ORIGINAL_ARTICLE
Total perfect codes, OO-irredundant and total subdivision in graphs
Let $G=(V(G),E(G))$ be a graph, $\gamma_t(G)$. Let $ooir(G)$ be the total domination and OO-irredundance number of $G$, respectively. A total dominating set $S$ of $G$ is called a $\textit{total perfect code}$ if every vertex in $V(G)$ is adjacent to exactly one vertex of $S$. In this paper, we show that if $G$ has a total perfect code, then $\gamma_t(G)=ooir(G)$. As a consequence, we determine the value of $ooir(G)$ for some classes of graphs.
http://bims.iranjournals.ir/article_778_fa2994302d0b573b33b69934d84dde37.pdf
2016-06-01
499
506
Total domination number
OO- irredundance number
total subdivision number
H.
Hosseinzadeh
hamideh.hosseinzadeh@gmail.com
1
Department of Mathematics, Alzahra University, P.O. Box 19834, Tehran, Iran.
AUTHOR
N.
Soltankhah
soltan@alzahra.ac.ir
2
Department of Mathematics, Alzahra University, P.O. Box 19834, Tehran, Iran.
LEAD_AUTHOR
E. J. Cockayne, S. Finbow and J. S. Swarts, OO-irredundance and maximum degree in paths and trees, J. Combin. Math. Combin. Comput. 73 (2010) 223--236.
1
O. Favaron, H. Karami and S. M. Sheikholeslami, Bounding the total domination subdivision number of a graph in terms of its order, J. Comb. Optim. 21 (2011), no. 2, 209--218.
2
H. Gavlas and K. Schultz, Efficient open domination. The Ninth Quadrennial International Conference on Graph Theory, Combinatorics, Algorithms and Applications, 11 pages, Electron. Notes Discrete Math., 11, Elsevier Sci. B. V., Amsterdam, 2002.
3
T. W. Haynes, S. M. Hedetniemi, S. T. Hedetniemi, D. P. Jacobs, J. Knisely and L. C. van der Merwe, Domination subdivision numbers, Discuss. Math. Graph Theory 21 (2001), no. 2, 239--253.
4
T. W. Haynes, S. T. Hedetniemi and P. J. Slater, Fundamentals of domination in graphs, Monographs and Textbooks in Pure and Applied Mathematics, Marcel Dekker, Inc., New York, 1998.
5
T. W. Haynes, S. T. Hedetniemi and L. C. van der Merwe, Total domination subdivision numbers, J. Combin. Math. Combin. Comput. 44 (2003) 115--128.
6
M. A. Henning, A survey of selected recent results on total domination in graphs, Discrete Math. 309 (2009), no. 1, 32--63.
7
M. A. Henning and A. Yeo, Total Domination in Graphs, Monographs in Mathematics, Springer, New York, 2013.
8
W. F. Klostermeyer and J. L. Goldwasser, Total perfect codes in grid graphs, Bull. Inst. Combin. Appl. 46 (2006) 61--68.
9
J. Lee, Independent perfect domination sets in Cayley graphs, J. Graph Theory 37 (2001), no. 4, 213--219.
10
N. Soltankhah, On the total domination subdivision numbers of grid graphs, Int. J. Contemp. Math. Sci. 5 (2010), no. 49-52, 2419--2432.
11
N. Soltankhah, Results on total domination and total restrained domination in grid graphs, Int. Math. Forum 5 (2010), no. 5-8, 319--332.
12
ORIGINAL_ARTICLE
The theory of matrix-valued multiresolution analysis frames
A generalization of matrix-valued multiresolution analysis (MMRA) to matrix-valued frames, and the constructions of matrix-valued frames are considered and characterized. A matrix-valued frame multiresolution analysis is defined in this paper. We provide necessary and sufficient conditions for constructing matrix-valued frames and Riesz bases of translates, and give the calculation method of matrix-valued dual Riesz basis. These conclusions are useful in providing theoretical basis for constructing matrix-valued frames and Riesz basis.
http://bims.iranjournals.ir/article_779_bb10aaa73cdd7d1d0904b351010f3dbf.pdf
2016-06-01
507
519
Matrix-valued wavelet
frame
wavelets
matrix-valued dual Riesz basis
P.
Zhao
pingzhao@bjtu.edu.cn
1
School of Science, Beijing Jiaotong University, Beijing, 100044, China.
LEAD_AUTHOR
C.
Zhao
yczhaochun@163.com
2
Faculty of Mathematics Science , Tianjin normal University, Tianjin, 300074, China
AUTHOR
A. S. Antolin and R. A. Zalik, Matrix-valued wavelets and multiresolution analysis, J. Appl. Funct. Anal. 7 (2012), no. 1-2, 13--25.
1
J. J. Benedetto and S. Li, The theory of multiresolution analysis frames and applications to filter banks, Appl. Comput. Harmon. Anal. 5 (1998), no. 4, 389--427.
2
Q. Chen, Z. X. Cheng and C. L. Wang, Existence and construction of compactly supported biorthogonal multiple vector-valued wavelets, J. Appl. Math. Comput. 22 (2006), no. 3, 101--115.
3
Q. Chen and Z. Shi, Construction and properties of orthogonal matrix valued waveletsand wavelet packets, Chaos, Solitons Fractals 37 (2008), no. 1 , 75--86.
4
L. Cui, B. Zhai and T. Zhang, Existence and design of biorthogonal matrix-valued wavelets, Nonlinear Anal. Real World Appl. 10 (2009), no. 5, 2679--2687.
5
J. Geronimo, D. P. Hardin and P. Massopust, Fractal functions and wavelet expansions based on several scaling functions, J. Approx. Theory 78 (1994), no. 3, 373--401.
6
P. Ginzberg and A. T. Walden, Matrix-valued and quaternion wavelets, IEEE Trans. Signal Process. 61 (2013), no. 6, 1357--1367.
7
Q. Jiang, On the design of multifilter banks and orthonormal multiwavelet bases, IEEE Trans. Signal Process. 46 (1998) 3292--3303.
8
W. Li and P. Zhao, A study on minimum-energy vector-valued wavelets tight frames, International Conference on Information Science and Technology (2012) 436--440.
9
A. Ron and Z. Shen, Frames and stable bases for shift-invariant subspaces of L2(Rd), Canad. J. Math. 47 (1995), no. 5, 1051--1094.
10
F. A. Shah and N. A. Sheikh, Construction of vector-valued multivariate wavelet frame packets, Thai J. Math. 10 (2012), no. 2, 401--414.
11
K. Slavakis and I. Yamada, Biorthogonal unconditional bases of compactly supported matrix valued wavelets, Numer. Funct. Anal. Optim. 22 (2001), no. 1-2, 223--253.
12
A. T. Walden and A. Serroukh, Wavelet analysis of matrix-valued time series, R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci. 458 (2002), no. 2017, 157--179.
13
X. G. Xia and B.W. Suter, Vector-valued wavelets and vector filter banks, IEEE Trans. Signal Process, 44 (1996) 508--518.
14
X. G. Xia, Orthonormal matrix valued wavelets and matrix Karhunen-Love expansion. Wavelets, multiwavelets, and their applications (San Diego, CA, 1997), 159--175, Contemp. Math., 216, Amer. Math. Soc., Providence, 1998.
15
R. Young, An introduction to nonharmonic Fourier series, Academic Press, Inc., New York, 1980.
16
P. Zhao, C. Zhao and P. G. Casazza, Perturbation of regular sampling in shift-invariant spaces for frames, IEEE Trans. Inf. Theory 52 (2006), no. 10, 4643--4648.
17
P. Zhao, G. Liu and C. Zhao, A matrix-valued wavelet KL-like expansion for wide-sense stationary random processes, IEEE Trans. Signal Process. 52 (2004), no. 4, 914--920.
18
ORIGINAL_ARTICLE
Polynomially bounded solutions of the Loewner differential equation in several complex variables
We determine the form of polynomially bounded solutions to the Loewner differential equation that is satisfied by univalent subordination chains of the form $f(z,t)=e^{\int_0^t A(\tau){\rm d}\tau}z+\cdots$, where $A:[0,\infty]\rightarrow L(\mathbb{C}^n,\mathbb{C}^n)$ is a locally Lebesgue integrable mapping and satisfying the condition $$\sup_{s\geq0}\int_0^\infty\left\|\exp\left\{\int_s^t [A(\tau)-2m(A(\tau))I_n]\rm {d}\tau\right\}\right\|{\rm d}t<\infty,$$ and $m(A(t))>0$ for $t\geq0$, where $m(A)=\min\{\mathfrak{Re}\left\langle A(z),z\right\rangle:\|z\|=1\}$. We also give sufficient conditions for $g(z,t)=M(f(z,t))$ to be polynomially bounded, where $f(z,t)$ is an $A(t)$-normalized polynomially bounded Loewner chain solution to the Loewner differential equation and $M$ is an entire function. On the other hand, we show that all $A(t)$-normalized polynomially bounded solutions to the Loewner differential equation are Loewner chains.
http://bims.iranjournals.ir/article_777_1bac89a6fb0e82c7a49584552cbe52f2.pdf
2016-06-01
521
537
Biholomorphic mapping
Loewner differential equation
polynomially bounded
subordination chain
parametric representation.
A.
Ebadian
a.ebadian@urmia.ac.ir
1
Department of Mathematics, Payame Noor University, P.O. Box 19395-3697, Tehran, Iran.
AUTHOR
S.
Rahrovi
sarahrovi@gmail.com
2
Department of Mathematics, Faculty of Basic Science, University of Bonab, P.O. Box 5551-761167, Bonab, Iran.
AUTHOR
S.
Shams
sa40shams@yahoo.com
3
Department of Mathematics, Urmia University, Urmia, Iran.
AUTHOR
J.
Sokol
jsokol@prz.edu.pl
4
Department of Mathematics, Rzesz'ow University of Technology, Poland.
LEAD_AUTHOR
L. Arosio, F. Bracci, H. Hamada and G. Kohr, An abstract approach to Loewner chains, J. Anal. Math. 119 (2013) 89--114.
1
J. Becker, Lownersche differentialgleichung und schlichtheitskriterien, Math. Ann. 202 (1973) 321--335.
2
J. Becker, Uber die Losungsstruktur einer differentialgleichung in der konformen abbildung, J. Reine Angew. Math. 285 (1976) 66--74.
3
F. Bracci, M. D. Contreras and S. D. Madrigal, Evolution families and the Loewner equation II, Complex hyperbolic manifolds, Math. Ann. 344 (2009), no. 4, 947--962.
4
N. Dunford and J. T. Schwartz, Linear Operators, I, John Wiley & Sons, Inc., New York, 1988.
5
P. Duren, I. Graham, H. Hamada and G. Kohr, Solutions for the generalized Loewner differential equation in several complex variables, Math. Ann. 347 (2010), no. 2, 411--435.
6
M. Elin, S. Reich and D. Shoikhet, Complex dynamical systems and the geometry of domains in Banach spaces, Dissertationes Math. 427 (2004) 62 pages.
7
I. Graham, H. Hamada and G. Kohr, Parametric representation of univalent mappings in several complex variables, Canad. J. Math. 54 (2002), no. 2, 324--351.
8
I. Graham, H. Hamada, G. Kohr and M. Kohr, Spirallike mappings and univalent subordination chains in Cn, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 7 (2008), no. 4, 717--740.
9
I. Graham, H. Hamada, G. Kohr and M. Kohr, Asymptotically spirallike mappings in several complex variables, J. Anal. Math. 105 (2008) 267--302.
10
I. Graham, H. Hamada, G. Kohr and M. Kohr, Parametric representation and asymptotic starlikeness in Cn, Proc. Amer. Math. Soc. 136 (2008), no. 11, 3963--3973.
11
I. Graham and G. Kohr, Geometric function theory in one and higher dimensions, Marcel Dekker, Inc., New York, 2003.
12
I. Graham, G. Kohr and M. Kohr, Loewner chains and prametric representation in several complex variables, J. Math. Anal. Appl. 281 (2003), no. 2, 425--438.
13
I. Graham, G. Kohr and J. A. Pfaltzgraff, The general solution of the Loewner differential equation on the unit ball in Cn, Contemp. Math. 382, Amer. Math. Soc., Providence, 2005.
14
S. Gong, Convex and starlike mappings in several complex variables, With a preface by David Minda. Mathematics and its Applications (China Series), 435, Kluwer Academic Publishers, Dordrecht, Science Press, Beijing, 1998.
15
K. E. Gustafson and O. K. M. Rao, Numerical range, The field of values of linear operators and matrices, Universitext, Springer-Verlag, New York, 1997.
16
H. Hamada, Polynomially bounded solutions to the Loewner differential equation in several complex variables, J. Math. Anal. Appl. 381 (2011), no. 1, 179--186.
17
H. Hmada and G. Kohr, Subordination chains and the growth theorem of spirallike mappings, Mathematica 42(65) (2000), no. 2, 153--161.
18
G. Kohr, Kernel convergence and biholomorphic mappings in several complex variables, Int. J. Math. Math. Sci. 2003 (2003), no. 67, 4229--4239.
19
E. Kubicka and T. Poreda, On the parametric representation of starlike maps of the unit ball in Cn into Cn, Demonstratio Math. 21 (1988), no. 2, 345--355.
20
J. A. Pfaltzgraff, Subordination chains and univalence of holomorphic mappings in Cn, Math. Ann. 210 (1974) 55--68.
21
J. A. Pfaltzgraff, Subordination chains and quasiconformal extension of holomorphic maps in Cn, Ann. Acad. Sci. Fenn. Ser. A I Math. 1 (1975) 13--25.
22
C. Pommereneke, Univalent functions, Vandenhoeck and Ruprecht, Gottingen, 1975
23
T. Poreda, On the univalent holomorphic maps of the unit polydisc in Cn which have the prametric representation, I- the geometrical properties, Ann. Univ. Mariae Curie Sk lodowska, Sect. A. 41 (1987) 105--113.
24
T. Poreda, On the univalent holomorphic maps of the unit polydisc in Cn which have the prametric representation, II- the necessary conditions and the sufficient conditions, Ann. Univ. Mariae Curie Sk lodowska, Sect. A. 41 (1987) 115--121.
25
T. Poreda, On the univalent subordination chains of holomorphic mappings in Banach spaces, Comment. Math. Prace Mat. 28 (1989), no. 2, 295--304.
26
T. Poreda, On generalized differential equations in Banach spaces, Dissertationes Math. 310 (1991) 50 pages.
27
S. Rahrovi, A. Ebadian and S. Shams, The non-normalized subordination chains with asymptotically spirallike mapping in several complex variables, General Math. 21 (2013), no. 2, 17--46.
28
S. Reich and D. Shoikhet, Nonlinear semigroups, Fixed points, and Geometry of Domains in Banach Spaces, Imperial College Press, London, 2005.
29
T. J. Suffridge, Starlikeness, convexity and other geometric properties of holomorphic maps in higher dimensions, Complex analysis (Proc. Conf., Univ. Kentucky, Lexington, Ky., 1976), 146--159. Lecture Notes in Math., 599, Springer, Berlin, 1977.
30
M. Voda, Solution of a Loewner chain equation in several complex variables, J. Math. Anal. Appl. 375 (2011), no. 1, 58--74.
31
ORIGINAL_ARTICLE
$k$-power centralizing and $k$-power skew-centralizing maps on triangular rings
Let $\mathcal A$ and $\mathcal B$ be unital rings, and $\mathcal M$ be an $(\mathcal A, \mathcal B)$-bimodule, which is faithful as a left $\mathcal A$-module and also as a right $\mathcal B$-module. Let ${\mathcal U}=Tri(\mathcal A, \mathcal M, \mathcal B)$ be the triangular ring and ${\mathcal Z}({\mathcal U})$ its center. Assume that $f:{\mathcal U}\rightarrow{\mathcal U}$ is a map satisfying $f(x+y)-f(x)-f(y)\in{\mathcal Z}({\mathcal U})$ for all $x,\ y\in{\mathcal U}$ and $k$ is a positive integer. It is shown that, under some mild conditions, the following statements are equivalent: (1) $[f(x),x^k]\in{\mathcal Z}({\mathcal U})$ for all $x\in{\mathcal U}$; (2) $[f(x),x^k]=0$ for all $x\in{\mathcal U}$; (3) $[f(x),x]=0$ for all $x\in{\mathcal U}$; (4) there exist a central element $z\in{\mathcal Z}({\mathcal U})$ and an additive modulo ${\mathcal Z}({\mathcal U})$ map $h:{\mathcal U}\rightarrow{\mathcal Z}({\mathcal U})$ such that $f(x)=zx+h(x)$ for all $x\in{\mathcal U}$. It is also shown that there is no nonzero additive $k$-skew-centralizing maps on triangular rings.
http://bims.iranjournals.ir/article_776_5f93e5da86761d28483d66373943f57e.pdf
2016-06-01
539
554
Triangular rings
centralizing maps
$k$-skew-centralizing maps
nest algebras
X. F.
Qi
xiaofeiqisxu@aliyun.com
1
Department of Mathematics, Shanxi University, Taiyuan 030006, P. R. China.
LEAD_AUTHOR
H. E. Bell and J. Lucier, On additive maps and commutativity in rings, Result Math.36 (1999), no. 1-2, 1--8.
1
M. Brešar, Centralizing mappings on von Neumann algebras, Proc. Amer. Math. Soc. 111 (1991), no. 2, 501--510.
2
M. Brešar, On skew-commuting mappings of rings, Bull. Austral. Math. Soc. 47 (1993), no. 2, 291--296.
3
M. Brešar, Centralizing mappings and derivations in prime rings, J. Algebra 156 (1993), no. 2, 385--394.
4
M. Brešar, On generalized biderivations and related maps, J. Algebra 172 (1995), no. 3, 764--786.
5
M. Brešar, Commuting maps: a survey, Taiwanese J. Math. 8 (2004), no. 3, 361--397.
6
M. Brešar and B. Hvala, On additive maps of prime rings, Bull. Austral. Math. Soc. 51 (1995), no. 3, 377--381.
7
C. W. Chen, M. T. Koşan and T. K. Lee, Decompositions of quotient rings and m-power commuting maps, Comm. Algebra 41 (2011), no. 5, 1865--1871.
8
W. S. Cheung, Commuting maps of triangular algebras, J. London Math. Soc. (2) 63 (2001), no. 1, 117--127.
9
K. R. Davidson, Nest Algebras, Pitman Research Notes in Mathematics, John Wiley & Sons, Inc., New York, 1988
10
N. Divinsky, On commuting automorphisms of rings, Trans. Roy. Soc. Canad. Sect. III (3) 49 (1955) 19--22.
11
Y. Q. Du and Y.Wang, k--commuting maps on triangular algebras, Linear Algebra Appl. 436 (2012), no. 5, 1367--1375.
12
H. G. Inceboz, M. T. Koşan and T. K. Lee, m-power commuting maps on semiprime rings, Comm. Algebra 42 (2014), no. 3, 1095--1110.
13
C. Lanski, An Engel condition with derivation, Proc. Amer. Math. Soc. 118 (1993) 75--80.
14
C. Lanski, An Engel condition with derivation for left ideals, Proc. Amer. Math. Soc. 125 (1997), no. 2, 339--345.
15
X. F. Qi and J. C. Hou, Characterization of k-commuting additive maps on rings, Linear Algebra Appl. 468 (2015) 48--62.
16
J. Vukman, Commuting and centralizing mappings in prime rings, Proc. Amer. Math. Soc. 109 (1990), no. 1, 47--52.
17
ORIGINAL_ARTICLE
On radical formula and Prufer domains
In this paper we characterize the radical of an arbitrary submodule $N$ of a finitely generated free module $F$ over a commutatitve ring $R$ with identity. Also we study submodules of $F$ which satisfy the radical formula. Finally we derive necessary and sufficient conditions for $R$ to be a Pr$\ddot{\mbox{u}}$fer domain, in terms of the radical of a cyclic submodule in $R\bigoplus R$.
http://bims.iranjournals.ir/article_797_18ddba9d7a3f373b64964a1c3fa7e85c.pdf
2016-06-01
555
563
Prime submodules
Radical of a submodule
Radical formula
Pr$ddot{mbox{u}}$fer domains
Dedekind domains
R.
Nekooei
rnekooei@uk.ac.ir
1
Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, P.O. Box 76169133, Kerman, Iran.
LEAD_AUTHOR
F.
Mirzaei
mirzaee0269@yahoo.com
2
Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, P.O. Box 76169133, Kerman, Iran.
AUTHOR
A. Azizi, Radical formula and prime submodules, J. Algebra 307 (2007), no. 1, 454--460.
1
D. Buyruk and D. P. Yilmaz, Modules over Pufer domains which satisfy the radical formula, Glasg. Math. J. 49 (2007), no. 1, 127--131.
2
S. Ceken and M. Alkan, On radical formula over free modules with two generators, Numerical Analysis and Applied Mathematics ICNAAM (2011) 333--336.
3
L. Fuchs and L. Salce, Modules over non-Noetherian domains, Mathematical Surveys and Monographs, American Mathematical Society, Providence, 2001.
4
R. Gilmer, Multiplicative Ideal Theory, Marcel Dekker, Inc., New York, 1972.
5
J. Jenkins and P. F. Smith, On the prime radical of a module over a commutative ring, Comm. Algebra 20 (1991), no. 12, 3593--3602.
6
K. H. Leung and S. H. Man, On commutative Noetherian rings which satisfy the radical formula, Glasgow Math. J. 39 (1997), no. 3, 285--293.
7
F. Mirzaei and R. Nekooei, On prime submodules of a finitely generated free module over a commutative ring, Communications In Algebra, Accepted.
8
A. Parkash, Arithmetical rings satisfy the radical formula, J. Commutative Algebra (2013), no. 2, 293--296.
9
H. Sharif, Y. Sharifi and S. Namazi, Rings satisfying the radical formula, Acta Math. Hungar. 71 (1996), no. 1-2, 103--108.
10
D. P. Yilmaz and P. F. Smith, Radical of submodules of free modules, Comm. Algebra 27 (1999), no. 5, 2253--2266.
11
ORIGINAL_ARTICLE
On cohomogeneity one nonsimply connected 7-manifolds of constant positive curvature
In this paper, we give a classification of non simply connected seven dimensional Reimannian manifolds of constant positive curvature which admit irreducible cohomogeneity-one actions. We characterize the acting groups and describe the orbits. The first and second homo-topy groups of the orbits have been presented as well.
http://bims.iranjournals.ir/article_798_57c6204c6001577ab8221c3c84ec415c.pdf
2016-06-01
565
584
Positively curved manifold
irreducible representation
cohomogeneity one action
M.
Zarei
masoumeh.zarei@modares.ac.ir
1
Department of Pure Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, P.O. Box 14115-134, Tehran, Iran.
AUTHOR
S.M.B.
Kashani
kashanism@yahoo.com
2
Tarbiat Modares University
LEAD_AUTHOR
H.
Abedi
h.abedi@basu.ac.ir
3
Mathematics Group, School of Sciences Bu-Ali Sina University, Hamedan, Iran.
AUTHOR
H. Abedi and S. M. B. Kashani, Cohomogeneity one Riemannian manifolds of constant positive curvature, J. Korean Math. Soc. 44 (2007), no. 4, 799--807.
1
G. E. Bredon, Introduction to Compact Transformation Groups, Academic Press, New York-London, 1972.
2
T. Brocker, T. Dieck, Representations of Compact Lie Groups, Springer-Verlag, New York, 1985.
3
F. Fang, Collapsed 5-manifolds with pinched positive sectional curvature, Adv. Math. 221 (2009), no. 3, 830--860.
4
K. Grove, B. Wilking and W. Ziller, Positively curved cohomogeneity one manifolds and 3-sasakian geometry, J. Differential Geom. 78 (2008), no. 1, 33--111.
5
B. C. Hall, Lie Groups, Lie Algebras, and Representations, Springer-Verlag, New York, 2003.
6
C. A. Hoelscher, Classification of cohomogeneity one manifolds in low dimensions, Pacific J. Math. 246 (2010), no. 1, 129--185.
7
H. Reckziegel, Horizontal lifts of isometric immersions into the bundle space of a pseudoRiemannian submersion, Global Differential Geometry and Global Analysis (1984), Lecture Notes in Mathematics, 1156 (1985), 264--279.
8
F. Mercuri, P. Piccione and D. Tausk, Stability of the Focal and the Geometric Index in semi Riemannian Geometry via the Maslov Index, Technical Report RT-MAT 99-08, Mathematics Department, University of Sao Paulo, Brazil, (1999).
9
W. D. Neumann, 3-Dimensional G-Manifolds with 2-dimensional prbits, Proc. Conf. on Transformation Groups (1968) 220--222.
10
B. O'Neill, Semi Riemannain Geometry, Accademic Press, Inc., California, 1983.
11
J. Parker, 4-dimensional G-manifolds with 3-dimensional orbit, Pacific J. Math. 125 (1986), no. 1, 187--204.
12
F. Podesta and L. Verdiani, Positively curved 7-dimensional manifolds, Quart. J. Math. Oxford 50 (1999) 494--507.
13
X. Rong, On the fundamental groups of compact manifolds of positive sectional curvature. Ann. of Math. (2) 143 (1996), no. 2, 397--411.
14
C. Searle, Cohomogeneity and positive curvature in low dimensions, Math. Z. 214 (1993), no. 3, 491--498.
15
K. Shankar, On the fundamental group of positively curved manifolds, J. Differential Geom. 49 (1998), no. 1, 179--182.
16
E. Straume, Compact connected Lie transformation groups on spheres with low cohomogeneity, I, Mem. Amer. Math. Soc. 119 (1996), no. 569, 93 pages.
17
L. Verdiani, cohomogeneity one Riemannian manifolds of even dimension with strictly positive curvature, I, Math. Z. 241 (2002), no. 2, 329--339.
18
L. Verdiani, cohomogeneity one manifolds of even dimension with strictly positive sectional curvature, J. Differential Geom. 68 (2004), no. 1, 31--72.
19
J. A. Wolf, Spaces of Constant Curvature, McGraw-Hill Book Co., New York-London-Sydney, 1967.
20
W. Ziller, Lie Groups, Representation Theory and Symmetric Spaces, Unpublished note, http://www.math.upenn.edu/wziller/math650/LieGroupsReps.pdf.
21
W. Ziller, On the geometry of cohomogeneity one manifolds with positive curvature, Riemannian topology and geometric structures on manifolds, 233--262, Progr. Math., 271, Birkhäuser Boston, Boston, 2009.
22
ORIGINAL_ARTICLE
Complete characterization of the Mordell-Weil group of some families of elliptic curves
The Mordell-Weil theorem states that the group of rational points on an elliptic curve over the rational numbers is a finitely generated abelian group. In our previous paper, H. Daghigh, and S. Didari, On the elliptic curves of the form $ y^2=x^3-3px$, Bull. Iranian Math. Soc. 40 (2014), no. 5, 1119--1133., using Selmer groups, we have shown that for a prime $p$ the rank of elliptic curve $y^2=x^3-3px$ is at most two. In this paper we go further, and using height function, we will determine the Mordell-Weil group of a family of elliptic curves of the form $y^2=x^3-3nx$, and give a set of its generators under certain conditions. We will introduce an infinite family of elliptic curves with rank at least two. The full Mordell-Weil group and the generators of a family (which is expected to be infinite under the assumption of a standard conjecture) of elliptic curves with exact rank two will be described.
http://bims.iranjournals.ir/article_799_3ad7f75a4be58868ac2adcc0d33b1d9f.pdf
2016-06-01
585
594
Elliptic Curve
Mordell-Weil Group
Generators
Height Function
H.
Daghigh
hassan@kashanu.ac.ir
1
Faculty of Mathematical Sciences, University of Kashan, P.O. Box 8731751167, Kashan, Iran.
LEAD_AUTHOR
S.
Didari
somayeh_didari@yahoo.com
2
Faculty of Mathematical Sciences, University of Kashan, P.O. Box 8731751167, Kashan, Iran.
AUTHOR
V. Bouniakowski, Sur les diviseurs numeriques invariables des functions rationelles entieres, Mem. Acad. Sci. St. Petersburg 6 (1857) 305--309.
1
H. Cohen, A Course in Computational Algebraic Number Theory, Springer-Verlag, Berlin, 1993.
2
J. Cannon, MAGMA Computational Algebra System, http://magma.maths.usyd.edu.au/magma/handbook/.
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H. Daghigh, and S. Didari, On the elliptic curves of the form y2 = x3 -3px , Bull. Iranian Math. Soc. 40 (2014), no. 5, 1119--1133.
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Y. Fujita, N. Terai, Generators for the elliptic curve y2 = x3 -nx, J. Theor. Nombres Bordeaux 23 (2011), no. 2, 403--416.
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Y. Fujita, Generators for the elliptic curve y2 = x3-nx of rank at least three, J. Number Theory 133 (2013), no. 5, 1645--1662.
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C. Hooley, On the power-free values of polynomials in two variables, Analytic number theory, 235--266, Cambridge University Press, Cambridge, 2009.
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J. Hoffstein, J. Pipher and J. H. Silverman, An Introduction to Mathematical Cryptography (Undergraduate Texts in Mathematics), Springer, New York, 2008.
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A. W. Knapp, Elliptic Curves, Princeton University Press, Princeton, 1992.
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T. Nagell, Zur Arithmetik der polynome, Abhandl. Math. Sem. Hamburg 1 (1922) 179--194.
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J. H. Silverman, The Arithmetic of Elliptic Curves, Graduate Texts in Mathematics, 106, Springer, Dordrecht, 2009.
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L. C. Washington, Elliptic curves: Number Theory and Cryptography, Chapman & Hall/CRC, Boca Raton, 2008.
18
ORIGINAL_ARTICLE
Involutiveness of linear combinations of a quadratic or tripotent matrix and an arbitrary matrix
In this article, we characterize the involutiveness of the linear combination of the forma1A1 +a2A2 when a1, a2 are nonzero complex numbers, A1 is a quadratic or tripotent matrix,and A2 is arbitrary, under certain properties imposed on A1 and A2.
http://bims.iranjournals.ir/article_800_4cbebc1a2c9731758eba450931c50d7d.pdf
2016-06-01
595
610
Quadratic matrix
involutive matrix
linear combination
X.
Liu
xiaojiliu72@126.com
1
College of Science, Guangxi University for Nationalities, Nanning 530006, P. R. China.
AUTHOR
J.
Benitez
jbenitez@mat.upv.es
2
Departamento de Matematica Aplicada, Instituto de Matematica Multidisciplinar, Universidad Politecnica de Valencia, Valencia 46022, Spain.
LEAD_AUTHOR
M.
Zhang
zhangmiao198658@163.com
3
College of Science, Guangxi University for Nationalities, Nanning 530006, P. R. China.
AUTHOR
M. Aleksiejczyk and A. Smoktunowicz, On properties of quadratic matrices, Math. Pannon. 11 (2000), no. 2, 239--248.
1
J. K. Baksalary, O. M. Baksalary and G. P. H. Styan, Idempotency of linear combinations of an idempotent and a tripotent matrix, Linear Algebra Appl. 354 (2002) 21--34.
2
J. K. Baksalary, O. M. Baksalary and H. Özdemir, A note on linear combinations of commuting tripotent matrices, Linear Algebra Appl. 388 (2004) 45--51.
3
J. K. Baksalary and O. M. Baksalary, When is a linear combination of two idempotent matrices the group involutory matrix?, Linear Multilinear Algebra 54 (2006), no. 6, 429--435.
4
A. Ben-Israel and T. N. E. Greville, Generalized Inverses: Theory and Applications, Wiley-Interscience, 2nd edition, New York, 1974.
5
J. Bentez and N. Thome, fkg-group periodic matrices, SIAM J. Matrix Anal. Appl. 28 (2005), no. 1, 9--25.
6
J. Bentez, X. Liu and T. Zhu, Nonsingularity and group invertibility of linear combinations of two k-potent matrices, Linear Multilinear Algebra 58 (2010)), no. 7-8, 1023--1035.
7
D. S. Cvetkovic-Ilic and C. Y. Deng, The Drazin invertibility of the difference and the sum of two idempotent operators, J. Comput. Appl. Math. 233 (2010), no. 8, 1717--1722.
8
C. Y. Deng, On properties of generalized quadratic operators, Linear Algebra Appl. 432 (2010), no. 4, 847--856.
9
C. Y. Deng, Characterizations and representations of the group inverse involving idempotents, Linear Algebra Appl. 434 (2011), no. 4, 1067--1079.
10
C. Y. Deng, On the Drazin inverses involving power commutativity, J. Math. Anal. Appl. 378 (2011), no. 1, 314--323.
11
C. Y. Deng, D.S. Cvetkovic-Ilic, Y. Wei, On invertibility of combinations of k-potent operators, Linear Algebra Appl. 437 (2012), no. 1, 376--387.
12
C. Y. Deng, Characterizations of the commutators and the anticommutator involving idempotents, Appl. Math. Comput. 221 (2013) 351--359.
13
R. A. Horn and C. R. Johnson, Matrix Analysis, Cambridge University Press, Cambridge, 1985.
14
X. Liu and J. Bentez, The spectrum of matrices depending on two idempotents, Appl. Math. Lett. 24 (2011), no. 10, 1640--1646.
15
X. Liu, L. Wu and J. Bentez, On the group inverse of linear combinations of two group invertible matrices, Electron. J. Linear Algebra 22 (2011) 490--503.
16
X. Liu, L. Wu and Y. Yu, The group inverse of the combinations of two idempotent matrices, Linear Multilinear Algebra 59 (2011), no. 1, 101--115.
17
S. K. Mitra, P. Bhimasankaram and S. B Malik, Matrix Partial Orders, Shorted Operators And Applications, World Scientiic Publishing Co., Hackensack, 2010.
18
H. Özdemir and T. Petik, On the spectra of some matrices derived from two quadratic matrices, Bull. Iranian Math. Soc. 39 (2013), no. 2, 225--238.
19
H. Özdemir, M. Sarduvan, A. Y. Özban and N. Guler, On idempotency and tripotency of linear combinations of two commuting tripotent matrices, Appl. Math. Comput. 207 (2009), no. 1, 197--201.
20
C. R. Rao and S. K. Mitra, Generalized Inverse of Matrices and Its Applications, John Wiley & Sons, Inc., New York-London-Sydney, 1971.
21
M. Sarduvan and H. Özdemir, On linear combinations of two tripotent, idempotent, and involutive matrices, Appl. Math. Comput. 200 (2008), no. 1, 401--406.
22
ORIGINAL_ARTICLE
Infinitely many solutions for a bi-nonlocal equation with sign-changing weight functions
In this paper, we investigate the existence of infinitely many solutions for a bi-nonlocal equation with sign-changing weight functions. We use some natural constraints and the Ljusternik-Schnirelman critical point theory on C1-manifolds, to prove our main results.
http://bims.iranjournals.ir/article_801_4e0cfaca570cffce5b5d67eec547dff4.pdf
2016-06-01
611
626
Infinitely many solutions
Nehari manifold
sign-changing weight function
Bi-nonlocal equation
Y.
Jalilian
y.jalilian@razi.ac.ir
1
Department of Mathematics, Razi University, Kermanshah, Iran.
LEAD_AUTHOR
C. O. Alves and F. J. S. A. Corrêa, On existence of solutions for a class of problem involving a nonlinear operator, Comm. Appl. Nonlinear Anal. 8 (2001), no. 2, 43--56.
1
C. O. Alves, F. J. S. A. Corrêa and T. F. Ma, Positive solutions for a quasilinear elliptic equation of Kirchhoff type, Comput. Math. Appl. 49 (2005), no. 1, 85--93.
2
G. Anello, A uniqueness result for a nonlocal equation of Kirchhoff type and some related open problem, J. Math. Anal. Appl. 373 (2011), no. 1, 248--251.
3
G. Anello, On a perturbed Dirichlet problem for a nonlocal differential equation of Kirchhoff type, Bound. Value Probl. 2011 (2011), Article ID 891430, 10 pages.
4
K. J. Brown and Y. Zhang, The Nehari manifold for a semilinear elliptic equation with a sign-changing weight function, J. Differential Equations 193 (2003), no. 2, 481--499.
5
A. Bonnet, A deformation lemma on a C1 manifold, Manuscripta Math. 81 (1993), no. 3-4, 339--359.
6
C. Y. Chen, Y. C. Kuo and T. F. Wu, The Nehari manifold for a Kirchhoff type problem involving sign-changing weight functions, J. Differential Equations 250 (2011), no, 4, 1876--1908.
7
S. J. Chen and L. Li, Multiple solutions for the nonhomogeneous Kirchhoff equation on RN, Nonlinear Anal. Real World Appl. 14 (2013), no. 3, 1477--1486.
8
B. Cheng, New existence and multiplicity of nontrivial solutions for nonlocal elliptic Kirchhoff type problems, J. Math. Anal. Appl. 394 (2012), no. 2, 488--495.
9
M. Chipot and J. F. Rodriguse, On a class of nonlocal nonlinear elliptic problems, RAIRO Model. Math. Anal. Numer. 29 (1992), no. 3, 447--468. F. J. S. A. Corra, M. Delgado and A. Suarez, Some non-local population models with
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non-linear diffusion, Rev. Integr. Temas Mat. 28 (2010), no. 1, 37--49.
11
F. J. S. A. Corrêa and S. D. B. Menezes, Existence of solutions to nonlocal and singular elliptic problems via Galerkin method, Electron. J. Differential Equations 2004 (2004), no. 19, 1--10.
12
F. J. S. A. Corrêa and G. M. Figueiredo, Existence and multiplicity of nontrivial solutions for a bi-nonlocal equation, Adv. Differential Equations 18 (2013), no. 5-6, 587--608.
13
P. Drabek and S. I. Pohozaev, Positive solutions for the p-Laplacian: application of the fibrering method, Proc. Roy. Soc. Edinburgh Sect. A 127 (1997), no. 4, 703--726.
14
G. M. Figueiredo, Existence of a positive solution for a Kirchhoff problem type with critical growth via truncation argument, J. Math. Anal. Appl. 401 (2013), no. 2, 706--713.
15
J. Furter and M. Grinfeld, Local vs. nonlocal interactions in population dynamics, J. Math. Biol. 27 (1989), no. 1, 65--80.
16
X. He and W. Zou, Existence and concentration behavior of positive solutions for a Kirchhoff equation in R3, J. Differential Equations 252 (2012), no. 2, 1813--1834.
17
G. Kirchhoff, Mechanik, Teubner, Leipzig, 1883.
18
P. H. Rabinowitz, Minimax Methods in Critical Point Theory with Applications to Differential Equations, CBMS Reg. Conf. Series Math., 65, Amer. Math. Soc., Providence, 1986.
19
M. Struwe, Variational Methods, Springer-Verlag, Berlin, 2008.
20
A. Szulkin, Ljusternik-Schnirelmann theory on C1-manifolds, Ann. Inst. H. Poincare Anal. Non Lineaire 5 (1988) 119--139.
21
L. Wang, On a quasilinear Schrodinger-Kirchhoff-type equation with radial potentials, Nonlinear Anal. 83 (2013) 58--68.
22
M. Willem, Minimax Theorems, BirkhäuserBoston, Inc., Boston, 1996.
23
ORIGINAL_ARTICLE
T-dual Rickart modules
We introduce the notions of T-dual Rickart and strongly T-dual Rickart modules. We provide several characterizations and investigate properties of each of these concepts. It is shown that every free (resp. finitely generated free) $R$-module is T-dual Rickart if and only if $\overline{Z}^2(R)$ is a direct summand of $R$ and End$(\overline{Z}^2(R))$ is a semisimple (resp. regular) ring. It is shown that, while a direct summand of a (strongly) T-dual Rickart module inherits the property, direct sums of T-dual Rickart modules do not. Moreover, when a direct sum of T-dual Rickart modules is T-dual Rickart, is included. Examplesillustrating the results are presented.
http://bims.iranjournals.ir/article_802_ff60a17a6bbe853afe2fa8050110df8e.pdf
2016-06-01
611
642
Dual Rickart modules
t-lifting modules
t-dual Baer modules
T-dual Rickart modules
strongly T-dual Rickart modules
S.
Ebrahimi Atani
ebrahimi@guilan.ac.ir
1
Department of Mathematics, University of Guilan, P.O. Box 1914, Rasht, Iran.
AUTHOR
M.
Khoramdel
mehdikhoramdel@gmail.com
2
Department of Mathematics, University of Guilan, P.O. Box 1914, Rasht, Iran.
LEAD_AUTHOR
S.
Dolati Pish Hesari
saboura_dolati@yahoo.com
3
Department of Mathematics, University of Guilan, P.O. Box 1914, Rasht, Iran.
AUTHOR
T. Amouzegar, D. K. Tütüncü and Y. Talebi, t-dual Baer modules and t-lifting modules, Vietnam J. Math. 42 (2014), no. 2, 159--169.
1
Sh. Asgari and A. Haghany, t-extending modules and t-Baer modules, Comm. Algebra 39 (2011), no. 5, 1605--1623.
2
K. I. Beidar and W. F. Ke, On essential extensions of direct sums of injective modules, Arch. Math. (Basel) 78 (2002), no. 2, 120--123.
3
G. F. Birkenmeier, J. K. Park and S. T. Rizvi, Modules with fully invariant submodules essential in fully invariant summands, Comm. Algebra 30 (2002), no. 4, 1833--1852.
4
G. F. Birkenmeier, B. J. Müller and S.T. Rizvi, Modules in which every fully invariant submodule is essential in a direct summands, Comm. Algebra, 30 (2002), no. 3, 1395--1415.
5
J. Clark, C. Lomp, N. Vanaja and R. Wisbauer, Lifting Modules, Frontiers in Mathematics, Birkhäuser Verlag, Basel, 2006.
6
S. Ebrahimi Atani, M. Khoramdel and S. Dolati Pish Hesari, t-Rickart modules, Colloq. Math. 128 (2012), no. 1, 87--100.
7
S. Ebrahimi Atani, M. Khoramdel and S. Dolati Pish Hesari , Strongly Extending Modules, Kyungpook Math. J. 54 (2014), 237--247.
8
K. R. Goodearl, Von Neumann Regular Rings, Monographs and studies in mathematics, Boston, Mass.-London, 1979.
9
A. Hattori, A foundation of torsion theory for modules over general rings, Nagoya Math. J. 17 (1960) 147--158.
10
I. Kaplansky, Rings of Operators, W. A. Benjamin, Inc., New York-Amsterdam 1968.
11
T. Y. Lam, Lectures on modules and rings, Graduate Texts in Mathematics, 189, Springer-Verlag, New York, 1999.
12
G. Lee, S. T. Rizvi and C. S. Roman, Rickart Modules, Comm. Algebra 38 (2010), no. 11, 4005--4027.
13
G. Lee, S. T. Rizvi and C. S. Roman, Dual Rickart Modules, Comm. Algebra 39 (2011), no. 11, 4036--4058.
14
A. V. Mikhalev and G. Pilz. The Concise Handbook of Algebra, Kluwer Academic Publishers, Dordrecht, 2002.
15
S. H. Mohamed and B. J. Müller, Continuous and Discrete Modules, London Math. Soc. Lecture Notes Series 147, Cambridge, University Press, Cambridge, 1990.
16
S. T. Rizvi and C. S. Roman, Baer and Quasi-Baer Modules, Comm. Algebra. 32 (2004), no. 1, 103--123.
17
S. T. Rizvi and C. S. Roman, On K-nonsingular modules and applications, Comm. Algebra 35 (2007), no. 9, 2960--2982.
18
Y. Talebi and N. Vanaja, The Torsion Theory Cogenerated by M-small Modules, Comm. Algebra 30 (2002), no. 3, 1449--1460.
19
D. K. Tütüncü, P. F. Smith and S. E. Toksoy, On dual Baer modules, Ring theory and its applications, 173--184, Contemp. Math., 609, Amer. Math. Soc., Providence, 2014.
20
D. K. Tütüncü and R. Tribak, On Dual Baer Modules, Glasg. Math. J. 52 (2010), no. 2, 261--269.
21
R. Ware, Endomorphism rings of projective modules, Trans. Amer. Math. Soc. 155 (1971) 233--256.
22
R. Wisbauer, Foundations of Module and Ring Theory, Gordon and Breach Science Publishers, Philadelphia, 1991.
23
ORIGINAL_ARTICLE
The existence of global attractor for a Cahn-Hilliard/Allen-Cahn equation
In this paper, we consider a Cahn-Hillard/Allen-Cahn equation. By using the semigroup and the classical existence theorem of global attractors, we give the existence of the global attractor in $H^k(0<=k<5)$ space of this equation, and it attracts any bounded subset of $H^k(\omega)$ in the $H^k$-norm.
http://bims.iranjournals.ir/article_803_0b5005164973791b8218766a77550508.pdf
2016-06-01
643
658
Cahn-Hilliard/Allen-Cahn equation
existence
global attractor
H.
Tang
tangtangth83@163.com
1
Department of Mathematics, Jilin University, Changchun 130012, P.R. China and School of Science, Changchun University, Changchun 130022, P.R. China.
LEAD_AUTHOR
C.
Liu
liucc@jlu.edu.cn
2
Department of Mathematics, Jilin University, Changchun 130012, P.R. China.
AUTHOR
Z.
Zhao
jczzx10@163.com
3
Department of Mathematics, Changchun Normal University, Chang-chun 130032, P.R. China and Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, P.R. China.
AUTHOR
R. A. Adams, Sobolev Spaces, Pure and Applied Mathematics, 65, Academic Press, A subsidiary of Harcourt Brace Jovanovich, Publishers, New York-London, 1975.
1
D. C. Antonopoulou, G. Karali and A. Millet, Existence and regularity of solution for a stochastic Cahn-Hilliard/Allen-Cahn equation with unbounded noise diffusion, J. Differential Equations 260 (2016), no. 3, 2383--2417.
2
J. L. Boldrini and P. N. Da Silva, A generalized solution to a Cahn-Hilliard/Allen-Cahn System, Electron. J. Differential Equations 2004 (2004), no. 126, 24 pages.
3
M. Gokieli and A. Ito, Global attractor for the Cahn-Hilliard/Allen-Cahn system, Non-linear Analysis 52 (2003), no. 7, 1821--1841.
4
M. Gokieli and L. Marcinkowski, Discrete Approximation of the Cahn-Hilliard/Allen-Cahn System with Logarithmic Entropy, Japan J. Indust. Appl. Math. 20 (2003), no. 3, 321--351.
5
G. Karali and M. A. Katsoulakis, The role of multiple microscopic mechanisms in cluster interface evolution, J. Differential Equations 235 (2007), no. 2, 418--438.
6
G. Karali and Y. Nagase, On the existence of solution for a Cahn-Hilliard/Allen-Cahn equation, Discrete Contin. Dyn. Syst. Ser. S 7 (2014), no. 1, 127--137.
7
G. Karali and T. Ricciardi, On the convergence of a fourth order evolution equation to the Allen-Cahn equation, Nonlinear Anal. 72 (2010), no. 11, 4271--4281.
8
D. Li and C. Zhong, Global attractor for the Cahn-Hilliard system with fast growing nonlinearity, J. Differential Equations 149 (1998), no. 2, 191--210.
9
T. Ma and S. Wang, Stability and Bifurcation of Nonlinear Evolution Equations, Science Press, Beijing, 2006.
10
A. Novick-Cohen and L. P. Hari, Geometric motion for a degenerate Allen-Cahn/Cahn-Hilliard system: The partial wetting case, Phys. D 209 (2005), no. 1-4, 205--235.
11
A. Novick-Cohen, Triple-junction motion for an Allen-Cahn/Cahn-Hilliard system, Phys. D 137 (2000), no. 1-2, 1--24.
12
L. Song, Y. Zhang and T. Ma, Global attractor of a modified Swift-Hohenberg equation in Hk spaces, Nonlinear Anal. 72 (2010), no. 1, 183--191.
13
L. Song, Y. Zhang and T. Ma, Global attractor of the Cahn-Hilliard equation in Hk spaces, J. Math. Anal. Appl. 355 (2009), no. 1, 53--62.
14
L. Song, Y. He and Y. Zhang, The existence of global attractors for semilinear parabolic equation in Hk spaces, Nonlinear Anal. 68 (2008), no. 11, 3541--3549.
15
R. Temam, Infinite-Dimensional Dynamical Systems in Mechanics and Physics, Springer-Verlag, New York, 1988
16
H. Wu and S. M. Zheng, Global attractor for the 1-D thin film equation, Asymptot. Anal. 51 (2007), no. 2, 101--111.
17
X. Zhao and C. Liu, The existence of global attractor for a fourth-order parabolic equation, Appl. Anal. 92 (2013), no. 1, 44--59.
18
ORIGINAL_ARTICLE
Nonlinear $*$-Lie higher derivations on factor von Neumann algebras
Let $\mathcal M$ be a factor von Neumann algebra. It is shown that every nonlinear $*$-Lie higher derivation $D={\phi_{n}}_{n\in\mathbb{N}}$ on $\mathcal M$ is additive. In particular, if $\mathcal M$ is infinite type $I$ factor, a concrete characterization of $D$ is given.
http://bims.iranjournals.ir/article_804_014d235291f660ccf7545720818e036c.pdf
2016-06-01
659
678
von Neumann algebra
nonlinear $*$-Lie higher derivation
additive $*$-higher derivation
F.
Zhang
zhfj888@126.com
1
School of Science, Xi'an University of Posts and Telecommunications, Xi'an 710121, P. R. China.
LEAD_AUTHOR
X.
Qi
xiaofeiqisxu@aliyun.com
2
Department of Mathematics, Shanxi University, Taiyuan 030006, P. R. China.
AUTHOR
J.
Zhang
jhzhang@snnu.edu.cn
3
College of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710062, P. R China.
AUTHOR
M. Brešar, Commuting traces of biadditive mappings, commutativity preserving mappings and Lie mappings, Trans. Amer. Math. Soc. 335 (1993), no. 2, 525--546.
1
Z. F. Bai and S. P. Du, The structure of nonlinear Lie derivation on von Neumann algebras, Linear Algebra Appl. 436 (2012), no. 7, 2701--2708.
2
L. Chen and J. H. Zhang, Nonlinear Lie derivations on upper triangular matrices, Linear Multilinear Algebra 56 (2008), no. 6, 725--730.
3
Y. Q. Du and Y. Wang, Lie derivations of generalized matrix algebras, Linear Algebra Appl. 437 (2012), no. 11, 2719--2726.
4
M. Ferrero and C. Haetinger, Higher derivations and a theorem by Herstein, Quaest. Math. 25 (2002), no. 2, 249--257.
5
M. Ferrero and C. Haetinger, Higher derivations of semiprime rings, Comm. Algebra 30 (2002), no. 5, 2321--2333.
6
N. Heerema, Higher derivations and automorphisms of complete local rings, Bull. Amer. Math. Soc. 76 (1970) 1212--1225.
7
F. Y. Lu and W. Jing, Characterizations of Lie derivations of B(X), Linear Algebra Appl. 432 (2010), no. 1, 89--99.
8
M. Mathieu and A. R. Villena, The structure of Lie derivations on C-algebras, J. Funct. Anal. 202 (2003), no. 2, 504--525.
9
A. Nakajima, On generalized higher derivations, Turkish J. Math. 24 (2000), no. 3, 295--311.
10
A. Nowicki, Inner derivations of higher orders, Tsukuba J. Math. 8 (1984), no. 2, 219--225.
11
X. F. Qi and J. C. Hou, Characterization of Lie derivations on prime rings, Comm. Algebra 39 (2011), no. 10, 3824--3835.
12
X. F. Qi and J. C. Hou, Lie higher derivations on nest algebras, Commun. Math. Res. 26 (2010), no. 2, 131--143.
13
A. Roy and R. Sridharan, Higher derivations and central simple algebras, Nagoya Math. J. 32 (1968) 21--30.
14
P. Šemrl, Additive derivations of some operator algebras, Illinois J. Math. 35 (1991), no. 2, 234--240.
15
F. Wei and Z. K. Xiao, Higher derivations of triangular algebras and its generalizations, Linear Algebra Appl. 435 (2011), no. 5, 1034--1054.
16
Z. K. Xiao and F. Wei, Nonlinear Lie higher derivations on triangular algebras, Linear Multilinear Algebra 60 (2012), no. 8, 979--994.
17
W. Y. Yu and J. H. Zhang, Nonlinear *-Lie derivations on factor von Neumann algebras, Linear Algebra Appl. 437 (2012), no. 8, 1979--1991.
18
W. Y. Yu and J. H. Zhang, Nonlinear Lie derivations of triangular algebras, Linear Algebra Appl. 432 (2010), no. 11, 2953--2960.
19
F. J. Zhang and J. H. Zhang, Nonlinear Lie derivations on factor von Neumann algebras, Acta Mathematica Sinica. (Chin. Ser) 54 (2011), no. 5, 791--802.
20
ORIGINAL_ARTICLE
Bounding cochordal cover number of graphs via vertex stretching
It is shown that when a special vertex stretching is applied to a graph, the cochordal cover number of the graph increases exactly by one, as it happens to its induced matching number and (Castelnuovo-Mumford) regularity. As a consequence, it is shown that the induced matching number and cochordal cover number of a special vertex stretching of a graph G are equal provided G is well-covered bipartite or weakly chordal graph.
http://bims.iranjournals.ir/article_805_81bd74ccf92af8a92a50edd4ec90271f.pdf
2016-06-01
679
685
Castelnuovo-Mumford regularity
Induced matching number
Cochordal cover number
M. R.
Fander
mohamadrezafander@yahoo.com
1
Science and Research Branch, Islamic Azad University (IAU), Tehran, Iran.
LEAD_AUTHOR
V. E. Alekseev, On the local restrictions effect on the complexity of inding the graph independence number, Combinatorial-Algebraic Methods in Applied Mathematics, 3--13,Gorkiy Univ. Press, Gorkiy, 1983.
1
V. E. Alekseev, R. Boliac, D. V. Korobitsyn and V. V. Lozin, NP-hard graph problems and boundary classes of graphs, Theoret. Comput. Sci. 389 (2007), no. 1-2, 219--236.
2
T. Biyikoglu and Y Civan, Bounding Castelnuovo-Mumford regularity of graphs via Lozin's transformation, arXiv:1302.3064.
3
R. Boliac, K. Cameron and V. V. Lozin, On computing the dissociation number and the induced matching number of bipartite graphs, Ars Combin. 72 (2004) 241--253.
4
J. A. Bondy and U. S. R. Murty, Graph Theory, Graduate Texts in Mathematics, 244, Springer, New York, 2008.
5
A. H. Busch, F. F. Dragan and R. Sritharan, New min-max theorems for weakly chordal and dually chordal graphs, Combinatorial Optimization and Applications, Part II (WeiliWu and Ovidiu Daescu, eds.) Lecture Notes in Computer Science, vol 6509, Springer,
6
Berlin 2010.
7
M. Katzman, Characteristic-independence of Betti numbers of graph ideals, J. Combin. Theory Ser. A 113 (2006), no. 3, 435--454.
8
D. V. Korobitsyn, On the complexity of determining the domination number in mono-genic classes of graphs, Diskret. Mat. 2 (1990), no. 3, 90--96 (in Russian), Translation in Discrete Math. Appl. 2 (1992), no. 2, 191--199.
9
D. N. Kozlov, Complexes of directed trees, J. Combin. Theory Ser. A 88 (1999), no. 1, 112--122.
10
M. Kummini, Regularity, depth and arithmetic rank of bipartite edge ideals, J. Algebraic Combin. 30 (2009), no. 4, 429--445.
11
V. V. Lozin, On maximum induced matchings in bipartite graphs, Inform. Process. Lett. 81 81 (2002), no. 1, 7--11.
12
V. V. Lozin and M. Gerber, On the jump number problem in hereditary classes of bipartite graphs, Order 17 (2000), no. 4, 377--385.
13
R. Woodroofe, Matchings, coverings, and Castelnuovo--Mumford regularity, J. Commut. Algebra 6 (2014), no. 2, 287--304.
14
ORIGINAL_ARTICLE
P-stability, TF and VSDPL technique in Obrechkoff methods for the numerical solution of the Schrodinger equation
Many simulation algorithms (chemical reaction systems, differential systems arising from the modeling of transient behavior in the process industries and etc.) contain the numerical solution of systems of differential equations. For the efficient solution of the above mentioned problems, linear multistep methods or Runge-Kutta technique are used. For the simulation of chemical procedures the radial Schrodinger equation is used frequently. In the present paper we will study a symmetric two-step Obrechkoff method, in which we will use of technique of VSDPL (vanished some of derivatives ofphase-lag), for the numerical integration of the one-dimensional Schrodinger equation. We will show superiority of new method in stability, accuracy and efficiency. So we present a stability analysis and an error analysis based on the radial Schrodinger equation. Also we will apply the new proposed method to the resonance problem of the radial Schrodinger equation.
http://bims.iranjournals.ir/article_806_30e8c4d6d6c54025669e5872bc7174c3.pdf
2016-06-01
687
706
P-stable
Phase-lag
Schr"{o}dinger equation
trigonometrically fitted
A.
Shokri
shokri@maragheh.ac.ir
1
Department of Mathematics, Faculty of Basic Science, University of Maragheh, P.O. Box 55181-83111, Maragheh, Iran.
LEAD_AUTHOR
H.
Saadat
hosein67saadat@yahoo.com
2
Department of Mathematics, Faculty of Basic Science, University of Maragheh, P.O. Box 55181-83111, Maragheh, Iran.
AUTHOR
S. D. Achar, Symmetric multistep Obrechkoff methods with zero phase-lag for periodic initial value problems of second order differential equations, J. Appl. Math. Comput. 218 (2011), no. 5, 2237--2248.
1
U. A. Ananthakrishnaiah, P-stable Obrechkoff methods with minimal phase-lag for periodic initial value problems, Math. Comput. 49 (1987), no. 180, 553--559.
2
M. M. Chawla and P. S. Rao, A Noumerov-type method with minimal phase-lag for the integration of second order periodic initial value problems, II, Explicit method, J. Comput. Appl. Math. 15 (1986), no. 3, 329--337.
3
M. M. Chawla, P. S. Rao and B. Neta, Two-step fourth order P-stable methods with phase-lag of order six for y”= f(t; y), J. Comput. Appl. Math. 16 (1986), no. 2, 233--236.
4
J. P. Coleman and L. Gr. Ixaru, P-stability and exponential-fitting methods for y”=f(x, y), IMA J. Numer. Anal. 16 (1995), no. 2, 179--199.
5
L. G. Ixaru and M. Rizea, Comparison of some four-step methods for the numerical solution of the Schrodinger equation, Comput. Phys. Commun. 38 (1985), no. 3, 329--337.
6
L. G. Ixaru and M. Rizea, A Numerov-like scheme for the numerical solution of the Schrodinger equation in the deep continuum spectrum of energies, Comput. Phys. Commun. 19 (1980), 23--27.
7
J. D. Lambert and I. A. Watson, Symmetric multistep methods for periodic initial value problems, J. Inst. Math. Appl. 18 (1976), no. 2, 189--202.
8
A. D. Raptis, Exponentially-fitted solutions of the eigenvalue Schrdinger equation with automatic error control, Comput. Phys. Comm. 28 (1983), no. 4, 427--431.
9
D. P. Sakas and T. E. Simos, Trigonometrically-fitted multiderivative methods for the numerical solution of the radial Schrodinger equation, Commun. Math. Comput. Chem. 53 (2005), no. 2, 299--320.
10
G. Saldanha and S. D. Achar, Symmetric multistep Obrechkoff methods with zero phase-lag for periodic initial value problems of second order differential equations, Appl. Math. Comput. 218 (2011), no. 5, 2237--2248.
11
T. E. Simos, A P-stable complete in phase Obrechkoff trigonometric fitted method for periodic initial value problems, Proc. Roy. Soc. London Ser. A 441 (1993), no. 1912, 283--289.
12
A. Shokri, An explicit trigonometrically fitted ten-step method with phase-lag of order infinity for the numerical solution of radial Schrodinger equation, Appl. Comput. Math. 14 (2015), no. 1, 63--74.
13
A. Shokri, The symmetric two-step P-stable nonlinear predictor-corrector methods for the numerical solution of second order initial value problems, Bull. Iranian Math. Soc. 41 (2015), no. 1, 201--215.
14
A. Shokri and H. Saadat, High phase-lag order trigonometrically fitted two-step Obrechkoff methods for the numerical solution of periodic initial value problems, Numer. Algorithms 68 (2015), no. 2, 337--354.
15
A. Shokri and H. Saadat, Trigonometrically fitted high-order predictor-corrector method with phase-lag of order infinity for the numerical solution of radial Schrodinger equation, J. Math. Chem. 52 (2014), no. 7, 1870--1894.
16
M. Van Daele and G. Vanden Berghe, P-stable exponentially fitted Obrechkoff methods of arbitrary order for second order differential equations, Numer. Algorithms 46 (2007), no. 4, 333--350.
17
G. Vanden Berghe and M. Van Daele, Exponentially-fitted Obrechkoff methods for second-order differential equations, Applied Numerical Mathematics 59 (2009), no. 3-4, 815--829.
18
Z. Wang, D. Zhao, Y. Dai and D. Wu, An improved trigonometrically fitted P-stable Obrechkoff method for periodic initial value problems, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 461 (2005), no. 2058, 1639--1658.
19
ORIGINAL_ARTICLE
On subdifferential in Hadamard spaces
In this paper, we deal with the subdifferential concept on Hadamard spaces. Flat Hadamard spaces are characterized, and necessary and suficient conditions are presented to prove that the subdifferential set in Hadamard spaces is nonempty. Proximal subdifferential in Hadamard spaces is addressed and some basic properties are high-lighted. Finally, a density theorem for subdifferential set is established.
http://bims.iranjournals.ir/article_807_c964b05ed4b54e1642cbd753e007a371.pdf
2016-06-01
707
717
Subdifferential
Hadamard Space
Flat space
Hilbert space
Convexity
M.
Soleimani-damaneh
soleimani@khayam.ut.ac.ir
1
{School of Mathematics, Statistics and Computer Science, College of Science, University of Tehran, Enghelab Avenue, Tehran, Iran.
LEAD_AUTHOR
M.
Movahedi
m.movahedi18@yahoo.com
2
Department of Mathematics, Faculty of Sciences, Alzahra University, Tehran, Iran.
AUTHOR
D.
Behmardi
behmardi@alzahra.ac.ir
3
Department of Mathematics, Faculty of Sciences, Alzahra University, Tehran, Iran.
AUTHOR
B. Ahmadi-kakavandi and M. Amini, Duality and subdifferential for convex functions on complete CAT(0) metric spaces, Nonlinear Anal. 73 (2010), no. 10, 3450--3455.
1
A. D. Aleksandrov, A theorem on triangles in a metric space and some of its applications, (Russian), Trudy Mat. Inst. Steklov. 38 (1951) 5--23.
2
C. D. Aliprantis and K. C. Border, Infinite dimensional analysis, 3rd Edition, Springer-Verlag, Berlin, 2006.
3
D. Azagra, J. Ferrera and F. Lopez-Mesas, Nonsmooth analysis and Hamilton-Jacobi equations on Riemannian manifolds, J. Funct. Anal. 220 (2005), no. 2, 304--361.
4
D. Azagra, J. Ferrera and F. Lopez-Mesas, A maximum principle for evolution Hamilton Jacobi equations on Riemannian manifolds, J. Math. Anal. Appl. 323 (2006), no. 1, 473--480.
5
M. Bacak, Convex Analysis and Optimization in Hadamard Spaces, Walter de Gruyter, Berlin, 2014.
6
W. Ballmann, Lectures on Spaces of Nonpositive Curvature, Birkhauser Verlag, Basel, 1995.
7
I. D. Berg and I.G. Nikolaev, Quasilinearization and curvature of Aleksandrov spaces, Geom. Dedicata 133 (2008) 195--218.
8
M. Bridson and A. Haeiger, Metric spaces of non-positive curvature, Grundlehren der Mathematischen Wissenschaften, 319, Springer-Verlag, Berlin, 1999.
9
D. Burago, Y. Burago and S. Ivanov, A course in metric geometry, in: Graduate studies in Math., 33, Amer. Math. Soc., Providence, 2001.
10
F. H. Clarke, Y. S. Ledyaev, R. J. Stern and P. R. Wolenski, Nonsmooth Analysis and Control Theory, Springer-Verlag, New York, 1998.
11
S. Dhompongsa and B. Panyanak, On Δ-convergence theorems in CAT(0) spaces, Comput. Math. Appl. 56 (2008), no. 10, 2572--2579.
12
J. Lurie, Notes on the Theory of Hadamard Spaces, Harvard University, http://www.math.harvard.edu/lurie/papers/hadamard.pdf.
13
B. S. Mordukhovich, Variational analysis and generalized differentiation I, Basic theory, Springer-Verlag, Berlin, Heidelberg, 2006.
14
R. T. Rockafellar, Convex Analysis, Princeton University Press, Princeton, 1970.
15
C. Zalinescu, Convex Analysis in General Vector Spaces, Publishing Co., Inc., River Edge, 2002.
16
ORIGINAL_ARTICLE
Iterative scheme based on boundary point method for common fixed point of strongly nonexpansive sequences
Let $C$ be a nonempty closed convex subset of a real Hilbert space $H$. Let ${S_n}$ and ${T_n}$ be sequences of nonexpansive self-mappings of $C$, where one of them is a strongly nonexpansive sequence. K. Aoyama and Y. Kimura introduced the iteration process $x_{n+1}=\beta_nx_n+(1-\beta_n)S_n(\alpha_nu+(1-\alpha_n)T_nx_n)$ for finding the common fixed point of ${S_n}$ and ${T_n}$, where $uin C$ is an arbitrarily (but fixed) element in $C$, $x_0\in C$ arbitrarily, ${\alpha_n}$ and ${\beta_n}$ are sequences in $[0,1]$. But in the case where $u\notin C$, the iterative scheme above becomes invalid because $x_n$ may not belong to $C$. To overcome this weakness, a new iterative scheme based on the thought of boundary point method is proposed and the strong convergence theorem is proved. As a special case, we can find the minimum-norm common fixed point of ${S_n}$ and ${T_n}$ whether $0\in C$ or $0\notin C$.
http://bims.iranjournals.ir/article_808_2c7750cdcd7019d6e876e332881bea9f.pdf
2016-06-01
719
730
minimum-norm common fixed point
strongly nonexpansive mappings
strong convergence
boundary point method
variational inequality
W.
Zhu
wlzhu152@163.com
1
College of Management and Economics, Tianjin University, Tianjin 300072, China.
AUTHOR
S.
Ling
lingshuai@tju.edu.cn
2
College of Management and Economics, Tianjin University, Tianjin 300072, China.
LEAD_AUTHOR
K. Aoyama and Y. Kimura, Strong convergence theorem for strongly nonexpansive sequences, Appl. Math. Comput. 217 (2011), no. 19, 7537--7545.
1
W. Takahashi and T. Tamura, Convergence theorems for a pair of nonexpansive mappings, J. Convex Anal. 5 (1998), no. 1, 45--56.
2
S. Takahashi, W. Takahashi and M. Toyoda, Strong convergence theorems for maximal monotone operators with nonlinear mappings in Hilbert spaces, J. Optim. Theory Appl. 147 (2010), no. 1, 27--41.
3
L. C. Zeng, N. C. Wong and J. C. Yao, Convergence analysis of iterative sequences for a pair of mappings in Banach spaces, Acta Math. Sin. (Engl. Ser.) 24 (2008), no. 3, 463--470.
4
Y. Yao and J. C. Yao, On modified iterative method for nonexpansive mappings and monotone mappings, Appl. Math. Comput. 186 (2007), no. 2, 1551--1558.
5
K. Aoyama, Y. Kimura, W. Takahashi and M. Toyoda, On a strongly nonexpansive sequence in Hilbert spaces, J. Nonlinear Convex Anal. 8 (2007), no. 3, 471--489.
6
S. Chandok, W. Sintunavarat and P. Kumam, Some coupled common fixed points for a pair of mappings in partially ordered G-metric spaces, Math. Sci. (Springer) 7 (2013), 7 pages.
7
W. Shatanawi and M. Postolache, Common fixed point results for mappings under non- linear contraction of cyclic form in ordered metric spaces, Fixed Point Theory Appl. 2013 (2013) 13 pages.
8
D. K. Patel, P. Kumam and D. Gopal, Some discussion on the existence of common fixed points for a pair of maps, Fixed Point Theory Appl. 2013 (2013) 17 pages.
9
H.-K. Xu, Viscosity approximation methods for nonexpansive mappings, J. Math. Anal. Appl. 298 (2004), no. 1, 279--291.
10
Hong-Kun Xu, Viscosity method for hierarchical fixed point approach to variational inequalities, Taiwanese J. Math. 14 (2010), no. 2, 463--478.
11
A. Mouda, Viscosity approximation methods for fixed-points problems, J. Math. Anal. Appl. 241 (2000), no. 1, 46--55.
12
R. Chen and Z. Zhu, Viscosity approximation method for accretive operator in Banach space, Nonlinear Anal. 69 (2008), no. 4, 1356--1363.
13
Rabian Wangkeeree, and Pakkapon Preechasilp, Viscosity approximation methods for nonexpansive semigroups in CAT(0) spaces, Fixed Point Theory Appl. 2013 (2013) 16 pages.
14
P. E. Mainge, The viscosity approximation process for quasi-nonexpansive mappings in Hilbert spaces, Comput. Math. Appl. 59 (2010), no. 1, 74--79.
15
J. S. Jung, Strong convergence of viscosity approximation methods for finding zeros of accretive operators in Banach spaces, Nonlinear Anal. 72 (2010), no. 1, 449--459.
16
J. S. Jung, Viscosity approximation methods for a family of finite nonexpansive mappings in Banach spaces, Nonlinear Anal. 64 (2006), no. 11, 2536--2552.
17
S. S. Chang, Viscosity approximation methods for a finite family of nonexpansive mappings in Banach spaces, J. Math. Anal. Appl. 323 (2006), no. 2, 1402--1416.
18
L. C. Ceng, H. K. Xu and J. C. Yao, The viscosity approximation method for asymptotically nonexpansive mappings in Banach spaces, Nonlinear Anal. 69 (2008), no. 4, 1402--1412.
19
J. Lou, L. J. Zhang and Z. He, Viscosity approximation methods for asymptotically nonexpansive mappings, Appl. Math. Comput. 203 (2008), no. 1, 171--177.
20
S. Takahashi and W. Takahashi, Viscosity approximation methods for equilibrium problems and fixed point problems in Hilbert spaces, J. Math. Anal. Appl. 331 (2007), no. 1, 506--515.
21
S. Plubtieng and T. Thammathiwat, A viscosity approximation method for equilibrium problems, fixed point problems of nonexpansive mappings and a general system of variational inequalities, J. Global Optim. 46 (2010), no. 3, 447--464.
22
K. Aoyama, An iterative method for a variational inequality problem over the common fixed point set of nonexpansive mappings, Nonlinear analysis and convex analysis, 21--28, Yokohama Publ., Yokohama, 2010.
23
C. M. Yanes and H. K. Xu, Strong convergence of the CQ method for fixed point iteration processes, Nonlinear Anal. 64 (2006), no. 11, 2400--2411.
24
S. Wang, A general iterative method for an infinite family of strictly pseudo-contractive mappings in Hilbert spaces, Appl. Math. Lett. 24 (2011), no. 6, 901--907.
25
T. Suzuki, Strong convergence theorems for infinite families of nonexpansive mappingsin general Banach spaces, Fixed Point Theory Appl. (2005), no. 1, 103--123.
26
S. Wang, Convergence and certain control conditions for hybrid iterative algorithms, Appl. Math. Comput. 219 (2013), no. 20, 10325--10332.
27
Y. Yao, Y. J. Cho and Y. C. Liou, Algorithms of common solutions for variational inclusions, mixed equilibrium problems and fixed point problems, European J. Oper. Res. 212 (2011), no. 2, 242--250.
28
H. K. Xu, Iterative algorithms for nonlinear operators, J. London Math. Soc. (2) 66 (2002), no. 1, 240--256.
29
S. He and W. Zhu, A modified Mann iteration by boundary point method for finding minimum-norm fixed point of nonexpansive mappings, Abstr. Appl. Anal. 2013 (2013), Article ID 768595, 6 pages.
30
ORIGINAL_ARTICLE
On strongly dense submodules
The submodules with the property of the title ( a submodule $N$ of an $R$-module $M$ is called strongly dense in $M$, denoted by $N\leq_{sd}M$, if for any index set $I$, $\prod _{I}N\leq_{d}\prod _{I}M$) are introduced and fully investigated. It is shown that for each submodule $N$ of $M$ there exists the smallest subset $D'\subseteq M$ such that $N+D'$ is a strongly dense submodule of $M$ and $D'\bigcap N=0$. We also introduce a class of modules in which the two concepts of strong essentiality and strong density coincide. It is also shown that for any module $M$, dense submodules in $M$ are strongly dense if and only if $M\leq_{sd} \tilde{E}(M)$, where $\tilde{E}(M)$ is the rational hull of $M$. It is proved that $R$ has no strongly dense left ideal if and only if no nonzero-element of every cyclic $R$-module $M$ has a strongly dense annihilator in $R$. Finally, some appropriate properties and new concepts related to strong density are defined and studied.
http://bims.iranjournals.ir/article_809_9508d8b8a48f740c5b8f741a57040ea9.pdf
2016-06-01
731
747
Strongly essential submodule
strongly dense submodule
singular submodule
special submodule
column submodule
E.
Ghashghaei
e.ghashghaei@yahoo.com
1
Department of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, Iran.
LEAD_AUTHOR
M.
Namdari
namdari@ipm.ir
2
Department of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, Iran.
AUTHOR
E. P. Armendariz, Rings with dcc on essential left ideals, Comm. Algebra. 8 (1980), no. 3, 299--308.
1
M. Behboodi, O. A. S. Karamzadeh and H. Koohy, Modules whose certain submodules are prime, Vietnam J. Math. 32 (2004), no. 3, 303--317.
2
G. D. Findlay and J. Lambek, A generalized ring of quotients, I, II, Canad. Math. Bull. 1 (1958), 77--85, 155--167.
3
M. Ghirati and O. A. S. Karamzadeh, On strongly essential submodules, Comm. Algebra. 36 (2008), no. 2, 564--580.
4
K. R. Goodearl and R. Jr. Warfield, An introduction to noncommutative Noetherian rings, second edition, Cambridge University Press, Cambridge, 2004.
5
O. A. S. Karamzadeh, M. Motamedi and S. M. Shahrtash, On rings with a unique proper essential right ideal, Fund. Math. 183 (2004), no. 3, 229--244.
6
T. Y. Lam, Lectures on Modules and Rings, Graduate Texts in Math., Springer-Verlag, 189, Berlin-Heidelberg-New York, 1999.
7
T. Y. Lam, Exercises in Modules and Rings, Problem Books in Math., Springer, New York, 2007.
8
J. Lambek and G. Michler, The torsion theory at a prime ideal of a right Noetherian ring, J. Algebra 25 (1973), no. 2, 364--389.
9
K. Louden, Maximal quotient rings of ring extensions, Pacific J. Math. 62 (1976), no. 2, 489--496.
10
L. B. Stenstrom, Rings of quotients, Die Grundlehren der Mathematischen Wissenschaften, Band 217. An introduction to methods of ring theory, Springer-Verlag, New York-Heidelberg, 1975.
11
H. H. Storrer, Goldman's primary decomposition, Lectures on ring and modules, Lecture Notes in Math., 246, Springer, Berlin, 1972.
12
J. M. Zelmanowitz, Representation of rings with faithful polyform modules, Comm. Algebra. 14 (1986), no. 6, 1141--1169.
13
ORIGINAL_ARTICLE
The power digraphs of safe primes
A power digraph, denoted by $G(n,k)$, is a directed graph with $Z_{n}={0,1,..., n-1}$ as the set of vertices and $L={(x,y):x^{k}\equiv y~(mod , n)}$ as the edge set, where $n$ and $k$ are any positive integers. In this paper, the structure of $G(2q+1,k)$, where $q$ is a Sophie Germain prime is investigated. The primality tests for the integers of the form $n=2q+1$ are established in terms of the structure of components of $G(n,k)$. The digraphs in which all components look like directed star graphs are completely classified. This work generalizes the results of M. Krizekek, L. Somer, Sophie Germain Little Suns, Math. Slovaca 54(5) (2004), 433-442.
http://bims.iranjournals.ir/article_810_0df6b481f1fb0fa44a9e1d04a5d4fa1a.pdf
2016-06-01
749
759
Iteration digraph
Carmichael lambda function
fixed point
Sophie Germain primes
Safe primes
U.
Ahmad
uzma.math@pu.edu.pk
1
Department of Mathematics, University of the Punjab, New Campus, Lahore, Pakistan.
LEAD_AUTHOR
S. M.
Husnine
syed.husnine@nu.edu.pk
2
Department of Humanities and Sciences, National University of Computer and Emerging Sciences(FAST), Lahore Campus, Lahore, Pakistan.
AUTHOR
U. Ahmad and S. Husnine, Characterization of Power Digraphs modulo n, Comment. Math. Univ. Carolin 48 (2011), no. 3, 359--367.
1
U. Ahmad and S. Husnine, On the Heights of Power Digraphs modulo n, Czechoslovak. Math. J. 62(137) (2012), no. 2, 541--556.
2
S. M. Husnine, U. Ahmad and L. Somer, On symmetries of Power digraphs, Util. Math 85 (2011) 257--271.
3
J. Kramer-Miller, Structural properties of power digraphs modulo n, Proceedings of the 2009 Midstates Conference on Undergraduate Research in Computer Science and Mathematics, 40-49, Oberlin, Ohio, 2009.
4
L. Somer and M. Krizek, On a connection of number theory with graph theory, Czechoslovak Math. J. 54(129) (2004), no. 2, 465--485.
5
M. Kritzek and L. Somer, Sophie Germain Little Suns, Math. Slovaca 54 (2004), no. 5, 433--442.
6
L. Somer and M. Kritzek, Structure of digraphs associated with quadratic congruences with composite moduli, Discrete Math. 306 (2006), no. 18, 2174--2185.
7
L. Somer and M. Kritzek, On semiregular digraphs of the congruence xk =y(mod n), Comment. Math. Univ. Carolin. 48 (2007), no. 1, 41--58.
8
L. Somer and M. Kritzek, On symmetric digraphs of the congruence xk=y (mod n), Discrete Math. 309 (2009), no. 8, 1999--2009.
9
B. Wilson, Power digraphs modulo n, Fibonacci Quart. 36 (1996), no. 3, 229--239.
10
ORIGINAL_ARTICLE
Applications of subordination theory to starlike functions
Let $p$ be an analytic function defined on the open unit disc $\mathbb{D}$ with $p(0)=1.$ The conditions on $\alpha$ and $\beta$ are derived for $p(z)$ to be subordinate to $1+4z/3+2z^{2}/3=:\varphi_{C}(z)$ when $(1-\alpha)p(z)+\alpha p^{2}(z)+\beta zp'(z)/p(z)$ is subordinate to $e^{z}$. Similar problems were investigated for $p(z)$ to lie in a region bounded by lemniscate of Bernoulli $|w^{2}-1|=1$ when the functions $(1-\alpha)p(z)+\alpha p^{2}(z)+\beta zp'(z)$ , $(1-\alpha)p(z)+\alpha p^{2}(z)+\beta zp'(z)/p(z)$ or $p(z)+\beta zp'(z)/p^{2}(z)$ is subordinate to $\varphi_{C}(z)$. Related results for $p$ to be in the parabolic region bounded by the $RE w=|w-1|$ are investigated.
http://bims.iranjournals.ir/article_811_b56bdeb24d06f65b35a6ba3a70fd9fd6.pdf
2016-06-01
761
777
convex and starlike functions
differential subordination
univalent functions
K.
Sharma
kanika.divika@gmail.com
1
Department of Mathematics, Atma Ram Sanatan Dharma College, University of Delhi, Delhi 110021, India.
AUTHOR
V.
Ravichandran
vravi68@gmail.com
2
Department of Mathematics, University of Delhi, Delhi--110007, India.
LEAD_AUTHOR
R. M. Ali, N. E. Cho, N. Jain and V. Ravichandran, Radii of starlikeness and convexity for functions with fixed second coefficient defined by subordination, Filomat 26 (2012), no. 3, 553--561.
1
R. M. Ali, N. E. Cho, V. Ravichandran and S. Sivaprasad Kumar, Differential subordi-nation for functions associated with the lemniscate of Bernoulli, Taiwanese J. Math. 16 (2012), no. 3, 1017--1026.
2
R. M. Ali, N. K. Jain and V. Ravichandran, Radii of starlikeness associated with the lemniscate of Bernoulli and the left-half plane, Appl. Math. Comput. 218 (2012), no. 11, 6557--6565.
3
A. W. Goodman, On uniformly convex functions, Ann. Polon. Math. 56 (1991), no. 1, 87--92.
4
W. Janowski, Some extremal problems for certain families of analytic functions, I, Ann. Polon. Math. 28 (1973) 297--326.
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W. Janowski, Extremal problems for a family of functions with positive real part and for some related families, Ann. Polon. Math. 23 (1970/1971) 159--177.
6
S. Sivaprasad Kumar, V. Kumar, V. Ravichandran and N. E. Cho, Sufficient conditions for starlike functions associated with the lemniscate of Bernoulli, J. Inequal. Appl. 2013 (2013) 13 pages.
7
W. C. Ma and D. Minda, A unified treatment of some special classes of univalent functions, Proceedings of the Conference on Complex Analysis (Tianjin, 1992), 157--169,
8
Conf. Proc. Lecture Notes Anal., I Int. Press, Cambridge, 1994.
9
R. Mendiratta, S. Nagpal and V. Ravichandran, A subclass of starlike functions associated with left-half of the lemniscate of Bernoulli, Internat. J. Math. 25 (2014), no. 9, 17 pages.
10
R. Mendiratta, S. Nagpal and V. Ravichandran, On a subclass of strongly starlike functions associated with exponential function, Bull. Malays. Math. Sci. Soc. 38 (2015), no. 1, 365--386.
11
S. S. Miller and P. T. Mocanu, Differential Subordinations, Monographs and Textbooks in Pure and Applied Mathematics, 225, Marcel Dekker, Inc., New York, 2000.
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E. Paprocki and J. Soko l, The extremal problems in some subclass of strongly starlike functions, Zeszyty Nauk. Politech. Rzeszowskiej Mat. 20 (1996) 89--94.
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Y. Polatoğlu and M. Bolcal, Some radius problem for certain families of analytic functions, Turkish J. Math. 24 (2000), no. 4, 401--412.
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V. Ravichandran, F. Rønning and T. N. Shanmugam, Radius of convexity and radius of starlikeness for some classes of analytic functions, Complex Variables Theory Appl. 33 (1997), no. 1-4, 265--280.
15
V. Ravichandran and K. Sharma, Sufficient conditions for starlikeness, J. Korean Math. Soc. 52 (2015), no. 4, 727--749.
16
M. S. Robertson, Certain classes of starlike functions, Michigan Math. J. 32 (1985), no. 2, 135--140.
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F. Rønning, Uniformly convex functions and a corresponding class of starlike functions, Proc. Amer. Math. Soc. 118 (1993), no. 1, 189--196.
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ORIGINAL_ARTICLE
Weak $F$-contractions and some fixed point results
In this paper we define weak $F$-contractions on a metric space into itself by extending $F$-contractions introduced by D. Wardowski (2012) and provide some fixed point results in complete metric spaces and in partially ordered complete generalized metric spaces. Some relationships between weak $F$-contractions and $\varphi$-contractions are highlighted. We also give some applications on fractal theory improving the classical Hutchinson-Barnsley's theory of iterated function systems. Some illustrative examples are provided.
http://bims.iranjournals.ir/article_812_f9360006c4cf94034e472005a0ef6475.pdf
2016-06-01
779
798
F-contraction
partially ordered metric space
generalized metric
iterated function system
fixed point theorem
N. A.
Secelean
nicolae.secelean@ulbsibiu.ro
1
Department of Mathematics and Informatics Faculty of Sciences, Lucian Blaga University of Sibiu, Romania.
LEAD_AUTHOR
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