Let be a simple and connected graph. A k-vertex separator [k-edge separator] is a subset of vertices [edges] whose deletion separates the vertex [edge] set of into two parts of equal cardinality, that are at distance greater than k in . Here we investigate the relation between the cardinality of these cutsets and the laplacian spectrum of . As a consequence of the study, we obtain the well-know...

We use three-dimensional simulations to study the statistics of supersonic turbulence in molecular clouds. Our numerical experiments describe driven turbulent flows with an isothermal equation of state, Mach numbers around 10, and various degrees of magnetization. We first support the so-called 1/3-rule of Kritsuk et al. (2007a) with our new data from a larger 2048 simulation. We then attempt t...

In our previous work, we have established the existence of transonic characteristic discontinuities separating supersonic flows from a static gas in two-dimensional steady compressible Euler flows under a perturbation with small total variation of the incoming supersonic flow over a solid right-wedge. It is a free boundary problem in Eulerian coordinates and, across the free boundary (character...

This study aims to investigate and optimize the effects of the main parameters including the particle size, gravity and magnetic separation combination, high gradient magnetic separation, magnetic field intensity, shaking table slope, washing water flow, and electrostatic separation upon the rare earth element (REE) recoveries from iron mine waste. The electron microprobe showed that high amoun...

Latin squares can be classified as odd or even according to the signs of the permutations given by their rows and columns. In this paper, the behaviour of the parities of a latin square under the action of the isotopy group (permuting rows, columns, and symbols) and the transformation group (interchanging rows, columns, and symbols) is analyzed. A rule is given that shows that the behaviour of ...

This paper deals with the well known classes of threshold and difference graphs, both characterized by separators, i.e. node weight functions and thresholds. We show how to maintain minimum the value of the separator when the input (threshold or difference) graph is fully dynamic, i.e. edges/nodes are inserted/removed. Moreover, exploiting the data structure used for maintaining the minimality ...

Polarization, solution-separator, charge transfer, and diffusion resistances of clean and used separator electrode assemblies were examined in microbial fuel cells using current–voltage curves and electrochemical impedance spectroscopy (EIS). Current–voltage curves showed the total resistance was reduced at low cathode potentials. EIS results revealed that at a set cathode potential of 0.3 V di...

In the present work we introduce a new are activity indicator, MAD and examine its characteristics by analyzing a set of successive three days' observations of a typical active region, AR2372. The computed MAD is compared with conventional activity indicator such as separator. It is found that (1) MAD traces very well the separator, (2) it singles out local discontinuity of magnetic eld lines a...