This paper focuses on the propagation of a few cycle optical pulses in graphene in a case of electromagnetic field. Electrons in the quantum formalism were considered and a change of dispersion law with Coulomb repuls...This paper focuses on the propagation of a few cycle optical pulses in graphene in a case of electromagnetic field. Electrons in the quantum formalism were considered and a change of dispersion law with Coulomb repulsion was taken into account. The effective equation was numerically analyzed and an influence of Coulomb repulsion was found. The amplification of few cycle optical pulses in graphene with applying of electromagnetic field to our system was discovered. Results about the amplification of pulse in graphene have been achieved.展开更多
S.W. Colomb proposed the conjecture——there exists a positive integer q_0 such that every non-zero element in GF(q) can be written as a sum of two primitive roots if q>q_0.Such a q_0 has been obtained, but quite l...S.W. Colomb proposed the conjecture——there exists a positive integer q_0 such that every non-zero element in GF(q) can be written as a sum of two primitive roots if q>q_0.Such a q_0 has been obtained, but quite large. In this paper we consider whether or not every non-zero element in GF(q) can be written as a sum of two primitive roots for any prime power q=p^n. We will prove that the answer of this question is in the affirmative for one of the following cases: (i) q>6.62×10, and q≠300690391, (ii) n>1 and q≠2~2.If prime power q<10500, the answer of this question is in the negative for q=2, 3, 4, 5,7, 11, 13, 19, 31, 43, 61 and in the affirmative for the others.展开更多
基金supported by the Russion Foundation for Basic Research under Grant No. 02-08-00663the Federal Target Program "Scientific and Pedagogical Manpower" for 2010-2013 under project No. NK-16(3)
文摘This paper focuses on the propagation of a few cycle optical pulses in graphene in a case of electromagnetic field. Electrons in the quantum formalism were considered and a change of dispersion law with Coulomb repulsion was taken into account. The effective equation was numerically analyzed and an influence of Coulomb repulsion was found. The amplification of few cycle optical pulses in graphene with applying of electromagnetic field to our system was discovered. Results about the amplification of pulse in graphene have been achieved.
文摘S.W. Colomb proposed the conjecture——there exists a positive integer q_0 such that every non-zero element in GF(q) can be written as a sum of two primitive roots if q>q_0.Such a q_0 has been obtained, but quite large. In this paper we consider whether or not every non-zero element in GF(q) can be written as a sum of two primitive roots for any prime power q=p^n. We will prove that the answer of this question is in the affirmative for one of the following cases: (i) q>6.62×10, and q≠300690391, (ii) n>1 and q≠2~2.If prime power q<10500, the answer of this question is in the negative for q=2, 3, 4, 5,7, 11, 13, 19, 31, 43, 61 and in the affirmative for the others.
