177,763 research outputs found

    Slice-polynomial functions and twistor geometry of ruled surfaces in CP 3

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    In the present paper we introduce the class of slice-polynomial functions: slice regular functions defined over the quaternions, outside the real axis, whose restriction to any complex half-plane is a polynomial. These functions naturally emerge in the twistor interpretation of slice regularity introduced in Gentili et al. (J Eur Math Soc 16(11):2323–2353, 2014) and developed in Altavilla (J Geom Phys 123:184–208, 2018). To any slice-polynomial function P we associate its companionP ∨ and its extension to the real axis P R , that are quaternionic functions naturally related to P. Then, using the theory of twistor spaces, we are able to show that for any quaternion q the cardinality of simultaneous pre-images of q via P, P ∨ and P R is generically constant, giving a notion of degree. With the brand new tool of slice-polynomial functions, we compute the twistor discriminant locus of a cubic scroll C in CP 3 and we conclude by giving some qualitative results on the complex structures induced by C via the twistor projection

    Twistor interpretation of slice regular functions

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    Given a slice regular function f:Ω⊂H→H, with Ω∩R≠∅, it is possible to lift it to surfaces in the twistor space CP3 of S4≃H∪{∞} (see Gentili et al., 2014). In this paper we show that the same result is true if one removes the hypothesis Ω∩R≠∅ on the domain of the function f. Moreover we find that if a surface S⊂CP3 contains the image of the twistor lift of a slice regular function, then S has to be ruled by lines. Starting from these results we find all the projective classes of algebraic surfaces up to degree 3 in CP3 that contain the lift of a slice regular function. In addition we extend and further explore the so-called twistor transform, that is a curve in Gr2(C4) which, given a slice regular function, returns the arrangement of lines whose lift carries on. With the explicit expression of the twistor lift and of the twistor transform of a slice regular function we exhibit the set of slice regular functions whose twistor transform describes a rational line inside Gr2(C4), showing the role of slice regular functions not defined on R. At the end we study the twistor lift of a particular slice regular function not defined over the reals. This example shows the effectiveness of our approach and opens some questions

    Sexual function after modified radical hysterectomy (Piver II/Type B) vs. classic radical hysterectomy (Piver III/Type C2) for early stage cervical cancer. A prospective study.

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    Introduction. When cervical cancer is detected at an early stage (International Federation of Gynecology and Obstetrics [FIGO] IA2-IB1), it can be successfully treated by radical surgery alone. Considering that most patients are young and sexually active at the moment of diagnosis and the long life expectancy of survivors after the treatment, quality of life (QoL) and sexual function are important issues for cancer survivors and caregivers. However, only a few studies have examined the QoL and sexual function in disease-free cervical cancer survivors, and there are no studies in the literature comparing prospectively sexual function after different types of radical hysterectomy. Aim. To compare sexual function in two groups of early stage cervical cancer survivors treated by radical surgery alone, undergoing two different types of radical hysterectomy. Methods. Patients treated by radical hysterectomy with systematic lymphadenectomy for early stage cervical cancer (FIGO IA2-IB1) have been enrolled and divided in two groups with regard to type of radical hysterectomy performed; S1: modified radical hysterectomy (Piver II/Type B), S2: classic radical hysterectomy (Piver III/ Type C2). Main Outcome Measure. Twenty-four months after surgery we assessed the sexual function using the European Organization for Research and Treatment of Cancer Cervix Cancer Module Questionnaire, which is a validated system for the assessment of disease- and treatment-specific issues that affect the QoL and sexual functioning of women who are treated for cervical cancer. Results. Of the 31 patients enrolled in the S1 group and 46 in the S2 group, 23 and 33 patients have been included, respectively. We observed significant differences between the two groups in terms of symptom experience, sexual/ vaginal functioning, sexual activity, and sexual enjoyment. There was not any significant difference regarding lymphedema, peripheral neuropathy, and sexual worry. Conclusion. Survivors of early stage cervical cancer treated by modified radical hysterectomy (Piver II/ Type B) have a better sexual function than those operated by classic radical hysterectomy (Piver III/ Type C2). Plotti F, Nelaj E, Sansone M, Antonelli E, Altavilla T, Angioli R, and Benedetti Panici P. Sexual function after modified radical hysterectomy (Piver II/Type B) vs. classic radical hysterectomy (Piver III/Type C2) for early stage cervical cancer: A prospective study. J Sex Med 2012;9:909–917

    Evaluation of the coordinative aspects attached to the foundations of the football of the young player

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    The scientific literature of reference for youth football analyzes the tests dedicated to measuring technical football skills because, unfortunately, it mainly focuses on the result of matches and sports performances as if it were equal to absolute football. Instead in youth football, the result of the game and athletic performance should be replaced by the acquisition of specific technical skills with the ball. For this reason, there should be a line of research that seeks the tool to measure the skill levels of the technical foundations of football in youth by borrowing the scientific aspects characteristic of the tests already validated and used for educational aspects. The aim of the study is to hypothesize tests derived from the elements of the ABC movement test (complete title) which provides for adaptability to measure the technical capacity of the technical base. The method is the creation and management of tests related to the coordination aspect through the help of the ABC movement. The results found were useful to understand the importance of the work focused on this topic and above all on the usefulness of these assessment tools

    BIOMECHANICAL ANALYSIS OF FOUNDAMENTALS IN BASKETBALL. THE REBOUND

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    Abstract Objetives. In view of a physical and athletic preparation, before technical-specific increasingly targeted, this work seeks to clarify from various points of view, the technical, tactical and mainly the biomechanical one, those that are the constituent elements of the fundamental of the rebound to order to optimize the specific preparation. In basketball, bouncing consist in the action of recovering the ball, after carrying out a wrong shot. It is of fundamental importance either in defense, giving the opportunity for a new ball possession and then you can set up a new offensive action as well as to have the opportunity to go in fast breack, or in attack since it offers players an additional opportunity shooting placing itself thus as one of the items among those that often give the final victory. For this reason a good basketball player has to learn to take care of this aspect of the game. Knowing how to defend the rebound is also a necessary feature during the competition; the player executing a cut off, looking at the place themselves in front of his opponent, holding it essentially away from the basket and jump effectively preventing him from rebounding

    Equivalence of slice semi-regular functions via Sylvester operators

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    The aim of this paper is to study some features of slice semi-regular functions mathcalRM(Omega)mathcal{RM}(Omega) on a circular domain OmegaOmega contained in the skew-symmetric algebra of quaternions mathbbHmathbb{H} via the analysis of a family of linear operators built from left and right *-multiplication on mathcalRM(Omega)mathcal{RM}(Omega); this class of operators includes the family of Sylvester-type operators mathcalSf,gmathcal{S}_{f,g}. Our strategy is to give a matrix interpretation of these operators as we show that mathcalRM(Omega)mathcal{RM}(Omega) can be seen as a 44-dimensional vector space on the field mathcalRMmathbbR(Omega)mathcal{RM}_{mathbb{R}}(Omega). We then study the rank of mathcalSf,gmathcal{S}_{f,g} and describe its kernel and image when it is not invertible. By using these results, we are able to characterize when the functions ff and gg are either equivalent under *-conjugation or intertwined by means of a zero divisor, thus proving a number of statements on the behaviour of slice semi-regular functions. We also provide a complete classification of idempotents and zero divisors on product domains of mathbbHmathbb{H}

    Pharmacogenomics of gemcitabine in non-small-cell lung cancer and other solid tumors

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    The validation of predictive biomarkers to tailor chemotherapy is a key issue in the development of effective treatment modalities against cancer. Examples of how genetics might affect drug response are offered by gemcitabine. A substantial number of potential biomarkers for sensitivity or resistance to gemcitabine have been proposed, including ribonucleotide reductase and cytidine deaminase polymorphisms, human equilibrative transporter-1 and ribonucleotide reductase gene-expression and AKT phosphorylation status. These markers displayed a significant relationship with disease response to the drug; however, their robustness needs to be evaluated within prospective studies. Moreover, recent trials of customized chemotherapy based on genetic markers have been carried out in non-small-cell lung cancer and promising pharmacogenetic determinants are gaining momentum, including BRCA1 and ERCC1. Hopefully, biomarkers to select patients most likely to respond to gemcitabine will be validated in the near future
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