Let β > 1 and let m > β be an integer. Each x ∈ Iβ := [0, m−1 β−1 ] can be represented in the form x = ∞ ∑ k=1 εkβ −k, where εk ∈ {0, 1, . . . , m − 1} for all k (a β-expansion of x). It is known that a.e. x ∈ Iβ has a continuum of distinct β-expansions. In this paper we prove that if β is a Pisot number, then for a.e. x this continuum has one and the same growth rate. We also link this rate to...

This paper examines two related models, which permit analytical investigation, to gain some insights into a relationship between endogenous growth and business cycle. Using two simple models which incorporate Fisher Black’s idea that a significant part of business cycle fluctuations is a consequence of an economy’s choice, we obtained a negative relationship between uncertainty and growth. Henc...

The growth rate and uniformity of Carbon Nano Tubes (CNTs) based on Chemical Vapor Deposition (CVD) technique is investigated by using a numerical model. In this reactor, inlet gas mixture, including xylene as carbon source and mixture of argon and hydrogen as  carrier gas enters into a horizontal CVD reactor at atmospheric pressure. Based on the gas phase and surface reactions, released carbon...

Let C be a rate (n ? r)=n convolutional code with canonical parity-check matrix H(D), and let w 0 denote the minimum average weight per edge over all nonzero cycles in the state diagram for C. The rate of growth per edge of the minimum distance between two nonmerged codewords is given by the value of w 0. For any code C, we show how to obtain an upper bound on w 0 from the columns of H(D). Inde...

inflation has always been an economic problem and different solutions have been proposed to control it. although it is said that “higher output lowers inflation rate” but it is true when other factors are constant. this study searches the answer to the following question: “what is the effect of inflation rate and output in a case that inflation rate and output growth has a volatility trend?” to...