# Bulletin of the Iranian Mathematical Society

Bulletin of the Iranian Mathematical Society > 2018 > 44 > 5 > 1267-1281

*b-*metric space endowed with a graph.

Bulletin of the Iranian Mathematical Society > 2018 > 44 > 5 > 1155-1161

*I*be the defining ideal of the set of all singular points of the union of lines in $$\mathcal {L}$$ L . In this note, the Waldschmidt constant of

*I*for some special cases of line arrangement $$\mathcal {L}$$ L is computed.

Bulletin of the Iranian Mathematical Society > 2018 > 44 > 5 > 1185-1193

*G*be a finite group and

*H*a subgroup of

*G*. We say that

*H*is

*s*-semipermutable in

*G*if $$HG_{p}=G_{p}H$$ HGp=GpH for any Sylow

*p*-subgroup $$G_{p}$$ Gp of

*G*with $$(p,|H|)=1$$ (p,|H|)=1 . In this paper, we consider the

*s*-semipermutability of prime-power order subgroups and prove the following result which generalizes some known results concerning

*s*-semipermutable subgroups.

**Theorem:**Suppose that...

Bulletin of the Iranian Mathematical Society > 2018 > 44 > 5 > 1163-1170

Bulletin of the Iranian Mathematical Society > 2018 > 44 > 5 > 1351-1386

Bulletin of the Iranian Mathematical Society > 2018 > 44 > 5 > 1315-1328

Bulletin of the Iranian Mathematical Society > 2018 > 44 > 5 > 1211-1216

*reciprocal distance*matrix of a connected graph, called the

*reciprocal distance Laplacian.*Let $$\delta _1\ge \delta _2\ge \cdots \ge \delta _{n-1}\ge \delta _n$$ δ1≥δ2≥⋯≥δn-1≥δn be the reciprocal distance Laplacian spectrum. In this short note, we show that $$\delta _1\le n$$ δ1≤n with equality if and only if the complement graph $$\overline{G}$$...

Bulletin of the Iranian Mathematical Society > 2018 > 44 > 5 > 1283-1294

Bulletin of the Iranian Mathematical Society > 2018 > 44 > 5 > 1217-1226

*R*belongs to the right (left) singular ideal of

*R*. In this paper, we investigate rings in which all nilpotent elements belong to the right singular ideal of

*R*.

Bulletin of the Iranian Mathematical Society > 2018 > 44 > 5 > 1329-1336

*X*of a topological vector space and an arbitrary set

*Y*. Our results extend the Knaster–Kuratowski–Mazurkiewicz Lemma, Ky Fan’s minimax inequality and Brézis–Nirenberg–Stampacchia Theorem.

Bulletin of the Iranian Mathematical Society > 2018 > 44 > 5 > 1117-1124

Bulletin of the Iranian Mathematical Society > 2018 > 44 > 5 > 1303-1314

Bulletin of the Iranian Mathematical Society > 2018 > 44 > 5 > 1243-1265

Bulletin of the Iranian Mathematical Society > 2018 > 44 > 5 > 1141-1153

Bulletin of the Iranian Mathematical Society > 2018 > 44 > 5 > 1195-1209

*P*-space. These spaces were introduced by Azarpanah and Motamedi in their study of the zero-divisor graph of rings of continuous functions. In this note, we explore...

Bulletin of the Iranian Mathematical Society > 2018 > 44 > 5 > 1171-1184

Bulletin of the Iranian Mathematical Society > 2018 > 44 > 5 > 1125-1139

Bulletin of the Iranian Mathematical Society > 2018 > 44 > 5 > 1337-1349

Bulletin of the Iranian Mathematical Society > 2018 > 44 > 5 > 1295-1301

*G*is a finite

*p*-group with $$p>2$$ p>2 and $$(|Z(G)|, |Z_3(G)|) \in \{ (p, p^4), (p^2, p^5) \}$$ (|Z(G)|,|Z3(G)|)∈{(p,p4),(p2,p5)} , then

*G*has a noninner automorphism of order

*p*, where $$Z_3(G)$$ Z3(G) is the third member of the upper central series of

*G*. In particular, there exists a noninner automorphism of order

*p*in some families of finite

*p*-groups of coclass 3.

Bulletin of the Iranian Mathematical Society > 2018 > 44 > 5 > 1227-1242

*j*,

*k*)-symmetric functions has many applications in the investigation of fixed points, estimation of the absolute values of some integrals and in obtaining results of the type of Cartan’s uniqueness theorem. The concept of $$\left( 2j,k\right) $$ 2j,k -symmetric functions extends the idea of even, odd,

*k*, 2

*k*, $$\left( j,k\right) $$ j,k -symmetric and conjugate functions. In this paper,...