On the Number of Solutions of Diagonal Equations over a Finite Field

AbstractIn this paper, we give a reduction theorem for the number of solutions of any diagonal equation over a finite field. Using this reduction theorem and the theory of quadratic equations over a finite field, we also get an explicit formula for the number of solutions of a diagonal equation over a finite field, under a certain natural restriction on the exponents

Detecting Majorana fermions by nonlocal entanglement between quantum dots

Nonlocal entanglement between two quantum dots can be generated through Majorana fermions. The two Majorana fermions at the ends of an one-dimensional topological superconductor form a nonlocal fermion level, coupling to the occupation states of two quantum dots put close to the two ends, and the entire system will come into an entangled state. After introducing a charging energy by a capacitor, entanglement of the entire system can manifest itself through the nonlocal entanglement between the two quantum dots. That is, when measuring the electron occupations of the quantum dots, the measurement result of one quantum dot will influence the measurement result of the other quantum dot. This nonlocal entanglement between the two quantum dots is a strong evidence of the nonlocal nature of the fermion level constructed by two Majorana fermions.Comment: 4 pages, 4 figure

2-Chloro-N-isopropyl-N-phenyl­acetamide

In the title compound, C11H14ClNO, the herbicide propachlor, there are significant differences between the three N—C bond lengths [N—Ccarbon­yl = 1.354 (3) Å, N—Cphen­yl = 1.444 (2) Å and N—Cisoprop­yl = 1.496 (3) Å], indicating the presence of π delocalization involving the carbonyl group. The N atom lies 0.074 (2) Å from the plane defined by the the three bonded C atoms

2-Hydr­oxy-1-methoxy­anthraquinone monohydrate

The title compound, C15H10O4·H2O, also known as alizarin 1-methyl ether monohydrate, was isolated from Morinda officinalis How. The anthraquinone ring system is almost planar, the dihedral angle between the two outer benzene rings being 3.07 (4)°. In the crystal structure, O—H⋯O hydrogen bonds link the organic mol­ecules and the water mol­ecules, forming a three-dimensional network