Let Ca be the central Cantor set obtained by removing a central interval of length 1 − 2a from the unit interval, and continuing this process inductively on each of the remaining two intervals. We prove that if log b/ log a is irrational, then dim(Ca + Cb) = min(dim(Ca) + dim(Cb), 1), where dim is Hausdorff dimension. More generally, given two self-similar sets K,K′ in R and a scaling parameter...

Milton Friedman argued that irrational traders will consistently lose money, won’t survive and, therefore, cannot influence long run equilibrium asset prices. Since his work, survival and price influence have been assumed to be the same. Often partial equilibrium analysis has been relied upon to examine the survival of irrational traders and to make inferences on their influence on prices. In t...

The idea that technological revolutions can explain major swings in stock market value is occupying an increasingly prominent role in the literature on the economics of financial markets. Both the 1990s and the 1920s stock market runups have been linked to the arrival of new technologies and the accumulation of intangible capital by firms (Robert Hall 2001; Bart Hobijn and Boyan Jovanovic 2001;...

In this essay, Sahand Shaibani employs a Freudian psychoanalytic approach to discuss the influence of irrational and emotive forces in the American judicial process. He argues that the adversarial legal process serves the important psychological function of sublimating aggression, and that trial courts present a forum for the recreation of the Oedipal triangle, wherein the judge is unconsciousl...

In this paper a class of nonparametric transfer function models is proposed to model nonlinear relationships between 'input' and 'output' time series. The transfer function is smooth with unknown functional forms, and the noise is assumed to be a stationary autoregressive-moving average (ARMA) process. The nonparametric transfer function is estimated jointly with the ARMA parameters. By modelin...

Direct volume rendering has been an active area of research for over two decades. Transfer function design remains a difficult task since current methods, such as traditional 1D and 2D transfer functions are not always effective for all datasets. Various 1D or 2D transfer function spaces have been proposed to improve classification exploiting different aspects, such as using the gradient magnit...

over time but instead depends partly on the elapsed time between individual input events. The biophysical mechanisms underlying this shortterm synaptic plasticity are numerous and complex (29). As a result of such variety, different synapses supplied with the same temporal pattern of inputs may respond very differently. Thus a synapse does not simply transmit impulses from the presynaptic to th...

BACKGROUND Irrational use of medicines has been an issue concerned all over the world and the outlooks in developing countries are more severe. This study aimed to assess the different patterns of irrational use of medicines and its influential factors in China and Vietnam. METHODS A systematic review was performed on both published and grey literatures in English, Chinese and Vietnamese lang...

Transfer functions are a standard description of onedimensional linear and time-invariant systems. They provide an alternative to the conventional representation by ordinary differential equations and are suitable for computer implementation. This article extends that concept to multidimensional (MD) systems, normally described by partial differential equations (PDEs). Transfer function modelin...

Let 0 be an irrational number, and a any number between 0 and 1 (0 included). Then it is well known that it is possible to find a sequence of positive integers wa as r —» oo . Now let f(n) denote a positive increasing function of n, integral when n is integral, such as n, n, n\ ..., 2, S, ...,n\, 2\ ..., 2", ..., and let fr denote the value of f(n) for n = nr. ...