Ramanujan also conjectured that congruences (1) exist for the cases A = 5 , 7 , or 11 . This conjecture was proved by Watson [17] for the cases of powers of 5 and 7 and Atkin [3] for the cases of powers of 11. Since then, the problem of finding more examples of such congruences has attracted a great deal of attention. However, Ramanujan-type congruences appear to be very sparse. Prior to the la...

The optimal power flow (OPF) problem determines an optimal operating point of the power network that minimizes a certain objective function subject to physical and network constraints. There has been a great deal of attention in convex relaxation of the OPF problem in recent years, and it has been shown that a semidefinite programming (SDP) relaxation can solve different classes of the nonconve...

The rise of a land power that is trying to develop its maritime forces has been viewed as an important conflict instigator among great powers. Great Britain shared similar concerns with the Germany at beginning 20th century. Power relations states in East Asia, during last two decades, share many similarities those pre-World War I Europe. This historical analogy provides abundant information re...

In this paper we determine the perfect powers that are sums of three fifth in an arithmetic progression. More precisely, completely solve Diophantine equation(x−d)5+x5+(x+d)5=zn,n≥2, where d,x,z∈Z and d=2a5b with a,b≥0.

In this paper, power control for two-tier small-cell networks in the uplink is investigated. We formulate the power control problem as a Stackelberg game, where the macrocell user equipment (MUE) acts as the leader and the small-cell user equipments (SUEs) as the followers. To reduce the cross-tier and co-tier interference and also the power consumption of both the MUE and SUEs, we propose to i...

Any active thing always needs power. All productive tools, machines or working systems, which are so-called productive force, would need proper driving (motive) power (force). The motive power is the heart or core of productive force, which would always want to correspond with a definite relation of production. The different driving powers (or energy resource) with power devices are completely ...

among others internal, regional, international, political, economic, technical, social and cultural factors are reasons that theorists introduce for beginning of integration at a region. by looking at the functions of the shanghai cooperation organization and the association of southeast asian nations (asean), we understand that there are two basic pragmatic factors, the support of the great po...

regulating relations with great powers constitutes one of the most significant issues of each country’s foreign policy. iran, the soviet :union: and later russia have failed to establish strategic relations, despite their efforts to enhance mutual relations since late 1980s. it is believed that iran found it politically expedient to have ties with moscow due to its disputed relations with the w...