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Open access

Bo Zhang and Yatsuka Nakamura

The Definition of Finite Sequences and Matrices of Probability, and Addition of Matrices of Real Elements

In this article, we first define finite sequences of probability distribution and matrices of joint probability and conditional probability. We discuss also the concept of marginal probability. Further, we describe some theorems of matrices of real elements including quadratic form.

Open access

Bo Zhang and Yatsuka Nakamura

Definition and some Properties of Information Entropy

In this article we mainly define the information entropy [3], [11] and prove some its basic properties. First, we discuss some properties on four kinds of transformation functions between vector and matrix. The transformation functions are LineVec2Mx, ColVec2Mx, Vec2DiagMx and Mx2FinS. Mx2FinS is a horizontal concatenation operator for a given matrix, treating rows of the given matrix as finite sequences, yielding a new finite sequence by horizontally joining each row of the given matrix in order to index. Then we define each concept of information entropy for a probability sequence and two kinds of probability matrices, joint and conditional, that are defined in article [25]. Further, we discuss some properties of information entropy including Shannon's lemma, maximum property, additivity and super-additivity properties.

Open access

Jianjun Li and Ru Bo Zhang

Abstract

The multi-autonomous underwater vehicle (AUV) distributed task allocation model of a contract net, which introduces an equilibrium coefficient, has been established to solve the multi-AUV distributed task allocation problem. A differential evolution quantum artificial bee colony (DEQABC) optimization algorithm is proposed to solve the multi-AUV optimal task allocation scheme. The algorithm is based on the quantum artificial bee colony algorithm, and it takes advantage of the characteristics of the differential evolution algorithm. This algorithm can remember the individual optimal solution in the population evolution and internal information sharing in groups and obtain the optimal solution through competition and cooperation among individuals in a population. Finally, a simulation experiment was performed to evaluate the distributed task allocation performance of the differential evolution quantum bee colony optimization algorithm. The simulation results demonstrate that the DEQABC algorithm converges faster than the QABC and ABC algorithms in terms of both iterations and running time. The DEQABC algorithm can effectively improve AUV distributed multi-tasking performance.

Open access

Bo Li, Yan Zhang and Artur Korniłowicz

Simple Continued Fractions and Their Convergents

The article introduces simple continued fractions. They are defined as an infinite sequence of integers. The characterization of rational numbers in terms of simple continued fractions is shown. We also give definitions of convergents of continued fractions, and several important properties of simple continued fractions and their convergents.

Open access

Bo Li, Yan Zhang and Xiquan Liang

Difference and Difference Quotient

In this article, we give the definitions of forward difference, backward difference, central difference and difference quotient, and some of their important properties.

Open access

Bo Zhang and Chunming Tang

Abstract

The detection of defects in yarn-dyed fabric is one of the most difficult problems among the present fabric defect detection methods. The difficulty lies in how to properly separate patterns, textures, and defects in the yarn-dyed fabric. In this paper, a novel automatic detection algorithm is presented based on frequency domain filtering and similarity measurement. First, the separation of the pattern and yarn texture structure of the fabric is achieved by frequency domain filtering technology. Subsequently, segmentation of the periodic units of the pattern is achieved by using distance matching function to measure the fabric pattern. Finally, based on the similarity measurement technology, the pattern’s periodic unit is classified, and thus, automatic detection of the defects in the yarn-dyed fabric is accomplished.

Open access

Bo Zhang, Hiroshi Yamazaki and Yatsuka Nakamura

The Relevance of Measure and Probability, and Definition of Completeness of Probability

In this article, we first discuss the relation between measure defined using extended real numbers and probability defined using real numbers. Further, we define completeness of probability, and its completion method, and also show that they coincide with those of measure.

Open access

Bo Li, Yan Zhang and Xiquan Liang

Several Differentiation Formulas of Special Functions. Part III

In this article, we give several differentiation formulas of special and composite functions including trigonometric function, inverse trigonometric function, polynomial function and logarithmic function.

Open access

Huyuan Zhang, Bo Yang, Guangwei Zhang and Xuechao Zhang

Abstract

Heavy metal pollutants in the leachate of waste landfill are a potential threat to the environment. In this study, the feasibility of using municipal sewage sludge as barrier material for the containment of heavy metal pollutants from solid waste landfills was evaluated by compaction test and hydraulic conductivity test concerning compaction property, impermeability and heavy metal retardation. Results of the compaction test showed that the maximum dry density of 0.79 g·cm−3 was achieved at the optimum water content of about 60%. The hydraulic conductivities of compacted sewage sludge permeated with synthetic heavy metal solutions were in the range of 1.3×10−8 – 6.2×10−9 cm·s−1, less than 1.0 ×10−7cm·s−1 recommended by regulations for barrier materials. Chemical analyses on the effluent from the hydraulic conductivity tests indicated that the two target heavy metals, Zn and Cd in the permeants were all retarded by compacted sewage sludge, which might be attributed to the precipitation and adsorption of heavy metal ions. The results of this study suggest that specially prepared material from sewage sludge could be used as a barrier for waste landfills for its low permeability and strong retardation to heavy metal pollutants.

Open access

Zhuo Wang, Bo Zhang and Tao Wang

Abstract

When an offshore oil field completed and put into production, new subsea pipelines and the new cable need to be established. Cable protection pipe clamp is used to fix cable protection pipe on the jacket. In order to avoid the problem of traditional steel structure clamp splice, counterpoint, fastening difficulty when installed cable protection pipe under water, reduce the risk and workload of under water, This paper develop a new type of portable connecting riser clamp -“backpack clamp” which solve the riser cable protection pipe difficult underwater installation problem. The main structure of backpack clamp used three valves type structure. The load characteristic of a clamping device was determined by the Morison equation which was a classical theory. Clamp device underwater mechanics analysis model was established. The minimum tension pre-tightening force was determined. The results show that the strength of the base meets the requirements after strength analysis with finite element analysis method, stability and strength experiments, which means the clamp based on resin matrix composite is feasible.