On the number of limit cycles bifurcating from a non-global degenerated center

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Lower bounds for the number of limit cycles of trigonometric Abel equations

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Limit cycles for cubic systems with a symmetry of order 4 and without in nite critical points

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Limit Cycles for a class of three dimensional polynomial differential systems

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On the upper bound of the number of limit cycles obtained by the second order averaging method I

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On the upper bound of the number of limit cycles obtained by the second order averaging method II

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Geometric tools to determine the hyperbolicity of limit cycles

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Multiplicity of limit cycles and analytic m-solutions for planar differential systems

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Renormalization and α-limit set for expanding Lorenz maps

We establish a one-to-one correspondence between the renormalizations and proper totally invariant closed sets (i.e., α-limit sets) of expanding Lorenz map, which enable us to distinguish periodic and non-periodic renormalizations. We describe the minimal renormalization by constructing the minimal totally invariant closed set, so that we can define the renormalization operator. Using consecutive renormalizations, we obtain complete topological characteriza- tion of α-limit sets and nonwandering set decomposition. For piecewise linear Lorenz map with slopes ≥ 1, we show that each renormalization is periodic and every proper α-limit set is countable.

On the existence and uniqueness of limit cycles in Liénard differential equations allowing discontinuities

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Rigorous derivation of a nonlinear diffusion equation as fast-reaction limit of a continuous coagulation-fragmentation model with diffusion

Weak solutions of the spatially inhomogeneous (diffusive) Aizenmann-Bak model of coagulation-breakup within a bounded domain with homogeneous Neumann boundary conditions are shown to converge, in the fast reaction limit, towards local equilibria determined by their mass. Moreover, this mass is the solution of a nonlinear diffusion equation whose nonlinearity depends on the (size-dependent) diffusion coefficient. Initial data are assumed to have integrable zero order moment and square integrable first order moment in size, and finite entropy. In contrast to our previous result [CDF2], we are able to show the convergence without assuming uniform bounds from above and below on the number density of clusters.

On Cooperative solutions of a generalized assignment game: limit theorems to the set of competitive equilibria

We study two cooperative solutions of a market with indivisible goods modeled as a generalized assignment game: Set-wise stability and Core. We first establish that the Set-wise stable set is contained in the Core and it contains the non-empty set of competitive equilibrium payoffs. We then state and prove three limit results for replicated markets. First, the sequence of Cores of replicated markets converges to the set of competitive equilibrium payoffs when the number of replicas tends to infinity. Second, the Set-wise stable set of a two-fold replicated market already coincides with the set of competitive equilibrium payoffs. Third, for any number of replicas there is a market with a Core payoff that is not a competitive equilibrium payoff.

alr approach for replacing values below the detection limit

All of the imputation techniques usually applied for replacing values below thedetection limit in compositional data sets have adverse effects on the variability. In thiswork we propose a modification of the EM algorithm that is applied using the additivelog-ratio transformation. This new strategy is applied to a compositional data set and theresults are compared with the usual imputation techniques

Market versus limit orders in an imperfectly competitive security

This paper analyzes the choice between limit and market orders in animperfectly competitive noisy rational expectations economy. There is a uniqueinsider, who takes into account the effect their trading has on prices. If theinsider behaves as a price taker, she will choose market orders if her privateinformation is very precise and she will choose limit orders otherwise. On thecontrary, if the insider recognizes and exploits her ability to affect themarket price, her optimal choice is to place limit orders whatever the precisionof her private information.