Let E/K be an elliptic curve defined over a number field, and let P ∈ E(K) be a point of infinite order. It is natural to ask how many integers n ≥ 1 fail to occur as the order of P modulo a prime of K. For K = Q, E a quadratic twist of y2 = x3 − x, and P ∈ E(Q) as above, we show that there is at most one such n ≥ 3.

Kinetic helicity is one of the invariants of the Euler equations that is associated with the topology of vortex lines within the fluid. In superfluids, the vorticity is concentrated along vortex filaments. In this setting, helicity would be expected to acquire its simplest form. However, the lack of a core structure for vortex filaments appears to result in a helicity that does not retain its k...

Near a nonresonant, elliptic fixed point, a symplectic map can be transformed into Birkhoff normal form. In these coordinates, the dynamics is represented entirely by the Lagrangian ‘‘frequency map’’ that gives the rotation number as a function of the action. The twist matrix, given by the Jacobian of the rotation number, describes the anharmonicity in the system. When the twist is singular the...

introduction left ventricular (lv) twist is believed to store potential energy and plays an important role in generating diastolic suction. recent advances in echocardiography techniques have allowed quantification of lv twist. the aim of the present study was to compare lv twist and torsion in healthy human subjects determined by velocity vector imaging (vvi) and tissue doppler imaging (tdi) a...

Recent advances in structural biochemistry have provided evidence that not only the geometric properties but also the elastic moduli of duplex DNA are strongly dependent on nucleotide sequence in a way that is not accounted for by classical rod models of the Kirchhoff type. A theory of sequence-dependent DNA elasticity is employed here to calculate the dependence of the equilibrium configuratio...

We prove local global compatibility (up to a quadratic twist) of Galois representations associated to holomorphic Hilbert-Siegel modular forms in many cases (induced from Borel or Klingen parabolic). For Siegel modular forms, when the local representation is an irreducible principal series we get local global compatibility without a twist. We achieve this by proving a version of rigidity (stron...

Scroll waves are three-dimensional excitation patterns that rotate around a central filament curve; they occur in many physical, biological, and chemical systems. We explicitly derive the equations of motion for scroll wave filaments in reaction-diffusion systems with isotropic diffusion up to third order in the filament's twist and curvature. The net drift components define at every instance o...

We used QCD factorization for the hadronic matrix elements to show that the existing data, in particular the branching ratios BR ( ?J/?K) and BR ( ?J/??), can be accounted for this approach. We analyzed the decay within the framework of QCD factorization. We have complete calculation of the relevant hard-scattering kernels for twist-2 and twist-3. We calculated this decays in a special scale ...

Suppose that f = ∑ n≥1 an(f)q n is a cusp form of weight 2k (k ∈ N). We denote by L(f, s) the L-function of f . For Re(s) sufficiently large, the value of L(f, s) is given by L(f, s) = ∑ n≥1 an(f) ns , and one can show that L(f, s) has analytic continuation to the entire complex plane. The value of L(f, s) at s = k will be of particular interest to us, and we will refer to this value as the cen...

A passive false twist unit (spiral) has been developed to assist with the handling lowstrength slivers on a high speed-spinning machine with a high-speed feed. In the first trial, a falsetwist simulator device was constructed to determine whether the passive false twist unit can be usedon high speed feeding with different can distance from the feeding device. In the second trial, theeffects of ...