Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X42420160801The geometric properties of a degenerate parabolic equation with periodic source term799808833ENG. GuoInstitute of Mathematics, Shanghai Normal University, Shanghai, 200235,
China and
Institute of Mathematics, Jimei University, Xiamen, 361021 China.J. Q. PanInstitute of Mathematics, Jimei University, Xiamen, 361021 China.Journal Article20140722In this paper, we discuss the geometric properties of solution and lower bound estimate of ∆um−1 of the Cauchy problem for a degenerate parabolic equation with periodic source term ut =∆um+ upsint. Our objective is to show that: (1)with continuous variation of time t, the surface ϕ = [u(x,t)]mδq is a complete Riemannian manifold floating in space RN+1and is tangent to the space RN at ∂H0(t); (2)the surface u = u(x,t) is tangent to the hyperplane W(t) at ∂Hu(t).Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X42420160801Constructing vertex decomposable graphs809817834ENE. LashaniDepartment of Mathematics, Science and Research
branch, Islamic Azad University(IAU), Tehran, Iran.A. Soleyman JahanDepartment of Mathematics, University of Kurdistan,
P.O. Box 66177-15175, Sanadaj, Iran.Journal Article20150327Recently, some techniques such as adding whiskers and attaching graphs to vertices of a given graph, have been proposed for constructing a new vertex decomposable graph. In this paper, we present a new method for constructing vertex decomposable graphs. Then we use this construction to generalize the result due to Cook and Nagel.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X42420160801A limited memory adaptive trust-region approach for large-scale unconstrained optimization819837835ENM. AhookhoshFaculty of Mathematics, University of Vienna, Oskar-Morge-nstern-Platz 1, 1090 Vienna, Austria.K. AminiDepartment of
Mathematics, Razi University, Kermanshah, Iran.M. KimiaeiDepartment of
Mathematics, Asadabad Branch, Islamic Azad University, Asadabad, Iran.M. R. PeyghamiK.N. Toosi University of Department of
Mathematics, K. N. Toosi University of Technology, P.O. Box 16315-1618, Tehran, Iran.Journal Article20131115This study concerns with a trust-region-based method for solving unconstrained optimization problems. The approach takes the advantages of the compact limited memory BFGS updating formula together with an appropriate adaptive radius strategy. In our approach, the adaptive technique leads us to decrease the number of subproblems solving, while utilizing the structure of limited memory quasi-Newton formulas helps to handle large-scale problems. Theoretical analysis indicates that the new approach preserves the global convergence to a first-order stationary point under classical assumptions. Moreover, the superlinear and the quadratic convergence rates are also established under suitable conditions. Preliminary numerical experiments show the effectiveness of the proposed approach for solving large-scale unconstrained optimization problems.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X42420160801Totally umbilical radical transversal lightlike hypersurfaces of Kähler-Norden manifolds of constant totally real sectional curvatures839854836ENG. NakovaDepartment of Algebra and Geometry,
Faculty of Mathematics and Informatics,
University of Veliko Tarnovo "St. Cyril and St. Methodius",
2 T. Tarnovski Str., 5003 Veliko Tarnovo, Bulgaria.Journal Article20150120In this paper we study curvature properties of semi - symmetric type of totally umbilical radical transversal lightlike hypersurfaces $(M,g)$ and $(M,widetilde g)$ of a K"ahler-Norden manifold $(overline M,overline J,overline g,overline { widetilde g})$ of constant totally real sectional curvatures $overline nu$ and $overline {widetilde nu}$ ($g$ and $widetilde g$ are the induced metrics on $M$ by the Norden metrics $overline g$ and $overline {widetilde g}$, respectively). We obtain a condition for $overline {widetilde nu}$ (resp. $overline nu$) which is equivalent to each<br />of the following conditions: $(M,g)$ $(resp., (M,widetilde g))$ is locally symmetric, semi-symmetric, Ricci semi-symmetric and almost Einstein. We construct an example of a totally umbilical radical transversal lightlike hypersurface, which is locally symmetric, semi-symmetric, Ricci semi-symmetric and almost Einstein.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X42420160801A note on inequalities for Tsallis relative operator entropy855859837ENL. ZouSchool of Mathematics and Statistics, Chongqing Three Gorges University, Chongqing, 404100, P. R. China.Y. JiangSchool of Mathematics and Statistics, Chongqing Three Gorges University, Chongqing, 404100, P. R. China.Journal Article20140921In this short note, we present some inequalities for relative operator entropy which are generalizations of some results obtained by Zou [Operator inequalities associated with Tsallis relative operator entropy, Math. Inequal. Appl. 18 (2015), no. 2, 401--406]. Meanwhile, we also show some new lower and upper bounds for relative operator entropy and Tsallis relative operator entropy.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X42420160801A module theoretic approach to zero-divisor graph with respect to (first) dual861872838ENE. MomtahanDepartment of Mathematics,
Yasouj University, Yasouj,75914, Iran.M. BaziarDepartment of Mathematics,
Yasouj University, Yasouj,75914, Iran.S. SafaeeyanDepartment of Mathematics,
Yasouj University, Yasouj,75914, Iran.Journal Article20130311Let $M$ be an $R$-module and $0 neq fin M^*={rm Hom}(M,R)$. We associate an undirected graph $gf$ to $M$ in which non-zero elements $x$ and $y$ of $M$ are adjacent provided that $xf(y)=0$ or $yf(x)=0$. We observe that over a commutative ring $R$, $gf$ is connected and diam$(gf)leq 3$. Moreover, if $Gamma (M)$ contains a cycle, then $mbox{gr}(gf)leq 4$. Furthermore if $|gf|geq 1$, then $gf$ is finite if and only if $M$ is finite. Also if $gf=emptyset$, then $f$ is monomorphism (the converse is true if $R$ is a domain). If $M$ is either a free module with ${rm rank}(M)geq 2$ or a non-finitely generated projective module there exists $fin M^*$ with ${rm rad}(gf)=1$ and ${rm diam}(gf)leq 2$. We prove that for a domain $R$ the chromatic number and the clique number of $gf$ are equal.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X42420160801Center--like subsets in rings with derivations or epimorphisms873878839ENH. E. BellDepartment of Mathematics, Brock University, St. Catharines, Ontario L2S 3A1, Canada.M. N. DaifDepartment of Mathematics, Al-Azhar University, Nasr City(11884), Cairo, Egypt.Journal Article20140601We introduce center-like subsets Z*(R,f), Z**(R,f) and Z1(R,f), where R is a ring and f is a map from R to R. For f a derivation or a non-identity epimorphism and R a suitably-chosen prime or semiprime ring, we prove that these sets coincide with the center of R.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X42420160801The Ramsey numbers of large trees versus wheels879880840END. ZhuSchool of Economics and Management, Southeast University, Nanjing 210093, P.R. China.L. ZhangSchool of Management and Engineering,
Nanjing University, Nanjing 210093, P.R. China.D. LiSchool of Management and Engineering,
Nanjing University, Nanjing 210093, P.R. China.Journal Article20141217For two given graphs $G_1$ and $G_2$, the Ramsey number $R(G_1,G_2)$ is the smallest integer n such that for any graph G of order n, either $G$ contains G1 or the complement of G contains $G_2$. Let Tn denote a tree of order n and Wm a wheel of order m+1. To the best of our knowledge, only $R(T_n,W_m)$ with small wheels are known. In this paper, we show that $R(T_n,W_m)=3n-2$ for odd m with $n>756m^{10}$.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X42420160801Coefficient estimates for a subclass of analytic and bi-univalent functions881889841ENA. ZirehDepartment of Mathematics, Shahrood University Of Technology, P.O. Box 316-36155, Shahrood, Iran.E. Analouei AudeganiDepartment of Mathematics, Mobarakeh Branch, Islamic Azad University, Mobarakeh, P.O. Box 84819-97817, Isfahan, Iran.Journal Article20150417In this paper, we introduce and investigate a subclass of analytic and bi-univalent functions in the open unit disk. Upper bounds for the second and third coefficients of functions in this subclass are founded. Our results, which are presented in this paper, generalize and improve those in related works of several earlier authors.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X42420160801Relative (co)homology of $F$-Gorenstein modules891902842ENC. ZhangDepartment of Mathematics, Northwest
School of Mathematics Sciences, Chongqing Normal University, Chongqing 400000, China.Z. LiDepartment of Mathematics, Northwest
Normal University, Lanzhou 730070, China.Journal Article20150305We investigate the relative cohomology and relative homology theories of $F$-Gorenstein modules, consider the relations between classical and $F$-Gorenstein (co)homology theories.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X42420160801On Black-Scholes equation; method of Heir-equations, nonlinear self-adjointness and conservation laws903921843ENM. S. HashemiDepartment of Mathematics, Basic Science Faculty,
University of Bonab, P.O. Box 55517-61167, Bonab, Iran.Journal Article20141201In this paper, Heir-equations method is applied to investigate nonclassical symmetries and new solutions of the Black-Scholes equation. Nonlinear self-adjointness is proved and infinite number of conservation laws are computed by a new conservation laws theorem.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X42420160801On the order of a module923931844ENS. HadjirezaeiDepartment of
Mathematics, Vali-e-Asr University of Rafsanjan, P.O. Box 7718897111, Rafsanjan, Iran.S. KarimzadehDepartment of
Mathematics, Vali-e-Asr University of Rafsanjan, P.O. Box 7718897111, Rafsanjan, Iran.Journal Article20140514Abstract. Let $(R,P)$ be a Noetherian unique factorization domain (UFD) and M be a finitely generated R-module. Let I(M)<br />be the first nonzero Fitting ideal of M and the order of M, denoted $ord_R(M)$, be the largest integer n such that $I(M) ⊆ P^n$. In this paper, we show that if M is a module of order one, then either M is isomorphic with direct sum of a free module and a cyclic module or M is isomorphic with a special module represented in the text. We also assert some properties of M while $ord_R(M) = 2.$Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X42420160801Sufficient conditions for univalence and starlikeness933939845ENM. N. NunokawaUniversity of Gunma, Hoshikuki-cho 798-8, Chuou-Ward, Chiba 260-0808, Japan.J. SokolDepartment of Mathematics, Rzeszow University of Technology, Al. Powstancow Warszawy 12, 35-959 Rzeszow, Poland.N. E. ChoDepartment of Applied Mathematics, College of Natural Sciences,
Pukyong National University, Busan 608-737, Korea.Journal Article20141031It is known that the condition $mathfrak {Re} left{zf'(z)/f(z)right}>0$, $|z|<1$ is a sufficient condition for $f$, $f(0)=f'(0)-1$ to be starlike in $|z|<1$. The purpose of this <br />work is to present some new sufficient conditions for univalence and starlikeness.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X42420160801On two problems concerning the Zariski topology of modules941948846ENH. Ansari-ToroghyDepartment of pure Mathematics,
Faculty of mathematical Sciences, University of Guilan,
P.O. Box 41335-19141, Rasht, Iran.R. Ovlyaee-SarmazdehDepartment of pure Mathematics,
Faculty of mathematical Sciences, University of Guilan,
P.O. Box 41335-19141, Rasht, Iran.Seyed Sajad PourmortazaviDepartment of pure Mathematics,
Faculty of mathematical Sciences, University of Guilan,
P. O. Box 41335-19141 Rasht, Iran.Journal Article20141218Let $R$ be an associative ring and let $M$ be a left $R$-module. Let $Spec_{R}(M)$ be the collection of all prime submodules of $M$ (equipped with classical Zariski topology). There is a conjecture which says that every irreducible closed subset of $Spec_{R}(M)$ has a generic point. In this article we give an affirmative answer to this conjecture and show that if $M$ has a Noetherian spectrum, then $Spec_{R}(M)$ is a spectral space.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X42420160801Complexes of $C$-projective modules949958847ENE. AmanzadehFaculty of Mathematical Sciences and Computer,
Kharazmi University, Tehran, Iran.M. T. DibaeiFaculty of Mathematical Sciences and Computer,
Kharazmi University, Tehran, Iran
and
School of Mathematics,
Institute for Research in Fundamental Sciences (IPM), P.O. Box
19395-5746, Tehran, Iran.Journal Article20150313Inspired by a recent work of Buchweitz and Flenner, we show that, for a semidualizing bimodule $C$, $C$--perfect complexes have the ability to detect when a ring is strongly regular. It is shown that there exists a class of modules which admit minimal resolutions of $C$--projective modules.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X42420160801Hyperstability of some functional equation on restricted domain: direct and fixed point methods959974848ENA. BahyryczAGH University of Science and Technology, Faculty of Applied Mathematics, Mickiewicza 30, 30-059 Krakow, Poland.Journal Article20140329The study of stability problems of functional equations was motivated by a question of S.M. Ulam asked in 1940. The first result giving answer to this question is due to D.H. Hyers. Subsequently, his result was extended and generalized in several ways.<br />We prove some hyperstability results for the equation <br /><br />g(ax+by)+g(cx+dy)=Ag(x)+Bg(y)<br /><br />on restricted domain. <br />Namely, we show, under some weak natural assumptions, that functions satisfying the above equation approximately (in some sense) must be actually solutions to it.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X42420160801On statistical type convergence in uniform spaces975986849ENB. T. BilalovDepartment of
Non-harmonic analysis, Institute of Mathematics and Mechanics of NAS of Azerbaijan, 9, B.Vahabzade Str., AZ 1141, Baku, Azerbaijan.T. Y. NazarovaDepartment of
Non-harmonic analysis, Institute of Mathematics and Mechanics of NAS of Azerbaijan, 9, B. Vahabzade Str., AZ 1141, Baku, Azerbaijan.Journal Article20141112The concept of ${mathscr{F}}_{st}$-fundamentality is introduced in uniform spaces, generated by some filter ${mathscr{F}}$. Its equivalence to the concept of ${mathscr{F}}$-convergence in uniform spaces is proved. This convergence generalizes many kinds of convergence, including the well-known statistical convergence.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X42420160801Polynomial evaluation groupoids and their groups987997850ENH. S. KimDepartment of Mathematics, Research Institute for Natural Sciences, Hanyang University, Seoul 04763, Korea.P. J. AllenDepartment of Mathematics, University of Alabama, Tuscaloosa, AL 35487-0350, USA.J. NeggersDepartment of Mathematics, University of Alabama, Tuscaloosa, AL 35487-0350, USA.Journal Article20130918In this paper, we show how certain metabelian groups can be found within polynomial evaluation groupoids. We show that every finite abelian group can be obtained as a polynomial evaluation groupoid.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X42420160801Strongly noncosingular modules9991013851ENY. Alagözİzmir Institute of Technology, Department
of Mathematics, 35430, İzmir, Turkey.Y. DurğunBitlis Eren University, Department of Mathematics, 13000, Bitlis, Turkey.Journal Article20150320An R-module M is called strongly noncosingular if it has no nonzero Rad-small (cosingular) homomorphic image in the sense of Harada. It is proven that (1) an R-module M is strongly noncosingular if and only if M is coatomic and noncosingular; (2) a right perfect ring R is Artinian hereditary serial if and only if the class of injective modules coincides with the class of (strongly) noncosingular R-modules; (3)absolutely coneat modules are strongly noncosingular if and only if R is a right Max-ring and injective modules are strongly noncosingular; (4) a commutative ring R is semisimple if and only if the class of injective modules coincides with the class of strongly noncosingular R-modules.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X42420160801On certain semigroups of transformations that preserve double direction equivalence10151024852ENL. DengSchool of Mathematical Science, Guizhou Normal University, Guiyang 550001, China.Journal Article20140225Let TX be the full transformation semigroups on the set X. For an equivalence E on X, let TE*(X) = {α ∈ TX : ∀(x, y) ∈ E ⇔ (xα, yα) ∈ E} It is known that TE*(X) is a subsemigroup of TX. In this paper, we discuss the Green's *-relations, certain *-ideal and certain Rees quotient semigroup for TE*(X).