2018-11-15T23:23:24Z
http://bims.iranjournals.ir/?_action=export&rf=summon&issue=82
Bulletin of the Iranian Mathematical Society
BIMS
1017-060X
1017-060X
2016
42
2
Bulletin of the Iranian Mathematical Society
2016
04
01
http://bims.iranjournals.ir/article_755_912ec75f54c027ac1de89d21bbf9662f.pdf
Bulletin of the Iranian Mathematical Society
BIMS
1017-060X
1017-060X
2016
42
2
Radical of $cdot$-ideals in $PMV$-algebras
F.
Forouzesh
In this paper, we introduce the notion of the radical of a $PMV$-algebra $A$ and we charactrize radical $A$ via elements of $A$. Also, we introduce the notion of the radical of a $cdot$-ideal in $PMV$-algebras. Several characterizations of this radical is given. We define the notion of a semimaximal $cdot$-ideal in a $PMV$-algebra. Finally we show that $A/I$ has no nilpotent elements if and only if $I$ is a semi-maximal $cdot$-ideal of $A$.
$PMV$-algebra
$cdot$-ideal
$cdot$-prime ideal
radical
2016
04
01
233
246
http://bims.iranjournals.ir/article_756_d1afd5d234b5acc222bd74060762df14.pdf
Bulletin of the Iranian Mathematical Society
BIMS
1017-060X
1017-060X
2016
42
2
Existence of solutions of boundary value problems for Caputo fractional differential equations on time scales
R. A.
Yan
S. R.
Sun
Z. L.
Han
In this paper, we study the boundary-value problem of fractional order dynamic equations on time scales, $$ ^c{Delta}^{alpha}u(t)=f(t,u(t)),;;tin [0,1]_{mathbb{T}^{kappa^{2}}}:=J,;;1
Fractional differential equation
Time scales
Boundary-value problem
Fixed-point theorem
2016
04
01
247
262
http://bims.iranjournals.ir/article_757_6c272666edd826df2c68e8aa2ebafd12.pdf
Bulletin of the Iranian Mathematical Society
BIMS
1017-060X
1017-060X
2016
42
2
Locally GCD domains and the ring $D+XD_S[X]$
G. W.
Chang
T.
Dumitrescu
M.
Zafruhhah
An integral domain $D$ is called a emph{locally GCD domain} if $D_{M}$ is a GCD domain for every maximal ideal $M$ of $D$. We study some ring-theoretic properties of locally GCD domains. E.g., we show that $D$ is a locally GCD domain if and only if $aDcap bD$ is locally principal for all $0neq a,bin D$, and flat overrings of a locally GCD domain are locally GCD. We also show that the t-class group of a locally GCD domain is just its Picard group. We study when a locally GCD domain is Pr"{u}fer or a generalized GCD domain. We also characterize locally factorial domains as domains $D$ whose minimal prime ideals of a nonzero principal ideal are locally principal and discuss conditions that make them Krull domains. We use the $D+XD_{S}[X]$ construction to give some interesting examples of locally GCD domains that are not GCD domains.
Locally GCD domain
generalized GCD domain
$D+XD_S[X]$
2016
04
01
263
284
http://bims.iranjournals.ir/article_758_519fca69eb4a638b55fe87c7eafe3be6.pdf
Bulletin of the Iranian Mathematical Society
BIMS
1017-060X
1017-060X
2016
42
2
Sufficiency and duality for a nonsmooth vector optimization problem with generalized $alpha$-$d_{I}$-type-I univexity over cones
H.
Jiao
In this paper, using Clarke’s generalized directional derivative and dI-invexity we introduce new concepts of nonsmooth K-α-dI-invex and generalized type I univex functions over cones for a nonsmooth vector optimization problem with cone constraints. We obtain some sufficient optimality conditions and Mond-Weir type duality results under the foresaid generalized invexity and type I cone-univexity assumptions.
Vector optimization
Type I univexity
Cones
Optimality
duality
2016
04
01
285
295
http://bims.iranjournals.ir/article_759_d37d71e77deecebe9efed9e81fb10b79.pdf
Bulletin of the Iranian Mathematical Society
BIMS
1017-060X
1017-060X
2016
42
2
A new approach for solving the first-order linear matrix differential equations
A.
Golbabai
S.
P. A. Beik
D.
K. Salkuyeh
Abstract. The main contribution of the current paper is to propose a new effective numerical method for solving the first-order linear matrix differential equations. Properties of the Legendre basis operational matrix of integration together with a collocation method are applied to reduce the problem to a coupled linear matrix equations. Afterwards, an iterative algorithm is examined for solving the obtained coupled linear matrix equations. Numerical experiments are presented to demonstrate the applicably and efficiency of our method.
Linear matrix differential equation
Legendre polynomials
Coupled linear matrix equations
Iterative algorithm
2016
04
01
297
314
http://bims.iranjournals.ir/article_760_2cfb83ffe97a3eb87e63d4a2121a528b.pdf
Bulletin of the Iranian Mathematical Society
BIMS
1017-060X
1017-060X
2016
42
2
An analytic solution for a non-local initial-boundary value problem including a partial differential equation with variable coefficients
M.
Jahanshahi
M.
Darabadi
This paper considers a non-local initial-boundary value problem containing a first order partial differential equation with variable coefficients. At first, the non-self-adjoint spectral problem is derived. Then its adjoint problem is calculated. After that, for the adjoint problem the associated eigenvalues and the subsequent eigenfunctions are determined. Finally the convergence of series solution and the uniqueness of this solution will be proved.
Partial Differential Equation
Boundary Value Problem
Self Adjoint Problem
Non-Self Adjoint Operators
Non-Local-Boundary Conditions
2016
04
01
315
326
http://bims.iranjournals.ir/article_761_706ebf130c6496e7db6e47caf0549442.pdf
Bulletin of the Iranian Mathematical Society
BIMS
1017-060X
1017-060X
2016
42
2
Trivially related lax pairs of the Sawada-Kotera equation
D.
Talati
We show that a recently introduced Lax pair of the Sawada-Kotera equation is not a new one but is trivially related to the known old Lax pair. Using the so-called trivial compositions of the old Lax pairs with a differentially constrained arbitrary operators, we give some examples of trivial Lax pairs of KdV and Sawada-Kotera equations.
Sawada-Kotera equation
Lax pair
integrability
2016
04
01
327
330
http://bims.iranjournals.ir/article_762_f60c4b68590b1689ee7d3635b080f175.pdf
Bulletin of the Iranian Mathematical Society
BIMS
1017-060X
1017-060X
2016
42
2
On Silverman's conjecture for a family of elliptic curves
K.
Nabardi
F.
Izadi
Let $E$ be an elliptic curve over $Bbb{Q}$ with the given Weierstrass equation $ y^2=x^3+ax+b$. If $D$ is a squarefree integer, then let $E^{(D)}$ denote the $D$-quadratic twist of $E$ that is given by $E^{(D)}: y^2=x^3+aD^2x+bD^3$. Let $E^{(D)}(Bbb{Q})$ be the group of $Bbb{Q}$-rational points of $E^{(D)}$. It is conjectured by J. Silverman that there are infinitely many primes $p$ for which $E^{(p)}(Bbb{Q})$ has positive rank, and there are infinitely many primes $q$ for which $E^{(q)}(Bbb{Q})$ has rank $0$. In this paper, assuming the parity conjecture, we show that for infinitely many primes $p$, the elliptic curve $E_n^{(p)}: y^2=x^3-np^2x$ has odd rank and for infinitely many primes $p$, $E_n^{(p)}(Bbb{Q})$ has even rank, where $n$ is a positive integer that can be written as biquadrates sums in two different ways, i.e., $n=u^4+v^4=r^4+s^4$, where $u, v, r, s$ are positive integers such that $gcd(u,v)=gcd(r,s)=1$. More precisely, we prove that: if $n$ can be written in two different ways as biquartic sums and $p$ is prime, then under the assumption of the parity conjecture $E_n^{(p)}(Bbb{Q})$ has odd rank (and so a positive rank) as long as $n$ is odd and $pequiv5, 7pmod{8}$ or $n$ is even and $pequiv1pmod{4}$. In the end, we also compute the ranks of some specific values of $n$ and $p$ explicitly.
Silverman's Conjecture
Elliptic Curve
Quadratic Twist
rank
Parity Conjecture
2016
04
01
331
340
http://bims.iranjournals.ir/article_763_4e8380b4a993b2881f9ee0d5d1e2181c.pdf
Bulletin of the Iranian Mathematical Society
BIMS
1017-060X
1017-060X
2016
42
2
Every class of $S$-acts having a flatness property is closed under directed colimits
H.
Qiao
L.
Wang
X.
Ma
Let $S$ be a monoid. In this paper, we prove every class of $S$-acts having a flatness property is closed underdirected colimits, it extends some known results. Furthermore this result implies that every $S$-act has a flatness cover if and only if it has a flatness precover.
Flatness property
colimit
closed
2016
04
01
341
351
http://bims.iranjournals.ir/article_764_8c92870856f42224b242cd3dc1feb5b5.pdf
Bulletin of the Iranian Mathematical Society
BIMS
1017-060X
1017-060X
2016
42
2
Partial proof of Graham Higman's conjecture related to coset diagrams
Q.
Mushtaq
A.
Razaq
Graham Higman has defined coset diagrams for PSL(2,ℤ). These diagrams are composed of fragments, and the fragments are further composed of two or more circuits. Q. Mushtaq has proved in 1983 that existence of a certain fragment γ of a coset diagram in a coset diagram is a polynomial f in ℤ[z]. Higman has conjectured that, the polynomials related to the fragments are monic and for a fixed degree, there are finite number of such polynomials. In this paper, we consider a family Ϝ of fragments such that each fragment in Ϝ contains one vertex fixed byF_v [(〖xy〗^(-1) )^(s_1 ) (xy)^(s_2 ) (〖xy〗^(-1) )^(s_3 ),(xy)^(q_1 ) (〖xy〗^(-1) )^(q_2 ) (xy)^(q_3 ) ]where s₁,s₂,s₃,q₁,q₂,q₃∈ℤ⁺, and prove Higman's conjecture for the polynomials obtained from the fragments in Ϝ.
Modular group
Coset diagrams
projective line over finite field
2016
04
01
353
369
http://bims.iranjournals.ir/article_765_b144cad7da2c8ab7c7be161d9bb12fe5.pdf
Bulletin of the Iranian Mathematical Society
BIMS
1017-060X
1017-060X
2016
42
2
Toroidalization of locally toroidal morphisms of 3-folds
R.
Ahmadian
A toroidalization of a dominant morphism $varphi: Xto Y$ of algebraic varieties over a field of characteristic zero is a toroidal lifting of $varphi$ obtained by performing sequences of blow ups of nonsingular subvarieties above $X$ and $Y$. We give a proof of toroidalization of locally toroidal morphisms of 3-folds.
Toroidalization
resolution of morphisms
principalization
2016
04
01
371
405
http://bims.iranjournals.ir/article_766_30a65aebf30dd4f836a00da605df90a7.pdf
Bulletin of the Iranian Mathematical Society
BIMS
1017-060X
1017-060X
2016
42
2
Finite groups with $X$-quasipermutable subgroups of prime power order
X.
Yi
X.
Yang
Let $H$, $L$ and $X$ be subgroups of a finite group $G$. Then $H$ is said to be $X$-permutable with $L$ if for some$xin X$ we have $AL^{x}=L^{x}A$. We say that $H$ is emph{$X$-quasipermutable } (emph{$X_{S}$-quasipermutable}, respectively) in $G$ provided $G$ has a subgroup $B$ such that $G=N_{G}(H)B$ and $H$ $X$-permutes with $B$ and with all subgroups (with all Sylow subgroups, respectively) $V$ of $B$ such that $(|H|, |V|)=1$. In this paper, we analyze the influence of $X$-quasipermutable and $X_{S}$-quasipermutable subgroups on the structure of $G$. Some known results are generalized.
$X$-quasipermutable subgroup
Sylow subgroup
$p$-soluble group
$p$-supersoluble group
$p$-nilpotent group
2016
04
01
407
416
http://bims.iranjournals.ir/article_767_7c8f57226de334e589c125523eea2281.pdf
Bulletin of the Iranian Mathematical Society
BIMS
1017-060X
1017-060X
2016
42
2
The augmented Zagreb index, vertex connectivity and matching number of graphs
A.
Ali
A.
Bhatti
Z.
Raza
Let $Gamma_{n,kappa}$ be the class of all graphs with $ngeq3$ vertices and $kappageq2$ vertex connectivity. Denote by $Upsilon_{n,beta}$ the family of all connected graphs with $ngeq4$ vertices and matching number $beta$ where $2leqbetaleqlfloorfrac{n}{2}rfloor$. In the classes of graphs $Gamma_{n,kappa}$ and $Upsilon_{n,beta}$, the elements having maximum augmented Zagreb index are determined.
augmented Zagreb index
vertex connectivity
matching number
spanning subgraph
2016
04
01
417
425
http://bims.iranjournals.ir/article_768_9ad3a73dc4b8f0abc057b82d03ab8eca.pdf
Bulletin of the Iranian Mathematical Society
BIMS
1017-060X
1017-060X
2016
42
2
The unit sum number of Baer rings
N.
Ashrafi
N.
Pouyan
In this paper we prove that each element of any regular Baer ring is a sum of two units if no factor ring of $R$ is isomorphic to $Z_2$ and we characterize regular Baer rings with unit sum numbers $omega$ and $infty$. Then as an application, we discuss the unit sum number of some classes of group rings.
unit sum number
regular Baer ring
$pi$-regular Baer ring
right perpetual ideal
2016
04
01
427
434
http://bims.iranjournals.ir/article_769_b7f142c271337a1f63d0a503031cec1d.pdf
Bulletin of the Iranian Mathematical Society
BIMS
1017-060X
1017-060X
2016
42
2
Existence of ground states for approximately inner two--parameter $C_0$--groups on $C^*$--algebras
R.
Abazari
A.
Niknam
In this paper, we generalize the definitions of approximately inner $C_0$-groups and their ground states to the two- parameter case and study necessary and sufficient conditions for a state to be ground state. Also we prove that any approximately inner two- parameter $C_0$--group must have at least one ground state. Finally some applications are given.
Two--parameter group
Approximately inner dynamical system
Tensor product
Ground state
2016
04
01
435
446
http://bims.iranjournals.ir/article_770_d466d7717510eb9caf6af9b237000141.pdf
Bulletin of the Iranian Mathematical Society
BIMS
1017-060X
1017-060X
2016
42
2
Remarks on microperiodic multifunctions
J.
Olko
It is well known that a microperiodic function mapping a topological group into reals, which is continuous at some point is constant. We introduce the notion of a microperiodic multifunction, defined on a topological group with values in a metric space, and study regularity conditions implying an analogous result. We deal with Vietoris and Hausdorff continuity concepts.Stability of microperiodic multifunctions is considered, namely we show that an approximately microperiodic multifunction is close to a constant one, provided it is continuous at some point. As a consequence we obtain stability result for an approximately microperiodic single-valued function.
multifunction
microperiodic function
functional inequality
functional inclusion
2016
04
01
447
459
http://bims.iranjournals.ir/article_771_daeaa7f55c0826ade1687602332086b4.pdf
Bulletin of the Iranian Mathematical Society
BIMS
1017-060X
1017-060X
2016
42
2
On cycles in intersection graphs of rings
N.
Hoseini
A.
Erfanian
A.
Azimi
M.
Farrokhi D. G.
Let $R$ be a commutative ring with non-zero identity. We describe all $C_3$- and $C_4$-free intersection graph of non-trivial ideals of $R$ as well as $C_n$-free intersection graph when $R$ is a reduced ring. Also, we shall describe all complete, regular and $n$-claw-free intersection graphs. Finally, we shall prove that almost all Artin rings $R$ have Hamiltonian intersection graphs. We show that such graphs are indeed pancyclic.
Intersection graph
cycle
claw
Hamiltonian
pancyclic
2016
04
01
461
470
http://bims.iranjournals.ir/article_772_474628f752047d413e00702e57860add.pdf
Bulletin of the Iranian Mathematical Society
BIMS
1017-060X
1017-060X
2016
42
2
On linear preservers of sgut-majorization on $textbf{M}_{n,m}$
A.
Ilkhanizadeh Manesh
Let $textbf{M}_{n,m}$ be the set of $n$-by-$m$ matrices with entries in the field of real numbers. A matrix $R$ in $textbf{M}_{n}=textbf{M}_{n,n}$ is a generalized row substochastic matrix (g-row substochastic, for short) if $Releq e$, where $e=(1,1,ldots,1)^t$. For $X,$ $Y in textbf{M}_{n,m}$, $X$ is said to be sgut-majorized by $Y$ (denoted by $X prec_{sgut} Y$) if there exists an $n$-by-$n$ upper triangular g-row substochastic matrix $R$ such that $X=RY$. This paper characterizes all linear preservers and strong linear preservers of $prec_{sgut}$ on $mathbb{R}^{n}$ and $textbf{M}_{n,m}$ respectively.
Linear preserver
Strong linear preserver
g-row substochastic matrices
sgut- majorization
2016
04
01
471
481
http://bims.iranjournals.ir/article_773_f2bdfc65aa79e88076d077bd50940a73.pdf
Bulletin of the Iranian Mathematical Society
BIMS
1017-060X
1017-060X
2016
42
2
Examples of non-quasicommutative semigroups decomposed into unions of groups
N.
Hosseinzadeh
H.
Doostie
Decomposability of an algebraic structure into the union of its sub-structures goes back to G. Scorza's Theorem of 1926 for groups. An analogue of this theorem for rings has been recently studied by A. Lucchini in 2012. On the study of this problem for non-group semigroups, the first attempt is due to Clifford's work of 1961 for the regular semigroups. Since then, N.P. Mukherjee in 1972 studied the decomposition of quasicommutative semigroups where, he proved that: a regular quasicommutative semigroup is decomposable into the union of groups. The converse of this result is a natural question. Obviously, if a semigroup $S$ is decomposable into a union of groups then $S$ is regular so, the aim of this paper is to give examples of non-quasicommutative semigroups which are decomposable into the disjoint unions of groups. Our examples are the semigroups presented by the following presentations: $$pi_1 =langle a,bmid a^{n+1}=a, b^3=b, ba=a^{n-1}brangle,~(ngeq 3),$$ $$pi_2 =langle a,bmid a^{1+p^alpha}=a, b^{1+p^beta}=b, ab=ba^{1+p^{alpha-gamma}}rangle$$where, $p$ is an odd prime, $alpha, beta$ and $gamma$ are integers such that $alpha geq 2gamma$, $beta geq gamma geq 1$ and $alpha +beta > 3$.
quasicommutative semigroups
finitely presented semigroups
decomposition
2016
04
01
483
487
http://bims.iranjournals.ir/article_774_d1f0dd06cdd8ca40e4a11a7315f27db4.pdf
Bulletin of the Iranian Mathematical Society
BIMS
1017-060X
1017-060X
2016
42
2
Pseudo Ricci symmetric real hypersurfaces of a complex projective space
S. k.
Hui
Y.
Matsuyama
Pseudo Ricci symmetric real hypersurfaces of a complex projective space are classified and it is proved that there are no pseudo Ricci symmetric real hypersurfaces of the complex projective space CPn for which the vector field ξ from the almost contact metric structure (φ, ξ, η, g) is a principal curvature vector field.
real hypersurface
complex projective space
pseudo Ricci symmetric
2016
04
01
489
497
http://bims.iranjournals.ir/article_775_19d72442dec53b5d5a278fded703c98e.pdf