Choice under Risk : Theory and Applications

Es útil para estudiantes de postgrado (Master y Doctorado) en cursos de Economía o de Microeconomía en los que se analicen problemas de Decisión en condiciones de Riesgo o Incertidumbre. El documento comienza explicando la Teoría de la Utilidad Esperada. A continuación se estudian la aversión al riesgo, los coeficientes de aversión absoluta y relativa al riesgo, la relación “más averso que” entre agentes económicos y los efectos riqueza sobre las decisiones en algunas relaciones de preferencia utilizadas frecuentemente en el análisis económico. La sección 4 se centra en la comparación entre alternativas arriesgadas en términos de rendimiento y riesgo, considerando la dominancia estocástica de primer y segundo orden y algunas extensiones posteriores de esas relaciones de orden. El documento concluye con doce ejercicios resueltos en los que se aplican los conceptos y resultados expuestos en las secciones anteriores a problemas de decisión en varios contextos

New Strain Gradient Theory And Analysis

A new strain gradient theory which is based on energy nonlocal model is proposed in this paper, and the theory is applied to investigate the size effects in thin metallic wire torsion, ultra-thin beam bending and micro-indentation of polycrystalline copper. First, an energy nonlocal model is suggested. Second, based on the model, a new strain gradient theory is derived. Third, the new theory is applied to analyze three representative experiments.

An extension of the two dimensional JKR theory to the case with a large contact width

In the Hertz and JKR theories, parabolic assumptions for the rounded profiles of the sphere or cylinder are adopted under the condition that the contact radius (width) should be very small compared to the radius of the sphere or cylinder. However, a large contact radius (width) is often found in experiments even under a zero external loading. We aim at extending the plane strain JKR theory to the case with a large contact width. The relation between the external loading and the contact width is given. Solutions for the Hertz, JKR and rounded-profile cases are compared and analyzed. It is found that when the ratio of a/R is approximately larger than about 0.4, the parabolic assumptions in the Hertz and JKR theories are no longer valid and the exact rounded profile function should be used.

The elasto-damage theory of the components assembling model

The potential energy in materials is well approximated by pair functional which is composed of pair potentials and embedding energy. During calculating material potential energy, the orientational component and the volumetric component are derived respectively from pair potentials and embedding energy. The sum of energy of all these two kinds of components is the material potential. No matter how microstructures change, damage or fracture, at the most level, they are all the changing and breaking atomic bonds. As an abstract of atomic bonds, these components change their stiffness during damaging. Material constitutive equations have been formulated by means of assembling all components' response functions. This material model is called the component assembling model. Theoretical analysis and numerical computing indicate that the proposed model has the capacity of reproducing some results satisfactorily, with the advantages of great conceptual simplicity, physical explicitness, and intrinsic induced anisotropy, etc.

Relating thermodynamics to information theory : the equality of free energy and mutual information

In this thesis we uncover a new relation which links thermodynamics and information theory. We consider time as a channel and the detailed state of a physical system as a message. As the system evolves with time, ever present noise insures that the "message" is corrupted. Thermodynamic free energy measures the approach of the system toward equilibrium. Information theoretical mutual information measures the loss of memory of initial state. We regard the free energy and the mutual information as operators which map probability distributions over state space to real numbers. In the limit of long times, we show how the free energy operator and the mutual information operator asymptotically attain a very simple relationship to one another. This relationship is founded on the common appearance of entropy in the two operators and on an identity between internal energy and conditional entropy. The use of conditional entropy is what distinguishes our approach from previous efforts to relate thermodynamics and information theory.

Deviation from standard inflationary cosmology and the problems in ekpyrosis

There are two competing models of our universe right now. One is Big Bang with inflation cosmology. The other is the cyclic model with ekpyrotic phase in each cycle. This paper is divided into two main parts according to these two models. In the first part, we quantify the potentially observable effects of a small violation of translational invariance during inflation, as characterized by the presence of a preferred point, line, or plane. We explore the imprint such a violation would leave on the cosmic microwave background anisotropy, and provide explicit formulas for the expected amplitudes $\langle a_{lm}a_{l'm'}^*\rangle$ of the spherical-harmonic coefficients. We then provide a model and study the two-point correlation of a massless scalar (the inflaton) when the stress tensor contains the energy density from an infinitely long straight cosmic string in addition to a cosmological constant. Finally, we discuss if inflation can reconcile with the Liouville's theorem as far as the fine-tuning problem is concerned. In the second part, we find several problems in the cyclic/ekpyrotic cosmology. First of all, quantum to classical transition would not happen during an ekpyrotic phase even for superhorizon modes, and therefore the fluctuations cannot be interpreted as classical. This implies the prediction of scale-free power spectrum in ekpyrotic/cyclic universe model requires more inspection. Secondly, we find that the usual mechanism to solve fine-tuning problems is not compatible with eternal universe which contains infinitely many cycles in both direction of time. Therefore, all fine-tuning problems including the flatness problem still asks for an explanation in any generic cyclic models.

Topics in bifurcation theory

I. Existence and Structure of Bifurcation Branches

The problem of bifurcation is formulated as an operator equation in a Banach space, depending on relevant control parameters, say of the form G(u,λ) = 0. If dimN(G_u(u_O,λ_O)) = m the method of Lyapunov-Schmidt reduces the problem to the solution of m algebraic equations. The possible structure of these equations and the various types of solution behaviour are discussed. The equations are normally derived under the assumption that G^O_λεR(G^O_u). It is shown, however, that if G^O_λεR(G^O_u) then bifurcation still may occur and the local structure of such branches is determined. A new and compact proof of the existence of multiple bifurcation is derived. The linearized stability near simple bifurcation and "normal" limit points is then indicated.

II. Constructive Techniques for the Generation of Solution Branches

A method is described in which the dependence of the solution arc on a naturally occurring parameter is replaced by the dependence on a form of pseudo-arclength. This results in continuation procedures through regular and "normal" limit points. In the neighborhood of bifurcation points, however, the associated linear operator is nearly singular causing difficulty in the convergence of continuation methods. A study of the approach to singularity of this operator yields convergence proofs for an iterative method for determining the solution arc in the neighborhood of a simple bifurcation point. As a result of these considerations, a new constructive proof of bifurcation is determined.