Bulletin of Iranian Mathematical Society
Volume:42 Issue: 1, 2016

ýIn this paperý, ýwe study spectral element approximation for a constrainedý ýoptimal control problem in one dimensioný. ýThe equivalent a posteriori error estimators are derived forý ýthe controlý, ýthe state and the adjoint state approximationý. ýSuch estimators can be used toý ýconstruct adaptive spectral elements for the control problems.

ýLet G G be a finite groupý. ýWe say that the derived covering number of G G is finite if and only if there exists a positive integer n n such that C n =G ′ Cn=G′ for all non-central conjugacy classes C C of G G ý. ýIn this paper we characterize solvable groups G G in which the derived covering number is finiteý.ý

ýLet G G be a finite groupý. ýThe degree pattern of G G denoted byý ýD(G) D(G) is defined as followsý: ýIf π(G)={p 1 ,p 2 ,...,p k } π(G)={p1,p2,...,pk} such thatý ýp 1

ýLet {X α :α∈Λ} {Xα:α∈Λ} be a collection of topological spacesý, ýand G α Gα be a grill on X α Xα for each α∈Λ α∈Λ ý. ýWe consider Tychonoff\rq{}s type Theorem for X=∏ α∈Λ X α X=∏α∈ΛXα via the above grills and a natural grill on X X ýrelated to these grills, and present a simple proof to this theoremý. ýThis immediately yields the classical theorem of Tychonoff. We shall also observe> that the above result is also equivalent to the Axiom of Choiceý.ý

Let R R be a right artinian ring or a perfect commutativeý ýringý. ýLet M M be a noncosingular self-generator ∑ ∑ -liftingý ýmoduleý. ýThen M M has a direct decomposition M=⊕ i∈I M i M=⊕i∈IMi ý, ýwhere each M i Mi is noetherian quasi-projective and eachý ýendomorphism ring End(M i ) End(Mi) is localý.

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, 29-40”.

Suppose T T and S S are Moore-Penrose invertible operators between Hilbert C*-module. Some necessary and sufficient conditions are given for the reverse order law (TS) dag =S dag T dag (TS)dag=SdagTdag to hold. In particular, we show that the equality holds if and only if Ran(T ∗ TS)subseteqRan(S) Ran(T∗TS)subseteqRan(S) and Ran(SS ∗ T ∗ )subseteqRan(T ∗ ), Ran(SS∗T∗)subseteqRan(T∗), which was studied first by Greville [{it SIAM Rev. 8 (1966) 518--521}] for matrices.

we investigate the problem of the existence of a frame for right ideals of a C*-algebra A, without the use of the Kasparov stabilization theorem. We show that this property can not characterize A as a C*-algebra of compact operators.

In this paper, a complete description concerning linear operators of Banach spaces with range in Lipschitz algebras lip a l(X) lipal(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.

Abstract In this paper, we study the generalized order- Jacobsthal sequences modulo for and the generalized order-k Jacobsthal-Padovan sequence modulo for . Also, we define the generalized order-k Jacobsthal orbit of a k-generator group for and the generalized order-k Jacobsthal-Padovan orbit a k-generator group for . Furthermore, we obtain the lengths of the periods of the generalized order-3 Jacobsthal orbit and the generalized order-3 Jacobsthal-Padovan orbit of the direct product, and the semidirect product .

ýWe say that a module M M is a \emph{cms-module} ifý, ýfor every cofinite submodule N N of M M ý, ýthere exist submodules K K and K ′ K′ of M M such that K K is a supplement of N N ý, ýand K K ý, ýK ′ K′ are mutual supplements in M M ý. ýIn this articleý, ýthe various properties of cms-modules are given as a generalization of ⊕ ⊕ -cofinitely supplemented modulesý. ýIn particularý, ýwe prove that a π π -projective module M M is a cms-module if and only if M M is ⊕ ⊕ -cofinitely supplementedý. ýFinallyý, ýwe show that every free R R -module is a cms-module if and only if R R is semiperfect.

In 2005, A. Abdollahi and A. Rejali, studied the relations between paradoxical decomposition and configuration for semigroups. In the present paper, we introduce one other concept of amenability type on semigroups and groups which includes amenability of semigroups and inner-amenability of groups. We have extend the previous known results to semigroups and groups satisfying this concept.

We introduce the class of “right almost V-rings” which is properly between the
classes of right V-rings and right good rings. A ring R is called a right almost V-ring if every simple R-module is almost injective. It is proved that R is a right almost V-ring if and only if
for every R-module M, any complement of every simple submodule of M is a direct summand. Moreover, R is a right almost V-ring if and only if for every simple R-module S, either S is injective or the injective hull of S is projective of length 2. Right Artinian right almost V-rings and right Noetherian right almost V-rings are characterized. A 2×2 upper triangular matrix ring over R is a right almost V-ring precisely when R is semisimple.

ýUsing Nehari manifold methods and Mountain pass theoremý, ýthe existence of nontrivial and radially symmetric solutions for a class of p p -Kirchhoff-type system are established.

ýThis paper presents two main results that the singular values of the Hadamard product of normal matrices A i Ai are weakly log-majorized by the singular values of the Hadamard product of |A i | |Ai| and the singular values of the sum of normal matrices A i Ai are weakly log-majorized by the singular values of the sum of |A i | |Ai| ý. ýSome applications to these inequalities are also givený. ýIn additioný, ýseveral related and new inequalities are obtainedý.

In this paper we provideý ýexistence results for positive solution toý ýDirichlet p(t)-Laplacian boundary value problemsý. ýThe sublinear andý ýsuperlinear cases are considerdý.

Semilinear stochastic evolution equations with multiplicative Levy noise are consideredý. ýThe drift term is assumed to be monotone nonlinear and with linear growthý. ýUnlike other similar worksý, ýwe do not impose coercivity conditions on coefficientsý. ýWe establish the continuous dependence of the mild solution with respect to initial conditions and also on coefficients. ýAs corollaries of the continuity resultý, ýwe derive sufficient conditions for asymptotic stability of the solutionsý, ýwe show that Yosida approximations converge to the solution and we prove that solutions have Markov propertyý. ýExamples on stochastic partial differential equations and stochastic delay differential equations are provided to demonstrate the theory developedý. ýThe main tool in our study is an inequality which gives a pathwise bound for the norm of stochastic convolution integralsý.

In this paper, under the condition that K K is concave, we characterize lacunary series in Q k Qk spaces. We improve a result due to H. Wulan and K. Zhu.

The main aim of this article is to study (v,k,λ)-symmetric designs admitting a flag-transitive and point-primitive 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).

In this paper we show that expansion of a Buchsbaum simplicial complex is CM t CMt , for an optimal integer tgeq1 tgeq1 . Also, by imposing extra assumptions on a CM t CMt simplicial complex, we prove that it can be obtained from a Buchsbaum complex.