Reduction of critical field for magnetic and orbital-ordering phase transition in impurity-substituted Nd0.45_{0.45}Sr0.55_{0.55}MnO3_3 crystal

We have investigated the Mn-site substitution effect in Nd$_{0.45}$Sr$_{0.55}$MnO$_3$ single crystal, which has an $A$-type layered antiferromagnetic ($A$-AFM) phase with the 3$d_{x^2-y^2}$-type orbital-order. Substitution of Fe or Ga for Mn-site suppresses both the $A$-AFM order and competing ferromagnetic (FM) correlation whereas Cr substitution suppresses only the $A$-AFM order but reactivates the underlying FM correlation via double-exchange mechanism along the AFM coupled $c$-direction. In Nd$_{0.45}$Sr$_{0.55}$Mn$_{0.95}$Cr$_{0.05}$O$_3$, the $A$-AFM state with the orbital-order is changed into the orbital-disordered three-dimensional FM metallic state by applying magnetic field of $\mu_0 H = 12$ T, which is much smaller than that of the parent compound Nd$_{0.45}$Sr$_{0.55}$MnO$_3$.Comment: 5 pages, 4 figures, to appear in APL Material

QC-level sets and quotients of Douglas algebras

AbstractThere is a QC-level set which coincides with a support set (under the continum hypothesis), and there are Douglas algebras B1 and B2 satisfying: both the unit balls of L∞B1 and B2H∞ + C have extreme points but not have exposed points

Quality Assurance Using ICT Best Practices in School-Based Assessment of Students’ Learning in Nigerian University Education

The paper emphasized strongly that ICTs best practices if adopted in School Based Assessment (S B A) would achieve quality assurance. Best practices are techniques that through experience and research have proven to reliably lead to a desired result. The study is a descriptive survey which sought to determine the potentials of ICTs best practices in SBA among others in Nigerina university education. The study was carried out in Federal and State universities in the South – South and South- East Zones of Nigeria. The sample size comprised of 140 lecturers drawn from the population of 345 respondents. Four research questions and three hypotheses guided the study. The instrument for data collection was a 38- item questionnaire developed by the researchers. The instrument was validated and reliability was computed to be 0.82; 0.86; 0.81 and 0.88 for the four sections respectively. The data were analyzed using mean and standard deviation to answer the research questions and Z- test statistic in testing the null hypotheses at 0.05 alpha level. The findings among others indicated that ICTs best practices in SBA have the potentials to achieve quality education. Based on the findings, recommendations were made which were that lecturers should be developed in the use of ICTs facilities for SBA and adequate ICTs facilities should be provided to aid e-assessment.Key words: Quality Assurance, ICTs best practices, School – Based Assessment, Nigerian University educatio

Linear sums of two composition operators on the Fock space

AbstractLinear sums of two composition operators of the multi-dimensional Fock space are studied. We show that such an operator is bounded only when both composition operators in the sum are bounded. So, cancelation phenomenon is not possible on the Fock space, in contrast to what have been known on other well-known function spaces over the unit disk. We also show the analogues for compactness and for membership in the Schatten classes. For linear sums of more than two composition operators the investigation is left open

Applications of Hilbert Module Approach to Multivariable Operator Theory

A commuting $n$-tuple $(T_1, \ldots, T_n)$ of bounded linear operators on a Hilbert space \clh associate a Hilbert module $\mathcal{H}$ over $\mathbb{C}[z_1, \ldots, z_n]$ in the following sense: $$\mathbb{C}[z_1, \ldots, z_n] \times \mathcal{H} \rightarrow \mathcal{H}, \quad \quad (p, h) \mapsto p(T_1, \ldots, T_n)h,$$where $p \in \mathbb{C}[z_1, \ldots, z_n]$ and $h \in \mathcal{H}$. A companion survey provides an introduction to the theory of Hilbert modules and some (Hilbert) module point of view to multivariable operator theory. The purpose of this survey is to emphasize algebraic and geometric aspects of Hilbert module approach to operator theory and to survey several applications of the theory of Hilbert modules in multivariable operator theory. The topics which are studied include: generalized canonical models and Cowen-Douglas class, dilations and factorization of reproducing kernel Hilbert spaces, a class of simple submodules and quotient modules of the Hardy modules over polydisc, commutant lifting theorem, similarity and free Hilbert modules, left invertible multipliers, inner resolutions, essentially normal Hilbert modules, localizations of free resolutions and rigidity phenomenon. This article is a companion paper to "An Introduction to Hilbert Module Approach to Multivariable Operator Theory".Comment: 46 pages. This is a companion paper to arXiv:1308.6103. To appear in Handbook of Operator Theory, Springe

集団遊びによる子どもたちの相互生成－物的環境からのアフォーダンスに焦点づけて－

本研究は，子どもたちの遊びやかかわりを生成させる要因について，明らかにすることが目的である。幼稚園に通う4，5歳児を対象に観察調査を行い，フィールドノートから得られた内容を分析した。その結果，31 の小項目，13 の大項目が抽出された。各大項目の関係を検討した結果，子どもたちのかかわりを生起させる要因として物的環境，子ども個人の日常の経験，保育者の関与の三つが抽出された。今回は，物的環境に着目し，子どもたちのかかわりを分析した。その結果，物的環境が，子どもたちのかかわりを生起させ，持続させることに大きな影響を与えていたことが明らかとなった

Backward shift invariant subspaces in the bidisc II

For every invariant subspace NI in the Hardy spaces H2 (f2 ), let Vz and Vw be mulitplication operators on AL Then it is known that the condition Vz V; v;vz on NI holds if and only if J;I is a Demling type invariant subspace. For a backward shift invariant subspace N in H2(f2), two operators Sz and Sw on N are defined by Sz = PN LzPN and Sw = PN Lw PN, where PN is the orthogonal projection from L2(f2) onto N. It is given a characterization of N satisfying szs1:J = s1:JsZ on N