Primitive complete normal bases: Existence in certain 2-power extensions and lower bounds

The present paper is a continuation of the author’s work (Hachenberger (2001) [3]) on primitivity and complete normality. For certain 2-power extensions E over a Galois field F_q, we are going to establish the existence of a primitive element which simultaneously generates a normal basis over every intermediate field of E/F_q. The main result is as follows: Letq≡3mod4and letm(q)≥3be the largest integer such that2^m(q)dividesq²−1; ifE=F_q^2l, wherel≥m(q)+3, then there exists a primitive element inEthat is completely normal overF_q.Our method not only shows existence but also gives a fairly large lower bound on the number of primitive completely normal elements. In the above case this number is at least 4⋅(q−1)^2l−2. We are further going to discuss lower bounds on the number of such elements in r-power extensions, where r=2 and q≡1mod4, or where r is an odd prime, or where r is equal to the characteristic of the underlying field.     

On Blaschke products with derivatives in Bergman spaces with normal weights

We generalize a well-known sufficient condition for interpolating sequences for the Hilbert Bergman spaces to other Bergman spaces with normal weights (as defined by Shields and Williams) and obtain new results regarding the membership of the derivative of a Blaschke product or a general inner function in such spaces. We also apply duality techniques to obtain further results of this type and obtain new results about interpolating Blaschke products.     

Y_(0.928)Pr_(0.072)Ba_2Cu_3O_7超导单晶的钉扎机制研究

研究了Y0.928 Pr0.072 Ba2 Cu3 O7(后文称YPBCO)单晶在不同温度下的磁特性,计算了不同温度下的钉扎力密度Fp对磁场的依赖关系.结果表明,在不同温度下的钉扎力密度可近似标度在同一条曲线上;标度函数和峰效应引起的最大Jc所对应的磁场与不可逆场的比值都表明,YPBCO单晶在磁通玻璃态的钉扎机制主要是样品中Pr的微观电子分布不均匀性引起的正常相面钉扎.     

Mathematical and numerical approaches to a one-dimensional dynamic thermoviscoelastic contact problem

In this paper, we propose numerical schemes for solving a nonlinear system which consists of a coupled partial differential equations and two conditions, called normal compliance contact condition and Barber’s heat exchange condition. The convergence of numerical trajectories is shown by using a time discretization and passing the limit of the time step size. The uniqueness of the weak solution is proved as well. We derive the extensive form of an energy balance which will be a criterion to examine numerical stability. An example is provided to present and discuss numerical results.     

Predicting terrain parameters for physics-based vehicle mobility models from cone index data

To provide terrain data for the development of physics-based vehicle mobility models, such as the Next Generation NATO Reference Mobility Model, there is a desire to make use of the vast amount of cone index (CI) data available. The challenge is whether the terrain parameters for physics-based vehicle mobility models can be predicted from CI data. An improved model for cone-terrain interaction has been developed that takes into account both normal pressure and shear stress distributions on the cone-terrain interface. A methodology based on Derivative-Free Optimization Algorithms (DFOA) has been developed in combination with the improved model to make use of continuously measured CI vs. sinkage data for predicting the three Bekker pressure-sinkage parameters, k_c, k_ϕ and n, and two cone-terrain shear strength parameters, c_c and ϕ_c. The methodology has been demonstrated on two types of soil, LETE sand and Keweenaw Research Center (KRC) soils, where continuous CI vs. sinkage measurements and continuous plate pressure vs. sinkage measurements are available. The correlations between the predicted pressure-sinkage relationships based on the parameters derived from continuous CI vs. sinkage measurements using the DFOA-based methodology and that measured were generally encouraging.     

Normal and non-normal Cayley graphs for symmetric groups

A Cayley graph is said to be an NNN-graph if its automorphism group contains two isomorphic regular subgroups where one is normal and the other is non-normal. In this paper, we show that there exist NNN-graphs among the Cayley graphs for symmetric groups $S_n$ if and only if $n?5$.     

Nekhoroshev type stability results for Hamiltonian systems with an additional transversal component

We prove exponential stability theorems of Nekhoroshev type for motion in the neighbourhood of an elliptic fixed point in Hamiltonian systems having an additional transverse component of arbitrary dimension, under certain conditions on this transverse component. We consider both the cases (i) of a strongly constrained motion, and (ii) of a weak perturbation.     

Robust errors-in-variables linear regression via Laplace distribution

Robust estimation procedures for linear and mixture linear errors-in-variables regression models are proposed based on the relationship between the least absolute deviation criterion and maximum likelihood estimation in a Laplace distribution. The finite sample performance of the proposed procedures is evaluated by simulation studies.     

Formation of iron(III) cluster complexes with a new (N2O2) Schiff base

Two new series of Fe(III) Schiff-base complexes have been prepared and characterized by elemental and thermogravimetric analyses, IR, electronic, ESR and Mössbauer spectra. The Fe(III) complexes possess octahedral, pseudo-octahedral or pseudo-tetrahedral geometries around Fe(III), depending on the nature of the Schiff-base ligand used.