ACECR at Tarbiat Modares University Iranian Journal of Mathematical Sciences and Informatics 1735-4463 6 2 2011 11 1 On the Decomposition of Hilbert Spaces 1 7 EN H.R. Afshin M.A. Ranjbar Basic relation between numerical range and Davis-Wielandt shell of an operator $A$ acting on a Hilbert space with orthonormal basis $xi={e_{i}|i in I}$ and its conjugate $bar{A}$ which is introduced in this paper are obtained. The results are used to study the relation between point spectrum, approximate spectrum and residual spectrum of $A$ and $bar{A}$. A necessary and sufficient condition for $A$ to be self-conjugate ($A=bar{A}$) is given using a subgroup of H.

ACECR at Tarbiat Modares University Iranian Journal of Mathematical Sciences and Informatics 1735-4463 6 2 2011 11 1 Properties of Central Symmetric X-Form Matrices 9 20 EN A.M. Nazari E. Afshari A. Omidi Bidgoli In this paper we introduce a special form of symmetric matrices that is called central symmetric $X$-form matrix and study some properties, the inverse eigenvalue problem and inverse singular value problem for these matrices.

ACECR at Tarbiat Modares University Iranian Journal of Mathematical Sciences and Informatics 1735-4463 6 2 2011 11 1 Shift Invariant Spaces and Shift Preserving Operators on Locally Compact Abelian Groups 21 32 EN R. Raisi Tousi R.A. Kamyabi Gol We investigate shift invariant subspaces of $L^2(G)$, where $G$ is a locally compact abelian group. We show that every shift invariant space can be decomposed as an orthogonal sum of spaces each of which is generated by a single function whose shifts form a Parseval frame. For a second countable locally compact abelian group $G$ we prove a useful Hilbert space isomorphism, introduce range functions and give a characterization of shift invariant subspaces of $L^2(G)$ in terms of range functions. Finally, we investigate shift preserving operators on locally compact abelian groups. We show that there is a one-to-one correspondence between shift preserving operators and range operators on $L^2(G)$ where $G$ is a locally compact abelian group.

ACECR at Tarbiat Modares University Iranian Journal of Mathematical Sciences and Informatics 1735-4463 6 2 2011 11 1 Deformation of Outer Representations of Galois Group II 33 41 EN Arash Rastegar This paper is devoted to deformation theory of "anabelian" representations of the absolute Galois group landing in outer automorphism group of the algebraic fundamental group of a hyperbolic smooth curve defined over a number-field. In the first part of this paper, we obtained several universal deformations for Lie-algebra versions of the above representation using the Schlessinger criteria for functors on Artin local rings. In the second part, we use a version of Schlessinger criteria for functors on the Artinian category of nilpotent Lie algebras which is formulated by Pridham, and explore arithmetic applications.

ACECR at Tarbiat Modares University Iranian Journal of Mathematical Sciences and Informatics 1735-4463 6 2 2011 11 1 Linear Preservers of Majorization 43 50 EN Fatemeh Khalooei Abbas Salemi For vectors $X, Yin mathbb{R}^{n}$, we say $X$ is left matrix majorized by $Y$ and write $X prec_{ell} Y$ if for some row stochastic matrix $R, ~X=RY.$ Also, we write $Xsim_{ell}Y,$ when $Xprec_{ell}Yprec_{ell}X.$ A linear operator $Tcolon mathbb{R}^{p}to mathbb{R}^{n}$ is said to be a linear preserver of a given relation $prec$ if $Xprec Y$ on $mathbb{R}^{p}$ implies that $TXprec TY$ on $mathbb{R}^{n}$. In this note we study linear preservers of $sim_{ell}$ from $mathbb{R}^{p}$ to $mathbb{R}^{n}.$ In particular, we characterize all linear preservers of $sim_{ell}$ from $mathbb{R}^{2}$ to $mathbb{R}^{n},$ and also, all linear preservers of $sim_{ell}$ from $mathbb{R}^{p}$ to $mathbb{R}^{p}.$

ACECR at Tarbiat Modares University Iranian Journal of Mathematical Sciences and Informatics 1735-4463 6 2 2011 11 1 On Schur Multipliers of Pairs and Triples of Groups with Topological Approach 51 65 EN Hanieh Mirebrahimi Behrooz Mashayekhy In this paper, using a relation between Schur multipliers of pairs and triples of groups, the fundamental group and homology groups of a homotopy pushout of Eilenberg-MacLane spaces, we present among other things some behaviors of Schur multipliers of pairs and triples with respect to free, amalgamated free, and direct products and also direct limits of groups with topological approach.

ACECR at Tarbiat Modares University Iranian Journal of Mathematical Sciences and Informatics 1735-4463 6 2 2011 11 1 The Hyper-Wiener Polynomial of Graphs 67 74 EN G.H. Fath-Tabar A.R. Ashrafi The distance $d(u,v)$ between two vertices $u$ and $v$ of a graph $G$ is equal to the length of a shortest path that connects $u$ and $v$. Define $WW(G,x) = 1/2sum_{{ a,b } subseteq V(G)}x^{d(a,b) + d^2(a,b)}$, where $d(G)$ is the greatest distance between any two vertices. In this paper the hyper-Wiener polynomials of the Cartesian product, composition, join and disjunction of graphs are computed.

ACECR at Tarbiat Modares University Iranian Journal of Mathematical Sciences and Informatics 1735-4463 6 2 2011 11 1 A Study of the Total Graph 75 80 EN Abolfazl Tehranian Hamid Reza Maimani Let R be a commutative ring with $Z(R)$ its set of zero-divisors. In this paper, we study the total graph of $R$, denoted by $T(Gamma(R))$. It is the (undirected) graph with all elements of R as vertices, and for distinct $x, yin R$, the vertices $x$ and $y$ are adjacent if and only if $x + yinZ(R)$. We study the chromatic number and edge connectivity of this graph.