On the inducibility of small trees

The quantity that captures the asymptotic value of the maximum number of appearances of a given topological tree (a rooted tree with no vertices of outdegree $1$) $S$ with $k$ leaves in an arbitrary tree with sufficiently large number of leaves is called the inducibility of $S$. Its precise value is known only for some specific families of trees, most of them exhibiting a symmetrical configuration. In an attempt to answer a recent question posed by Czabarka, Sz\'ekely, and the second author of this article, we provide bounds for the inducibility $J(A_5)$ of the $5$-leaf binary tree $A_5$ whose branches are a single leaf and the complete binary tree of height $2$. It was indicated before that $J(A_5)$ appears to be `close' to $1/4$. We can make this precise by showing that $0.24707\ldots \leq J(A_5) \leq 0.24745\ldots$. Furthermore, we also consider the problem of determining the inducibility of the tree $Q_4$, which is the only tree among $4$-leaf topological trees for which the inducibility is unknown

Improved estimators for dispersion models with dispersion covariates

In this paper we discuss improved estimators for the regression and the dispersion parameters in an extended class of dispersion models (J{\o}rgensen, 1996). This class extends the regular dispersion models by letting the dispersion parameter vary throughout the observations, and contains the dispersion models as particular case. General formulae for the second-order bias are obtained explicitly in dispersion models with dispersion covariates, which generalize previous results by Botter and Cordeiro (1998), Cordeiro and McCullagh (1991), Cordeiro and Vasconcellos (1999), and Paula (1992). The practical use of the formulae is that we can derive closed-form expressions for the second-order biases of the maximum likelihood estimators of the regression and dispersion parameters when the information matrix has a closed-form. Various expressions for the second-order biases are given for special models. The formulae have advantages for numerical purposes because they require only a supplementary weighted linear regression. We also compare these bias-corrected estimators with two different estimators which are also bias-free to the second-order that are based on bootstrap methods. These estimators are compared by simulation

Coolant passage heat transfer with rotation

In current and advanced gas turbine engines, increased speeds, pressures and temperatures are used to reduce specific fuel consumption and increase thrust/weight ratios. Hence, the turbine airfoils are subjected to increased heat loads escalating the cooling requirements to satisfy life goals. The efficient use of cooling air requires that the details of local geometry and flow conditions be adequately modeled to predict local heat loads and the corresponding heat transfer coefficients. The objective of this program is to develop a heat transfer and pressure drop data base, computational fluid dynamic techniques and correlations for multi-pass rotating coolant passages with and without flow turbulators. The experimental effort is focused on the simulation of configurations and conditions expected in the blades of advanced aircraft high pressure turbines. With the use of this data base, the effects of Coriolis and buoyancy forces on the coolant side flow can be included in the design of turbine blades

Phase relaxation of Faraday surface waves

Surface waves on a liquid air interface excited by a vertical vibration of a fluid layer (Faraday waves) are employed to investigate the phase relaxation of ideally ordered patterns. By means of a combined frequency-amplitude modulation of the excitation signal a periodic expansion and dilatation of a square wave pattern is generated, the dynamics of which is well described by a Debye relaxator. By comparison with the results of a linear theory it is shown that this practice allows a precise measurement of the phase diffusion constant.Comment: 5 figure

Beauty, elegance, grace, and sexiness compared

Beauty is the single most frequently and most broadly used aesthetic virtue term. The present study aimed at providing higher conceptual resolution to the broader notion of beauty by comparing it with three closely related aesthetically evaluative concepts which are likewise lexicalized across many languages: elegance, grace(fulness), and sexiness. We administered a variety of questionnaires that targeted perceptual qualia, cognitive and affective evaluations, as well as specific object properties that are associated with beauty, elegance, grace, and sexiness in personal looks, movements, objects of design, and other domains. This allowed us to reveal distinct and highly nuanced profiles of how a beautiful, elegant, graceful, and sexy appearance is subjectively perceived. As aesthetics is all about nuances, the fine-grained conceptual analysis of the four target concepts of our study provides crucial distinctions for future research

The evidence of quasi-free positronium state in GiPS-AMOC spectra of glycerol

We present the results of processing of Age-Momentum Correlation (AMOC) spectra that were measured for glycerol by the Gamma-induced positron spectroscopy (GiPS) facility. Our research has shown that the shape of experimental s(t) curve cannot be explained without introduction of the intermediate state of positronium (Ps), called quasi-free Ps. This state yields the wide Doppler line near zero lifetimes. We discuss the possible properties of this intermediate Ps state from the viewpoint of developed model. The amount of annihilation events produced by quasi-free Ps is estimated to be less than 5% of total annihilations. In the proposed model, quasi-free Ps serves as a precursor for trapped Ps of para- and ortho-states