PUBLICATIONS

[1] L. Corgnier, A. D'Adda & A. Prástaro, Regge pole vs.resonance duality and boostrap calculations, Nuovo Cimento 57A(4)(1968), 881-885. DOI: 10.1007/BF02751394.

[2] A. Prástaro & P. Parrini, A mathematical model for spinning molten polymer and conditions of spinning, Tex. Res. J. 45(2)(1975), 118-127. DOI: 10.1177/004051757504500206.

[3] A. Prástaro & P. Parrini, Ein mathematisches Modell für das Verspinnen geschmolzener Polymerer und für die Spinnbedingungen, Colloid & Polymer Science 255(6)(1977), 624-633. DOI: 10.1007/BF01549886.

[4] A. Prástaro, A mathematical model for spinning viscoelastic molten polymers, Riv. Mat. Univ. Parma 4(2)(1976), 295-313. Zbl 0375.73034.

[5] A. Prástaro, Modello matematico sulla formazione della melt-fracture nei polimeri fusi, Quad. Ing. Chim. Ital. Suppl. 13(3-4)(1977), 37-44. (Chemical Abstracts: Collective Index 2000.)

[6] A. Prástaro, Geometrodynamics of some non-relativistic incompressible fluids, Stochastica 3(2)(1979), 15-31. MR0556645(81b:76014); Zbl 0427.76003.

[7] A. Prástaro, Spazi derivativi e fisica del continuo in relativitá generale, Atti Accad. Sci. Torino Suppl. 114(1980/81), 289-292. MR0670263(83h:58013).

[8] A. Prástaro, On the general structure of continuum physics.I: Derivative spaces, Boll. Unione Mat. Ital. (5)17-B(1980), 704-726. MR0580551(81m:73012); Zbl 0438.58004.

[9] A. Prástaro, On the general structure of continuum physics.II: Differential operators, Boll. Unione Mat. Ital. (5)S.-FM(1981), 69-106. MR0641760(83c:73002a); Zbl 0478.58004.

[10] A. Prástaro, On the general structure of continuum physics.III: The physical picture, Boll. Unione Mat. Ital. (5)S.-FM(1981), 107-129. MR0641761(83c:73002b); Zbl 0478.58005.

[11] A. Prástaro, On the intrinsic expression of Euler-Lagrange operator, Boll. Unione Mat. Ital. (5)18-A(1981), 411-416. MR0633674(842:58049); Zbl 0471.58012.

[12] A. Prástaro, Dynamic conservation laws and the Korteweg-De Vries equation, Atti convegno su onde e stabilità nei mezzi continui, Catania 1981, Quaderni CNR-GNFM, Catania (1982), 272-274.

[13] A. Prástaro, Spinor super bundles of geometric objects on spinG space-time structures, Boll. Unione Mat. Ital. (6)1-B(1982), 1015-1028. MR0683489(84c:53036); Zbl 0501.53023.

[14] A. Prástaro, Gauge geometrodynamics, Riv. Nuovo Cimento 5(4) (1982), 1-122. DOI: 10.1007/BF02740593 MR0693882(84e:83045); Zbl 0695.58028.

[15] A. Prástaro, Geometry and existence theorems for incompressible fluids, Geometrodynamics Proceedings 1983, A. Prástaro (ed.), Pitagora Ed., Bologna (1984), 65-90. MR0823718(87g:58034).

[16] A. Prástaro, Geometrodynamics of non-relativistic continuous media.I: Space-time structures, Rend. Sem. Mat. Univ. Politec. Torino 40(2)(1982), 89-117. MR0724201(85e:53095); Zbl 0525.53036.

[17] A. Prástaro, Geometrodynamics of non-relativistic continuous media.II: Dynamic and constitutive structures, Rend. Sem. Mat. Univ. Politec. Torino 43(1)(1985), 89-116. MR08559851(87m:53091); Zbl 0609.53042.

[18] A. Prástaro, A geometric point of view for the quantization of non-linear field theories, Atti VI Convegno Nazionale di Relatività Generale e Fisica della Gravitazione, Firenze 1984 (R. Fabbri and M. Modugno eds.), Pitagora Ed., Bologna (1986), 289-292.

[19] A. Prástaro, Dynamic conservation laws, Geometrodynamics Proceedings 1985, A. Prástaro (ed.), World Scientific Publishing, Singapore (1985), 283-420. MR0825784(87g:53109); Zbl 0645.58038. [About ''Geometrodynamics'' see also Wikipedia.]

[20] A. Prástaro & T. Regge, The group structure of supergravity, Ann. Inst. H. Poincaré Phys. Thèor. 44(1)(1986), 39-89. MR0834019(87i:83104); Zbl 0588.53066.

[21] V. Marino & A. Prástaro, On the geometric generalization of the Noether theorem,, Lecture Notes in Math. 1209, Springer-Verlag, Berlin (1986), 222-234. DOI: 10.1007/BFb0076634. MR0863759(88j:58142); Zbl 0603.53058.

[22] A. Prástaro, Quantum gravity and group model gauge theory, Journées Relativistes, Toulouse, France 1986, A. Crumeyrolle (ed.), Univ. Paul Sabatier Toulouse (1986), 213-222. [ Recent results on the quantum geometrodynamics. Proceedings General Relativity and Gravitation, vol.1. July, 4-9, 1983, Padova - Italy. (B. Bertotti, F. de Felice & A. Pascolini eds.) CNR - Roma (1983), 1145.]

[23] V. Marino & A. Prástaro, On the conservation laws of PDE's, Rep. Math. Phys. 26(2)(1987/8), 211-225. DOI: 10.1016/0034-4877(88)90024-9. MR0991720(91b:58097); Zbl 0695.58029.

[24] A. Prástaro, On the quantization of Newton equation, Atti IX Congresso AIMETA, Bari 1988, AIMETA(1988), 13-16.

[25] A. Prástaro, Wholly cohomological PDE's, International Conference on Differential Geometry and Applications, Dubrovnick (Yu), 1988, Univ. Beograd & Univ. Novi Sad (1989), 305-314. MR1040078(91c:58151); Zbl 0695.58030.

[26] A. Prástaro, Geometry of quantized PDE's, Differential Geometry and Applications, J. Janyska & D. Krupka (eds.), World Scientific Publishing, NJ, (1990), 392-404. MR1062046(91m:58175); Zbl 0796.35006.

[27] A. Prástaro, , On the singular solutions of PDE's, Atti X Congresso Nazionale AIMETA, Pisa 1990, AIMETA(1990), 17-20.

[28] A. Prástaro, Cobordism of PDE's, Boll. Unione Mat. Ital. (7)5-B(1991), 977-1001. MR1146783(93a:57037); Zbl 0746.57015.

[29] A. Prástaro, Quantum geometry of PDE's, Rep. Math. Phys. 30(3) (1991), 273-354. DOI: 10.1016/0034-4877(91)90063-S. MR1198655(94e:58150); Zbl 0771.58024.

[30] A. Prástaro, Geometry of super PDE's, Geometry of Partial Differential Equations, A. Prástaro & Th. M. Rassias (eds.), World Scientific Publishing, River Edge, NJ, (1994), 259-315. MR1340222(96g:58025); Zbl 0879.58080.

[31] V. Lychagin & A. Prástaro, Singularities for Cauchy data,characteristics, cocharacteristics and integral cobordism, Differential Geom. Appl. 4(3)(1994), 283-300. DOI: 10.1016/0926-2245(94)00017-4. MR1299399(96b:58122); Zbl 0808.58039.

[32] A. Prástaro & Th. M. Rassias, On a geometric approach to an equation of J. D'Alembert, Geometry of Partial Differential Equations, A. Prástaro & Th. M. Rassias (eds.), World Scientific Publishing, River Edge, NJ, (1994), 316-322. MR1340223(96g:35131); Zbl 0879.35038.

[33] A. Prástaro, Th. M. Rassias & J. Šimša, Geometry of the J. D'Alembert equation, in Finite Sums Decompositions in Mathematical Analysis, Th. M. Rassias & J. Šimša (eds.), J. Wiley (1995), 133-159. MR 96k:26006; Zbl 0859.26005.

[34] A. Prástaro & Th. M. Rassias, A geometric approach to an equation of J. D'Alembert, Proc. Amer. Math. Soc. 123(5)(1995), 1597-1606. DOI: 10.2307/2161153.MR1232143(95f:58007); Zbl 0839.58068.

[35] A. Prástaro, Geometry of quantized super PDE's, The Interplay Between Differential Geometry and Differential Equations, V. Lychagin (ed.), Amer. Math. Soc. Transl. 2/167(1995), 165-192. MR1343988(96d:58159); Zbl 0844.58012.

[36] A. Prástaro, Quantum geometry of super PDE's, Rep. Math. Phys. 37(1)(1996), 23-140. DOI: 10.1016/0034-4877(96)88921-X. MR1394861(97e:58235); Zbl 0887.58064.

[37] A. Prástaro, (Co)bordism in PDEs and quantum PDEs, Rep. Math. Phys. 38(3)(1996), 443-455. DOI: 10.1016/S0034-4877(97)84894-X. MR1437641(97m:58004); Zbl 0885.58094.

[38] A. Prástaro, Quantum and integral (co)bordisms in partial differential equations, Acta Appl. Math. 51(3) (1998), 243-302. DOI: 10.1023/A:1005986024130. MR1625961(99d:58183); Zbl 0924.58103.

[39] A. Prástaro, Quantum and integral bordism groups in the Navier-Stokes equation. New Developments in Differential Geometry, Budapest 1996, J. Szenthe (ed.), Kluwer Academic Publishers, Dordrecht (1998), 343-360. MR1670467(2000h:58065); Zbl 0937.35133.

[40] A. Prástaro & Th. M. Rassias, On the set of solutions of the generalized d'Alembert equation, C. R. Acad. Sci. Paris 328(I-5)(1999), 389-394. DOI: 10.1016/S0764-4442(99)80177-3. MR1678135(2000a:3508); Zbl 0931.35031.

[41] A. Prástaro & Th. M. Rassias, A geometric approach of the generalized d'Alembert equation, J. Comput. Appl. Math. 113(1-2)(2000), 93-122. DOI: 10.1016/S0377-0427(99)00247-2. MR1735816(2001c:58079); Zbl 0936.35011.

[42] A. Prástaro, (Co)bordism groups in PDEs, Acta Appl. Math. 59(2) (1999), 111-201. DOI: 10.1023/A:1006346916360. MR1741657(2001m:58046); Zbl 0949.35011.

[43] A. Prástaro, (Co)bordism groups in quantum PDEs, Acta Appl. Math. 64(2)(2000), 111-217. DOI: 10.1023/A:1010685903329. MR1826643(2002e:58037); Zbl 0978.58016.

[44] A. Prástaro, Theorems of existence of local and global solutions of PDEs in the category of noncommutative quaternionic manifolds, Quaternionic Structures in Mathematics and Physics, S. Marchiafava, P. Piccinni & M. Pontecorvo (eds.), World Scientific Publishing, Singapore (2001), 329-337. MR1848673(2002f:58007); Zbl 0978.81038.

[45] A. Prástaro, Local and global solutions of the Navier-Stokes equation, Steps in Differential Geometry, Proceedings of the Colloquium on Differential Geometry, 25-30 July, 2000, Debrecen, Hungary, L. Kozma, P. T. Nagy & L. Tomassy (eds.), Univ. Debrecen (2001), 263-271. MR1859305(2002d:53008); Zbl 0983.3510.

[46] A. Prástaro, Navier-Stokes equation: Global existence and uniqueness. (A geometric way to solve the ''(NS)-problem''.), published as: Addendum I: Bordism Groups and the (NS)-Problem, in Quantized Partial Differential Equations, World Scientific Publishing, River Edge, NJ, (2004), 377-434.

[47] A. Prástaro & Th. M. Rassias, A geometric approach to a noncommutative generalized d'Alembert equation, C. R. Acad. Sc. Paris 330(I-7)(2000), 545-550. DOI: 10.1016/S0764-4442(00)00238-X. MR1760436(2001d:58026); Zbl 0966.35105.

[48] A. Prástaro & Th. M. Rassias, Results on the J. d'Alembert equation, Ann. Acad. Paed. Cracoviensis. Studia Math. (4)1(2001)117-128. Zbl 1137.58308.

[49] A. Prástaro, Quantum manifolds and integral (co)bordism groups in quantum partial differential equations, Nonlinear Anal. Theory Methods Appl. 47/4(2001), 2609-2620. DOI: 10.1016/S0362-546X(01)00382-0. MR1972386(2004c:35343); Zbl 1042.35610.

[50] A. Prástaro, Dirac quantization, Encyclopaedia Math. Suppl.III., M. Hazwinkel (ed.), Kluwer Academic Publishers, Dordrecht (2002), 127-129. DOI: 10.1007/978-0-306-48373-8.

[51] A. Prástaro, Integral bordisms and Green kernels in PDEs, Cubo 4(2)(2002), 316-370. MR1928829(2003g:58056).

[52] A. Prástaro & Th. M. Rassias, On the Ulam stability in geometry of PDE's, Functional Equations Inequality and Applications, Th. M. Rassias (ed.), Kluwer Academic Publishers, Dordrecht (2003), 139-147. MR2042561(2004k:58034); Zbl 1059.39024.

[53] A. Prástaro & Th. M. Rassias, Ulam stability in geometry of PDE's, Nonlinear Funct. Anal. Appl. 8(2)(2003), 259-278. MR1994707(2004g:35179); Zbl 1906.39028.

[54] A. Prástaro, Quantum super Yang-Mills equations: Global existence and mass-gap, Dynamic Syst. Appl. 4(2004), 227-232. (Eds. G. S. Ladde, N. G. Madhin & M. Sambandham), Dynamic Publishers, Inc., Atlanta, USA. ISBN:1-890888-00-1. MR2117787(2005m:81203); Zbl 1067.81097.

[55] A. Prástaro, Geometry of PDE's. I: Integral bordism groups in PDE's, J. Math. Anal. Appl. 319(2)(2006), 547-566. DOI: 10.1016/j.jmaa.2005.06.044. MR2227923(2007d:58031); Zbl 1100.35007.

[56] A. Prástaro, Geometry of PDE's. II: Variational PDE's and integral bordism groups, J. Math. Anal. Appl. 321(2)(2006), 930-948.DOI: 10.1016/j.jmaa.2005.08.037. MR2241487(2007d:58032); Zbl 1160.58301.

[57] A. Prástaro, Conservation laws in quantum super PDE's, Proceedings of the Conference on Differential & Difference Equations and Applications (eds. R. P. Agarwal & K. Perera), Hindawi Publishing Corporation, New York (2006), 943-952. MR2309427(2008b:58041); Zbl 1131.35381.

[58] A. Prástaro, (Co)bordism groups in quantum super PDE's. I: Quantum supermanifolds, Nonlinear Anal. Real World Appl. 8(2)(2007), 505-536. DOI: 10.1016/j.nonrwa.2005.12.008. MR2289563(2008j:58052); Zbl 1152.58313.

[59] A. Prástaro, (Co)bordism groups in quantum super PDE's. II: Quantum super PDE's, Nonlinear Anal. Real World Appl. 8(2)(2007), 480-504. DOI: 10.1016/j.nonrwa.2005.12.007. MR2289562(2008j:58053); Zbl 1152.58312.

[60] A. Prástaro, (Co)bordism groups in quantum super PDE's. III: Quantum super Yang-Mills equations, Nonlinear Anal. Real World Appl. 8(2)(2007), 447-479. DOI: 10.1016/j.nonrwa.2005.12.006. MR2289561(2009b:58082); Zbl 1152.58311.

[61] R. Agarwal & A. Prástaro, Geometry of PDE's. III(I): Webs on PDE's and integral bordism groups.The general theory, Adv. Math. Sci. Appl. 17(1)(2007), 239-266. MR237378(2009j:58026); Zbl 1143.53017.

[62] R. Agarwal & A. Prástaro, Geometry of PDE's. III(II): Webs on PDE's and integral bordism groups. Applications to Riemannian geometry PDE's, Adv. Math. Sci. Appl. 17(1)(2007), 267-285. MR2337379(2009j:58027); Zbl 1140.53005.

[63] A. Prástaro, Geometry of PDE's. IV: Navier-Stokes equation and integral bordism groups, J. Math. Anal. Appl. 338(2)(2008), 1140-1151. DOI: 10.1016/j.jmaa.2007.06.009. MR2386488(2009j:58028); Zbl 1135.35064.

[64] A. Prástaro, (Un)stability and bordism groups in PDE's, Banach J. Math. Anal. 1(1)(2007), 139-147. MR2350203(2009e:58036); Zbl 1130.58014.

[65] A. Prástaro, Extended crystal PDE's stability.I: The general theory, Math. Comput. Modelling 49(9-10)(2009), 1759-1780. DOI: 10.1016/j.mcm.2008.07.020.. Zbl 1171.35322.

[66] A. Prástaro, Extended crystal PDE's stability.II: The extended crystal MHD-PDE's, Math. Comput. Modelling 49(9-10)(2009), 1781-1801. DOI: 10.1016/j.mcm.2008.07.021.. Zbl 1171.35323.

[67] A. Prástaro, On the extended crystal PDE's stability.I: The n-d'Alembert extended crystal PDE's, Appl. Math. Comput. 204(1)(2008), 63-69. DOI: 10.1016/j.amc.2008.05.141. MR2458340(2010h:58058); Zbl 1161.35054.

[68] A. Prástaro, On the extended crystal PDE's stability.II: Entropy-regular-solutions in MHD-PDE's, Appl. Math. Comput. 204(1)(2008), 82-89. DOI: 10.1016/j.amc.2008.05.142. MR2458342(2010h:58059); Zbl 1161.35462.

[69] A. Prástaro, On quantum black-hole solutions of quantum super Yang-Mills equations, Dynamic Syst. Appl. 5(2008), 407-414. (Eds. G. S. Ladde, N. G. Madhin, C. Peng & M. Sambandham), Dynamic Publishers, Inc., Atlanta, USA. ISBN: 1-890888-01-6. MR2468173(2010g:83040).

[70] A. Prástaro, Surgery and bordism groups in quantum partial differential equations.I: The quantum Poincaré conjecture, Nonlinear Anal. Theory Methods Appl. 71(12)(2009), 502-525. DOI: 10.1016/j.na.2008.11.077. MR2671857.

[71] A. Prástaro, Surgery and bordism groups in quantum partial differential equations.II: Variational quantum PDE's, Nonlinear Anal. Theory Methods Appl. 71(12)(2009), 526-549. DOI: 10.1016/j.na.2008.10.063. MR2671858.

[72] R. P. Agarwal & A. Prástaro, Singular PDE's geometry and boundary value problems, J. Nonlinear Conv. Anal. 9(3)(2008), 417-460. MR2478974(2010b:58030); Zbl 1171.35006.

[73] R. P. Agarwal & A. Prástaro, On singular PDE's geometry and boundary value problems, Appl. Anal. 88(8)(2009), 1115-1131. DOI: 10.1080/00036810902943612. MR2568427(2010k:58033); Zbl 1180.35012.

[74] A. Prástaro, Extended crystal PDE's, arXiv: 0811.3693[math.AT].

[75] A. Prástaro, Quantum extended crystal PDE's, Nonlinear Studies 18(3)(2011), 447-485. arXiv: 1105.0166[math.AT].

[76] A. Prástaro, Quantum extended crystal super PDE's, arXiv: 0906.1363[math.AT].

[77] A. Prástaro, Exotic heat PDE's, Commun. Math. Anal. 10(1)(2011), 64-81. arXiv: 1006.4483[math.GT].

[78] A. Prástaro, Exotic heat PDE's.II. Essays in Mathematics and its Applications. (Dedicated to Stephen Smale.) (Eds. P. M. Pardalos and Th. M. Rassias.) Springer, New York, (to appear). arXiv: 1009.1176[math.AT].

[79] A. Prástaro, Exotic n-d'Alembert PDE's and stability. Stability, Approximation and Inequalities. (Dedicated to Themistocles M. Rassias for his 60th birthday.) (Eds. G. Georgiev (USA), P. Pardalos (USA) and H. M. Srivastava (Canada)), Springer, New York, (to appear). arXiv: 1011.0081[math.AT].

[80] A. Prástaro, Exotic PDE's. arXiv: 1101.0283[math.AT].

[81] A. Prástaro, Quantum exotic PDE's. arXiv: 1106.0862[math.AT].

MONOGRAPHS AND TEXTS

[82] A. Prástaro, Geometry of PDEs and Mechanics, World Scientific Publishing, River Edge, NJ, 1996, 760 pp. ISBN 9810225202. MR1412798(98e:55182); Zbl 0866.35007.

 This book gives the theory of partial differential equations (PDE's) from a modern geometric point of view so that PDE's can be characterized by using either techniques of differential geometry or algebraic topology. This allows us to recognize the richness of the structure of PDE's. It presents for the first time, a geometric theory of noncommutative (quantum) PDE's and gives a general application of this theory to quantum field theory and quantum supergravity.

CONTENTS. Algebraic Geometry. Differential Equations (PDEs). Mechanics. Continuum Mechanics. Quantum Field Theory. Geometry of Quantum PDEs.

[83] A. Prástaro, Elementi di Meccanica Razionale, Edizione 2010, Aracne Editrice, Roma, 2010, 446 pp. ISBN 978-88-548-3601-3.

 This monography is addressed to Italian university students in Mathematics, Physics and Engineering. It develops with a modern geometric language the methods of classical mechanics and geometry of (partial) differential equations. The presentation, even if elementary, gives the actual mathematics situation in classical mechanics.

INDICE. Algebra. Equazioni Differenziali. Connessioni Differenziali. Spazio-tempo Galileiano. Dinamica. Equazioni Cardianali. Equazioni di Lagrange. Dinamica dei Sistemi Rigidi. Esercizi. Meccanica dei Continui. Reottica. Relatività Ristretta. Esercizi Complementari: Esercizi di Geometria; Esercizi di Meccanica dei Sistemi Discreti o Rigidi; Esercizi di Meccanica dei Sistemi Continui.

[84] A. Prástaro, Quantized Partial Differential Equations, World Scientific Publishing, River Edge, NJ, 2004, 500 pp. ISBN 981-238-764-1. MR2086084(2005f:58036); Zbl 1067.58022.

 This monography presents, for the first time, a systematic formulation of the geometric theory of noncommutative PDE's which is suitable enough to be used for a mathematical description of quantum dynamics and quantum field theory. A geometric theory of supersymmetric quantum PDE's is also considepink, in order to describe quantum supergravity. Covariant and canonical quantizations of (super) PDE's are shown to be founded on the geometric theory of PDE's and to produce quantum (super) PDE's by means of functors from the category of commutative (super) PDE's to the category of quantum (super) PDE's. Global properties of solutions to (super) (commutative) PDE's are obtained by means of their integral bordism groups. In particular the (quantum) Navier-Stokes problem and the (quantum)Yang-Mills problem are considepink showing that their solutions can be obtained in the framework of the integral bordism groups for such equations.

CONTENTS. Quantized PDE's I: Noncommutative Manifolds: Algebraic Topology; Quantum Algebras; Quantum Manifolds; Quantum Supermanifolds. Quantized PDE's II: Noncommutative PDE's: Quantum PDE's; The Quantum Navier-Stokes Equation; Quantum Super PDE's; The Quantum Super Yang-Mills Equations. Quantized PDE's III: Quantizations of Commutative PDE's: Integral (Co)bordism groups in PDE's; Algebraic Geometry of PDE's; Spectral Measures of PDE's; Quantizations of PDE's; Covariant and Canonical Quantizations of PDE's. Addendum I: Bordism groups and the (NS)-problem. Addendum II: Bordism groups and Variational PDE's.

BOOKS (EDITOR AND COAUTHOR)

[85] A. Prástaro, Geometrodynamics Proceedings 1983, Pitagora Ed., Bologna 1984. ISBN 88-371-0286-0. MR0823711(86m:58007).

 CONTENTS. S. Benenti, The Hamilton-Jacobi Equation for a Hamiltonian Action. A. Crumeyrolle, Twisteurs sans Twisteurs. H. P. Kunzle, General Covariance and Minimal Gravitational Coupling in Newtonian Space-Time. J. M. Masqué, Canonical Cartan Equation for Higher Order Variational Problems. J. P. Pommaret, Bäcklund Problem and Group Theory. J. P. Pommaret, Group Structure of Non-linear Field Theories. A. Prástaro, Geometry and Existence Theorems for Incompressible Fluids. W. M. Tulczyjew, Relativistic Hydrodynamics as a Symplectic Field Theory.

[86] A. Prástaro, Geometrodynamics Proceedings 1985, World Scientific Publishing, Singapore 1985. ISBN 9971-978-63-6. MR0825784(86m:58008); Zbl 0637.00006.

 CONTENTS. S. Benenti & W. M. Tulczyiew, A Geometrical Interpretation of the 1-cocycles of a Lie Group. Y. Choquet-Bruhat, Supermanifolds and Supergravities. A. Crumeyrolle, Self-dual Yang-Mills Fields and the Penrose Transform in the Spinor Context. J. Czyz, On Smooth and Analytic Functions in Gauge Field Theory. G. F. Dell'Antonio, An Application of Topological Methods to the Study of Periodic Solutions of Hamiltonian Systems. L. Dabrowski, Introducing Spinors, Isospinors, etc. in Globally Nontrivial Space-times. H. Goldschmidt, The Radon Transform on Compact Symmetric Spaces. J. Kijowski, Unconstrained Degrees of Freedom of Gravitational Field and the Positivity of Gravitational Energy. M. Iosifescu & H. Scutaru, Polynomial Identities Satisfied by Realizations of Lie Algebras. G. Marmo, Free Motions in Multidimensional Universes. T. Milnor, Harmonically Immersed Lorentz Surfaces. M. Mintchev, On the Symmetries Properties of Constrained Hamiltonian Systems. J. M. Masqué, On a Property of Higher Order Poincaré-Cartan Forms in the Constructive Approach . J. E. Nelson & T. Regge, Covariant Canonical Formalism for Gravity Theories. A. Nijenhuis, Invariant Differentiation Techniques. A. Pérez-Rendòn, A Utiyama Type Theorem in the C-K-S Gauge Approach to Gravity I. A. Prástaro, Dynamic Conservation Laws. M. Puta, The Doulbeault-Kostant Complex and Geometric Quantization. A. Smolski, Symplectic Origin of Some Properties of Generally Covariant Field Theories. S. Sternberg, Symplectic Scattering Theory.

[87] A. Prástaro & Th. M. Rassias, Geometry in Partial Differential Equations, World Scientific Publishing, River Edge, NJ, 1994. ISBN 978-981-02-1407-4. MR1340208(96a:58003); Zbl 0867.00017.

 CONTENTS. F. Bethuel & J.-M. Chidaglia, Some Applications of the Corea Formula to Partial Differential Equations. F. Bethuel & O. Rey, Large Solutions for the Equation of Surfaces of Prescribed Mean Curvature. M. Bialy & L. Polterovich, Optical Hamiltonian Functions. M. Craioveanu, M. Puta & Th. M. Rassias, On the Geometry of the Hodge-de Rham Laplace Operator. J. Donato, Minimal Surfaces in Economic Theory. B. Doubrov & A. Hushner, The Morimoto Problem. P. B. Giley, Asymptotic Expansions in Spectral Geometry. I. S. Krasil'shchik & P. H. M. Kersten, Deformations and Recursion Operators for Evolution Equations. B. A. Kupershmidt, Geometric Hamiltonian Forms for the Kadomtsev-Petviashvili and Zabolotskaya-Khokhlov Equations. A. Kushner, Classification of Mixed Type Momnge-Ampere Equations. V. Lychagin & V. Rubtsov, Non-Holonomic Filtration: Algebraic and Geometric Aspects of Non-Integrability. V. Lychagin & L. Zilbergleit, Spencer Cohomologies. P. E. Parker, Hawking's Relation via Fourier Integral Operators. A. Prástaro, Geometry of Super PDE's. A. Prástaro & Th. M. Rassias, On a Geometric Approach to an Equation of J.d'Alembert. M. Puta, Geometric Prequantization of the Einstein's Vacuum Field. Y. R. Romanovsky, On Differential Equations and Cartan's Projective Connections. Yu I. Sapronov, Smooth Marginal Analysis of Bifurcation of Extremals. C. S. Sharma, On the Schrödinger Equation for an N-Electron Atom. V. E. Shemarulin, Higher Symmetries and Conservation Laws of Euler-Darboux Equations. K. S. Stelle, Strings and Menbranes. V. S. Titov, Methods for Solving Two-Dimensional Nonstationary MHD Equations at Small Alfven-Mach Numbers.

PATENTS

[88] A. Prástaro et al., 28/5/1975 - No 23.797 A/75. Process of production of fibrous structures with high degree of birefringence.

The present invention refers to a process to produce fibrous structures having an high degreee of monoaxial orientation, by means of controlled extrusion of solutions, emulsions, suspensions of fibrogenous thermoplastic polymers. In particular, one fixes the optimum conditions of the extrusor design in order to obtain a birefringence higher than 0.1 × 10-4.

[89] A. Prástaro et al., 11/7/1975 - No 25.334 A/75. Process of production of synthetic polymers by means of flash-spinning of polymers solutions.

The present invention refers to a process to produce fibrous structures of synthetic polymers, in the form of plexus-filament of single little fibers, by means of the technique of the ''flash-spinning'' of polymers solutions. In particular, one fixes the optimum thermodynamical conditions to obtain plexus-filaments that extend ranges previously found by USA-patents. This has been possible by using a new mathematical model of flash-spinning, purposely formulated, and put on informatic support. Of particular importance has been the discovery of metastable states in the extruded solution, similar to ones used in the bubble-chambers for dedecting sub-atomic collisions. These thermodynamical conditions, beside some suitable dynamical conditions, allow us to get optimum control conditions in such a process.

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