Instability of equilibrium points of some Lagrangian systems

In this work we show that, if L is a natural Lagrangian system such that the k-jet of the potential energy ensures it does not have a minimum at the equilibrium and such that its Hessian has rank at least n - 2, then there is an asymptotic trajectory to the associated equilibrium point and so the equilibrium is unstable. This applies, in particular, to analytic potentials with a saddle point and a Hessian with at most 2 null eigenvalues. The result is proven for Lagrangians in a specific form, and we show that the class of Lagrangians we are interested can be taken into this specific form by a subtle change of spatial coordinates. We also consider the extension of this results to systems subjected to gyroscopic forces. (C) 2008 Elsevier Inc. All rights reserved.

Ca(2+)-mediated thiolysis of peptide-resin linkage as an option for preparing protected peptide thioesters

A mild new procedure for preparing protected peptide thioesters, based oil Ca(2+)-assisted thiolysis of peptide-Kaiser oxime resin (KOR) linkage, is described. Ac-Ile-Ser(Bzl)-Asp(OcHx)-SR (Ac: acetyl; Bzl: benzyl; cHx: cyclohexyl), model peptide, was readily released from the resin by incubating the peptide-KOR at 60 degrees C in mixtures of DMF with n-butanethiol [R = (CH(2))(3)CH(3)] or ethyl 3-mercaptopropionate [R = (CH(2))(2)COOCHCH(3)] containing Ca(CH(3)COO)(2). After serine and aspartic acid side-chain deprotection under acid conditions, Ac-Ile-Ser-Asp-S(CH(2))(2)COOCH(2)CH(3) was successfully obtained with good quality and high yield. This type of C-terminal modified peptide may act as an excellent acyl donor in peptide segment condensation by the thioester method, native chemical ligation and enzymatic methods. (c) 2008 Elsevier Ltd. All rights reserved.

Structural parameters of polyacrylamide hydrogels obtained by the Equilibrium Swelling Theory

In this paper, the synthesis and structural characterization of a series of polyacrylamide hydrogels with different degrees of reticulation are reported. Although the Equilibrium Swelling Theory was recognized as a simple and reliable tool for the determination of structural hydrogels network parameters like equilibrium degree of swelling, cross-link ratio and mesh size, this is the first application of this methodology for polyacrylamide hydrogels. By changing the total monomer content in the synthesis solution (%T) from 5 to 30%, at a fixed value of cross-linker content in the total monomer amount (%C) of 5%, the final parameter obtained, the mesh size, can be tuned from 2 to 0.3 nm. It was also possible to change the mesh size (0.19-0.35) by varying %C from 5 to 12% (at %T = 20%). Scanning Electron Microscopy images for the most different formulations are shown and corroborate data obtained from the theory. (c) 2008 Elsevier Ltd. All rights reserved.

Solvatochromism in Binary Mixtures: First Report on a Solvation Free Energy Relationship between Solvent Exchange Equilibrium Constants and the Properties of the Medium

We have employed UV-vis spectroscopy in order to investigate details of the solvation of six solvatochromic indicators, hereafter designated as ""probes"", namely, 2,6-diphenyl-4-(2,4,6-triphenylpyridinium-1-yl) phenolate (RB); 4-[(E)-2-(1-methylpyridinium-4-yl)ethenyl] phenolate, MePM; 1-methylquinolinium-8-olate, QB; 2-bromo-4-[(E)-2-(1-methylpyridinium-4-yl)ethenyl] phenolate, MePMBr, 2,6-dichloro-4-(2,4,6-triphenylpyridinium-1-yl) phenolate (WB); and 2,6-dibromo-4-[(E)-2-(1-methylpyridinium-4-yl)ethenyl] phenolate, MePMBr,, respectively. These can be divided into three pairs, each includes two probes of similar pK(a) in water and different lipophilicity. Solvation has been studied in binary mixtures, BMs, of water, W, with 12 protic organic solvents, S, including mono- and bifunctional alcohols (2-alkoxyethanoles, unsaturated and chlorinated alcohols). Each medium was treated as a mixture of S, W, and a complex solvent, S-W, formed by hydrogen bonding. Values of lambda(max) (of the probe intramolecular charge transfer) were converted into empirical polarity scales, E(T)(probe) in kcal/mol, whose values were correlated with the effective mole fraction of water in the medium, chi w(effective). This correlation furnished three equilibrium constants for the exchange of solvents in the probe solvation shell; phi(W/S) (W substitutes S): phi(S-W/W) (S-W substitutes W), and phi(S-W/S) (S-W substitutes S), respectively. The values of these constants depend on the physicochemical properties of the probe and the medium. We tested, for the first time, the applicability of a new solvation free energy relationship: phi = constant + a alpha(BM) + b beta(BM) + s(pi*(BM) + d delta) + p log P(BM), where a, b, s, and p are regression coefficients alpha(BM), beta(BM), and pi*(BM) are solvatochromic parameters of the BM, delta is a correction term for pi*, and log P is an empirical scale of lipophilicity. Correlations were carried out with two-, three-, and four-medium descriptors. In all cases, three descriptors gave satisfactory correlations; use of four parameters gave only a marginal increase of the goodness of fit. For phi(W/S), the most important descriptor was found to be the lipophilicity of the medium; for phi(S-W/W) and phi(S-W/S), solvent basicity is either statistically relevant or is the most important descriptor. These responses are different from those of E(T)(probe) of many solvatochromic indicators in pure solvents, where the importance of solvent basicity is usually marginal, and can be neglected.

Pricing and competition in the Swedish retail market for electricity

Sweden, together with Norway, Finland and Denmark, have created a multi-national electricity market called NordPool. In this market, producers and retailers of electricity can buy and sell electricity, and the retailers then offers this electricity to end consumers such as households and industries. Previous studies have shown that pricing at the NordPool market is functioning quite well, but no other study has to my knowledge studied if pricing in the retail market to consumers in Sweden is well functioning. If the market is well functioning, with competition and low transaction costs when changing electricity retailer, we would expect that a homogeneous good such as electricity would be sold at the approximately same price, and that price changes would be highly correlated, in this market. Thus, the aim of this study is to test whether the price of Vattenfall, the largest energy firm in the Swedish market, is highly correlated to the price of other firms in the Swedish retail market for electricity. Descriptive statistics indicate that the price offered by Vattenfall is quite similar to the price of other firms in the market. In addition, regression analysis show that the correlation between the price of Vattenfall and other firms is as high as 0.98.

Local concavifiability of preferences and determinacy of equilibrium

In this paper we consider strictly convex monotone continuous complete preorderings on R+n that are locally representable by a concave utility function. By Alexandroff 's (1939) theorem, this function is twice dífferentiable almost everywhere. We show that if the bordered hessian determinant of a concave utility representation vanishes on a null set. Then demand is countably rectifiable, that is, except for a null set of bundles, it is a countable union of c1 manifolds. This property of consumer demand is enough to guarantee that the equilibrium prices of apure exchange economy will be locally unique, for almost every endowment. We give an example of an economy satisfying these conditions but not the Katzner (1968) - Debreu (1970, 1972) smoothness conditions.

Tests of conditional asset pricing models in the brazilian stock market

In this paper, we test a version of the conditional CAPM with respect to a local market portfolio, proxied by the Brazilian stock index during the period 1976-1992. We also test a conditional APT modeI by using the difference between the 3-day rate (Cdb) and the overnight rate as a second factor in addition to the market portfolio in order to capture the large inflation risk present during this period. The conditional CAPM and APT models are estimated by the Generalized Method of Moments (GMM) and tested on a set of size portfolios created from individual securities exchanged on the Brazilian markets. The inclusion of this second factor proves to be important for the appropriate pricing of the portfolios.

Competitive equilibrium hyperinflation under rational expectations

This paper shows that a competitive equilibrium model, where a representative agent maximizes welfare, expectations are rational and markets are in equilibrium can account for several hyperinflation stylized facts. The theory is built by combining two hypotheses, namely, a fiscal crisis that requires printing money to finance an increasing public deficit and a predicted change in an unsustainable fiscal regime.

Arbitrage Pricing Theory (APT) e variáveis macroeconômicas: um estudo empírico sobre o mercado acionário brasileiro

Este trabalho utiliza retornos mensais de 10 portfólios de ações negociadas na Bovespa entre 1987 e 1997, a fim de testar a validade empírica do modelo APT. Foram criadas variáveis macroeconômicas como fatores de variância comum aos diversos portfólios. Além destes fatores serem estatisticamente significantes para explicar a relação entre os retornos dos diversos portfólios de uma maneira geral, foram encontradas evidências no sentido de validar o APT.

Estimating the term structure of volatility and fixed income derivative pricing

Estimating the parameters of the instantaneous spot interest rate process is of crucial importance for pricing fixed income derivative securities. This paper presents an estimation for the parameters of the Gaussian interest rate model for pricing fixed income derivatives based on the term structure of volatility. We estimate the term structure of volatility for US treasury rates for the period 1983 - 1995, based on a history of yield curves. We estimate both conditional and first differences term structures of volatility and subsequently estimate the implied parameters of the Gaussian model with non-linear least squares estimation. Results for bond options illustrate the effects of differing parameters in pricing.

Bubbles, collateral and monetary equilibrium

Consider an economy where infinite-lived agents trade assets collateralized by durable goods. We obtain results that rule out bubbles when the additional endowments of durable goods are uniformly bounded away from zero, regardless of whether the asset’s net supply is positive or zero. However, bubbles may occur, even for state-price processes that generate finite present value of aggregate wealth. First, under complete markets, if the net supply is being endogenously reduced to zero as a result of collateral repossession. Secondly, under incomplete markets, for a persistent positive net supply, under the general conditions guaranteeing existence of equilibrium. Examples of monetary equilibria are provided.

A stochastic discount factor approach to asset pricing using panel data

Using the Pricing Equation, in a panel-data framework, we construct a novel consistent estimator of the stochastic discount factor (SDF) mimicking portfolio which relies on the fact that its logarithm is the ìcommon featureîin every asset return of the economy. Our estimator is a simple function of asset returns and does not depend on any parametric function representing preferences, making it suitable for testing di§erent preference speciÖcations or investigating intertemporal substitution puzzles.

A general-equilibrium closed-form solution to the welfare costs of inflation (Forthcoming, Revista Brasileira de Economia)

This work presents closed-form solutions to Lucasís (2000) generalequilibrium expression for the welfare costs of ináation, as well as to the di§erence between the general-equlibrium measure and Baileyís (1956) partial-equilibrium measure. In Lucasís original work only numerical solutions are provided.

Nash equilibrium under knightian uncertainty: breaking down backward induction (extensively revised version)

We define Nash equilibrium for two-person normal form games in the presence of uncertainty, in the sense of Knight(1921). We use the fonna1iution of uncertainty due to Schmeidler and Gilboa. We show tbat there exist Nash equilibria for any degree of uncertainty, as measured by the uncertainty aversion (Dow anel Wer1ang(l992a». We show by example tbat prudent behaviour (maxmin) can be obtained as an outcome even when it is not rationaliuble in the usual sense. Next, we break down backward industion in the twice repeated prisoner's dilemma. We link these results with those on cooperation in the finitely repeated prisoner's dilemma obtained by Kreps-Milgrom-Roberts-Wdson(1982), and withthe 1iterature on epistemological conditions underlying Nash equilibrium. The knowledge notion implicit in this mode1 of equilibrium does not display logical omniscience.