The problem on the set-theoretical solutions to the quantum Yang-Baxter equation was presented byDrinfel'd as a main unsolved problem in quantum group theory. The set-theoretical solutions are a natural extensiono...The problem on the set-theoretical solutions to the quantum Yang-Baxter equation was presented byDrinfel'd as a main unsolved problem in quantum group theory. The set-theoretical solutions are a natural extensionof the usual (linear) solutions. In this paper, we not only give a further study on some known set-theoretical solutions(the Venkov's solutions), but also find a new kind of set-theoretical solutions which have a geometric interpretation.Moreover, the new solutions lead to the metahomomorphisms in group theory.展开更多
Considering that the uncertain information has serious influences on the safety of structural systems and is always limited, it is reasonable that the uncertainties are generally described as interval sets. Based on t...Considering that the uncertain information has serious influences on the safety of structural systems and is always limited, it is reasonable that the uncertainties are generally described as interval sets. Based on the non-probabilistic set-theoretic theory, which is applied to measuring the safety of structural components and further combined with the branch-and-bound method for the probabilistic reliability analysis of structural systems, the non-probabilistic branch-and-bound method for determining the dominant failure modes of an uncertain structural system is given. Meanwhile, a new system safety measuring index obtained by the non-probabilistic set-theoretic model is investigated. Moreover, the compatibility between the classical probabilistic model as well as the proposed interval-set model will be discussed to verify the physical meaning of the safety measure in this paper. Some numerical examples are utilized to illustrate the validity and feasibility of the developed method.展开更多
The aim of this paper is to evaluate the fatigue reliability with hybrid uncertain parameters based on a residual strength model. By solving the non-probabilistic setbased reliability problem and analyzing the reliabi...The aim of this paper is to evaluate the fatigue reliability with hybrid uncertain parameters based on a residual strength model. By solving the non-probabilistic setbased reliability problem and analyzing the reliability with randomness, the fatigue reliability with hybrid parameters can be obtained. The presented hybrid model can adequately consider all uncertainties affecting the fatigue reliability with hybrid uncertain parameters. A comparison among the presented hybrid model, non-probabilistic set-theoretic model and the conventional random model is made through two typical numerical examples. The results show that the presented hybrid model, which can ensure structural security, is effective and practical.展开更多
Similarity measurement is one of key operations to retrieve “desired” images from an image database. As a famous psychological similarity measure approach, the Feature Contrast (FC) model is defined as a linear comb...Similarity measurement is one of key operations to retrieve “desired” images from an image database. As a famous psychological similarity measure approach, the Feature Contrast (FC) model is defined as a linear combination of both common and distinct features. In this paper, an adaptive feature contrast (AdaFC) model is proposed to measure similarity between satellite images for image retrieval. In the AdaFC, an adaptive function is used to model a variable role of distinct features in the similarity measurement. Specifically, given some distinct features in a satellite image, e.g., a COAST image, they might play a significant role when the image is compared with an image including different semantics, e.g., a SEA image, and might be trivial when it is compared with a third image including same semantics, e.g., another COAST image. Experimental results on satellite images show that the proposed model can consistently improve similarity retrieval effectiveness of satellite images including multiple geo-objects, for example COAST images.展开更多
Cycle sets were introduced to reduce non-degenerate unitary Yang-Baxter maps to an algebraic system with a single binary operation. Every finite cycle set extends uniquely to a finite cycle set with a compatible abeli...Cycle sets were introduced to reduce non-degenerate unitary Yang-Baxter maps to an algebraic system with a single binary operation. Every finite cycle set extends uniquely to a finite cycle set with a compatible abelian group structure. Etingof et al. introduced affine Yang-Baxter maps. These are equivalent to cycle sets with a specific abelian group structure. Abelian group structures have also been essential to get partial results for the still unsolved retraction problem. We introduce two new classes of cycle sets with an underlying abelian group structure and show that they can be transformed into each other while keeping the group structure fixed. This leads to a proper extension of the retractibility conjecture and new evidence for its truth.展开更多
This paper addresses a set-theoretic method for the detection of data corruption cyber-attacks on the load frequency control loop of a networked power system. The system consists of several interconnected control area...This paper addresses a set-theoretic method for the detection of data corruption cyber-attacks on the load frequency control loop of a networked power system. The system consists of several interconnected control areas forming a power grid. Based on the overall discrete-time network dynamics, a convex and compact polyhedral robust invariant set is extracted and is used as a set-induced anomaly detector. If the state vector exits the invariant set,then an alarm will be activated, and the potential threat is considered disclosed. The attack scenario used to assess the efficiency of the proposed anomaly detector concerns corrupted frequency sensor measurements transmitted to the automatic generation control unit of a compromised control area. Simulation studies highlight the ability of a set-theoretic approach to disclose persistent and intermittent attack patterns even when they occur at the same time with changes in the power load demand.展开更多
This is the first part of a series of two articles.In this paper we enumerate and classify the left braces of size p^(2)q,where p and q are distinct prime numbers,by the classification of regular subgroups of the holo...This is the first part of a series of two articles.In this paper we enumerate and classify the left braces of size p^(2)q,where p and q are distinct prime numbers,by the classification of regular subgroups of the holomorph of the abelian groups of the same order.We also provide the formulas that define the constructed braces.展开更多
文摘The problem on the set-theoretical solutions to the quantum Yang-Baxter equation was presented byDrinfel'd as a main unsolved problem in quantum group theory. The set-theoretical solutions are a natural extensionof the usual (linear) solutions. In this paper, we not only give a further study on some known set-theoretical solutions(the Venkov's solutions), but also find a new kind of set-theoretical solutions which have a geometric interpretation.Moreover, the new solutions lead to the metahomomorphisms in group theory.
基金National Nature Science Foundation of China(No.11002013)Defense Industrial Technology Development Program(Nos.A2120110001,B2120110011)the Aeronautical Science Foundation of China(No.2012ZA51010)
文摘Considering that the uncertain information has serious influences on the safety of structural systems and is always limited, it is reasonable that the uncertainties are generally described as interval sets. Based on the non-probabilistic set-theoretic theory, which is applied to measuring the safety of structural components and further combined with the branch-and-bound method for the probabilistic reliability analysis of structural systems, the non-probabilistic branch-and-bound method for determining the dominant failure modes of an uncertain structural system is given. Meanwhile, a new system safety measuring index obtained by the non-probabilistic set-theoretic model is investigated. Moreover, the compatibility between the classical probabilistic model as well as the proposed interval-set model will be discussed to verify the physical meaning of the safety measure in this paper. Some numerical examples are utilized to illustrate the validity and feasibility of the developed method.
基金supported by the National Natural Science Foundation of China (90816024, 10872017 and 10876100)the 111 Project (B07009)the Innovation Foundation of Beihang University for PhD Graduates
文摘The aim of this paper is to evaluate the fatigue reliability with hybrid uncertain parameters based on a residual strength model. By solving the non-probabilistic setbased reliability problem and analyzing the reliability with randomness, the fatigue reliability with hybrid parameters can be obtained. The presented hybrid model can adequately consider all uncertainties affecting the fatigue reliability with hybrid uncertain parameters. A comparison among the presented hybrid model, non-probabilistic set-theoretic model and the conventional random model is made through two typical numerical examples. The results show that the presented hybrid model, which can ensure structural security, is effective and practical.
文摘Similarity measurement is one of key operations to retrieve “desired” images from an image database. As a famous psychological similarity measure approach, the Feature Contrast (FC) model is defined as a linear combination of both common and distinct features. In this paper, an adaptive feature contrast (AdaFC) model is proposed to measure similarity between satellite images for image retrieval. In the AdaFC, an adaptive function is used to model a variable role of distinct features in the similarity measurement. Specifically, given some distinct features in a satellite image, e.g., a COAST image, they might play a significant role when the image is compared with an image including different semantics, e.g., a SEA image, and might be trivial when it is compared with a third image including same semantics, e.g., another COAST image. Experimental results on satellite images show that the proposed model can consistently improve similarity retrieval effectiveness of satellite images including multiple geo-objects, for example COAST images.
文摘Cycle sets were introduced to reduce non-degenerate unitary Yang-Baxter maps to an algebraic system with a single binary operation. Every finite cycle set extends uniquely to a finite cycle set with a compatible abelian group structure. Etingof et al. introduced affine Yang-Baxter maps. These are equivalent to cycle sets with a specific abelian group structure. Abelian group structures have also been essential to get partial results for the still unsolved retraction problem. We introduce two new classes of cycle sets with an underlying abelian group structure and show that they can be transformed into each other while keeping the group structure fixed. This leads to a proper extension of the retractibility conjecture and new evidence for its truth.
文摘This paper addresses a set-theoretic method for the detection of data corruption cyber-attacks on the load frequency control loop of a networked power system. The system consists of several interconnected control areas forming a power grid. Based on the overall discrete-time network dynamics, a convex and compact polyhedral robust invariant set is extracted and is used as a set-induced anomaly detector. If the state vector exits the invariant set,then an alarm will be activated, and the potential threat is considered disclosed. The attack scenario used to assess the efficiency of the proposed anomaly detector concerns corrupted frequency sensor measurements transmitted to the automatic generation control unit of a compromised control area. Simulation studies highlight the ability of a set-theoretic approach to disclose persistent and intermittent attack patterns even when they occur at the same time with changes in the power load demand.
基金supported by UBACyT 20020171000256BA and PICT 2016-2481.
文摘This is the first part of a series of two articles.In this paper we enumerate and classify the left braces of size p^(2)q,where p and q are distinct prime numbers,by the classification of regular subgroups of the holomorph of the abelian groups of the same order.We also provide the formulas that define the constructed braces.
