1. What is an elliptic curve? 2 2. Mordell-Weil Groups 5 2.1. The Group Law on a Smooth, Plane Cubic Curve 5 2.2. Reminders on Commutative Groups 8 2.3. Some Elementary Results on Mordell-Weil Groups 9 2.4. The Mordell-Weil Theorem 11 2.5. K-Analytic Lie Groups 13 3. Background on Algebraic Varieties 15 3.1. Affine Varieties 15 3.2. Projective Varieties 18 3.3. Homogeneous Nullstellensätze 20 3...

Due to the continuing high suicide rates among young men, there is a need understand help-seeking behaviour and engagement with tailored prevention interventions. The aim of this study was compare younger older men who attended therapeutic centre for in suicidal crisis. In case series study, data were collected from 546 referred into community-based service North West England. Of 337 (52%) rece...

Under 5 years . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.1 5 to 9 years . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.8 10 to 14 years . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 3.5 15 to 19 years . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 5.6 20 to 24 years . . . . . . . . . . . . . . . . . . . . . . . ...

Under 5 years . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 6.6 5 to 9 years . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 5.7 10 to 14 years . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 7.7 15 to 19 years . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 10.1 20 to 24 years . . . . . . . . . . . . . . . . . . . . . . ...

rewriting system, 16irreflexive, 33weakly irreflexive, 33with typing, 37, 40with very weak typing, 40with weak typing, 40abstract rewriting systemsIn, 16I, 16abstract typing system, 38 bound variable, 52, 90, 137BV, 52, 90, 137 categoriesArs, 17Arst, 41Arstw, 41Carst, 46Carst""'' 46Carstw, 46Spec, 88Ats, 38common-reduct...

Data on human papillomavirus (HPV) type distribution in invasive and pre-invasive cervical cancer is essential to predict the future impact of HPV16/18 vaccines and HPV-based screening tests. A meta-analyses of HPV type distribution in invasive cervical cancer (ICC) and high-grade squamous intraepithelial lesions (HSIL) identified a total of 14,595 and 7,094 cases, respectively. In ICC, HPV16 w...

Atlantic bluefin tuna (ABFT) are highly valued and heavily exploited, and critical uncertainties regarding their population structure hinder effective management. Evidence supports the existence of two breeding populations of ABFT; a western population in the Gulf of Mexico and an eastern population in the Mediterranean Sea; both of which migrate and mix in the North Atlantic. Conventional tagg...

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Abstract A field experiment was conducted to grow the wheat crop during fall season 2020 in Karbala province, north of Ain Al-Tamr District two locations different textures and parent materials. The first site (calcareous soil) with a sandy loam texture, is located at (44° 40′ 37′) east longitude (32° 41′ 34′) latitude, an altitude 32 m above sea level, area 20 hectares. As for second location ...

John Baez, Computations and the periodic table By now there is an extensive network of interlocking analogies between physics, topology, logic and computer science, which can be seen most easily by comparing the roles that symmetric monoidal closed categories play in each subject. However, symmetric monoidal categories are just the n = 1, k = 3 entry of a hypothesized ”periodic table” of k-tupl...