Essential coverings and triangulations

Sunto In questo lavoro si danno condizioni sufficienti per un ricoprimento di una varietà differenziabile V affinchè il suo nerbo abbia lo stesso tipo P.L. di V e si prova l'esistenza di una larga classe di siffatti ricoprimenti.

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The author is member of G.N.S.A.G.A. of the C.N.R. and partially supported by a N.A.T.O.-C.N.R. fellowship.     

On the Banach spaces with the property (V*) of Pelczynski

Summary We consider the Banach spaces with the property (V*) of Pelczynski giving a sufficient condition for a Banach space to have this property as well as a characterization of Banach lattices with the same property. Several other results are given which are concerning relationships among that property and other famous isomorphic properties of Banach spaces. Also a characterization of Banach spaces with property (V*) using Schauder decompositions is given. Some result concerning lifting of that property from a Banach space E to L¹(, E) is presented, too.Work performed under the auspices of G.N.A.F.A. of C.N.R. and partially supported by M.P.I. of Italy (40%).     

A uniqueness result for a nonlinear hyperbolic equation

Summary We prove the uniqueness of the solution of a Cauchy problem for a nonlinear and non-local hyperbolic equation, which arises in a model of the dynamic of cardiac muscle.The authors were supported by G.N.A.F.A., G.N.I.M. and I.A.N. of C.N.R. and by M.P.I.     

Algorithms for parametric nonconvex programming

In this paper, we consider a general family of nonconvex programming problems. All of the objective functions of the problems in this family are identical, but their feasibility regions depend upon a parameter . This family of problems is called a parametric nonconvex program (PNP). Solving (PNP) means finding an optimal solution for every program in the family. A prototype branch-and-bound algorithm is presented for solving (PNP). By modifying a prototype algorithm for solving a single nonconvex program, this algorithm solves (PNP) in one branch-and-bound search. To implement the algorithm, certain compact partitions and underestimating functions must be formed in an appropriate manner. We present an algorithm for solving a particular (PNP) which implements the prototype algorithm by forming compact partitions and underestimating functions based upon rules given by Falk and Soland. The programs in this (PNP) have the same concave objective function, but their feasibility regions are described by linear constraints with differing right-hand sides. Computational experience with this algorithm is reported for various problems.The author would like to thank Professors R. M. Soland, T. L. Morin, and P. L. Yu for their helpful comments. Thanks also go to two anonymous reviewers for their useful comments concerning an earlier version of this paper.     

Existence,uniqueness and a priori estimates for a nonlinear integro-differential equation

The paper deals with the explicit calculus and the properties of the fundamental solution K of a parabolic operator related to a semilinear equation that models reaction diffusion systems with excitable kinetics. The initial value problem in all of the space is analyzed together with continuous dependence and a priori estimates of the solution. These estimates show that the asymptotic behavior is determined by the reaction mechanism. Moreover it’s possible a rigorous singular perturbation analysis for discussing travelling waves with their characteristic times. This work has been performed under the auspices of the G.N.F.M. of I.N.D.A.M. and M.I.U.R. (P.R.I.N. 2007) “Waves and stability in continuous media”.     

Nonzero-sum differential games (the noncooperative variant)

One presents the fundamental results of the theory of noncooperative differential games: necessary and sufficient equilibrium conditions, existence theorems, properties of equilibrium solutions, numerical methods. One indicates applications to concrete problems in economics, the mechanics of controlled motions, and to strategic games.Translated from Itogi Nauki i Tekhniki, Matematicheskii Analiz, Vol. 15, pp. 199–266, 1977.The authors are grateful to É. M. Vaisbord, A. F. Koaonenko, V. S. Molostvov, V. P. Patsyukov, V. A. Plotnikov, V. V. Podinovskii, R. A. Polyak, and R. T. Yanushevskii for the problems in Sec. 11 and for the remarks which have been taken into account in the final editing of the survey.     

Arcs in Minkowski planes

The aim of this paper is to study some properties of k-arcs in Minkowski planes focalizing the attention on problems of existence and completness.Work done under the auspicies of G.N.S.A.G.A. supported by 40% grants of M.U.R.S.T.In memoriam Giuseppe Tallini     

Some new examples of flocks of Q+(3,q)

Three new examples of non-linear flocks of the non-singular ruled quadric Q⁺(3,q) of PG(3,q) are given.This paper was written while the author was a member of G.N.S.A.G.A. of C.N.R., with partial financial support from M.P.I.     

Classical r-matrices and quantization

The construction of quantum integrals of motion for systems with linear Poisson brackets given by classical r-matrices is described.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 133, pp. 228–235, 1984.The author is grateful to A. G. Reiman, N. Yu. Reshetikhin, and E. K. Sklyanin for numerous fruitful discussions.     

Invariants,orbits and symmetric spaces

Lavoro svolto nell'ambito del G.N.S.A.G.A. del C.N.R. con contributo del M.P.I. fondi 40%.     

The Cauchy problem for a class of pseudodifferential equations over p-adic field

In this paper, some classes much more general than the one in [N.M. Chuong, Yu.V. Egorov, A. Khrennikov, Y. Meyer, D. Mumford (Eds.), Harmonic, Wavelet and p-Adic Analysis, World Scientific, Singapore, 2007] of Cauchy problems for an interesting class of pseudodifferential equations over p-adic fields are studied. The used functions belong to mixed classes of real and p-adic functions. Even for p-adic partial differential equations such problems in such function spaces have not been discussed yet. The established mathematical foundation requires very complicated and very difficult proofs. Days after days, these equations occur increasingly in mathematical physics, quantum mechanics. Explicit solutions of such problems are very needed for specialists on applied mathematics, physics, and engineering.     

A note on the extension of BV functions in metric measure spaces

In this note, a classical extension result for BV functions due to Yu.D. Burago and V.G. Maz'ja [Yu.D. Burago, V.G. Maz'ja, Potential Theory and Function Theory for Irregular Regions, Seminars in Math., vol. 3, V.A. Steklov Math. Inst., Leningrad, 1969 (translated from Russian)] is generalized to the abstract setting of doubling metric measure spaces endowed with a differentiation structure called D-structure.     

Systems of quasi-equilibrium problems with lower and upper bounds

In this work, we consider systems of quasi-equilibrium problems with lower and upper bounds and establish the existence of their solutions by using some known maximal element theorems for a family of multivalued maps. Our problems are more general than the one posed in [G. Isac, V.M. Sehgal, S.P. Singh, An alternative version of a variational inequality, Indian J. Math. 41 (1999) 25–31]. As a particular case, we also get the answer to the problem raised in [G. Isac, V.M. Sehgal, S.P. Singh, An alternative version of a variational inequality, Indian J. Math. 41 (1999) 25–31].     

The infinitesimal and generalized Hodge Conjecture for some families of sextic threefolds

This paper deals with some families of projective hypersurfaces of degree 6 and dimension 3, left invariant under certain actions of the group of the cubic roots of unity. The general Grothendieck-Hodge conjecture, for the families above and for their intersections, is verified. In particular certain families of elliptic curves on the general element of these families are closely investigated and their degeneration at the Fermat point is studied. These results are used to verify the general Infinitesimal Hodge Conjecture extending to the general type case a similar conjecture due to A. Albano and S. Katz. Research partially supported by italian M.U.R.S.T., by the Science Project “Geom. of Alg. Var.” and by G.N.S.A.G.A. (C.N.R.)     

Penetrative convection in a fluid layer with throughflow

Linear and nonlinear stability analyses of vertical throughflow in a fluid layer, where the density is quadratic in temperature, are studied. To avoid the loss of key terms a weighted functional is used in the energy analysis. Both conditional and unconditional thresholds are derived. When the throughflow is ascending the linear and nonlinear boundaries show substantial agreement. The linear boundary remains close to the conditional nonlinear boundary for descending throughflow, whilst the unconditional threshold begins to diverge. Grant sponsors: Leverhulme Trust: grant number F/00128/AK, EPSRC: grant number GR/S34601/01. This work has been performed under the auspicies of the G.N.F.M. of I.N.D.A.M. and M.I.U.R. (P.R.I.N. 2005): Propagazione non lineare e stabilita’ nei processi termodinamici del continuo.     

A note on norm-one projections onto subspaces of finite codimension ofl ∞

Research partially supported by Italian Ministero della Pubblica Istruzione (M.P.I.) and G.N.A.F.A. (C.N.R.)     

Programming language ALGOL 68

The basic concepts of ALGOL 68 are presented. The prospects for its use and mathematical questions related to its implementation are discussed.Translated from Itogi Nauki i Tekhniki. Teoriya Veroyatnostei, Matematicheskaya Statistika, Teoreticheskaya Kibernetika, Vol. 15, pp. 163–232, 1978.The authors are grateful to V. L. Leites, V. B. Yakovlev, V. M. Gushchin, V. M. Kurochkin, N. N. Nepeivoda, M. R. Levinson, and É. A. Aslanyan for discussion of various aspects of the present work.     

Regular boundary value problems for complete second order elliptic differential-operator equations in UMD Banach spaces

We consider coerciveness and Fredholmness of nonlocal boundary value problems for complete second order elliptic differential-operator equations in UMD Banach spaces. In some special cases, the main coefficients of the boundary conditions may be bounded operators and not only complex numbers. Then, we prove an isomorphism, in particular, maximal L _p -regularity, of the problem with a linear parameter in the equation. In both cases, the boundary conditions may also contain unbounded operators in perturbation terms. Finally, application to regular nonlocal boundary value problems for elliptic equations of the second order in non-smooth domains are presented. Equations and boundary conditions may contain differential-integral parts. The spaces of solvability are Sobolev type spaces W _p,q ^2,2. The first author is a member of G.N.A.M.P.A. and the paper fits the 60% research program of G.N.A.M.P.A.-I.N.D.A.M.; The third author was supported by the Israel Ministry of Absorption.     

Strongly-cyclic branched coverings of knots via (g, 1)-decompositions

Strongly-cyclic branched coverings of knots are studied by using their (g, 1)-decompositions. Necessary and sufficient conditions for the existence and uniqueness of such coverings are obtained. It is also shown that their fundamental groups admit geometric g-words cyclic presentations. Work performed under the auspices of G.N.S.A.G.A. of I.N.d.A.M. of Italy and supported by M.U.R.S.T., by the University of Bologna, funds for selected research topics. The third named author was also supported by the INTAS project “CalcoMet-GT” 03-51-3663, the grant of RFRB, and the grant of SB RAN.     

Approximation of a bending plate problem with a boundary unilateral constraint

Summary We study a variational formulation of the unilaterally supported bent plate problem and we analyze the approximation of the problem by a mixed finite element method. We proveO(h) andO(h|lnh|^1/2) error bounds respectively for the moments and the displacement.Work partially supported by M.P.I., by G.N.I.M. of C.N.R. and by I.A.N. of C.N.R. of Pavia