ORIGINAL_ARTICLE
The geometric properties of a degenerate parabolic equation with periodic source term
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
2016-08-01
799
808
Degenerate parabolic equation
~Riemannian manifold
~Periodic source term
G.
Guo
gwg0518@sina.com
1
Institute of Mathematics, Shanghai Normal University, Shanghai, 200235, China and Institute of Mathematics, Jimei University, Xiamen, 361021 China.
AUTHOR
J. Q.
Pan
jqpan@jmu.edu.cn
2
Institute of Mathematics, Jimei University, Xiamen, 361021 China.
LEAD_AUTHOR
A. Bjorner and M. Wachs, Shellable nonpure complexes and posets, I, Trans. Amer. Math. Soc. 348 (1996), no. 4, 1299--1327.
1
D. Cook II, U. Nagel, Cohen-Macaulay graph and face vector of ag complexes, SIAM J. Discrete Math. 26 (2012), no. 1, 89--101.
2
A. Dochtermann and A. Engstom, Algebraic properties of edge ideals via combinatorial topology, Electron. J. Combin. 16 (2009), no. 2, Special volume in honor of Anders Bjorner, 24 pages.
3
D. Hang, N. C^ong Minh and T. Nam Trung, On the Cohen-Macaulay graphs and girth, preprint, (2013), arXiv:1204.5561v2, 16 pages.
4
T. Hibi, A. Higashitani, K. Kimura and A. B. O'Keefe, Algebraic study on Cameron Walker graphs, J. Algebra 422 (2015) 257--269.
5
A. Mousivand, S. A. S. Fakhari and S. Yassemi, A new construction for Cohen-Macaulay graphs, Comm. Algebra 43 (2015), no. 12, 5104--5112.
6
B. Randerath and L. Volkmann, A characterization of well covered block-cactus graphs, Australas. J. Combin. 9 (1994) 307--314.
7
J. Scott Provan and Louis J. Billera, Decompositions of simplicial complexes related to diameters of convex polyhedra, Math. Oper. Res. 5 (1980), no. 4, 576--594.
8
R. H. Villarreal, Cohen-Macaulay graphs, Manuscripta Math. 66 (1990), no. 3, 277--293.
9
R.Woodroofe, Vertex decomposable graphs and obstructions to shellability, Proc. Amer. Math. Soc. 137 (2009), no. 10, 3235--3246.
10
ORIGINAL_ARTICLE
Constructing vertex decomposable graphs
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
2016-08-01
809
817
Finite graph
well-covered graph
independence complex
edge ideal
vertex decomposable graph
E.
Lashani
lashani@iau-doroud.ac.ir
1
Department of Mathematics, Science and Research branch, Islamic Azad University(IAU), Tehran, Iran.
LEAD_AUTHOR
A.
Soleyman Jahan
solymanjahan@gmail.com
2
Department of Mathematics, University of Kurdistan, P.O. Box 66177-15175, Sanadaj, Iran.
AUTHOR
A. Bjorner and M. Wachs, Shellable nonpure complexes and posets, I, Trans. Amer. Math. Soc. 348 (1996), no. 4, 1299--1327.
1
D. Cook II, U. Nagel, Cohen-Macaulay graph and face vector of ag complexes, SIAM J. Discrete Math. 26 (2012), no. 1, 89--101.
2
A. Dochtermann and A. Engstrom, Algebraic properties of edge ideals via combinatorial topology, Electron. J. Combin. 16 (2009), no. 2, Special volume in honor of Anders Bjorner, 24 pages.
3
D. Hang, N. C^ong Minh and T. Nam Trung, On the Cohen-Macaulay graphs and girth, preprint, (2013), arXiv:1204.5561v2, 16 pages.
4
T. Hibi, A. Higashitani, K. Kimura and A. B. O'Keefe, Algebraic study on Cameron Walker graphs, J. Algebra 422 (2015) 257--269.
5
A. Mousivand, S. A. S. Fakhari and S. Yassemi, A new construction for Cohen-Macaulay graphs, Comm. Algebra 43 (2015), no. 12, 5104--5112.
6
B. Randerath and L. Volkmann, A characterization of well covered block-cactus graphs, Australas. J. Combin. 9 (1994) 307--314.
7
J. Scott Provan and Louis J. Billera, Decompositions of simplicial complexes related to diameters of convex polyhedra, Math. Oper. Res. 5 (1980), no. 4, 576--594.
8
R. H. Villarreal, Cohen-Macaulay graphs, Manuscripta Math. 66 (1990), no. 3, 277--293.
9
R.Woodroofe, Vertex decomposable graphs and obstructions to shellability, Proc. Amer. Math. Soc. 137 (2009), no. 10, 3235--3246.
10
ORIGINAL_ARTICLE
A limited memory adaptive trust-region approach for large-scale unconstrained optimization
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
2016-08-01
819
837
Unconstrained optimization
trust-region framework
compact quasi-Newton representation
limited memory technique
adaptive strategy
M.
Ahookhosh
masoud.ahookhosh@univie.ac.at
1
Faculty of Mathematics, University of Vienna, Oskar-Morge-nstern-Platz 1, 1090 Vienna, Austria.
AUTHOR
K.
Amini
kamini@razi.ac.ir
2
Department of Mathematics, Razi University, Kermanshah, Iran.
LEAD_AUTHOR
M.
Kimiaei
morteza.kimiaei@gmail.com
3
Department of Mathematics, Asadabad Branch, Islamic Azad University, Asadabad, Iran.
AUTHOR
M. R.
Peyghami
peyghami@kntu.ac.ir
4
K.N. Toosi University of Department of Mathematics, K. N. Toosi University of Technology, P.O. Box 16315-1618, Tehran, Iran.
AUTHOR
M. Ahookhosh and K. Amini, A nonmonotone trust region method with adaptive radius for unconstrained optimization problems, Comput. Math. Appl. 60 (2010), no. 3, 411--422.
1
M. Ahookhosh, H. Esmaeili and M. Kimiaei, An effective trust-region-based approach for symmetric nonlinear systems, Int. J. Comput. Math. 90 (2013), no. 3, 671--690.
2
K. Amini and M. Ahookhosh, A hybrid of adjustable trust-region and nonmonotone algorithms for unconstrained optimization, Appl. Math. Model. 38 (2014), no. 9-10, 2601--2612.
3
K. Amini and M. Ahookhosh, Combination adaptive trust region method by non-monotone strategy for unconstrained nonlinear programming, Asia-Pac. J. Oper. Res. 28 (2011), no. 5, 585--600.
4
N. Andrei, An unconstrained optimization test functions collection, Adv. Model. Optim. 10 (2008), no. 1, 147--161.
5
D. Ataee Tarzanagh, M. R. Peyghami and H. Mesgarani, A new nonmonotone trust region method for unconstrained optimization equipped by an efficient adaptive radius, Optim. Methods Softw. 29 (2014), no. 4, 819--836.
6
F. Bastin, V. Malmedy, M. Mouffe, Ph. L. Toint and D. Tomanos, A retrospective trust-region method for unconstrained optimization, Math. Programming 123 (2008), no. 2, 395--418.
7
J. V. Burke, A. Wiegmann and L. Xu, Limited memory BFGS updating in a trust-region framework, SIAM Journal on Optimization. submitted, 2008.
8
R. H. Byrd, P. Lu and J. Nocedal, A limited memory algorithm for bound constrained optimization, SIAM J. Sci. Comput. 16 (1995), no. 5, 1190--1208.
9
R. Byrd, J. Nocedal and R. Schnabel, Representation of quasi-Newton matrices and their use in limited memory methods, Math. Programming 63 (1994), no. 2, 129--156.
10
A. R. Conn, N. I. M. Gould and Ph. L. Toint, LANCELOT. A Fortran package for large scale nonlinear optimization (release A), Springer Series in Computational Mathematics, 17, Springer-Verlag, Berlin, 1992.
11
A. R. Conn, N. I. M. Gould and Ph. L. Toint, Trust-Region Methods, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, 2000.
12
E. Dolan and J. J. Morfie, Benchmarking optimization software with performance profiles, Math. Program. 21 (2002), no. 2, 201--213.
13
H. Esmaeili and M. Kimiaei, An efficient adaptive trust-region method for systems of nonlinear equations, Int. J. Comput. Math. 92 (2015), no. 1, 151--166.
14
H. Esmaeili and M. Kimiaei, A new adaptive trust-region method for system of nonlinear equations, Appl. Math. Model. 38 (2014), no. 11--12, 3003--3015.
15
R. Fletcher, Practical Method of Optimization, Wiley, NewYork, 2000.
16
N. Gould, S. Lucidi, M. Roma and Ph. L. Toint, Solving the trust-region subproblem using the Lanczos method, SIAM J. Optim. 9 (1999), no. 2, 504--525.
17
N. I. M. Gould, D. Orban and A. Sartenaer and P. L. Toint, Sensitivity of trust-region algorithms to their parameters, 4OR 3 (2005), no. 3, 227--241.
18
D. C. Liu and J. Nocedal, On the limited memory BFGS method for large scale optimization, Math. Programming 45 (1989), no. 3, 503--528.
19
L. Kaufman, Reduced storage, quasi-Newton trust region approaches to function optimization, SIAM J. Optim. 10 (1999), no. 1, 56--69.
20
J. L. Morales and J. Nocedal, Enriched methods for large-scale unconstrained optimization, Comput. Optim. Appl. 21 (2002), no. 2, 143--154.
21
J. L. Morales and J. Nocedal, L-BFGS-B: Remark on Algorithm 778: L-BFGS-B, FOR-TRAN routines for large scale bound constrained optimization, to appear in ACM Trans.Math. Software, 2011.
22
J. J. Morfie, B. S. Garbow and K. E. Hillstrom, Testing Unconstrained Optimization Software, ACM Trans. Math. Software 7 (1981) 17--41.
23
S. G. Nash and J. Nocedal, A numerical study of the limited memory BFGS method and the truncated Newton method for large scale optimization, SIAM J. Optim. 1 (1991), no. 3, 358--372.
24
J. Nocedal, Updating quasi-Newton matrices with limited storage, Mathematics of Computation. 35 (1980), no. 151, 773--782.
25
J. Nocedal and S. J. Wright, Numerical Optimization, Springer, New York, 2006.
26
J. Nocedal and Y. Yuan, Combining trust region and line search techniques, in: Y. Yuan (Ed.), Advanced in nonlinear programming, 153--175, Kluwer Acad. Publ., Dordrecht, 1998.
27
M. J. D. Powell, A new algorithm for unconstrained optimization, In: Rosen JB, Mangasarian OL, Ritter K (eds) Nonlinear programming, 31--66, Academic Press, New York, 1970.
28
M. J. D. Powell, On the global convergence of trust region algorithms for unconstrained minimization, Math. Programming 29 (1984) 297--303.
29
A. Sartenaer, Automatic determination of an initial trust region in nonlinear programming, SIAM J. Sci. Statist. Comput. 18 (1997), no. 6, 1788--1803.
30
R. B. Schnabel and E. Eskow, A new modified Cholesky factorization, SIAM J. Sci. Statist. Comput. 11 (1990), no. 6, 1136--1158.
31
G. A. Schultz, R. B. Schnabel and R. H. Byrd, A family of trust-region-based algorithms for unconstrained minimization with strong global convergence, SIAM J. Numer. Anal. 22 (1985), no. 1, 47--67.
32
Z. J. Shi and J. H. Guo, A new trust region method with adaptive radius, Comput. Optim. Appl., 213 (2008), no. 2, 509--520.
33
T. Steihaug, The conjugate gradient method and trust regions in large scale optimization, SIAM J. Numer. Anal. 20 (1983), no. 3, 626--637.
34
X. S. Zhang, J. L. Zhang and L. Z. Liao, An adaptive trust region method and its convergence, Sci. China Ser. A 45 (2002), no. 5, 620--631.
35
C. Zhu, R. H. Byrd and J. Nocedal, Algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound-constrained optimization, ACM Trans. Math. Software 23 (1997), no. 4, 550--560.
36
http://users.eecs.northwestern.edu/ nocedal/lbfgsb.html
37
ORIGINAL_ARTICLE
Totally umbilical radical transversal lightlike hypersurfaces of Kähler-Norden manifolds of constant totally real sectional curvatures
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
2016-08-01
839
854
Kähler-Norden manifold
totally real sectional curvature
radical transversal lightlike hypersurface
totally umbilical lightlike hypersurface
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.
LEAD_AUTHOR
A. Borisov and G. Ganchev, Curvature properties of Kaehlerian manifolds with B-metric, 220{226, Proc. of 14th Spring Conference of UBM, Sunny Beach, 1985.
1
K. L. Duggal and A. Bejancu, Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications, Kluwer Academic Publishers Group, Dordrecht, 1996.
2
K. L. Duggal and B. Sahin, Differential Geometry of Lightlike Submanifolds, Birkhäuser Verlag, Basel, 2010.
3
G. T. Ganchev and A. Borisov, Note on the almost complex manifolds with a Norden metric, C. R. Acad. Bulgare Sci. 39 (1986), no. 5, 31{34.
4
G. T. Ganchev, K. Gribachev and V. Mihova, B-connections and their conformal invariants on conformally Kahler manifolds with B-metric, Publ. Inst. Math. (Beograd) (N.S.) 42 (1987), no. 56, 107{121.
5
D. H. Jin, The curvatures of lightlike hypersurfaces of an indefinite Kenmotsu manifold, BJGA 17 (2012), no. 1, 49{57.
6
G. Nakova, Some lightlike submanifolds of almost complex manifolds with Norden metric, J. Geom. 103 (2012), no. 2, 293{312.
7
G. Nakova, Radical transversal lightlike hypersurfaces of almost complex manifolds with Norden metric, J. Geom. 104 (2013), no. 3, 539{556.
8
A. Norden, On a class of four-dimensional A-spaces (in Russian), Izv. Vyss. Ucebn. Zaved. Matematika 17 (1960) 145{157.
9
B. Sahin, Lightlike hypersurfaces of semi-Euclidean spaces satisfying curvature conditions of semisymmetry type, Turkish J. Math. 31 (2007), no. 2, 139{162.
10
ORIGINAL_ARTICLE
A note on inequalities for Tsallis relative operator entropy
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
2016-08-01
855
859
Relative operator entropy
Tsallis relative operator entropy
operator inequalities
L.
Zou
limin-zou@163.com
1
School of Mathematics and Statistics, Chongqing Three Gorges University, Chongqing, 404100, P. R. China.
LEAD_AUTHOR
Y.
Jiang
yyy_j123456@163.com
2
School of Mathematics and Statistics, Chongqing Three Gorges University, Chongqing, 404100, P. R. China.
AUTHOR
S. Furuichi, K. Yanagi and K. Kuriyama, A note on operator inequalities of Tsallis relative operator entropy, Linear Algebra Appl. 407 (2005), no. 1, 19--31.
1
T. Furuta, Furuta's inequality and its application to the relative operator entropy, J. Operator Theory 30 (1993), no. 1, 21--30.
2
T. Furuta, Invitation to Linear Operators, Taylor & Francis, London and New York, 2001.
3
T. Furuta, Reverse inequalities involving two relative operator entropies and two relative entropies, Linear Algebra Appl. 403 (2005), no. 1, 24--30.
4
T. Furuta, Two reverse inequalities associated with Tsallis relative operator entropy via generalized Kantorovich constant and their applications, Linear Algebra Appl. 412 (2006), no. 2-3, 526--537.
5
K. Yanagi, K. Kuriyama and S. Furuichi, Generalized Shannon inequalities based on Tsallis relative operator entropy, Linear Algebra Appl. 394 (2005), no. 1, 109--118.
6
L. Zou, Operator inequalities associated with Tsallis relative operator entropy, Math. Inequal. Appl. 18 (2015), no. 2, 401--406.
7
ORIGINAL_ARTICLE
A module theoretic approach to zero-divisor graph with respect to (first) dual
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
2016-08-01
861
872
Zero-divisor graph
Clique number
Chromatic number
Module
E.
Momtahan
momtahan_e@hotmail.com
1
Department of Mathematics, Yasouj University, Yasouj,75914, Iran.
LEAD_AUTHOR
M.
Baziar
mbaziar@yu.ac.ir
2
Department of Mathematics, Yasouj University, Yasouj,75914, Iran.
AUTHOR
S.
Safaeeyan
safaeeyan@yu.ac.ir
3
Department of Mathematics, Yasouj University, Yasouj,75914, Iran.
AUTHOR
S. Akbari and A. Mohammadian, On zero-divisor graphs of finite rings, J. Algebra 314 (2007), no. 1, 168--184.
1
D. F. Anderson, M. C. Axtell and J. A. Stickles, Zero-divisor graphs in commutative rings, Commutative Algebra, Noetherian and Non-Noetherian Perspective, 23--45, Springer, New York, 2011.
2
D. F. Anderson, A. D. F. Anderson, A. Frazier, A. Lauve and P. S. Livingston, The zero-divisor graph of a commutative ring, II, 61--72, Lecture Notes in Pure and Appl. Math., 220, Dekker, New York, 2001.
3
D. F. Anderson and P. S. Livingston, The zero-divisor graph of a commutative ring, J. Algebra. 217 (1999), no. 2, 434--447.
4
D. D. Anderson and M. Naseer, Beck's coloring of a commutative ring, J. Algebra. 159 (1993), no. 2, 500--514.
5
M. Baziar, E. Momtahan and S. Safaeeyan, A zero-divisor graph for modules with respect to their (first) dual, J. Algebra Appl. 12 (2013), no. 2, 11 pages.
6
M. Baziar, E. Momtahan and S. Safaeeyan, Zero-divisor graph of abelian groups, J. Algebra Appl. 13 (2014), no. 6, 13 pages.
7
I. Beck, Coloring of commutative rings, J. Algebra 116 (1988), no. 1, 208--226.
8
M. Behboodi, Zero divisor graphs for modules over commutative rings, J. Commut. Algebra 4 (2012), no. 2, 175--197.
9
M. Behboodi and Z. Rakeei, The annihilating-ideal graph of commutative rings I, J. Algebra Appl. 10 (2011), no. 4, 727--739.
10
M. Behboodi and Z. Rakeei, The annihilating-ideal graph of commutative rings II, J. Algebra Appl. 10 (2011), no. 4, 741--753.
11
F. DeMeyer, T. McKenzie and K. Schneider, The zero-divisor graph of a commutative semigroup, Semigroup Forum 65 (2002), no. 2, 206--214.
12
T. G. Lucas, The diameter of a zero divisor graph, J. Algebra 301 (2006), no. 1, 3533--3558.
13
H. R. Maimani, M. R. Pournaki, A. Tehranian and S. Yassemi, Graphs attached to rings revisited, Arab. J. Sci. Eng. 36 (2011), no. 6, 997--1012.
14
S. B. Mulay, Cycles and symmetries of zero-divisors, Comm. Algebra 30 (2002), no. 7, 3533--3558.
15
S. P. Redmond, The zero-divisor graph of a non-commutative ring, Internat. J. Commutative Rings 1 (2002), no. 4, 203--211.
16
S. P. Redmond, An ideal based zero-divisor graph of a commutative ring, Comm. Algebra 31 (2003), no. 9, 4425--4443.
17
S. Safaeeyan, M. Baziar and E. Momtahan, A generalization of the zero-divisor graph for modules, J. Korean Math. Soc. 51 (2014), no. 1, 87--98.
18
D. B. West, Introduction to Graph Theory, 2nd ed., Prentice Hall, Upper Saddle River, 2001.
19
R. Wisbauer, Foundations of Modules and Rings Theory, Gordon and Breach Science Publishers, Philadelphia, 1991.
20
Z. Xue and S. Liu, Zero-divisor graphs of partially ordered sets, App. Math. Letters 23 (2010), no. 4, 449--452.
21
ORIGINAL_ARTICLE
Center--like subsets in rings with derivations or epimorphisms
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
2016-08-01
873
878
Prime ring
semiprime ring
derivation
epimorphism
center-like subset
H. E.
Bell
hbell@brocku.ca
1
Department of Mathematics, Brock University, St. Catharines, Ontario L2S 3A1, Canada.
AUTHOR
M. N.
Daif
nagydaif@yahoo.com
2
Department of Mathematics, Al-Azhar University, Nasr City(11884), Cairo, Egypt.
LEAD_AUTHOR
H. E. Bell and M. N. Daif, On commutativity and strong commutativity--preserving maps, Canad. Math. Bull. 37 (1994), no. 4, 443--447.
1
H. E. Bell and M. N. Daif, On derivations and commutativity in prime rings, Acta Math. Hungar. 66 (1995), no. 4, 337--343.
2
H. E. Bell and A. A. Klein, On some centre-like subsets of rings, Math. Proc. R. Ir. Acad. 105 (2005), no. 1, 17--24.
3
H. E. Bell and A. A. Klein, Neumann near-rings and Neumann centers, New Zealand J. Math. 35 (2006), no. 1 , 31--36.
4
H. E. Bell and W. S. Martindale III, Centralizing mappings of semiprime rings, Canad Math. Bull. 30 (1987), no. 1, 92--101.
5
J. Bergen and I. N. Herstein, The algebraic hypercenter and some applications, J. Algebra 85 (1983), no. 1, 217--242.
6
M. Chacron, A commutativity theorem for rings, Proc. Amer. Math. Soc. 59 (1976), no. 2, 211--216.
7
C. L. Chuang and T. K. Lee, On the one-sided version of hypercenter theorem, Chinese J. Math. 23 (1995), no. 3, 211--223.
8
A. Giambruno, Some generalizations of the center of a ring, Rend. Circ. Mat. Palermo (2) 27 (1978), no. 2, 270--282.
9
A. Giambruno, On the symmetric hypercenter of a ring, Canad. J. Math. 36 (1984), no. 3, 421--435.
10
I. N. Herstein, On the hypercenter of a ring, J. Algebra 36 (1975), no. 1, 151--157.
11
I. N. Herstein, Rings with Involution, Univ. Chicago Press, Chicago, 1976.
12
I. N. Herstein, A note on derivations II, Canad. Math. Bull. 22 (1979), no. 4, 509--511.
13
ORIGINAL_ARTICLE
The Ramsey numbers of large trees versus wheels
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
2016-08-01
879
880
Ramsey number
tree
wheel
D.
Zhu
dongmeizhu2013@126.com
1
School of Economics and Management, Southeast University, Nanjing 210093, P.R. China.
AUTHOR
L.
Zhang
zhanglm@nju.edu.cn
2
School of Management and Engineering, Nanjing University, Nanjing 210093, P.R. China.
LEAD_AUTHOR
D.
Li
leedongxin@163.com
3
School of Management and Engineering, Nanjing University, Nanjing 210093, P.R. China.
AUTHOR
J. A. Bondy and U. S. R. Murty, Graph Theory, Graduate Texts in Mathematics, 244, Springer, New York, 2008.
1
E. T. Baskoro, Surahmat, S. M. Nababan and M. Miller, On Ramsey numbers for trees versus wheels of five or six vertices, Graphs Combin. 18 (2002), no. 4, 717--721.
2
S. A. Burr, P. Erdos, R. J. Faudree, C. C. Rousseau and R. H. Schelp, Ramsey numbers for the pair sparse graph-path or cycle, Trans. Amer. Math. Soc. 269 (1982), no. 2, 501--512.
3
Y. Chen, Y. Zhang and K. Zhang, The Ramsey numbersR(Tn;W6) for Δ(Tn) ≥n-3, Appl. Math. Lett. 17 (2004), no. 3, 281--285.
4
Y. Chen, Y. Zhang and K. Zhang, The Ramsey numbers of Trees versus W6 or W7, European J. Combin. 27 (2006), no. 4, 558--564.
5
Y. Chen, Y. Zhang and K. Zhang, The Ramsey numbersR(Tn;W6) for small n, Util. Math. 67 (2005) 269--284.
6
Y. Chen, Y. Zhang and K. Zhang, The Ramsey Numbers R(Tn;W6) for Tn without certain deletable sets, J. Syst. Sci. Complex 18 (2005), no. 1, 95--101.
7
S. P. Radziszowski, Small Ramsey numbers, Electron. J. Combin. (2014), DS1.14.
8
Y. Zhang, Y. Chen and K. Zhang, The Ramsey numbers for trees of high degree versus a wheel of order nine, manuscript (2009).
9
ORIGINAL_ARTICLE
Coefficient estimates for a subclass of analytic and bi-univalent functions
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
2016-08-01
881
889
Analytic functions
Bi-Univalent Functions
Coefficient estimates
starlike functions
Koebe one-quarter theorem
A.
Zireh
azireh@shahroodut.ac.ir
1
Department of Mathematics, Shahrood University Of Technology, P.O. Box 316-36155, Shahrood, Iran.
LEAD_AUTHOR
E.
Analouei Audegani
e_analoei@ymail.com
2
Department of Mathematics, Mobarakeh Branch, Islamic Azad University, Mobarakeh, P.O. Box 84819-97817, Isfahan, Iran.
AUTHOR
R. M. Ali, S. K. Lee, V. Ravichandran and S. Subramaniam, Coefficient estimates for bi-univalent Ma-Minda starlike and convex functions, Appl. Math. Lett. 25 (2012), no. 3, 344--351.
1
D. A. Brannan and J. G. Clunie (Eds.), Aspects of contemporary complex analysis, Proceedings of the NATO Advanced Study Institute held at the University of Durham, Academic Press, New York-London, 1980.
2
P. L. Duren, Univalent Functions, Springer-Verlag, New York, Berlin, 1983.
3
T. Hayami and S. Owa, Coefficient bounds for bi-univalent functions, Panamer. Math. J. 22 (2012), no. 4 , 15--26.
4
B. A. Frasin and M. K. Aouf, New subclasses of bi-univalent functions, Appl. Math. Lett. 24 (2011), no. 9, 1569--1573.
5
B. A. Frasin, Coefficient bounds for certain classes of bi-univalent functions, Hacet. J. Math. Stat. 43 (2014), no. 3, 383--389.
6
C. Y. Gao and S. Q. Zhou, Certain subclass of starlike functions, Appl. Math. Comput. 187 (2007), no. 1, 176--182.
7
A. W. Kedzierawski, Some remarks on bi-univalent functions, Ann. Univ. Mariae Curie-Sklodowska Sect. A. 39 (1985) 77--81.
8
M. Lewin, On a coefficient problem for bi-univalent functions, Proc. Amer. Math. Soc. 18 (1967) 63--68.
9
H. M. Srivastava, A. K. Mishra and P. Gochhayat, Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett. 23 (2010), no. 10, 1188--1192.
10
E. Netanyahu, The minimal distance of the image boundary from the origin and the second coefficient of a univalent function in jzj < 1, Arch. Rational Mech. Anal. 32 (1969) 100--112.
11
D. L. Tan, Coefficient estimates for bi-univalent functions, Chinese Ann. Math. Ser. A. 5 (1984), no. 5, 559--568.
12
Q. H. Xu, Y. C. Gui and H. M. Srivastava, Coefficient estimates for a certain subclass of analytic and bi-univalent functions, Appl. Math. Lett. 25 (2012), no. 6, 990--994.
13
Q. H. Xu, H. G. Xiao and H. M. Srivastava, A certain general subclass of analytic and bi-univalent functions and associated coefficient estimate problems, Appl. Math. Comput. 218 (2012), no. 23, 11461--11465.
14
D. G. Yang and J. L. Liu, A class of analytic functions with missing coefficients, Abstr. Appl. Anal. 2011, Article ID 456729, 16 pages.
15
ORIGINAL_ARTICLE
Relative (co)homology of $F$-Gorenstein modules
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
2016-08-01
891
902
$F$-Gorenstein projective module
$F$-Gorenstein injective module
relative cohomology
relative homology
C.
Zhang
zhangcx@nwnu.edu.cn
1
Department of Mathematics, Northwest School of Mathematics Sciences, Chongqing Normal University, Chongqing 400000, China.
LEAD_AUTHOR
Z.
Li
792252531@qq.com
2
Department of Mathematics, Northwest Normal University, Lanzhou 730070, China.
AUTHOR
M. Auslander and M. Bridger, Stable Module Theory, Mem. Amer. Math. Soc. 94, Amer. Math. Soc., Providence, 1969.
1
M. Auslander and ø. Solberg, Relative homology and representation theory I. Relative homology and homologically finite subcategories, Comm. Algebra 21 (1993), no. 9, 2995--3031.
2
M. Auslander and ø. Solberg, Relative homology and representation theory II. Relative cotilting theory, Comm. Algebra 21 (1993), no. 9, 3033--3079.
3
M. Auslander and ø. Solberg, Relative homology and representation theory III. Cotilting modules and Wedderburn correspondence, Comm. Algebra 21 (1993), no. 9, 3081--3097.
4
M. Auslander and ø. Solberg, Gorenstein algebras and algebras with dominant dimension at least 2, Comm. Algebra 21 (1993), no. 11, 3897--3934.
5
L. L. Avramov and A. Martsinkovsky, Absolute, relative, and Tate cohomology of modules of finite Gorenstein dimension, Proc. London Math. Soc. (3) 85 (2002), no. 2, 393--440.
6
E. E. Enochs and O. M. G. Jenda, Gorenstein injective and projective modules, Math. Z. 220 (1995), no. 4, 611--633.
7
E. E. Enochs and O. M. G. Jenda, Relative homological algebra, De Gruyter Expositions in Mathematics no. 30, Walter de Gruyter & Co., Berlin, 2000.
8
R. Hartshorne, Algebraic Geometry, Graduate Texts in Mathematics, 52, Springer-Verlag, New York-Heidelberg, 1977.
9
H. Holm, Gorenstein derived functors, Proc. Amer. Math. Soc. 132 (2004), no. 7, 1913--1923.
10
H. Holm, Gorenstein homological dimensions, J. Pure Appl. Algebra 189 (2004), no. 1-3, 167--193.
11
S. Sather-Wagstaff, T. Sharif and D. White, Stability of Gorenstein categories, J. London Math. Soc. (2) 77 (2008), no. 2, 481--502.
12
X. Tang, On F-Gorenstein dimensions, J. Algebra Appl. 13 (2014), no. 6, 14 pages.
13
ORIGINAL_ARTICLE
On Black-Scholes equation; method of Heir-equations, nonlinear self-adjointness and conservation laws
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
2016-08-01
903
921
Black-Scholes equation
Heir-equation
nonclassical symmetry
Nonlinear self-adjointness
Conservation law
M. S.
Hashemi
hashemi_math396@yahoo.com
1
Department of Mathematics, Basic Science Faculty, University of Bonab, P.O. Box 55517-61167, Bonab, Iran.
LEAD_AUTHOR
F. Allassia and M. C. Nucci, Symmetries and heir equations for the laminar boundary layer model, J. Math. Anal. Appl. 201 (1996), no. 3, 911--942.
1
F. Black and M. S. Scholes, The pricing of options and corporate liabilities, J. Political Econ. 81 (1973), no. 3, 637--654.
2
G. W. Bluman and S. C. Anco, Symmetry and Integration Methods for Differential Equations, Springer-Verlag, New York, 2002.
3
G. W. Bluman and J. D. Cole, The general similarity solution of the heat equation, J. Math. Mech. 18 (1969) 1025--1042.
4
Y. Bozhkov and S. Dimas, Group classification of a generalized Black-Scholes-Merton equation, Commun. Nonlinear. Sci. Numer. Simul. 19 (2014), no. 7, 2200--2211.
5
Y. Bozhkov and K. A. A. Silva, Nonlinear self-adjointness of a 2D generalized second order evolution equation, Nonlinear Anal. 75 (2012), no. 13, 5069--5078.
6
R. M. Edelstein and K.S. Govinder, Conservation laws for the Black-Scholes equation, Nonlinear Anal. Real World Appl. 10 (2009), no. 6, 3372--3380.
7
I. L. Freire, and J. C. S. Sampaio, Nonlinear self-adjointness of a generalized fifth-order KdV equation, J. Phys. A 45 (2012), no. 3, 32001-32007.
8
I. L. Freire and J. C. S. Sampaio, On the nonlinear self-adjointness and local conservation laws for a class of evolution equations unifying many models, Commun. Nonlinear Sci. Numer. Simul. 19 (2014), no. 2, 350--360.
9
I. L. Freire, New classes of nonlinearly self-adjoint evolution equations of third- and fifth-order, Commun. Nonlinear Sci. Numer. Simul. 18 (2013), no. 3, 493--499.
10
L. R. Galiakberova N. H. and Ibragimov, Nonlinear self-adjointness of the Krichever-Novikov equation, Commun. Nonlinear. Sci. Numer. Simul. 19 (2014), no. 2, 361--363.
11
M. L. Gandarias, Weak self-adjoint differential equations, J. Phys. A: Math. Theor. 44 (2011) 262001.
12
M. L. Gandarias, M. Redondo and M. S. Bruzon, Some weak self-adjoint Hamilton-Jacobi-Bellman equations arising in financial mathematics, Nonlinear Anal. Real World Appl. 13 (2012), no. 1, 340-347.
13
R. K. Gazizov and N. H. Ibragimov, Lie Symmetry Analysis of Differential Equations in Finance, Nonlinear Dynam. 17 (1998), no. 4, 387--407.
14
J. Goard, Generalised conditional symmetries and Nucci's method of iterating the non-classical symmetries method, Appl. Math. Lett. 16 (2003), no. 4, 481--486.
15
G. Guthrie, Constructing Miura transformations using symmetry groups, Research Report 85 (1993) 1--27.
16
J. G. Hara, C. Sophocleous and P. G. L. Leach, Symmetry analysis of a model for the exercise of a barrier option, Commun. Nonlinear. Sci. Numer. Simul. 18 (2013), no. 9, 2367--2373.
17
M. S. Hashemi, A. Haji-Badali and P. Vafadar, Group Invariant Solutions and Conser-vation Laws of the Fornberg-Whitham Equation, Z. Naturforsch. 69 (2014) 489--496.
18
M. S. Hashemi and M. C. Nucci, Nonclassical symmetries for a class of reaction-diffusion equations: the method of heir-equations, J. Nonlinear Math. Phys. 20 (2013), no. 1, 44--60.
19
N. H. Ibragimov, A new conservation theorem, J. Math. Anal. Appl. 333 (2007), no. 1, 311--328.
20
N. H. Ibragimov, Quasi-self-adjoint differential equations, Arch. ALGA. 4 (2007) 55--60.
21
N. H. Ibragimov, M. Torrisi and R. Tracina', Self-adjointness and conservation laws of a generalized Burgers equation, J. Phys. A 44 (2011), no. 14, 145201, 5 pages.
22
A. H. Kara and F. M. Mahomed, The relationship between symmetries and conservation laws, Int. J. Theor. Phys. 39 (2000) 23--40.
23
Y. Liu and D. S. Wang, Symmetry analysis of the option pricing model with dividend yield from financial markets, Appl. Math. Lett. 24 (2001), no. 4, 481--486.
24
S. Martini, N. Ciccoli and M. C. Nucci, Group analysis and heir-equations of a mathematical model for thin liquid films, J. Nonlinear Math. Phys. 16 (2009), no. 1, 77--92.
25
M. C. Nucci, Iterating the nonclassical symmetries method, Physica D. 78 (1994), no. 1-2, 124--134.
26
M. C. Nucci, Nonclassical symmetries as special solutions of heir-equations, J. Math. Anal. Appl. 279 (2003), no. 1, 168--179.
27
M. C. Nucci, Nonclassical symmetries and Backlund transformations, J. Math. An. Appl. 178 (1993), no. 1, 294--300.
28
P. J. Olver, Direct reduction and differential constraints, Proc. R. Soc. Lond. A. 444 (1994), no. 1922, 509--523.
29
C. A. Pooe, F. M. Mahomed and C. Wafo soh, Invariant solutions of the Black-Scholes equation, Math. Comput. Appl. 8 (2003), no. 1-3, 63--70.
30
R. Tracina, On the nonlinear self-adjointness of the Zakharov-Kuznetsov equation, Commun. Nonlinear Sci. Numer. Simul. 19 (2014) 377--382.
31
E. M. Vorob'ev, Partial symmetries and integrable multidimensional differential equations, Differential Equations 25 (1989), no. 3, 322--325.
32
ORIGINAL_ARTICLE
On the order of a module
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
2016-08-01
923
931
Fitting ideals
minimal free presentation
order of a module
S.
Hadjirezaei
s.hajirezaei@vru.ac.ir
1
Department of Mathematics, Vali-e-Asr University of Rafsanjan, P.O. Box 7718897111, Rafsanjan, Iran.
LEAD_AUTHOR
S.
Karimzadeh
karimzadeh@vru.ac.ir
2
Department of Mathematics, Vali-e-Asr University of Rafsanjan, P.O. Box 7718897111, Rafsanjan, Iran.
AUTHOR
N. Bourbaki, Commutative Algebra, Springer-Verlag, Berlin, 1998.
1
D. A. Buchsbaum and D. Eisenbud, What makes a complex exact? J. Algebra 25 (1973) 259--268.
2
D. Eisenbud, Commutative Algebra with a View toward Algebraic Geometry, Springer-verlag, New York, 1995.
3
S. Hadjirezaei and S. Hedayat, On the first nonzero Fitting ideal of a module over a UFD, Comm. Algebra 41 (2013), no. 1, 361--366.
4
V. Kodiyalam, Integrally closed modules over two-dimensional regular local ring, Trans. Amer. math. soc. 347 (1995), no. 9, 3551--3573.
5
J. Lipman, On the Jacobian ideal of the module of differentials, Proc. Amer. Math. Soc. 21 (1969) 423--426.
6
J. Ohm, On the first nonzero Fitting ideal of a module, J. Algebra 320 (2008), no. 1, 417--425.
7
Y. Tiras and M. Alkan, Prime modules and submodules, Comm. Algebra 31 (2003), no. 11, 5253--5261.
8
ORIGINAL_ARTICLE
Sufficient conditions for univalence and starlikeness
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
2016-08-01
933
939
Analytic functions
convex functions
starlike functions
univalent functions
M. N.
Nunokawa
mamoru_nuno@doctor.nifty.jp
1
University of Gunma, Hoshikuki-cho 798-8, Chuou-Ward, Chiba 260-0808, Japan.
AUTHOR
J.
Sokol
jsokol@prz.edu.pl
2
Department of Mathematics, Rzeszow University of Technology, Al. Powstancow Warszawy 12, 35-959 Rzeszow, Poland.
AUTHOR
N. E.
Cho
necho@pknu.ac.kr
3
Department of Applied Mathematics, College of Natural Sciences, Pukyong National University, Busan 608-737, Korea.
LEAD_AUTHOR
S. N. Kudryashov, On some criteria of schlichtness of analytic functions (Russian), Mat. Zametki 13 (1973) 359--366.
1
S. S. Miller and P. T. Mocanu, Differential subordinations and univalent functions, Michigan Math. J. 32 (1985) 185--195.
2
R. Nevanlinna, Uber die konforme Abbildund Sterngebieten, Oversikt av Finska-Vetenskaps Societen Forhandlingar, 63 (A) (1921), no. 6, 48--403.
3
M. Nunokawa, On properties of non-Caratheodory functions, Proc. Japan Acad. Ser. A 68 (1992), no. 6, 152--153.
4
M. Nunokawa, On the order of strongly starlikeness of strongly convex functions, Proc. Japan Acad. Ser. A Math. Sci. 69 (1993), no. 7, 234--237.
5
S. Ozaki, On the theory of multivalent functions II, Sci. Rep. Tokyo Bunrika Daigaku A 4 (1941) 45--87.
6
J. A. Pfaltzgraff, M. O. Reade and T. Umezawa, Sufficient Conditions for Univalence, Ann. Fac. Sci. de Kinshasa, Zare; Sec. Math. Phys. 2 (1976), no. 2, 94--100.
7
R. Singh and R. Singh, Some sufficient conditions for univalence and starlikeness, Colloq. Math. 47 (1982) no. 2, 309--314.
8
J. Sokol, On sufficient condition to be in a certain subclass of starlike functions defined by subordination, Appl. Math. Comput. 190 (2007), no. 1, 237--241.
9
J. Sokol, Starlikeness of Hadamard product of certain analytic functions, Appl. Math. Comp. 190 (2007), no. 2, 1157--1160.
10
J. Sokol, On a condition for alpha-starlikeness, J. Math. Anal. Appl. 352 (2009), 696--701.
11
J. Sokol, M. Nunokawa, On some sufficient condition for starlikeness, J. Inequal. Appl. 2012, 2012:282.
12
E. Study, Konforme Abbildung Einfachzusammenhangender Bereiche, B. C. Teubner, Leipzig und Berlin, 1913.
13
T. Umezawa, On the theory of univalent functions, Tohoku Math. J. (2) 7 (1955) 212--228.
14
ORIGINAL_ARTICLE
On two problems concerning the Zariski topology of modules
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
2016-08-01
941
948
Prime spectrum
classical Zariski topology
spectral space
H.
Ansari-Toroghy
ansari@guilan.ac.ir
1
Department of pure Mathematics, Faculty of mathematical Sciences, University of Guilan, P.O. Box 41335-19141, Rasht, Iran.
LEAD_AUTHOR
R.
Ovlyaee-Sarmazdeh
ovlyaee@guilan.ac.ir
2
Department of pure Mathematics, Faculty of mathematical Sciences, University of Guilan, P.O. Box 41335-19141, Rasht, Iran.
AUTHOR
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.
AUTHOR
H. Ansari-Toroghy and S. Keyvani, On the maximal spectrum of a module and Zariski topology, Bull. Malaysian Math. Soc. 21 (2015), no. 1, 303--316.
1
H. Ansari-Toroghy and R. Ovlyaee-Sarmazdeh, On the prime spectrum of X-injective modules, Comm. Algebra 38 (2010), no. 7, 2606--2621.
2
H. Ansari-Toroghy and R. Ovlyaee-Sarmazdeh, On the prime spectrum of a module and Zariski topologies, Comm. Algebra 38 (2010), no. 12, 4461--4475.
3
M. F. Atiyah and I. G. Macdonald, Introduction to Commutative Algebra, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1969
4
M. Behboodi and M. R. Haddadi, Clasical Zariski topology of modules and spectral spaces I, Int. Electron. J. Algebra 4 (2008) 104--130.
5
M. Behboodi and M. R. Haddadi, Classical Zariski topology of modules and spectral spaces II, Int. Electron. J. Algebra 4 (2008) 131--148.
6
N. Bourbaki, Commutative Algebra, Addison-Wesley Publishing Co., Reading, Mass, 1972.
7
M. Hochster, Prime ideal structure in commutative rings, Trans. Amer. Math. Soc. 142 (1969) 43--60.
8
C. P. Lu, Prime submodules of modules, Comment. Math. Univ. St. Paul 33 (1984), no. 1, 61--69.
9
C. P. Lu, Spectra of modules, Comm. Algebra 23 (1995), no. 10, 3741--3752.
10
C. P. Lu, Saturations of submodules, Comm. Algebra 31 (2003), no. 6, 2655--2673.
11
C. P. Lu, A module whose prime spectrum has the surjective natural map, Houston J. Math 33 (2007), no. 1, 125--143.
12
C. P. Lu, Modules with Noetherian spectrum, Comm. Algebra 38 (2010), no. 3, 807--828.
13
A. Marcelo, J. Masque, Prime submodules, the descent invariant, and modules of finite length, J. Algebra 189 (1997), no. 2, 273--293.
14
R. L. McCasland, M. E. Moore and P. F. Smith, On the spectrum of a module over a commutative ring, Comm. Algebra 25 (1997), no. 1, 79--103.
15
J. Ohm and R. L. Pendleton, Ring with Noetherian spectrum, Duke. Math. J 35 (1968), no. 1, 631--639.
16
N. Van Sanh, L. P. Thao, N. F. A. Al-Meyahi, and K. P. Shum, Zariski topology of prime spectrum of a module, 461--477, Proceedings of the International Conference on Algebra, 2010.
17
ORIGINAL_ARTICLE
Complexes of $C$-projective modules
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
2016-08-01
949
958
Semidualizing
$C$--projective
$mathcal P_C$--resolution
$C$--perfect complex
strongly regular
E.
Amanzadeh
en.amanzadeh@gmail.com
1
Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, Iran.
LEAD_AUTHOR
M. T.
Dibaei
dibaeimt@ipm.ir
2
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.
AUTHOR
E. Amanzadeh and M. T. Dibaei, Auslander class, GC and C--projective modules modulo exact zero-divisors, Comm. Algebra 43 (2015), no. 10, 4320--4333.
1
L. L. Avramov and A. Martsinkovsky, Absolute, relative, and Tate cohomology of modules of inite Gorenstein dimension, Proc. London Math. Soc. (3) 85 (2002), no. 2, 393--440.
2
R-O. Buchweitz and H. Flenner, Strong global dimension of commutative rings and schemes, J. Algebra 422 (2015) 741--751.
3
L. W. Christensen and H. B. Foxby, Hyperhomological algebra with applications to commutative rings, http://www.math.ttu.edu/~lchriste/download/918-final.pdf
4
M. T. Dibaei and M. Gheibi, Sequence of exact zero--divizors, arXiv:1112.2353v3 (2012).
5
E. E. Enochs and O. M. G. Jenda, Relative homological algebra, 30, Walter de Gruyter & Co., Berlin, 2000.
6
S. I. Gelfand and Y. I. Manin, Methods of Homological Algebra, Springer-Verlag, Berlin, 1996.
7
H. Holm and P. Jørgensen, Semi-dualizing modules and related Gorenstein homological dimensions, J. Pure Appl. Algebra 205 (2006), no. 2, 423--445.
8
H. Holm and D. White, Foxby equivalence over associative rings, J. Math. Kyoto Univ. 47 (2007), no. 4, 781--808.
9
J. J. Rotman, An Introduction to Homological Algebra, Springer Universitext, Second Edition, New York, 2009.
10
S. Sather-Wagstaff, Semidualizing modules, http://www.ndsu.edu/pubweb/~ssatherw/DOCS/sdm.pdf
11
S. Sather-Wagstaff, T. Sharif and D. White, Stability of Gorenstein categories, J. Lond. Math. Soc. (2) 77 (2008), no. 2, 481--502.
12
R. Takahashi and D. White, Homological aspects of semidualizing modules, Math. Scand. 106 (2010), no. 1, 5--22.
13
D. White, Gorenstein projective dimension with respect to a semidualizing module, J. Commut. Algebra 2 (2010), no. 1, 111--137.
14
ORIGINAL_ARTICLE
Hyperstability of some functional equation on restricted domain: direct and fixed point methods
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
2016-08-01
959
974
Hyperstability
linear equation
quadratic equation
p-Wright affine function
fixed point theorem
A.
Bahyrycz
bahyrycza@gmail.com
1
AGH University of Science and Technology, Faculty of Applied Mathematics, Mickiewicza 30, 30-059 Krakow, Poland.
LEAD_AUTHOR
T. Aoki, On the stability of the linear transformation in Banach spaces, J. Math. Soc. Japan 2 (1950) 64--66.
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A. Bahyrycz and M. Piszczek, Hyperstability of the Jensen functional equation, Acta Math. Hungar. 142 (2014), no. 2, 353--365.
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B. Bouikhalene and E. Elqorachi, Ulam-Gavruta-Rassias stability of the Pexider functional equation, Int. J. Appl. Math. Stat. 7 (2007) 27--39.
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D. Bourgin, Approximately isometric and multiplicative transformations on continuous function rings, Duke Math. J. 16 (1949) 385--397.
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J. Brzdęk, J. Chudziak and Zs. Pales, A fixed point approach to stability of functional equations, Nonlinear Anal. 74 (2011), no. 17, 6728--6732.
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J. Brzdęk, Stability of the equation of the p-Wright affine functions, Aequationes Math. 85 (2013), no. 3, 497--503.
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J. Brzdęk and A. Fosner, Remarks on the stability of Lie homomorphisms, J. Math. Anal. Appl. 400 (2013), no. 2, 585--596.
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J. Brzdęk, Hyperstability of the Cauchy equation on restricted domains, Acta Math. Hungar. 141 (2013), no. 1-2, 58--67.
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L. Cadariu and V. Radu, Fixed point and the stability of Jensen's functional equation, JIPAM. J. Inequal. Pure Appl. Math. 4 (2003), Article ID 4, 7 pages.
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38
ORIGINAL_ARTICLE
On statistical type convergence in uniform spaces
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
2016-08-01
975
986
${\mathscr{F}}$-convergence
${\mathscr{F}}_{st}$- fundamentality
statistical convergence
a uniform space
B. T.
Bilalov
b_bilalov@mail.ru
1
Department of Non-harmonic analysis, Institute of Mathematics and Mechanics of NAS of Azerbaijan, 9, B.Vahabzade Str., AZ 1141, Baku, Azerbaijan.
LEAD_AUTHOR
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.
AUTHOR
S. Aytar and S. Pehlivan, Statistically monotonic and statistically bounded sequences of fuzzy numbers, Inform. Sci. 176, (2006), no. 6, 734--744.
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35
ORIGINAL_ARTICLE
Polynomial evaluation groupoids and their groups
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
2016-08-01
987
997
polynomial evaluation groupoids
group evaluation polynomial
group
H. S.
Kim
heekim@hanyang.ac.kr
1
Department of Mathematics, Research Institute for Natural Sciences, Hanyang University, Seoul 04763, Korea.
LEAD_AUTHOR
P. J.
Allen
pallen@as.ua.edu
2
Department of Mathematics, University of Alabama, Tuscaloosa, AL 35487-0350, USA.
AUTHOR
J.
Neggers
jneggers@as.ua.edu
3
Department of Mathematics, University of Alabama, Tuscaloosa, AL 35487-0350, USA.
AUTHOR
P. J. Allen, H. S. Kim and J. Neggers, Smarandache algebras and their subgroups, Bull. Iranian Math. Soc. 38 (2012), no. 4, 1063--1077.
1
T. W. Hungerford, Algebra, Holt, Rinehart and Winston, Inc., New York-Montreal, Que.-London, 1974.
2
ORIGINAL_ARTICLE
Strongly noncosingular modules
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
2016-08-01
999
1013
coclosed submodules
(non) cosingular modules
coatomic modules
Y.
Alagöz
yusufalagoz@iyte.edu.tr
1
İzmir Institute of Technology, Department of Mathematics, 35430, İzmir, Turkey.
AUTHOR
Y.
Durğun
yilmaz.durgun@math.uzh.ch
2
Bitlis Eren University, Department of Mathematics, 13000, Bitlis, Turkey.
LEAD_AUTHOR
F. W. Anderson and K. R. Fuller, Rings and Categories of Modules, Second edition. Graduate Texts in Mathematics, 13, Springer-Verlag, New York, 1992.
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G. Azumaya, Characterizations of semi-perfect and perfect modules, Math. Z., 140 (1974) 95--103.
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G. Baccella, Generalized V -rings and von Neumann regular rings, Rend. Sem. Mat. Univ. Padova 72 (1984) 117--133.
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E. Büyükaşik, and Y. Durgun, Coneat submodules and coneat-at modules, J. Korean Math. Soc., 51 (2014), no. 6, 1305--1319.
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G. F. Birkenmeier, J. K. Park and Y. S. Park, International Symposium on Ring Theory. Proceedings of the 3rd Korea-China-Japan Symposium and the 2nd Korea-Japan Joint Seminar held in Kyongju, Edited by Gary F. Birkenmeier, Jae Keol Park and Young Soo Park, Trends in Mathematics, Birkhäuser Boston, Inc., Boston, 2001.
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J. Clark, C. Lomp, N. Vanaja and R. Wisbauer, Lifting Modules, Birkhäuser Verlag, Basel, 2006.
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L. Fuchs, Neat submodules over integral domains, Period. Math. Hungar. 64 (2012), no. 2, 131--143.
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K. R. Goodearl, Singular torsion and the splitting properties, Memoirs of the American Mathematical Society, 124, Amer. Math.Soc., Providence, 1972.
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M. Harada, Nonsmall modules and noncosmall modules, Ring theory (Proc. Antwerp Conf. (NATO Adv. Study Inst.), Univ. Antwerp, Antwerp, 1978, 669--690, Lecture Notes in Pure and Appl. Math., 51, Dekker, New York, 1979.
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T. A. Kalati and D. . Tütüncü, A note on noncosingular lifting modules, Ukrainian Math. J. 64 (2013) no. 11, 1776--1779.
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F. Kasch, Moduln und Ringe, Mathematische Leitfaden, B. G. Teubner, Stuttgart, 1977.
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T. Y. Lam, A first course in noncommutative rings, Second edition, Graduate Texts in Mathematics, 131, Springer-Verlag, New York, 2001.
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T. Y. Lam, Lectures on modules and rings, Graduate Texts in Mathematics, 189,Springer-Verlag, New York, 1999.
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C. Lomp, On the splitting of the dual Goldie torsion theory, Algebra and its applications (Athens, OH, 1999), 377--386, Contemp. Math., 259, Amer. Math. Soc., Providence, 2000.
17
V. D. Nguyen, V. H. Dinh, P. F. Smith and R. Wisbauer, Extending Modules, John Wiley & Sons, Inc., New York, 1994.
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A. Tuganbaev, Max rings and V -rings, Handbook of algebra, 3, 565--584, North-Holland, Amsterdam, 2003.
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D. K. Tütüncü and R. Tribak, On T -noncosingular modules, Bull. Aust. Math. Soc. 80 (2009), no. 3, 462--471.
29
D. K. Tütüncü and N. O. Ertas, and Tribak, R. and Smith, P. F., Some rings for which the cosingular submodule of every module is a direct summand, Turkish J. Math. 38 (2014), no. 4, 649--657.
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R. Wisbauer, Foundations of Module and Ring Theory, Gordon and Breach, 1991.
32
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H. Zöschinger, Schwach-injektive moduln, Period. Math. Hungar. 52 (2006), no. 2, 105--128.
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H. Zöschinger, Koatomare Moduln, Math. Z. 170 (1980), no. 3, 221--232.
35
H. Zöschinger, Kosingulre und kleine Moduln, (German) Comm. Algebra 33 (2005), no.10, 3389--3404.
36
ORIGINAL_ARTICLE
On certain semigroups of transformations that preserve double direction equivalence
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
2016-08-01
1015
1024
Transformation semigroups
Equivalence
Green's *-relations
*-Ideal
Rees quotient semigroup
L.
Deng
denglunzhi@163.com
1
School of Mathematical Science, Guizhou Normal University, Guiyang 550001, China.
LEAD_AUTHOR
L. Z. Deng, J. W. Zeng and B. Xu, Green's relations and regularity for semigroups of transformations that preserve double direction equivalence, Semigroup Forum 80 (2010), no. 3, 416--425.
1
J. B. Fountain, Abundant semigroups, Proc. London Math. Soc. (3) 44 (1982), no. 1, 103--129.
2
J. A. Green, On the structure of semigroups, Ann. of Math. (2) 54 (1951) 136--172.
3
H. S. Pei and H. J. Zhou, Abundant semigroups of transformations preserving an equivalence relation, Algebra Colloq. 18 (2011), no. 1, 77--82.
4
A. Umar, On certain infinite semigroups of order-decreasing transformations, Comm. Algebra 25 (1997), no. 9, 2987--2999.
5
A. Umar, On the semigroups of order-decreasing finite full transformations, Proc. Roy. Soc. Edinburgh Sect. A 120 (1992), no. 1-2, 129--142.
6