Book crossing numbers of the complete graph and small local convex crossing numbers

A $k$-page book drawing of a graph $G$ is a drawing of $G$ on $k$ halfplanes with common boundary $l$, a line, where the vertices are on $l$ and the edges cannot cross $l$. The $k$-page book crossing number of the graph $G$, denoted by $\nu_k(G)$, is the minimum number of edge-crossings over all $k$-page book drawings of $G$. Let $G=K_n$ be the complete graph on $n$ vertices. We improve the lower bounds on $\nu_k(K_n)$ for all $k\geq 14$ and determine $\nu_k(K_n)$ whenever $2 < n/k \leq 3$. Our proofs rely on bounding the number of edges in convex graphs with small local crossing numbers. In particular, we determine the maximum number of edges that a convex graph with local crossing number at most $\ell$ can have for $\ell\leq 4$.Comment: Version 2 extends our result on the maximum number of edges on a convex graph with local crossing number at most c for c=4. In This in turn improves most of the bounds in Version

Thermo-mechanical analysis of dental silicone polymers

Soft lining materials are used to replace the inner surface of a conventional complete denture, especially for weak elderly patients, with delicate health who cannot tolerate the hard acrylic denture base. Most of these patients have fragile supporting mucosa, excessive residual ridge resorption, particularly on the mandibular arch. The application of a soft liner to the mandibular denture allows absorbing impact forces during mastication and relieving oral mucosa. Actually, the silicone rubbers constitute the main family of commercialised soft lining materials. This study was conducted to understand the relationships between the mechanical properties and the physical structure of polysiloxanes. For this purpose, a series of polysiloxanes of various chemical compositions have been investigated. The evolution of their physical structure as a function of temperature has been followed by differential scanning calorimetry (DSC). In order to facilitate comparisons, the mechanical modulus has been analysed upon the same heating rate using dynamic mechanical analysis (DMA). Polysiloxanes actually commercialised as soft denture liners are three-dimensional networks: the flexibility of chains allows a crystalline organisation in an amorphous phase leading to the low value of the shear modulus. The dynamic mechanical analysis shows that they are used in the rubbery state. So, polysiloxanes have steady mechanical properties during physiological utilisation

On publicness theory and its implications for supply chain integration:The case of criminal justice supply chains

The literature has extensively discussed whether and how public organizations differ from private ones. Publicness theory argues that the degree of publicness is determined by ownership, funding, goal setting, and control structure of an organization. However, these theoretical ideas have not yet been extended to the interorganizational level. The need for further research is reflected in the sustained debate on the applicability of for-profit management approaches in public contexts and supply chains. Starting from the premise of the dimensional publicness theory, this study focuses on theory elaboration. We focus our empirical study on the criminal justice supply chain, which encompasses the process of bringing a criminal case to court. This chain provides an interesting public case to explore how specific dimensions of publicness affect or limit supply chain integration mechanisms. The results of our series of embedded cases focusing on Dutch criminal justice supply chains show that control structures, embodied in laws and regulations, define the governance of relationships between supply chain partners. In addition to these formalized ties, extensive known for-profit information and operational integration mechanisms can be observed, along with limited relational integration. Surprisingly, although similar integration mechanisms are used as in for-profit contexts, integration serves a different role in several of the relationships investigated: dealing with tensions stemming from the specific goal setting and stakeholders of criminal justice chains. Although our findings specifically relate to criminal justice supply chains, they have important implications for other supply chains using contracts and laws and those being selective in applying supply chain integration in cases of contrasting objectives. Moreover, we provide a stepping-stone for the extension of publicness theory to the interorganizational level

Distribution of airway narrowing responses across generations and at branching points, assessed in vitro by anatomical optical coherence tomography

Background: Previous histological and imaging studies have shown the presence of variability in the degree of bronchoconstriction of airways sampled at different locations in the lung (i.e., heterogeneity). Heterogeneity can occur at different airway generations and at branching points in the bronchial tree. Whilst heterogeneity has been detected by previous experimental approaches, its spatial relationship either within or between airways is unknown.Methods: In this study, distribution of airway narrowing responses across a portion of the porcine bronchial tree was determined in vitro. The portion comprised contiguous airways spanning bronchial generations (#3-11), including the associated side branches. We used a recent optical imaging technique, anatomical optical coherence tomography, to image the bronchial tree in three dimensions. Bronchoconstriction was produced by carbachol administered to either the adventitial or luminal surface of the airway. Luminal cross sectional area was measured before and at different time points after constriction to carbachol and airway narrowing calculated from the percent decrease in luminal cross sectional area.Results: When administered to the adventitial surface, the degree of airway narrowing was progressively increased from proximal to distal generations (r = 0.80 to 0.98, P < 0.05 to 0.001). This 'serial heterogeneity' was also apparent when carbachol was administered via the lumen, though it was less pronounced. In contrast, airway narrowing was not different at side branches, and was uniform both in the parent and daughter airways.Conclusions: Our findings demonstrate that the bronchial tree expresses intrinsic serial heterogeneity, such that narrowing increases from proximal to distal airways, a relationship that is influenced by the route of drug administration but not by structural variations accompanying branching sites

Dielectric relaxations in PEEK by combined dynamic dielectric spectroscopy and thermally stimulated current

The molecular dynamics of a quenched poly (ether ether ketone) (PEEK) was studied over a broad frequency range from 10-3 to 106 Hz by combining dynamic dielectric spectroscopy (DDS) and thermo-stimulated current (TSC) analysis. The dielectric relaxation losses e00 KK has been determined from the real part e0 T(x) thanks to Kramers–Kronig transform. In this way, conduction and relaxation processes can be analyzed independently. Two secondary dipolar relaxations, the c and the b modes, corresponding to non-cooperative localized molecular mobility have been pointed out. The main a relaxation appeared close to the glass transition temperature as determined by DSC; it has been attributed to the delocalized cooperative mobility of the free amorphous phase. The relaxation times of dielectric relaxations determined with TSC at low frequency converge with relaxation times extracted from DDS at high frequency. This correlation emphasized continuity of mobility kinetics between vitreous and liquid state. The dielectric spectroscopy exhibits the ac relaxation, near 443 K, which has been associated with the rigid amorphous phase confined by crystallites. This present experiment demonstrates coherence of the dynamics of the PEEK heterogeneous amorphous phase between glassy and liquid state and significantly improve the knowledge of molecular/dynamic structure relationships

The importance of Real-Life research in Respiratory Medicine: Manifesto of the Respiratory Effectiveness Group:Endorsed by the International Primary Care Respiratory Group and the World Allergy Organization

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Morality tales: young women's narratives on offending, self-worth and desistance

This article emerges from a study of female offenders’ participation in police-facilitated restorative justice in one county in England. The qualitative study, presented here, is based on life history interviews with twelve women and focuses on three morality tales that emerged through narrative analysis: ‘offending as play,’ ‘the strong woman’ and ‘work and a normal life.’ The women used these tales to protect self-worth and justify ‘bad’ behavior in order to counter professional responses which they viewed as stigmatising. The paper concludes with implications for practice with girls and women who offend, which may benefit police, probation and social workers