The problem of determining when an integral quadratic form represents every positive integer has received much attention in recent years, culminating in the 15 and 290 Theorems of Bhargava-Conway-Schneeberger and Bhargava-Hanke. For ternary quadratic forms, there are always local obstructions, but one may ask whether there are ternary quadratic forms which represent every locally represented in...

We investigate topological and combinatorial structures of Lyubich and Minsky’s affine and hyperbolic 3-laminations associated with the hyperbolic and parabolic quadratic maps. We begin by showing that hyperbolic rational maps in the same hyperbolic component have quasi-isometrically the same 3-laminations. Then we describe the topological and combinatorial changes of laminations associated wit...

We study the problem of the existence of arithmetic progressions of three cubes over quadratic number fields Q( √ D), where D is a squarefree integer. For this purpose, we give a characterization in terms of Q( √ D)-rational points on the elliptic curve E : y = x − 27. We compute the torsion subgroup of the Mordell–Weil group of this elliptic curve over Q( √ D) and we give an explicit answer, i...

Theory is developed for linear-quadratic at infinity generating families for Legendrian knots in R3 . It is shown that the unknot with maximal Thurston–Bennequin invariant of −1 has a unique linear-quadratic at infinity generating family, up to fiber-preserving diffeomorphism and stabilization. From this, invariant generating family polynomials are constructed for 2–component Legendrian links w...

background: left ventricular (lv) twist is due to oppositely directed apical and basal rotation and has been proposed as a sensitive marker of lv function. we sought to assess the impact of chronic pure mitral regurgitation (mr) on the torsional mechanics of the left human ventricle using tissue doppler imaging. methods: nineteen severe mr patients with a normal lv ejection fraction and 16 non-...

ab initio calculation at hf/6-31g* level of theory for geometry optimization and mp2/6-31g*//hf/6-31g* for a single point total energy calculation are reported for the important energyminimumconformations and transition-state geometries of of cyclodeca-1,2,3-triene (1). the mostfavorable conformation of 1 is a unsymmetrical twist-chair (1-tc) structure. degenerateinterconversion of 1-tc with it...

For a fixed odd prime p and a representation ̺ of the absolute Galois group of Q into the projective group PGL2(Fp), we provide the twisted modular curves whose rational points supply the quadratic Q-curves of degree N prime to p that realize ̺ through the Galois action on their p-torsion modules. The modular curve to twist is either the fiber product of the modular curves X0(N) and X(p) or a cer...

Symmetric ordering and Weyl realizations for non-commutative quantum Minkowski spaces are reviewed. of Lie deformed corresponding star products, as well twist to realization coproduct momenta, presented. Drinfeld twists understood in Hopf algebroid sense also discussed. A few examples given. We show that the original Snyder space, there exists symmetric but no realization. Quadratic deformation...

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