On the Two Obstacles Problem in Orlicz-Sobolev Spaces and Applications

We prove the Lewy-Stampacchia inequalities for the two obstacles problem in abstract form for T-monotone operators. As a consequence for a general class of quasi-linear elliptic operators of Ladyzhenskaya-Uraltseva type, including p(x)-Laplacian type operators, we derive new results of $C^{1,\alpha}$ regularity for the solution. We also apply those inequalities to obtain new results to the N-membranes problem and the regularity and monotonicity properties to obtain the existence of a solution to a quasi-variational problem in (generalized) Orlicz-Sobolev spaces

Dirac Equation with vector and scalar potentials via Supersymmetry in Quantum Mechanics

In this work, a spin $\frac 12$ relativistic particle described by a generalized potential containing both the Coulomb potential and a Lorentz scalar potential in Dirac equation is investigated in terms of the generalized ladder operators from supersymmetry in quantum mechanics. This formalism is applied for the generalized Dirac-Coulomb problem, which is an exactly solvable potential in relativistic quantum mechanics. We obtain the energy eigenvalues and calculate explicitly the energy eigenfunctions for the ground state and the first excited state.Comment: 14 pages, to be submitted to Phys. Lett.

Influence of network topology on cooperative problem-solving systems

The idea of a collective intelligence behind the complex natural structures built by organisms suggests that the organization of social networks is selected so as to optimize problem-solving competence at the group-level. Here we study the influence of the social network topology on the performance of a group of agents whose task is to locate the global maxima of NK fitness landscapes. Agents cooperate by broadcasting messages informing on their fitness and use this information to imitate the fittest agent in their influence networks. In the case those messages convey accurate information on the proximity of the solution (i.e., for smooth fitness landscapes) we find that high connectivity as well as centralization boost the group performance. For rugged landscapes, however, these characteristics are beneficial for small groups only. For large groups, it is advantageous to slow down the information transmission through the network to avoid local maximum traps. Long-range links and modularity have marginal effects on the performance of the group, except for a very narrow region of the model parameters

The Network of Inter-Regional Direct Investment Stocks across Europe

We propose a methodological framework to study the dynamics of inter-regional investment flow in Europe from a Complex Networks perspective, an approach with recent proven success in many fields including economics. In this work we study the network of investment stocks in Europe at two different levels: first, we compute the inward-outward investment stocks at the level of firms, based on ownership shares and number of employees; then we estimate the inward-outward investment stock at the level of regions in Europe, by aggregating the ownership network of firms, based on their headquarter location. Despite the intuitive value of this approach for EU policy making in economic development, to our knowledge there are no similar works in the literature yet. In this paper we focus on statistical distributions and scaling laws of activity, investment stock and connectivity degree both at the level of firms and at the level of regions. In particular we find that investment stock of firms is power law distributed with an exponent very close to the one found for firm activity. On the other hand investment stock and activity of regions turn out to be log-normal distributed. At both levels we find scaling laws relating investment to activity and connectivity. In particular, we find that investment stock scales with connectivity in a similar way as has been previously found for stock market data, calling for further investigations on a possible general scaling law holding true in economical networks.Comment: 27 pages, 17 figure

Stability and limit theorems for sequences of uniformly hyperbolic dynamics

In this paper we obtain an almost sure invariance principle for convergent sequences of either Anosov diffeomorphisms or expanding maps on compact Riemannian manifolds and prove an ergodic stability result for such sequences. The sequences of maps need not correspond to typical points of a random dynamical system. The methods in the proof rely on the stability of compositions of hyperbolic dynamical systems. We introduce the notion of sequential conjugacies and prove that these vary in a Lipschitz way with respect to the generating sequences of dynamical systems. As a consequence, we prove stability results for time-dependent expanding maps that complement results in [Franks74] on time-dependent Anosov diffeomorphisms.Comment: 16 pages, 3 figure

Generalized splines in R^n and optimal control

We have found an inconsistency in our previous version of the paper "Generalized splines in R^n and optimal control". We give a new-time-dependent definition of spline curves in R^n which results from solving a non-autonomous linear quadratic optimal control problem (P) where the matrix B(t) is assumed to be rectangular with maximum rank. Nevertheless, our results are only valid if B(t) is a square (nonsingular) matrix. This was pointed out to us by Andrey Sarychev. We have proceeded with the necessary corrections. %%%%%%%%%%%%%%%%%% We give a new time-dependent definition of spline curves in R^n, which extends a recent definition of vector-valued splines introduced by Rodrigues and Silva Leite for the time-independent case. Previous results are based on a variational approach, with lengthy arguments, which do not cover the non-autonomous situation. We show that the previous results are a consequence of the Pontryagin maximum principle, and are easily generalized using the methods of optimal control. Main result asserts that vector-valued splines are related to the Pontryagin extremals of a non-autonomous linear-quadratic optimal control problem.Comment: This research was partially presented, as an oral communication, at the Second Junior European Meeting on "Control Theory and Stabilization", Dipartimento di Matematica del Politecnico di Torino, Torino, Italy, 3-5 December 2003. To appear on Rend. Sem. Mat. Univ. Pol. Torino, Vol. 64 (2006) No.

On the dynamics and entropy of the push-forward map

In this work we study the main dynamical properties of the push-forward map, a transformation in the space of probabilities P(X) induced by a map T: X \to X, X a compact metric space. We also establish a connection between topological entropies of T and of the push-forward map.Comment: 20 page

Multifractal regime transition in a modified minority game model

The search for more realistic modeling of financial time series reveals several stylized facts of real markets. In this work we focus on the multifractal properties found in price and index signals. Although the usual Minority Game (MG) models do not exhibit multifractality, we study here one of its variants that does. We show that the nonsynchronous MG models in the nonergodic phase is multifractal and in this sense, together with other stylized facts, constitute a better modeling tool. Using the Structure Function (SF) approach we detected the stationary and the scaling range of the time series generated by the MG model and, from the linear (nonlinear) behavior of the SF we identified the fractal (multifractal) regimes. Finally, using the Wavelet Transform Modulus Maxima (WTMM) technique we obtained its multifractal spectrum width for different dynamical regimes.Comment: 14 pages, 6 figure

Combinatorial Solution of One-Dimensional Quantum Systems

We give a self-contained exposition of the combinatorial solution of quantum mechanical systems of coupled spins on a one-dimensional lattice. Using Trotter formula, we write the partition function as a generating function of a spanning subgraph of a two-dimensional lattice and solve the combinatorial problem by the method of Pfaffians provided the weights satisfy the so-called free fermion condition. The free energy and the ground state energy as a function of the inverse temperature, couplings J and magnetic fields h, for the XY model in a transverse field with period p=1 and 2, is then obtained.Comment: Number of figures: 9 (eps

Two possible circumbinary planets in the eclipsing post-common envelope system NSVS 14256825

We present an analysis of eclipse timings of the post-common envelope binary NSVS 14256825, which is composed of an sdOB star and a dM star in a close orbit (P_{orb} = 0.110374 days). High-speed photometry of this system was performed between July, 2010 and August, 2012. Ten new mid-eclipse times were analyzed together with all available eclipse times in the literature. We revisited the (O-C) diagram using a linear ephemeris and verified a clear orbital period variation. On the assumption that these orbital period variations are caused by light travel time effects, the (O-C) diagram can be explained by the presence of two circumbinary bodies, even though this explanation requires a longer baseline of observations to be fully tested. The orbital periods of the best solution would be P_c ~ 3.5 years and P_d ~ 6.9 years. The corresponding projected semi-major axes would be a_c i_c ~ 1.9 AU and a_d i_d ~ 2.9 AU. The masses of the external bodies would be M_c ~ 2.9 M_{Jupiter} and M_d ~ 8.1 M_{Jupiter}, if we assume their orbits are coplanar with the close binary. Therefore NSVS 14256825 might be composed of a close binary with two circumbinary planets, though the orbital period variations is still open to other interpretations.Comment: 16 pages, 3 figures, 4 tables. Accepted for publication in Ap