The application of NIR Raman spectroscopy in the assessment of serum thyroid-stimulating hormone in rats

Serum blood samples of euthyroid and thyroidectomized rats treated with thyrotropin-releasing hormone (TRH) were analyzed on aluminum substrates using the near-infrared Raman spectroscopy (830 nm). Spectra of thyroid-stimulating hormone (TSH), TRH and prolactin standards were obtained. Differences between Raman spectra profiles of control and Tx + TRH samples groups were found. These differences were confirmed by the linear discriminant analysis (LDA), which presents a good classification between groups. It is supposed that these differences are produced by the increment of TSH in the thyroidectomized rats.     

Dominated, diagonal polynomials on ℓ p spaces

We show that the r-dominated polynomials on _p(2 p ) are integral on ₁, and give examples proving that the converse is not true. We characterize when the 2-homogeneous, diagonal polynomials on _p(1 < p ) are r-dominated. We prove that, unlike the linear case, there are nuclear polynomials which are not 1-dominated.Received: 6 June 2004; revised: 28 September 2004     

Properties of In2S3 thin films deposited onto ITO/glass substrates by chemical bath deposition

In₂S₃ films have been chemically deposited on ITO coated glass substrates by chemical bath deposition, using different deposition times and precursor concentrations. The bilayers are intended for photovoltaic applications. Different characterization methods have been employed: optical properties of the films were investigated from transmittance measurements, structural properties by XRD and micro-Raman, and surface morphology by SEM microscopy analysis. Also, the direct and indirect band-gaps and the surface gap states were studied with surface photovoltage spectroscopy (SPS). We proposed that electronic properties of the In₂S₃ samples are controlled by two features: shallow tail states and a broad band centred at 1.5 eV approximately. Their relation with the structure is discussed, suggesting that their origin is related to defects created on the S sub-lattice, and then both defects are intrinsic to the material.     

A branch and cut algorithm for the hierarchical network design problem

The Hierarchical Network Design Problem consists of locating a minimum cost bi-level network on a graph. The higher level sub-network is a path visiting two or more nodes. The lower level sub-network is a forest connecting the remaining nodes to the path. We optimally solve the problem using an ad hoc branch and cut procedure. Relaxed versions of a base model are solved using an optimization package and, if binary variables have fractional values or if some of the relaxed constraints are violated in the solution, cutting planes are added. Once no more cuts can be added, branch and bound is used. The method for finding valid cutting planes is presented. Finally, we use different available test instances to compare the procedure with the best known published optimal procedure, with good results. In none of the instances we needed to apply branch and bound, but only the cutting planes.     

Data Envelopment Analysis of multiple response experiments

Taguchi method is the usual strategy in robust design and involves conducting experiments using orthogonal arrays and estimating the combination of factor levels that optimizes a given performance measure, typically a signal-to-noise ratio. The problem is more complex in the case of multiple responses since the combinations of factor levels that optimize the different responses usually differ. In this paper, an Artificial Neural Network, trained with the experiments results, is used to estimate the responses for all factor level combinations. After that, Data Envelopment Analysis (DEA) is used first to select the efficient (i.e. non-dominated) factor level combinations and then for choosing among them the one which leads to a most robust quality loss penalization. Mean Square Deviations of the quality characteristics are used as DEA inputs. Among the advantages of the proposed approach over traditional Taguchi method are the non-parametric, non-linear way of estimating quality loss measures for unobserved factor combinations and the non-parametric character of the performance evaluation of all the factor combinations. The proposed approach is applied to a number of case studies from the literature and compared with existing approaches.     

On the Hilbert scheme of the moduli space of vector bundles over an algebraic curve

Let M(n, ξ) be the moduli space of stable vector bundles of rank n ≥ 3 and fixed determinant ξ over a complex smooth projective algebraic curve X of genus g ≥ 4. We use the gonality of the curve and r-Hecke morphisms to describe a smooth open set of an irreducible component of the Hilbert scheme of M(n, ξ), and to compute its dimension. We prove similar results for the scheme of morphisms ${M or_P (\mathbb{G}, M(n, \xi))}$ and the moduli space of stable bundles over ${X \times \mathbb{G}}$ , where ${\mathbb{G}}$ is the Grassmannian ${\mathbb{G}(n - r, \mathbb{C}^n)}$ . Moreover, we give sufficient conditions for ${M or_{2ns}(\mathbb{P}^1, M(n, \xi))}$ to be non-empty, when s ≥ 1.     

Rigidity of symmetric products

Given a metric continuum X, we consider the following hyperspaces of X  : 2^X$2^X$, _Cn(X)$C_n(X)$ and _Fn(X)$F_n(X)$ (n∈N$n\in \mathbb{N}$). Let _F1(X)={{x}:x∈X}$F_1(X)=\{\{x\}:x\in X\}$. A hyperspace K(X)$K(X)$ of X   is said to be rigid provided that for every homeomorphism h:K(X)→K(X)$h:K(X)\to K(X)$ we have that h(_F1(X))=_F1(X)$h(F_1(X))=F_1(X)$. In this paper we study under which conditions a continuum X   has a rigid hyperspace _Fn(X)$F_n(X)$.     

“Everything is Math in the Whole World”: Integrating Critical and Community Knowledge in Authentic Mathematical Investigations with Elementary Latina/o Students

This critical ethnographic study of an after-school mathematics club for elementary-aged Latina/o youth focuses on connecting critical, community, and mathematical knowledge in the context of authentic, community-based investigations. We present cases of two extended projects to highlight tensions and dilemmas that emerged, particularly tensions related to ensuring rich mathematics in the contexts of projects that were personally and socially meaningful to the students. Our analysis offers insights into critical mathematics education with elementary aged students, and has the potential to counter dominant deficit perspectives of Latina/o youth. Additionally, the findings of this study inform critical approaches to teaching mathematics in schools attended by marginalized students in order to reverse prevalent trends of our educational system failing these students.     

Try to See It My Way: The Discursive Function of Idiosyncratic Mathematical Metaphor

What are the nature, forms, and roles of metaphors in mathematics instruction? We present and closely analyze three examples of idiosyncratic metaphors produced during one-to-one tutorial clinical interviews with 11-year-old participants as they attempted to use unfamiliar artifacts and procedures to reason about realistic probability problems. Our interpretations of these episodes suggest that metaphor is both spurred by and transformative of joint engagement in situated activities: metaphor serves individuals as semiotic means of objectifying and communicating their own evolving understanding of disciplinary representations and procedures, and its multimodal instantiation immediately modifies interlocutors' attention to and interaction with the artifacts. Instructors steer this process toward normative mathematical views by initiating, modifying, or elaborating metaphorical constructions. We speculate on situation parameters affecting students' utilization of idiosyncratic resources as well as how socio-mathematical license for metaphor may contribute to effective instructional discourse.     

Asplund Operators and p-Integral Polynomials

We introduce the Banach ideals of p-integral and of p-nuclear polynomials for 1 ≤ p ≤ + ∞, extending to the polynomial setting the well known notions of p-integral and p-nuclear operators. For p = 1, we recover the Pietsch integral and nuclear polynomials, respectively. Given a Banach space E, let K be a compact Hausdorff space such that there is an embedding h : E → C(K). Let R _h be the polynomial from E into C(K) given by R _h (x) : = h(x) ^m for all ${x \epsilon E}$ . We prove that a polynomial is p-integral (1 ≤ p ≤ + ∞) if and only if it factors through a polynomial of the form R _h followed by the canonical inclusion of C(K) into L _p (K, μ) for some finite measure μ. We also prove that a polynomial P is p-integral if and only if we may write ${P = T \circ R_{h}}$ where T is a p-integral operator on a C(K) space. We show that P is ∞-integral if and only if it factors in the form ${P = T \circ R_{h}}$ where T is a weakly compact operator on a C(K) space. Analogous results are true if we replace C(K) by L _∞ (Ω, μ) for some finite measure space (Ω, Σ, μ). It is proved that a polynomial ${P \epsilon \mathcal{P}(^{m}E, F)}$ is p-integral if and only if its linearization is well defined and p-integral on ${\bigotimes ^{m}_{{\epsilon}_{s}}, s^{E}}$ . It is also shown that a p-integral polynomial may be extended to a p-integral polynomial on every larger space, and the extension has the same p-integral norm. We give a factorization theorem for p-nuclear polynomials. Finally, we prove that a polynomial P is p-nuclear if and only if it may be written in the form ${P = Q \circ A}$ where A is a compact operator and Q is a p-integral polynomial, if and only ${P = Q^{\prime} \circ H}$ with H an Asplund operator and Q′ a p-integral polynomial. This extends a result obtained by C. Cardassi in the linear case.