Bound states in the continuum provide a remarkable example of how simple problem solved about century ago quantum mechanics can drive research on whole spectrum resonant phenomena wave physics. Due to their huge radiative lifetime, bound have found multiple applications various areas physics devoted processes, including hydrodynamics, atomic physics, and acoustics. In this review paper, we pres...

Elaborating on a previous work by Marolf et al, we relate some exact results in quantum field theory and statistical mechanics to the Bekenstein universal bound on entropy. Specifically, we consider the relative entropy between the vacuum and another state, both reduced to a local region. We propose that, with the adequate interpretation, the positivity of the relative entropy in this case cons...

One of the fundamental physical limits on speed time evolution a quantum state is known in form celebrated Mandelstam–Tamm inequality. This inequality gives an answer to question how fast isolated system can evolve from its initial orthogonal one. In turn, Fleming bound extension that optimal for between non-orthogonal and final states. present work, we are concerned not with single but whole (...

In this paper we obtain an upper bound and also a lower bound for maximum edges of strongly 2 multiplicative graphs of order n. Also we prove that triangular ladder the graph obtained by duplication of an arbitrary edge by a new vertex in path and the graphobtained by duplicating all vertices by new edges in a path and some other graphs are strongly 2 multiplicative

The physical sense of tight knots provided by the SONO algorithm is discussed. A method allowing one to predict their length is presented. An upper bound for the minimum length of a smooth trefoil knot is determined.

in this paper, we show that in each nite dimensional hilbert space, a frame of subspaces is an ultra bessel sequence of subspaces. we also show that every frame of subspaces in a nite dimensional hilbert space has frameness bound.

Sufficient number of linear and noisy measurements for exact and approximate sparsity pattern/support set recovery in the high dimensional setting is derived. Although this problem as been addressed in the recent literature, there is still considerable gaps between those results and the exact limits of the perfect support set recovery. To reduce this gap, in this paper, the sufficient con...

In this paper, the problem of two-machine flow shop scheduling to minimize total energy costs under time-of-use tariffs is investigated. As the objective function of this study is not a regular measure, allowing intentional idle-time can be advantageous. So this study considers two approaches, one for non-delay version of the problem and the other one for a situation when inserting intentional ...