Composite Fractional Trapezoidal Rule with Romberg Integration

The aim of this research is to demonstrate a novel scheme for approximating the Riemann-Liouville fractional integral operator.This would be achieved by first establishing a fractional-order version of the 2-point Trapezoidal rule and then by proposing another fractional-order version of the(n+1)-composite Trapezoidal rule.In particular,the so-called divided-difference formula is typically employed to derive the 2-point Trapezoidal rule,which has accordingly been used to derive a more accurate fractional-order formula called the(n+1)-composite Trapezoidal rule.Additionally,in order to increase the accuracy of the proposed approximations by reducing the true errors,we incorporate the so-called Romberg integration,which is an extrapolation formula of the Trapezoidal rule for integration,into our proposed approaches.Several numerical examples are provided and compared with a modern definition of the Riemann-Liouville fractional integral operator to illustrate the efficacy of our scheme.

Cluster-based composition rule for Laves phase-related BCC solid solution hydrogen storage alloys

A new cluster line approach for the composition rule of Laves phase-related BCC solid solution hydrogen-storage alloys was presented. The cluster line in a ternary phase diagram refers to a straight composition line linking a specific binary cluster to the third element. In the Laves phase-related BCC solid solution alloy system such as Ti-Cr-V, Ti-Cr tends to form binary Cr2Ti Laves phase while Ti-V and Cr-V to form solid solutions. This Laves phase is characterized by a close-packing icosahedral cluster Cr7Ti6. A cluster line Cr7Ti6-V is then constructed in this system. Alloy rods with a diameter of 3 mm of compositions along this line were prepared by copper-mould suction method. The alloy structure is found to vary with the V contents. Furthermore, the P-C-T measurements indicate that the cluster-line (Cr7Ti6)1-xVx alloys have large hydrogen storage capacities.

INTERSECTION POINT RULE OF THE RETENTION VALUE AND MOBILE PHASE COMPOSITION OF THE HOMOLOGUES IN REVERSED-PHASE HIGH-PERFORMANCE LIQUID CHROMATOGRAPHY

Based on the intersection point rule of the retention value and normal boiling point of homologues in reversed-phase high-performance liquid chromatography(RPLC), the intersection point rule of the retention value of homologues and mobile phase composition has been derived, and was testified by a lot of experimental data from the literature. With this newly proposed equation, we can use the retention value of the compound in one mobile phase composition to predict its retention value in any other mobile phase composition. For fourteen groups of homologues in five mobile phase compositions on five Kinds of columns, the overall average absolute error of 721 data sets is 2.8%.

The Rectangle Rule for Computing Cauchy Principal Value Integral on Circle

The classical composite rectangle (constant) rule for the computation of Cauchy principle value integral with the singular kernel is discussed. We show that the superconvergence rate of the composite midpoint rule occurs at certain local coodinate of each subinterval and obtain the corresponding superconvergence error estimate. Then collation methods are presented to solve certain kind of Hilbert singular integral equation. At last, some numerical examples are provided to validate the theoretical analysis.

Flexible Job Shop Composite Dispatching Rule Mining Approach Based on an Improved Genetic Programming Algorithm

To obtain a suitable scheduling scheme in an effective time range,the minimum completion time is taken as the objective of Flexible Job Shop scheduling Problems(FJSP)with different scales,and Composite Dispatching Rules(CDRs)are applied to generate feasible solutions.Firstly,the binary tree coding method is adopted,and the constructed function set is normalized.Secondly,a CDR mining approach based on an Improved Genetic Programming Algorithm(IGPA)is designed.Two population initialization methods are introduced to enrich the initial population,and a superior and inferior population separation strategy is designed to improve the global search ability of the algorithm.At the same time,two individual mutation methods are introduced to improve the algorithm’s local search ability,to achieve the balance between global search and local search.In addition,the effectiveness of the IGPA and the superiority of CDRs are verified through comparative analysis.Finally,Deep Reinforcement Learning(DRL)is employed to solve the FJSP by incorporating the CDRs as the action set,the selection times are counted to further verify the superiority of CDRs.

Differently implicational α-universal triple I restriction method of (1, 2, 2) type

From the viewpoints of both fuzzy system and fuzzy reasoning, a new fuzzy reasoning method which contains the α- triple I restriction method as its particular case is proposed. The previous α-triple I restriction principles are improved, and then the optimal restriction solutions of this new method are achieved, especially for seven familiar implications. As its special case, the corresponding results of α-triple I restriction method are obtained and improved. Lastly, it is found by examples that this new method is more reasonable than the α-triple I restriction method.

Mathematical Foundation of Basic Algorithms of Fuzzy Reasoning

Algorithm of fuzzy reasoning has been successful applied in fuzzy control,but its theoretical foundation of algorithms has not been thoroughly investigated. In this paper,structure of basic algorithms of fuzzy reasoning was studied, its rationality was discussed from the viewpoint of logic and mathematics, and three theorems were proved. These theorems shows that there always exists a mathe-~matical relation (that is, a bounded real function) between the premises and the conclusion for fuzzy reasoning, and in fact various algorithms of fuzzy reasoning are specific forms of this function. Thus these results show that algorithms of fuzzy reasoning are theoretically reliable.

Soil Parameter Identification for Wheel-terrain Interaction Dynamics and Traversability Prediction

This paper presents a novel technique for identifying soil parameters for a wheeled vehicle traversing unknown terrain. The identified soil parameters are required for predicting vehicle drawbar pull and wheel drive torque, which in turn can be used for traversability prediction, traction control, and performance optimization of a wheeled vehicle on unknown terrain. The proposed technique is based on the Newton Raphson method. An approximated form of a wheel-soil interaction model based on Composite Simpson＇s Rule is employed for this purpose. The key soil parameters to be identified are internal friction angle, shear deformation modulus, and lumped pressure-sinkage coefficient. The fourth parameter, cohesion, is not too relevant to vehicle drawbar pull, and is assigned an average value during the identification process. Identified parameters are compared with known values, and shown to be in agreement. The identification method is relatively fast and robust. The identified soil parameters can effectively be used to predict drawbar pull and wheel drive torque with good accuracy. The use of identified soil parameters to design a traversability criterion for wheeled vehicles traversing unknown terrain is presented.

Support optimal scheduling with weighted random forest for operation resources

Operation-related resources are lots of manpower and material with the characteristics of high cost and high income in hospitals,and scheduling optimization is a very important research issue in medical service.In this paper,to cope with the actualities of operation resources scheduling,such as poor planning,lack of standardized scheduling rules,chaotic use of the operating rooms,and many human interference factors,we propose a systematic approach to optimize scheduling problems based on multiple characteristics of operating resources.We frst design a framework that includes the composite dispatching rules(CDR),optimization ideology,and feedback mechanism,in which the CDR integrates fexible operating time,hold-up time of medical facilities,available time of medical staf,and multiple constraints.The optimization ideology is carried out through a learning model based on the weighted random forest(WRF)algorithm.The feedback mechanism enables the approach to realize closed-loop optimizations adaptively.Finally,the superiority of the systematic scheduling approach(SSA)is analyzed through numerical experiments on a simulation platform.Results of the simulation experiments show that the proposed scheduling method can improve performances signifcantly,especially in the waiting time of patients.