The minimizing of the Nielsen root classes

Given a map f: X→Y and a Nielsen root class, there is a number associated to this root class, which is the minimal number of points among all root classes which are H-related to the given one for all homotopies H of the map f. We show that for maps between closed surfaces it is possible to deform f such that all the Nielsen root classes have cardinality equal to the minimal number if and only if either N R[f]≤1, or N R[f]>1 and f satisfies the Wecken property. Here N R[f] denotes the Nielsen root number. The condition “f satisfies the Wecken property is known to be equivalent to |deg(f)|≤N R[f]/(1−χ(M ₂)−χ(M ₁0/(1−χ(M ₂)) for maps between closed orientable surfaces. In the case of nonorientable surfaces the condition is A(f)≤N R[f]/(1−χ(M ₂)−χ(M ₂)/(1−χ(M ₂)). Also we construct, for each integer n≥3, an example of a map f: K _n →N from an n-dimensionally connected complex of dimension n to an n-dimensional manifold such that we cannot deform f in a way that all the Nielsen root classes reach the minimal number of points at the same time.     

Zirconium phosphate dispersed on a cellulose fiber surface: preparation, characterization, and selective adsorption of Li+, Na+, and K+ from aqueous solution

Highly dispersed zirconium phosphate was prepared by reacting Cel/ZrO(2) (ZrO(2)=6.7 wt%; 0.56 mmol g(-1) of zirconium atom per gram of the material) with phosphoric acid. High power decoupling magic angle spinning (HPDEC-MAS)(31)P NMR and X-ray photoelectron spectroscopy data indicated that HPO(2-)(4) is the species present on the fiber surface. The X-ray diffraction patterns showed that zirconium hydrogen phosphate particles were amorphous and had an ion-exchange capacity, determined by ammonia gas adsorption, of 0.30 mmol g(-1). The ion-exchange capacities for Li(+), Na(+), and K(+) ions were determined from ion-exchange isotherms at 298 K and showed the following values (in mmol g(-1)): Li(+)=0.01, Na(+)=0.23, and K(+)=0.30. The higher affinity of the surface hydrogen phosphate particles for Na(+) and K(+) is due to its lamelar structure which permits easier diffusion of these two ions whose hydrated radii are smaller than that of Li(+).     

On the nuclearity of integral operators

Let X be a nonempty measurable subset of and consider the restriction of the usual Lebesgue measure σ of to X. Under the assumption that the intersection of X with every open ball of has positive measure, we find necessary and sufficient conditions on a L²(X)-positive definite kernel in order that the associated integral operator be nuclear. Taken nuclearity for granted, formulas for the trace of the operator are derived. Some of the results are re-analyzed when K is just an element of .      

Influence of plant densities and fertilization on maize grains by near-infrared spectroscopy

Near-infrared spectroscopy is a rapid process analytical technology for measuring a wide range of constituents of biological materials. The objective of the current study was to investigate maize grains grown under different levels of fertilization and plant densities using near-infrared spectroscopy. Maize grains from the same plant density had their protein content increased with doses of nitrogen. In addition, it was observed the decrease in protein content with the increase in plant densities. Except for ash content, models for the assessed parameters indicated that near-infrared spectra has the potential for fast assessment of maize grains.     

Strong surjectivity of mappings of some 3-complexes into $$ M_{Q_8 } $$

Let K be a CW-complex of dimension 3 such that H ³(K;ℤ) = 0 and the orbit space of the 3-sphere with respect to the action of the quaternion group Q ₈ determined by the inclusion Q ₈ ⊆ . Given a point a ∈ , we show that there is no map f:K → which is strongly surjective, i.e., such that MR[f,a]=min{#(g ⁻¹(a))|g ∈ [f]} ≠ 0.      

A topological invariant for pairs of maps

In this paper we develop the notion of contact orders for pairs of continuous self-maps (f, g) from ℝⁿ, showing that the set Con(f, g) of all possible contact orders between f and g is a topological invariant (we remark that Con(f, id) = Per(f)). As an interesting application of this concept, we give sufficient conditions for the graphs of two continuous self-maps from ℝ intersect each other. We also determine the ordering of the sets Con(f, 0) and Con(f, h), for h ∈ Hom(ℝ) such that f ∘ h = h ∘ f. For this latter set we obtain a generalization of Sharkovsky’s theorem.     

SBA-16负载金属氧化物催化剂合成、表征及催化CO氧化反应活性

将V2O5, CeO2和CuO分散到提取自稻米壳的SBA-16上,考察了其催化CO氧化反应活性,并采用X射线衍射、扫描电镜、透射电镜、程序升温还原和紫外漫反射光谱对所制催化剂进行了表征。结果表明,掺杂CuO的介孔氧化硅是一种有前景的催化剂,其CO转化率可达98%以上。     

Primeness property for graded central polynomials of verbally prime algebras

Let F be an infinite field. The primeness property for central polynomials of $M_n(F)$ was established by A. Regev, i.e., if the product of two polynomials in distinct variables is central then each factor is also central. In this paper we consider the analogous property for $M_n(F)$ and determine, within the elementary gradings with commutative neutral component, the ones that satisfy this property, namely the crossed product gradings. Next we consider $M_n(R)$, where R admits a regular grading, with a grading such that $M_n(F)$ is a homogeneous subalgebra and provide sufficient conditions – satisfied by $M_n(E)$ with the trivial grading – to prove that $M_n(R)$ has the primeness property if $M_n(F)$ does. We also prove that the algebras $M_{a,b}(E)$ satisfy this property for ordinary central polynomials. Hence we conclude that, over a field of characteristic zero, every verbally prime algebra has the primeness property.     

Oxidation kinetics of nickel nano crystallites obtained by controlled thermolysis of diaquabis(ethylenediamine)nickel(II) nitrate

The metal complex, [Ni(en)₂(H₂O)₂](NO₃)₂ (en = ethylenediamine), was decomposed in a static furnace at 200 °C by autogenous decomposition to obtain phase pure metallic nickel nanocrystallites. The nickel metal thus obtained was studied by XRD, IR spectra, SEM and CHN analysis. The nickel crystallites are in the nanometer range as indicated by XRD studies. The IR spectral studies and CHN analyses show that the surface is covered with a nitrogen containing species. Thermogravimetric mass gain shows that the product purity is high (93%). The formed nickel is stable and resistant to oxidation up to 350 °C probably due to the coverage of nitrogen containing species. Activation energy for the oxidation of the prepared nickel nanocrystallites was determined by non-isothermal methods and was found to depend on the conversion ratio. The oxidation kinetics of the nickel crystallites obeyed a Johnson–Mehl–Avrami mechanism probably due to the special morphology and crystallite strain present on the metal.     

Removable singularities for sections of Riemannian submersions of prescribed mean curvature

We will prove that isolated singularities of sections with prescribed mean curvature of a Riemannian submersion fibered by geodesics of a vertical Killing field, are removable. Also we obtain information on the growth of the difference of two sections , having the same prescribed mean curvature and u=v on ∂Ω. This generalizes Theorem 2 of [P. Collin, R. Krust, Le problème de Dirichlet l'équation des surfaces minimales sur des domaines non bornés, Bull. S.M.F. 119 (4) (1991) 443-462].