Hyperbolic manifolds that fibre algebraically up to dimension 8

We construct some cusped finite-volume hyperbolic n-manifolds M-n that fibre algebraically in all the dimensions 5 <= n <= 8. That is, there is a surjective homomorphism pi(1)(M-n) -> Z with finitely generated kernel. The kernel is also finitely presented in the dimensions n = 7,8, and this leads to the first examples of hyperbolic n-manifolds (M) over tilde (n) whose fundamental group is finitely presented but not of finite type. These n-manifolds (M) over tilde (n) have infinitely many cusps of maximal rank and, hence, infinite Betti number b(n-1). They cover the finite-volume manifold M-n. We obtain these examples by assigning some appropriate colours and states to a family of right-angled hyperbolic polytopes P-5, ..., P-8, and then applying some arguments of Jankiewicz, Norin and Wise [18] and Bestvina and Brady [7]. We exploit in an essential way the remarkable properties of the Cosset polytopes dual to P-n, and the algebra of integral octonions for the crucial dimensions n = 7,8

Hyperbolic manifolds that fiber algebraically up to dimension 8

We construct some cusped finite-volume hyperbolic $n$-manifolds $M_n$ that fiber algebraically in all the dimensions $5\leq n \leq 8$. That is, there is a surjective homomorphism $\pi_1(M_n) \to \mathbb Z$ with finitely generated kernel. The kernel is also finitely presented in the dimensions $n=7, 8$, and this leads to the first examples of hyperbolic $n$-manifolds $\widetilde M_n$ whose fundamental group is finitely presented but not of finite type. These $n$-manifolds $\widetilde M_n$ have infinitely many cusps of maximal rank and hence infinite Betti number $b_{n-1}$. They cover the finite-volume manifold $M_n$. We obtain these examples by assigning some appropriate colours and states to a family of right-angled hyperbolic polytopes $P_5, \ldots, P_8$, and then applying some arguments of Jankiewicz, Norin, Wise and Bestvina, Brady. We exploit in an essential way the remarkable properties of the Gosset polytopes dual to $P_n$, and the algebra of integral octonions for the crucial dimensions $n=7,8$.Comment: 40 pages, 21 figure

Hyperbolic 5-manifolds that fiber over S^1

We exhibit some finite-volume cusped hyperbolic 5-manifolds that fiber over the circle. These include the smallest hyperbolic 5-manifold known, discovered by Ratcliffe and Tschantz. As a consequence, we build a finite type subgroup of a hyperbolic group that is not hyperbolic

Global Stability and Plus-Global Stability. An Application to Forward Neural Networks

A necessary and sufficient condition for a discrete dynamical system to be globally stable and plus-globally stable are first established in Section 2. The V-condition is introduced and Theorems 3.5 and 3.7 are presented in Section 3. The two theorems link the V-condition to the most relevant properties of globally stable and plus-globally stable discrete dynamical systems. In Section 4 we provide a simple application to a convergence problem for forward neural networks

The use of India ink in tissue-simulating phantoms

The optical properties of India ink, an absorber often used in preparation of tissue simulating phantoms, have been investigated at visible and near infrared wavelengths. The extinction coefficient has been obtained from measurements of collimated transmittance and from spectrophotometric measurements, the absorption coefficient from multidistance measurements of fluence rate in a diffusive infinite medium with small concentrations of added ink. Measurements have been carried out on samples of India ink from five different brands, and for some brands also from different batches. As also reported in previously published papers the results we have obtained showed large inter-brand and inter-batch variations for both the absorption and the extinction coefficient. On the contrary, our results showed small variations for the ratio between the absorption and the extinction coefficient. The albedo is therefore similar for all samples: The values averaged over all samples investigated were 0.161, 0.115, and 0.115 at λ = 632.8, 751, and 833 nm respectively, with maximum deviations of 0.044, 0.019, and 0.035. These results indicate that, using the values we have obtained for the albedo, it should be possible to obtain with uncertainty smaller than about 4% the absorption coefficient of a sample of unknown ink from simple measurements of extinction coefficient. A similar accuracy is not easily obtained with the complicated procedures necessary for measurements of absorption coefficient

Critical concepts, practice recommendations, and research perspectives of pixantrone therapy in non-Hodgkin lymphoma: a SIE, SIES, and GITMO consensus paper

Objectives: In this paper, we present a review of critical concepts and research perspectives and produce recommendations on the optimal use of pixantrone in non-Hodgkin lymphoma (NHL) by group discussion from an expert panel appointed by the Italian Society of Hematology and the affiliate societies, Societa Italiana di Ematologia Sperimentale and Gruppo Italiano Trapianto di Midollo Osseo. Methods: Recommendations were produced using the Delphi process. Scientific evidence on pixantrone efficacy was analyzed using Grades of Recommendation, Assessment, Development, and Evaluation (GRADE) methodology in the areas where at least one randomized trial was published. The following key issues were addressed for practical recommendations: pixantrone monotherapy in aggressive relapsed or refractory non-Hodgkin B-cell lymphomas and toxicity risk management in patients candidates to pixantrone. Results and conclusions: After a balanced and value-oriented discussion, the panel agreed that the benefit/risk profile was in favor of pixantrone in the treatment of adult patients with multiply relapsed or refractory aggressive NHL B-cell lymphomas. Pixantrone was deemed to be contraindicated in patients with uncontrolled cardiovascular disease. Despite a low rate of cardiotoxicity of pixantrone reported in clinical trials, the panel recommended that all patients receiving pixantrone should undergo periodical cardiac monitoring

Effetti termici nella metrologia a coordinate

La norma UNI EN ISO 10360-2:2010 prescrive: “I limiti per le condizioni ambientali ammesse che possono avere influenza sulle misurazioni, quali condizioni di temperatura, umidità dell’aria e vibrazione nel luogo di installazione, devono essere specificati: - dal fabbricante, nel caso di prove di accettazione; - dall’utilizzatore, nel caso di prove di riverifica periodica. In entrambi i casi, l'utilizzatore è libero di scegliere le condizioni ambientali nelle quali saranno eseguite le prove secondo la ISO 10360-2, all'interno dei limiti specificati.” La presente Guida si prefigge l’obiettivo di rendere disponibile all’utilizzatore di Macchine di Misura a Coordinate (di seguito CMM) una serie di indicazioni e informazioni relative principalmente alla grandezza di influenza temperatura ed ai suoi effetti nelle misurazioni dimensionali. Affinché si possano ottenere le prestazioni dichiarate sui cataloghi, il costruttore di CMM dichiara, insieme alle specifiche tecniche della macchina, anche alcuni parametri ambientali che ritiene debbano essere mantenuti entro i limiti specificati.Ci si trova quindi subito di fronte al dilemma: • Si è in grado di rispettare le condizioni ambientali prescritte? • oppure si può soprassedere ed accontentarsi di prestazioni finali diverse? E quali saranno queste nuove prestazioni? Alle prime domande ne seguono altre: • serve ottenere dalla macchina il massimo delle prestazioni dichiarate dal Costruttore oppure ci si può accontentare di qualcosa in meno? • Tutte le volte che si effettuano misurazioni si è in grado di ricondurre i risultati delle misurazioni alla temperatura di riferimento? Nel prossimo paragrafo vengono proposte alcune problematiche che sono frequentemente oggetto di domande da parte degli utilizzatori di CMM e alle quali la presente guida propone delle risposte, frutto di analisi ed esperienze maturate da coloro che hanno redatto articoli nelle riviste di settore. Il capitolo 2 indica quali sono i riferimenti per terminologia e definizioni. I capitoli 3, 4, 5, 6, 7 e 8 sono il corpo centrale della guida e descrivono il fenomeno temperatura da un punto di vista fisico. Il capitolo 9 presenta invece un'ampia bibliografia comprendendo nel contempo termini di riferimenti normativi, nonché articoli scritti da esperti del settore in vari ambiti: tutto ciò allo scopo di fornire materiale utile sia per un approfondimento dei temi trattati nella stessa guida, sia per supportare (grazie soprattutto alle esperienze già maturate e descritte nei vari articoli) coloro i quali si trovassero ad affrontare per la prima volta simili tematiche