We are interested in a linearized inverse scattering problem considered by Symes and Nolan [10] for the marine data acquisition geometry. This arises as follows: a vessel carries an acoustic source (airgun) and recording instruments (hydrophones). The airgun sends acoustic waves through the ocean to the subsurface and the reflections occur when the sound waves encounter singularities in the mat...

Convolutional stabilizer codes promise to make quantum communication more reliable with attractive online encoding and decoding algorithms. This paper introduces a new approach to convolutional stabilizer codes based on direct limit constructions. Two families of quantum convolutional codes are derived from generalized Reed-Solomon codes and from ReedMuller codes. A Singleton bound for pure con...

The RV Investigator is Australia’s new noise quietened Marine National Facility (MNF) vessel built to comply with the DNV silent-R specification. This radiated noise specification was based on the ICES 209 CRR specification designed with the main goal of minimising vessel avoidance for fisheries surveys. Noise quietening was specified for RV Investigator to improve the acoustic detection of ins...

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We solve one of the oldest problems in the theory of quantum stabilizer codes by proving the non-existence of quantum [[13,5,4]]-codes.

Let K〈x, y〉 be the free associative algebra of rank 2 over an algebraically closed constructive field of any characteristic. We present an algorithm which decides whether or not two elements in K〈x, y〉 are equivalent under an automorphism of K〈x, y〉. A modification of our algorithm solves the problem whether or not an element in K〈x, y〉 is a semiinvariant of a nontrivial automorphism. In partic...

In this paper by definition of generalized action of generalized Lie groups (top spaces) on a manifold, the concept of stabilizer of the top spaces is introduced. We show that the stabilizer is a top space, moreover we find the tangent space of a stabilizer. By using of the quotient spaces, the dimension of some top spaces are fined.

A base of a permutation group G on a set Ω is a subset B of Ω such that the pointwise stabilizer of B in G is trivial. The base size of G, denoted by b(G), is the minimal cardinality of a base. Let G = Sn or An acting primitively on a set with point stabilizer H. In this note we prove that if H acts primitively on {1, . . . , n}, and does not contain An, then b(G) = 2 for all n ≥ 13. Combined w...

We show how to convert a quantum stabilizer code to a one-way or two-way entanglement distillation protocol. The proposed conversion method is a generalization of those of Shor-Preskill and Nielsen-Chuang. The recurrence protocol and the quantum privacy amplification protocol are equivalent to the protocols converted from [[2, 1]] stabilizer codes. We also give an example of a two-way protocol ...

Observational and experimental studies were conducted on the dispersal of fouling organisms on a replica of a 16th-century sailing vessel along an 800 km transect from Yaquina Bay, Oregon to San Francisco Bay, California. The vessel sailed between four bays at slow speeds (3.5 to 4 knots), resided in each bay for approximately 30 d, and spent 1 to 3 d in the open ocean travelling between ports....