scholarly journals ARITHMETIC-GEOMETRIC MEANS FOR HYPERELLIPTIC CURVES AND CALABI–YAU VARIETIES

2010 ◽  
Vol 21 (07) ◽  
pp. 939-949 ◽  
Author(s):  
KEIJI MATSUMOTO ◽  
TOMOHIDE TERASOMA
Keyword(s):  
Projective Space ◽  
Hyperelliptic Curve ◽  
Geometric Mean ◽  
Hyperelliptic Curves ◽  
Double Cover ◽  
The Other ◽  
Geometric Means ◽  
Dimensional Projective Space ◽  
Period Integral ◽  
Generalized Arithmetic

In this paper, we define a generalized arithmetic-geometric mean μg among 2g terms motivated by 2τ-formulas of theta constants. By using Thomae's formula, we give two expressions of μg when initial terms satisfy some conditions. One is given in terms of period integrals of a hyperelliptic curve C of genus g. The other is by a period integral of a certain Calabi–Yau g-fold given as a double cover of the g-dimensional projective space Pg.

scholarly journals A quadratic transformation of the three-dimensional space of all conics through two points of a projective plane

2009 ◽  
Vol 42 (3) ◽  
Author(s):  
Giorgio Donati
Keyword(s):  
Projective Space ◽  
Projective Plane ◽  
Dimensional Space ◽  
Three Dimensional ◽  
The Other ◽  
Quadratic Transformation ◽  
Pencil Of Conics ◽  
Dimensional Projective Space ◽  
Three Dimensional Space

AbstractUsing the Steiner’s method of projective generation of conics and its dual we define two projective mappings of a double contact pencil of conics into itself and we prove that one is the inverse of the other. We show that these projective mappings are induced by quadratic transformations of the three-dimensional projective space of all conics through two distinct points of a projective plane.

On Topological Properties of Some Coverings. An Addendum to a Paper of Lanteri and Struppa

1992 ◽  
Vol 44 (1) ◽  
pp. 206-214
Author(s):  
Jarosław A. Wiśniewski
Keyword(s):  
Line Bundle ◽  
Projective Space ◽  
Betti Numbers ◽  
Ample Line Bundle ◽  
Double Cover ◽  
Topological Properties ◽  
Surjective Morphism ◽  
Projective Manifolds ◽  
Dimensional Projective Space ◽  
Complex Projective

AbstractLet π: X′ → X be a finite surjective morphism of complex projective manifolds which can be factored by an embedding of X′ into the total space of an ample line bundle 𝓛 over X. A theorem of Lazarsfeld asserts that Betti numbers of X and X′ are equal except, possibly, the middle ones. In the present paper it is proved that the middle numbers are actually non-equal if either 𝓛 is spanned and deg π ≥ dim X, or if X is either a hyperquadric or a projective space and π is not a double cover of an odd-dimensional projective space by a hyperquadric.

Explicit Hyperelliptic Curves With Real Multiplication and Permutation Polynomials

1991 ◽  
Vol 43 (5) ◽  
pp. 1055-1064 ◽  
Author(s):  
Walter Tautz ◽  
Jaap Top ◽  
Alain Verberkmoes
Keyword(s):  
Cyclotomic Field ◽  
Prime Numbers ◽  
Explicit Construction ◽  
Hyperelliptic Curves ◽  
Double Cover ◽  
The Other ◽  
Roots Of Unity ◽  
Permutation Polynomials ◽  
Endomorphism Algebra ◽  
Real Multiplication

AbstractThe aim of this paper is to present a very explicit construction of one parameter families of hyperelliptic curves C of genus (p−1 )/ 2, for any odd prime number p, with the property that the endomorphism algebra of the jacobian of C contains the real subfield Q(2 cos(2π/p)) of the cyclotomic field Q(e2π i/p).Two proofs of the fact that the constructed curves have this property will be given. One is by providing a double cover with the pth roots of unity in its automorphism group. The other is by explicitly writing down equations of a correspondence in C x C which defines multiplication by 2cos(2π/ p) on the jacobian of C. As a byproduct we obtain polynomials which define bijective maps Fℓ → Fℓ for all prime numbers in certain congruence classes.

Assessment of the exposure of swimmers to microbiological contaminants in fresh waters

1997 ◽  
Vol 35 (11-12) ◽  
pp. 157-163 ◽  
Author(s):  
G. J. Medema ◽  
I. A. van Asperen ◽  
A. H. Havelaar
Keyword(s):  
Geometric Mean ◽  
Microbiological Quality ◽  
The Other ◽  
Pollution Level ◽  
Intestinal Infection ◽  
E Coli ◽  
Faecal Pollution ◽  
Run Off ◽  
Thermotolerant Coliforms ◽  
Mean Concentration

As part of a prospective cohort study among triathletes to determine a relationship between the microbiological quality of fresh bathing water and the risk of acquiring an intestinal infection, the exposure of the triathletes to microbiological contaminants was assessed. Waters were collected at seven triathlons (swimming course 1–1.5km) held in the summer of 1993 and 1994 to have a range of water qualities. All were influenced by sewage effluents, most also by agricultural run-off. Samples were collected several weeks before the event to establish a sampling programme (1993) and during the actual exposure of the triathletes (1993 and 1994) and examined for thermotolerant coliforms alone (samples preceding the event) and for E. coli, faecal enterococci, Staphylococcus aureus, F-specific RNAphages, enteroviruses (1993 and 1994) and for thermophilic Campylobacter, Salmonella, Aeromonas, Plesiomonas shigelloides and Pseudomonas aeruginosa (1993). The samples taken in the weeks before the exposure showed significant differences in thermotolerant coliform concentration between locations, depths and times. Also during swimmer exposure, significant differences occurred in microorganism levels at the different sampling points over the swimming course. As the triathletes swam as a group, they were exposed to approximately the same water at the same time. The geometric mean concentration was used to characterise each site. In the epidemiological study, the risk of an intestinal infection correlated with the concentration of thermotolerant coliforms and E. coli but not with the other parameters. The geometric mean concentration of thermotolerant coliforms at the triathlons ranged from 11–330/100mL and 54–1,200/100mL E. coli. Ranking of the seven sites by faecal pollution level, based on the geometric mean concentration of a faecal indicator, resulted in a different ranking for each indicator. At the fresh water sites studied, only the ratio between the geometric mean density of E. coli and thermotolerant coliforms was constant. The ratio between the other parameters related to faecal pollution (faecal enterococci, F-specific RNA phages, enteroviruses) varied considerably. Water quality standards relating to faecal pollution can only be based on parameters that show a significant correlation with risk of intestinal illness.

scholarly journals Two algebraic deformations of a K3 surface

1981 ◽  
Vol 82 ◽  
pp. 1-26
Author(s):  
Daniel Comenetz
Keyword(s):  
Hyperelliptic Curve ◽  
Double Cover ◽  
Rational Curves ◽  
K3 Surface ◽  
Quartic Surface ◽  
Quadric Cone ◽  
Birational Model ◽  
Affine Line ◽  
Characteristic 2 ◽  
General Member

Let X be a nonsingular algebraic K3 surface carrying a nonsingular hyperelliptic curve of genus 3 and no rational curves. Our purpose is to study two algebraic deformations of X, viz. one specialization and one generalization. We assume the characteristic ≠ 2. The generalization of X is a nonsingular quartic surface Q in P3 : we wish to show in § 1 that there is an irreducible algebraic family of surfaces over the affine line, in which X is a member and in which Q is a general member. The specialization of X is a surface Y having a birational model which is a ramified double cover of a quadric cone in P3.

Transformations depending on sets of associated points

1952 ◽  
Vol 48 (3) ◽  
pp. 383-391
Author(s):  
T. G. Room
Keyword(s):  
Projective Space ◽  
Projective Plane ◽  
Three Dimensional ◽  
Cubic Curves ◽  
Birational Transformations ◽  
Quadric Surfaces ◽  
Base Points ◽  
Dimensional Projective Space ◽  
Quartic Curves

This paper falls into three sections: (1) a system of birational transformations of the projective plane determined by plane cubic curves of a pencil (with nine associated base points), (2) some one-many transformations determined by the pencil, and (3) a system of birational transformations of three-dimensional projective space determined by the elliptic quartic curves through eight associated points (base of a net of quadric surfaces).

scholarly journals GALOIS THEORY OF THE CANONICAL THETA STRUCTURE

2011 ◽  
Vol 07 (01) ◽  
pp. 173-202
Author(s):  
ROBERT CARLS
Keyword(s):  
Galois Theory ◽  
Theoretical Foundation ◽  
Abelian Varieties ◽  
Geometric Mean ◽  
Null Point ◽  
Point Counting ◽  
Characteristic 2 ◽  
Theoretic Characterization ◽  
Generalized Arithmetic

In this article, we give a Galois-theoretic characterization of the canonical theta structure. The Galois property of the canonical theta structure translates into certain p-adic theta relations which are satisfied by the canonical theta null point of the canonical lift. As an application, we prove some 2-adic theta identities which describe the set of canonical theta null points of the canonical lifts of ordinary abelian varieties in characteristic 2. The latter theta relations are suitable for explicit canonical lifting. Using the theory of canonical theta null points, we are able to give a theoretical foundation to Mestre's point counting algorithm which is based on the computation of the generalized arithmetic geometric mean sequence.

scholarly journals Biases Associated with Four Stream Substrate Samplers

1991 ◽  
Vol 48 (10) ◽  
pp. 1882-1886 ◽  
Author(s):  
Michael K. Young ◽  
Wayne A. Hubert ◽  
Thomas A. Wesche
Keyword(s):  
Particle Size ◽  
Geometric Mean ◽  
The Other ◽  
Substrate Composition ◽  
Mean Particle Size ◽  
Core Samples ◽  
Freeze Core ◽  
Single Probe ◽  
Core Sampler ◽  
Stream Substrate

We compared samples collected from 10 substrates of various compositions with a single-probe freeze-core sampler, a triple-probe freeze-core sampler, a McNeil sampler, and a shovel. The accuracy with which these devices sampled particles larger than 50 mm in diameter varied; they were oversampled by the freeze-core devices, sampled in proportion to their availability by a shovel, and sampled inconsistently by the McNeil sampler. The geometric mean particle size and variance of single-probe freeze-core samples consistently exceeded those of samples collected with the other devices. Most sample means also exceeded the test substrate means. By excluding the proportions of particles larger than 50 mm in diameter in our analyses, we found that proportions of several particles sizes in samples collected by different methods differed significantly from the actual proportions in test substrates. There were few differences between the single- and triple-probe freeze-core samples or between McNeil and shovel samples. All four samplers were biased, but the McNeil sampler most frequently produced samples that approximated the true substrate composition.

scholarly journals Pharmacokinetic Interactions between the Hormonal Emergency Contraception, Levonorgestrel (Plan B), and Efavirenz

2012 ◽  
Vol 2012 ◽  
pp. 1-4 ◽  
Author(s):  
Monica L. Carten ◽  
Jennifer J. Kiser ◽  
Awewura Kwara ◽  
Samantha Mawhinney ◽  
Susan Cu-Uvin
Keyword(s):  
Geometric Mean ◽  
Liver Function Tests ◽  
Open Label ◽  
Time Curve ◽  
Geometric Means ◽  
Concentration Time ◽  
Plan B ◽  
Effective Contraception ◽  
Grade 3 ◽  
Hiv Negative

Objectives. Compare the Plan B levonorgestrel (LNG) area under the concentration- time curve (AUC12) prior to and with efavirenz (EFV).Design. Prospective, open-label, single-arm, equivalence study.Methods. Healthy HIV-negative subjects underwent 12 hr intensive pharmacokinetic (PK) sampling following single dose LNG alone and after 14 days of EFV. Geometric means, Geometric Mean Ratios, and 90% confidence intervals (CI) are reported for PK Parameters.T-tests were utilized. Clinical parameters and liver function tests (LFTs) were assessed.Results. 24 women enrolled and 21 completed the study. With EFV, LNG AUC12was reduced 56% (95% CI: 49%, 62%) from 42.9 to 17.8 ng*hr/mL, and maximum concentration (Cmax⁡) was reduced 41% (95% CI: 33%, 50%) from 8.4 to 4.6 ng/mL. LNG was well tolerated with no grade 3 or 4 treatment-related toxicities.Conclusions. EFV significantly reduced LNG exposures. Higher LNG doses may be required with EFV. These results reinforce the importance of effective contraception in women taking EFV.

The geometry and algebra of the representations of the Lorentz group

1968 ◽  
Vol 303 (1474) ◽  
pp. 381-396 ◽  
Keyword(s):  
Projective Space ◽  
Lorentz Group ◽  
Point Of View ◽  
Normal Curve ◽  
Geometrical Representation ◽  
Spinor Space ◽  
Dimensional Projective Space ◽  
And Algebra ◽  
Rational Normal Curve ◽  
Formal Point

In this paper a (2j + l)-spinor analysis is developed along the lines of the 2-spinor and 3-spinor ones. We define generalized connecting quantities A μv (j) which transform like (j, 0) ⊗ (j -1, 0) in spinor space and like second rank tensors under transformations in space-time. The general properties of the A uv are investigated together with algebraic relations involving the Lorentz group generators, J μv . The connexion with 3j symbols is discussed. From a purely formal point of view we introduce a geometrical representation of a (2j +1)-spinor as a point in a 2j dimensional projective space. Then, for example, the charge con­jugate of a (2j + l)-spinor is just the polar of the corresponding point with respect to a certain rational, normal curve in the projective space. It is suggested that this representation will prove useful.

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