In an interval containing the origin we study a Brownian motion which returns to zero as soon as it reaches the boundary. We determine explicitly its transition probability, prove it is ergodic and calculate the decay rate to equilibrium. It is shown that the process solves the martingale problem for certain asymmetric boundary conditions and can be regarded as a diffusion on an eight shaped do...

Linear Neutral Time-Delay Systems Anna Maria Perdon and Maria Anderlucci DIIGA, Università Politecnica delle Marche, Via Brecce Bianche, 60131 Ancona, Italy (e-mail: [email protected] [email protected]). Abstract The problem of state reconstruction is discussed for linear neutral systems with a finite number of commensurable point delays. Using as models systems with coefficients in a r...

In this paper we study the Hausdorff volume in a non equiregular sub-Riemannian manifold and we compare it with a smooth volume. We first give the Lebesgue decomposition of the Hausdorff volume. Then we study the regular part, show that it is not commensurable with the smooth volume, and give conditions under which it is a Radon measure. We finally give a complete characterization of the singul...

Let d be a square-free positive integer, let Od denote the ring of integers in Q( √ −d), and let Qd denote the Bianchi orbifold H/PSL(2,Od). A non-compact finite volume hyperbolic 3-manifold X is called arithmetic if X and Qd are commensurable, that is to say they share a common finite sheeted cover (see [26] Chapter 8 for more on this). If N is a closed orientable 3-manifold and L ⊂ N a link, ...

We study differential equations satisfied by modular forms of two variables associated to Γ1×Γ2, where Γi (i = 1, 2) are genus zero subgroups of SL2(R) commensurable with SL2(Z), e.g., Γ0(N) or Γ0(N)∗ for some N . In some examples, these differential equations are realized as the Picard–Fuchs differential equations of families of K3 surfaces with large Picard numbers, e.g., 19, 18, 17, 16. Our ...

In this paper, Java programming with applets for internet-based control education of two mechanical systems are presented. First, a new multi-objective optimization method is applied to obtain the Pareto frontiers of some non-commensurable objective functions in the design of linear state feedback controllers for an inverted pendulum and a ball–beam system. Second, the simulations of the proble...

First, we apply Thurston’s construction of pseudo-Anosov homeomorphisms to grid graphs and obtain translation surfaces whose Veech groups are commensurable to (m, n,∞) triangle groups. Many (if not all) of the surfaces we construct were first discovered by Bouw and Möller, however our treatment of the surfaces differs. We construct these surfaces by gluing together polygons in two ways. We use ...

A Hamiltonian that approaches the study of the three-body problem in general relativity is obtained. We use it to study the relativistic version of the circular restricted three-body problem in which the first body is the heaviest and the third body is a test-particle. We focus on the orbits around the 3:2 resonance. We show that, in spite of the notable difference between the relativistic and ...

Abstract The class of abelian p -groups with minimal full inertia, that is, satisfying the property fully inert subgroups are commensurable invariant is investigated, as well groups not this property; it known both direct sums cyclic and torsion-complete first type. It proved “small" endomorphism ring do satisfy concrete examples them provided via Corner’s realization theorems. Closure properti...