Experimental and statistical assessments of the mechanical strength reliability of gamma alumina catalyst supports

The mechanical strength of solid catalysts is considered an important factor in terms of ensuring the reliable performance of industrial reactors. In this work, a pelletizing method was used to form gamma alumina support for catalysts. Response surface methodology (RSM) was employed to analyze and model the effects of various manufacturing parameters on the crushing strength of the supports. These parameters were binder concentration, compaction pressure, calcination temperature, and drying mode. The suggested model was verified by applying an analysis of variance to assess its validity with regard to crushing strength. The mechanical reliability of various supports was also determined by calculating their Weibull modulus values through linear regression of the Weibull equation. The material with the highest mechanical strength reliability will have both a high mean crushing strength and a high Weibull modulus, and the best values obtained for a support in this work were 70.7 MPa and 6.63, respectively. The conditions used to form this sample were: 20 mass% binder concentration, 861 MPa compaction pressure, 466 °C calcination temperature, and gentle drying.     

GBS operators of bivariate Bernstein‐Durrmeyer–type on a triangle

The purpose of the present paper is to define the GBS (Generalized Boolean Sum) operators associated with the two‐dimensional Bernstein‐Durrmeyer operators introduced by Zhou 1992 and study its approximation properties. Furthermore, we show the convergence and comparison of convergence with the GBS of the Bernstein‐Kantorovich operators proposed by Deshwal et al 2017 by numerical examples and illustrations.     

Kobayashi’s and Teichmuller’s Metrics and Bers Complex Manifold Structure on Circle Diffeomorphisms

Given a modulus of continuity ω,we consider the Teichmuller space TC1+ω as the space of all orientation-preserving circle diffeomorphisms whose derivatives are ω-continuous functions modulo the space of Mobius transformations preserving the unit disk.We study several distortion properties for diffeomorphisms and quasisymmetric homeomorphisms.Using these distortion properties,we give the Bers complex manifold structure on the Teichm(u| ")ller space TC^1+H as the union of over all0 <α≤1,which turns out to be the largest space in the Teichmuller space of C1 orientation-preserving circle diffeomorphisms on which we can assign such a structure.Furthermore,we prove that with the Bers complex manifold structure on TC^1+H ,Kobayashi’s metric and Teichmuller’s metric coincide.     

λ-Kantorovich算子的逼近性质

首先在无穷空间上构造了一类新的λ-Szász-Kantorovich算子,通过分析计算得到了该类算子矩的估计及Korovkin型逼近性质;其次,利用连续模和K-泛函的等价关系给出了收敛速度的刻画;最后,借助于Holder不等式建立了Lipschitz连续函数的收敛定理.     

Value function,relaxation, and transversality conditions in infinite horizon optimal control

We investigate the value function $V:{\mathbb{R}}_{+}\times {\mathbb{R}}^n\to {\mathbb{R}}_{+}\cup \{+\infty \}$ of the infinite horizon problem in optimal control for a general—not necessarily discounted—running cost and provide sufficient conditions for its lower semicontinuity, continuity, and local Lipschitz regularity. Then we use the continuity of $V(t,?)$ to prove a relaxation theorem and to write the first order necessary optimality conditions in the form of a, possibly abnormal, maximum principle whose transversality condition uses limiting/horizontal supergradients of $V(0,?)$ at the initial point. When $V(0,?)$ is merely lower semicontinuous, then for a dense subset of initial conditions we obtain a normal maximum principle augmented by sensitivity relations involving the Fréchet subdifferentials of $V(t,?)$. Finally, when V is locally Lipschitz, we prove a normal maximum principle together with sensitivity relations involving generalized gradients of V for arbitrary initial conditions. Such relations simplify drastically the investigation of the limiting behavior at infinity of the adjoint state.     

A note on Baskakov-Kantorovich type operators preserving e−x

In this paper, we give a generalization of the Baskakov-Kantorovich type operators that reproduce functions e₀ and e^−x. We discuss uniform convergence of this generalization by means of the modulus of continuity and establish quantitive asymptotic formula.     

Efficient Use of Carbon Fibers as Heating Elements for Curing of Epoxy Matrix Composites

The aim of this study is to achieve a fully cured thermoset matrix that is heated by a direct electric current passing through the reinforcement fibers i.e., the Joule heating effect. Two types of fibers were used as heating elements for curing the epoxy resins. Kanthal resistance fibers were used as reference heating elements and subsequently, they were replaced by a Torayca Carbon Tow of the same radius. The specimens were cured by the heat produced by a direct electric current passing through the fibers and achieving temperatures of 50 °C and 70 °C. Specimens cured in a conventional oven were also manufactured, to compare the resistance heating method to the conventional one. Next, all specimens were mechanically characterized in a quasi-static three-point bending mode of loading and experimental results were compared to derive useful conclusions concerning the applicability of the technique to polymer/composite materials mass production. Finally, a preliminary economical study concerning power consumption needed for the application of both the traditional oven curing and the carbon fibers heating elements use for the manufacturing of the same amounts of materials is presented, showing a maximum financial benefit that can be achieved, on the order of 68%.     

Vibration analysis of foam plates based on cell volume distribution

In this paper, vibration analysis of irregular-closed-cell foam plates is per-formed. A cell volume distribution coefficient is introduced to modify the original Gibson-Ashby equations of effective Young’s modulus of foam materials. A Burr distribution is imported to describe the cell volume distribution situation. Three Burr distribution pa-rameters are obtained and related to the cell volume range and the diversity. Based on the plate theory and the effective modulus theory, the natural frequency of foam plates is calculated with the change of the cell volume distribution parameters. The relationship between the frequencies and the cell volumes are derived. The scale factor of the average cell size is introduced and proved to be an important factor to the performance of the foam plate. The result is shown by the existing theory of size effects. It is determined that the cell volume distribution has an impact on the natural frequency of the plate structure based on the cell volume range, the diversity, and the average size, and the impact can lead to optimization of the synthesis procedure.     

Ti、TiN、TiO2改性层的纳米力学性能测试与分析

采用等离子表面合金化技术,分别在316L不锈钢表面制备出渗Ti改性层、渗TiN改性层和TiO2改性层薄膜.使用连续刚度法,从截面方向和表面方向对改性层进行纳米压痕实验,研究改性层的纳米力学性能.实验测得材料在压痕过程中的载荷—位移曲线以及硬度和模量随压入深度的连续变化值.结果表明,改性层纳米力学特性表现为各向异性;TiN改性层的力学性能表现良好.TiO2改性层由渗Ti改性层经氧化制成,二者的弹性模量和硬度在截面方向上变化规律相似,在表面方向上数值相近.