Cyclic orbit codes are constant dimension subspace codes that arise as the orbit of a cyclic subgroup of the general linear group acting on subspaces in the given ambient space. With the aid of the largest subfield over which the given subspace is a vector space, the cardinality of the orbit code can be determined, and estimates for its distance can be found. This subfield is closely related to...

BACKGROUND Identifying the potential for drug-induced kidney injury is essential for the successful research and development of new drugs. Newer and more sensitive preclinical drug-induced kidney injury biomarkers are now qualified for use in rat toxicology studies, but biomarkers for clinical studies are still undergoing qualification. The current studies investigated biomarkers in healthy vol...

The stabilizer formalism allows the efficient description of a sizeable class of pure as well as mixed quantum states of n-qubit systems. That same formalism has important applications in the field of quantum error correcting codes, where mixed stabilizer states correspond to projectors on subspaces associated with stabilizer codes. In this paper, we derive efficient reduction procedures to obt...

Design of power system stabilizer for enhancement power system stability is proposed. The effect of the proposed PSS on the synchronizing and damping torque coefficients is proved. To study the effectiveness of the proposed linear quadratic regulator (LQR) power system stabilizer, a sample power system in a linearized model is simulated and subjected to different operating conditions. The Linea...

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...

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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...