Open-loop stabilizability of infinite-dimensional systems

In this paper we study open-loop stabilizability, a general notion of stabilizability for linear differential equations =Ax+Bu in an infinite-dimensional state space. This notion is sufficiently general to be implied by exact controllability, by optimizability, and by various general definitions of closedloop stabilizability. Here,A is the generator of a strongly continuous semigroup, and we make very few a priori restrictions on the class of controlsu. Our results hinge upon the control operatorB being smoothly left-invertible, which is a very mild restriction when the input space is finite-dimensional. Since open-loop stabilizability is a weak concept, lack of open-loop stability is quites strong. A focus of this paper is to give necessary conditions for open-loop stabilizability, thus identifying classes of systems which are not open-loops stabilizable. First we give useful frequency domain conditions that are equivalent to our definitions of open-loop stabilizability, and lead to a version of the Hautus test for open-loop stabilizability. When the input space is finite-dimensional, we give necessary conditions for open-loop stabilizability which involve spectral properties ofA. We show that these results are not true if the conditions onB are weakened. We obtain analogous results for discrete-time systems. We show that, for a class of systems without spectrum determined growth, optimizability is impossible. Finally, we show that a system is open-loop stabilizable with a class of controlu if and only if the system with the sameA but a more boundedB is open-loop stabilizable with a larger class of controls. This work was partially supported by NSF Grant DMS-9623392.     

Some modifications of the Weiss–Staffans perturbation theorem

For boundary control systems in factor form, a version of the Weiss perturbation result is derived and formulated as an exponential stability robustness result (Theorem 3.1 ). An example of a heating rod control, illustrating its application, is given. Next, a generalization of the Weiss perturbation to a class of retarded systems of the neutral type is presented (Theorem 4.1 ). The characteristic feature of this generalization is that it allows to deal with a dynamic perturbation rather than a static one. Using this result, we get a new derivation of an exponential stability criterion. We also show that some parabolic systems without the admissibility of control operator still admit a weakened version of the Weiss perturbation result (Theorem 5.1 ). This result is a consequence of the necessary and sufficient conditions for generation of an analytic exponentially stable semigroup and some frequency‐domain estimates and is illustrated in details by an example of an unloaded electric ‐transmission line. Copyright © 2016 John Wiley & Sons, Ltd.     

关于BCI－代数中元素的轨道

讨论了ＢＣＩ－代数中关于元素的轨道的几个问题，给出了在Ｏ（０）为理想时，Ｏ（ａ）＝Ｏ（ｂ）的充要条件。说明Ｘ关于Ｏ（０）的商代数就是Ｐ（Ｘ）．     

Key factors affecting Fe density in Fe-fortified-parboiled rice: Parboiling conditions,storage duration,external Fe-loading rate and genotypic differences

The present study evaluated the key factors affecting the efficiency of iron (Fe) penetration into the endosperm in parboiled rice of different varieties. It also investigated effects of storage time on Fe bio-accessibility, rice colour and Fe retention after rinsing. Rice grains of three varieties were fortified with an increasing range of Fe-fortification rates during the parboiling process, under two typical parboiling conditions, which are ambient soaking temperature for 24 h and 60 °C soaking temperature for 6 h at neutral (6.0–6.5) and acidic pH (3.0–3.5). Soaking of paddy rice, at 60 °C in acidic water for 6 h before steaming, was found to be better for maximising the Fe concentration in white-parboiled rice than the former ambient soaking. Under this parboiling condition, adding 250 mg Fe kg⁻¹ of paddy rice, at soaking, produced the most desirable Fe concentration in white rice, ranging from 17.5 to 25.4 mg kg⁻¹ among the rice varieties tested. The concentrations of Fe in parboiled white rice exhibited an exponential increase with increasing concentrations of Fe in the soaking water in all varieties, which were linearly related to Fe concentration of brown rice (r = 0.96∗∗, p < 0.01). The colour of the parboiled rice fortified with Fe was initially light yellow, with variation among rice varieties, but it did become slightly darker after 16 weeks of storage, probably because of Fe oxidisation. This may be related to decreasing bio-accessibility after 20 weeks of storage. Storage, however, did not affect the total Fe retention after rinsing, though the retention rate was variety-dependent. Information about parboiling will provide the basis for formulating an optimal industry protocol for producing Fe-fortified-parboiled rice, which can be further refined in pilot studies on the industrial scale.     

Uniform Stability and Stabilization of Linear Thermoelastic Systems

The object of this work is the study of uniform stability and stabilization of linear thermoelastic systems. We construct an explicit stabilizer feedback for the thermoelastic system and use a Lyapunov function to prove the exponential stability.     

Unification in partially commutative semigroups

Unification algorithms have been constructed for semigroups and commutative semigroups. This paper considers the intermediate case of partially commutative semigroups. We introduce classesN and of such semigroups and justify their use. We present an equation-solving algorithm for any member of the classN. This algorithm is relative to having an algorithm to determine all non-negative solutions of a certain class of diophantine equations of degree 2 which we call -equations. The difficulties arising when attempting to solve equations in members of the class are discussed, and we present arguments that strongly suggest that unification in these semigroups is undecidable.     

Volterra算子的交换子

本文引进了Ｖｏｌｔｅｒｒａ套定义的套代数中的一个部分等距算子半群｛Ｖｔ：ｔ∈［０，１］｝，证明了Ｖｏｌｔｅｒｒａ算子Ｖ是｛Ｖｔ：ｔ∈［０，１］｝在［０，１］上的积分，Ｖ＊的交换子是｛Ｖ＊ｔ：ｔ∈［０，１］｝的强算子拓扑闭包．     

Enriched Air or Pure Oxygen as Oxidant for Gas‐to‐Liquid Process with Microchannel Reactors

The syngas production step is one of the most costly steps in a gas‐to‐liquid plant. Commonly, oxygen is used as an oxidant in the reforming step. However, through the introduction of microchannel reactors, the use of enriched air may be justified. The merits of using enriched air versus pure oxygen are analyzed by utilizing an autothermal reformer, with microchannel reactors in the once‐through Fischer‐Tropsch (FT) step. Pure oxygen is provided by a cryogenic air separation unit (ASU) and enriched air by use of air separation membranes. Pure oxygen requires a smaller FT reactor volume, which means lower reactor costs at the expense of having a costly cryogenic ASU to produce pure oxygen. The operating cost of the ASU is lower than that of the air membrane, but the installed cost is higher.     

The Correction Capability of the Berlekamp–Massey–Sakata Algorithm with Majority Voting

Sakata’s generalization of the Berlekamp–Massey algorithm applies to a broad class of codes defined by an evaluation map on an order domain. In order to decode up to the minimum distance bound, Sakata’s algorithm must be combined with the majority voting algorithm of Feng, Rao and Duursma. This combined algorithm can often decode far more than (d _min −1)/2 errors, provided the errors are in general position. We give a precise characterization of the error correction capability of the combined algorithm. We also extend the concept behind Feng and Rao’s improved codes to decoding of errors in general position. The analysis leads to a new characterization of Arf numerical semigroups.     

INDUCTION OF MUTAGENIC EFFECT IN SOMATIC AND GERM CELLS BY ENRICHED URANIUM

Enriched uranium(UO2F2) accumulated in organism could cause chromosome aberrations in somatic cells, its rates on bone marrow cells were elevated when the dose of 235UO2F2 was increased. Among the types of induced aberrations, chromatid breakage was predominant, accompanied with a few chromosome breakage and translocation. At the same time mitosis index of metaphase cells was depressed. Chromatid delation and chromatid exchange were induced in peripheral blood lymphocytes. The important type of aberrations in spermatogonia was break. For primary spermatocytes the most significant aberration was multivalents which resulted either from chromatid interchanges or reciprocal translocations. 235UO2F2 could result in DNA breakage in germ cells. The sensitivity of germ cells at various stages to 235UO2F2. was different. At 12d after exposure the amount of sperm DNA eluted reached the peak. When the treating time was fixed, elution of sperm DNA from treated animals increased with the increasing doses. 235UO2F2. could also result in sperm abnormalities. Especially at 13 to 36 d after treatment the rates of sperm abnormalities were significantly elevated.