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L. Gǎvruţa (2012) introduced a special kind of frames, named K-frames, where K is an operator, in Hilbert spaces, which is significant in frame theory and has many applications. In this paper, first of all, we have introduced the notion of approximative K-atomic decomposition in Banach spaces. We gave two characterizations regarding the existence of approximative K-atomic decompositions in Banach spaces. Also some results on the existence of approximative K-atomic decompositions are obtained. We discuss several methods to construct approximative K-atomic decomposition for Banach Spaces. Further, approximative _d-frame and approximative _d-Bessel sequence are introduced and studied. Two necessary conditions are given under which an approximative _d-Bessel sequence and approximative _d-frame give rise to a bounded operator with respect to which there is an approximative K-atomic decomposition. Example and counter example are provided to support our concept. Finally, a possible application is given.

In the past few decades, the content-based image retrieval (CBIR), which focuses on the exploration of image feature extraction methods, has been widely investigated. The term of feature extraction is used in two cases: application-based feature expression and mathematical approaches for dimensionality reduction. Feature expression is a technique of describing the image color, texture and shape information with feature descriptors; thus, obtaining effective image features expression is the key to extracting high-level semantic information. However, most of the previous studies regarding image feature extraction and expression methods in the CBIR have not performed systematic research. This paper aims to introduce the basic image low-level feature expression techniques for color, texture and shape features that have been developed in recent years.

First, this review outlines the development process and expounds the principle of various image feature extraction methods, such as color, texture and shape feature expression. Second, some of the most commonly used image low-level expression algorithms are implemented, and the benefits and drawbacks are summarized. Third, the effectiveness of the global and local features in image retrieval, including some classical models and their illustrations provided by part of our experiment, are analyzed. Fourth, the sparse representation and similarity measurement methods are introduced, and the retrieval performance of statistical methods is evaluated and compared.

The core of this survey is to review the state of the image low-level expression methods and study the pros and cons of each method, their applicable occasions and certain implementation measures. This review notes that image peculiarities of single-feature descriptions may lead to unsatisfactory image retrieval capabilities, which have significant singularity and considerable limitations and challenges in the CBIR.

A comprehensive review of the latest developments in image retrieval using low-level feature expression techniques is provided in this paper. This review not only introduces the major approaches for image low-level feature expression but also supplies a pertinent reference for those engaging in research regarding image feature extraction.

The main purpose of this paper is to research the e‐government architecture issue as a means of addressing the interoperability gap. It will incorporate the new knowledge acquired in the e‐government integration methodology of the interconnectivity of cross‐layers. These layers include the vertical direction of strategy, business, process, service and information.

The methodology used in this research as it progressed was component‐base driven and involved the exploration of vertical e‐government integration and common service interoperability between business and IT. The realization of this methodology first required a technical foundation setup followed by a business semantics study and a new concept of enterprise integration. The lack of interconnectivity between these layers is the main concerns with the implication that e‐government architecture needs a robust micro‐mechanism of semantic messaging and metadata to coordinate across layers.

E‐government architecture became pervasive in the twenty‐first century due to its significant growth in terms of huge volume transactions, the citizens' new service concept, and sophisticated businesses. Enterprise architecture mainly mediates between business and IT to minimize the gap by improving governance, agility and business integrity. All of these disciplines and principles should be applied to attain e‐government transformation and vertical interoperability and common services provisioning are the major findings in the research.

This paper contribute new concept of enterprise vertical integration in e‐government. The integrated solution of coherence of approaches forms the basis of this new concept; it serves as the backbone in vertical integration and addresses the e‐government enterprise gap. It is expected to provide further insights into micro process integration across e‐government enterprise layers.

A mature adoption of a service-oriented architecture (SOA) goes steadily through different levels of maturity, whereby each level has its own types of services (e.g. software services or business services). However, the identification of such services is not an easy task even though there exist many service identification methods (SIMs). This paper aims to propose a new approach to select SIMs. The proposed selection approach for SIMs uses the desired SOA maturity level as the main guidance to assist the organizations in selecting a suitable SIM for each level of SOA maturity.

The methodology consists of three activities: surveying and selecting a suitable evaluation framework for SIMs, surveying and selecting a suitable SOA maturity model (SOAMM) and using the selected evaluation framework to decide a suitable SIM for the desired SOA maturity level with respect to the selected SOAMM.

Welke’s SOAMM and two existing evaluation frameworks for SIMs were found suitable to validate the proposed selection approach for SIMs. The two selected frameworks utilized the proposed selection approach to different degrees. To fully utilize the proposed selection approach, a comprehensive evaluation framework is required that addresses the most significant aspects of the existing SIMs.

In this research, the authors propose a new way of using Welke’s SOAMM to guide the organizations in selecting a suitable SIM from the existing evaluation frameworks for SIMs based on the desired SOA maturity level. In addition, the proposed selection approach improves the applicability of the existing evaluation frameworks, as it provides the organizations with a new way to select the methods.

The purpose of this article is to present a new application of pursuit‐based analysis for diagnosing rolling element bearing faults.

Intelligent diagnosis of rolling element bearing faults in rotating machinery involves the procedure of feature extraction using modern signal processing techniques and artificial intelligence technique‐based fault detection and identification. This paper presents a comparative study of both the basis and matching pursuits when applied to fault diagnosis of rolling element bearings using vibration analysis.

Fault features were extracted from vibration acceleration signals and subsequently fed to a feed forward neural network (FFNN) for classification. The classification rate and mean square error (MSE) were calculated to evaluate the performance of the intelligent diagnostic procedure. Results from the basis pursuit fault diagnosis procedure were compared with the classification result of a matching pursuit feature‐based diagnostic procedure. The comparison clearly illustrates that basis pursuit feature‐based fault diagnosis is significantly more accurate than matching pursuit feature‐based fault diagnosis in detecting these faults.

Intelligent diagnosis can reduce the reliance on experienced personnel to make expert judgements on the state of the integrity of machines. The proposed method has the potential to be extensively applied in various industrial scenarios, although this application concerned rolling element bearings only. The principles of the application are directly translatable to other parts of complex machinery.

This work presents a novel intelligent diagnosis strategy using pursuit features and feed forward neural networks. The value of the work is to ease the burden of making decisions on the integrity of plant through a manual program in condition monitoring and diagnostics particularly of complex pieces of plant.

Paley's and Hardy's inequality are proved on a Hardy-type space for the Fourier–Dunkl expansions based on a complete orthonormal system of Dunkl kernels generalizing the classical exponential system defining the classical Fourier series.

Although the difficulties related to the Dunkl settings, the techniques used by K. Sato were still efficient in this case to establish the inequalities which have expected similarities with the classical case, and Hardy and Paley theorems for the Fourier–Bessel expansions due to the fact that the Bessel transform is the even part of the Dunkl transform.

Paley's inequality and Hardy's inequality are proved on a Hardy-type space for the Fourier–Dunkl expansions.

This work is a participation in extending the harmonic analysis associated with the Dunkl operators and it shows the utility of BMO spaces to establish some analytical results.

Dunkl theory is a generalization of Fourier analysis and special function theory related to root systems. Establishing Paley and Hardy's inequalities in these settings is a participation in extending the Dunkl harmonic analysis as it has many applications in mathematical physics and in the framework of vector valued extensions of multipliers.

This information will be useful in the selection of materials and technology for the detection and removal of mercury ions at a low cost and with high sensitivity and selectivity. The purpose of this study is to provide the useful information for selection of materials and technology to detect and remove the mercury ions from water with high sensitivity and selectivity. The purpose of this study is to provide the useful information for selection of materials and technology to detect and remove the mercury ions from water with high sensitivity and selectivity.

Different nano- and bio-materials allowed for the development of a variety of biosensors – colorimetric, chemiluminescent, electrochemical, whole-cell and aptasensors – are described. The materials used for their development also make it possible to use them in removing heavy metals, which are toxic contaminants, from environmental water samples.

This review focuses on different technologies, tools and materials for mercury (heavy metals) detection and remediation to environmental samples.

This review gives up-to-date and systemic information on modern nanotechnology methods for heavy metal detection. Different recognition molecules and nanomaterials have been discussed for remediation to water samples. The present review may provide valuable information to researchers regarding novel mercury ions detection sensors and encourage them for further research/development.

The purpose of this paper is to provide a fault diagnosis method for rolling bearings. Rolling bearings are widely used in industrial appliances, and their fault diagnosis is of great importance and has drawn more and more attention. Based on the common failure mechanism of failure modes of rolling bearings, this paper proposes a novel compound data classification method based on the discrete wavelet transform and the support vector machine (SVM) and applies it in the fault diagnosis of rolling bearings.

Vibration signal contains large quantity of information of bearing status and this paper uses various types of wavelet base functions to perform discrete wavelet transform of vibration and denoise. Feature vectors are constructed based on several time-domain indices of the denoised signal. SVM is then used to perform classification and fault diagnosis. Then the optimal wavelet base function is determined based on the diagnosis accuracy.

Experiments of fault diagnosis of rolling bearings are carried out and wavelet functions in several wavelet families were tested. The results show that the SVM classifier with the db4 wavelet base function in the db wavelet family has the best fault diagnosis accuracy.

This method provides a practical candidate for the fault diagnosis of rolling bearings in the industrial applications.

Collaboration is a common phenomenon in human society. The best way of collaborations can make the group achieve the best interests. Because of the low cost and high repeatability of simulation, it is a good method to explore the best way of collaborations by means of simulation. The traditional simulation is difficult to adapt to the crowd intelligence network simulation, so the crowd collaborations simulation is proposed.

In this paper, the atomic swarm intelligence unit and collective swarm intelligence unit are proposed to represent the behavior of individuals and groups in physical space and the interaction between them.

To explore the best collaboration mode of the group, a framework of crowd collaborations simulation is proposed, which decomposes the big goal into the small goals by constructing the cooperation chain and analyzes the cooperation results and feeds them back to the next simulation.

Two kinds of swarm intelligence units are used to represent the simulated individuals in the group, and the pattern is used to represent individual behavior. It is suitable for the simulation of collaboration problems in various types and situations.

The application of smart contract can greatly reduce transaction costs and improve transaction efficiency. The existing smart contract are expensive, single application scenario and inefficient. This paper aims to propose a new smart contract model to solve these problems.

By investigating the research history, models and platforms, this paper summarizes the shortcomings of existing smart contracts. Based on the content and architecture of traditional contract, a smart contract model with wider application scope is designed.

In this paper, several models are used to describe the operation mechanism of smart contracts. To facilitate computer execution, a decomposition method is proposed, which divides smart contracts into several sub-contracts. Then, the advantages and deployment methods of smart contract are discussed. On this basis, a specific example is given to illustrate how the application of smart contract will change our life.

Smart contract is gradually applied to more fields. In this paper, the structure and operation mechanism of smart contract system in reality are given, which will be beneficial to the application of smart contract to more complex systems.