1,354,291 research outputs found
Spinor super-bundles of geometric objects on spin^G space-times.
No full textSpinorial fibre bundles are built on space-times manifolds of type spin that are fully covariant in the sense introduced by A. Prastaro. These fibre bundles generalize ones previously
introduced by the same author and are very useful in a unified field theory
(Co)bordism groups in quantum PDE's
No full textA theory of noncommutative manifolds (\textit{quantum manifolds}) is formulated, and for such manifolds a geometric theory of quantum PDEs (QPDEs) is formulated. In particular, a criterion of formal integrability is given that
extends to QPDEs previous one given by H. Goldschmidt for PDEs and by A. Prastaro for super PDEs. A general theory of integral (co)bordism for QPDEs is developed, that extends previous one for PDEs formulated by A. Prastaro.
Then, non-commutative Hopf algebras, (\textit{full quantum -Hopf algebras, }), are canonically associated to any QPDE whose elements represent all the
possible invariants that can be recognized for such a structure.
Many examples of QPDEs are considered where we apply our theory. In particular, applications to quantum supergravity are considered. Existence of (quantum) tunnel
effects for quantum superstrings in supergravity is proved
Geometry of quantized super PDE's.
No full textIn this paper we announce some results
on the geometrization of super PDE's, i.e., PDE's defined in the
category of supermanifolds. These results generalize previous ones
for PDE's by A. Prastaro
On the general structure of continuum physics, II.
No full textIn order to give an intrinsic and axiomatic formulation of continuum physics, the differential operators are studied in the language of \textit{derivative spaces} as introduced by A. Prastaro. Useful generalizations of differential operators
are given by introducing \textit{derivative operators} and {\it
functional differential operators}. Finally differential equations
are considered as suitable subspaces of derivative spaces
Quantum geometry of PDE's.
No full textIn this paper we present the formal quantization of PDE's, as introduced by A. Prastaro, is recast in categorial language. Formal quantization results as a canonical functor defined on the category of differential equations. Furthermore, a Dirac-quantization can be interpreted as a covering in the category of differential equations. A quantum (pre-)spectral measure is a functor that can be factorized by means of formal quantization and a (pre-)spectral measure. A relation between canonical Dirac-quantization and singular solutions of PDE's is given. It is also proved that the knowledge of B\"aklund correspondences, as well as the conservation laws, can aid the procedure of canonical quantization of PDE's. Physically interesting examples are considered. In particular, we give the canonical quantization of an anharmonic oscillator. A general theory of quantum tunneling effects in PDE's is given. In particular, quantum cobordism has been related with Leray-Serre spectral sequences of PDE's
Quantum geometry of super PDE's.
No full textIn order to extend to super PDEs the theory of quantization of PDEs as given by A. Prastaro, we first develop a geometric theory for super PDEs (see also a companion paper on this subject by the same author). Superspaces and supermanifolds are introduced by using the concept of weak differentiability as usually given for locally convex spaces. This allows us to consider in algebraic way superdual spaces and superderivative spaces and to develop a formal theory for super PDEs that directly extends the previous ones for standard manifolds of finite dimension. In particular, we give a criterion of formal superintegrability for super PDEs, and show that a geometric theory of singular supersolutions, with singularities of Thom--Boardman type, can be formulated in the framework of super PDEs too. These results generalize the previous ones obtained for ordinary manifolds by H.Goldschmidt and by Moscow's mathematical school. Conservation superlaws associated to super PDEs are considered and related with some spectral sequences and wholly cohomological character of these equations. Then, the quantization of super PDEs is formulated on the ground of quantum cobordism. This is made in order to give an intrinsic and fully covariant geometric formulation of unified quantum field
theory. In particular, a theory of quantum supergravity is
developed. We explain how canonical quantization and quantum
tunneling effects arise in super PDEs. Furthermore, we explicitly
extend previous results of Witten and Atiyah in topological quantum field theory to our geometric framework for super PDEs. Obstructions to existence of quantum cobords in super PDEs are given by means of supercharacteristic classes. These results can be considered as a generalization of the recent results obtained by Gibbons and Hawking
A mathematical model for spinning viscoelastic molten polymers.
No full textA mathematical model for spinning viscoelastic materials is proposed. This work can be considered the continuation of some previous papers by A. Prastaro, which treated the case of newtonian materials. The viscoelastic system, as more
differs from the newtonian as the elastic component is present; thus the viscoelastic mathematical model can be not be inferred from the analysis of the previous paper; on the contrary the viscoelastic model includes, as particular case, the newtonian model. The spinning process was analysed by adding the rheological equation for viscoelastic materials to the set of simultaneous partial differential equations describing a general molten spinning process. We gave the steady-state numerical solutions, i.e. the filament croos-section , filament temperature and filament tension , as function of position and we related them to the parameters which influence the process of spinning: material parameters and spinning conditions parameters. We related the yarn
birefringence to the same parameters also. Moreover, we proposed to investigate which bounds impose the spinnability
criterion on the viscoelastic paramaters and which conditions
realize the maximum yarn production with fixed denier and section
Singularities for Cauchy data, characteristics, cocharacteristics and integral cobordism,
No full textA generalization of the classical concept of characteristic for partial differential equations (PDE) is given in the framework of the geometric formal theory for PDE's. In particular, it is given a relation between singularities of Cauchy data and characteristics in order to obtain integral manifolds (solutions) generated by means of characteristics. In this direction it is shown that to any PDE we can associate a "dual" equation having the same characteristics. These equations can be related by means of a sort of B\"acklund transformation. Furthermore, a criterion that relates characteristics and integral cobordism (or quantum cobordism as introduced by A. Prastaro) is given. Al relation between quantum cobordism in non-linear PDE's and Green's functions is given too
Elementi di Meccanica Razionale.
No full textThis 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
ELEMENTI DI MECCANICA RAZIONALE
No full textThis 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
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