Encryption methods using formal power series rings

Recently there has been a great deal of work on noncommutative algebraic cryptography. This involves the use of noncommutative algebraic objects as the platforms for encryption systems. Most of this work, such as the Anshel-Anshel-Goldfeld scheme, the Ko-Lee scheme and the Baumslag-Fine-Xu Modular group scheme use nonabelian groups as the basic algebraic object. Some of these encryption methods have been successful and some have been broken. It has been suggested that at this point further pure group theoretic research, with an eye towards cryptographic applications, is necessary.In the present study we attempt to extend the class of noncommutative algebraic objects to be used in cryptography. In particular we explore several different methods to use a formal power series ring R && x1; :::; xn && in noncommuting variables x1; :::; xn as a base to develop cryptosystems. Although R can be any ring we have in mind formal power series rings over the rationals Q. We use in particular a result of Magnus that a finitely generated free group F has a faithful representation in a quotient of the formal power series ring in noncommuting variables.

A systematic and feasible method for computing nuclear contributions to electrical properties of polyatomic molecules

An analytic method to evaluate nuclear contributions to electrical properties of polyatomic molecules is presented. Such contributions control changes induced by an electric field on equilibrium geometry (nuclear relaxation contribution) and vibrational motion (vibrational contribution) of a molecular system. Expressions to compute the nuclear contributions have been derived from a power series expansion of the potential energy. These contributions to the electrical properties are given in terms of energy derivatives with respect to normal coordinates, electric field intensity or both. Only one calculation of such derivatives at the field-free equilibrium geometry is required. To show the useful efficiency of the analytical evaluation of electrical properties (the so-called AEEP method), results for calculations on water and pyridine at the SCF/TZ2P and the MP2/TZ2P levels of theory are reported. The results obtained are compared with previous theoretical calculations and with experimental values

Systematic study of the static electrical properties of the CO molecule: influence of the basis set size and correlation energy

The influence of the basis set size and the correlation energy in the static electrical properties of the CO molecule is assessed. In particular, we have studied both the nuclear relaxation and the vibrational contributions to the static molecular electrical properties, the vibrational Stark effect (VSE) and the vibrational intensity effect (VIE). From a mathematical point of view, when a static and uniform electric field is applied to a molecule, the energy of this system can be expressed in terms of a double power series with respect to the bond length and to the field strength. From the power series expansion of the potential energy, field-dependent expressions for the equilibrium geometry, for the potential energy and for the force constant are obtained. The nuclear relaxation and vibrational contributions to the molecular electrical properties are analyzed in terms of the derivatives of the electronic molecular properties. In general, the results presented show that accurate inclusion of the correlation energy and large basis sets are needed to calculate the molecular electrical properties and their derivatives with respect to either nuclear displacements or/and field strength. With respect to experimental data, the calculated power series coefficients are overestimated by the SCF, CISD, and QCISD methods. On the contrary, perturbation methods (MP2 and MP4) tend to underestimate them. In average and using the 6-311 + G(3df) basis set and for the CO molecule, the nuclear relaxation and the vibrational contributions to the molecular electrical properties amount to 11.7%, 3.3%, and 69.7% of the purely electronic μ, α, and β values, respectively

Elastic scattering of fast electrons and positrons by atoms

Elastic scattering of relativistic electrons and positrons by atoms is considered in the framework of the static field approximation. The scattering field is expressed as a sum of Yukawa terms to allow the use of various approximations. Accurate phase shifts have been computed by combining Bühring¿s power-series method with the WKB and Born approximations. This combined procedure allows the evaluation of differential cross sections for kinetic energies up to several tens of MeV. Numerical results are used to analyze the validity of several approximate methods, namely the first- and second-order Born approximations and the screened Mott formula, which are frequently adopted as the basis of multiple scattering theories and Monte Carlo simulations of electron and positron transport.

Compositional Time Series: An Application

The composition of the labour force is an important economic factor for a country.Often the changes in proportions of different groups are of interest.I this paper we study a monthly compositional time series from the Swedish LabourForce Survey from 1994 to 2005. Three models are studied: the ILR-transformed series,the ILR-transformation of the compositional differenced series of order 1, and the ILRtransformationof the compositional differenced series of order 12. For each of thethree models a VAR-model is fitted based on the data 1994-2003. We predict the timeseries 15 steps ahead and calculate 95 % prediction regions. The predictions of thethree models are compared with actual values using MAD and MSE and the predictionregions are compared graphically in a ternary time series plot.We conclude that the first, and simplest, model possesses the best predictive power ofthe three models

Lag-one autocorrelation in short series: Estimation and hypothesis testing

In the first part of the study, nine estimators of the first-order autoregressive parameter are reviewed and a new estimator is proposed. The relationships and discrepancies between the estimators are discussed in order to achieve a clear differentiation. In the second part of the study, the precision in the estimation of autocorrelation is studied. The performance of the ten lag-one autocorrelation estimators is compared in terms of Mean Square Error (combining bias and variance) using data series generated by Monte Carlo simulation. The results show that there is not a single optimal estimator for all conditions, suggesting that the estimator ought to be chosen according to sample size and to the information available of the possible direction of the serial dependence. Additionally, the probability of labelling an actually existing autocorrelation as statistically significant is explored using Monte Carlo sampling. The power estimates obtained are quite similar among the tests associated with the different estimators. These estimates evidence the small probability of detecting autocorrelation in series with less than 20 measurement times.

Countervailing power? Collusion in markets with decentralized trade

We consider the collective incentives of buyers and sellers to form cartels in markets where trade is realized through decentralized pairwise bargaining. Cartels are coalitions of buyers or sellers that limit market participation and compensate inactive members for abstaining from trade. In a stable market outcome, cartels set Nash equilibrium quantities and cartel memberships are immune to defections. We prove that the set of stable market outcomes is non-empty and we provide its full characterization. Stable market outcomes are of two types: (i) at least one cartel actively restrains trade and the levels of market participation are balanced, or (ii) only one cartel, eventually the cartel that forms on the long side of the market, is active and it reduces trade slightly below the opponent's.

I want you! An experiment studying the selection effect when assigning distributive power.

We study whether selection affects motivation. In our experiment subjects first answer a personality questionnaire. They then play a 3-person game. One of the three players decides between an outside option assigning him a positive amount, but leaving the two others empty-handed and allowing one of the other two players to distribute a pie. Treatments differ in the procedure by which distributive power is assigned: to a randomly determined or to a knowingly selected partner. Before making her decision the selecting player could consult the personality questionnaire of the other two players. Results show that knowingly selected players keep less for themselves than randomly selected ones and reward the selecting player more generously.

Demand elasticity and market power in the spanish electricity market

In this paper we check whether generator's bid behavior at the Spanish whosale electricity market is consistent with the hypothesis of profit maximization on their residual demands. Using OMEL data, we find the arc-elacticity of the residual demand around the system marginal price. The results suggest thet the larger firms are not actually profit-msximization. We argue how the regulatory environment may drive these results. Finally, we repeat the analysis for the first session of the intra-day market where presumably firms may not have the same incentives as in the day-ahead market.

Two algorithms to find a power integral basis

"Vegeu el resum a l'inici del fitxer adjunt."

Co-movements between US and UK stock prices: the roles of macroeconomic information and time-series varying conditional correlations

This paper provides evidence on the sources of co-movement in monthly US and UK stock price movements by investigating the role of macroeconomic and financial variables in a bivariate system with time-varying conditional correlations. Crosscountry communality in response is uncovered, with changes in the US Federal Funds rate, UK bond yields and oil prices having similar negative effects in both markets. Other variables also play a role, especially for the UK market. These effects do not, however, explain the marked increase in cross-market correlations observed from around 2000, which we attribute to time variation in the correlations of shocks to these markets. A regime-switching smooth transition model captures this time variation well and shows the correlations increase dramatically around 1999-2000. JEL classifications: C32, C51, G15 Keywords: international stock returns, DCC-GARCH model, smooth transition conditional correlation GARCH model, model evaluation.

Price level convergence, purchasing power parity and multiple structural breaks: an application to US cities

This article provides a fresh methodological and empirical approach for assessing price level convergence and its relation to purchasing power parity (PPP) using annual price data for seventeen US cities. We suggest a new procedure that can handle a wide range of PPP concepts in the presence of multiple structural breaks using all possible pairs of real exchange rates. To deal with cross-sectional dependence, we use both cross-sectional demeaned data and a parametric bootstrap approach. In general, we find more evidence for stationarity when the parity restriction is not imposed, while imposing parity restriction provides leads toward the rejection of the panel stationar- ity. Our results can be embedded on the view of the Balassa-Samuelson approach, but where the slope of the time trend is allowed to change in the long-run. The median half-life point estimate are found to be lower than the consensus view regardless of the parity restriction.

Political alliances and organisational change in political parties: a framework for analysis

This article sets out a theoretical framework for the study of organisational change within political alliances. To achieve this objective it uses as a starting point a series of premises, the most notable of which include the definition of organisational change as a discrete, complex and focussed phenomenon of changes in power within the party. In accordance with these premises, it analyses the synthetic model of organisational change proposed by Panebianco (1988). After examining its limitations, a number of amendments are proposed to adapt it to the way political alliances operate. The above has resulted in the design of four new models. In order to test its validity and explanatory power in a preliminary manner, the second part looks at the organisational change of the UDC within the CiU alliance between 1978 and 2001. The discussion and conclusions reached demonstrate the problems of determinism of the Panebianco model and suggest, tentatively, the importance of the power balance within the alliance as a key factor.

Water scarcity, social power and the production of an elite suburb: the political ecology of water in Matadepera, Catalonia

This article investigates the history of land and water transformations in Matadepera, a wealthy suburb of metropolitan Barcelona. Analysis is informed by theories of political ecology and methods of environmental history; although very relevant, these have received relatively little attention within ecological economics. Empirical material includes communications from the City Archives of Matadepera (1919-1979), 17 interviews with locals born between 1913 and 1958, and an exhaustive review of grey historical literature. Existing water histories of Barcelona and its outskirts portray a battle against natural water scarcity, hard won by heroic engineers and politicians acting for the good of the community. Our research in Matadepera tells a very different story. We reveal the production of a highly uneven landscape and waterscape through fierce political and power struggles. The evolution of Matadepera from a small rural village to an elite suburb was anything but spontaneous or peaceful. It was a socio-environmental project well intended by landowning elites and heavily fought by others. The struggle for the control of water went hand in hand with the land and political struggles that culminated – and were violently resolved - in the Spanish Civil War. The displacement of the economic and environmental costs of water use from few to many continues to this day and is constitutive of Matadepera’s uneven and unsustainable landscape. By unravelling the relations of power that are inscribed in the urbanization of nature (Swyngedouw, 2004), we question the perceived wisdoms of contemporary water policy debates, particularly the notion of a natural scarcity that merits a technical or economic response. We argue that the water question is fundamentally a political question of environmental justice; it is about negotiating alternative visions of the future and deciding whose visions will be produced.