In this work, a weighted H lder function that approximates a Jacobi polynomial which solves the second order singular Sturm-Liouville equation is discussed. This is generally equivalent to the Jacobean translations and the moduli of smoothness. This paper aims to focus on improving methods of approximation and finding the upper and lower estimates for the degree of approximation in weighted H lder spaces by modifying the modulus of continuity and smoothness. Moreover, some properties for the moduli of smoothness with direct and inverse results are considered.

The temperature control process of electric heating furnace (EHF) systems is a quite difficult and changeable task owing to non-linearity, time delay, time-varying parameters, and the harsh environment of the furnace. In this paper, a robust temperature control scheme for an EHF system is developed using an adaptive active disturbance rejection control (AADRC) technique with a continuous sliding-mode based component. First, a comprehensive dynamic model is established by using convection laws, in which the EHF systems can be characterized as an uncertain second order system. Second, an adaptive extended state observer (AESO) is utilized to estimate the states of the EHF system and total disturbances, in which the observer gains are updated

A novel demountable shear connector for precast steel-concrete composite bridges is presented. The connector uses high-strength steel bolts, which are fastened to the top flange of the steel beam with the aid of a special locking nut configuration that prevents bolts from slipping within their holes. Moreover, the connector promotes accelerated construction and overcomes the typical construction tolerance issues of precast structures. Most importantly, the connector allows bridge disassembly. Therefore, it can address different bridge deterioration scenarios with minimum disturbance to traffic flow including the following: (1) precast deck panels can be rapidly uplifted and replaced; (2) connectors can be rapidly removed and replaced; and (