Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X42220160401Radical of $\cdot$-ideals in $PMV$-algebras233246756ENF.ForouzeshFaculty of Mathematics and computing, Higher Education complex of Bam, Bam, Iran.Journal Article20140822In 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 $A$.http://bims.iranjournals.ir/article_756_d1afd5d234b5acc222bd74060762df14.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X42220160401Existence of solutions of boundary value problems for Caputo fractional differential equations on time scales247262757ENR. A.YanSchool of Mathematical Sciences, University of Jinan, Jinan, Shandong 250022, P R ChinaS. R.SunSchool of Mathematical Sciences, University of Jinan, Jinan,
Shandong 250022, P R ChinaZ. L.HanSchool of Mathematical Sciences, University of Jinan, Jinan, Shandong 250022, P R ChinaJournal Article20140226In this paper, we study the boundary-value problem of fractional order dynamic equations on time scales,<br /> $$<br /> ^c{\Delta}^{\alpha}u(t)=f(t,u(t)),\;\;t\in<br /> [0,1]_{\mathbb{T}^{\kappa^{2}}}:=J,\;\;1<\alpha<2,<br /> $$ $$ u(0)+u^{\Delta}(0)=0,\;\;u(1)+u^{\Delta}(1)=0, $$<br /> where $\mathbb{T}$ is a general time scale with $0,1\in \mathbb{T}$, $^c{\Delta}^{\alpha}$ is the Caputo $\Delta$-fractional derivative. We investigate the existence and uniqueness of solution for the problem by Banach's fixed point theorem and Schaefer's fixed point theorem. We also discuss the existence of positive solutions of the problem by using the Krasnoselskii theorem.http://bims.iranjournals.ir/article_757_6c272666edd826df2c68e8aa2ebafd12.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X42220160401Locally GCD domains and the ring $D+XD_S[X]$263284758ENG. W.ChangDepartment of Mathematics Education, Incheon National University,
Incheon 406-772, Republic of Korea.T.DumitrescuFacultatea de Matematica si Informatica, University of Bucharest, 14 Academiei Str., Bucharest, RO 010014, RomaniaM.ZafruhhahDepartment of Mathematics, Idaho State University, Poca-tello, ID 83209, USAJournal Article20140709An 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 $aD\cap bD$ is locally principal for all $0\neq a,b\in D$, 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.http://bims.iranjournals.ir/article_758_519fca69eb4a638b55fe87c7eafe3be6.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X42220160401Sufficiency and duality for a nonsmooth vector optimization problem with generalized $\alpha$-$d_{I}$-type-I univexity over cones285295759ENH.JiaoSchool of Mathematics and Statistics, Yangtze Normal University, Chongqing 408100, P. R. China.Journal Article20131005In 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.http://bims.iranjournals.ir/article_759_d37d71e77deecebe9efed9e81fb10b79.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X42220160401A new approach for solving the first-order linear matrix differential equations297314760ENA.GolbabaiSchool of Mathematics, Iran
University of Science and Technology, P.O. Box 16846-13114,
Tehran, Iran.S.P. A. BeikSchool of Mathematics, Iran
University of Science and Technology, P.O. Box 16846-13114,
Tehran, IranD.K. SalkuyehFaculty of Mathematical Sciences, University of Guilan, Rasht, IranJournal Article20130804Abstract. 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.http://bims.iranjournals.ir/article_760_2cfb83ffe97a3eb87e63d4a2121a528b.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X42220160401An analytic solution for a non-local initial-boundary value problem including a partial differential equation with variable coefficients315326761ENM.JahanshahiDepartment of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran.M.DarabadiDepartment of Mathematics, Azarbaijan Shahid Madani University, Tabriz, IranJournal Article20140909This 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.http://bims.iranjournals.ir/article_761_706ebf130c6496e7db6e47caf0549442.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X42220160401Trivially related lax pairs of the Sawada-Kotera equation327330762END.TalatiSama Technical and Vocational Training College, Islamic Azad university, Urmia Branch, Urmia, Iran.Journal Article20140702We 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.http://bims.iranjournals.ir/article_762_f60c4b68590b1689ee7d3635b080f175.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X42220160401On Silverman's conjecture for a family of elliptic curves331340763ENK.NabardiDepartment of
Mathematics, Azarbaijan Shahid Madani University,
Tabriz 53751-71379, Iran.F.IzadiDepartment of
Mathematics, Azarbaijan Shahid Madani University, P. O. Box 53751-71379,
Tabriz , Iran.Journal Article20130620Let $E$ 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 $E^{(D)}$.<br /> 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<br /> 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 $p\equiv5, 7\pmod{8}$ or $n$ is even and $p\equiv1\pmod{4}$.<br /> In the end, we also compute the ranks of some specific values of $n$ and $p$ explicitly.http://bims.iranjournals.ir/article_763_4e8380b4a993b2881f9ee0d5d1e2181c.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X42220160401Every class of $S$-acts having a flatness property is closed under directed colimits341351764ENH.QiaoCollege of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, P. R. China.L.WangCollege of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, P. R. China.X.MaCollege of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, P. R. China.Journal Article20140123Let $S$ 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.http://bims.iranjournals.ir/article_764_8c92870856f42224b242cd3dc1feb5b5.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X42220160401Partial proof of Graham Higman's conjecture related to coset diagrams353369765ENQ.MushtaqVice Chancellor, The Islamia University of Bahawalpur, Pakistan.A.RazaqDepartment of Mathematics, Govt. Post Graduate College Jauharabad, Pakistan.Journal Article20131201Graham 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 by<br />F_v [(〖xy〗^(-1) )^(s_1 ) (xy)^(s_2 ) (〖xy〗^(-1) )^(s_3 ),(xy)^(q_1 ) (〖xy〗^(-1) )^(q_2 ) (xy)^(q_3 ) ]<br />where s₁,s₂,s₃,q₁,q₂,q₃∈ℤ⁺, and prove Higman's conjecture for the polynomials obtained from the fragments in Ϝ.http://bims.iranjournals.ir/article_765_b144cad7da2c8ab7c7be161d9bb12fe5.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X42220160401Toroidalization of locally toroidal morphisms of 3-folds371405766ENR.AhmadianSchool of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5746, Tehran, Iran.Journal Article20141210A toroidalization of a dominant morphism $\varphi: X\to Y$ 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.http://bims.iranjournals.ir/article_766_30a65aebf30dd4f836a00da605df90a7.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X42220160401Finite groups with $X$-quasipermutable subgroups of prime power order407416767ENX.YiDepartment of Mathematics, Zhejiang Sci-Tech University, 310018, Hangzhou, P. R. China.X.YangDepartment of Mathematics, Zhejiang Sci-Tech University, 310018, Hangzhou, P. R. China.Journal Article20141201Let $H$, $L$ and $X$ be subgroups of a finite group $G$. Then $H$ is said to be $X$-permutable with $L$ if for some<br />$xin X$ 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.http://bims.iranjournals.ir/article_767_7c8f57226de334e589c125523eea2281.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X42220160401The augmented Zagreb index, vertex connectivity and matching number of graphs417425768ENA.AliDepartment of Mathematics, National University of Computer and
Emerging Sciences, B-Block, Faisal Town, Lahore, Pakistan.A.BhattiDepartment of Mathematics, National University of Computer and
Emerging Sciences, B-Block, Faisal Town, Lahore, Pakistan.Z.RazaDepartment of Mathematics, National University of Computer
and Emerging Sciences, B-Block, Faisal Town, Lahore, Pakistan.and Department of Mathematics, College of Sciences, University
of Sharjah, Sharjah, United Arab Emirates.Journal Article20140322Let $\Gamma_{n,\kappa}$ be the class of all graphs with $n\geq3$ vertices and $\kappa\geq2$ vertex connectivity. Denote by $\Upsilon_{n,\beta}$ the family of all connected graphs with $n\geq4$ vertices and matching number $\beta$ where $2\leq\beta\leq\lfloor\frac{n}{2}\rfloor$. In the classes of graphs $\Gamma_{n,\kappa}$ and $\Upsilon_{n,\beta}$, the elements having maximum augmented Zagreb index are determined.http://bims.iranjournals.ir/article_768_9ad3a73dc4b8f0abc057b82d03ab8eca.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X42220160401The unit sum number of Baer rings427434769ENN.AshrafiSemnan UniversityFaculty of Mathematics, Statistics and
Computer Science,
Semnan University, Semnan, Iran.N.PouyanFaculty of Mathematics, Statistics and Computer Science,
Semnan
University, Semnan, Iran.Journal Article20131104In 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 <br />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.http://bims.iranjournals.ir/article_769_b7f142c271337a1f63d0a503031cec1d.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X42220160401Existence of ground states for approximately inner two--parameter $C_0$--groups on $C^*$--algebras435446770ENR.AbazariDepartment of
Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran.A.NiknamDepartment of
Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran.Journal Article20131213In 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.http://bims.iranjournals.ir/article_770_d466d7717510eb9caf6af9b237000141.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X42220160401Remarks on microperiodic multifunctions447459771ENJ.OlkoAGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Kraków, Poland.Journal Article20140220It 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.<br /><br />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.http://bims.iranjournals.ir/article_771_daeaa7f55c0826ade1687602332086b4.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X42220160401On cycles in intersection graphs of rings461470772ENN.HoseiniDepartment of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran.A.ErfanianDepartment of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran.A.AzimiDepartment of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran.M.Farrokhi D. G.Department of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran.Journal Article20131105Let $R$ 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.http://bims.iranjournals.ir/article_772_474628f752047d413e00702e57860add.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X42220160401On linear preservers of sgut-majorization on $\textbf{M}_{n,m}$471481773ENA.Ilkhanizadeh ManeshDepartment of
Mathematics, Vali-e-Asr
University of Rafsanjan, P.O. Box 7713936417, Rafsanjan, Iran.Journal Article20140414Let $\textbf{M}_{n,m}$ 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 $Re\leq e$, 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.http://bims.iranjournals.ir/article_773_f2bdfc65aa79e88076d077bd50940a73.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X42220160401Examples of non-quasicommutative semigroups decomposed into unions of groups483487774ENN.HosseinzadehDepartment of
Mathematics, Tehran Science and Research Branch, Islamic Azad
University, P.O. Box 14515/1775, Tehran, Iran.H.DoostieDepartment of
Mathematics, Tehran Science and Research Branch, Islamic Azad
University, P.O. Box 14515/1775, Tehran, Iran.Journal Article20140605Decomposability 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 <br />groups. Our examples are the semigroups presented by the following presentations: $$\pi_1 =\langle a,b\mid a^{n+1}=a, b^3=b, ba=a^{n-1}b\rangle,~(n\geq 3),$$ <br />$$\pi_2 =\langle a,b\mid a^{1+p^\alpha}=a, b^{1+p^\beta}=b, ab=ba^{1+p^{\alpha-\gamma}}\rangle$$where, $p$ is an odd prime, $\alpha, \beta$ and $\gamma$ are integers such that $\alpha \geq 2\gamma$, $\beta \geq \gamma \geq 1$ and $\alpha +\beta > 3$.http://bims.iranjournals.ir/article_774_d1f0dd06cdd8ca40e4a11a7315f27db4.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X42220160401Pseudo Ricci symmetric real hypersurfaces of a complex projective space489497775ENS. K.HuiDepartment of Mathematics, Sidho Kanho Birsha University, Purulia-723104, West Bengal, India.\newline
Department of Mathematics, Bankura University, Bankura-722155, West Bengal, India.Y.MatsuyamaDepartment of Mathematics, Chuo University, Faculty of Science and Engineering, 1-13-27 Kasuga, Bunkyo-ku, Tokyo 112-8551, Japan.Journal Article20140508Pseudo 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.http://bims.iranjournals.ir/article_775_19d72442dec53b5d5a278fded703c98e.pdf