In this paper, we state some results on product of operators with closed ranges and we solve the operator equation $TXS^*-SX^*T^*= A$ in the general setting of the adjointable operators between Hilbert $C^*$-modules, when $TS = 1$. Furthermore, by using some block operator matrix techniques, we nd explicit solution of the operator equation $TXS^*-SX^*T^*= A$.

We consider the assignment problem between two sets of $N$ random points on a smooth, two-dimensional manifold $\Omega$ unit area. It is known that average cost scales as $E_{\Omega}(N)\sim\frac{1}{2\pi}\ln N$ with correction at most order $\sqrt{\ln N\ln\ln N}$. In this paper, we show that, within linearization approximation field-theoretical formulation problem, first $\Omega$-dependent const...

Partial, or set-valued classification assigns instances to sets of classes, making it possible reduce the probability misclassification while still providing useful information. This paper reviews approaches partial based on Dempster–Shafer theory belief functions. To define utility predictions, we propose extend matrix using an Ordered Weighted Average operator, allowing us model decision make...

Automated storage and retrieval systems (AS/RSs) are material handling systems that are frequently used in manufacturing and distribution centers. The modelling of the retrieval–travel time of an AS/RS (expected product delivery time) is practically important, because it allows us to evaluate and improve the system throughput. The free-fall-flow-rack AS/RS has emerged as a new technology for dr...

‎in this paper we try to extend geometric concepts in the context of operator valued tensors‎. ‎to this end‎, ‎we aim to replace the field of scalars $ mathbb{r} $ by self-adjoint elements of a commutative $ c^star $-algebra‎, ‎and reach an appropriate generalization of geometrical concepts on manifolds‎. ‎first‎, ‎we put forward the concept of operator-valued tensors and extend semi-riemannian...

We define a utility-based framework for joint channel assignment, topology control and routing in multi-rate multi-radio wireless mesh networks, and present a greedy algorithm for solving the corresponding optimization problem. A key and novel feature of the proposed approach is the support for different target objectives, which are defined as utility functions of the MAC layer throughput, that...

A $it{weighted~slant~Toep}$-$it{Hank}$ operator $L_{phi}^{beta}$ with symbol $phiin L^{infty}(beta)$ is an operator on $L^2(beta)$ whose representing matrix consists of all even (odd) columns from a weighted slant Hankel (slant weighted Toeplitz) matrix, $beta={beta_n}_{nin mathbb{Z}}$ be a sequence of positive numbers with $beta_0=1$. A matrix characterization for an operator to be $it{weighte...

We construct a quantum searching model of signed edge driven by walk. The time evolution operator this walk provides weighted adjacency matrix induced the assignment sign to each edge. This can be regarded as so-called coloring. Then an application, under arbitrary coloring which gives matching on complete graph $$n+1$$ vertices we consider search colored from set graph. show that finds within...