We provide an exposition of supercompact Radin forcing and present several methods for iterating Radin forcing. In this paper we give an exposition of supercompact Radin forcing using coherent sequences of ultrafilters. This version of Radin forcing includes as special cases the Prikry forcing and Magidor forcing, both the measurable and supercompact versions. We also introduce some methods for...

We show that bounded forcing axioms (for instance, the Bounded Proper Forcing Axiom and the Bounded Semiproper Forcing Axiom) are consistent with the existence of (!2; !2)-gaps and thus do not imply the Open Coloring Axiom. They are also consistent with Jensen’s combinatorial principles for L at the level !2, and therefore with the existence of an !2-Suslin tree. We also show that the axiom we ...

In this paper we consider MIMO broadcast channels with separable variance profile modelling antenna correlation at both transmit and receive sides. For large number of antennas we derive the theoretical sum-rate capacity when the transmitter performs zero-forcing or regularized zero-forcing precoding. In particular, we apply the results to volumelimited devices where the correlation originates ...

A natural question to ask is whether this result has an analogue in the context of large cardinals. The purpose of this article is to provide the strongest such analogue not ruled out by limitations imposed by the existence of Woodin cardinals. To describe the latter limitations we consider the forcing P , described as follows. Let δ be inaccessible and consider the language L(δ): (a) n ∈ R bel...

In a systematic study, we compare the density statistics in high resolution numerical experiments of supersonic isothermal turbulence, driven by the usually adopted solenoidal (divergence-free) forcing and by compressive (curl-free) forcing. We find that for the same rms Mach number, compressive forcing produces much stronger density enhancements and larger voids compared to solenoidal forcing....

The dependence of mixing efficiency on time-varying forcing is studied by direct numerical simulation (DNS) of Kelvin-Helmholtz (KH) instability. Timedependent forcing fields are designed to mimic a breaking internal wave by solving the equations of motion in a tilted coordinate frame and allowing the tilt angle to vary in time. Mixing efficiency Γc is defined as the ratio of potential energy g...

We present results of a high resolution 3-dimensional numerical simulation of compressively driven supersonic turbulence. A detailed analysis of the fractal mass dimension, which is extracted from data of the density field, yields values of Df ≈ 2.6− 2.7. This is significantly higher than what is usually assumed in the literature (Df ≈ 2.35). However, this value is traditionally obtained by app...

For a given graph G, the zero forcing number of Z(G), is smallest cardinality any set S vertices on which repeated applications rule results in all being included S. The as follows: if vertex v S, and exactly one neighbor u not then added to next iteration. failed was introduced by Fetcie, Jacob, Saavedra defined largest fails force graph. In 2021, Gomez et al. proved that there were 15 graphs ...

The controllability for complex network system is to find the minimum number of leaders achieve effective control global networks. In this paper, problem directed a family matrices carrying structure under hypercube considered. relationship between and signed zero forcing set established. networks obtained by computing graph.