2016
42
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Equivalent a posteriori error estimates for spectral element solutions of constrained optimal control problem in one dimension
2
2
In this paper, we study spectral element approximation for a constrained optimal control problem in one dimension. The equivalent a posteriori error estimators are derived for the control, the state and the adjoint state approximation. Such estimators can be used to construct adaptive spectral elements for the control problems.
1

1
18


X.
Ye
School of Science, Jimei University, 361021 Xiamen, China.
School of Science, Jimei University
China (P. R. C.)
xingyangye@163.com
Optimal control problem
spectral element method
a posteriori error estimates
control constraint
polynomial inverse estimates
[M. Ainsworth and J. T. Oden, A posteriori error estimation in finite element analysis, Comput. Methods Appl. Mech. Engrg. 142 (1997), no. 12, 188. ##I. Babuska and W. C. Rheinboldt, A posteriori error estimates for the finite element method, Internat. J. Numer. Methods Engrg. 12, no. 10, 15971615, 1978. ##I. Babuska and W. C. Rheinboldt, Error estimates for adaptive finite element computa tions, SIAM J. Numer. Anal. 15 (1978), no. 4, 736754. ##I. Babuska and T. Strouboulis, The Finite Element Method and its Reliability, The Clarendon Press, Oxford University Press, New York, 2001. ##I. Babuska and G. N. Gatica, A residualbased a posteriori error estimator for the StokesDarcy coupled problem, SIAM J. Numer. Anal. 48 (2010), no. 2, 498523. ##R. Becker, H. Kapp and R. Rannacher, Adaptive finite element methods for optimal control of partial differential equations: Basic concept, SIAM J. Control Optim. 39 (2000), no. 1, 113132. ##C. Bernardi and Y. Maday, Spectral Methods, Handbook of Numerical Analysis, 209 485, Handb. Numer. Anal., V, NorthHolland, Amsterdam, 1997. ##C. Bernardi, N. Fietier and G. R. Owens, An error indicator for mortar element solutions to the Stokes problem, IMA J. Numer. Anal. (2001), no. 4, 857886. ##C. Bernardi, Indicateurs d'erreur en hN version des elements spectraux, RAIRO Model. Math. Anal. Numer 30 (1996), no. 1, 138. ##C. Canuto, M. Y. Hussaini, A. Quarteroni and T. A. Zang, Spectral methods. Fundamentals in single domains. Scientific Computation, SpringerVerlag, Berlin, 2006. ##Y. Chen, N. Yi and W. Liu, A LegendreGalerkin spectral method for optimal control problems governed by elliptic equations, SIAM J. Numer. Anal. 46 (2008), no. 5, 22542275. ##Y. P. Chen, F. L. Huang, N. Y. Yi and W. B. Liu, A LegendreGalerkin spectral method for optimal control problems governed by Stokes Equations, SIAM J. Numer. Anal. 49 (2011), no. 4, 16251648. ##Y. P. Chen and Y. J. Lin, A posteriori error estimates for hp finite element solutions of convex optimal control problems, J. Comput. Appl. Math. 235 (2011), no. 12, 34353454. ##Q. Du, L. Ju, L. Tian and K. Zhou, A posteriori error analysis of finite element method for linear nonlocal diffusion and peridynamic models, Math. Comp. 82 (2013), no. 284, 18891922. ##L. Ge, W. Liu and D. Yang, Adaptive finite element approximation for a constrained optimal control problem via multimeshes, J. Sci. Comput. 41 (2009), no. 2, 238255. ##R. Ghanem and H. Sissaoui, A posteriori error estimate by a spectral method of an elliptic optimal control problem, J. Comput. Math. Optim. 2 (2006), no. 2, 111125. ##W. Gong, W. B. Liu and N. N. Yan, A posteriori error estimates of hpFEM for optimal control problems, Int. J. Numer. Anal. Model. 8 (2011), no. 1, 4869. ##B. Guo, Recent progress on aposteriori error analysis for the p and hp finite element methods, Contemporary Mathematics 383 (2005) 4762. ##K. Kohls, A. Rosch and K. G. Siebert, A posteriori error analysis of optimal control problems with control constraints, SIAM J. Control Optim. 52 (2014), no. 3, 18321861. ##J. L. Lions, Optimal Control of Systems Governed by Partial Differential Equations, SpringerVerlag, New YorkBerlin, 1971. ##R. Li, W. Liu, H. Ma and T. Tang, Adaptive finite element approximation for distributed elliptic optimal control problems, SIAM J. Control Optim., 41 (2002), no. 5, 13211349. ##W. Liu and N. Yan, A posteriori error estimates for convex boundary control problems, SIAM J. Numer. Anal. 39 (2001), no. 1, 7399. ##J. M. Melenk and B. I. Wohlmuth, On residualbased a posteriori error estimation in hpFEM, Adv. Comput. Math. 15 (2001), no. 14, 311331. ##C. Schwab, pand hpFinite Element Methods, Oxford Univ. Press, New York, 1998. ##A. Veeser, Efficient and reliable a posteriori error estimators for elliptic obstacle problems, SIAM J. Numer. Anal. 39 (2001), no. 1, 146167.##]
Some connections between powers of conjugacy classes and degrees of irreducible characters in solvable groups
2
2
Let $G$ be a finite group. We say that the derived covering number of $G$ is finite if and only if there exists a positive integer $n$ such that $C^n=G'$ for all noncentral conjugacy classes $C$ of $G$. In this paper we characterize solvable groups $G$ in which the derived covering number is finite.
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19
25


S.
M. Robati
Department of
Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, Iran
Department of
Mathematics, Faculty
Iran
sajjad.robati@gmail.com
Conjugacy classes
irreducible characters
solvable groups
[M. Bianchi, A. G. B. Mauri, M. Herzog, G. Qian and W. Shi, Characterization of nonnilpotent groups with two irreducible character degrees, J. Algebra 284 (2005), no. 1, 326332. ##M. R. Darafsheh and S. M. Robati, Powers of irreducible characters and conjugacy classes in finite groups, J. Algebra Appl. 13 (2014), no. 8, 9 pages. ##L. Dornhoff, Group representation theory, Part A: Ordinary representation theory, Marcel Dekker, Inc., New York, 1971. ##I. M. Isaacs, Character theory of finite groups, Academic Press, New YorkSan FranciscoLondon, 1976. ##K. Ishikawa, On finite pgroups which have only two conjugacy lengths, Israel J. Math. 129 (2002) 119123. ##B. Srinivasan, The characters of the finite symplectic group Sp(4; q), Trans. Amer. Math. Soc. 131 (1968) 488525.##]
Characterization of some projective special linear groups in dimension four by their orders and degree patterns
2
2
Let $G$ be a finite group. The degree pattern of $G$ denoted by $D(G)$ is defined as follows: If $pi(G)={p_{1},p_{2},...,p_{k}}$ such that $p_{1}<p_{2}<...<p_{k}$, then $D(G):=(deg(p_{1}),deg(p_{2}),...,deg(p_{k}))$, where $deg(p_{i})$ for $1leq ileq k$, are the degree of vertices $p_{i}$ in the prime graph of $G$. In this article, we consider a finite group $G$ under assumptions $G=L_{4}(2^{n})$ and $D(G)=D(L_{4}(2^{n}))$, where $nin{5, 6, 7}$ and we prove that $Gcong L_{4}(2^{n})$.
1

27
36


M.
Sajjadi
Department of Mathematics, Payame Noor University,
Iran.
Department of Mathematics, Payame
Iran
masa.irsh@gmail.com


M.
Bibak
Department of Mathematics, Payame Noor University,
Iran.
Department of Mathematics, Payame
Iran
m.bibak62@gmail.com


G. R.
Rezaeezadeh
Department
of Mathematics, University
of Shahrekord, Shahrekord, Iran.
Department
of Mathematics,
Iran
gh.rezaeezadeh@yahoo.com;rezaeezadeh@sci.sku.ac.ir
Degree pattern
prime graph
projective special linear group
On Tychonoff's type theorem via grills
2
2
Let ${X_{alpha}:alphainLambda}$ be a collection of topological spaces, and $mathcal {G}_{alpha}$ be a grill on $X_{alpha}$ for each $alphainLambda$. We consider Tychonoffrq{}s type Theorem for $X=prod_{alphainLambda}X_{alpha}$ via the above grills and a natural grill on $X$ related to these grills, and present a simple proof to this theorem. This immediately yields the classical theorem of Tychonoff. We shall also observe> that the above result is also equivalent to the Axiom of Choice.
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37
41


A.
Talabeigi
Department of Mathematics, Payam Noor University, Tehran, Iran.
Department of Mathematics, Payam
Iran
talabeigi@phd.pnu.ac.ir;talabeigi.amin@gmail.com
Tychonoff's theorem
grills
Axiom of Choice
On the decomposition of noncosingular $sum$lifting modules
2
2
Let $R$ be a right artinian ring or a perfect commutativering. Let $M$ be a noncosingular selfgenerator $sum$liftingmodule. Then $M$ has a direct decomposition $M=oplus_{iin I} M_i$,where each $M_i$ is noetherian quasiprojective and eachendomorphism ring $End(M_i)$ is local.
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43
48


T.
Amouzegar
Department of
Mathematics, Quchan University of Advanced Technology, Quchan, Iran.
Department of
Mathematics, Quchan
Iran
t.amoozegar@yahoo.com
Noncosingular module
lifting module
$sum$lifting module
Erratum: Coupled fixed point results for weakly related mappings in partially ordered metric spaces
2
2
In this note we point out and rectify some errors in a recently published paper “N. Singh, R. Jain: Coupled Fixed Point Results For Weakly Related Mappings In Partially Ordered Metric Spaces, Bull. Iranian Math. Soc. 40 (2014), no. 1, 2940”.
1

49
52


M.
Jain
Department of Mathematics, Ahir College, Rewari 123401, India.
Department of Mathematics, Ahir
India
manish_261283@rediffmail.com


N.
Gupta
HAS Department, YMCAUST, Faridabad, India.
HAS Department, YMCAUST, Farid
India
neetuymca@yahoo.co.in


S.
Kumar
Department of Mathematics, DCRUST, Murthal, Sonepat, India.
Department of Mathematics, DCRUST,
India
sanjuciet@rediffmail.com
Coupled fixed point
common coupled fixed point
partially ordered space
weakly related mappings
The reverse order law for MoorePenrose inverses of operators on Hilbert C*modules
2
2
Suppose $T$ and $S$ are MoorePenrose invertible operators betweenHilbert C*module. Some necessary and sufficient conditions are given for thereverse order law $(TS)^{ dag} =S^{ dag} T^{ dag}$ to hold.In particular, we show that the equality holds if and only if $Ran(T^{*}TS) subseteq Ran(S)$ and $Ran(SS^{*}T^{*}) subseteq Ran(T^{*}),$ which was studied first by Greville [{it SIAM Rev. 8 (1966) 518521}] for matrices.
1

53
60


K.
Sharifi
Department of Mathematics, Shahrood University of Technology, and, Mathematisches Institut, Fachbereich Mathematik und Informatik der Universitat Munster, Einsteinstrasse 62, 48149 Munster, Germany.
Department of Mathematics, Shahrood University
Iran
sharifi.kamran@gmail.com


Behnaz
A. Bonakdar
Department of Mathematics, International Campus of Ferdowsi University, Mashhad, Iran.
Department of Mathematics,
Iran
b.a.bonakdar1@gmail.com
Bounded adjointable operator
Hilbert C*module
generalized inverse
reverse order law
Frames in right ideals of $C^*$algebras
2
2
we investigate the problem of the existence of a frame forright ideals of a C*algebra A, without the use of the Kasparov stabilizationtheorem. We show that this property can not characterize A as a C*algebraof compact operators.
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61
67


M. B.
Asadi
School of Mathematics, Statistics and Computer Science,
College of Science, University of Tehran, Tehran,
Iran, and, School of Mathematics, Institute for Research in Fundamental Sciences
School of Mathematics, Statistics
Iran
mb.asadi@gmail.com
Hilbert C*modules
frames
C*algebras
Linear operators of Banach spaces with range in Lipschitz algebras
2
2
In this paper, a complete description concerning linear operators of Banach spaces with range in Lipschitz algebras $lip_al(X)$ is provided. Necessary and sufficient conditions are established to ensure boundedness and (weak) compactness of these operators. Finally, a lower bound for the essential norm of such operators is obtained.
1

69
78


H.
Mahyar
Department of Mathematics, Faculty of Mathematical Sciences and
Computer, Kharazmi University, 50, Taleghani Ave., 15618, Tehran, Iran.
Department of Mathematics, Faculty
Iran
mahyar@khu.ac.ir


A.
Golbaharan
Department of Mathematics, Faculty of Mathematical Sciences and
Computer, Kharazmi University, 50, Taleghani Ave., 15618, Tehran, Iran.
Department of Mathematics, Faculty
Iran
golbaharan_azin@yahoo.com
Lipschitz algebra
compact linear operator
weakly compact linear operator
essential norm
The Jacobsthal Sequences in Finite Groups
2
2
Abstract In this paper, we study the generalized order Jacobsthal sequences modulo for and the generalized orderk JacobsthalPadovan sequence modulo for . Also, we define the generalized orderk Jacobsthal orbit of a kgenerator group for and the generalized orderk JacobsthalPadovan orbit a kgenerator group for . Furthermore, we obtain the lengths of the periods of the generalized order3 Jacobsthal orbit and the generalized order3 JacobsthalPadovan orbit of the direct product, and the semidirect product .
1

79
89


Ö
Deveci
Department of Mathematics, Faculty of Science
and Letters, Kafkas University, 36100 Kars, Turkey.
Department of Mathematics, Faculty
Turkey
odeveci36@hotmail.com


E.
Karaduman
Department of Mathematics, Faculty of Science, Ataturk University, 25240 Erzurum, Turkey.
Department of Mathematics, Faculty
Turkey
eduman@atauni.edu.tr


G.
Sağlam
Department of Mathematics, Faculty of Science
and Letters, Kafkas University, 36100 Kars, Turkey.
Department of Mathematics, Faculty
Turkey
saglamgencay25@hotmail.com
Length
Jacobsthal sequence
finite group
A generalization of $oplus$cofinitely supplemented modules
2
2
We say that a module $M$ is a emph{cmsmodule} if, for every cofinite submodule $N$ of $M$, there exist submodules $K$ and $K^{'}$ of $M$ such that $K$ is a supplement of $N$, and $K$, $K^{'}$ are mutual supplements in $M$. In this article, the various properties of cmsmodules are given as a generalization of $oplus$cofinitely supplemented modules. In particular, we prove that a $pi$projective module $M$ is a cmsmodule if and only if $M$ is $oplus$cofinitely supplemented. Finally, we show that every free $R$module is a cmsmodule if and only if $R$ is semiperfect.
1

91
99


B.
Koşar
Ondokuz Mayis University, Samsun, Turkey.
Ondokuz Mayis University, Samsun,
Turkey
bernak@omu.edu.tr


B. N.
Türkmen
Amasya University, Faculty of Art and Science, Ipekkoy, Amasya, Turkey.
Amasya University, Faculty of Art
Turkey
burcunisancie@hotmail.com
Supplements
cofinite submodule
($oplus$)cofinitely supplemented module
Amenability of groups and semigroups characterized by configuration
2
2
In 2005, A. Abdollahi and A. Rejali, studied the relations betweenparadoxical decomposition and configuration for semigroups. In thepresent paper, we introduce one other concept of amenability typeon semigroups and groups which includes amenability of semigroupsand inneramenability of groups. We have extend the previous knownresults to semigroups and groups satisfying this concept.
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101
112


A.
Tavakoli
Department of Mathematics, Meymeh Branch, Islamic Azad
University, Meymeh, Iran.
Department of Mathematics, Meymeh Branch,
Iran
at4300125@gmail.com


A.
Rejali
Department of Mathematics, University of Isfahan, Isfahan, Iran.
Department of Mathematics, University
Iran
rejali@sci.ui.ac.ir
Amenability
configuration
paradoxical decomposition
semigroup
Rings for which every simple module is almost injective
2
2
We introduce the class of “right almost Vrings” which is properly between the classes of right Vrings and right good rings. A ring R is called a right almost Vring if every simple Rmodule is almost injective. It is proved that R is a right almost Vring if and only if for every Rmodule M, any complement of every simple submodule of M is a direct summand. Moreover, R is a right almost Vring if and only if for every simple Rmodule S, either S is injective or the injective hull of S is projective of length 2. Right Artinian right almost Vrings and right Noetherian right almost Vrings are characterized. A 2×2 upper triangular matrix ring over R is a right almost Vring precisely when R is semisimple.
1

113
127


Sh.
Asgari
Department of Mathematical Sciences, University of Isfahan, Isfahan, Iran, and School of Mathematics, Institute for Research in Fundamental Sciences (IPM), Tehran, Iran.
Department of Mathematical Sciences,
Iran
sh_asgari@ipm.ir


M.
ArabiKakavand
Department of Mathematical Sciences, Isfahan University of Technology, Isfahan, Iran.
Department of Mathematical Sciences,
Iran
m.arabikakavand@math.iut.ac.ir


H.
Khabazian
Department of Mathematical Sciences, Isfahan University of Technology, Isfahan, Iran.
Department of Mathematical Sciences,
Iran
khabaz@cc.iut.ac.ir
Almost injective modules
$V$rings
almost $V$rings
On nonlocal elliptic system of $p$Kirchhofftype in $mathbb{R}^N$
2
2
Using Nehari manifold methods and Mountain pass theorem, the existence of nontrivial and radially symmetric solutions for a class of $p$Kirchhofftype system are established.
1

129
141


L.
Liu
College of Sciences, Hohai University,
Nanjing 210098, P.R. of China.
College of Sciences, Hohai University&l
China, R. O. C.
liulihua11111@163.com


C.
Chen
College of Sciences, Hohai University,
Nanjing 210098, P.R. of China.
College of Sciences, Hohai University&l
China (P. R. C.)
cshengchen@hhu.edu.cn
$p$Kirchhofftype elliptic system
Nehari manifold
mountain pass theorem
Weak logmajorization inequalities of singular values between normal matrices and their absolute values
2
2
This paper presents two main results that the singular values of the Hadamard product of normal matrices $A_i$ are weakly logmajorized by the singular values of the Hadamard product of $A_{i}$ and the singular values of the sum of normal matrices $A_i$ are weakly logmajorized by the singular values of the sum of $A_{i}$. Some applications to these inequalities are also given. In addition, several related and new inequalities are obtained.
1

143
153


D.
Chen
School of Mathematical Sciences, Huaibei Normal University, Huaibei 235000, P.R. China.
School of Mathematical Sciences, Huaibei
China (P. R. C.)
djcmaths@163.com


Y.
Zhang
School of Mathematical Sciences, Huaibei Normal University, Huaibei 235000, P.R. China.
School of Mathematical Sciences, Huaibei
China (P. R. C.)
zhangyunmaths@163.com
Unitarily invariant norms
singular values
weak logmajorization
normal matrices
Hadamard product
Positive solution for Dirichlet $p(t)$Laplacian BVPs
2
2
In this paper we provide existence results for positive solution to Dirichlet p(t)Laplacian boundary value problems. The sublinear and superlinear cases are considerd.
1

155
173


A.
Benmezai
Faculty of Mathematics, USTHB, Algiers, Algeria.
Faculty of Mathematics, USTHB,
Algeria
aehbenmezai@gmail.com


S.
Mechrouk
Faculty of Sciences, UMB, Boumerdes, Algeria.
Faculty of Sciences, UMB,
Algeria
mechrouksalima@yahoo.fr
P(t)Laplacian
Positive solutions, Fixed point index theory
Continuous dependence on coefficients for stochastic evolution equations with multiplicative Levy Noise and monotone nonlinearity
2
2
Semilinear stochastic evolution equations with multiplicative L'evy noise are considered. The drift term is assumed to be monotone nonlinear and with linear growth. Unlike other similar works, we do not impose coercivity conditions on coefficients. We establish the continuous dependence of the mild solution with respect to initial conditions and also on coefficients. As corollaries of the continuity result, we derive sufficient conditions for asymptotic stability of the solutions, we show that Yosida approximations converge to the solution and we prove that solutions have Markov property. Examples on stochastic partial differential equations and stochastic delay differential equations are provided to demonstrate the theory developed. The main tool in our study is an inequality which gives a pathwise bound for the norm of stochastic convolution integrals.
1

175
194


E.
Salavati
Department of
Mathematical Sciences, Sharif University of Technology, P.O. Box 1136511155, Tehran, Iran.
Department of
Mathematical Sciences,
Iran
erfan.salavati@gmail.com,salavati@mehr.sharif.ir


B.
Zangeneh
Department of
Mathematical Sciences, Sharif University of Technology, P.O. Box 1136511155, Tehran, Iran.
Department of
Mathematical Sciences,
Iran
zangeneh@sharif.ir
Stochasic evolution equations
monotone nonlinearity
stochastic convolution integrals
L'evy processes
A note on lacunary series in $mathcal{Q}_K$ spaces
2
2
In this paper, under the condition that $K$ is concave, we characterize lacunary series in $Q_{k}$ spaces. We improve a result due to H. Wulan and K. Zhu.
1

195
200


J.
Zhou
School of Sciences,
Anhui University of Science and Technology,
Huainan, Anhui 232001, China.
School of Sciences,
Anhui University
China (P. R. C.)
hope189@163.com
$mathcal{Q}_K$ spaces
lacunary series
concave
Flagtransitive Pointprimitive symmetric designs and three dimensional projective special linear groups
2
2
The main aim of this article is to study (v,k,λ)symmetric designs admitting a flagtransitive and pointprimitive automorphism group G whose socle is PSL(3,q). We indeed show that the only possible design satisfying these conditions is a Desarguesian projective plane PG(2,q) and G > PSL(3,q).
1

201
221


S. H.
Alavi
Department of Mathematics, Faculty of Science, BuAli Sina University, Hamedan, Iran newline and newline School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 193955746,
Department of Mathematics, Faculty
Iran
alavi.s.hassan@gmail.com


M.
Bayat
Department of Mathematics, Faculty of Science, BuAli Sina University, Hamedan Iran.
Department of Mathematics, Faculty
Iran
mohsen0sayex24@gmail.com
automorphism group
pointprimitive
flagtransitive
Symmetric design
CohenMacaulayness in codimension for simplicial complexes and expansion functor
2
2
In this paper we show that expansion of a Buchsbaum simplicial complex is $CM_t$, for an optimal integer $tgeq 1$. Also, by imposing extra assumptions on a $CM_t$ simplicial complex, we provethat it can be obtained from a Buchsbaum complex.
1

223
232


R.
RahmatiAsghar
Department of Mathematics, Faculty of Basic Sciences, University of Maragheh,
P.O. Box 5518183111, Maragheh, Iran, and, School of Mathematics, Institute for
Research in Fundamental Sciences (IPM), P.O. Box 193955746, Tehran, Iran.
Department of Mathematics, Faculty of Basic
Iran
rahmatiasghar.r@gmail.com
$CM_t$ simplicial complex
expansion functor
simple graph