Inclusion matrices and chains

Given integers t, k, and v such that 0?t?k?v, let Wtk(v) be the inclusion matrix of t-subsets vs. k-subsets of a v-set. We modify slightly the concept of standard tableau to study the notion of rank of a finite set of positive integers which was introduced by Frankl. Utilizing this, a decomposition of the poset ²[v] into symmetric skipless chains is given. Based on this decomposition, we construct an inclusion matrix, denoted by , which is row-equivalent to Wtk(v). Its Smith normal form is determined. As applications, Wilson's diagonal form of Wtk(v) is obtained as well as a new proof of the well-known theorem on the necessary and sufficient conditions for existence of integral solutions of the system Wtkx=b due to Wilson. Finally we present another inclusion matrix with similar properties to those of which is in some way equivalent to Wtk(v).     

A note on the Jacobian conjecture

In this paper we consider the Jacobian conjecture for a map of complex affine spaces of dimension . It is well known that if is proper, then the conjecture will hold. Using topological arguments, specifically Smith theory, we show that the conjecture holds if and only if is proper onto its image.

     

Smith-fuzzy fractional control of systems with time delay

The fractional calculation is over 300 years old, but only in the last decades its application arisen in many areas of science and engineering. The explanation for this expansion in the scientific and tecnologic worlds is due to the good results obtained in solving different problems, which have overcome the classics. On the other hand, in the control area there was an increasing interest in the development of new strategies, which resulted in new algorithms where the use of the fractional calculus revealed an helpfull tool. In this paper we apply the fractional order concepts into two systems with time delay. Several algorithms are investigated and compared, when integrated within a Smith predictor structure and with an optimal fuzzy fractional PD^β+I controller in which the parameters are tuned by a genetic algorithm. Simulations are presented assessing the performance of the proposed fractional schemes.     

Issues with the Smith–Wilson method

We analyse various features of the Smith–Wilson method used for discounting under the EU regulation Solvency II, with special attention to hedging. In particular, we show that all key rate duration hedges of liabilities beyond the Last Liquid Point will be peculiar. Moreover, we show that there is a connection between the occurrence of negative discount factors and singularities in the convergence criterion used to calibrate the model. The main tool used for analysing hedges is a novel stochastic representation of the Smith–Wilson method.     

一种新的RFID射频前端振荡器的设计方法

为解决RFID低功耗、小体积的问题,提出了一种新的RFID射频前端振荡器的设计方法.分析了晶体管稳定性的变化规律,提出了采用晶体管和无源网络产生振荡的方法,在增加正反馈使反射系数最佳的情况下给出了振荡器的电路结构.对射频振荡器进行仿真,结果表明,调谐网络和终端网络对振荡器的性能有影响,反射系数增大可缩短起振时间,调谐网络电阻增大将加大噪声,可以综合利用史密斯圆图和复平面上的稳定性边界有效分配性能指标.研究结果为RFID在低复杂度下改善振荡器的性能提出了一种新的途径.     

Plasma impedance monitoring for real time endpoint detection of bulk materials etched in ICP tool

Plasma impedance monitoring (PIM) based on electrical measurements is successfully used as an alternative to determine real time detection endpoint during plasma etching of structured bulk materials. In this paper we present the results with this technique for the endpoint detection during the etching of various materials.The endpoint conditions are tested in the sixth harmonic components of the electrical plasma parameters with an RF sensor. The endpoint is determined when an electrical parameter transition is observed. This transition corresponds to the change of the total reactor impedance, and allows the etching of the doped layer to stop on the bulk substrate.Using a Smith chart we determine the best harmonics/electrical monitoring couple parameters for processes on various materials. Resistivity measurements are used before and after etching in order to confirm the usefulness of the PIM method.In this paper, we also demonstrate how to monitor a real time control of non-uniformity during the reactive ion etching (RIE) process in the case of gallium arsenide etching.     

Generalized equivalence of pairs of matrices

Pairs (A ₁ B ₁) and (A ₂ B ₂) of matrices over a principal ideal domain R are called the generalized equivalent pairs if A ₂=UA ₁ V ₁ B ₂=UB ₁ V ₂ for some invertible matrices U V ₁ V ₂ over R. A special form is established to which a pair of matrices can be reduced by means of generalized equivalent transformations. Besides necessary and sufficient conditions are found, under which a pair of matrices is generalized equivalent to a pair of diagonal matrices. Applications are made to study the divisibility of matrices and multiplicative property of the Smith normal form.     

On the structure invariants of proper rational matrices with prescribed finite poles

Abstract

The algebraic structure of matrices defined over arbitrary fields whose elements are rational functions with no poles at infinity and prescribed finite poles is studied. Under certain very general conditions, they are shown to be matrices over an Euclidean domain that can be classified according to the corresponding invariant factors. The relationship between these invariants and the local Wiener–Hopf factorization indices will be clarified. This result can be seen as an extension of the classical theorem on pole placement by Rosenbrock in control theory.     

史密斯图偏振表示及其计算机程序

本文给出了史密斯图上表示任意振偏光偏振态的公式，史密斯图等效于Ｐｏｉｎｃａｒｅ球。讨论了史密斯图的特性。描述了绘制史密斯图ＱＵＩＣＫＢＡＳＩＣ计算机程序，一个例子讨论了史密斯图的应用。     

Estimation of high performance in Schmitt triggers with stacking power‐gating techniques in 45 nm CMOS technology

In the complementary metal oxide semiconductor (CMOS) nanoscale technology ground bounce noise and power consumption are becoming important metric. In presented paper, low leakage Schmitt trigger circuits are proposed for wave shaping or cleaning process with low ground bounce noise. Schmitt trigger play important role in communication electronics. Power‐gating and stacking power‐gating techniques have provided for maintaining the parameter of Schmitt trigger. An ideal approach has been investigated with stacking power‐gating technique. For further reduction in peak of ground bounce noise during sleep to active (power) mode transition, we have performed simulations using cadence specter 45 nm standard CMOS technology at nominal temperature (27°C) with supply voltage V_dd = 0.7 V and input voltage vary from 0.7 V to 1.5 V. The simulation results show that a proposed design provide efficient 6 T and 4 T Schmitt triggers in term of minimum leakage power (8.18 fW), active power (17.80 pW), ground bounce noise (1.65 μV) and propagation delay (1.98 ns), transconductance (4.51 × 10^?14 S), voltage gain (29.44 dB), hysteresis width (11.07 V) and efficiency (64.68%). Reported devices use for low‐power communication systems. Copyright © 2013 John Wiley & Sons, Ltd.