Periodic points of holomorphic maps via Lefschetz numbers

In this paper we study the set of periods of holomorphic maps on compact manifolds, using the periodic Lefschetz numbers introduced by Dold and Llibre, which can be computed from the homology class of the map. We show that these numbers contain information about the existence of periodic points of a given period; and, if we assume the map to be transversal, then they give us the exact number of such periodic orbits. We apply this result to the complex projective space of dimension n and to some special type of Hopf surfaces, partially characterizing their set of periods. In the first case we also show that any holomorphic map of CP(n) of degree greater than one has infinitely many distinct periodic orbits, hence generalizing a theorem of Fornaess and Sibony. We then characterize the set of periods of a holomorphic map on the Riemann sphere, hence giving an alternative proof of Baker's theorem.

Single-valued solutions for the Böhm-Bawerk horse market game

Single-valued solutions for the case of two-sided market games without product differentiation, also known as Böhm-Bawerk horse market games, are analyzed. The nucleolus is proved to coincide with the tau-value, and is thus the midpoint of the core. Moreover a characterization of this setof games in terms of the assignment matrix is provided.

Time consistent Pareto solutions in common access resource gameswith asymmetric players

In the analysis of equilibrium policies in a di erential game, if agents have different time preference rates, the cooperative (Pareto optimum) solution obtained by applying the Pontryagin's Maximum Principle becomes time inconsistent. In this work we derive a set of dynamic programming equations (in discrete and continuous time) whose solutions are time consistent equilibrium rules for N-player cooperative di erential games in which agents di er in their instantaneous utility functions and also in their discount rates of time preference. The results are applied to the study of a cake-eating problem describing the management of a common property exhaustible natural resource. The extension of the results to a simple common property renewable natural resource model in in nite horizon is also discussed.

Heterogeneous discounting in consumption-investment problems. Time consistent solutions

[cat] En aquest treball s'analitza un model estocàstic en temps continu en el que l'agent decisor descompta les utilitats instantànies i la funció final amb taxes de preferència temporal constants però diferents. En aquest context es poden modelitzar problemes en els quals, quan el temps s'acosta al moment final, la valoració de la funció final incrementa en comparació amb les utilitats instantànies. Aquest tipus d'asimetria no es pot descriure ni amb un descompte estàndard ni amb un variable. Per tal d'obtenir solucions consistents temporalment es deriva l'equació de programació dinàmica estocàstica, les solucions de la qual són equilibris Markovians. Per a aquest tipus de preferències temporals, s'estudia el model clàssic de consum i inversió (Merton, 1971) per a les funcions d'utilitat del tipus CRRA i CARA, comparant els equilibris Markovians amb les solucions inconsistents temporalment. Finalment es discuteix la introducció del temps final aleatori.

Coalitionally monotonic set-solutions for cooperative TU games

A static comparative study on set-solutions for cooperative TU games is carried out. The analysis focuses on studying the compatibility between two classical and reasonable properties introduced by Young (1985) in the context of single valued solutions, namely core-selection and coalitional monotonicity. As the main result, it is showed that coalitional monotonicity is not only incompatible with the core-selection property but also with the bargaining-selection property. This new impossibility result reinforces the tradeoff between these kinds of interesting and intuitive economic properties. Positive results about compatibility between desirable economic properties are given replacing the core selection requirement by the core-extension property.

Aggregate monotonic stable single-valued solutions for cooperative games

[cat] En aquest treball caracteritzem les solucions puntuals de jocs cooperatius d'utilitat transferible que compleixen selecció del core i monotonia agregada. També mostrem que aquestes dues propietats són compatibles amb la individualitat racional, la propietat del jugador fals i la propietat de simetria. Finalment, caracteritzem les solucions puntuals que compleixen les cinc propietats a l'hora.

Velocity fluctuations of fracturelike disruptions of associating polymer solutions

Velocity has been measured as a function of time for propagating crack tips as water is injected into solutions of end-capped associating polymers in a rectanguar Hele-Shaw cell. Measurements were performed for flows with different values of cell gap, channel width, polymer molecular weight, and polymer concentration. The condition for the onset of fracturelike behavior is well described by a Deborah number which uses the shear-thinning shear rate of the polymer solution as a characteristic frequency for network relaxation. At low molecular weight, the onset of fracturelike pattern evolution is accompanied by an abrupt jump in tip velocity, followed by a lower and approximately constant acceleration. At high molecular weight, the transition to fracturelike behavior involves passing through a regime that may be understood in terms of stick-slip dynamics. The crack-tip wanders from side to side and fluctuates (in both speed and velocity along the channel) with a characteristic frequency which depends linearly on the invading fluid injection rate.

Velocity-jump instabilities in Hele-Shaw flow of associating polymer solutions

We study fracturelike flow instabilities that arise when water is injected into a Hele-Shaw cell filled with aqueous solutions of associating polymers. We explore various polymer architectures, molecular weights, and solution concentrations. Simultaneous measurements of the finger tip velocity and of the pressure at the injection point allow us to describe the dynamics of the finger in terms of the finger mobility, which relates the velocity to the pressure gradient. The flow discontinuities, characterized by jumps in the finger tip velocity, which are observed in experiments with some of the polymer solutions, can be modeled by using a nonmonotonic dependence between a characteristic shear stress and the shear rate at the tip of the finger. A simple model, which is based on a viscosity function containing both a Newtonian and a non-Newtonian component, and which predicts nonmonotonic regions when the non-Newtonian component of the viscosity dominates, is shown to agree with the experimental data.

Periodic forcing of scroll rings and control of Winfree turbulence in excitable media

By simulations of the Barkley model, action of uniform periodic nonresonant forcing on scroll rings and wave turbulence in three-dimensional excitable media is investigated. Sufficiently strong rapid forcing converts expanding scroll rings into the collapsing ones and suppresses the Winfree turbulence caused by the negative tension of wave filaments. Slow strong forcing has an opposite effect, leading to expansion of scroll rings and induction of the turbulence. These effects are explained in the framework of the phenomenological kinematic theory of scroll waves.

Fréedericksz transition in a periodic magnetic field

We study the Fréedericksz transition in a twist geometry under the effect of a periodic modulation of the magnitude of the applied magnetic field. We find a shift of the effective instability point and a time-periodic state with anomalously large orientational fluctuations. This time-periodic state occurs below threshold and it is accompanied by a dynamically stabilized spatial pattern. Beyond the instability the emergence of a transient pattern can be significantly delayed by a fast modulation, allowing the observation of pattern selection by slowing down the reorientational dynamics.

Electronic structure of a neutral oxygen vacancy in SrTiO3

The electronic structure of an isolated oxygen vacancy in SrTiO3 has been investigated with a variety of ab initio quantum mechanical approaches. In particular we compared pure density functional theory (DFT) approaches with the Hartree-Fock method, and with hybrid methods where the exchange term is treated in a mixed way. Both local cluster models and periodic calculations with large supercells containing up to 80 atoms have been performed. Both diamagnetic (singlet state) and paramagnetic (triplet state) solutions have been considered. We found that the formation of an O vacancy is accompanied by the transfer of two electrons to the 3d(z2) orbitals of the two Ti atoms along the Ti-Vac-Ti axis. The two electrons are spin coupled and the ground state is diamagnetic. New states associated with the defect center appear in the gap just below the conduction band edge. The formation energy computed with respect to an isolated oxygen atom in the triplet state is 9.4 eV.

Electronic and magnetic structure of LaMnO3 from hybrid periodic density-functional theory

The electronic and magnetic structures of the LaMnO3 compound have been studied by means of periodic calculations within the framework of spin polarized hybrid density-functional theory. In order to quantify the role of approximations to electronic exchange and correlation three different hybrid functionals have been used which mix nonlocal Fock and local Dirac-Slater exchange. Periodic Hartree-Fock results are also reported for comparative purposes. The A-antiferromagnetic ground state is properly predicted by all methods including Hartree-Fock exchange. In general, the different hybrid methods provide a rather accurate description of the band gap and of the two magnetic coupling constants, strongly suggesting that the corresponding description of the electronic structure is also accurate. An important conclusion emerging from this study is that the nature of the occupied states near the Fermi level is intermediate between the Hartree-Fock and local density approximation descriptions with a comparable participation of both Mn and O states.

Ab initio study of MF2 (M=Mn, Fe, Co, Ni) rutile-type compounds using the periodic unrestricted Hartree-Fock approach

The ab initio periodic unrestricted Hartree-Fock method has been applied in the investigation of the ground-state structural, electronic, and magnetic properties of the rutile-type compounds MF2 (M=Mn, Fe, Co, and Ni). All electron Gaussian basis sets have been used. The systems turn out to be large band-gap antiferromagnetic insulators; the optimized geometrical parameters are in good agreement with experiment. The calculated most stable electronic state shows an antiferromagnetic order in agreement with that resulting from neutron scattering experiments. The magnetic coupling constants between nearest-neighbor magnetic ions along the [001], [111], and [100] (or [010]) directions have been calculated using several supercells. The resulting ab initio magnetic coupling constants are reasonably satisfactory when compared with available experimental data. The importance of the Jahn-Teller effect in FeF2 and CoF2 is also discussed.

Diffusive transport in spatially periodic hydrodynamic flows

We calculate the effective diffusion coefficient in convective flows which are well described by one spatial mode. We use an expansion in the distance from onset and homogenization methods to obtain an explicit expression for the transport coefficient. We find that spatially periodic fluid flow enhances the molecular diffusion D by a term proportional to D-1. This enhancement should be easy to observe in experiments, since D is a small number.