Bulletin of Iranian Mathematical Society
Volume:41 Issue: 4, 2015

‎Let M n be an n(n≥3) -dimensional complete connected and‎ ‎oriented spacelike hypersurface in a de Sitter space or an anti-de‎ ‎Sitter space‎, ‎S and K be the squared norm of the second‎ ‎fundamental form and Gauss-Kronecker curvature of M n ‎. ‎If S or‎ ‎K is constant‎, ‎nonzero and M n has two distinct principal‎ ‎curvatures one of which is simple‎, ‎we obtain some‎ ‎characterizations of the Riemannian products‎: ‎S n−1 (a)×‎‎H 1 (a 2 −1 − − − − − √) ‎, ‎or H n−1 (a)×H 1 (1−a 2 − − − − − √) ‎.

The group 2 6 cdot G 2 (2) is a maximal subgroup of the Rudvalis group Ru of index 188500 and has order 774144 = 2 12. 3 3. 7. In this paper, we construct the character table of the group 2 6 cdot G 2 (2) by using the technique of Fischer-Clifford matrices.

‎In this work we prove Malliavin differentiability for the solution to an SDE with locally Lipschitz and semi-monotone drift‎. ‎To prove this formula‎, ‎we construct a sequence of SDEs with globally Lipschitz drifts and show that the p -moments of their Malliavin derivatives are uniformly bounded‎.

‎Using several examples of positive definite functions‎, ‎some inequalities for the numerical radius of‎ ‎matrices are investigated‎. ‎Also‎, ‎some open problems are stated‎.

Let A be a C ∗ -algebra and Z(A) the‎ ‎center of A ‎. ‎A sequence {L n} ∞ n=0 of‎ ‎linear mappings on A with L 0 =I ‎, ‎where I is the‎ ‎identity mapping‎ ‎on A ‎, ‎is called a Lie higher derivation if‎ ‎L n [x,y]=∑ i+j=n [L i x,L j y] for all x,y∈‎A and all n⩾0 ‎. ‎We show that‎ ‎{L n} ∞ n=0 is a Lie higher derivation if and only if‎ ‎there exist a higher derivation‎ ‎{D n: A→A} ∞ n=0 and a‎ ‎sequence of linear mappings {Δ n: A→‎‎Z(A)} ∞ n=0 ‎such that Δ 0 =0 ‎, ‎Δ n ([x,y])=0 and L n =D n +Δ n for every‎ ‎x,y∈A and all n≥0 ‎.

In this paper we focus on a special class of commutative local‎ ‎rings called SPAP-rings and study the relationship between this‎ ‎class and other classes of rings‎. ‎We characterize the structure of‎ ‎modules and especially‎, ‎the prime submodules of free modules over‎ ‎an SPAP-ring and derive some basic properties‎. ‎Then we answer the‎ ‎question of Lam and Reyes about strongly Oka ideals family‎. ‎Finally‎, ‎we characterize the structure of SPAP-ring in special‎ ‎cases‎.

We consider properties of residuated lattices with universal quantifier and show that, for a residuated lattice X, (X,forall) is a residuated lattice with a quantifier if and only if there is an m -relatively complete substructure of X. We also show that, for a strong residuated lattice X, bigcapP lambda, |,P lambda rmisanmrm−filter=1 and hence that any strong residuated lattice is a subdirect product of a strong residuated lattice with a universal quantifier X/P lambda, where P lambda is a prime m -filter. As a corollary of this result, we prove that every strong monadic MTL-algebra (BL- and MV-algebra) is a subdirect product of linearly ordered strong monadic MTL-algebras (BL- and MV-algebras, respectively).

‎Inspired by the work of Suzuki in‎ ‎[T. Suzuki‎, ‎A generalized Banach contraction principle that characterizes metric completeness‎, Proc‎. ‎Amer‎. ‎Math‎. ‎Soc. ‎136 (2008)‎, ‎1861--1869]‎, ‎we prove a fixed point theorem for contractive mappings‎ ‎that generalizes a theorem of Geraghty in [M.A‎. ‎Geraghty‎, ‎On contractive mappings‎, ‎Proc‎. ‎Amer‎. ‎Math‎. ‎Soc., ‎40 (1973)‎, ‎604--608] ‎and characterizes metric completeness‎. ‎We introduce the family A of all nonnegative functions‎ ‎ϕ with the property that‎, ‎given a metric space (X,d) and a mapping T:X→X ‎, ‎the condition‎ ‎‎x,y∈X, x≠y, d(x,Tx)≤d(x,y) ⟹\‎‎d(Tx,Ty)<ϕ(d(x,y))‎,‎ ‎implies that the iterations x n =T n x ‎, ‎for any choice of initial point x∈X ‎, ‎form a Cauchy sequence in X ‎. ‎We show that the family of L-functions‎, ‎introduced by Lim in [T.C‎. ‎Lim‎, ‎On characterizations of Meir-Keeler contractive maps‎, Nonlinear Anal.‎, 46 (2001)‎, ‎113--120]‎, ‎and the family‎ ‎of test functions‎, ‎introduced by Geraghty‎, ‎belong to A ‎. ‎We also prove‎ ‎a Suzuki-type fixed point theorem for nonlinear contractions‎.

In this paper‎, ‎we study some properties of analytic extension of a n th roots of M -hyponormal operator‎. ‎We show that every analytic extension of a n th roots of M -hyponormal operator is subscalar of order 2k+2n ‎. ‎As a consequence‎, ‎we get that if the spectrum of such operator T has a nonempty interior in C ‎, ‎then T has a nontrivial invariant subspace‎. ‎Finally‎, ‎we show that the sum of a n th roots of M -hyponormal operator and an algebraic operator of order k which are commuting is subscalar of order 2kn+2 ‎.

In this paper, we classify the indecomposable non-nilpotent solvable Lie algebras with N(R n, m,r) nilradical,by using the derivation algebra and the automorphism group of N(R n, m,r). We also prove that these solvable Lie algebras are complete and unique, up to isomorphism.

‎Let X=(‎‎‎‎x 1 ‎‎x 2 …… x n−1 x n x n x n+1 ‎‎) be the Hankel matrix of size 2×n and let G be a closed graph on the vertex set [n]. We study the binomial ideal I G ⊂K[x 1, …,x n+1] which is generated by all the 2 -minors of X which correspond to the edges of G. We show that I G is Cohen-Macaulay‎. ‎We find the minimal primes of I G and show that I G is a set theoretical complete intersection‎. ‎Moreover‎, ‎a sharp upper bound for the regularity of I G is given‎.‎

In this paper‎, ‎we study convergence behavior of the global FOM (Gl-FOM) and global GMRES (Gl-GMRES) methods for solving the matrix equation AXB=C where A and B are symmetric positive definite (SPD)‎. ‎We present some new theoretical results of these methods such as computable exact expressions and upper bounds for the norm of the error and residual‎. ‎In particular‎, ‎the obtained upper bounds for the Gl-FOM method help us to predict the behavior of the Frobenius norm of the Gl-FOM residual‎. ‎We also explore the worst-case convergence behavior of these methods‎. ‎Finally‎, ‎some numerical experiments are given to show the performance of the theoretical results‎.

In this paper, we first introduce some function spaces, with certain locally convex topologies, closely related to the space of real-valued continuous functions on X, where X is a C -distinguished topological space. Then, we show that their dual spaces can be identified in a natural way with certain spaces of Radon measures.

Let P n (x)=sum n i=0 A i x i be a random algebraic polynomial, where A 0, A 1, cdots is a sequence of independent random variables belong to the domain of attraction of the normal law. Thus A j 's for j=0,1cdots possesses the characteristic functions exp−frac12t 2 H j (t), where H j (t) 's are complex slowly varying functions. Under the assumption that there exist a real positive slowly varying function H(cdot) and positive constants t 0, C ast and C ast that C ast H(t)leqmboxRe[H j (t)]leqC ast H(t),;tleqt 0, ;j=1,cdots,n, we find that while the variance of coefficients are bounded, real zeros are concentrated around pm1, and the expected number of real zeros of P n (x) round the origin at a distance (logn) (−s) of pm1 are at most of order Oleft((logn) s log(logn)right).

‎In this paper‎, ‎we find matrix representation of a class of sixth order Sturm-Liouville problem (SLP) with separated‎, ‎self-adjoint boundary conditions and we show that such SLP have finite spectrum‎. ‎Also for a given matrix eigenvalue problem HX=λVX ‎, ‎where H is a block tridiagonal matrix and V is a block diagonal matrix‎, ‎we find a sixth order boundary value problem of Atkinson type that is equivalent to matrix eigenvalue problem.

‎The aim of this paper is to study the convergence of solutions of the‎ ‎following second order difference inclusion‎ {exp −1 u i u i+1 +θ i exp −1 u i u i−1 ∈c i A(u i),i⩾1u 0 =x∈M‎,‎‎‎sup i⩾0 d(u i, x)<+∞‎,‎ ‎to a singularity of a multi-valued maximal monotone vector field A ‎on a Hadamard manifold M ‎, ‎where {c i} and {θ i} are‎ ‎sequences of positive real numbers and x is an arbitrary fixed‎ ‎point in M ‎. ‎The results of this paper extend previous results in‎ ‎the literature from Hilbert spaces to Hadamard manifolds for general‎ ‎maximal monotone‎, ‎strongly monotone multi-valued vector fields and‎ ‎subdifferentials of proper‎, ‎lower semicontinuous and geodesically‎ ‎convex functions f:M→]−∞,+∞] ‎. ‎In the recent case‎, ‎when A=∂f ‎, ‎we show that the sequence {u i} ‎, ‎given by‎ ‎the equation‎, ‎converges to a point of the solution set of the‎ ‎following constraint minimization problem‎ ‎Min x∈M f(x).