Infinite-variate wide-sense Markov processes and functional analysis for bounded operator-forming vectors

Let p, q be arbitrary parameter sets, and let $\text{H}$ be a Hilbert space. We say that x = (xⁱ)_i?q, xⁱ ? $\text{H}$, is a bounded operator-forming vector (?$\text{H}$_F^q) if the Gram matrix 〈x, x〉 = [(xⁱ, x^j)]_i?q,j?q is the matrix of a bounded (necessarily ≥ 0) operator on $\text{l}{}_{\mathrm{q}}{}^2$, the Hilbert space of square-summable complex-valued functions on q. Let A be p × q, i.e., let A be a linear operator from $\text{l}{}_{\mathrm{q}}{}^2$ to $\text{l}{}_{\mathrm{p}}{}^2$. Then exists a linear operator ǎ from (the Banach space) $\text{H}$_F^q to $\text{H}$_F^p on $\text{D}$(A) = {x:x ? $\text{H}$_F^q, $\text{A〈x, x〉}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ is p × q bounded on $\text{l}{}_{\mathrm{q}}{}^2$} such that y = ǎx satisfies y^j?σ(x) = {space spanned by the xⁱ}, 〈y, x〉 = A〈x, x〉 and $\text{〈y, y〉 = A〈x, x〉}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(A〈x, x〉}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{)}{}^1$. This is a generalization of our earlier [J. Multivariate Anal.4 (1974), 166–209; 6 (1976), 538–571] results for the case of a spectral measure concentrated on one point. We apply these tools to investigate q-variate wide-sense Markov processes.     

Some new domains with complete Kähler metrics of negative curvature

We add to the known examples of complete Kähler manifolds with negative sectional curvature by showing that the following three classes of domains in euclidean spaces also belong: perturbations of ellipsoidal domains in ?ⁿ, intersections of complex-ellipsoidal domains in ?², and intersections of fractional linear transforms of the unit ball in ?². In the process, we prove the following theorem in differential geometry: in the intersection of two complex-ellipsoidal domains in ?², the sum of the Bergman metrics is a Kähler metric with negative curvature operator.     

The Spearman footrule and a Markov chain property

An equivalent representation of the Spearman footrule is considered and a characterization in terms of a Markov chain is established. A martingale approach is thereby incorporated in the study of the asymptotic normality of the statistics.     

Peripheral and ADI hopscotch methods for two dimensional parabolic and elliptic equations with a mixed term

The peripheral and ADI hopscotch methods are extended to solve problems in two space dimensions with a mixed derivative term. The method is compared numerically with existing hopscotch methods.     

Balance theorems for height-2 posets

We prove that every height-2 finite poset with three or more points has an incomparable pair {x, y} such that the proportion of all linear extensions of the poset in which x is less than y is between 1/3 and 2/3. A related result of Komlós says that the containment interval [1/3, 2/3] shrinks to [1/2, 1/2] in the limit as the width of height-2 posets becomes large. We conjecture that a poset denoted by V _m ⁺ maximizes the containment interval for height-2 posets of width m+1.     

Structural and elastic properties of the filled tetrahedral semiconductors LiZnX (X=N, P, and As)

We report on first-principles study of the structural and elastic properties of the Nowotny-Juza filled tetrahedral compounds LiZnX (X=N, P, As) using the full-potential linearized augmented plane wave method within the local density approximations. Our results indicate that the energetically favourable α-LiZnX materials are slightly softer than their binary analogous GaX and the sound speeds are quantitatively similar for LiZnAs and GaAs.     

Spectroscopic and magnetic properties of Fe3Fe4(AsO4)6

The infrared (IR) and ⁵⁷Fe-Mössbauer spectra of Fe₃^IIFe₄^III(AsO₄)₆ were recorded and analyzed on the basis of its structural characteristics. The IR spectrum presents a high complexity, showing an important number of bands and splittings, as a consequence of the presence of three structurally independent AsO₄³⁻ groups. The analysis of the four quadrupole signals shown by the Mössbauer spectrum allowed to attain a detailed insight into the cation distribution over the available crystallographic sites. The alternating current susceptibility measurements indicate a paramagnetic to ferrimagnetic transition in the material at about 59 K.     

双酚A人工抗原的光谱表征及免疫鉴定研究

双酚A(bisphenol A,BPA)是一种酚类环境雌激素,即使极低剂量残留对人类健康也有危害。为了建立其简单快速并适应现场检测的免疫分析方法,必须先合成它的人工抗原并进行鉴定。通过对双酚A进行结构修饰,用碳二亚胺将结构修饰了的双酚A与牛血清蛋白相偶联,经透析得到纯的双酚A人工抗原并冷冻干燥备用。然后用紫外光谱、红外光谱和免疫方法对人工抗原进行鉴定。结果表明,合成的人工抗原紫外光谱图中具有蛋白质和双酚A的特征吸收峰;人工抗原红外光谱图中呈现双酚A和牛血清蛋白的红外特征吸收峰;通过竞争ELISA试验表明用合成的人工抗原免疫的Balb/c小鼠血清中产生了双酚A的抗体。三种方法综合鉴定结果表明双酚A人工抗原合成成功,该人工抗原可以进一步用于制备抗双酚A的单克隆抗体。     

Lee–Yang Problems and the Geometry of Multivariate Polynomials

We describe all linear operators on spaces of multivariate polynomials preserving the property of being non-vanishing in open circular domains. This completes the multivariate generalization of the classification program initiated by Pólya–Schur for univariate real polynomials and provides a natural framework for dealing in a uniform way with Lee–Yang type problems in statistical mechanics, combinatorics, and geometric function theory.     

Structural and magnetic ordering in the VxNb1+yS2 system

The influence of composition on the structural ordering and magnetism in the V_xNb_1+yS₂ system has been investigated by X-ray diffraction and magnetic measurements. Stoichiometric V_1/3NbS₂ did not exhibit the structural ordering of vanadium between the NbS₂ layers. In the ordered structure, the vanadium composition deviated from the ideal value of to both higher and lower values, while the niobium composition was in the range of 0.05?y?0.18. Excess niobium, y>0, is thought to play an essential role in the structural ordering in this system. For samples with excess niobium and ordered structures, a magnetic transition was observed at 20-50 K, depending on the composition. The spontaneous magnetization of 3-5×10⁻³ μ_B/V atom is thought to be intrinsic to this system. The magnetization curves consisted of a constant and a proportional parts of the magnetic field, which correspond to the spontaneous magnetization and high-field susceptibility, respectively. The magnetization curves and the temperature dependencies of the high-field susceptibility were quite similar to those of the canted antiferromagnetic NiS₂. A correlation between the structural and magnetic ordering is suggested.