eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2016-04-01
42
2
233
246
756
Radical of $cdot$-ideals in $PMV$-algebras
F. Forouzesh
frouzesh@bam.ac.ir
1
Faculty of Mathematics and computing, Higher Education complex of Bam, Bam, Iran.
In this paper, we introduce the notion of the radical of a $PMV$-algebra $A$ and we charactrize radical $A$ via elements of $A$. Also, we introduce the notion of the radical of a $cdot$-ideal in $PMV$-algebras. Several characterizations of this radical is given. We define the notion of a semimaximal $cdot$-ideal in a $PMV$-algebra. Finally we show that $A/I$ has no nilpotent elements if and only if $I$ is a semi-maximal $cdot$-ideal of $A$.
http://bims.iranjournals.ir/article_756_d1afd5d234b5acc222bd74060762df14.pdf
$PMV$-algebra
$cdot$-ideal
$cdot$-prime ideal
radical
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2016-04-01
42
2
247
262
757
Existence of solutions of boundary value problems for Caputo fractional differential equations on time scales
R. A. Yan
yanrian89@163.com
1
S. R. Sun
sshrong@163.com
2
Z. L. Han
hanzhenlai@163.com
3
School of Mathematical Sciences, University of Jinan, Jinan, Shandong 250022, P R China
School of Mathematical Sciences, University of Jinan, Jinan, Shandong 250022, P R China
School of Mathematical Sciences, University of Jinan, Jinan, Shandong 250022, P R China
In this paper, we study the boundary-value problem of fractional
order dynamic equations on time scales,
$$
^c{Delta}^{alpha}u(t)=f(t,u(t)),;;tin
[0,1]_{mathbb{T}^{kappa^{2}}}:=J,;;1
http://bims.iranjournals.ir/article_757_6c272666edd826df2c68e8aa2ebafd12.pdf
Fractional differential equation
Time scales
Boundary-value problem
Fixed-point theorem
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2016-04-01
42
2
263
284
758
Locally GCD domains and the ring $D+XD_S[X]$
G. W. Chang
whan@incheon.ac.kr
1
T. Dumitrescu
tiberiu@fmi.unibuc.ro
2
M. Zafruhhah
mzafrullah@usa.net
3
Department of Mathematics Education, Incheon National University, Incheon 406-772, Republic of Korea.
Facultatea de Matematica si Informatica, University of Bucharest, 14 Academiei Str., Bucharest, RO 010014, Romania
Department of Mathematics, Idaho State University, Poca-tello, ID 83209, USA
An integral domain $D$ is called a emph{locally GCD domain} if $D_{M}$ is aGCD domain for every maximal ideal $M$ of $D$. We study somering-theoretic properties of locally GCD domains. E.g., we show that $%D$ is a locally GCD domain if and only if $aDcap bD$ is locally principalfor all $0neq a,bin D$, and flat overrings of a locally GCD domain arelocally GCD. We also show that the t-class group of a locally GCD domain isjust its Picard group. We study when a locally GCD domain is Pr"{u}fer or ageneralized GCD domain.We also characterize locally factorial domains as domains $D$ whose minimal prime idealsof a nonzero principal ideal are locally principal and discuss conditions that make them Krull domains.We use the $D+XD_{S}[X]$ construction to give someinteresting examples of locally GCD domains that are not GCD domains.
http://bims.iranjournals.ir/article_758_519fca69eb4a638b55fe87c7eafe3be6.pdf
locally GCD domain
generalized GCD domain
$D+XD_S[X]$
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2016-04-01
42
2
285
295
759
Sufficiency and duality for a nonsmooth vector optimization problem with generalized $alpha$-$d_{I}$-type-I univexity over cones
H. Jiao
jiaohh361@126.com
1
School of Mathematics and Statistics, Yangtze Normal University, Chongqing 408100, P. R. China.
In this paper, using Clarke’s generalized directional derivative and dI-invexity we introduce new concepts of nonsmooth K-α-dI-invex and generalized type I univex functions over cones for a nonsmooth vector optimization problem with cone constraints. We obtain some sufficient optimality conditions and Mond-Weir type duality results under the foresaid generalized invexity and type I cone-univexity assumptions.
http://bims.iranjournals.ir/article_759_d37d71e77deecebe9efed9e81fb10b79.pdf
Vector optimization
Type I univexity
Cones
Optimality
duality
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2016-04-01
42
2
297
314
760
A new approach for solving the first-order linear matrix differential equations
A. Golbabai
golbabai@iust.ac.ir
1
S. P. A. Beik
panjehali@iust.ac.ir
2
D. K. Salkuyeh
salkuyeh@gmail.com
3
School of Mathematics, Iran University of Science and Technology, P.O. Box 16846-13114, Tehran, Iran.
School of Mathematics, Iran University of Science and Technology, P.O. Box 16846-13114, Tehran, Iran
Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran
Abstract. The main contribution of the current paper is to propose a new effective numerical method for solving the first-order linear matrix differential equations. Properties of the Legendre basis operational matrix of integration together with a collocation method are applied to reduce the problem to a coupled linear matrix equations. Afterwards, an iterative algorithm is examined for solving the obtained coupled linear matrix equations. Numerical experiments are presented to demonstrate the applicably and efficiency of our method.
http://bims.iranjournals.ir/article_760_2cfb83ffe97a3eb87e63d4a2121a528b.pdf
Linear matrix differential equation
Legendre polynomials
Coupled linear matrix
equations
Iterative algorithm
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2016-04-01
42
2
315
326
761
An analytic solution for a non-local initial-boundary value problem including a partial differential equation with variable coefficients
M. Jahanshahi
jahanshahi@azaruniv.edu
1
M. Darabadi
m.darabadi@azaruni.edu
2
Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran.
Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran
This paper considers a non-local initial-boundary value problem containing a first order partial differential equation with variable coefficients. At first, the non-self-adjoint spectral problem is derived. Then its adjoint problem is calculated. After that, for the adjoint problem the associated eigenvalues and the subsequent eigenfunctions are determined. Finally the convergence of series solution and the uniqueness of this solution will be proved.
http://bims.iranjournals.ir/article_761_706ebf130c6496e7db6e47caf0549442.pdf
Partial Differential Equation
Boundary Value
Problem
Self Adjoint Problem
Non-Self Adjoint Operators
Non-Local-Boundary Conditions
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2016-04-01
42
2
327
330
762
Trivially related lax pairs of the Sawada-Kotera equation
D. Talati
talati@eng.ankara.edu.tr
1
Sama Technical and Vocational Training College, Islamic Azad university, Urmia Branch, Urmia, Iran.
We show that a recently introduced Lax pair of the Sawada-Kotera equation is nota new one but is trivially related to the known old Lax pair. Using the so-called trivialcompositions of the old Lax pairs with a differentially constrained arbitrary operators,we give some examples of trivial Lax pairs of KdV and Sawada-Kotera equations.
http://bims.iranjournals.ir/article_762_f60c4b68590b1689ee7d3635b080f175.pdf
Sawada-Kotera equation
Lax pair
integrability
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2016-04-01
42
2
331
340
763
On Silverman's conjecture for a family of elliptic curves
K. Nabardi
nabardi@azaruniv.edu
1
F. Izadi
izadi@azaruniv.edu
2
Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz 53751-71379, Iran.
Department of Mathematics, Azarbaijan Shahid Madani University, P. O. Box 53751-71379, Tabriz , Iran.
Let $E$ be an elliptic curve over $Bbb{Q}$ with the given Weierstrass equation $ y^2=x^3+ax+b$. If $D$ is a squarefree integer, then let $E^{(D)}$ denote the $D$-quadratic twist of $E$ that is given by $E^{(D)}: y^2=x^3+aD^2x+bD^3$. Let $E^{(D)}(Bbb{Q})$ be the group of $Bbb{Q}$-rational points of $E^{(D)}$. It is conjectured by J. Silverman that there are infinitely many primes $p$ for which $E^{(p)}(Bbb{Q})$ has positive rank, and there are infinitely many primes $q$ for which $E^{(q)}(Bbb{Q})$ has rank $0$. In this paper, assuming the parity conjecture, we show that for infinitely many primes $p$, the elliptic curve $E_n^{(p)}: y^2=x^3-np^2x$ has odd rank and for infinitely many primes $p$, $E_n^{(p)}(Bbb{Q})$ has even rank, where $n$ is a positive integer that can be written as biquadrates sums in two different ways, i.e., $n=u^4+v^4=r^4+s^4$, where $u, v, r, s$ are positive integers such that $gcd(u,v)=gcd(r,s)=1$. More precisely, we prove that: if $n$ can be written in two different ways as biquartic sums and $p$ is prime, then under the assumption of the parity conjecture $E_n^{(p)}(Bbb{Q})$ has odd rank (and so a positive rank) as long as $n$ is odd and $pequiv5, 7pmod{8}$ or $n$ is even and $pequiv1pmod{4}$. In the end, we also compute the ranks of some specific values of $n$ and $p$ explicitly.
http://bims.iranjournals.ir/article_763_4e8380b4a993b2881f9ee0d5d1e2181c.pdf
Silverman's Conjecture
Elliptic Curve
Quadratic Twist
Rank
Parity Conjecture
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2016-04-01
42
2
341
351
764
Every class of $S$-acts having a flatness property is closed under directed colimits
H. Qiao
qiaohs@nwnu.edu.cn
1
L. Wang
wanglm@nwnu.edu.cn
2
X. Ma
maxin263@126.com
3
College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, P. R. China.
College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, P. R. China.
College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, P. R. China.
Let $S$ be a monoid. In this paper, we prove every class of $S$-acts having a flatness property is closed underdirected colimits, it extends some known results. Furthermore thisresult implies that every $S$-act has a flatness cover if and only if it has a flatness precover.
http://bims.iranjournals.ir/article_764_8c92870856f42224b242cd3dc1feb5b5.pdf
Flatness
property
colimit
closed
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2016-04-01
42
2
353
369
765
Partial proof of Graham Higman's conjecture related to coset diagrams
Q. Mushtaq
pir_qmushtaq@yahoo.com
1
A. Razaq
makenqau@gmail.com
2
Vice Chancellor, The Islamia University of Bahawalpur, Pakistan.
Department of Mathematics, Govt. Post Graduate College Jauharabad, Pakistan.
Graham Higman has defined coset diagrams for PSL(2,ℤ). These diagrams are composed of fragments, and the fragments are further composed of two or more circuits. Q. Mushtaq has proved in 1983 that existence of a certain fragment γ of a coset diagram in a coset diagram is a polynomial f in ℤ[z]. Higman has conjectured that, the polynomials related to the fragments are monic and for a fixed degree, there are finite number of such polynomials. In this paper, we consider a family Ϝ of fragments such that each fragment in Ϝ contains one vertex fixed byF_v [(〖xy〗^(-1) )^(s_1 ) (xy)^(s_2 ) (〖xy〗^(-1) )^(s_3 ),(xy)^(q_1 ) (〖xy〗^(-1) )^(q_2 ) (xy)^(q_3 ) ]where s₁,s₂,s₃,q₁,q₂,q₃∈ℤ⁺, and prove Higman's conjecture for the polynomials obtained from the fragments in Ϝ.
http://bims.iranjournals.ir/article_765_b144cad7da2c8ab7c7be161d9bb12fe5.pdf
Modular group
Coset diagrams
projective line over finite field
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2016-04-01
42
2
371
405
766
Toroidalization of locally toroidal morphisms of 3-folds
R. Ahmadian
ahmadian@ipm.ir
1
School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5746, Tehran, Iran.
A toroidalization of a dominant morphism $varphi: Xto Y$ of algebraic varieties over a field of characteristic zero is a toroidal lifting of $varphi$ obtained by performing sequences of blow ups of nonsingular subvarieties above $X$ and $Y$. We give a proof of toroidalization of locally toroidal morphisms of 3-folds.
http://bims.iranjournals.ir/article_766_30a65aebf30dd4f836a00da605df90a7.pdf
Toroidalization
resolution of morphisms
principalization
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2016-04-01
42
2
407
416
767
Finite groups with $X$-quasipermutable subgroups of prime power order
X. Yi
yxlyixiaolan@163.com
1
X. Yang
yangxue0222@126.com
2
Department of Mathematics, Zhejiang Sci-Tech University, 310018, Hangzhou, P. R. China.
Department of Mathematics, Zhejiang Sci-Tech University, 310018, Hangzhou, P. R. China.
Let $H$, $L$ and $X$ be subgroups of a finite group$G$. Then $H$ is said to be $X$-permutable with $L$ if for some$xin X$ we have $AL^{x}=L^{x}A$. We say that $H$ is emph{$X$-quasipermutable } (emph{$X_{S}$-quasipermutable}, respectively) in $G$ provided $G$ has a subgroup$B$ such that $G=N_{G}(H)B$ and $H$ $X$-permutes with $B$ and with all subgroups (with all Sylowsubgroups, respectively) $V$ of $B$ such that $(|H|, |V|)=1$. Inthis paper, we analyze the influence of $X$-quasipermutable and$X_{S}$-quasipermutable subgroups on the structure of $G$. Some known results are generalized.
http://bims.iranjournals.ir/article_767_7c8f57226de334e589c125523eea2281.pdf
$X$-quasipermutable subgroup
Sylow subgroup
$p$-soluble group
$p$-supersoluble group
$p$-nilpotent group
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2016-04-01
42
2
417
425
768
The augmented Zagreb index, vertex connectivity and matching number of graphs
A. Ali
akbarali.maths@gmail.com
1
A. Bhatti
akhlaq.ahmad@nu.edu.pk
2
Z. Raza
zahid.raza@nu.edu.pk
3
Department of Mathematics, National University of Computer and Emerging Sciences, B-Block, Faisal Town, Lahore, Pakistan.
Department of Mathematics, National University of Computer and Emerging Sciences, B-Block, Faisal Town, Lahore, Pakistan.
Department of Mathematics, National University of Computer and Emerging Sciences, B-Block, Faisal Town, Lahore, Pakistan.and Department of Mathematics, College of Sciences, University of Sharjah, Sharjah, United Arab Emirates.
Let $Gamma_{n,kappa}$ be the class of all graphs with $ngeq3$ vertices and $kappageq2$ vertex connectivity. Denote by $Upsilon_{n,beta}$ the family of all connected graphs with $ngeq4$ vertices and matching number $beta$ where $2leqbetaleqlfloorfrac{n}{2}rfloor$. In the classes of graphs $Gamma_{n,kappa}$ and $Upsilon_{n,beta}$, the elements having maximum augmented Zagreb index are determined.
http://bims.iranjournals.ir/article_768_9ad3a73dc4b8f0abc057b82d03ab8eca.pdf
augmented Zagreb index
vertex connectivity
matching number
spanning subgraph
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2016-04-01
42
2
427
434
769
The unit sum number of Baer rings
N. Ashrafi
nashrafi@semnan.ac.ir
1
N. Pouyan
neda.pouyan@gmail.com
2
Semnan UniversityFaculty of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran.
Faculty of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran.
In this paper we prove that each element of any regular Baer ring is a sum of two units if no factor ring of R is isomorphic to Z_2 and we characterize regular Baer rings with unit sum numbers $omega$ and $infty$. Then as an application, we discuss the unit sum number of some classes of group rings.
http://bims.iranjournals.ir/article_769_b7f142c271337a1f63d0a503031cec1d.pdf
unit sum number
regular Baer ring
$pi$-regular Baer
ring
right perpetual ideal
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2016-04-01
42
2
435
446
770
Existence of ground states for approximately inner two--parameter $C_0$--groups on $C^*$--algebras
R. Abazari
rasoolabazari@gmail.com
1
A. Niknam
niknam@um.ac.ir
2
Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran.
Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran.
In this paper, we generalize the definitions of approximately inner $C_0$-groups and their ground states to the two- parameter case and study necessary and sufficient conditions for a state to be ground state. Also we prove that any approximately inner two- parameter $C_0$--group must have at least one ground state. Finally some applications are given.
http://bims.iranjournals.ir/article_770_d466d7717510eb9caf6af9b237000141.pdf
Two--parameter group
Approximately inner dynamical system
Tensor product
Ground state
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2016-04-01
42
2
447
459
771
Remarks on microperiodic multifunctions
J. Olko
olko@agh.edu.pl
1
AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Kraków, Poland.
It is well known that a microperiodic function mapping a topological group into reals, which is continuous at some point is constant. We introduce the notion of a microperiodic multifunction, defined on a topological group with values in a metric space, and study regularity conditions implying an analogous result. We deal with Vietoris and Hausdorff continuity concepts.Stability of microperiodic multifunctions is considered, namely we show that an approximately microperiodic multifunction is close to a constant one, provided it is continuous at some point. As a consequence we obtain stability result for an approximately microperiodic single-valued function.
http://bims.iranjournals.ir/article_771_daeaa7f55c0826ade1687602332086b4.pdf
multifunction
microperiodic function
functional inequality
functional inclusion
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2016-04-01
42
2
461
470
772
On cycles in intersection graphs of rings
N. Hoseini
nesa.hoseini@gmail.com
1
A. Erfanian
erfanian@math.um.ac.ir
2
A. Azimi
ali.azimi61@gmail.com
3
M. Farrokhi D. G.
m.farrokhi.d.g@gmail.com
4
Department of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran.
Department of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran.
Department of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran.
Department of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran.
Let $R$ be a commutative ring with non-zero identity. We describe all $C_3$- and $C_4$-free intersection graph of non-trivial ideals of $R$ as well as $C_n$-free intersection graph when $R$ is a reduced ring. Also, we shall describe all complete, regular and $n$-claw-free intersection graphs. Finally, we shall prove that almost all Artin rings $R$ have Hamiltonian intersection graphs. We show that such graphs are indeed pancyclic.
http://bims.iranjournals.ir/article_772_474628f752047d413e00702e57860add.pdf
Intersection graph
cycle
claw
Hamiltonian
pancyclic
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2016-04-01
42
2
471
481
773
On linear preservers of sgut-majorization on $textbf{M}_{n,m}$
A. Ilkhanizadeh Manesh
a.ilkhani@vru.ac.ir
1
Department of Mathematics, Vali-e-Asr University of Rafsanjan, P.O. Box 7713936417, Rafsanjan, Iran.
Abstract. Let Mn;m be the set of n-by-m matrices with entries inthe field of real numbers. A matrix R in Mn = Mn;n is a generalizedrow substochastic matrix (g-row substochastic, for short) if Re e, where e = (1; 1; : : : ; 1)t. For X; Y 2 Mn;m, X is said to besgut-majorized by Y (denoted by X sgut Y ) if there exists ann-by-n upper triangular g-row substochastic matrix R such thatX = RY . This paper characterizes all linear preservers and stronglinear preservers of sgut on Rn and Mn;m respectively.
http://bims.iranjournals.ir/article_773_f2bdfc65aa79e88076d077bd50940a73.pdf
Linear preserver
Strong linear preserver
g-row substochastic matrices
sgut-
majorization
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2016-04-01
42
2
483
487
774
Examples of non-quasicommutative semigroups decomposed into unions of groups
N. Hosseinzadeh
narges.hosseinzadeh@gmail.com
1
H. Doostie
doostih@khu.ac.ir
2
Department of Mathematics, Tehran Science and Research Branch, Islamic Azad University, P.O. Box 14515/1775, Tehran, Iran.
Department of Mathematics, Tehran Science and Research Branch, Islamic Azad University, P.O. Box 14515/1775, Tehran, Iran.
Decomposability of an algebraic structure into the union of its sub-structures goes back to G. Scorza's Theorem of 1926 for groups. An analogue of this theorem for rings has been recently studied by A. Lucchini in 2012. On the study of this problem for non-group semigroups, the first attempt is due to Clifford's work of 1961 for the regular semigroups. Since then, N.P. Mukherjee in 1972 studied the decomposition of quasicommutative semigroups where, he proved that: a regular quasicommutative semigroup is decomposable into the union of groups. The converse of this result is a natural question. Obviously, if a semigroup $S$ is decomposable into a union of groups then $S$ is regular so, the aim of this paper is to give examples of non-quasicommutative semigroups which are decomposable into the disjoint unions of groups. Our examples are the semigroups presented by the following presentations: $$pi_1 =langle a,bmid a^{n+1}=a, b^3=b, ba=a^{n-1}brangle,~(ngeq 3),$$ $$pi_2 =langle a,bmid a^{1+p^alpha}=a, b^{1+p^beta}=b, ab=ba^{1+p^{alpha-gamma}}rangle$$where, $p$ is an odd prime, $alpha, beta$ and $gamma$ are integers such that $alpha geq 2gamma$, $beta geq gamma geq 1$ and $alpha +beta > 3$.
http://bims.iranjournals.ir/article_774_d1f0dd06cdd8ca40e4a11a7315f27db4.pdf
quasicommutative semigroups
finitely presented semigroups
decomposition
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2016-04-01
42
2
489
497
775
Pseudo Ricci symmetric real hypersurfaces of a complex projective space
S. k. Hui
shyamal_hui@yahoo.co.in
1
Y. Matsuyama
matuyama@math.chuo-u.ac.jp
2
Department of Mathematics, Sidho Kanho Birsha University, Purulia-723104, West Bengal, India.\newline Department of Mathematics, Bankura University, Bankura-722155, West Bengal, India.
Department of Mathematics, Chuo University, Faculty of Science and Engineering, 1-13-27 Kasuga, Bunkyo-ku, Tokyo 112-8551, Japan.
Pseudo Ricci symmetric real hypersurfaces of a complex projective space are classified and it is proved that there are no pseudo Ricci symmetric real hypersurfaces of the complex projective space CPn for which the vector field ξ from the almost contact metric structure (φ, ξ, η, g) is a principal curvature vector field.
http://bims.iranjournals.ir/article_775_19d72442dec53b5d5a278fded703c98e.pdf
real hypersurface
complex projective space
pseudo Ricci symmetric