On classification of singular matrix difference equations of mixed order

This paper is concerned with singular matrix difference equations of mixed order. The existence and uniqueness of initial value problems for these equations are derived, and then the classification of them is obtained with a similar classical Weyl's method by selecting a suitable quasi-difference. An equivalent characterization of this classification is given in terms of the number of linearly independent square summable solutions of the equation. The influence of off-diagonal coefficients on the classification is illustrated by two examples. In particular, two limit point criteria are established in terms of coefficients of the equation.Comment: 27 page

Computing resource allocation in three-tier IoT fog networks: a joint optimization approach combining Stackelberg game and matching

Fog computing is a promising architecture to provide economical and low latency data services for future Internet of Things (IoT)-based network systems. Fog computing relies on a set of low-power fog nodes (FNs) that are located close to the end users to offload the services originally targeting at cloud data centers. In this paper, we consider a specific fog computing network consisting of a set of data service operators (DSOs) each of which controls a set of FNs to provide the required data service to a set of data service subscribers (DSSs). How to allocate the limited computing resources of FNs to all the DSSs to achieve an optimal and stable performance is an important problem. Therefore, we propose a joint optimization framework for all FNs, DSOs, and DSSs to achieve the optimal resource allocation schemes in a distributed fashion. In the framework, we first formulate a Stackelberg game to analyze the pricing problem for the DSOs as well as the resource allocation problem for the DSSs. Under the scenarios that the DSOs can know the expected amount of resource purchased by the DSSs, a many-to-many matching game is applied to investigate the pairing problem between DSOs and FNs. Finally, within the same DSO, we apply another layer of many-to-many matching between each of the paired FNs and serving DSSs to solve the FN-DSS pairing problem. Simulation results show that our proposed framework can significantly improve the performance of the IoT-based network systems

Enhanced Thermal Conductivity for Nanofluids Containing Silver Nanowires with Different Shapes

Nanofluids are the special agents to enhance the heat transfer property of the common fluids, and most of the thermal additives are the spherical nanoparticles. Up to now, the 1D thermal additives are not well exploited. In this paper, a kind of silver nanowires (AgNWs) with well-distributed shape and aspect ratio is synthesized. The results show that when we use the AgNWs prepared by the poly-vinyl-pyrrolidone (PVP) with a specific molecular weight of 40000, the thermal conductivity enhancement of nanofluids prepared by that kind of silver nanowires is as high as 13.42% when loading 0.46 vol.% AgNWs, and the value of the thermal conductivity is 0.2843 W/m·K, which is far more than the case when loading the same volume of spherical silver particles. Besides, we use H&C model to fit the experimental results and the experimental results are consistent with the model

Distributed resource allocation for data center networks: a hierarchical game approach

The increasing demand of data computing and storage for cloud-based services motivates the development and deployment of large-scale data centers. This paper studies the resource allocation problem for the data center networking system when multiple data center operators (DCOs) simultaneously serve multiple service subscribers (SSs). We formulate a hierarchical game to analyze this system where the DCOs and the SSs are regarded as the leaders and followers, respectively. In the proposed game, each SS selects its serving DCO with preferred price and purchases the optimal amount of resources for the SS's computing requirements. Based on the responses of the SSs' and the other DCOs', the DCOs decide their resource prices so as to receive the highest profit. When the coordination among DCOs is weak, we consider all DCOs are noncooperative with each other, and propose a sub-gradient algorithm for the DCOs to approach a sub-optimal solution of the game. When all DCOs are sufficiently coordinated, we formulate a coalition game among all DCOs and apply Kalai-Smorodinsky bargaining as a resource division approach to achieve high utilities. Both solutions constitute the Stackelberg Equilibrium. The simulation results verify the performance improvement provided by our proposed approaches

Thermal Conductivity of Composite Materials Containing Copper Nanowires

The development of thermal conductive polymer composite is necessary for the application in thermal management. In this paper, the experimental and theoretical investigations have been conducted to determine the effect of copper nanowires (CuNWs) and copper nanoparticles (CuNPs) on the thermal conductivity of dimethicone nanocomposites. The CuNWs and CuNPs were prepared by using a liquid phase reduction method, and they were characterized through scanning electron microscopy (SEM) and X-ray diffraction (XRD). The experimental data show that the thermal conductivity of composites increases with the increase of filler. With the addition of 10 vol.% CuNWs, the thermal conductivity of the composite is 0.41 W/m/K. The normalized thermal conductivity enhancement factor is 2.73, much higher than that of the analogue containing CuNPs (1.67). These experimental data are in agreement with Nan’s model prediction. Due to the high aspect ratio of 1D CuNWs, they can construct thermal networks more effectively than CuNPs in the composite, resulting in higher thermal conductivity