Microwave field effect transistor

Electrodes of a high power, microwave field effect transistor are substantially matched to external input and output networks. The field effect transistor includes a metal ground plane layer, a dielectric layer on the ground plane layer, a gallium arsenide active region on the dielectric layer, and substantially coplanar spaced source, gate, and drain electrodes having active segments covering the active region. The active segment of the gate electrode is located between edges of the active segments of the source and drain electrodes. The gate and drain electrodes include inactive pads remote from the active segments. The pads are connected directly to the input and output networks. The source electrode is connected to the ground plane layer. The space between the electrodes and the geometry of the electrodes extablish parasitic shunt capacitances and series inductances that provide substantial matches between the input network and the gate electrode and between the output network and the drain electrode. Many of the devices are connected in parallel and share a common active region, so that each pair of adjacent devices shares the same source electrodes and each pair of adjacent devices shares the same drain electrodes. The gate electrodes for the parallel devices are formed by a continuous stripe that extends between adjacent devices and is connected at different points to the common gate pad

Classified Stable Matching

We introduce the {\sc classified stable matching} problem, a problem motivated by academic hiring. Suppose that a number of institutes are hiring faculty members from a pool of applicants. Both institutes and applicants have preferences over the other side. An institute classifies the applicants based on their research areas (or any other criterion), and, for each class, it sets a lower bound and an upper bound on the number of applicants it would hire in that class. The objective is to find a stable matching from which no group of participants has reason to deviate. Moreover, the matching should respect the upper/lower bounds of the classes. In the first part of the paper, we study classified stable matching problems whose classifications belong to a fixed set of ``order types.'' We show that if the set consists entirely of downward forests, there is a polynomial-time algorithm; otherwise, it is NP-complete to decide the existence of a stable matching. In the second part, we investigate the problem using a polyhedral approach. Suppose that all classifications are laminar families and there is no lower bound. We propose a set of linear inequalities to describe stable matching polytope and prove that it is integral. This integrality allows us to find various optimal stable matchings using Ellipsoid algorithm. A further ramification of our result is the description of the stable matching polytope for the many-to-many (unclassified) stable matching problem. This answers an open question posed by Sethuraman, Teo and Qian

APPLICATION OF PRICE ELASTICITIES TO FARM POLICY ANALYSIS: COMMENT

Demand and Price Analysis,

New Osmosis Law and Theory: the New Formula that Replaces van't Hoff Osmotic Pressure Equation

This article derived a new abstract concept from the osmotic process and concluded it via "osmotic force" with a new law -- "osmotic law". The "osmotic law" describes that, in an osmotic system, osmolyte moves osmotically from the side with higher "osmotic force" to the side with lower "osmotic force". In addition, it was proved mathematically that the osmotic process could be explained perfectly via "osmotic force" and "osmotic laws", which can prevent the difficulties in using current "osmotic pressure" concept to explain the osmotic process and phenomenon. A theory and equation to describe the curve of osmotic pressure vs. different ideal solution concentrations are also derived, which can overcome the limitedness and incompleteness of van't Hoff osmotic pressure formula (a linear equation) which is applicable to ideal dilute solution only