On the computation of scaling coefficients of Daubechies' wavelets

In the present paper, Daubechies' wavelets and the computation of their scaling coefficients are briefly reviewed. Then a new method of computation is proposed. This method is based on the work [7] concerning a new orthonormality condition and relations among scaling moments, respectively. For filter lengths up to 16, the arising system can be explicitly solved with algebraic methods like Gröbner bases. Its simple structure allows one to find quickly all possible solutions.     

The representation dimension of domestic weakly symmetric algebras

Auslander’s representation dimension measures how far a finite dimensional algebra is away from being of finite representation type. In [1], M. Auslander proved that a finite dimensional algebra A is of finite representation type if and only if the representation dimension of A is at most 2. Recently, R. Rouquier proved that there are finite dimensional algebras of an arbitrarily large finite representation dimension. One of the exciting open problems is to show that all finite dimensional algebras of tame representation type have representation dimension at most 3. We prove that this is true for all domestic weakly symmetric algebras over algebraically closed fields having simply connected Galois coverings.     

一个来自振动理论反问题的矩阵方程

§ 1　ＩｎｔｒｏｄｕｃｔｉｏｎＬｅｔＲｎ×ｍｄｅｎｏｔｅｔｈｅｒｅａｌｎ×ｍｍａｔｒｉｘｓｐａｃｅ ,Ｒｎ×ｍｒ ｉｔｓｓｕｂｓｅｔｗｈｏｓｅｅｌｅｍｅｎｔｓｈａｖｅｒａｎｋｒ ,ＯＲｎ×ｎｔｈｅｓｅｔｏｆａｌｌｎ×ｎｏｒｔｈｏｇｏｎａｌｍａｔｒｉｃｅｓ,ＳＲｎ×ｎ(ＳＲｎ×ｎ≥ ,ＳＲｎ×ｎ>)ｔｈｅｓｅｔｏｆａｌｌｎ×ｎｒｅａｌｓｙｍｍｅｔｒｉｃ (ｓｙｍｍｅｔｒｉｃｐｏｓｉｔｉｖｅｓｅｍｉｄｅｆｉｎｉｔｅ ,ｐｏｓｉｔｉｖｅｄｅｆｉｎｉｔｅ)ｍａｔｒｉｃｅｓ.ＴｈｅｎｏｔａｔｉｏｎＡ>0 (≥ 0 ,<0 ,≤ 0 )ｍ…     

逼近严格伪压缩映象不动点的Ishikawa迭代程序

Let(X,‖·‖ ) be a Banach space.Let K be a nonempty closed,convex subset of Xand T∶K→K.Assume that T is Lipschitzian,i.e.there exists L>0 such that‖ T(x) -T(y)‖≤ L‖ x -y‖for all x,y∈K.Withoutloss of generality,assume that L≥ 1 .Assume also that T is strictly pseudocontractive.According to[1 ] this may be statedas:there exists k∈ (0 ,1 ) such that‖ x -y‖≤‖ x -y + r[(I -T -k I) x -(I -T -k I) y]‖for all r>0 and all x,y∈ K.Throughout,let N denote the set of positive in…     

LD泵浦固体激光器基模振荡光的场分布噪音

通过调整泵浦光直径,使得LD端面泵浦固体激光器的振荡光工作于基模.在排除高阶横模的条件下,测量了由于热透镜的不稳定引起的光场场分布的噪音.实验发现,基模振荡光的高斯半径、光束指向角都在波动,而且光斑存在畸变波动.对一个未采取抑制措施的2W连续LD端面泵浦Nd:YAG固体激光器进行了测量.结果表明,在总功率不变的情况下,激光束峰值点附近的光强波动达到6.3%;激光的高斯半径波动达到5.8%;激光的指向角波动达到0.3mrad.     

Rhythmic pattern formations in gels and Matalon—Packter law: A fresh perspective

The periodic precipitation pattern formation in gelatinous media is interpreted as a moving boundary problem. The time law, spacing law and width law are revisited on the basis of the new scenario. The explicit dependence of the geometric structure on the initial concentrations of the reactants is derived. Matalon—Packter law, which relates the spacing coefficient with the initial concentrations is reformulated removing many ambiguities and impractical parameters. Experimental results are discussed to establish the significance of moving boundary concept in the diffusion controlled pattern forming systems     

Hysteresis and Eddy-current Relaxation in SiFe Materials

The rate-dependent effects in metallic ferromagnetic materials with magnetization processes attributed to domain-walls motion were studied. The experimental method for eddy-current relaxation time determination was proposed. Some discrepancies between the data and theoretical predictions were observed and discussed. The origin of these discrepancies is accounted for by the decrease of viscous-type relaxation process as the rate of change of averaged magnetization is approaching zero.