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 $TXS^*-SX^*T^*= A$.

‎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...

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 propose a simple gauge-mediated supersymmetry breaking model in which suitable soft breaking masses are dynamically generated without relying on a messenger sector. This model is constructed as an extention of the 3-2 model and needs no ne-tuning of parameters. The dynamical supersymmetry breaking sector contains non-renormalizable interactions and vector-like elds. Non-renormalizable terms ...

In the last years the traditional scenario of “Big Bang” has been deeply modified by the study of the quantum features of the Universe evolution, proposing again the problem of using “local” physical laws on cosmic scale, with particular regard to the cosmological constant role. The “group extention” method shows that the De Sitter group univocally generalizes the Poincarè group, formally justi...

The peculiar anatomical features of the common peroneal nerve and its nutrient vessels render it particularly susceptible to injuries near the lateral aspect of the knee joint (Sunderland, 1968). Numerous aetiopathologic factors have been enumerated as the possible causes of injuries to this nerve at this site such as; posterior-dislocation of the proximal tibio-fibular joint (Lyle, 1925); frac...

Increasingly large-scale clusters of SMPs continue to become majority platform in HPC field. Such a cluster environment, there may be load imbalances due to several reasons and mis-placement of data which bring performance bottlenecks. To overcome these problems, some dynamic load balancing mechanisms are needed. In this paper, we report our ongoing work on dynamic load balancing extention to O...