On the complete integrability and linearization of nonlinear ordinary differential equations - Part II: Third order equations

We introduce a method for finding general solutions of third-order nonlinear differential equations by extending the modified Prelle-Singer method. We describe a procedure to deduce all the integrals of motion associated with the given equation so that the general solution follows straightforwardly from these integrals. The method is illustrated with several examples. Further, we propose a powerful method of identifying linearizing transformations. The proposed method not only unifies all the known linearizing transformations systematically but also introduces a new and generalized linearizing transformation (GLT). In addition to the above, we provide an algorithm to invert the nonlocal linearizing transformation. Through this procedure the general solution for the original nonlinear equation can be obtained from the solution of the linear ordinary differential equation.Comment: Submitted to Proceedings of the Royal Society London Series A, 21 page

Reaction-diffusion systems with a nonlinear rate of growth

In the literature there are quite a few elegant approaches which have been proposed to find (he first integrals of nonlinear differential equations. Recently, the modified Prelle-Singer method for finding the first integrals of second-order nonlinear ordinary differential equations (ODEs) has attracted considerable attention. Many researchers used this method to derive the first integrals to various systems. In this thesis, we are concerned with the first integrals for reaction-diffusion systems with a nonlinear rate of growth. Under certain parametric conditions we express the first integrals explicitly by applying an analytical method as well as the modified Prelle-Singer method

Certifying Confluence of Almost Orthogonal CTRSs via Exact Tree Automata Completion

Suzuki et al. showed that properly oriented, right-stable, orthogonal, and oriented conditional term rewrite systems with extra variables in right-hand sides are confluent. We present our Isabelle/HOL formalization of this result, including two generalizations. On the one hand, we relax proper orientedness and orthogonality to extended proper orientedness and almost orthogonality modulo infeasibility, as suggested by Suzuki et al. On the other hand, we further loosen the requirements of the latter, enabling more powerful methods for proving infeasibility of conditional critical pairs. Furthermore, we formalized a construction by Jacquemard that employs exact tree automata completion for non-reachability analysis and apply it to certify infeasibility of conditional critical pairs. Combining these two results and extending the conditional confluence checker ConCon accordingly, we are able to automatically prove and certify confluence of an important class of conditional term rewrite systems

Linearization of hybrid Chi using program counters

The language χ was developed some years back as a modelling and simulation language for industrial systems [1, 2]. Originally, the language χ included fea-tures for modelling discrete event systems only. Later on it was extended with features to model dynamic behavior of a system as well [3, 4]. Hybrid χ wa

Stock Prices and Monetary Policy Shocks: A General Equilibrium Approach

Recent empirical literature documents that unexpected changes in the nominal interest rates have a significant effect on stock prices: a 25-basis point increase in the Fed funds rate is associated with an immediate decrease in broad stock indices that may range from 0.5 to 2.3 percent, followed by a gradual decay as stock prices revert towards their long-run expected value. In this paper, we assess the ability of a general equilibrium New Keynesian asset-pricing model to account for these facts. The model we consider allows for staggered price and wage setting, as well as time-varying risk aversion through habit formation. We find that the model predicts a stock market response to policy shocks that matches empirical estimates, both qualitatively and quantitatively. Our findings are robust to a range of variations and parameterizations of the model.Monetary policy; Asset prices; New Keynesian general equilibrium model.

Effective Action Studies of Quantum Hall Spin Textures

We report on analytic and numerical studies of spin textures in quantum Hall systems using a long-wavelength effective action for the magnetic degrees of freedom derived previously. The majority of our results concern skyrmions or solitons of this action. We have constructed approximate analytic solutions for skyrmions of arbitrary topological and electric charge and derived expressions for their energies and charge and spin radii. We describe a combined shooting/relaxational technique for numerical determination of the skyrmion profiles and present results that compare favorably with the analytic treatment as well as with Hartree-Fock studies of these objects. In addition, we describe a treatment of textures at the edges of quantum Hall systems within this approach and provide details not reported previously.Comment: 13 pages, 10 figure

Linearized Einstein theory via null surfaces

Recently there has been developed a reformulation of General Relativity - referred to as {\it the null surface version of GR} - where instead of the metric field as the basic variable of the theory, families of three-surfaces in a four-manifold become basic. From these surfaces themselves, a conformal metric, conformal to an Einstein metric, can be constructed. A choice of conformal factor turns them into Einstein metrics. The surfaces are then automatically characteristic surfaces of this metric. In the present paper we explore the linearization of this {\it null surface theory} and compare it with the standard linear GR. This allows a better understanding of many of the subtle mathematical issues and sheds light on some of the obscure points of the null surface theory. It furthermore permits a very simple solution generating scheme for the linear theory and the beginning of a perturbation scheme for the full theory.Comment: 22 page

Money and Risk Aversion in a DSGE Framework: A Bayesian Application to the Euro Zone

In this paper, we set up and test a model of the Euro zone, with a special emphasis on the role of money. The model follows the New Keynesian DSGE framework, money being introduced in the utility function with a non-separability assumption. By using bayesian estimation techniques, we shed light on the determinants of output and inflation, but also of the interest rate, real money balances, flexible-price output and flexible-price real money balances variances. The role of money is investigated further. We find that its impact on output depends on the degree of agents’ risk aversion, increases with this degree, and becomes significant when risk aversion is high enough. The direct impact of the money variable on inflation variability is essentially minor whatever the risk aversion level, the interest rate (monetary policy) being the overwhelming explanatory factor.Bayesian Estimation; DSGE Model; Euro Area; Money