Fn−k+1H 2n−2k+1(X)∼= F n−k+1A2n−2k+1(X)c dFn−k+1A2n−2k(X) . If (Zt )t∈C is a flat family of codimension k algebraic cycles on X parametrized by a smooth irreducible curve C, the map t → kX(Zt − Z0) factors through a homomorphism from the Jacobian J (C) to J 2k−1(X), and one can show that the image of this morphism is a complex subtorus of J 2k−1(X) whose tangent space is contained in Hk−1,k(X) ...

Let G be a simple Lie group of real rank one, with Iwasawa decomposition KAN̄ and Bruhat big cell NMAN̄ . Then the space G/MAN̄ may be (almost) identified with N and with K/M , and these identifications induce the (generalised) Cayley transform C : N → K/M . We show that C is a conformal map of Carnot–Caratheodory manifolds, and that composition with the Cayley transform, combined with multiplicat...

We describe methods of estimating the entire Lyapunov spectrum of a spatially extended system from multivariate time-series observations. Provided that the coupling in the system is short range, the Jacobian has a banded structure and can be estimated using spatially localized reconstructions in low embedding dimensions. This circumvents the "curse of dimensionality" that prevents the accurate ...

By solving the Yamabe equation with the discrete surface Ricci flow method, we can conformally parameterize a multiple boundary surface by a multi-hole disk. The resulting parameterizations do not have any singularities and they are intrinsic and stable. For applications in brain mapping research, first, we convert a cortical surface model into a multiple boundary surface by cutting along selec...

We establish some notation. Let N be prime and set S = SpecZ[1/2N ]. Denote by XQ = X0(N)/Q and JQ = J0(N) the usual modular curve and its Jacobian over Q, where we normalize the embedding XQ →֒ JQ by requiring ∞ 7→ 0. XQ is the generic fiber of the (smooth) S-curve X = X0(N)/S , and JQ has Néron model J = NéronS(J0(N)), which is in fact an abelian scheme over S. The Néron mapping property gives...

Let K be a perfect field of characteristic p > 0, A1 := K〈x, ∂ | ∂x−x∂ = 1〉 be the first Weyl algebra and Z := K[X := x, Y := ∂] be its centre. It is proved that (i) the restriction map res : AutK(A1) → AutK(Z), σ 7→ σ|Z , is a monomorphism with im(res) = Γ := {τ ∈ AutK(Z) | J (τ) = 1} where J (τ) is the Jacobian of τ (note that AutK(Z) = K ∗ ⋉ Γ and if K is not perfect then im(res) 6= Γ); (ii)...

The article presents the results of the study of nonlinear market prices dynamic, simulated using game theory model, maps and theory of bifurcation. Market pricing is presented as a two-dimensional map. Qualitative analyses of the firms’ pricing system properties using the fixed points, analysis of the trajectories near these fixed points were fulfilled Simulation of the market prices dynamic s...

Let X be a complex projective surface with arbitrary singularities. We construct a generalized Abel–Jacobi map A0(X) → J 2(X) and show that it is an isomorphism on torsion subgroups. Here A0(X) is the appropriate Chow group of smooth 0-cycles of degree 0 on X, and J 2(X) is the intermediate Jacobian associated with the mixed Hodge structure on H 3(X). Our result generalizes a theorem of Roitman...