In this note, I study a comparison map between a motivic and étale cohomology group of an elliptic curve over Q just outsie the range of Voevodsky's isomoprhism theorem. I show that the property of the map being an isomorphism is equivalent to certain arithmetical properties of the elliptic curve.

The toric residue mirror conjecture of Batyrev and Materov [2] for Calabi-Yau hypersurfaces in Gorenstein toric Fano varieties expresses a toric residue as a power series whose coefficients are certain integrals over moduli spaces. This conjecture was proved independently by Szenes and Vergne [10] and Borisov [5]. We build on the work of these authors to generalize the residue mirror map to not...

We propose an angular map driven active contouring based on curve evolution using level sets to extract object from natural color images. The constraint parameters to stop the intrinsically evolving curve on the angular map of the color space (RGB used) are derived based upon a modified minimal partition problem.

background and objective: obstructive sleep apnea (osa) is the most common type of sleep-disordered breathing. multivariable apnea prediction (map) index consists of three questions about the frequency of osa symptoms plus body mass index (bmi), age and sex that categorizes the patients to low and high risk for osa using a formula. objective map index was calculated by discounting the questions...

The use of elliptic curve cryptography (ECC) when used as a public-key cryptosystem for encryption is such that if one has a message to encrypt, then they attempt to map it to some point in the prime subgroup of the elliptic curve by systematically modifying the message in a deterministic manner. The applications typically used for ECC are the key-exchange, digital signature or a hybrid encrypt...

Production and prediction of land-use/land cover changes (LULCC) map are among the significant issues regarding input of many environmental and hydrological models. Among various introduced methods, similarity-weighted instance-based machine learning algorithm (SimWeight) and Markov-chain with lower complexity and proper performnce are frequently used. The main aim of this study is utilizing Si...

Let C be a curve of genus 2 and ψ1 : C −→ E1 a map of degree n, from C to an elliptic curve E1, both curves defined over C. This map induces a degree n map φ1 : P 1 −→ P 1 which we call a Frey-Kani covering. We determine all possible ramifications for φ1. If ψ1 : C −→ E1 is maximal then there exists a maximal map ψ2 : C −→ E2, of degree n, to some elliptic curve E2 such that there is an isogeny...

We provide a patch to complete the proof of the Voevodsky-Rost Theorem, that the norm residue map is an isomorphism. (This settles the motivic Bloch-Kato conjecture).

We present temperature and metallicity maps of the Perseus cluster core obtained with the Chandra X-ray Observatory. We find an overall temperature rise from ∼ 3.0 keV in the core to ∼ 5.5 keV at 120 kpc and a metallicity profile that rises slowly from ∼ 0.5 solar to ∼ 0.6 solar inside 60 kpc, but drops to ∼ 0.4 solar at 120 kpc. Spatially resolved spectroscopy in small cells shows that the tem...

Using the notion of equivariant Kirwan map, as defined by Goldin [3], we prove that — in the case of Hamiltonian torus actions with isolated fixed points — Tolman and Weitsman’s description of the kernel of the Kirwan map can be deduced directly from the residue theorem of [6] and [7]. A characterization of the kernel of the Kirwan map in terms of residues of one variable (i.e. associated to Ha...