On generalized covering and avoidance properties of finite groups and saturated fusion systems

A subgroup $A$ of a finite group $G$ is said to be a $CAP$-subgroup of $G$, if for any chief factor $H/K$ of $G$, either $A H= AK$ or $A\cap H = A \cap K$. Let $p$ be a prime, $S$ be a $p$-group and $\mathcal{F}$ be a saturated fusion system over $S$. Then $\mathcal{F}$ is said to be supersolvable, if there exists a series of $S$, namely $1 = S_0 \leq S_1 \leq \cdots \leq S_n = S$, such that $S_{i+1}/S_i$ is cyclic, and $S_i$ is strongly $\mathcal{F}$-closed for any $i=0,1,\cdots,n$. In this paper, we first introduce the concept of strong $p$-$CAP$-subgroups, and investigate the properties of finite groups under the assumption that some subgroups of $G$ are partial $CAP$-subgroups or strong $(p)$-$CAP$-subgroups, and obtain some criteria for a group $G$ to be $p$-supersoluble. Then, we investigate the characterizations for supersolvability of $\mathcal{F}_S (G)$ under the assumption that some subgroups of $G$ are partial $CAP$-subgroups or strong $(p)$-$CAP$-subgroups of $G$, and obtain some criteria for a fusion system $\mathcal{F}_S (G)$ to be $p$-supersolvable

Free vibration analysis of thin-walled rectangular box beams based on generalized coordinates

An eight degree-of-freedom dynamic theory is presented for the free vibration analysis of thin-walled rectangular box beams. With the newly proposed parameters to prescribe the cross-section deformations, governing differential equations of the thin-walled rectangular beam are deduced using the principle of minimum potential energy. For the finite element implementation, two different displacement fields are constructed with generalized coordinates to formulate the stiffness matrix and the mass matrix, respectively. Dynamic equations of motion are deduced with Hamilton’s principle, and approximated with C0 continuous interpolation functions. The validity of this study is confirmed both by published literature and by extensive finite element solutions from MSC/NASTRAN

On zeros of characters of finite groups

summary:For a finite group $G$ and a non-linear irreducible complex character $\chi$ of $G$ write $\upsilon (\chi )=\{g\in G\mid \chi (g)=0\}$. In this paper, we study the finite non-solvable groups $G$ such that $\upsilon (\chi )$ consists of at most two conjugacy classes for all but one of the non-linear irreducible characters $\chi$ of $G$. In particular, we characterize a class of finite solvable groups which are closely related to the above-mentioned question and are called solvable $\varphi$-groups. As a corollary, we answer Research Problem $2$ in [Y. Berkovich and L. Kazarin: Finite groups in which the zeros of every non-linear irreducible character are conjugate modulo its kernel. Houston J. Math.\ 24 (1998), 619--630.] posed by Y. Berkovich and L. Kazarin

Experimental investigation of feedforward inverse control with disturbance observer for acceleration tracking of electro-hydraulic shake table

Electro-hydraulic shake tables (EHSTs) are indispensable equipments in laboratory for evaluating structural performance subject to vibration environment. A novel feedforward inverse control with disturbance observer strategy is proposed in this paper in order to improve the acceleration tracking performance of the EHST system. The EHST system is firstly controlled by the three variable controller (TVC) to obtain a coarse time waveform replication accuracy, and then the parametric transfer function of the TVC controlled EHST system is identified with the H1 estimation method and complex curving fitting technology. Next, the zero magnitude error tracking control technology is employed to deal with the estimated non-minimum phase transfer function so as to design a stable and casual inverse model, and the proposed controller comprised of feedforward inverse controller and disturbance observer is further established based on the designed inverse model. Therefore, the proposed algorithm combines the virtues of feedforward inverse control and disturbance observer. The proposed algorithm is firstly programmed by MATLAB/Simulink software and then is compiled to an Advantech computer with real-time operating system for implementation. Finally, experiments are carried out on a unidirectional EHST system and the results demonstrate that a better acceleration tracking performance is achieved with the proposed controller than with the other conventional controllers

The influence of SS-quasinormality of some subgroups on the structure of finite groups

AbstractThe following concept is introduced: a subgroup H of the group G is said to be SS-quasinormal (Supplement-Sylow-quasinormal) in G if H possesses a supplement B such that H permutes with every Sylow subgroup of B. Groups with certain SS-quasinormal subgroups of prime power order are studied. For example, fix a prime divisor p of |G| and a Sylow p-subgroup P of G, let d be the smallest generator number of P and Md(P) denote a family of maximal subgroups P1,…,Pd of P satisfying ⋂i=1d(Pi)=Φ(P), the Frattini subgroup of P. Assume that the group G is p-solvable and every member of some fixed Md(P) is SS-quasinormal in G, then G is p-supersolvable

Finite groups with few vanishing elements

Let G be a finite group, and Irr(G) the set of irreducible complex characters of G. We say that an element g G is a vanishing element of G if there exists χ in Irr(G) such that χ(g)= 0. Let Van(G) denote the set of vanishing elements of G, that is, Van(G)= {g G|χ(g)=0 for some χ Irr (G)}. In this paper, we investigate the finite groups G with the following property: Van(G) contains at most four conjugacy classes of G

Experimental investigation of feedforward inverse control with disturbance observer for acceleration tracking of electro-hydraulic shake table

Electro-hydraulic shake tables (EHSTs) are indispensable equipments in laboratory for evaluating structural performance subject to vibration environment. A novel feedforward inverse control with disturbance observer strategy is proposed in this paper in order to improve the acceleration tracking performance of the EHST system. The EHST system is firstly controlled by the three variable controller (TVC) to obtain a coarse time waveform replication accuracy, and then the parametric transfer function of the TVC controlled EHST system is identified with the H1 estimation method and complex curving fitting technology. Next, the zero magnitude error tracking control technology is employed to deal with the estimated non-minimum phase transfer function so as to design a stable and casual inverse model, and the proposed controller comprised of feedforward inverse controller and disturbance observer is further established based on the designed inverse model. Therefore, the proposed algorithm combines the virtues of feedforward inverse control and disturbance observer. The proposed algorithm is firstly programmed by MATLAB/Simulink software and then is compiled to an Advantech computer with real-time operating system for implementation. Finally, experiments are carried out on a unidirectional EHST system and the results demonstrate that a better acceleration tracking performance is achieved with the proposed controller than with the other conventional controllers

The Transformation from Translucent into Transparent Rare Earth Ions Doped Oxyfluoride Glass-Ceramics with Enhanced Luminescence

Article reporting a scenario where a translucent Er3+−Yb3+ doped oxyfluoride precursor glass-ceramic (P-GC) becomes transparent with increasing crystal size and crystallinity