CERTAIN COMMUTATIVITY CONDITIONS FOR RINGS WITH UNITY

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Generalized q-Schur algebras and quantum Frobenius

The quantum Frobenius map and it splitting are shown to descend to maps between generalized q-Schur algebras at a root of unity. We also define analogs of q-Schur algebras for any affine algebra, and prove the corresponding results for them.     

Modeling quasi-static crack growth with the extended finite element method Part II: Numerical applications

In Part I [Int. J. Solids Struct., 2003], we described the implementation of the extended finite element method (X-FEM) within Dynaflow™, a standard finite element package. In our implementation, we focused on two-dimensional crack modeling in linear elasticity. For crack modeling in the X-FEM, a discontinuous function and the near-tip asymptotic functions are added to the finite element approximation using the framework of partition of unity. This permits the crack to be represented without explicitly meshing the crack surfaces and crack propagation simulations can be carried out without the need for any remeshing. In this paper, we present numerical solutions for the stress intensity factor for crack problems, and also conduct crack growth simulations with the X-FEM. Numerical examples are presented with a two-fold objective: first to show the efficacy of the X-FEM implementation in Dynaflow™; and second to demonstrate the accuracy and versatility of the method to solve challenging problems in computational failure mechanics.     

基于单位分解法的无网格数值流形方法

在数值流形方法和单位分解法的基础上，提出了无网格数值流形方法. 无网格数值流形 方法在分析时采用了双重覆盖系统，即数学覆盖和物理覆盖. 数学覆盖提供的节点形成求解 域的有限覆盖和单位分解函数；而物理覆盖描述问题的几何区域及其域内不连续性. 与原有 的数值流形方法相比，无网格数值流形方法的数学覆盖形状更加灵活，可以用一系列节点的 影响域来建立数学覆盖和单位分解函数，具有无网格方法的特性，从而摆脱了传统的数值流 形方法中网格所带来的困难. 与无网格方法相比，由于采用了有限覆盖技术，试函数的构造 不受域内不连续的影响，克服了原有的无网格方法在处理不连续问题时所遇到的困难. 详细推导了无网格数值流形方法的试函数和求解方程，最后给出了算例，验证了该方法的正 确性.     

Representation and extension of states on MV-algebras

MV-algebras stand for the many-valued Łukasiewicz logic the same as Boolean algebras for the classical logic. States on MV-algebras were first mentioned [20] in probability theory and later also introduced in effort to capture a notion of `an average truth-value of proposition' [15] in Łukasiewicz many-valued logic. In the presented paper, an integral representation theorem for finitely-additive states on semisimple MV-algebra will be proven. Further, we shall prove extension theorems concerning states defined on sub-MV-algebras and normal partitions of unity generalizing in this way the well-known Horn-Tarski theorem for Boolean algebras. The author gratefully acknowledges the support of grant 201/02/1540 of the Grant Agency of the Czech Republic and the partial support by the project 1M6798555601 of the Ministry of Education, Youth and Sports of the Czech Republic.     

单位根上重Hermite插值多项式的逼近阶

设ｆ（ｚ）在｜ｚ｜≤１解析，在｜ｚ｜≤１连续．本文得到了基于单位根的扩充Ｈｅｒｍｉｔｅ插值多项式在｜ｚ｜≤１上一致收敛于ｆ（ｚ）的逼近阶和在｜ｚ｜＝１上平均收敛于ｆ（ｚ）的逼近阶，且一般说来，阶还是精确的．进而说明，重数不同的插值多项式的逼近阶不同于重数相同的插值多项式的逼近阶．     

The partition‐of‐unity method for linear diffusion and convection problems: accuracy,stabilization and multiscale interpretation

We investigate the effectiveness of the partition‐of‐unity method (PUM) for convection–diffusion problems. We show that for the linear diffusion equation, an exponential enrichment function based on an approximation of the analytic solution leads to improved accuracy compared to the standard finite‐element method. It is illustrated that this approach can be more efficient than using polynomial enrichment to increase the order of the scheme. We argue that the PUM enrichment, can be interpreted as a subgrid‐scale model in a multiscale framework, and that the choice of enrichment function has consequences for the stabilization properties of the method. The exponential enrichment is shown to function as a near optimal subgrid‐scale model for linear convection. Copyright © 2003 John Wiley & Sons, Ltd.     

NLCC controller for SEPIC-based micro-wind energy conversion system

The growth of the power industry is gaining greater momentum as the usage of the non-conventional energy sources that include fuel, solar, and wind energies, increases. Wind energy conversion systems (WECSs) are gaining more popularity and are expected to be able to control the power at the output. This paper describes the current control (CC), non-linear carrier charge control (NLCCC), and fuzzy logic control (FLC) applied to the single-ended primary inductor converter (SEPIC)-based WECS. The current controller has an inherent overcurrent protection with better line noise rejection. The pulses for the switch of the SEPIC are obtained by comparing the current flowing through it with the virtual current reference. FLC is also investigated for the micro-wind energy conversion system (μWECS), since it improves the damping characteristics of WECS over a wide range of operating points. This cannot attain the unity power factor rectification. In this paper, NLCCC is proposed for high-power factor rectifier-based SEPIC in continuous conduction mode (CCM) for μWECS. The proposed converter provides an output voltage with low input current ripple due to the presence of the inductor at the input side. By comparing the signal proportional to the integral of switch current with a periodic non-linear carrier wave, the duty ratio of the converter switch is determined for the NLCC controller. By selecting the shape of the periodic non-linear carrier wave the input-line current can be made to follow the input-line voltage. This work employs a parabolic carrier waveform generator. The output voltage is regulated for changes in the wind speed. The results obtained prove the effectiveness of the NLCC controller in improving the power factor.     

大学物理教学中不应忽视电磁学与狭义相对论的内在联系

文章指出大学物理教学中关于电磁学和狭义相对论的缺憾,并提出了可行的教学方案.由此可以使学生深化对电磁场的认识,同时深刻理解狭义相对论时空观的内在意义.     

Eventually constant solutions of a rational difference equation

We describe all the solutions of a rational difference equation from Putnam’s mathematical competition, which are eventually equal to its positive equilibrium . As a consequence we give a new, elegant and short proof of the fact that the equation has a positive solution which is not eventually equal to one. Moreover, we show that almost all solutions of the equation are not eventually equal to one.