Sur la discrétisation de notions de longueur et de temps dans l'élaboration de la Mécanique

Summary To represent, by a discrete set, the time-space in which we want to describe a phenomenon (euclidian or relativistic), for reasons due to duality, we are led to use coordinates taken from a finite field. For reasons due to orientation, we have to choose the characteristic. The stone in which the coordinates of a ? positive vector ? have to be chosen, contain as high a number of points as we like, provided that p be chosen sufficiently large. The notions of kinematics then result from the theory of the formal series.

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A Dario Graffi pour son 70-ème anniversaire

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Entrata in Redazione il 29 luglio 1975.     

New approach to optimal control of stochastic Volterra integral equations

ABSTRACT

We study optimal control of stochastic Volterra integral equations (SVIE) with jumps by using Hida-Malliavin calculus.

• We give conditions under which there exist unique solutions of such equations.

• Then we prove both a sufficient maximum principle (a verification theorem) and a necessary maximum principle via Hida-Malliavin calculus.

• As an application we solve a problem of optimal consumption from a cash flow modelled by an SVIE.

     

Spectral dimension of spheres

Abstract

In this paper, we associate a growth graph to a homogeneous space of a compact group. Under certain assumptions, we show that the spectral dimension of a homogeneous space is greater than or equal to summability of the length operator associated with the growth graph. Using this, we compute spectral dimension of spheres.

Communicated by Miriam Cohen     

Remarks on Weak-Type Estimates for Certain Grand Square Functions

In this note we extend weak-type estimates obtained recently by A. K. Lerner to certain grand square functions by using a simple argument in terms of real variables. In this way, we improve a weak-type L¹-estimate for grand Littlewood–Paley operators due to N. N. Osipov.

     

Sulla instabilità gravitazionale secondo Jeans di un plasma dissipativo in presenza di effetto Hall

Summary In this paper we study Jeans' gravitational instability of a dissipative Hall plasma, i.e., of a viscous, heat-conducting plasma with finite electrical conductivity, described by the magnetofluiddynamic equations in the presence of the Hall effect. The critical value of the wavelength is determined and the condition for the gravitational instability is discussed. Several noteworthy particular cases are then examined.

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Facoltà di Ingegneria dell'Università.

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Entrata in Redazione il 7 settembre 1977.     

P-twisted affine Lie algebra and its realiza tions by twisted vertex operators

In this paper, we define a P-twisted affine Lie algebra, and construct its realizations by twisted vertex operators.

     

Anelli Henseliani topologici - II

Summary In the present work we study some problems about henselian triples and henselization which have been introduced in our article [18]. Mainly we prove that henselian triples coincide with strong henselian triples and give a new formulation of the Hensel lemma, stronger than that we gave in [18]. Then we investigate some properties of henselian triples (changement of ideal or of topology, ecc.) and prove commutativity with quotient.

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Lavoro eseguito nell'ambito dei contratti di ricerca del Comitato Nazionale per la Matematica del C.N.R.

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Entrata in Redazione il 27 maggio 1971.     

Gruppi con complessi a normalità transitiva

Summary In a group we consider P-, Q-, R-complexes, which satisfy to some weaker conditions than subgroups and we introduce the concept of normality. We investigate T_P-, T_Q-, T_R-groups (analogous to the well-known T-groups), where the property of being a normal P-, Q-, R-complex is somehow transitive. More precisely we determine these types of groups, which are nilpotent (they coincide with some Dedekind groups) and we state criteria to check or to characterize such groups in general and in some particular cases.

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A BeniaminoSegre per il suo 70° genetliaco.

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Questo lavoro è stato eseguito nell'ambito del Gruppo Nazionale per le Strutture Algebriche e Geometriche e loro Applicazioni del C.N.R.; Istituto matematico dell'Università di Milano.

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Entrata in Redazione il 4 dicembre 1973.     

Alcune soluzioni esatte delle equazioni della magnetofluidodinamica per il moto stazionario di un fluido viscoso,incomprimibile e a conducibilità elettrica finita

Summary With regard to the non-linear equations of Magneto-Fluid Dynamics in this paper we examine the steady, axially symmetric motion of an incompressible, homogeneous, viscous and electrically conducting fluid when such a fluid moves also around the axis of symmetry. We give some classes of exact solutions and then we generalize the problem taking also in account the Hall effect.

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A Dario Graffi nel suo 70^o compleanno

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Entrata in Redazione il 23 gennaio 1975.

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Istituto Matematico dell'Università di Siena.     

Mean-field stochastic control with elephant memory in finite and infinite time horizon

ABSTRACT

Our purpose of this paper is to study stochastic control problems for systems driven by mean-field stochastic differential equations with elephant memory, in the sense that the system (like the elephants) never forgets its history. We study both the finite horizon case and the infinite time horizon case.

• In the finite horizon case, results about existence and uniqueness of solutions of such a system are given. Moreover, we prove sufficient as well as necessary stochastic maximum principles for the optimal control of such systems. We apply our results to solve a mean-field linear quadratic control problem.

• For infinite horizon, we derive sufficient and necessary maximum principles.

  As an illustration, we solve an optimal consumption problem from a cash flow modelled by an elephant memory mean-field system.

     

Anelli Henseliani topologici

Summary In the present work we give a generalization of the concept of ? ring henselian with respect to its idealm ?, by introducing the concept of ? ring henselian with respect to the idealm and the linear topology τ ?. Then we get the henselization of a triple (A,m, τ) (ring, ideal, linear topology) and investigate its relations with completion, mainly in the ?m-adic ? situation. Among our results there is also a reformulation, with less restrictive hypothesis, of the Hensel lemma as it is given in Bourbaki.

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Entrata in Redazione il 24 marzo 1971.

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Lavoro eseguito nell'ambito dei Contratti di ricerca del Comitato Nazionale per la matematica del C.N.R.     

Eine gruppentheoretische Kennzeichnung ebener kommutativer punktiert-affiner Inzidenzgruppen

In this paper we give a group-theoretical characterization of plane commutative punctured affine incidence groups as introduced by G.P. Kist in [1].

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Herrn Professor Dr. WERNER BURAU zum 70. Geburtstag     

Gruppi semiextraspeciali di esponentep

Summary Semi-extraspecial groups are defined by B. Beisiegel in [1] as a generalization of extraspecial groups. In this paper we characterize these groups in some different ways and we prove several their properties. Connections between these groups and other algebraic and geometrical structures are investigated, and two important subclasses are characterized in geometrical terms.

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Lavoro eseguito nell'ambito dei progetti ministeriali di ricerca.     

Projection theorems in hyperbolic space

We establish Marstrand-type projection theorems for orthogonal projections along geodesics onto m-dimensional subspaces of the hyperbolic n-space by a geometric argument. Moreover, we obtain a Besicovitch–Federer type characterization of purely unrectifiable sets in terms of these hyperbolic orthogonal projections.

     

Onde di discontinuità ed equazioni costitutive nei corpi elastici isotropi sottoposti a deformazioni finite

Summary We consider an elastic isotropic material with finite deformations. The existence of a double wave (therefore exceptional because the field equations are in the conservative form) for all the deformations and the discontinuity propagation direction is required. This because in the linear theory there exists a double wave, furthermore, because in many non-linear theories of Mathematical physics there exists at least one exceptional wave (this wave doesn’t produce shocks). This request implies conditions for the response function in the constitutive equations. Furthermore, under these assumptions, we can determine explicitly all the possible propagation speeds. Therefore we can find theorems generalizing (in the case of the imposed conditions) those ones obtained by Truesdell and Green for the principal waves (whose unit normal has the direction of the eigenvectors of the deformation matrix). In the last part of this work we examine the case of a hyperelastic material and we determine some classes of possible thermodynamic potentials.

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Entrata in Redazione il 18 febbraio 1976.

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Lavoro eseguito nell’ambito dei contratti del C.N.R. - Gruppo Nazionale per la Fisica Matematica.     

Evolution Inclusions Governed by Time-Dependent Maximal Monotone Operators with a Full Domain

In this paper, we study the existence of solutions for evolution inclusions governed by time-dependent maximal monotone operators with a full domain. Without assumptions concerning time-regularity on the time-dependent maximal monotone operators, and by using the Moreau-Yosida regularization technique, we establish the existence of solutions in Hilbert spaces. The theoretical result is applied to prove the existence of solutions for semicoercive sweeping processes with velocity constraint.

     

Doubly Feller Property of Brownian Motions with Robin Boundary Condition

In this paper, we consider first order Sobolev spaces with Robin boundary condition on unbounded Lipschitz domains. Hunt processes are associated with these spaces. We prove that the semigroup of these processes are doubly Feller. As a corollary, we provide a condition for semigroups generated by these processes being compact.

     

On co-isosimple modules and co-isoradical of modules

Abstract

In this paper we study “co-isosimple” modules, that is, those modules which are isomorphic to all of its non-zero quotients modules. This allows us to define and study “isomaximal” submodules, “isomax” modules and the “co-isoradical” of a module. We study some of its basic properties and we give a characterization of left V-ring using these concepts.

Communicated by Alberto Facchini     

Spectrum structure and decay rate estimates on the Landau equation with Coulomb potential

In this paper we first deduce the estimates on the linearized Landau operator with Coulomb potential and then analyze its spectrum structure by using semigroup theory and linear operator perturbation theory. Based on these estimates, we give the precise time decay rate estimates on the semigroup generated by the linearized Landau operator so that the optimal time decay rates of the nonlinear Landau equation follow. In addition, we present a similar result for the non-angular cutoff Boltzmann equation with soft potentials.

     

The Existence Of Nonhomogeneous,Viscous And Incompressible Flow In Unbounded Domains

The existence of global (in time) solution {ρu,p} (density, velocity field and pressure) of a partial differential problem modelling the behaviour of a viscous, nonhomogenous and incompressible flow has been recently obtained viscous, nonhomogenous and incompressible flow has been recently obtained by J. Simon. In his most general result, he finds a solution which satifies an initial condition in an appropriate weak sense. In this paper, we present an extension of this result to the case of arbitrary unbounded three–dimensional fluid domains.

1. Introduction.

2. The main result.

3. Some technical Lemmas.

4. Proof of Theorem 1.

4.1 The existence and properties of {ρR, U^R PR}

4.2 Some estimates for ρR,U^R and their time derivatives.

4.3 Further estimates.

4.4 The choice of a convergent sequence and conclusions.

References.