/3/4/3/6/34363841/morera_-_hamiltons_equations.pdf">G. Morera</a>, "On Hamilton's dynamical equations," Atti della R. Acc. delle sci. <strong>39</strong> (1903-04), 342-355.</font><br /><br /><font size="5"><font size="4"><a href="/uploads/3/4/3/6/34363841/morera_-_transf_ham_eq_i_and_ii.pdf">G. Morera</a>, "On the transformation of Hamilton’s differential equations. Notes I and II," Rend. Real. Accad. Lincei (5) <strong>12</strong> (1903), 113-122; pp. 149-152.</font></font><br /><br /><font size="4"><a href="/uploads/3/4/3/6/34363841/hamel_-_geodesics_are_straight_lines.pdf">G. Hamel</a>, "On the geometries in which the lines are shortest," Math. Ann. <strong>57</strong> (1903), 231-264.</font><br /><br /><font size="5"><font size="4"><a href="/uploads/3/4/3/6/34363841/bolza_-_second_var_isoperim.pdf">O. Bolza</a>, "On the second variation for isoperimetric problems," Math. <strong>57</strong> (1903), 44-47.</font></font><br /><br /><font size="4"><a href="/uploads/3/4/3/6/34363841/yoshiye_-_calc_var_and_pdes.pdf">T. Yoshiye</a>, "Applications of the calculus of variations to partial differential equations with two independent variables," Math. Ann. <strong>57</strong> (1903), 185-194.</font><br /><br /><font size="4"><a href="/uploads/3/4/3/6/34363841/thome_-_linear_des_in_cv.pdf">L. W. Thome</a>, "On an application of the theory of linear differential equations to the calculus of variations," J. reine angew. Math. 125 (1903), 1-27.<br /><br /><a href="/uploads/3/4/3/6/34363841/hahn_-_remarks_on_cv.pdf">H. Hahn</a>, "Remarks concerning the calculus of variations," Math. Ann. <strong>58</strong> (1904), 148-168.<br /><br /><a href="/uploads/3/4/3/6/34363841/thome_-_linear_des_in_cv_-_supp.pdf">L. W. Thome</a>, "On an application of the theory of linear differential equations to the calculus of variations (supplement)," J. reine angew. Math. 128 (1905), 33-44.</font><br /><br /><font size="4"><a href="/uploads/3/4/3/6/34363841/hahn_-_remarks_on_cv.pdf">H. Hans</a>, "Remarks concerning the calculus of variations," Math. Ann. <strong>58</strong> (1904), 148-168.</font><br /><br /><font size="4"><a href="/uploads/3/4/3/6/34363841/levi-civita_-_hj_by_sep_var.pdf">T. Levi-Civita</a>, "On the integration of the Hamilton-Jacobi equation by separation of variables," Math. Ann. <strong>59</strong> (1904), 383-397.</font><br /><br /><font size="5"><font size="4"><a href="/uploads/3/4/3/6/34363841/frechet_-_hamilton-jacobi_eq.pdf">M. Frechet</a>, "On an extension of the Jacobi-Hamilton method," Annali di mat. pura ed appl. (3) <strong>11</strong> (1904), 187-199.</font></font><br /><br /><font size="5"><font size="4"><a href="/uploads/3/4/3/6/34363841/kurschak_-_kinetic_potential.pdf">J. Kurschak</a>, "The existence conditions for the generalized kinetic potential," Math. Ann. <strong>62</strong> (1906), 148-155.</font></font><br /><br /><font size="5"><font size="4"><a href="/uploads/3/4/3/6/34363841/mayer_-_hilbert_independence_thm.pdf">A. Mayer</a>, "On Hilbert's independence theorem in the theory of the maximum and minimum of a simple integral," Math. Ann. <strong>58</strong> (1904), 235-248; "..., Part II," <em>ibid.</em> <strong>62</strong> (1906), 335-350.</font></font><br /><br /><font size="4"><a href="/uploads/3/4/3/6/34363841/hilbert_-_calc_var.pdf">D. Hilbert</a>, "On the calculus of variations," Math. Ann. <strong>62</strong> (1906), 351-370.<br /><br /><a href="/uploads/3/4/3/6/34363841/egorov_-_mayer_problem.pdf">D. Egorov</a>, "The sufficient conditions for the extremum in the theory of the Mayer problem," Math. Ann. <strong>62</strong> (1906), 371-380.</font><br /><br /><font size="4"><a href="/uploads/3/4/3/6/34363841/goursat_-_integral_invariants.pdf">E. Goursat</a>, "On integral invariants," J. math. pures et appl. (6) <strong>4</strong> (1908), 331-365.</font><br /><br /><br /><font size="4"><a href="/uploads/3/4/3/6/34363841/hahn_-_second_variation.pdf">H. Hahn</a>, "On the connection between the theories of the second variation and Weierstrass's theory of the calculus of variations," Rend. Circ. Matem. Palermo (1909), 49-78.</font><br /><br /><font size="5"><font size="4"><a href="/uploads/3/4/3/6/34363841/vergne_-_integral_invariants.pdf">H. Vergne</a>, "On certain properties of systems of differential equations," Ann. sci. de l’E.N.S. (3) <strong>27</strong> (1910), 543-563.</font></font><br /><br /><font size="5"><font size="4"><a href="/uploads/3/4/3/6/34363841/richardson_-_jacobi_crit_and_oscil_props_-_1.pdf">R. G. D. Richardson</a>, "The Jacobi criterion in the calculus of variations and the oscillatory properties of second-order linear differential equations," Math. Ann. <strong>68</strong> (1910), 279-304.</font></font><br /><br /><font size="4"><a href="/uploads/3/4/3/6/34363841/de_donder_-_gen_of_poisson_-_i.pdf">Th. De Donder</a>, "Generalization of Poisson's theorem," C. R. Acad. Sci. Paris <strong>148</strong> (1910), 610-612.<br /><br /><a href="/uploads/3/4/3/6/34363841/de_domder_-_gen_of_poisson_-_ii.pdf">Th. De Donder</a>, " On Poisson's theorem and Lie's differential invariants," C. R. Acad. Sci. Paris <strong>151</strong> (1910), 371-373.<br /><br /><a href="/uploads/3/4/3/6/34363841/de_donder_-_int_inv_and_math_phys.pdf">Th. De Donder</a>, "On relative integral invariants and their applications to mathematical physics," Bull. Acad. roy. Belgique, classe de sci. (5) <strong>1</strong> (1911), 50-70.</font><br /><br /><font size="4"><a href="/uploads/3/4/3/6/34363841/bolza_-_independence_theorem.pdf">O. Bolza</a>, "On Hilbert's independence theorem for the Lagrange variational problem," Ren
266d. Circ. matem. Palermo (1) <strong>31</strong> (1911), 257-272.<br /><br /><a href="/uploads/3/4/3/6/34363841/radon_-_maxima_and_minima.pdf">J. Radon</a>, "Some questions concerning the theory of maxima and minima of multiple integrals," Monats. Math. Phys. <strong>22</strong> (1911), 53-63.</font><br /><br /><font size="4"><a href="/uploads/3/4/3/6/34363841/de_donder_-_hamilton-volterra_equations.pdf">Th. De Donder</a>, "On the canonical Hamilton-Volterra equations," Mem. Acad. roy. Belg., Cl. de Sc. (2) <strong>3</strong>, fasc. IV, 1911.</font><br /><br /><font size="5"><font size="4"><a href="/uploads/3/4/3/6/34363841/dallacqua_-_integ_of_hj_by_sep_var.pdf">F. A. Dall'Acqua</a>, "The Hamilton-Jacobi equations that can be integrated by separation of variables," Rend. Circ. mat. Palermo (1) <strong>33</strong> (1912), 341-351.</font></font><br /><br /><font size="4"><a href="/uploads/3/4/3/6/34363841/de_donder_-_hilbert_ind._int.pdf">Th. De Donder</a>, "On Hilbert's independence theorem," C. R. Acad. Sci. Paris <strong>156</strong> (1913), 609-611, 868-870,</font><br /><br /><font size="4"><a href="/uploads/3/4/3/6/34363841/goursat_-_integral_invariants_-_ii.pdf">E. Goursat</a>, "On some points regarding the theory of integral invariants," J. math. pures et appl. (7) <strong>1</strong> (1915), 241-259.</font><br /><br /><font size="5"><font size="4"><a href="/uploads/3/4/3/6/34363841/prange_-_hj_theory.pdf">G. Prange</a>, <em>The Hamilton-Jacobi Theory for Double Integrals</em>, Dietrich, Gottingen, 1915.</font></font><br /><br /><font size="5"><font size="4"><a href="/uploads/3/4/3/6/34363841/kneser_-_contrib_to_cv.pdf">A. Kneser</a>, "Contributions to the theory of the calculus of variations: The connection between the Weierstrass and Jacobi-Hamilton methods and a theory of integration of Cauchy," Archiv der Math. und Phys. <strong>24</strong> (1915), 26-57.</font></font><br /><br /><font size="4"><a href="/uploads/3/4/3/6/34363841/noether_-_invariant_variational_problems.pdf">E. Noether</a><span>, "On invariant variational problems," Gottinger Nachrichten (1918), 235-257.</span><br /><br /><font size="4"><a href="/uploads/3/4/3/6/34363841/bessel-hagen_-_invariance_of_em.pdf">E. Bessel-Hagen</a>, "On the conservation laws of electrodynamics," Math. Ann. <strong>84</strong> (1921), 258-276.</font><br /><br /><font color="#000000"><a href="/uploads/3/4/3/6/34363841/cartan_-_lessons_on_integral_invariants.pdf">E. Cartan</a>, <em>Lessons on integral invariants</em>, Hermann and Co., Paris, 1922.</font></font><br /><br /><font size="4"><a href="/uploads/3/4/3/6/34363841/caratheodory_-_envelopes_of_extremals.pdf">C. Caratheodory</a>, "On the envelopes of the extremals of a field in a multidimensional space," <strong>4</strong> (1923), 23-31.</font><br /><br /><font size="4"><a href="/uploads/3/4/3/6/34363841/caratheodory_-_method_of_geod_equid.pdf">C. Caratheodory</a>, "The method of geodetic equidistants and the Lagrange problem," Acta Math. <strong>47</strong> (1925), 199-236.</font><br /><br /><font size="5"><font size="4"><a href="/uploads/3/4/3/6/34363841/haar_-_adjoint_problems.pdf">A. Haar</a>, "On adjoint variational problems and adjoint extremal surfaces," Math. Ann. <strong>100</strong> (1928), 481-502.</font></font><br /><br /><font size="5"><font size="4"><a href="/uploads/3/4/3/6/34363841/caratheodory_-_cv_for_multiple_integrals.pdf">C. Caratheodory</a>, On the calculus of variations for multiple integrals," Acta Szeged Sect. Sci. Math. <strong>4</strong> (1929), 193-216.</font></font><br /><br /><font size="4"><a href="/uploads/3/4/3/6/34363841/paquet_-_diff_forms_in_calc_var.pdf">P. V. Paquet</a>, "The exterior differential forms <em>Wn</em> in the calculus of variations," Bull. Acad. roy. Belg., Cl. sc. (5) <strong>27</strong> (1941), 65-84.<br /><br /><a href="/uploads/3/4/3/6/34363841/dedecker_-_batemans_method_for_inverse_problem.pdf">P. Dedecker</a>, "On Bateman’s method in the inverse problem in the calculus of variations," Bull. Acad. roy. Belgique (Cl. des Sc.) (5) <strong>35</strong> (1949), 774-792.<br /><br /><a href="/uploads/3/4/3/6/34363841/dedecker_-_inverse_problem.pdf">P. Dedecker</a>, "On an inverse problem in the calculus of variations," Bull. Acad. roy. Belgique, classe de sciences <strong>38</strong> (1950), 63-70.<br /><br /><a href="/uploads/3/4/3/6/34363841/dedecker_-_bjerknes_theorem.pdf">P. Dedecker</a>, <em>On the circulation theorem of V. Bjerknes and the theory of integral invariants</em>, Institut royale Météorologique de Belgique, Brussells, 1951.</font><br /><br /><font size="4"><a href="/uploads/3/4/3/6/34363841/boerner_-_caratheodorys_approach.pdf">H. Boerner</a>, " Caratheodory's approach to the calculus of variations," Jber. Deutsch. Math. Ver. <strong>56</strong> (1953), 31-58.<br /><br /><a href="/uploads/3/4/3/6/34363841/velte_-_multiple_integrals.pdf">W. Velte</a>, "On the calculus of variations for multiple integrals," Math. Zeit. <strong>60</strong> (1954), 367-383.</font><br /><br /><font size="4"><a href="/uploads/3/4/3/6/34363841/dedecker_-_helmholtz-cartan_invariant.pdf">P. Dedecker</a>, "The Helmholtz-Cartan theorem for a simple integral of higher order," Study group on solitons, partial differential equations, and spectral methods, (16 – 27 July 1979), International Centre for Theoretical Physics, Trieste, Italy.</font><br /><br /><font size="4"> <strong>Differential equations</strong></font><br /><br /><font size="4"><a href="/uploads/3/4/3/6/34363841/monge_-_pdes.pdf">G. Monge</a>, "Integrating ordinary differential equations by integrating partial differential equations," Hist. Acad. Roy. Sci. (1784), 502-576.</font><br /><br /><font size="5"><font size="4"><a href="/uploads/3/4/3/6/34363841/monge_-_addition_-_pdes.pdf">G. Monge</a>, "On the integration of first-order partial difference equations in three variables," Supplement to <em>Application de l'Analyse a la Geometrie,</em>5th ed., Bachelier, Paris, 1850.</font></font><br /><br /><font size="4"><a href="/uploads/3/4/3/6/34363841/mayer_-_jacobi-hamilton_method.pdf">A. Mayer</a>, "On the Jacobi-Hamilton method for integrating first-order partial differential equations," Math. Ann. <strong>3</strong> (1871), 436-452.<br /><br /><a href="/uploads/3/4/3/6/34363841/morera_-_pfaff_method.pdf">G. Morera</a>, "The Pfaff method for integrating first-order partial differential equations," Rend. Reale Istituto Lombardo di scienze (2) <strong>16</strong> (1883), 637-644, 691-699.</font><br /><br /><font size="5"><font size="4"><a href="/uploads/3/4/3/6/34363841/biermann_-_pfaff_systems.pdf">O. Biermann</a>, "On <em>n</em> simultaneous differential equations of the form (...) = 0," Zeit. Math. Phys. <strong>30</strong> (1885), 234-244.</font></font><br /><br /><font size="4"><a href="/uploads/3/4/3/6/34363841/picard_-_lin_des_and_alg._groups.pdf"><font size="3">E. Picard</font></a>, "On linear differential equations and algebraic groups of transformations," Ann. fac. sci. Toulouse (1) <strong>1</strong> (1887), pp. A1-A15.<br /><br /><a href="/uploads/3/4/3/6/34363841/picard_-_galois_theory.pdf">E. Picard</a>, "On the groups of transformations of linear differential equations," Math. Ann. <strong>46</strong> (1895), 161-166.<br /><br /><a href="/uploads/3/4/3/6/34363841/picard_-_galois_theory_and_des.pdf">E. Picard</a>, "On the extension of Galois’s ideas to the theory of differential equations (Extract from a latter addressed to Mr. Klein)," Math. Ann. <strong>47</strong> (1896), 161-162.</font><br /><br /><br /><font size="5"><font size="4">P. Painleve, <em>Integrating the Differential Equations of Mechanics</em>, Hermann, Paris, 1895. <a href="/uploads/3/4/3/6/34363841/painleve_-_book_-_chap._1-12.pdf">Chaps. 1-12</a>, <a href="/uploads/3/4/3/6/34363841/painleve_-_book_-_chap._13-17.pdf">Chaps. 13-17</a>.</font></font><br /><br /><font size="5"><font size="4"><a href="/uploads/3/4/3/6/34363841/beudon_-_characteristic_surfaces.pdf">J. Beudon</a>, "On the characteristics of partial differential equations," Bull. Soc. Math. France <strong>25</strong> (1897), 108-120.<br /><br /><a href="/uploads/3/4/3/6/34363841/goursat_-_on_a_pde.pdf">E. Goursat</a>, "On a partial differential equation," Bull. Soc. Math. France <strong>25</strong> (1897), 36-48.</font></font><br /><br /><font size="4"><a href="/uploads/3/4/3/6/34363841/morera_-_canonical_equations.pdf">G. Morera</a>, "Canonical systems of total differential equations in the theory of groups of transformations," Atti Reale Accad. sci. di Torino <strong>38</strong> (1902-03), 940-953.<br /><br /><a href="/uploads/3/4/3/6/34363841/morera_-_iopdes_in_involution.pdf">G. Morera</a>, "On systems of first-order partial differential equations in involution," Rend. Reale Istituto Lombardo di scienze (2) <strong>36</strong> (1903), 775-790.</font><br /><br /><font size="5"><font size="4"><a href="/uploads/3/4/3/6/34363841/vessiot_-_odes.pdf">E. Vessiot</a>, "Ordinary differential equations. Elementary integration methods," <em>Encykl. math. Wiss., </em>B. G. Teubner, Leipzig, 1899-1916, Art. II A 4b., pp. 232-293.</font></font><br /><br /><font size="4"><a href="/uploads/3/4/3/6/34363841/weber_-_pdes.pdf">E. von Weber</a>, "Partial differential equations," <em>Encycl. math. Wiss.</em>, II A 5, ed. H. Burkhardt, W. Wirtinger, and R. Fricke, B. G. Teubner, Leipzig, 1899-1916.<br /><br /><a href="/uploads/3/4/3/6/34363841/bocher_-_bvps_for_odes.pdf">M. Bocher</a>, "Boundary-value problems for ordinary differential equations," from <em>Encyklopadie der mathematischen Wissenschaften</em>, II A 7.a, eds. H. Burkhardt, W. Wirtinger, and R. Fricke, B. G. Teubner, Leipzig, 1899-1916, pp. 437-463.
266</font><br /><br /><font size="4"><a href="/uploads/3/4/3/6/34363841/bocher_-_sturmian_theory.pdf">M. Bocher</a>, <em>Lectures on Sturm's Method in the Theory of Linear Differential Equations and their Modern Developments</em>, Gauthier-Villars, Paris, 1917.</font><br /><br /><font size="5"><font size="4"><a href="/uploads/3/4/3/6/34363841/levi-civita_-_characteristics.pdf">T. Levi-Civita</a>, <em>Characteristics of differential systems and wave propagation, </em>Alcan, Paris, 1932.</font></font><br /><br /><font size="4"><span> <span style="font-weight:bold">Contact transformations</span></span><br /><br /><font color="#000000"><a href="/uploads/3/4/3/6/34363841/mayer_-_lies_contact_transformations.pdf">A. Mayer</a>, "On Lie's contact transformations," Gott. Nachr. 13 (1874), 317-331.</font></font><br /><br /><font size="5"><font size="4"><a href="/uploads/3/4/3/6/34363841/mathieu_-_mathieu_transf.pdf">E. Mathieu</a>, "On the canonical differential equations of mechanics," J. pures appl. (2) <strong>19</strong> (1874), 265-306.</font></font><br /><br /><font size="4"><font color="#000000"><a href="/uploads/3/4/3/6/34363841/lie_-_contact_transformations.pdf">S. Lie</a>, "Foundations of an invariant theory of contact transformations," Math. Ann. <strong>8</strong> (1875), 215-303.</font></font><br /><br /><font size="5"><font size="4"><a href="/uploads/3/4/3/6/34363841/lie_-_pert._theory_and_cont._transf.pdf">S. Lie</a>, "Perturbation theory and contact transformations," Arch. for Math. Christiania <strong>2</strong> (1877), 129-156; <em>Gesammelte Abhandlungen</em>, art. XX, pp. 296-319.</font></font><br /><br /><font size="4"><span><a href="/uploads/3/4/3/6/34363841/lie_-_infinitesimal_contact_transformations_in_mechanics.pdf">S. Lie</a>, “The infinitesimal contact transformations of mechanics,” Berichte über die Verhandlunen Königlich Sächsisschen Gesellschaft der Wissenschaft zu Leipzig, Mathematische-Physische Classe, v. <strong>41</strong> (1889), 145-146.</span><br /><br /><a href="/uploads/3/4/3/6/34363841/lie_-_contrib._gen._transf._groups.pdf">S. Lie</a>, "Contributions to the general theory of transformations," Leip. Ber. (1895); Ges. Abh., v. VI, art XXIII.<br /><br /><a href="/uploads/3/4/3/6/34363841/lie_-_inf._contact_trans._of_optics.pdf">S. Lie</a>, "The infinitesimal contact transformations of optics," Leip. Ber. (1896); Ges. Abh., v. VI, art. XXIV.<br /><br /><a href="/uploads/3/4/3/6/34363841/vessiot_-_icts.pdf">E. Vess</a><a href="/uploads/3/4/3/6/34363841/vessiot_-_icts.pdf">iot</a>, “On the mechanical interpretation of infinitesimal contact transformations,” Bull. Soc. Math. de France <strong>34</strong> (1906), 230-269.<br /><br /><a href="/uploads/3/4/3/6/34363841/vessiot_-_multiplicities_and_calc._var..pdf">E. Vessiot</a>, “On the theory of multiplicities and the calculus of variations,” Bull. Soc. Math. France <strong>40</strong> (1912), 68-139.<br /><br /><a href="/uploads/3/4/3/6/34363841/engel_-_contact_transformations.pdf">F. Engel</a>, “Lie’s theory invariant of contact transformations and its extensions,” from the Jahresbericht der deutschen Mathematiker-Vereinigung, v. 5, H. Liebmann and<br />F. Engel, <em>Die Berührungstransformationen</em>, <em>Geschichte und Invariantentheorie</em>, B. G. Teubner, Leipzig, 1914.<br /><br /><a href="/uploads/3/4/3/6/34363841/liebmann_-_contact_transformations.pdf">H. Liebmann</a>, “The development of the theory of contact transformations,” from the Jahresbericht der deutschen Mathematiker-Vereinigung, v. 5, H. Liebmann and F. Engel, <em>Die Berührungstransformationen</em>, <em>Geschichte und Invariantentheorie</em>, B. G. Teubner, Leipzig, 1914.<br /><br /><a href="/uploads/3/4/3/6/34363841/schouten_-_contact_transf._i.pdf">J. A. Schouten</a>, "On the differential geometry of the group of contact transformations: I. Doubly-homogeneous treatment of contact transformations." Proc. Kon. Akad. Wet. Amsterdam <strong>40</strong> (1937), 100-107.<br /><br />.<a href="/uploads/3/4/3/6/34363841/schouten_-_contact_transf._ii.pdf">J. A. Schouten</a>, "On the differential geometry of the group of contact transformations: II. Normal form and main theorems for doubly-homogeneous contact transformations." Proc. Kon. Akad. Wet. Amsterdam <strong>40</strong> (1937), 236-245.<br /><br /><a href="/uploads/3/4/3/6/34363841/schouten_-_contact_transf._iii.pdf">J. A. Schouten</a>, "On the differential geometry of the group of contact transformations: III. Infinitesimal doubly-homogeneous contact transformations and their relationship to mechanics and electrodynamics." Proc. Kon. Akad. Wet. Amsterdam <strong>40</strong> (1937), 470-480.<br /><br /><a href="/uploads/3/4/3/6/34363841/schouten_-_contact_transf._iv.pdf">J. A. Schouten and J. Haantjes</a>, "On the differential geometry of the group of contact transformations: IV. Covariant derivatives in K2n-1." Proc. Kon. Akad. Wet. Amsterdam <strong>41</strong> (1938), 577-584.<br /><br /><a href="/uploads/3/4/3/6/34363841/hoelder_-_icts.pdf">E. Hölder</a>, “The infinitesimal contact transformations of the variational calculus,” Jber. Deutsche Math.-Verein <strong>49</strong> (1939), 162-178.<br /><br /> <strong>The Pfaff and Monge problems</strong><br /><br /><a href="/uploads/3/4/3/6/34363841/jacobi_-_pfaff_method_of_integration.pdf">C. G. J. Jacobi</a>, “On the Pfaffian method of integrating an ordinary linear differential equation in 2<em>n</em> variables by means of a system of <em>n</em> equations,” J. f. Reine und Angew. Math. <strong>2</strong> (1827), 347-357.</font><br /><br /><font size="5"><font size="4"><a href="/uploads/3/4/3/6/34363841/serret_-_solving_the_problem....pdf">J.-A. Serret</a>, "On the integration of the equation <em>dx</em>2 + <em>dy</em>2 + <em>dz</em>2 = <em>ds</em>2," J. math. pures appl. <strong>13</strong> (1848), 353-368.</font></font><br /><br /><font size="4"><a href="/uploads/3/4/3/6/34363841/bonnet_-_on_a_theorem_of_jacobi.pdf">O. Bonnet</a>, "On a theorem of Jacobi that relates to the integration of first-order partial difference equations," C. R. Acad. Sci. Paris <strong>45</strong> (1857), 581-585.</font><br /><font size="5"><font size="4"><a href="/uploads/3/4/3/6/34363841/mayer_-_unrestricted_integrable_systs.pdf">A. Mayer</a>, "On unrestricted integrable systems of linear total differential equations and the simultaneous integration of linear partial differential equations," Math. Ann. <strong>5</strong> (1872), 448-470.</font></font><br /><br /><font size="4"><a href="/uploads/3/4/3/6/34363841/mayer_-_lie_method_of_integration.pdf">A. Mayer</a>, “On an extension of Lie’s integration method,” Math. Ann. <strong>8</strong> (1875), 313-318.<br /><br /><a href="/uploads/3/4/3/6/34363841/mayer_-_weilers_method_of_integrating_pdes.pdf">A. Mayer</a><a href="/uploads/3/4/3/6/34363841/mayer_-_weilers_method_of_integrating_pdes.pdf">
266,</a> “On Weiler’s method of integrating partial differential equations of first order,” Math. Ann. <strong>9</strong> (1875), 347-370.<br /><br /><a href="/uploads/3/4/3/6/34363841/mayer_-_pfaff_problem.pdf">A. Mayer</a><a href="/uploads/3/4/3/6/34363841/mayer_-_pfaff_problem.pdf">,</a> “On Pfaff’s solution of the Pfaff problem.” Math. Ann. <strong>17</strong> (1880), 523-530.<br /><br /><font color="#000000">G. Darboux, "<a href="/uploads/3/4/3/6/34363841/darboux_-_pfaff_problem_i.pdf">On the Pfaff problem</a>," Bull. sci. math. astron. (2) <strong>6</strong> (1882), 14-36,<br /> "<a href="/uploads/3/4/3/6/34363841/darboux_-_pfaff_problem_ii.pdf">On the Pfaff problem (cont.)</a>," Bull. sci. math. astron. (2) <strong>6</strong> (1882), 49-62.</font><br /><br /><a href="/uploads/3/4/3/6/34363841/voss_-_geometrical_interp_of_eq._p__0..pdf">A. Voss</a>, "Geometrical interpretation of the differential equation <em>P dx </em>+ <em>Q dy</em> + <em>R dz</em> = 0," Math. Ann. <strong>16</strong> (1880), 556-559.<br /><br /><a href="/uploads/3/4/3/6/34363841/morera_-_pfaff_method.pdf">G. Morera</a>, "The Pfaff method for integrating first-order partial differential equations," Rend. Reale Istituto Lombardo di scienze (2) <strong>16</strong> (1883), 637-644, 691-699.</font><br /><br /><font size="4"><a href="/uploads/3/4/3/6/34363841/voss_-_on_the_theory_of_general_point-plane_systems.pdf">A. Voss</a>, "On the theory of general point-plane systems," Math. Ann. <strong>23</strong> (1884), 45-81.<br /><br /><font size="5"><font size="4"><a href="/uploads/3/4/3/6/34363841/darboux_-_monge_problem.pdf">G. Darboux</a>, "On the solution of the equation <em>dx</em>2 + <em>dy</em>2 + <em>dz</em>2 = <em>ds</em>2 and some analogous equations," J. Math. pure appl. (4) <strong>3</strong> (1887), 305-325.</font></font><br /><br /><a href="/uploads/3/4/3/6/34363841/engel_-_pfaff_systems_1.pdf">F. Engel</a>, "On the invariant theory of systems of Pfaff equations," Ber. Verh. Sachs. Ges. Wiss. <strong>41</strong> (1889), 157-176.<br /><br /><a href="/uploads/3/4/3/6/34363841/engel_-_pfaff_systems_2.pdf">F. Engel</a>, "On the invariant theory of systems of Pfaff equations (second communication)," Ber. Verh. Sachs. Ges. Wiss. <strong>42</strong> (1890), 192-207.</font><br /><br /><font size="5"><font size="4"><a href="/uploads/3/4/3/6/34363841/weber_-_pfaff_systems.pdf">E. von Weber</a>, "On the invariant theory of systems of PFAFF equations," Ber. Verh. Kon. Ges. Wiss. <strong>50</strong> (1898), 207-229.</font></font><br /><br /><font size="5"><font size="4"><a href="/uploads/3/4/3/6/34363841/lie_-_geom_of_monge_eq..pdf">S. Lie</a>, "On the geometry of a Monge equation," Ber. Verh. Kon.Ges. Wiss. Leipzig <strong>50</strong> (1898), 1-3.</font></font><br /><br /><font size="4"><font color="#000000"><a href="/uploads/3/4/3/6/34363841/cartan_-_on_the_pfaff_problem.pdf">E. Cartan</a>, "On certain differential expressions and the Pfaff problem," Ann. sci. de l'E.N.S. (3) <strong>16</strong> (1899), 239-332.</font></font><br /><br /><font size="4"><font color="#000000"><a href="/uploads/3/4/3/6/34363841/cartan_-_systems_of_total_diff_eqs.pdf">E. Cartan,</a> "On the integration of systems of total differential equations," Ann. sci. de l'E.N.S. (3) <strong>18</strong>
266 (1901), 241-311.</font><br /><br /><a href="/uploads/3/4/3/6/34363841/goursat_-_the_monge_problem.pdf">E. Goursat</a>, "On the Monge problem," Bull. Soc. Math. <strong>33</strong> (1905), 2101-210.<br /><br /><font size="5"><font size="4"><a href="/uploads/3/4/3/6/34363841/bottasso_-_the_monge_problem.pdf">M. Botasso</a>, "On a solution to the Monge problem that relates to the equation<em> f</em> (<em>dx</em>1, <em>dx</em>2, …, <em>dxn</em>) with variable coefficients," C. R. Acad. Sci. Paris <strong>140</strong> (1905), 1579-1582.<br /><br /><a href="/uploads/3/4/3/6/34363841/hilbert_-_class_of_a_diff_eq.pdf">D. Hilbert</a>, "On the concept of the class of a differential equation," Math. Ann. <strong>73</strong> (1913), 95-108.</font></font></font><br /><br /><font size="5"><font size="4"><a href="/uploads/3/4/3/6/34363841/cartan_-_underdetermined_systems.pdf">E. Cartan</a>, "On the integration of certain undetermined systems of differential equations," J. reine angew. Math. <strong>145</strong> (1915), 86-91.</font></font><br /><br /><font size="4"><font size="5"><font size="4"><a href="/uploads/3/4/3/6/34363841/vessiot_-_new_theory_of_integration.pdf">E. Vessiot</a>, <font size="5"><font size="4">"On a new theory of general integration problems," Bull. Soc. math. France <strong>52</strong> (1924), 336-395.<br /><br /><a href="/uploads/3/4/3/6/34363841/vessiot_-_sheaves_of_inf_trans.pdf">E. Vessiot</a>, "On the integration of sheaves of infinitesimal transformations in the case where the degree of the derived sheaf is <em>n</em> + 1, if the degree of the sheaf is <em>n</em>," Ann. sci. de l'E.N.S. (3) <strong>45</strong> (1928), 189-253.</font></font><br /><br /><a href="/uploads/3/4/3/6/34363841/goursat_-_monge_prob_sev_var.pdf">E. Goursat</a>, "On a Monge problem with several independent variables," C. R. Acad. Sci. Paris <strong>186</strong> (1928), 1469-1472.</font></font><br /><br /><font color="#000000"><a href="/uploads/3/4/3/6/34363841/zervos_-_the_monge_problem.pdf" target="_blank">P. Zervos</a>, "The Monge Problem," Mem. Math. Sci., fasc. LIII, Gauthier-VIllars, Paris, 1932.</font><br /><br /><font color="#000000"><a href="/uploads/3/4/3/6/34363841/kaehler_-_systems_of_diff_eqs.pdf">E. Kaehler</a>, <em>Introduction to the theory of systems of differential equations</em>, B. G. Teubner, Leipzig, 1934.</font><br /><br /><a href="/uploads/3/4/3/6/34363841/levi-civita_-_pfaff_syst.pdf">T. Levi-Civita</a>, "On the stationary solutions of Pfaffian systems," Rend. Acc. Lincei (6) <strong>19</strong> (1934), Nota I, pp. 261-267; Nota II, pp. 470-477.<br /><br /> <span style="font-weight:bold"><span>Backlund transformations</span></span><br /><br /><span><a href="/uploads/3/4/3/6/34363841/backlund_-_on_surface_transformations.pdf">A. V. Backlund</a>, "On surface transformations," Math. Ann. 9 (1875), 297-320.</span><br /><br /><font color="#000000"><a href="/uploads/3/4/3/6/34363841/backlund_-_on_the_theory_of_surface_transformations.pdf">A. V. Backlund</a>, "On the theory of surface transformations," Math. Ann. <strong>19</strong> (1882), 387-422.</font><br /><br /><font color="#000000"><a href="/uploads/3/4/3/6/34363841/clairin_-_backlund_transformations.pdf">J. Clairin</a>, "On the Backlund transformations," Ann. sci. de l'E.N.S. (3) <strong>19</strong> (1902), 3-63.</font><br /><br /><span><a href="/uploads/3/4/3/6/34363841/goursat_-_the_backlund_problem.pdf">E. Goursat</a>, "The Backlund Problem,: Mem. Sci. Math., fasc. VI, Gauthier-Villars, Paris, 1925.</span><br /><br /><span> <em>Book:Selected papers on geodesic fields, </em><span style="font-weight:bold">translated and edited by D. H. Delphenich, 2011</span><br /><br /> (File consists of two parts: <a href="/uploads/3/4/3/6/34363841/geodesic_fields_-_pt._1.pdf">I</a> and <a href="/uploads/3/4/3/6/34363841/geodesic_fields_-_pt._2.pdf">II</a>)<br /><br /> <span style="font-weight:bold">Contents</span><br /><br />A. Clebsch, “On the second variation of multiple integrals,” J. de Crelle, <strong>56</strong> (1859), 122-149.<br /><br />J. Hadamard, “On a question in the calculus of variations,” Bull. Soc. Math. de France <strong>30</strong> (1902), 253-256.<br /><br />J. Hadamard, “On some questions in the calculus of variations,” Bull. Soc. Math. de France <strong>33</strong> (1905), 73-80.<br /><br />D. Hilbert, “On the calculus of variations,” Math. Ann. <strong>69</strong> (1906), 351-370; Ges. Abh. v. III, pp. 38-55.<br /><br />C. Carathéodory, “On the calculus of variations for multiple integrals,” Acta Szeged <strong>4</strong> (1929), 193-216.<br /><br />H. Weyl, “Observations on Hilbert’s independence problem and Born’s quantization of field equations,” Phys. Rev. <strong>46</strong> (1934), 505-508.<br /><br />H. Weyl, “Geodesic fields in the calculus of variations for multiple integrals,” Ann. Math. <strong>36</strong> (1935), 607-629.<br /><br />H. Boerner, “On extremals and geodesic fields in the calculus of variations for multiple integrals,” Math. Ann. <strong>112</strong> (1936), 187-220.<br /><br />J. Géhéniau, “Generalization of the Weierstrass excess formula, as deduced from the Hilbert-de Donder independence theorem,”
266 Bull. Acad. Roy. Belg. <strong>21</strong> (1935), pp. 385 and 504.<br /><br />Th. Lepage, “On the geodesic fields of the calculus of variations,” Bull. Acad. Roy. Belg. <strong>22</strong> (1936), 716-729.<br /><br />R. Debever, “Mayer fields in the calculus of variations of multiple integrals,” Bull. Acad. Roy. Belg. <strong>23</strong> (1937), 809-815.<br /><br />E. Hölder,”The infinitesimal contact transformation of the variational calculus,” Jber. d. deutsche Math.-Verein. <strong>49</strong> (1939), 162-178.<br /><br />H. Boerner, “Calculus of variations from Stokes’s theorem,” Math. Zeit. <strong>46</strong> (1940), 709-719.<br /><br />H. Boerner, “On the Legendre condition and field theory in the calculus of variations for multiple integrals,” Math. Zeit. <strong>46</strong> (1940), 720-742.<br /><br />Th. Lepage, “On the geodesic fields of multiple integrals,” Bull. Acad. Roy. Belg. <strong>27</strong> (1941), 27-46.<br /><br />Th. Lepage, “Stationary fields, geodesic fields, and integrable forms,” Bull. Acad. Roy. Belg. <strong>28</strong> (1942), 73-94.<br /><br />L. van Hove, “On the de Donder-Weyl fields and their construction by the method of characteristics,” Bull. Roy. Acad. Belg. <strong>31</strong> (1945), 278-285.<br /><br />L. van Hove, “On the Carathéodory fields and their construction by the method of characteristics,” Bull. Roy. Acad. Belg. <strong>31</strong> (1945), 625-638.<br /><br />P. Dedecker, “Calculus of variations, differential forms, and geodesic fields,” Coll. Intl. du C.N.R.S., Strasbourg, 1953.</span></font></div> 267</div> 268 269 <div class="clear"></div> 270 </div> 271 </div> 272 <div id="footer"> 273 <div class='wsite-elements wsite-footer'> 274<div><div class="wsite-multicol"><div class="wsite-multicol-table-wrap" style="margin:0 -15px;"> 275 <table class="wsite-multicol-table"> 276 <tbody class="wsite-multicol-tbody"> 277 <tr class="wsite-multicol-tr"> 278 <td class="wsite-multicol-col" style="width:50%; padding:0 15px;"> 279 280 281 282<div class="wsite-spacer" style="height:50px;"></div> 283 284 285 286 </td> <td class="wsite-multicol-col" style="width:50%; padding:0 15px;"> 287 288 289 290<div class="wsite-spacer" style="height:50px;"></div> 291 292 293 294 </td> </tr> 295 </tbody> 296 </table> 297</div></div></div> 298 299<div class="paragraph"><a href='http://www.ipage.com/' target='_blank'>Web Hosting</a> by iPage</div></div> 300 301 <div class="clear"></div> 302 </div> 303 </div> 304</div> 305 <div id="customer-accounts-app"></div> 306
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