Let A and B be positive semidefinite matrices. We investigate the conditions under which the Lieb-Thirring inequality can be extended to singular values. That is, for which values of p does the majorisation σ(BpAp) ≺w σ((BA) p) hold, and for which values its reversed inequality σ(BpAp) ≻w σ((BA) p).

We extend the perturbation theory of Vǐsik, Ljusternik and Lidskĭı for eigenvalues of matrices, using methods of min-plus algebra. We show that the asymptotics of the eigenvalues of a perturbed matrix is governed by certain discrete optimisation problems, from which we derive new perturbation formulæ, extending the classical ones and solving cases which where singular in previous approaches. Ou...

We first prove Kato's inequalities for the Laplacian and a Schr$\ddot{o}$dinger-type operator on smooth functions closed Riemannian manifolds. then apply result to establish some new domination spectral zeta their related kernels $n$-dimensional unit spheres using majorisation techniques. Our results are generalisations of comparison surfaces

Resource theories provide a framework for thermodynamics beyond the thermodynamic limit. For systems with definite energy, the key resource is purity. In this paper we formulate three alternative resource theories of purity in the framework of general probabilistic theories (GPTs). Each resource theory corresponds to a different choice of free operations, including i) random reversible operatio...

fracture system in carbonate reservoirs is very complex. understanding the features of fractures such as dip, strike and the other parameters can help to distinguish the behaviour of reservoir in any exploration and production plan. image log is the best way to investigate feature planes like fracture and bedding. image log in one of drilled well #10x393 of bangestan reservoir in gachsaran oilf...

The concept of majorisation is explored as a tool to characterize the performance quantum Otto engine in quasi-static regime. For working substance form spin arbitrary magnitude, yields necessary and sufficient condition for operation engine, provided canonical distribution medium at hot reservoir majorised by its cold reservoir. case spin-1/2 interacting with an via isotropic Heisenberg exchan...

Let A,B be two positive definite matrices. The Fan-Lidskii majorisations can be subsumed as the symmetric norm rearrangement inequalities ‖A↓ +B↑‖ ‖A+B‖ ‖A↓ +B↓‖ where the up/down arrows on A,B mean the diagonal matrices with the same eigenvalues in decreasing/increasing order down to the diagonal. We refine these relations with sums of type A +UBU∗ and A +VBV∗ for two unitary matrices U,V asso...

The composite autoregressive system can be used to estimate a speech source-filter decomposition in a rigorous manner, thus having potential use in glottal inverse filtering. By introducing a suitable prior, spectral tilt can be introduced into the source component estimation to better correspond to human voice production. However, the current expectationmaximisation based composite autoregress...