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...

This paper deals with a CMOS based artificial neuron implemented by threshold elements. We consider the artificial neuron as a threshold element with controlled inputs having weights formed during a learning process. A so-called β-driven threshold element is used for in the scheme of the neuron. Functioning of this element is described in a specific ratio form. The β-driven implementation is ba...

A novel fluorescence sensor of NR-β-CD@AuNPs was prepared for the trace detection of nitrite in quantities as low as 4.25 × 10-3 μg∙mL-1 in an aqueous medium. The fluorescence was due to the host-guest inclusion complexes between neutral red (NR) molecules and gold nanoparticles (AuNPs), which were modified by per-6-mercapto-beta-cyclodextrins (SH-β-CDs) as both a reducing agent and a stabilize...

The effect of concentration of reduction agent of sodium borohydrate (NaBH4) on the properties of silicon nanoparticles synthesized via microemulsion route is reported. In this work, the concentration of the silicon tetrachloride (SiCl4) that served as silicon source with sodium hydroxide (NaOH) and polyethylene glycol (PEG) as stabilizer and surfactant, respectively, are keep fixed. Four sampl...

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 ...

Generic cosmetic creams (oil-in-water emulsions) were prepared using dry Bacterial Cellulose and Carboxymethyl (BC:CMC) to study the possibility of partially or completely replacing surfactants, while ensuring a long-term stability required organoleptic characteristics. BC:CMC was benchmarked against two hydrocolloidal Avicel products (PC-591 PC-611), commonly used as thickeners stabilizing aid...

A 22-year-old male diagnosed with bipolar affective disorder presented to us with a 3rd episode mania resistant to both olanzapine and haloperidol as well as electroconvulsive therapy. He, however, responded to chlorpromazine (CPZ) which was also effective as a mood stabilizer. The patient had a relapse of his illness when CPZ was stopped and responded again when it was started. The case demons...