125,065 research outputs found
Stepanov-like C(n)-pseudo almost automorphy and applications to some nonautonomous higher-order differential equations
No full textTyt. z nagł.References p. 468-470.In this paper we introduce and study a new concept called Stepanov-like C(n)-pseudo almost automorphy, which generalizes in a natural fashion both the notions of C(n)-pseudo almost periodicity and that of C(n)-pseudo almost automorphy recently introduced in the literature by the authors. Basic properties of these new functions are investigated. Furthermore, we study and obtain the existence of C(N+m)-pseudo almost automorphic solutions to some nonautonomous higher-order systems of differential equations with Stepanov-like C(m)-pseudo almost automorphic coefficients.Dostępny również w formie drukowanej.SŁOWA KLUCZOWE : KEYWORDS: pseudo almost automorphic C(n)-pseudo almost automorphy, Stepanov-like C(n)-pseudo almost automorphy, exponential dichotomy
Further properties of Stepanov--Orlicz almost periodic functions
No full textsummary:We revisit the concept of Stepanov--Orlicz almost periodic functions introduced by Hillmann in terms of Bochner transform. Some structural properties of these functions are investigated. A particular attention is paid to the Nemytskii operator between spaces of Stepanov--Orlicz almost periodic functions. Finally, we establish an existence and uniqueness result of Bohr almost periodic mild solution to a class of semilinear evolution equations with Stepanov--Orlicz almost periodic forcing term
Stepanov-like almost automorphic solutions for nonautonomous evolution equations
No full textWe study the convolution of Stepanov-like almost automorphic functions and L^1 functions. Also we consider nonautonomous evolution equations, with a periodic operator coefficient and Stepanov-like almost automorphic forcing, and show that, under certain assumptions, any bounded mild solution is almost automorphic.Mathematic
On the Dirichlet problem with several volume constraints on the level sets
No full textWe consider minimization problems involving the Dirichlet integral under an arbitrary number of volume constraints on the level sets and a generalized boundary condition. More precisely, given a bounded open domain Ω ⊂ Rn with smooth boundary, we study the problem of minimizing fΩ |∇u|2 among all those functions u ∈ H1 that simultaneously satisfy n-dimensional measure constraints on the level sets of the kind |{u = li}| = α1, i = 1,..., k, and a generalized boundary condition u ∈. Here, Κ is a closed convex subset of H1 such that Κ + H01 = Κ; the invariance of Κ under H01 provides that the condition u ∈ Κ actually depends only on the trace of u along δΩ. By a penalization approach, we prove the existence of minimizers and their Hölder continuity, generalizing previous results that are not applicable when a boundary condition is prescribed. Finally, in the case of just two volume constraints, we investigate the Γ-convergence of the above (rescaled) functionals when the total measure of the two prescribed level sets tends to saturate the whole domain Ω. It turns out that the resulting Γ-limit functional can be split into two distinct parts: the perimeter of the interface due to the Dirichlet energy that concentrates along the jump, and a boundary integral term due to the constraint u ∈ Κ. In the particular case where Κ = H1 (i.e. when no boundary condition is prescribed), the boundary term vanishes and we recover a previous result due to Ambrosio et al
On a higher-order evolution equation with a Stepanov-bounded solution
No full textWe study strong solutions u:ℝ→X, a Banach space X, of the nth-order evolution equation u(n)−Au(n−1)=f, an infinitesimal generator of a strongly continuous group A:D(A)⊆X→X, and a given forcing term f:ℝ→X. It is shown that if X is reflexive, u and u(n−1) are Stepanov-bounded, and f is Stepanov almost periodic, then u and all derivatives u′,…,u(n−1) are strongly almost periodic. In the case of a general Banach space X, a corresponding result is obtained, proving weak almost periodicity of u, u′,…,u(n−1)
A generalization of an inequality of Stepanov
No full textAbstractLet Γn(p) denote a random graph with n vertices in which any two vertices, independently of the others, are connected by an edge with probability p = 1 − q where 0 ≤ q ≤ 1. Denote by Qn(q) the probability that Γn(p) is connected. In 1970 V. E. Stepanov proved that Qn(q) ≤ (1−qn)n−1 for n ≥ 1. In this paper a simple proof is given for a general inequality related to the connectedness of Γn(p) which contains Stepanov's inequality as a particular case
Valerij L. Stepanov, N. H. Bunge : sud´ba reformatora
No full textNikolaj H. Bunge, professeur d’économie à l’université de Kiev et ministre des Finances pendant les années 1880, constitue une figure cruciale de la Russie impériale. Cependant, à la différence d’autres ministres réformateurs tels que Witte et Stolypin, Bunge a été relativement négligé par l’historiographie russe aussi bien qu’ « occidentale ». L’ouvrage de Valerij L. Stepanov comble dès lors un vide important, et de manière très efficace. L’auteur a en effet dépouillé un très grand nombre de..
Flows of measures generated by vector fields
No full textWe show that for a large class of measurable vector fields in the sense of N. Weaver (i.e. derivations over the algebra of Lipschitz functions), the notion of a flow of the given positive Borel measure similar to the classical one generated by a smooth vector field (in a space with smooth structure) may be defined in a reasonable way, so that the measure flows along'' the appropriately understood integral curves of the given vector field and the classical continuity equation is satisfied in the weak sense
RECONSTRUCTION OF MANIFOLD EMBEDDINGS INTO EUCLIDEAN SPACES VIA INTRINSIC DISTANCES
No full textWe consider the problem of reconstructing an embedding of a compact connected Riemannian manifold in a Euclidean space up to an almost isometry, given the information on intrinsic distances between points from its “sufficiently large” subset. This is one of the classical manifold learning problems. It happens that the most popular methods to deal with such a problem, with a long history in data science, namely, the classical Multidimensional scaling (MDS) and the Maximum variance unfolding (MVU), actually miss the point and may provide results very far from an isometry; moreover, they may even give no bi-Lipshitz embedding. We will provide an easy variational formulation of this problem, which leads to an algorithm always providing an almost isometric embedding with the distortion of original distances as small as desired (the parameter regulating the upper bound for the desired distortion is an input parameter of this algorithm)
V.P. Stepanov (éd.) : La Noblesse de service en Russie dans la deuxième moitié du XVIIIe siècle (1765-1795)., 2003
No full textPrébet Jacques, Zaborov Piotr. V.P. Stepanov (éd.) : La Noblesse de service en Russie dans la deuxième moitié du XVIIIe siècle (1765-1795)., 2003. In: Dix-huitième Siècle, n°36, 2004. Femmes des Lumières. p. 631
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