For the familiar Fibonacci sequence | deened by f 1 = f 2 = 1, and f n = f n?1 + f n?2 for n > 2 | f n increases exponentially with n at a rate given by the golden ratio (1 + p 5)=2 = 1:61803398 : : :. But for a simple modiication with both additions and subtractions | the random Fibonacci sequences deened by t 1 = t 2 = 1, and for n > 2, t n = t n?1 t n?2 , where each sign is independent and e...

We develop a transfer matrix formalism for two-dimensional pure gravity. By taking the continuum limit, we obtain a “Hamiltonian formalism” in which the geodesic distance plays the role of time. Applying this formalism, we obtain a universal function which describes the fractal structures of two dimensional quantum gravity in the continuum limit. Recent developments of two-dimensional gravity h...

Model-based diagnostic reasoning often leads to a large number of diagnostic hypotheses. The set of diagnoses can be reduced by taking into account extra observations (passive monitoring), measuring additional variables (probing) or executing additional tests (sequential diagnosis/test sequencing). In this paper we combine the above approaches with techniques from Automated Test Pattern Generat...

Model-based diagnostic reasoning often leads to a large number of diagnostic hypotheses. The set of diagnoses can be reduced by taking into account extra observations (passive diagnosis), measuring additional variables (probing) or executing additional tests (sequential testing/test sequencing). In this paper we combine the above approaches, as well as from Automated Test Pattern Generation (AT...

Compositional explanatory variables should not be directly used in a linear regression model because any inference statistic can become misleading. While various approaches for this problem were proposed, here an approach based on the isometric logratio (ilr) transformation is used. It turns out that the resulting model is easy to handle, and that parameter estimation can be done like in usual ...

A fundamental aspect of harmonic analysis on Euclidean spaces deals with various classes of real or complex-valued functions, such as the C classes of functions which are continuous and continuously differentiable up to order k, where k is a nonnegative integer. If k = 0, this simply means that the function is continuous. Of course continuity of a function makes sense on any metric space, or on...

We study a chemical gelation model in two dimensions which includes both monomer aggregations and bond fluctuations. Our numerical simulation shows that a sol-gel transition occurs when an initial monomer concentration is above a critical concentration. Fractal aggregates grow until the sol-gel transition occurs. After the gelation, however, bond fluctuations break the fractal structure and an ...

Gear’s normal contact stiffness played an important role in the mechanical equipment. In this paper, the M-B fractal model is modified and the contact surface coefficient is put forward to set up the fractal model, considering the influence of friction, which could be used to calculate accurately the involute arc cylindrical gears’ normal contact stiffness based on the fractal theory and Hertz ...

In a colloidal suspension with attractive interaction, particles form aggregates that settle to the bottom of the container. As the concentration of particles is increased, the overlapping of the aggregates (flocs) produces a continuous network throughout the suspension before settling occurs and a colloidal gel is formed. Colloidal gels may be divided into hard gels and soft gels. 1 Hard gels ...