A Handheld low-mass, impact instrument to measure nondestructive firmness of fruit

A portable, handheld impact firmness sensor was designed for nondestructive measurement of fruit firmness while the fruit remain attached to the tree or for use in other remote locations where the use of a benchtop instrument would be impractical. The instrument design was based on the low-mass, constant velocity, impact-type measurement concept. Validation tests of the handheld sensor using `Bartlett' pears from orchards in California and Washington showed excellent agreement (r2 = 0.92 and 0.96, respectively) with both ASAE Standard method S368.2 for determining the apparent modulus of intact fruit and the impact firmness scores from a commercial benchtop impact firmness instrument

Natural equilibrium states for multimodal maps

This paper is devoted to the study of the thermodynamic formalism for a class of real multimodal maps. This class contains, but it is larger than, Collet-Eckmann. For a map in this class, we prove existence and uniqueness of equilibrium states for the geometric potentials $-t \log|Df|$, for the largest possible interval of parameters $t$. We also study the regularity and convexity properties of the pressure function, completely characterising the first order phase transitions. Results concerning the existence of absolutely continuous invariant measures with respect to the Lebesgue measure are also obtained

Secondary dentin formation mechanism: The effect of attrition

Human dentin consists of a primary layer produced during tooth formation in early child-hood and a second layer which first forms upon tooth eruption and continues throughout life, termed secondary dentin (SD). The effect of attrition on SD formation was considered to be confined to the area subjacent to attrition facets. However, due to a lack of three‐dimensional methodologies to demonstrate the structure of the SD, this association could not be determined. Therefore, in the current study, we aimed to explore the thickening pattern of the SD in relation to the amount of occlusal and interproximal attrition. A total of 30 premolars (50–60 years of age) with varying attrition rates were evaluated using micro‐computerized tomography. The results revealed thickening of the SD below the cementoenamel junction (CEJ), mostly in the mesial and distal aspects of the root (p < 0.05). The pattern of thickening under the tooth cervix, rather than in proximity to attrition facets, was consistent regardless of the attrition level. The amount of SD thickening mildly corre-lated with occlusal attrition (r = 0.577, p < 0.05) and not with interproximal attrition. The thickening of the SD below the CEJ coincided with previous finite element models, suggesting that this area is mostly subjected to stress due to occlusal loadings. Therefore, we suggest that the SD formation might serve as a compensatory mechanism aimed to strengthen tooth structure against deflection caused by mechanical loading. Our study suggests that occlusal forces may play a significant role in SD formation

Statistical stability of equilibrium states for interval maps

We consider families of multimodal interval maps with polynomial growth of the derivative along the critical orbits. For these maps Bruin and Todd have shown the existence and uniqueness of equilibrium states for the potential $\phi_t:x\mapsto-t\log|Df(x)|$, for $t$ close to 1. We show that these equilibrium states vary continuously in the weak$^*$ topology within such families. Moreover, in the case $t=1$, when the equilibrium states are absolutely continuous with respect to Lebesgue, we show that the densities vary continuously within these families.Comment: More details given and the appendices now incorporated into the rest of the pape

The Analyticity of a Generalized Ruelle's Operator

In this work we propose a generalization of the concept of Ruelle operator for one dimensional lattices used in thermodynamic formalism and ergodic optimization, which we call generalized Ruelle operator, that generalizes both the Ruelle operator proposed in [BCLMS] and the Perron Frobenius operator defined in [Bowen]. We suppose the alphabet is given by a compact metric space, and consider a general a-priori measure to define the operator. We also consider the case where the set of symbols that can follow a given symbol of the alphabet depends on such symbol, which is an extension of the original concept of transition matrices from the theory of subshifts of finite type. We prove the analyticity of the Ruelle operator and present some examples

The Lyapunov spectrum is not always concave

We characterize one-dimensional compact repellers having nonconcave Lyapunov spectra. For linear maps with two branches we give an explicit condition that characterizes non-concave Lyapunov spectra

Equilibrium states for potentials with \sup\phi - \inf\phi < \htop(f)

In the context of smooth interval maps, we study an inducing scheme approach to prove existence and uniqueness of equilibrium states for potentials $\phi$ with he `bounded range' condition \sup \phi - \inf \phi < \htop, first used by Hofbauer and Keller. We compare our results to Hofbauer and Keller's use of Perron-Frobenius operators. We demonstrate that this `bounded range' condition on the potential is important even if the potential is H\"older continuous. We also prove analyticity of the pressure in this context.Comment: Added Lemma 6 to deal with the disparity between leading eigenvalues and operator norms. Added extra references and corrected some typo

Almost-additive thermodynamic formalism for countable Markov shifts

We introduce a definition of pressure for almost-additive sequences of continuous functions defined over (non-compact) countable Markov shifts. The variational principle is proved. Under certain assumptions we prove the existence of Gibbs and equilibrium measures. Applications are given to the study of maximal Lypaunov exponents of product of matrices

Operator renewal theory and mixing rates for dynamical systems with infinite measure

We develop a theory of operator renewal sequences in the context of infinite ergodic theory. For large classes of dynamical systems preserving an infinite measure, we determine the asymptotic behaviour of iterates $L^n$ of the transfer operator. This was previously an intractable problem. Examples of systems covered by our results include (i) parabolic rational maps of the complex plane and (ii) (not necessarily Markovian) nonuniformly expanding interval maps with indifferent fixed points. In addition, we give a particularly simple proof of pointwise dual ergodicity (asymptotic behaviour of $\sum_{j=1}^nL^j$) for the class of systems under consideration. In certain situations, including Pomeau-Manneville intermittency maps, we obtain higher order expansions for $L^n$ and rates of mixing. Also, we obtain error estimates in the associated Dynkin-Lamperti arcsine laws.Comment: Preprint, August 2010. Revised August 2011. After publication, a minor error was pointed out by Kautzsch et al, arXiv:1404.5857. The updated version includes minor corrections in Sections 10 and 11, and corresponding modifications of certain statements in Section 1. All main results are unaffected. In particular, Sections 2-9 are unchanged from the published versio