LM-g splines

As an extension of the notion of an L-g spline, three mathematical structures called LM-g splines of types I, II, and III are introduced. Each is defined in terms of two differential operators the coefficients a_j, J = 0,…, n − 1, and b_i, I = 0,…, m, are sufficiently smooth; and b_m is bounded away from zero on [0, T]. Each of the above types of splines is the solution of an optimization problem more general than the one used in the definition of the L-g spline and hence it is recognized as an entity which is distinct from and more general mathematically than the L-g spline. The LM-g splines introduced here reduce to an L-g spline in the special case in which m = 0 and b₀ = constant ≠ 0. After the existence and uniqueness conditions, characterization, and best approximation properties for the proposed splines are obtained in an appropriate reproducing kernel Hilbert space framework, their usefulness in extending the range of applicability of spline theory to problems in estimation, optimal control, and digital signal processing are indicated. Also, as an extension of recent results in the generalized spline literature, state variable models for the LM-g splines introduced here are exhibited, based on which existing least squares algorithms can be used for the recursive calculation of these splines from the data.     

Disk Noise Measurement System for Optical Disks

We developed a system to measure disk noise as a function of both radial and angular position. In order to obtain an accurate disk noise measurement, crosstalk and intersymbol interference were avoided by recording regularly repeating pit patterns and the influence of electronic and laser noise was removed by averaging techniques. We found the system’s mapping ability and its high sensitivity to be very useful in investigating disk noise phenomena in the mastering process. We used the system to assess the accuracy and reproducibility of the photopolymerization replication and Al vapor deposition processes. Also, we investigated the choice of photoresist and found that photoresists with the combination of the narrowest molecular weight distribution and the highest photo-active compound content resulted in the lowest disk noise levels. Our system can, in principle, be adapted to evaluate magneto-optical and phase change disks.     

On a dual submanifold homomorphism

In this paper we develop a technique to study the homomorphisma: MU _* (B U₁)→M U_*?2 (B U₁) defined by assigning to the class off: M→B U ₁ the class off _oi: N→B U₁, wherei: N→M is the submanifold dual tof*(γ₁)?f*(γ₁), and γ₁→B U is the 3 universal line boundle. So that we can present a (σ_n), where σ_nis the class of the classifying map of the canonical line boundle overC P ⁿ, in terms of the σ_i’s and chosen generators of Π_★(M U).     

Spin echo MRI in the evaluation of hearts with a double outlet right ventricle: usefulness and limitations

The surgical approach to a double outlet right ventricle (DORV) is dependent on the spatial relationship of the semilunar valves, outflow tracts and ventricular septal defect (VSD). The purpose of the study was to assess the value of MRI for the evaluation of cardiovascular anatomy in patients before and after surgery for DORV. Spin echo MRI was performed in 12 patients with DORV (eight preoperative and four postoperative patients). Thin-section MRI was performed in three orthogonal planes and selected angulated views were obtained. Conventional imaging by color Doppler echocardiography and cine-angiocardiography and surgical findings, when present, served as the reference standards. The results found that the spatial relationship between semilunar valves and VSD was accurately assessed by MRI in eight out of eight preoperative patients. In the four postoperative cases MRI depicted the morphology of both outflow tracts and provided adequate information on their patency. Of the eight preoperative patients, five have undergone corrective surgery and the MRI findings were confirmed. MRI provided additional information to conventional imaging preoperatively in three cases in which the VSD opened into the outlet portion of the DORV, without there being a direct relation to a semilunar valve. In two preoperative cases in which the VSD was directly committed to the aorta, conventional imaging was conclusive. MRI was unable to depict aberrant chordae tendineae in four out of four cases. We conclude that MRI provides accurate additional anatomic information in patients with DORV, which is helpful in presurgical planning as well as during follow-up. Spin echo MRI does not visualize aberrant chordae tendineae.     

Accurate masses of unstable rare-earth isotopes by ISOLTRAP

Direct mass measurements of neutron-deficient rare-earth isotopes in the vicinity of ¹⁴⁶Gd were performed with the Penning trap mass spectrometer ISOLTRAP at ISOLDE/CERN. This paper reports on the measurement of more than 40 isotopes of the elements praseodymium, neodymium, promethium, samarium, europium, dysprosium and holmium, that have been measured with a typical accuracy of m 14 keV. An atomic mass evaluation has been performed taking into account other experimental mass values via a least-squares adjustment. The results of the adjustment are discussed. Received: 18 April 2000 / Accepted: 12 July 2000     

On the maximum cardinality of a consistent set of arcs in a random tournament

For any tournament T on n vertices, let h(T) denote the maximum number of edges in the intersection of T with a transitive tournament on the same vertex set. Sharpening a previous result of Spencer, it is proved that, if T_n denotes the random tournament on n vertices, then, $\text{P}$$\text{(h(T}{}_{\mathrm{n}}\text{) ≤}\text{1}\text{2}\text{(}{}_2{}^{\mathrm{n}}\text{) + 1.73n}{}^{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{) → 1}$ as n → ∞.     

Is the new ECTS system better than the traditional one? An application to the ECTS pilot-project at the University Pablo de Olavide

At the meeting of the joint Bologna Declaration, EU representatives agreed on the establishment of a common European Higher Education Area by 2010. Since then, several universities have implemented pilot projects, although no formal research has been carried out to analyse their results. In this study, we analysed one of these pilot-projects with two objectives. First, we examined the performance of the new system as compared to that of the traditional system. We used a procedure based on a modified model of Data Envelopment Analysis that is able to distinguish students’ efficiency (managerial efficiency) from efficiency based on the educational programme used (programme efficiency). Then we analysed whether the different systems perform differently for different types of students.     

Melting of heterogeneous vortex matter: The vortex ‘nanoliquid’

Disorder and porosity are parameters that strongly influence the physical behavior of materials, including their mechanical, electrical, magnetic and optical properties. Vortices in superconductors can provide important insight into the effects of disorder because their size is comparable to characteristic sizes of nanofabricated structures. Here we present experimental evidence for a novel form of vortex matter that consists of inter-connected nanodroplets of vortex liquid caged in the pores of a solid vortex structure, like a liquid permeated into a nanoporous solid skeleton. Our nanoporous skeleton is formed by vortices pinned by correlated disorder created by high-energy heavy ion irradiation. By sweeping the applied magnetic field, the number of vortices in the nanodroplets is varied continuously from a few to several hundred. Upon cooling, the caged nanodroplets freeze into ordered nanocrystals through either a first-order or a continuous transition, whereas at high temperatures a uniform liquid phase is formed upon delocalization-induced melting of the solid skeleton. This new vortex nanoliquid displays unique properties and symmetries that are distinct from both solid and liquid phases.     

MAS NMR spectra of quadrupolar nuclei in disordered solids: the Czjzek model

Structural disorder at the scale of two to three atomic positions around the probe nucleus results in variations of the EFG and thus in a distribution of the quadrupolar interaction. This distribution is at the origin of the lineshape tailing toward high fields which is often observed in the MAS NMR spectra of quadrupolar nuclei in disordered solids. The Czjzek model provides an analytical expression for the joint distribution of the NMR quadrupolar parameters upsilon(Q) and eta from which a lineshape can be predicted. This model is derived from the Central Limit Theorem and the statistical isotropy inherent to disorder. It is thus applicable to a wide range of materials as we have illustrated for 27Al spectra on selected examples of glasses (slag), spinels (alumina), and hydrates (cement aluminum hydrates). In particular, when relevant, the use of the Czjzek model allows a quantitative decomposition of the spectra and an accurate extraction of the second moment of the quadrupolar product. In this respect, it is important to realize that only rotational invariants such as the quadrupolar product can make sense to describe the quadrupolar interaction in disordered solids.