受控双向远程量子控制

融合远程量子控制与双向受控隐形传态的思想,率先提出了受控双向远程控制（CBRQC）的一个概念。利用五量子纠缠,提出执行任意单量子算子对的两个CBRQC方案。这两个方案是概率的,而在第一个方案中,增加局域Pauli算子将导致该方案成功概率和内在效率都翻倍。对于双向传送算子的限制集,两个确定的方案被提出,其中一个总体优于其他方案,并且这两个方案的成功概率和效率都可大大提高。从量子及经典资源消耗、必要的操作复杂性、成功概率和内在效率五个方面对这些方案进行了比较,阐明了选择量子通道的原因,指出提出的方案是安全的,并说明了在现有技术的分析下该方案的实验可行性。     

Generalized Definite Set Constraints

Set constraints (SC) are logical formulae in which atoms are inclusions between set expressions. Those set expressions are built over a signature , variables and various set operators. On a semantical point of view, the set constraints are interpreted over sets of trees built from and the inclusion symbol is interpreted as the subset relation over those sets. By restricting the syntax of those formulae and/or the set of operators that can occur in set expressions, different classes of set constraints are obtained. Several classes have been proposed and studied for some problems such as satisfiability and entailment. Among those classes, we focus in this article on the class of definite SC's introduced by Heintze and Jaffar, and the class of co-definite SC's studied by Charatonik and Podelski. In spite of their name, those two classes are not dual from each other, neither through inclusion inversion nor through complementation. In this article, we propose an extension for each of those two classes by means of an intentional set construction, so called membership expression. A membership expression is an expression {x| (x)}. The formula (x) is a positive first-order formula built from membership atomst in S in which S is a set expression. We name those two classes respectively generalized definite and generalized co-definite set constraints. One of the main point concerning those so-extended classes is that the two generalized classes turn out to be dual through complementation. First, we prove in this article that generalized definite set constraints is a proper extension of the definite class, as it is more expressive in terms of sets of solutions. But we show also that those extensions preserve some main properties of the definite and co-definite class. Hence for instance, as definite set constraints, generalized definite SC's have a least solution whereas the generalized co-definite SC's have a greatest solution, just as co-definite ones. Furthermore, we devise an algorithm based on tree automata that solves the satisfiability problem for generalized definite set constraints. Due to the dualization, the algorithm solves the satisfiability problem for generalized co-definite set constraints as well. This algorithm proves first that for those generalized classes, the satisfiability problem remains DEXPTIME-complete. It provides also a proof for regularity of the least solution of generalized definite constraints and so, by dualization for the greatest solution for the generalized co-definite SC's.     

On operations of soft sets

Soft set theory, proposed by Molodtsov, has been regarded as an effective mathematical tool to deal with uncertainties. In this paper, first we prove that certain De Morgan’s law hold in soft set theory with respect to different operations on soft sets. Then, we discuss the basic properties of operations on soft sets such as intersection, extended intersection, restricted union and restricted difference. Moreover, we illustrate their interconnections between each other. Also we define the notion of restricted symmetric difference of soft sets and investigate its properties. The main purpose of this paper is to extend the theoretical aspect of operations on soft sets.     

A new interpretation of complex membership grade

Complex fuzzy sets utilize a complex degree of membership, represented in polar coordinates, which is a combination of a degree of membership in a fuzzy set along with a crisp phase value that denotes position within the set. The compound value carries more information than a traditional fuzzy set and enables efficient reasoning. In this paper, we present a new and generalized interpretation of a complex grade of membership, where a complex membership grade defines a complex fuzzy class. The new definition provides rich semantics that is not readily available through traditional fuzzy sets or complex fuzzy sets and is not limited to a compound of crisp cyclical data with fuzzy data. Furthermore, the two components of the complex fuzzy class carry fuzzy information. A complex class is represented either in Cartesian or in polar coordinates where both axes induce fuzzy interpretation. Another novelty of the scheme is that it enables representing an infinite set of fuzzy sets. The paper provides the new definition of complex fuzzy classes along with axiomatic definition of basic operations on complex fuzzy classes. In addition, coordinate transformation as well as an extension from two‐dimensional fuzzy classes to n‐dimensional fuzzy classes are presented. © 2011 Wiley Periodicals, Inc.     

Exclusive disjunctive soft sets

Soft sets theory, initiated by Molodtsov, is an emerging tool to deal with uncertain problems and has been studied by scholars in both theory and practice. This paper proposes the notion of exclusive disjunctive soft sets and studies some of its operations, such as, restricted/relaxed AND operations, dependency between exclusive disjunctive soft sets and bijective soft sets, exclusive disjunctive soft decision systems, reduction of exclusive disjunctive soft decision systems, core of exclusive disjunctive soft decision systems, decision rules in exclusive disjunctive decision soft sets. Moreover, this study gives an application of exclusive disjunctive soft sets, which shows that it can be applied to attribute reduction of incomplete information system.     

Easy sets and hard certificate schemes

Can easy sets only have easy certificate schemes? In this paper, we study the class of sets that, for all NP certificate schemes (i.e., NP machines), always have easy acceptance certificates (i.e., accepting paths) that can be computed in polynomial time. We also study the class of sets that, for all NP certificate schemes, infinitely often have easy acceptance certificates. In particular, we provide equivalent characterizations of these classes in terms of relative generalized Kolmogorov complexity, showing that they are robust. We also provide structural conditions – regarding immunity and class collapses – that put upper and lower bounds on the sizes of these two classes. Finally, we provide negative results showing that some of our positive claims are optimal with regard to being relativizable. Our negative results are proven using a novel observation: We show that the classical “wide spacing” oracle construction technique yields instant non-bi-immunity results. Furthermore, we establish a result that improves upon Baker, Gill, and Solovay's classical result that holds in some relativized world. Received: 12 January 1996 / 9 January 1997     

Algebraic Structures of Rough Sets in Representative Approximation Spaces

In this paper a generalized notion of an approximation space is considered. By an approximation space we mean an ordered pair (U, ), where U is a finite nonempty set and is a covering of U. According to connections between rough sets and concepts we define two types of approximation operations. Hence we obtain two families of rough sets. We show that these families form lattices in special types of representative approximation spaces. The operations on rough sets defined in the above lattices are analogous to classical operations on sets.     

Number of curves in the generalized Edwards form with minimal even cofactor of the curve order

We analyze properties of points of orders 2, 4, and 8 of a curve in the generalized Edwards form. Arithmetic for group operations with singular points of these curves is introduced. We propose a classification of curves in the Edwards form into three disjoint classes. Formulas for the number of curves of order 4n of different classes are obtained. Works of other authors are critically analyzed.     

Quantum secret sharing using orthogonal multiqudit entangled states

In this work, we investigate the distinguishability of orthogonal multiqudit entangled states under restricted local operations and classical communication. According to these properties, we propose a quantum secret sharing scheme to realize three types of access structures, i.e., the (n, n)-threshold, the restricted (3, n)-threshold and restricted (4, n)-threshold schemes (called LOCC-QSS scheme). All cooperating players in the restricted threshold schemes are from two disjoint groups. In the proposed protocol, the participants use the computational basis measurement and classical communication to distinguish between those orthogonal states and reconstruct the original secret. Furthermore, we also analyze the security of our scheme in four primary quantum attacks and give a simple encoding method in order to better prevent the participant conspiracy attack.     

A Novel Indefinite Kernel Dimensionality Reduction Algorithm: Weighted Generalized Indefinite Kernel Discriminant Analysis

Kernel methods are becoming increasingly popular for many real-world learning problems. And these methods for data analysis are frequently considered to be restricted to positive definite kernels. In practice, however, indefinite kernels arise and demand application in pattern analysis. In this paper, we present several formal extensions of kernel discriminant analysis (KDA) methods which can be used with indefinite kernels. In particular they include indefinite KDA (IKDA) based on generalized singular value decomposition (IKDA/GSVD), pseudo-inverse IKDA, null space IKDA and range space IKDA. Similar to the case of LDA-based algorithms, IKDA-based algorithms also fail to consider that different contribution of each pair of class to the discrimination. To remedy this problem, weighted schemes are incorporated into IKDA extensions in this paper and called them weighted generalized IKDA algorithms. Experiments on two real-world data sets are performed to test and evaluate the effectiveness of the proposed algorithms and the effect of weights on indefinite kernel functions. The results show that the effect of weighted schemes is very significantly.     

Research on arithmetic operations over generalized orthopair fuzzy sets

The four fundamental operations of arithmetic for real (and complex) numbers are well known to everybody and quite often used in our daily life. And they have been extended to classical and generalized fuzzy environments with the demand of practical applications. In this paper, we present the arithmetic operations, including addition, subtraction, multiplication, and division operations, over -rung orthopair membership grades, where subtraction and division operations are both defined in two different ways. One is by solving the equation involving addition or multiplication operations, whereas the other is by determining the infimum or supremum of solutions of the corresponding inequality. Not all of -rung orthopairs can be performed by the former method but by the latter method, and it is proved that the former is a special case of the latter. Moreover, the elementary properties of arithmetic operations as well as mixed operations are extensively investigated. Finally, these arithmetic operations are pointwise defined on -rung orthopair fuzzy sets in which the membership degree of each element is a -rung orthopair.     

Julia集的广义同步

研究了两个不同的Julia集耦合实现广义同步的问题. 不同于以往对Julia集的研究仅限于对一个独立的Julia集的性质, 制图等方面的讨论, 本文提出了两个不同的Julia集广义同步的思想, 并以经典的复二次多项式系统z_n+1 = z²_n+c为例, 分别采用线性和非线性耦合的方法对该系统不同参数的Julia集进行了广义同步. 仿真结果表明了方法的有效性.     

Methods for saving and restoring register values across function calls

The method used to save and restore the values of registers across function calls can affect performance and influence the design of specific instructions. This paper describes the results of an experiment that empirically evaluated six different schemes for saving and restoring registers on CISC machines. The methods do not require special hardware or interprocedural analysis to be performed. The six schemes were logically divided into two classes. Three of the techniques do not require the compiler to perform data-flow analysis, whereas the other three schemes do. Within each class one scheme delegates the responsibility of preserving the state of the registers to the calling function. The second scheme of each class delegates the responsibility of saving the registers to the function being called. In the third scheme of the two classes, the registers are partitioned into two disjoint sets. The calling function is responsible for preserving register values in one of the sets whereas the called function is responsible for the other set. For each class the third scheme is shown to produce the most effective code.     

Deterministic joint remote preparation of arbitrary two- and three-qubit entangled states

We present several schemes for joint remote preparation of arbitrary two- and three-qubit entangled states with complex coefficients via two and three GHZ states as the quantum channel, respectively. In these schemes, two senders (or N senders) share the original state which they wish to help the receiver to remotely prepare. To complete the JRSP schemes, some novel sets of mutually orthogonal basis vectors are introduced. It is shown that, only if two senders (or N senders) collaborate with each other, and perform projective measurements under suitable measuring basis on their own qubits, respectively, the receiver can reconstruct the original state by means of some appropriate unitary operations. The advantage of the present schemes is that the success probability in all the considered JRSP can reach 1.     

Generalized intuitionistic fuzzy geometric interaction operators and their application to decision making

Considering that there may exist some interactions between membership function and non-membership function of different intuitionistic fuzzy sets, we present some new operational laws from the probability point of view and give a geometric interpretation of the new operations. Based on which, a new class of generalized intuitionistic fuzzy aggregation operators are developed, including the generalized intuitionistic fuzzy weighted geometric interaction averaging (GIFWGIA) operator, the generalized intuitionistic fuzzy ordered weighted geometric interaction averaging (GIFOWGIA) operator and the generalized intuitionistic fuzzy hybrid geometric interaction averaging (GIFHGIA) operator. The properties of these new generalized aggregation operators are investigated. Moreover, approaches to multiple attributes decision making are given based on the generalized aggregation operators under intuitionistic fuzzy environment, and an example is illustrated to show the validity and feasibility of new approach. Finally, we give a systematic comparison between the work of this paper and that of other papers.     

Semantics analysis through elementary meanings

Abstract. Thesaurus is a collection of words classified according to some relatedness measures among them. In this paper, we lay the theoretical foundations of thesaurus construction through elementary meanings of words. The concept of elementary meanings has been advocated and utilized in compiling Webster's Collegiate Thesaurus. If each word is supplied with elementary meanings so that all its meanings are covered by them in a standard fashion, we can define various similarity measures for a given set of words. Here we take an axiomatic way to analyze semantic structure of word groups. Assuming an abstract semantic world, we deduce closed sets as generalized synonym sets. That is, we show that under certain natural axioms, we only need to consider closed sets as far as the semantics are concerned. We also show that the set of generalized synonyms described as a certain pair of closed sets has a lattice structure. In order to have a flexible thesaurus, we also analyze structure changes corresponding to three basic environmental changes: A new word-meaning relation is added, a new word or a new meaning is included with its word-meaning relations. Actually we give algorithms to have updated lattice structure from previous one for the three operations. Received: 5 May 1996 / 21 February 2000     

Two nonparametric models for fusing heterogeneous fuzzy data

Two models are discussed that integrate heterogeneous fuzzy data of three types: real numbers, real intervals, and real fuzzy sets. The architecture comprises three modules: 1) an encoder that converts the mixed data into a uniform internal representation; 2) a numerical processing core that uses the internal representation to solve a specified task; and 3) a decoder that transforms the internal representation back to an interpretable output format. The core used in this study is fuzzy clustering, but there are many other operations that are facilitated by the models. Two schemes for encoding the data and decoding it after clustering are presented. One method uses possibility and necessity measures for encoding and several variants of a center of gravity defuzzification method for decoding. The second approach uses piecewise linear splines to encode the data and decode the clustering results. Both procedures are illustrated using two small sets of heterogeneous fuzzy data     

Arithmetic of complex sets

Let \(\mathbb{I}\) (?) be the set of all real closed intervals and letΩ ₁:= {+, ?, ×, /} be the set of arithmetic operators of ?. By extendingΩ ₁ from ? to \(\mathbb{I}\) (?) as usual one finds that \(\mathbb{I}\) (?) is closed with respect to the operations fromΩ ₁ (R. E. Moore [9]). In the literature several possibilities are discussed to go over from complex numbers to “complex intervals”: rectangles (Alefeld [1] et al.), discs (Henrici [4] et al.) or ellipses (Kahan [5] et al.). In all three cases the resulting sets are not closed with respect toΩ ₁, since the multiplication and division of such “intervals” does not lead to sets of the same kind. In what follows the question is treated whether there are classes of complex sets (“generalized intervals”) which are closed with respect toΩ ₁ or to subsets ofΩ ₁. One such class is easy to find. Also the shape of the sets involved is discussed. If it is assumed however that the sets under consideration are described by a finite number of parameters then there isno such class closed underΩ ₁.     

Modifiers based on some t-norms in fuzzy logic

Modifiers generated by n-placed functions are considered. The subject matter of modifiers are fuzzy sets, i.e. membership functions defined on the unit interval I = [0, 1]. Two sets of modifiers are considered as example cases. One of them is a set of modifiers generated by t-norms and t-conorms. Here different dual pairs of norms create modifiers of different grade of strength. These norms are examples of two-placed functions. Another case is to generate a series of modifiers using only one DeMorgan class of norms. Norms are generalized to be n-placed functions. The place number n takes effect to the strength of a modifier. Two different DeMorgan classes are taken into the consideration. The first steps to the direction of many-valued modifier logics are taken.