This terminology is explained by Bogomolov decomposition theorem which states that, up to a finite étale covering, each holomorphic symplectic manifold is a product of several irreducible ones and a torus. Let X be a holomorphic symplectic manifold with a holomorphic symplectic form ω. Let D be a smooth divisor on X. At each point of D, the restriction of ω to D has one-dimensional kernel. This...

The Mortonor z-curve is one example for a space filling curve: Given a level of refinement L ∈ N0, it maps the interval [0, 2)∩Z one-to-one to a set of d-dimensional cubes of edge length 2−L that form a subdivision of the unit cube. Similar curves have been proposed for triangular and tetrahedral unit domains. In contrast to the Hilbert curve that is continuous, the Morton-type curves produce j...

A tetrahedral curve is an unmixed, usually non-reduced, one-dimensional subscheme of projective 3-space whose homogeneous ideal is the intersection of powers of the ideals of the six coordinate lines. The second and third authors have shown that these curves have very nice combinatorial properties, and they have made a careful study of the even liaison classes of these curves. We build on this ...

In this research, 272977 test day records collected from 659 herds during years 2001 to 2011 by the Iranian animal breeding center were used. In the first section the ability of different models to predict daily milk yield from alternative milk recording was tested. The result showed that a complex model including noon milking time plus the effect of lactation curve of Ali and Schaeffer functio...

We study conditions for a d –Kummer pullback of a Picard–Fuchs equation in a twisted symmetric square of the universal elliptic curve over X0(N) W to be of type D3. Our main result says that the only possible pairs (N, d) are exactly those for which there exists a Fano threefold with one-dimensional Picard group whose index is d and whose anticanonical degree is 2d2N. We give some modular formu...

angiotensin i-converting enzyme (ace) gene polymorphism; genotype dd or d allele may be involved with an increased susceptibility to type 2 diabetes and diabetic nephropathy (dn). we examined the frequency of ace gene polymorphism in 170 patients (85 type 2 diabetes with nephropathy and 85 without it) in tehran, iran. dna was extracted from the white blood cells and the i/d polymorphism of the ...

Let $E$ be an elliptic curve over $Bbb{Q}$ with the given Weierstrass equation $ y^2=x^3+ax+b$. If $D$ is a squarefree integer, then let $E^{(D)}$ denote the $D$-quadratic twist of $E$ that is given by $E^{(D)}: y^2=x^3+aD^2x+bD^3$. Let $E^{(D)}(Bbb{Q})$ be the group of $Bbb{Q}$-rational points of $E^{(D)}$. It is conjectured by J. Silverman that there are infinitely many primes $p$ for which $...

The coupled Kadomtsev–Petviashvili system associated with an elliptic curve, proposed by Date, Jimbo, and Miwa [J. Phys. Soc. Jpn., 52:766–771, 1983], is reinvestigated within the direct linearization framework, which provides us more insights into integrability of this model from perspective a general linear integral equation. As result, we successfully construct for not only Lax pair composed...