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This paper is devoted to study the existence of center-stable manifolds for some planar fractional differential equations of Caputo type with relaxation factor. After giving some necessary estimation for Mittag–Leffler functions, some existence results for center-stable manifolds are established under the mild conditions by virtue of a suitable Lyapunov–Perron operator. Moreover, an explicit example is given to illustrate the above result. Finally, high-dimensional case is considered.

Aiming at the bad video quality which caused by the diversity of users cooperation willingness and the limited transmission rate of multicast due to the worst channel quality of user, a model is proposed for cooperative D2D communications that combines social relationships and physical conditions between users. Additionally the corresponding D2D pairing for cooperative video transmission algorithm based on stable matching in this model is also given. To this end the importance and status of each dimension is measured by the weight function. The weight function is used to establish dynamic social relationships between users combined with physical distance. Thus unicast throughput and delay are derived by considering the social relationships and physical conditions. The preference information are generated by designing the utility function of cooperation, the users form a stable matching by dynamic negotiation. Finally, it is proved that the proposed algorithm is stable and weak Pareto optimal. Simulation results demonstrate that D2D communications can be enhanced by considering social aspects, and that the performance of the proposed algorithm can be improved with lower computation complexity compared to the traditional cooperative scheme.

In this paper, we consider the existence and uniqueness of solutions to the nonlocal boundary value problem for semi-linear differential equations involving Hilfer fractional derivative. With the help of properties of Hilfer fractional calculus, Mittag-Leffler functions, and fixed point methods, we derive existence and uniqueness results. Finally, examples are given to illustrate our theoretical results.

Due to the poor robustness and high complexity of the concentrated dictionary learning (CDL) algorithm, this paper addresses these issues using denoising deep extreme learning machine based on autoencoder (DDELM-AE) and approximate k singular value decomposition (AK-SVD). Different from the CDL algorithm, on input, DDELM-AE is added for enhancing denoising ability and AK-SVD replaces K-SVD for improving running speed. Additionally, experimental results show that the improved algorithm is more efficient than the original CDL algorithm in terms of running time, denoising ability, and stability.

Clustering analysis of massive data in wireless multimedia sensor networks (WMSN) has become a hot topic. However, most data clustering algorithms have difficulty in obtaining latent nonlinear correlations of data features, resulting in a low clustering accuracy. In addition, it is difficult to extract features from missing or corrupted data, so incomplete data are widely used in practical work. In this paper, the optimally designed variational autoencoder networks is proposed for extracting features of incomplete data and using high-order fuzzy c-means algorithm (HOFCM) to improve cluster performance of incomplete data. Specifically, the feature extraction model is improved by using variational autoencoder to learn the feature of incomplete data. To capture nonlinear correlations in different heterogeneous data patterns, tensor based fuzzy c-means algorithm is used to cluster low-dimensional features. The tensor distance is used as the distance measure to capture the unknown correlations of data as much as possible. Finally, in the case that the clustering results are obtained, the missing data can be restored by using the low-dimensional features. Experiments on real datasets show that the proposed algorithm not only can improve the clustering performance of incomplete data effectively, but also can fill in missing features and get better data reconstruction results.

This paper intends to reduce the communication cost, while ensuring data prediction accuracy and data transmission efficiency in wireless sensor networks (WSNs). A data fusion scheme using clustering and prediction algorithms is proposed. Initially, nodes are clustered by using historical data, and then they are linked based on the actual geographical distance. Next, during the data fusion process, the base station and sensor nodes both use the online recurrent extreme learning machine (OR-ELM) to predict the future sensing data, which can guarantee that the data sequence in the base station and sensor nodes are synchronous. If the prediction fails, data will be transmitted to other nodes in the link and forwarded. Finally, experimental results reveal that the proposed data fusion scheme not only can effectively predict the sensor data, but also can reduce spatial and temporal redundant transmissions with low computational cost.

In this paper, we investigate Ulam-Hyers stability, Practical-Ulam-Hyers stability and Practical-Ulam-Hyers-Rassias stability of nonlocal fractional Langevin equations involving Riemann-Liouville fractional integral with positive constant coefficients. By utilizing an explicit bound of Mittag-Leffler function with two parameters and analytical methods, the practical stability results are presented via a generalized Gronwall inequality. Finally, two examples are given to illustrate our theoretical results.

In this paper, we study P-type, PIα-type, and D-type iterative learning control for fractional impulsive evolution equations in Banach spaces. We present triple convergence results for open-loop iterative learning schemes in the sense of λ-norm through rigorous analysis. The proposed iterative learning control schemes are effective to fractional hybrid infinite-dimensional distributed parameter systems. Finally, an example is given to illustrate our theoretical results. Copyright © 2015 John Wiley & Sons, Ltd.

In this paper, we consider periodic boundary value problems for two new type nonlinear impulsive evolution equations on Banach spaces. By using the theory of semigroup, a mixed type Gronwall inequality and fixed point methods, we establish several sufficient conditions on the existence of mild solutions for such problems. Finally, examples are given to illustrate our main results.

In this paper, we first present $$\beta $$ -Ulam–Hyers–Rassias stability results for nonautonomous impulsive evolution equations on a compact interval and an unbounded interval. Second, we give some extensions of $$\beta $$ -Ulam–Hyers–Rassias stability for infinite impulses case. Finally, we give two examples to illustrate our results.

In this paper, we apply asymptotic behavior on Mittag-Leffler functions $\mathbb{E}_{\alpha}(z)$ and $\mathbb{E}_{\alpha,\alpha}(z)$ for $z>0$ to discuss exp-type Ulam-Hyers stability of ${}^{\mathrm{c}} D_{t}^{\alpha}x(t)=\lambda x(t)+f(t,x(t))$ for the case $\lambda>0$ on a finite time interval $[0,1]$ and an unbounded interval $(1,\infty)$ .

In this paper, we investigate a new class of fractional differential equations with non-instantaneous impulses. We give a suitable formula of piecewise continuous solutions and present the concept of β-Ulam-Hyers stability. We present existence and β-Ulam-Hyers stability results on a compact interval.

With the advance in wireless Internet and mobile computing, location-based services (LBS)--the capability to deliver location-aware content to subscribers on the basis of the positioning capability of the wireless infrastructure--are emerging as key value-added services that telecom operators can offer. To support efficient and effective development and deployment of innovative location-aware applications, a flexible and resilient middleware should be built as the enabling infrastructure. This paper presents the research and efforts made in the IBM China Research Laboratory toward developing an infrastructure that supports location-aware services. This infrastructure is based on a proposed location operating reference model (LORE), which addresses many major aspects of building location-aware services, including positioning, location modeling, location-dependent query processiug, tracking, and intelligent location-aware message notification. Three key components of the infrastructure--the location server, a moving object database, and a spatial publish/subscribe engine--are introduced in detail. The location server has a common location adapter framework that supports heterogeneous positioning techniques and industry-standard location application program interfaces (APIs). The moving object database manages the location stream and processes the location-based queries. The spatial publish/subscribe engine enables intelligent location-aware message notification. We also present some location-aware application demonstrations that leverage the LORE infrastructure. Part of our work has been tested in pilot projects with leading carriers in China and has been integrated into the IBM WebSphere® Everyplace® Suite.

In this paper, we study periodic BVPs for fractional order impulsive evolution equations. The existence and boundedness of piecewise continuous mild solutions and design parameter drift for periodic motion of linear problems are presented. Furthermore, existence results of piecewise continuous mild solutions for semilinear impulsive periodic problems are showed. Finally, an example is given to illustrate the results.

This paper describes the concept and the theoretical foundations of the Social Learning based on Social Networking in the network era firstly. Secondly, the main characteristics of Social Learning are discussed from the perspective of Social Networking. And then based on the above discussion, the paper emphatically analyzes the social learning elements and the relationships between them, and puts forward a model of social learning initially.

The major requests for telecom network are efficiency, security, and reliability of service. Data service, running on the telecom network, is a most prominent revenue source for telecom operators. But traditional interface for data service delivery platform cannot completely meet these requirements. Web services, as a promising distributed computing technology, is regarded as the best candidate to design these interfaces. However, whether Web services technology can satisfy the telecom major requirements, especially security request, is still a question for telecom operators. This paper discusses the multiple aspects of Web service security, provides Web service security performance experiment results based on data size and different security policies, and gives suggestions on how to apply Web service security technology to data service delivery platform interface design

Advances in wireless Internet and mobile computing require a new service model for location aware services to support push services and personalization services based on mobility patterns of mobile users. This paper presents a prototype of CAMEL (Continuous, Active Monitor Engine for Location-based Services), a high performance location stream engine to manage large numbers of moving objects in support of intelligent location aware services. We introduce the location model employed by CAMEL, the component architecture and key components of CAMEL, including a Database component, Location Listener, Query Engine, Location Filter, Trigger Handler and Data Server. Also we present an enhanced processing algorithm using Max-Velocity constraint for improving performance of Binary Moving Object Trigger.

Investigation shows that a huge number of spatial data exists in current business databases. Traditional data warehousing and OLAP, however, could not exploit the spatial information to get deep insight into the business data in decision making. In this paper, we propose a novel approach to enabling spatial OLAP by aggregating on the spatial hierarchy. A spatial index mechanism is employed to derive the spatial hierarchy for pre-aggregation and materialization, which in turn are leveraged by the OLAP system to efficiently answer spatial OLAP queries. Our prototype system shows that the proposed approach could be integrated easily into the existing data warehouse and OLAP systems to support spatial analysis. Preliminary experiment results are also presented.

Advances in wireless Internet and mobile computing require a new service model for location aware services supporting push services and personalization services based on mobility patterns of mobile users. This paper presents a prototype of CAMEL (Continuous, Active Monitor Engine for Location-based Services), a high performance location management engine to support such intelligent location aware services. We introduce the location model employed by CAMEL, the component architecture and key components of CAMLE, including a Database component, Location Listener, Query Engine, Location Filter, Trigger Handler and Data Server. The component-based architecture facilitates easy deployment of CAMEL for meeting different service model, such as push service, moving object monitor and moving object data warehousing. Two spatial trigger processing mechanisms for Single Moving Object Trigger and Binary Moving Object Trigger, which play an important role in push-based location aware service, are presented in detail and their performance is analyzed.