The Sylow theorems hold for finite extra loops, as does P. Hall’s theorem for finite solvable extra loops. Every finite nonassociative extra loop Q has a nontrivial center, Z(Q). Furthermore, Q/Z(Q) is a group whenever |Q| < 512. Loop extensions are used to construct an infinite nonassociative extra loop with a trivial center and a nonassociative extra loop Q of order 512 such that Q/Z(Q) is no...

We construct vortex loop operators in the three-dimensional N = 6 supersymmetric Chern-Simons theory recently constructed by Aharony, Bergman, Jafferis and Maldacena. These disorder loop operators are specified by a vortex-like singularity for the scalar and gauge fields along a one dimensional curve in spacetime. We identify the 1/2, 1/3 and 1/6 BPS loop operators in the Chern-Simons theory wi...

We study the quantum fermions+gravity system, that is, the gravitational counterpart of QED. We start from the standard Einstein-Weyl theory, reformulated in terms of Ashtekar variables; and we construct its non-perturbative quantum theory by extending the loop representation of general relativity. To this aim, we construct the fermion equivalent to the loop variables, and we define the quantum...

We construct a family of representations central extension loop group and affine Lie algebra for $\frak {sl}_n$ study their relations with highest weight modules. also Whittaker functionals on our prepresentations.

Objectives: The aim of the present study was to reconstruct determining validity, and score The Stanford Diagnostic Reading Test fourth edition (SDRT4) in the sixth grade students. Methods: The population of the study was all sixth grades of the 19 educational districts from Tehran, 571 students (255 boys and 316 girls) were selected by using a random multi-cluster sampling. The data were an...

The gravitational back-reaction on a certain type of rigidly-rotating cosmic string loop, first discovered by Allen, Casper and Ottewill, is studied at the level of the weak-field approximation. The near-field metric perturbations are calculated and used to construct the self-acceleration vector of the loop. Although the acceleration vector is divergent at the two kink points on the loop, its n...

Loop is a powerful program construct in classical computation, but its power is still not exploited fully in quantum computation. The exploitation of such power definitely requires a deep understanding of the mechanism of quantum loop programs. In this paper, we introduce a general scheme of quantum loops. The computational process of a quantum loop is then described. Moreover, the notions of t...

A Hamilton loop is a loop in which every subloop is normal. This definition is somewhat broader than the analogous definition of group theory where a Hamiltonian group is restricted to be non-Abelian. The structure of a Hamiltonian group is well known [4, pp. 129-131 ]l —it is the direct product of an Abelian group whose elements have odd order, an Abelian group with exponent 2, and a quaternio...

BACKGROUND Natural history of osteoporotic vertebral compression fractures (OVCFs), that is, collapse, loads the rigid pedicle screw rod construct in the absence of anterior column reconstruction, often leading to implant back outs. Semi rigid spinal loop rectangle and sublaminar wire construct allows controlled axial collapse and does not require anterior column reconstruction. MATERIALS AND...