eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2016-08-01
42
4
799
808
833
The geometric properties of a degenerate parabolic equation with periodic source term
G. Guo
gwg0518@sina.com
1
J. Q. Pan
jqpan@jmu.edu.cn
2
Institute of Mathematics, Shanghai Normal University, Shanghai, 200235, China and Institute of Mathematics, Jimei University, Xiamen, 361021 China.
Institute of Mathematics, Jimei University, Xiamen, 361021 China.
In 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).
http://bims.iranjournals.ir/article_833_3a19f3cfd152e71e5060b6ee86fda34e.pdf
Degenerate parabolic equation
~Riemannian manifold
~Periodic source term
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2016-08-01
42
4
809
817
834
Constructing vertex decomposable graphs
E. Lashani
lashani@iau-doroud.ac.ir
1
A. Soleyman Jahan
solymanjahan@gmail.com
2
Department of Mathematics, Science and Research branch, Islamic Azad University(IAU), Tehran, Iran.
Department of Mathematics, University of Kurdistan, P.O. Box 66177-15175, Sanadaj, Iran.
Recently, 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.
http://bims.iranjournals.ir/article_834_0e4d232717c9878e672368f90111370c.pdf
Finite graph
well-covered graph
independence complex
edge ideal
vertex decomposable graph
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2016-08-01
42
4
819
837
835
A limited memory adaptive trust-region approach for large-scale unconstrained optimization
M. Ahookhosh
masoud.ahookhosh@univie.ac.at
1
K. Amini
kamini@razi.ac.ir
2
M. Kimiaei
morteza.kimiaei@gmail.com
3
M. R. Peyghami
peyghami@kntu.ac.ir
4
Faculty of Mathematics, University of Vienna, Oskar-Morge-nstern-Platz 1, 1090 Vienna, Austria.
Department of Mathematics, Razi University, Kermanshah, Iran.
Department of Mathematics, Asadabad Branch, Islamic Azad University, Asadabad, Iran.
K.N. Toosi University of Department of Mathematics, K. N. Toosi University of Technology, P.O. Box 16315-1618, Tehran, Iran.
This 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.
http://bims.iranjournals.ir/article_835_05d125fc7788d3d72bb2e454b7c9ae39.pdf
Unconstrained optimization
trust-region framework
compact quasi-Newton representation
limited memory technique
adaptive strategy
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2016-08-01
42
4
839
854
836
Totally umbilical radical transversal lightlike hypersurfaces of Kähler-Norden manifolds of constant totally real sectional curvatures
G. Nakova
gnakova@gmail.com
1
Department 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.
In 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 eachof 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.
http://bims.iranjournals.ir/article_836_492ff15de80235a366b9a8fbf01ab827.pdf
Kähler-Norden manifold
totally real sectional curvature
radical transversal lightlike hypersurface
totally umbilical lightlike hypersurface
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2016-08-01
42
4
855
859
837
A note on inequalities for Tsallis relative operator entropy
L. Zou
limin-zou@163.com
1
Y. Jiang
yyy_j123456@163.com
2
School of Mathematics and Statistics, Chongqing Three Gorges University, Chongqing, 404100, P. R. China.
School of Mathematics and Statistics, Chongqing Three Gorges University, Chongqing, 404100, P. R. China.
In 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.
http://bims.iranjournals.ir/article_837_df4210a6e2cdcbb39f8414109f5622bf.pdf
Relative operator entropy
Tsallis relative operator entropy
operator inequalities
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2016-08-01
42
4
861
872
838
A module theoretic approach to zero-divisor graph with respect to (first) dual
E. Momtahan
momtahan_e@hotmail.com
1
M. Baziar
mbaziar@yu.ac.ir
2
S. Safaeeyan
safaeeyan@yu.ac.ir
3
Department of Mathematics, Yasouj University, Yasouj,75914, Iran.
Department of Mathematics, Yasouj University, Yasouj,75914, Iran.
Department of Mathematics, Yasouj University, Yasouj,75914, Iran.
Let $M$ 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.
http://bims.iranjournals.ir/article_838_871ce9b57fe08bf9203f8e500d1cd9ef.pdf
Zero-divisor graph
Clique number
Chromatic number
Module
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2016-08-01
42
4
873
878
839
Center--like subsets in rings with derivations or epimorphisms
H. E. Bell
hbell@brocku.ca
1
M. N. Daif
nagydaif@yahoo.com
2
Department of Mathematics, Brock University, St. Catharines, Ontario L2S 3A1, Canada.
Department of Mathematics, Al-Azhar University, Nasr City(11884), Cairo, Egypt.
We 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.
http://bims.iranjournals.ir/article_839_3782dc4a21cf87ae977f69355ec9216b.pdf
Prime ring
semiprime ring
derivation
epimorphism
center-like subset
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2016-08-01
42
4
879
880
840
The Ramsey numbers of large trees versus wheels
D. Zhu
dongmeizhu2013@126.com
1
L. Zhang
zhanglm@nju.edu.cn
2
D. Li
leedongxin@163.com
3
School of Economics and Management, Southeast University, Nanjing 210093, P.R. China.
School of Management and Engineering, Nanjing University, Nanjing 210093, P.R. China.
School of Management and Engineering, Nanjing University, Nanjing 210093, P.R. China.
For 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 $n>756m^{10}$.
http://bims.iranjournals.ir/article_840_30a26766892a2873e795eb8000b43f23.pdf
Ramsey number
tree
wheel
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2016-08-01
42
4
881
889
841
Coefficient estimates for a subclass of analytic and bi-univalent functions
A. Zireh
azireh@shahroodut.ac.ir
1
E. Analouei Audegani
e_analoei@ymail.com
2
Department of Mathematics, Shahrood University Of Technology, P.O. Box 316-36155, Shahrood, Iran.
Department of Mathematics, Mobarakeh Branch, Islamic Azad University, Mobarakeh, P.O. Box 84819-97817, Isfahan, Iran.
In 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.
http://bims.iranjournals.ir/article_841_1f6a850b3488d0952e36fdcc558e5e53.pdf
Analytic functions
Bi-Univalent Functions
Coefficient estimates
starlike functions
Koebe one-quarter theorem
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2016-08-01
42
4
891
902
842
Relative (co)homology of $F$-Gorenstein modules
C. Zhang
zhangcx@nwnu.edu.cn
1
Z. Li
792252531@qq.com
2
Department of Mathematics, Northwest School of Mathematics Sciences, Chongqing Normal University, Chongqing 400000, China.
Department of Mathematics, Northwest Normal University, Lanzhou 730070, China.
We investigate the relative cohomology and relative homology theories of $F$-Gorenstein modules, consider the relations between classical and $F$-Gorenstein (co)homology theories.
http://bims.iranjournals.ir/article_842_da59dead14e2b930104ab3b6393aba8e.pdf
$F$-Gorenstein projective module
$F$-Gorenstein injective module
relative cohomology
relative homology
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2016-08-01
42
4
903
921
843
On Black-Scholes equation; method of Heir-equations, nonlinear self-adjointness and conservation laws
M. S. Hashemi
hashemi_math396@yahoo.com
1
Department of Mathematics, Basic Science Faculty, University of Bonab, P.O. Box 55517-61167, Bonab, Iran.
In 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.
http://bims.iranjournals.ir/article_843_9440a70bdefec0826847378e3637ce93.pdf
Black-Scholes equation
Heir-equation
nonclassical symmetry
Nonlinear self-adjointness
Conservation law
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2016-08-01
42
4
923
931
844
On the order of a module
S. Hadjirezaei
s.hajirezaei@vru.ac.ir
1
S. Karimzadeh
karimzadeh@vru.ac.ir
2
Department of Mathematics, Vali-e-Asr University of Rafsanjan, P.O. Box 7718897111, Rafsanjan, Iran.
Department of Mathematics, Vali-e-Asr University of Rafsanjan, P.O. Box 7718897111, Rafsanjan, Iran.
Abstract. Let $(R,P)$ be a Noetherian unique factorization domain (UFD) and M be a finitely generated R-module. Let I(M)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 $ord_R(M) = 2.$
http://bims.iranjournals.ir/article_844_8c5b86ca03124119d8397dde84a956c0.pdf
Fitting ideals
minimal free presentation
order of a module
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2016-08-01
42
4
933
939
845
Sufficient conditions for univalence and starlikeness
M. N. Nunokawa
mamoru_nuno@doctor.nifty.jp
1
J. Sokol
jsokol@prz.edu.pl
2
N. E. Cho
necho@pknu.ac.kr
3
University of Gunma, Hoshikuki-cho 798-8, Chuou-Ward, Chiba 260-0808, Japan.
Department of Mathematics, Rzeszow University of Technology, Al. Powstancow Warszawy 12, 35-959 Rzeszow, Poland.
Department of Applied Mathematics, College of Natural Sciences, Pukyong National University, Busan 608-737, Korea.
It 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 work is to present some new sufficient conditions for univalence and starlikeness.
http://bims.iranjournals.ir/article_845_7d14220cd3142ab48ef16685f5904494.pdf
Analytic functions
convex functions
starlike functions
univalent functions
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2016-08-01
42
4
941
948
846
On two problems concerning the Zariski topology of modules
H. Ansari-Toroghy
ansari@guilan.ac.ir
1
R. Ovlyaee-Sarmazdeh
ovlyaee@guilan.ac.ir
2
Seyed Sajad Pourmortazavi
mortazavi@phd.guilan.ac.ir
3
Department of pure Mathematics, Faculty of mathematical Sciences, University of Guilan, P.O. Box 41335-19141, Rasht, Iran.
Department of pure Mathematics, Faculty of mathematical Sciences, University of Guilan, P.O. Box 41335-19141, Rasht, Iran.
Department of pure Mathematics, Faculty of mathematical Sciences, University of Guilan, P. O. Box 41335-19141 Rasht, Iran.
Let $R$ 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.
http://bims.iranjournals.ir/article_846_1769c60f5d1f171166300f224d7e2683.pdf
Prime spectrum
classical Zariski topology
spectral space
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2016-08-01
42
4
949
958
847
Complexes of $C$-projective modules
E. Amanzadeh
en.amanzadeh@gmail.com
1
M. T. Dibaei
dibaeimt@ipm.ir
2
Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, Iran.
Faculty 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.
Inspired 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.
http://bims.iranjournals.ir/article_847_8072eb9287f684dfb94b1ec60af8979a.pdf
Semidualizing
$C$--projective
$mathcal P_C$--resolution
$C$--perfect complex
strongly regular
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2016-08-01
42
4
959
974
848
Hyperstability of some functional equation on restricted domain: direct and fixed point methods
A. Bahyrycz
bahyrycza@gmail.com
1
AGH University of Science and Technology, Faculty of Applied Mathematics, Mickiewicza 30, 30-059 Krakow, Poland.
The 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.We prove some hyperstability results for the equation g(ax+by)+g(cx+dy)=Ag(x)+Bg(y)on restricted domain. Namely, we show, under some weak natural assumptions, that functions satisfying the above equation approximately (in some sense) must be actually solutions to it.
http://bims.iranjournals.ir/article_848_f70737eade2a159a95d98ee8c93435c2.pdf
Hyperstability
linear equation
quadratic equation
p-Wright affine function
fixed point theorem
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2016-08-01
42
4
975
986
849
On statistical type convergence in uniform spaces
B. T. Bilalov
b_bilalov@mail.ru
1
T. Y. Nazarova
tubunazarova@mail.ru
2
Department of Non-harmonic analysis, Institute of Mathematics and Mechanics of NAS of Azerbaijan, 9, B.Vahabzade Str., AZ 1141, Baku, Azerbaijan.
Department of Non-harmonic analysis, Institute of Mathematics and Mechanics of NAS of Azerbaijan, 9, B. Vahabzade Str., AZ 1141, Baku, Azerbaijan.
The 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.
http://bims.iranjournals.ir/article_849_7288695c066460ba0ef6f0e26ae1a84a.pdf
${\mathscr{F}}$-convergence
${\mathscr{F}}_{st}$- fundamentality
statistical convergence
a uniform space
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2016-08-01
42
4
987
997
850
Polynomial evaluation groupoids and their groups
H. S. Kim
heekim@hanyang.ac.kr
1
P. J. Allen
pallen@as.ua.edu
2
J. Neggers
jneggers@as.ua.edu
3
Department of Mathematics, Research Institute for Natural Sciences, Hanyang University, Seoul 04763, Korea.
Department of Mathematics, University of Alabama, Tuscaloosa, AL 35487-0350, USA.
Department of Mathematics, University of Alabama, Tuscaloosa, AL 35487-0350, USA.
In 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.
http://bims.iranjournals.ir/article_850_1eb6e61f83e959712c8e2809e47d56a9.pdf
polynomial evaluation groupoids
group evaluation polynomial
group
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2016-08-01
42
4
999
1013
851
Strongly noncosingular modules
Y. Alagöz
yusufalagoz@iyte.edu.tr
1
Y. Durğun
yilmaz.durgun@math.uzh.ch
2
İzmir Institute of Technology, Department of Mathematics, 35430, İzmir, Turkey.
Bitlis Eren University, Department of Mathematics, 13000, Bitlis, Turkey.
An 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.
http://bims.iranjournals.ir/article_851_d18ecbcc8e8e4b588b255c42f726eb89.pdf
coclosed submodules
(non) cosingular modules
coatomic modules
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2016-08-01
42
4
1015
1024
852
On certain semigroups of transformations that preserve double direction equivalence
L. Deng
denglunzhi@163.com
1
School of Mathematical Science, Guizhou Normal University, Guiyang 550001, China.
Let 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).
http://bims.iranjournals.ir/article_852_a64e6817281df6609cd01af3d32c5d45.pdf
Transformation semigroups
Equivalence
Green's *-relations
*-Ideal
Rees quotient semigroup