The BLI (boundary layer ingestion) concept for propulsion seeks to improve the energy efficiency of aircraft propulsion. This is achieved by accelerating low momentum flow ingested from boundary layers and wakes developed over the fuselage through the fan. A major challenge that needs to be overcome to realise the benefits is that the fan needs to work efficiently in distorted flow. Understanding the effects of distortion on the aerodynamic performance and the distortion transfer through the fan is therefore essential to future designs. A BLI fan, designed at reduced scale, is used for analytic modelling and experiments in a rig designed for this purpose. The test rig replicates BLI conditions for a fan installed at the aircraft tail cone. An unsteady model that includes all blades and vanes of the fan, as well as the nacelle and the by-pass duct of the test rig is used for CFD (computational fluid dynamics) simulations. Test results are used to confirm that the CFD model is representative of the aerodynamics of the fan. The tests are conducted using varying fan operating conditions but also tests with an added distortion screen. Analysis results are then used to investigate the effects of distortion on the fan efficiency, as well as on the overall efficiency. The fan efficiency is found to be moderately decreased depending on the level of and extent of inlet circumferential distortion. In terms of overall energy efficiency, a net improvement over a similar fan in clean inlet flow is found.

Decision makers have been found to bias their interpretation of incoming information to support an emerging judgment (predecisional information distortion). This is a robust finding in human judgment, and was recently also established and measured in physicians’ diagnostic judgments (Kostopoulou et al. 2012). The two studies reported here extend this work by addressing the constituent modes of distortion in physicians. Specifically, we studied whether and to what extent physicians distort information to strengthen their leading diagnosis and/or to weaken a competing diagnosis. We used the “stepwise evolution of preference” method with three clinical scenarios, and measured distortion on separate rating scales, one for each of the two competing diagnoses per scenario.

In Study 1, distortion in an experimental group was measured against the responses of a separate control group. In Study 2, distortion in a new experimental group was measured against participants’ own, personal responses provided under control conditions, with the two response conditions separated by a month. The two studies produced consistent results. On average, we found considerable distortion of information to weaken the trailing diagnosis but little distortion to strengthen the leading diagnosis. We also found individual differences in the tendency to engage in either mode of distortion. Given that two recent studies found both modes of distortion in lay preference (Blanchard, Carlson & Meloy, 2014; DeKay, Miller, Schley & Erford, 2014), we suggest that predecisional information distortion is affected by participant and task characteristics. Our findings contribute to the growing research on the different modes of predecisional distortion and their stability to methodological variation.

A design of a sub-scale Boundary Layer Ingestion (BLI) fan for a transonic test rig is presented. The fan is intended to be used in flow conditions with varying distortion patterns representative of a BLI application on an aircraft. The sub-scale fan design is based on a design study of a full-scale fan for a BLI demonstration project for a Fokker 100 aircraft. CFD results from the full-scale fan design and the ingested distortion pattern from CFD analyses of the whole aircraft are used as inputs for this study. The sub-scale fan is designed to have similar performance characteristics to the full-scale fan within the capabilities of the test facility. The available geometric rig envelope in the test facility necessitates a reduction in geometric scale and consideration of the operating conditions. Fan blades and vanes are re-designed for these conditions in order to mitigate the effects of the scaling. The effects of reduced size, increased relative tip clearance and thicknesses of the blades and vanes are evaluated as part of the step-by-step adaption of the design to the sub-scale conditions. Finally, the installation effects in the rig are simulated including important effects of the by-pass flow on the running characteristics and the need to control the effective fan nozzle area in order to cover the available fan operating range. The predicted operating behaviour of the fan as installed in the coming transonic test rig gives strong indication that the sub-scale fan tests will be successful.

Let G be the group $\text {PAff}_{+}(\mathbb R/\mathbb Z)$ of piecewise affine circle homeomorphisms or the group ${\operatorname {\mathrm {Diff}}}^{{\kern1pt}\infty }(\mathbb R/\mathbb Z)$ of smooth circle diffeomorphisms. A constructive proof that all irrational rotations are distorted in G is given.

A continuum of stochastic dominance rules, also referred to as fractional stochastic dominance (SD), was introduced by Müller, Scarsini, Tsetlin, and Winkler (2017) to cover preferences from first- to second-order SD. Fractional SD can be used to explain many individual behaviors in economics. In this paper we introduce the concept of fractional pure SD, a special case of fractional SD. We investigate further properties of fractional SD, for example the generating processes of fractional pure SD via $\gamma$ -transfers of probability, Yaari’s dual characterization by utilizing the special class of distortion functions, the separation theorem in terms of first-order SD and fractional pure SD, Strassen’s representation, and bivariate characterization. We also establish several closure properties of fractional SD under quantile truncation, under comonotonic sums, and under distortion, as well as its equivalence characterization. Examples of distributions ordered in the sense of fractional SD are provided.

We improve a recent construction of Andrés Navas to produce the first examples of $C^2$ -undistorted diffeomorphisms of the interval that are $C^{1+\alpha }$ -distorted (for every ${\alpha < 1}$ ). We do this via explicit computations due to the failure of an extension to class $C^{1+\alpha }$ of a classical lemma related to the work of Nancy Kopell.

Despite the great progress in data transmission systems using dielectric waveguides (DWGs) in the millimeter-wave (mm-wave) frequency band (30–300 GHz), the signal distortions caused by DWGs have not yet been fully understood. However, such investigations would help to optimize DWGs as a transmission channel in order to further increase data rate and transmission distance of such systems without the need for more complex transceivers. Therefore, this paper presents a detailed study of the expected signal distortions caused by frequency-dependent attenuation and frequency-dependent group delay of circular DWGs at mm-wave frequencies. Based on a low-complexity digital transmission system, the effects of DWGs on the signal-to-noise ratio and the intersymbol interference at the receiver are evaluated. The figures and equations given in this paper allow the reader to easily calculate the channel properties and signal distortions for a wide range of circular DWGs without the need of finite element method solver or other time-consuming numerical simulations. Finally, design recommendations are given to minimize signal distortions for transmitting signals along DWGs.

Frequent large losses from recent catastrophes have caused great concerns among insurers/reinsurers, who then turn to seek mitigations of such catastrophe risks by issuing catastrophe (CAT) bonds and thereby transferring the risks to the bond market. Whereas, the pricing of CAT bonds remains a challenging task, mainly due to the facts that the CAT bond market is incomplete and that the pricing usually requires knowledge about the tail of the risks. In this paper, we propose a general pricing framework based on a product pricing measure, which combines a distorted probability measure that prices the catastrophe risks underlying the CAT bond with a risk-neutral probability measure that prices interest rate risk. We also demonstrate the use of the peaks over threshold (POT) method to uncover the tail risk. Finally, we conduct case studies using Mexico and California earthquake data to demonstrate the applicability of our pricing framework.

A synthetic analogue, Ca(Ti0.6Al0.2Ta0.16Nb0.04)OSiO4, of an aluminoan tantalian titanite previously described from Craveggia pegmatite (Piemonte, Italy) has been prepared by a ceramic synthesis technique and its crystal structure determined by Rietveld analysis of the powder X-ray diffraction pattern. The synthetic Al-Ta-Nb-rich titanite adopts space group A2/a implying that substitutions at the single octahedral site destroy the coherence of the off-centering of octahedral chains in the titanite structure resulting in a P 21/a → A2/a phase transition. Unit-cell dimensions obtained for the Al-Ta-Nb-rich titanite are: a = 7.0649(1) Å; b = 8.7187(1) Å; c = 6.5701(1) Å; β = 113.755(1)°, V = 370.41(1) Å3. The extensive replacement of Ti by Al, Ta and Nb results in a considerable decrease in the distortion of all coordination polyhedra in the structure of this titanite. These structural data suggest that a solid solution CaTi1-x(Alx /2 [Ta,Nb]x /2)OSiO4 (0 ≤ x ≤ 0.4) adopting the titanite structure might exist.

Bannisterite is a modulated 2:1-type phyllosilicate having ten octahedral sites with hydroxyl groups in trans, cis and combined trans-cis configurations. Each octahedral site, depending on its proximity to the layer modulation, is exposed to a different degree of distortion. The electric field gradient at the Fe site and the site distortion are used to propose a model for the site assignment and oxidation mechanism in bannisterite. The results show that two models are compatible with the experimental results of fitting the spectrum of bannisterite. However, the model which allows for site distortion accounts better for the observed line overlap of the [6]Fe2+ sites. Accordingly, the octahedral sites with a greater degree of distortion are assigned to the [6]Fe2+ with lower electric quadrupole splitting, and the octahedral sites with lower site distortion are assigned to the [6]Fe2+ with higher electric quadrupole splitting. Moreover, the ease of oxidation decreases in the order trans > trans-cis > cis.

In this paper we prove uniqueness theorems for mappings $F\in W_{\text{loc}}^{1,n}(\mathbb{B}^{n};\mathbb{R}^{n})$ of finite distortion $1\leq K(x)=\Vert \mathit{DF}(x)\Vert ^{n}/J_{F}(x)$ satisfying some integrability conditions. These types of theorems fundamentally state that if a mapping defined in $\mathbb{B}^{n}$ has the same boundary limit $a$ on a ‘relatively large’ set $E\subset \unicode[STIX]{x2202}\mathbb{B}^{n}$, then the mapping is constant. Here the size of the set $E$ is measured in terms of its $p$-capacity or equivalently its Hausdorff dimension.

The formulation of optimal reinsurance policies that take various practical constraints into account is a problem commonly encountered by practitioners. In the context of a distortion-risk-measure-based optimal reinsurance model without moral hazard, this article introduces and employs a variation of the Neyman–Pearson Lemma in statistical hypothesis testing theory to solve a wide class of constrained optimal reinsurance problems analytically and expeditiously. Such a Neyman–Pearson approach identifies the unit-valued derivative of each ceded loss function as the test function of an appropriate hypothesis test and transforms the problem of designing optimal reinsurance contracts to one that resembles the search of optimal test functions achieved by the classical Neyman–Pearson Lemma. As an illustration of the versatility and superiority of the proposed Neyman–Pearson formulation, we provide complete and transparent solutions of several specific constrained optimal reinsurance problems, many of which were only partially solved in the literature by substantially more difficult means and under extraneous technical assumptions. Examples of such problems include the construction of the optimal reinsurance treaties in the presence of premium budget constraints, counterparty risk constraints and the optimal insurer–reinsurer symbiotic reinsurance treaty considered recently in Cai et al. (2016).

For a fixed $K\,\gg \,1$ and $n\,\in \,\mathbb{N}$, $n\,\gg \,1$ we study metric spaces which admit embeddings with distortion $\le \,K$ into each $n$-dimensional Banach space. Classical examples include spaces embeddable into log $n$-dimensional Euclidean spaces, and equilateral spaces.

We prove that good embeddability properties are preserved under the operation of metric composition of metric spaces. In particular, we prove that $n$-point ultrametrics can be embedded with uniformly bounded distortions into arbitrary Banach spaces of dimension $\log \,n$.

The main result of the paper is a new example of a family of finite metric spaces which are not metric compositions of classical examples and which do embed with uniformly bounded distortion into any Banach space of dimension $n$. This partially answers a question of G. Schechtman.

This paper describes the progress in frequency-domain linear prediction coding (LPC)-based audio coding schemes. Although LPC was originally used only for time-domain speech coders, it has been applied to frequency-domain coders since the late 1980s. With the progress in associated technologies, the frequency-domain LPC-based audio coding scheme has become more promising, and it has been used in speech/audio coding standards, such as MPEG-D unified speech and audio coding and 3GPP enhanced voice services since 2010. Three of the latest investigations on the representations of LPC envelopes in frequency-domain coders are shown. These are the harmonic model, frequency-resolution warping and the Powered All-Pole Spectral Envelope, all of which are aiming at further enhancement of the coding efficiency.