Searcharxiv⌕ Search

arXiv subjects

M. Khosravi

Publications and source records attributed to M. Khosravi.

7 recordsLinked to original sources
arXiv2023

A study of $4-$cycle systems

A $4-$cycle system is a partition of the edges of the complete graph $K_n$ into $4-$cycles. Let ${ C}$ be a collection of cycles of length 4 whose edges partition the edges of $K_n$. A set of 4-cycles $T_1 \subset C$ is called a 4-cycle trade if there exists a set $T_2$ of edge-disjoint 4-cycles on the same vertices, such that $({C} \setminus T_1)\cup T_2$ also is a collection of cycles of length 4 whose edges partition the edges of $K_n$. We study $4-$cycle trades of volume two (double-diamonds) and three and show that the set of all 4-CS(9) is connected with respect of trading with trades of volume 2 (double-diamond) and 3. In addition, we present a full rank matrix whose null-space is containing trade-vectors.

math.CO↗
arXiv2023

Some Hadamard product inequalities for accretive matrices

In this paper, we obtain some new matrix inequalities involving Hadamard product. Also some Hadamard product inequalities for accretive matrices involving the matrix means, positive unital linear maps and matrix concave functions are investigated. Among other results, it is shown that if $A, B, C, D$ are $n\times n$ positive definite matrices, then \begin{equation*} \left(αA+βB\right)^r\circ\left(αC+βD\right)^{1-r}\leq α\left(A^r\circ C^{1-r}\right)+β\left(B^r\circ D^{1-r}\right), \end{equation*} where $r \in (-1, 0) \cup (1, 2)$ and $" \circ "$ stands for the Hadamard product.

math.FA↗
arXiv2023

Operator mean inequalities for sector matrices

In this note, some inequalities involving operator means of sectorial matrices are proved which are generalizations and refinements of previous known results. Among them, let $A$ and $B$ be two accretive matrices with $A,B\in\mathcal{S}_θ$, $0 < mI \leqslant A, B \leqslant MI$ for positive real numbers $ M, m, \, σ$ be an operator mean and $σ^{*}$ be the adjoint mean of $ σ.$ If $σ^*\leqslant σ_1,σ_2\leqslant σ$ and $Φ$ is a positive unital linear map, then $$Φ^{p}\Re(A σ_{1} B) \leqslant \sec^{2p}θα^{p} Φ^{p}\Re(A σ_{2} B),$$ where $$ α= \max \left \lbrace K, 4^{1-\frac{2}{p}}K \right \rbrace,$$ and $ K= \frac{(M+m)^2}{4mM}$ is the Kantorovich constant.

math.FA↗
arXiv2017

Connected zero forcing sets and connected propagation time of graphs

The zero forcing number $Z(G)$ of a graph $G$ is the minimum cardinality of a set $S$ with colored (black) vertices which forces the set $V(G)$ to be colored (black) after some times. "color change rule": a white vertex is changed to a black vertex when it is the only white neighbor of a black vertex. In this case, we say that the black vertex forces the white vertex. We investigate here the concept of connected zero forcing set and connected zero forcing number. We discusses this subject for special graphs and some products of graphs. Also we introduce the connected propagation time. Graphs with extreme minimum connected propagation times and maximum propagation times $|G|-1$ and $|G|-2$ are characterized.

math.CO↗
arXiv2009

Reverse triangle inequality in Hilbert $C^*$-modules

We prove several versions of reverse triangle inequality in Hilbert $C^*$-modules. We show that if $e_1, ..., e_m$ are vectors in a Hilbert module ${\mathfrak X}$ over a $C^*$-algebra ${\mathfrak A}$ with unit 1 such that $ =0 (1\leq i\neq j \leq m)$ and $\|e_i\|=1 (1\leq i\leq m)$, and also $r_k,ρ_k\in\Bbb{R} (1\leq k\leq m)$ and $x_1, ..., x_n\in {\mathfrak X}$ satisfy $$0\leq r_k^2 \|x_j\|\leq {Re}< r_ke_k,x_j> ,\quad0\leq ρ_k^2 \|x_j\| \leq {Im}< ρ_ke_k,x_j> ,$$ then [\sum_{k=1}^m(r_k^2+ρ_k^2)]^{1/2}\sum_{j=1}^n \|x_j\|\leq\|\sum_{j=1}^nx_j\|, and the equality holds if and only if \sum_{j=1}^n x_j=\sum_{j=1}^n\|x_j\|\sum_{k=1}^m(r_k+iρ_k)e_k .

math.FA↗
arXiv2009

Bessel type inequalities in Hilbert C*-modules

Regarding the generalizations of the Bessel inequality in Hilbert spaces which are due to Bombiari and Boas--Bellman, we obtain a version of the Bessel inequality and some generalizations of this inequality in the framework of Hilbert $C^*$-modules.

math.FA↗