A Borsuk-Ulam type theorem for sphere bundles over stunted projective spaces

A CW complex B is described as I-trivial if there does not exist a Z₂-map from Si−1 to S(α) for any vector bundle α over B and any integer i with i>dimα. For n>1, we determine all positive integers m for which the stunted projective space is I-trivial, where F=R,C or H.     

Prescribing valuations of the order of a point in the reductions of abelian varieties and tori

Let G be the product of an abelian variety and a torus defined over a number field K. Let R be a K-rational point on G of infinite order. Call nR the number of connected components of the smallest algebraic K-subgroup of G to which R belongs. We prove that nR is the greatest positive integer which divides the order of for all but finitely many primes p of K. Furthermore, let m>0 be a multiple of nR and let S be a finite set of rational primes. Then there exists a positive Dirichlet density of primes p of K such that for every ? in S the ?-adic valuation of the order of equals v?(m).     

A Chebysheff recursion formula for Coxeter polynomials

A polynomial f(T)∈Z[T] is represented by q(T)∈Z[T] if ; f(T) is graphically represented if for χ_M(T) the characteristic polynomial of a symmetric matrix M. Many instances of Coxeter polynomialsf_A(T), for A a finite dimensional algebra, are (graphically) representable. We study the case of extended canonical algebras A, see [H. Lenzing, J.A. de la Peña, Extended canonical algebras and Fuchsian singularities, in press], show that the corresponding polynomials f_A(T) are representable and satisfy a Chebysheff type recursion formula. We get consequences for the eigenvalues of the Coxeter transformation of A showing, for instance, that at most four eigenvalues may lie outside the unit circle.     

On generalized Lie derivations of Lie ideals of prime algebras

Let A be a prime algebra of characteristic not 2 with extended centroid C, let R be a noncentral Lie ideal of A and let B be the subalgebra of A generated by R. If f,d:R→A are linear maps satisfying that

     

Generalized Bowen-Franks groups of integral matrices with the same zeta function

In this paper the relation between the zeta function of an integral matrix and its generalized Bowen-Franks groups is studied. Suppose that A and B are nonnegative integral matrices whose invertible part is diagonalizable over the field of complex numbers and A and B have the same zeta function. Then there is an integer m, which depends only on the zeta function, such that, for any prime q such that gcd(q,m)=1, for any g(x)∈Z[x] with g(0)=1, the q-Sylow subgroup of the generalized Bowen-Franks group BF_g(x)(A) and BF_g(x)(B) are the same. In particular, if m=1, then zeta function determines generalized Bowen-Franks groups.     

A variational inequality theory for demicontinuous S-contractive maps with applications to semilinear elliptic inequalities

A variational inequality theory for demicontinuous S-contractive maps in Hilbert spaces is established by employing the ideas of Granas' topological transversality. Such a variational inequality theory has many properties similar to those of fixed point theory for demicontinuous weakly inward S-contractive maps and to those of fixed point index for condensing maps. The variational inequality theory will be applied to study the existence of positive weak solutions and eigenvalue problems for semilinear second-order elliptic inequalities with nonlinearities which satisfy suitable lower bound conditions involving the critical Sobolev exponent. There has been little discussion for such elliptic inequalities involving the critical Sobolev exponent in the literature.     

103-configurations and projective realizability of multiplied configurations

Some remarks on 10₃-configurations which contain the complete graph K ₄ are given, on their representations, and on projective realizability. Results are applied to show a class of configurations that cannot be realized in any Pappian projective space.      

四元数的复数形式及其在6R机器人反解中的应用

把四元数应用于平面旋转的特殊情况,并把旋转角度的正弦、余弦改写为复指数形式,导出平面四元数的两个复数形式的基.利用这两个基可以把表示三维变换的四元数和对偶四元数改造为复数形式,得到复数形式四元数的4个基和复数形式对偶四元数的8个基,以及它们之间乘法运算的运算法则.通过把它们应用到空间$6R$机器人的位移反解问题,证明了Dixon结式展开后的次数为16次,而不是形式上的24次,并且得到单变量的16次方程.     

基于R/S分析的专利申请量年增长率的相关性研究

Hurst指数是描述分数布朗运动的重要指标.利用R/S分析方法计算出我国专利申请量年增长率的Hurst指数稳定在0.62附近,分形维数稳定在1.38附近.表明我国专利申请量年增长率时间序列,服从分数布朗运动,专利申请量年增长率具有长期相关性.历史数据的影响力随时间间隔的长度增长而缩小,当间隔长度达到10年以上时,历史数据的影响力趋于稳定.     

Rapid determination of aluminum by UV-vis diffuse reflectance spectroscopy with application of suitable adsorbents

Diffuse reflectance spectroscopy (DRS) can be used as a rapid and sensitive method for the quantitative determination of low amounts of aluminum. In this analytical technique, the analyte in samples are extracted onto a solid sorbent matrix loaded with a colorimetric reagent and then quantified directly on the adsorbent surface. Alternatively, colored aluminum complexes formed in solution can also be immobilized onto adsorbent surface and be measured by DRS technique. Octadecyl silica disk, methyltrioctylammonium chloride–naphthalene and MCM-41 were examined as adsorbents. Eriochrome cyanine R and quinalizarin were used as coloring reagents. Optimal sorption conditions were found for each system of analyte–reagent–adsorbent. The concentration of analyte is determined using the appropriate form of the Kubelka–Munk function. We obtained for each of the aluminium–reagent–adsorbent system a calibration curve by plotting the absorbance versus the log 10²[Al³⁺] μg ml⁻¹. The linear dynamic range extends over two orders of magnitude within 0.01–15 μg ml⁻¹ with little differences in the range and in the correlation coefficients among the adsorbents. We consider that for a rapid determination of aluminum a spot-test-DRS combination with a detection limit of 1.0 × 10⁻² μg ml⁻¹ is the more facile and preferred technique.