On a nonlinear recurrent relation

We study the limiting behavior for the solutions of a nonlinear recurrent relation which arises from the study of Navier-Stokes equations. Some stability theorems are also shown concerning a related class of linear recurrent relations.Comment: to appear in Journal of Statistical Physic

An intelligent component database for behavioral synthesis

This paper describes an intelligent component database system that delivers components to synthesis tools when given a set of attributes and constraints. Requirements of a component server are defined and an implementation is described. Our experiments demonstrate that such a component sever can replace component libraries and component catalogs with hundreds of pages

On general systems with network-enhanced complexities

In recent years, the study of networked control systems (NCSs) has gradually become an active research area due to the advantages of using networked media in many aspects such as the ease of maintenance and installation, the large flexibility and the low cost. It is well known that the devices in networks are mutually connected via communication cables that are of limited capacity. Therefore, some network-induced phenomena have inevitably emerged in the areas of signal processing and control engineering. These phenomena include, but are not limited to, network-induced communication delays, missing data, signal quantization, saturations, and channel fading. It is of great importance to understand how these phenomena influence the closed-loop stability and performance properties

Neutrino masses and superheavy dark matter in the 3-3-1-1 model

In this work, we interpret the 3-3-1-1 model when the B-L and 3-3-1 breaking scales behave simultaneously as the inflation scale. This setup not only realizes the previously-achieved consequences of inflation and leptogenesis, but also provides new insights in superheavy dark matter and neutrino masses. We argue that the 3-3-1-1 model can incorporate a scalar sextet, which induces both small masses for the neutrinos via a combined type I and II seesaw and large masses for the new neutral fermions. Additionally, all the new particles have the large masses in the inflation scale. The lightest particle among the W-particles that have abnormal (i.e., wrong) B-L number in comparison to those of the standard model particles may be a superheavy dark matter as it is stabilized by the W-parity. The dark matter candidate may be a Majorana fermion, a neutral scalar, or a neutral gauge boson, which was properly created in the early universe due to the gravitational effects on the vacuum or the thermal production after cosmic inflation.Comment: 34 pages, improved with discussions on inflation and reheating as well as presentation, matches published version in EPJ

Determination of a Type of Permutation Binomials over Finite Fields

Let f=a\x+\x^{3q-2}\in\Bbb F_{q^2}[\x], where $a\in\Bbb F_{q^2}^*$. We prove that $f$ is a permutation polynomial of $\Bbb F_{q^2}$ if and only if one of the following occurs: (i) $q=2^e$, $e$ odd, and $a^{\frac{q+1}3}$ is a primitive $3$rd root of unity. (ii) $(q,a)$ belongs to a finite set which is determined in the paper