Let (X, d, T ) be a dynamical system, where (X, d) is a compact metric space and T : X → X is a continuous map. We assume that the dynamical system satisfies g-almost product property and the uniform separation property. We compute the topological pressure of saturated sets under these two conditions. If the uniform separation property does not hold, we compute the topological pressure of the set of generic points. We give an application of these results to multifractal analysis and finally get a conditional variational principle. Keywordsuniform separation property, g-almost product property, topological pressure of non-compact sets, variational principle, BS-dinmension MSC(2000): 37B45, 37C45Citation: Pei Y, Chen E C. On the variational principle for the topological pressure for certain non-compact sets.

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Large rectangular flue pipes installed in coal-fired power plants usually need inner supports to ensure their stability. The design and arrangement of inner supports in rectangular flue pipe before electrostatic precipitator have an impact on precipitators effectiveness and lifespan. Currently, there are two schemes used for setting inner supports in China. One is National Standard Specification (NSS) and the other is an American Combustion Engineering company design criterion (CE). No work has been done on the comparison of these two types of inner supports, especially with consideration of ash deposition. In this paper, the effect of ash deposition on pressure drop and velocity distribution in practical production are carried out, which are adopted flue pipes volume 1/8 and 1/16 as the ash layer. The numerical results show that the ash deposition volume have effect on pressure loss of the straight flue pipes. However, the effect depends on the inner supports type.

This paper investigates the multifractal structure due to the recurrence under the [Formula: see text]th Bowen metric on the dynamical system. It is shown that the set with the given lower and upper recurrence rates can have the full topological pressure, if the system [Formula: see text] with specification property is non-minimal, and [Formula: see text] is positively expansive.

The topological pressure for subadditive sequence of discontinuous functions is defined on any invariant subset having a nested family of subsets in the compact metric space. Two subadditive variational principles associated with two different relatively weak conditions are developed for the defined topological pressure. As an application, we give an example on systems with nonzero Lyapunov exponents.