The Seventh Vasil Popov Prize awarded to
Andriy Bondarenko of
Kyiv National Taras Shevchenko University, Ukraine
A B S T R A C T S
CLASSICAL HERMITE AND LAGUERRE POLYNOMIALS AND THE ZERO-DISTRIBUTION OF RIEMANN'S ζ-FUNCTION
Peter Rusev
pkrusev@math.bas.bg
2000 Mathematics Subject Classification: 11M26, 33C45, 42A38.
Key words:
Hermite polynomials, Laguerre polynomials, holomorphic extension, Riemann's hypothesis.
Necessary and sufficient conditions for absence of zeros of the function ζ(s), s=σ+it, in the half-plane σ<θ,
1/2≤θ<1 are proposed in terms of representations of holomorphic functions by series in Hermite and Laguerre polynomials as well as in terms of Fourier and Hankel integral transforms.
STRUCTURES DE CONTACT INVARIANTES
Saad Aggoun
saad.aggoun@yahoo.fr
2000 Mathematics Subject Classification: 37J55, 53D10, 53D17, 53D35.
Key words:
Contact structures, Contact forms, Reeb vector field, Poisson
Brackets, infinitesimal Automorphism.
Abstract: Let M be a compact manifold of three dimension with a contact
structure [ω]. The Lie algebra A([ω]) of infinitesimal automorphisms of [ω] is of infinite dimension. In this paper we study the sub-algebra of A([ω) of finite dimensions.
MANGASARIAN-TYPE SUFFICIENT OPTIMALITY CONDITIONS~FOR AGE-STRUCTURED CONTROL PROBLEMS WITH STATE~CONSTRAINTS. AN APPLICATION TO INVESTMENT IN VINTAGE CAPITAL
Vladimir Krastev
v_krastev@mail.ru
2000 Mathematics Subject Classification: 49K20, 49K21, 49N90, 49M30.
Key words:
Age-structured optimal control with state constraints, sufficient conditions for optimality, vintage capital goods, shooting method.
We consider a class of age-structured control problems with state constraints, nonlocal dynamics and boundary conditions, defined on finite time intervals. For these problems we suggest Mangasarian-type sufficient conditions for the optimality of the control. As an application we consider a model with a state constraint of optimal investment in vintage capital goods. To solve this model we suggest a numerical method and we prove that this method converges to an optimal solution.
TAIL BEHAVIOR OF HÖ$LDER NORMS OF STOCHASTIC PROCESSES AND WEAK CONVERGENCE OF MAXIMA IN HÖ$LDER SPACES
Stilian A. Stoev
sstoev@umich.edu
2000 Mathematics Subject Classification:
60F17, 60G17, 60G70.
Key words:
Max-stable processes, Hölder norm, heavy-tails, tail behavior, Ciesielski isomorphism.
Our main goal was to establish functional limit theorems for component-wise maxima of iid processes taking values in Hölder spaces. Given that the finite-dimensional distributions converge, the key technical challenge is to establish tightness. The classical tightness conditions of Lamperti apply, provided that one can control the tail-behavior of Hölder norms. We do so, by using a powerful isomorphism theorem due to Ciesielski, which relates H\"older norms to superma of sequences. As a consequence, we obtain estimates for the tail probabilities of Hölder norms for light, moderate and heavy-tailed stochastic processes. The established inequalities are of independent interest since they provide explicit bounds on the tail probabilities of Hölder norms and suprema of stochastic processes under simple conditions on the bivariate distributions.
We illustrate the results with sufficient conditions for the Hölder regularity of several classes of doubly stochastic max-stable processes of Schlather and Brown-Resnick types. Some extensions to the case of weak convergence in Besov spaces are also considered.
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