The general Randic index Rα(G) of a (chemical) graph G, is defined as the sum of the weights (d(u)d(v))α of all edges uv of G, where d(u) denotes the degree of a vertex u in G and α an arbitrary real number, which is called the Randic index or connectivity index (or branching index) for α = −1/2 proposed by Milan Randic in 1975. The paper outlines the results known for the (general) Randic index of (chemical) graphs. Some very new results are released. We classify the results into the following categories: extremal values and extremal graphs of Randic index, general Randic index, zeroth-order general Randic index, higher-order Randic index. A few conjectures and open problems are mentioned.

A Survey on the Randic Index

Intelligent spindles are core components of the next-generation of intelligent/smart machine tools in the Industry 4.0 Era. The purpose of this paper is to clarify the concept of intelligent spindles and provide an in-depth review of the state-of-the-art of related technologies. A new integrated concept for intelligent spindles is proposed, followed by descriptions of required characteristics, key enabling technologies and expected intelligent functions. Relevant research that may be beneficial to the development of intelligent spindles is reviewed from six thrust areas, which include monitoring and control of tool condition, chatter, spindle collision, temperature/thermal error, spindle balance, and spindle health. Finally, current limitations and challenges are discussed, and future trends of intelligent spindles are prospected from various perspectives.

The concept and progress of intelligent spindles: A review

Spacecraft trajectory optimization: A review of models, objectives, approaches and solutions

In this paper, a novel fractional-order fuzzy sliding mode control strategy is developed to realize the deployment of the tethered satellite system (TSS) with input saturation. The considered TSS is modeled as an underactuated system. By decoupling the underactuated system into two subsystems, a fractional-order and a constrained integer-order sliding surfaces are designed for the actuated and unactuated subsystems, respectively. Then, a new hybrid sliding manifold is obtained by coupling the two subsliding surfaces. Adaptive fuzzy algorithm is used to regulate the coupling coefficient in the newly proposed hybrid sliding manifold in order to procure satisfactory performance. Meanwhile, the saturation nonlinearity of control input is also considered. The asymptotic stability of the closed-loop system is demonstrated theoretically. With the existence of fractional order, the presented controller can perform faster and more smooth tether deployment when compared with conventional ones. Finally, the effectiveness and superiority of the proposed control approach are validated by illustrative simulations.

Fractional-Order Fuzzy Sliding Mode Control for the Deployment of Tethered Satellite System Under Input Saturation

A series of curved microstrip antennae with defected ground structure for multiband are proposed, which are more smaller, conveniently conformal, wider radiation beam and suitable for WLAN terminal for difierent environment. The relation between the main geometry parameters and the antennas' characters are studied with the cavity model method and EM simulation, and the optimum size antenna is achieved later. If keeping the other parameters but increasing the curving angle fi, the return loss is almost good at f = 2:45GHz, but poor at f = 5:25GHz and 5.8GHz. After slight tuning the key parameters, these curved antennae all can work at f = 2:45GHz, 5.25GHz and 5.8GHz, and their patterns in the plane that is vertical to the curve axes become more wider or even omni- directional with the curving angle fi increasing, which are verifled by experiment, their measured gain are 2dB{6.3dB.

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The development of curved microstrip antenna with defected ground structure

Fractional order sliding mode control for tethered satellite deployment with disturbances

The fast and accurate modeling for machine errors is an important step for the implementation of error compensation. In this article, a new approach for real-time compensation of geometric and ther...

Geometric and thermal error compensation for CNC milling machines based on Newton interpolation method

Bicyclic graphs with the first three smallest and largest values of the first general Zagreb index

A new ultra wideband antenna fed by coplanar waveguide (CPW) is presented in this paper. A fractal structure is constructed to obtain ultra wideband (UWB) performance. The parameters and characteristics of the antenna and the simulation results show that the 6:1 or more bandwidth is achieved with the second order iterative antenna structure.

Wei Wang

Papers

Fractional order sliding mode control for tethered satellite deployment with disturbances

Geometric and thermal error compensation for CNC milling machines based on Newton interpolation method

Bicyclic graphs with the first three smallest and largest values of the first general Zagreb index

Design of a CPW-fed Ultra Wideband Crown Circular Fractal Antenna

Multiple solar sail formation flying around heliocentric displaced orbit via consensus