Characterizations of two kinds of hemirings based on probability spaces

The notion of falling fuzzy \(h\)-interior ideals of a hemiring is introduced and some related properties are investigated. A special attention is given to two kinds of certain and impossible probability spaces. Finally, we investigate some characterizations of \(h\)-semisimple and \(h\)-quasi-hemiregular hemirings based on independent (perfect positive correlation) probability spaces.     

The characterizations of h-hemiregular hemirings and h-intra-hemiregular hemirings

In this paper, the concepts of fuzzy h-bi-ideals and fuzzy h-quasi-ideals of a hemiring are introduced, and related properties are investigated. The notion of h-intra-hemiregularity of a hemiring, which is a generalization of the notion of intra-regularity of a ring, is provided. Some characterizations of h-hemiregular hemirings, h-intra-hemiregular hemirings and hemirings that are both h-hemiregular and h-intra-hemiregular are derived in terms of fuzzy left, fuzzy right h-ideals, fuzzy h-bi-ideals and fuzzy h-quasi-ideals.     

Characterizations of detectability notions in terms of discontinuous dissipation functions

We consider a new Lyapunov-type characterization of detectability for non-linear systems without controls, in terms of lower-semicontinuous (not necessarily smooth, or even continuous) dissipation functions, and prove its equivalence to the GASMO (global asymptotic stability modulo outputs) and UOSS (uniform output-to-state stability) properties studied in previous work. The result is then extended to provide a construction of a discontinuous dissipation function characterization of the IOSS (input-to-state stability) property for systems with controls. This paper complements a recent result on smooth Lyapunov characterizations of IOSS. The utility of non-smooth Lyapunov characterizations is illustrated by application to a well-known transistor network example.     

On fuzzy h-ideals in \Upgamma-hemirings

By means of a kind of new idea, we introduce the concepts of some kinds of fuzzy h-ideals in \Upgamma\Upgamma-hemirings. Some new characterization theorems of these kinds of fuzzy h-ideals of a \Upgamma\Upgamma-hemiring are also given. In particular, we show that the h-hemiregular \Upgamma\Upgamma-hemirings can be described by using these kinds of fuzzy h-ideals.     

Fuzzy h-ideals in h-hemiregular and h-semisimple \Upgamma-hemirings

In this paper, we introduce the concepts of some kinds of fuzzy h-ideals in \Upgamma\Upgamma-hemirings and obtain some of their related properties. In particular, the characterizations of prime fuzzy h-ideals in \Upgamma\Upgamma-hemirings are discussed. Finally, we show that the h-hemiregular and h-semisimple \Upgamma\Upgamma-hemirings can be described by using these kinds of fuzzy h-ideals.     

Fuzzy h-ideals of hemirings

A characterization of an h-hemiregular hemiring in terms of a fuzzy h-ideal is provided. Some properties of prime fuzzy h-ideals of h-hemiregular hemirings are investigated. It is proved that a fuzzy subset ζ of a hemiring S is a prime fuzzy left (right) h-ideal of S if and only if ζ is two-valued, ζ(0) = 1, and the set of all x in S such that ζ(x) = 1 is a prime (left) right h-ideal of S. Finally, the similar properties for maximal fuzzy left (right) h-ideals of hemirings are considered.     

耦合的含立方非线性项系统的鞍结分岔控制

讨论了一个两自由度的含立方非线性项的受迫振动系统,设计了反馈控制器,对弱非线性系统用近似解析方法求出了控制系统的幅值控制方程,得到了控制参数与幅值的函数关系,实现了反馈控制法在多自由度非线性系统的鞍结分岔控制中的应用,证实了多尺度摄动法对多自由度非线性系统鞍结分岔控制的有效性和适用性.     

Characterizations of context-sensitive languages and other language classes in terms of symport/antiport P systems

We give “syntactic’’ characterizations of context-sensitive languages (CSLs) in terms of some restricted models of symport/antiport P systems. These are the first such characterizations of CSLs in terms of P systems. In particular, we show the following for any language L over a binary alphabet:

(1)

Let m   be any integer ≥1$\ge 1$. Then L is a CSL if and only if it can be accepted by a restricted symport/antiport P system with m membranes and multiple number of symbols (objects). Moreover, holding the number of membranes at m, there is an infinite hierarchy in computational power (within the class of binary CSLs) with respect to the number of symbols.     

On the transfer matrix of a neutral system: Characterizations of exponential stability in input—output terms

This paper investigates the stability of linear autonomous multivariable neutral systems from an input—output viewpoint. Several frequency-domain and input—output characterizations for exponential stability of neutral systems are given. We provide two examples which illustrate that the behaviour of neutral systems may be quite different from that of retarded systems. Moreover we give necessary and sufficient conditions for the transfer functions of a neutral system to belong to certain algebras of meromorphic functions introduced in this paper.     

Generalized fuzzy h-bi-ideals and h-quasi-ideals of hemirings

A new kind of generalized fuzzy h-ideals of a hemiring, namely, the (∈,∈∨q)-fuzzy h-bi-ideal (resp., h-quasi-ideal) is studied and the relationships between these generalized fuzzy h-ideals are described. Some characterization theorems of prime and semiprime (∈,∈∨q)-fuzzy h-bi-ideals (resp., h-quasi-ideals) of a hemiring are also given. In particular, we show that the h-hemiregular hemirings and h-intra-hemiregular hemirings can be described by using some of their generalized fuzzy h-ideals. Finally, the implication-based fuzzy h-bi-ideals (resp., h-quasi-ideals) of a hemiring are considered.     

量子自动机的刻画

澄清了各类量子自动机之间的相互关系,并给出了量子自动机的各种等价刻画定理.引入G-量子自动机、g-量子自动机、(广义)量子自动机及G-量子文法和g-量子文法,并阐明了它们与其他量子自动机之间的等价关系.在一定条件下讨论了G(g)-量子自动机与G(g)-量子文法的等价性,从而解决了关于量子文法产生量子正规语言的问题.讨论了量子语言与正规语言的关系,特别是回答了Gudder提出的两个公开问题.最后,给出了一种减少状态空间维数的方法.     

Characterizations of regular and context-free matrices

The u-v theorem for context-free languages is extended to prove an intercalation theorem for the family of context-free matrix languages. A row-wise iteration factor theorem is proved for the families of regular and context-free matrix languages. Characterizations of regular and context-free matrix languages are given in terms of vertical regular sequences and simple operations on vertical regular sequences. Closure of regular and context-free matrix languages under array nondeterministic finite state transducer mappings is established and an image theorem proved. This is used to give another characterization of regular matrix languages. Further it is shown that the family of regular matrix languages is a principal abstract family of matrices (AFM). The effect of string control and array control on these families are examined.     

NMG-代数中同态核的结构刻画

逻辑代数上的Bosbach态与Riečan态是经典概率论中Kolmogorov公理的两种不同方式的多值化推广,也是概率计量逻辑中语义计量化方法的代数公理化,是非经典数理逻辑领域中的重要研究分支.现已证明具有Glivenko性质的逻辑代数上的Bosbach态与Riečan态等价,并且逻辑代数的Glivenko性质是研究态算子的构造和存在性的重要工具,因而是态理论中的研究热点之一.研究了NMG-代数基于核算子的Glivenko性质,证明NMG-代数具有核基Glivenko性质的充要条件是该核算子是从此NMG-代数到其像集代数的同态,并给出NMG-代数中同态核的结构刻画.这里,NMG-代数是刻画序和三角模<（[0,1/2,T_NM]）,（[1/2,1,T_M]）>的逻辑系统NMG的语义逻辑代数.     

Characterizations and extensions of pushdown translations

A device called a pushdown assembler has been recently introduced and has been shown capable of defining exactly the syntax directed translations (SDT's). The output operation of the pushdown assembler can be extended in a natural way to obtain a more powerful device called a type B pushdown assembler (or B-machine). A B-machine can define SDT's more simply and directly than the original pushdown assembler. B-machines can also define many interesting translations which are not SDT's. In this paper the B-machine is defined and compared with the original pushdown assembler. The properties of B-machine translations are investigated and it is shown that, as with SDT's, there exists a natural infinite hierarchy of B-machine translations.