scholarly journals Kummer surfaces and the computation of the Picard group

2012 ◽  
Vol 15 ◽  
pp. 84-100 ◽  
Author(s):  
Andreas-Stephan Elsenhans ◽  
Jörg Jahnel
Keyword(s):  
Abelian Varieties ◽  
Upper Bounds ◽  
Picard Group ◽  
A Value ◽  
Kummer Surfaces

AbstractWe test R. van Luijk’s method for computing the Picard group of a K3 surface. The examples considered are the resolutions of Kummer quartics in ℙ3. Using the theory of abelian varieties, the Picard group may be computed directly in this case. Our experiments show that the upper bounds provided by van Luijk’s method are sharp when sufficiently many primes are used. In fact, there are a lot of primes that yield a value close to the exact one. However, for many but not all Kummer surfaces V of Picard rank 18, we have ${\rm rk}\,{\rm Pic}(V_{\overline {\mathbb F}_{\hspace *{-.8pt}p}}) \geq 20$ for a set of primes of density at least 1/2.

RELIABLE INTERNET-BASED MASTER-WORKER COMPUTING IN THE PRESENCE OF MALICIOUS WORKERS

2012 ◽  
Vol 22 (01) ◽  
pp. 1250002 ◽  
Author(s):  
ANTONIO FERNÁNDEZ ANTA ◽  
CHRYSSIS GEORGIOU ◽  
LUIS LÓPEZ ◽  
AGUSTÍN SANTOS
Keyword(s):  
Lower Bounds ◽  
Distributed System ◽  
High Probability ◽  
Upper Bounds ◽  
The Internet ◽  
Decision Strategy ◽  
Single Task ◽  
Asymptotically Optimal ◽  
A Value ◽  
Probability Of Success

We consider a Master-Worker distributed system where a master processor assigns, over the Internet, tasks to a collection of n workers, which are untrusted and might act maliciously. In addition, a worker may not reply to the master, or its reply may not reach the master, due to unavailabilities or failures of the worker or the network. Each task returns a value, and the goal is for the master to accept only correct values with high probability. Furthermore, we assume that the service provided by the workers is not free; for each task that a worker is assigned, the master is charged with a work-unit. Therefore, considering a single task assigned to several workers, our objective is to have the master processor to accept the correct value of the task with high probability, with the smallest possible amount of work (number of workers the master assigns the task). We probabilistically bound the number of faulty processors by assuming a known probability p < 1/2 of any processor to be faulty. Our work demonstrates that it is possible to obtain, with provable analytical guarantees, high probability of correct acceptance with low work. In particular, we first show lower bounds on the minimum amount of (expected) work required, so that any algorithm accepts the correct value with probability of success 1 - ε, where ε ≪ 1 (e.g., 1/n). Then we develop and analyze two algorithms, each using a different decision strategy, and show that both algorithms obtain the same probability of success 1 - ε, and in doing so, they require similar upper bounds on the (expected) work. Furthermore, under certain conditions, these upper bounds are asymptotically optimal with respect to our lower bounds.

VARIATIONS ON A THEME OF ROMANOFF

1996 ◽  
Vol 07 (03) ◽  
pp. 373-391 ◽  
Author(s):  
M. RAM MURTY ◽  
MICHAEL ROSEN ◽  
JOSEPH H. SILVERMAN
Keyword(s):  
Abelian Varieties ◽  
Number Fields ◽  
Upper Bounds ◽  
Log P ◽  
Variations On A Theme

Fix an integer a≥2. For each m≥1, let fa(m) be the smallest power f so that af≡1 (mod m). We give explicit upper bounds for the series Σm1/mfa(m)ε and Σplog(p)/pfa(p)ε, generalizing and strengthening results of Romanoff, Landau, Erdös and Turan. We also prove analogous results over number fields and for abelian varieties.

scholarly journals Moduli spaces of abstract and embedded Kummer varieties

2021 ◽  
pp. 2150054
Author(s):  
Mattia Galeotti ◽  
Sara Perna
Keyword(s):  
Equivalence Class ◽  
Moduli Space ◽  
Moduli Spaces ◽  
Abelian Varieties ◽  
The Other ◽  
Dimension Formula ◽  
Moduli Stacks ◽  
Other Hand ◽  
Kummer Surfaces ◽  
General Fact

In this paper, we investigate the construction of two moduli stacks of Kummer varieties. The first one is the stack [Formula: see text] of abstract Kummer varieties and the second one is the stack [Formula: see text] of embedded Kummer varieties. We will prove that [Formula: see text] is a Deligne-Mumford stack and its coarse moduli space is isomorphic to [Formula: see text], the coarse moduli space of principally polarized abelian varieties of dimension [Formula: see text]. On the other hand, we give a modular family [Formula: see text] of embedded Kummer varieties embedded in [Formula: see text], meaning that every geometric fiber of this family is an embedded Kummer variety and every isomorphic class of such varieties appears at least once as the class of a fiber. As a consequence, we construct the coarse moduli space [Formula: see text] of embedded Kummer surfaces and prove that it is obtained from [Formula: see text] by contracting the locus swept by a particular linear equivalence class of curves. We conjecture that this is a general fact: [Formula: see text] could be obtained from [Formula: see text] via a contraction for all [Formula: see text].

Observations of the Thermal Decomposition of Brucite

1968 ◽  
Vol 26 ◽  
pp. 446-447
Author(s):  
P. L. Burnett ◽  
W. R. Mitchell ◽  
C. L. Houck
Keyword(s):  
Thermal Decomposition ◽  
Magnesium Oxide ◽  
Basal Plane ◽  
Magnesium Ions ◽  
A Value ◽  
Reaction Proceeds

Natural Brucite (Mg(OH)2) decomposes on heating to form magnesium oxide (MgO) having its cubic ﹛110﹜ and ﹛111﹜ planes respectively parallel to the prism and basal planes of the hexagonal brucite lattice. Although the crystal-lographic relation between the parent brucite crystal and the resulting mag-nesium oxide crystallites is well known, the exact mechanism by which the reaction proceeds is still a matter of controversy. Goodman described the decomposition as an initial shrinkage in the brucite basal plane allowing magnesium ions to shift their original sites to the required magnesium oxide positions followed by a collapse of the planes along the original <0001> direction of the brucite crystal. He noted that the (110) diffraction spots of brucite immediately shifted to the positions required for the (220) reflections of magnesium oxide. Gordon observed separate diffraction spots for the (110) brucite and (220) magnesium oxide planes. The positions of the (110) and (100) brucite never changed but only diminished in intensity while the (220) planes of magnesium shifted from a value larger than the listed ASTM d spacing to the predicted value as the decomposition progressed.

Field-assisted ionization theory for microscopists

1994 ◽  
Vol 52 ◽  
pp. 820-821
Author(s):  
Patrick P. Camus
Keyword(s):  
Electric Field ◽  
Electron Tunneling ◽  
Ionization Probability ◽  
Critical Distance ◽  
Tunneling Probability ◽  
Field Ionization ◽  
Radius Of Curvature ◽  
Field Evaporation ◽  
A Value ◽  
Ion Emission

The theory of field ion emission is the study of electron tunneling probability enhanced by the application of a high electric field. At subnanometer distances and kilovolt potentials, the probability of tunneling of electrons increases markedly. Field ionization of gas atoms produce atomic resolution images of the surface of the specimen, while field evaporation of surface atoms sections the specimen. Details of emission theory may be found in monographs.Field ionization (FI) is the phenomena whereby an electric field assists in the ionization of gas atoms via tunneling. The tunneling probability is a maximum at a critical distance above the surface,xc, Fig. 1. Energy is required to ionize the gas atom at xc, I, but at a value reduced by the appliedelectric field, xcFe, while energy is recovered by placing the electron in the specimen, φ. The highest ionization probability occurs for those regions on the specimen that have the highest local electric field. Those atoms which protrude from the average surfacehave the smallest radius of curvature, the highest field and therefore produce the highest ionizationprobability and brightest spots on the imaging screen, Fig. 2. This technique is called field ion microscopy (FIM).

Vitamin A Value of Plant Food Provitamin A - Evaluated by the Stable Isotope Technologies

2014 ◽  
Vol 84 (Supplement 1) ◽  
pp. 25-29 ◽  
Author(s):  
Guangwen Tang
Keyword(s):  
Stable Isotope ◽  
Vitamin A ◽  
Provitamin A ◽  
Animal Origin ◽  
Plant Food ◽  
Plant Foods ◽  
A Value ◽  
Provitamin A Carotenoids ◽  
Β Carotene

Humans need vitamin A and obtain essential vitamin A by conversion of plant foods rich in provitamin A and/or absorption of preformed vitamin A from foods of animal origin. The determination of the vitamin A value of plant foods rich in provitamin A is important but has challenges. The aim of this paper is to review the progress over last 80 years following the discovery on the conversion of β-carotene to vitamin A and the various techniques including stable isotope technologies that have been developed to determine vitamin A values of plant provitamin A (mainly β-carotene). These include applications from using radioactive β-carotene and vitamin A, depletion-repletion with vitamin A and β-carotene, and measuring postprandial chylomicron fractions after feeding a β-carotene rich diet, to using stable isotopes as tracers to follow the absorption and conversion of plant food provitamin A carotenoids (mainly β-carotene) in humans. These approaches have greatly promoted our understanding of the absorption and conversion of β-carotene to vitamin A. Stable isotope labeled plant foods are useful for determining the overall bioavailability of provitamin A carotenoids from specific foods. Locally obtained plant foods can provide vitamin A and prevent deficiency of vitamin A, a remaining worldwide concern.

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