COMPLETE ISOMORPHIC CLASSIFICATIONS OF SOME SPACES OF COMPACT OPERATORS

This paper is a continuation and a complement of our previous work on isomorphic classification of some spaces of compact operators. We improve the main result concerning extensions of the classical isomorphic classification of the Banach spaces of continuous functions on ordinals. As an application, fixing an ordinal a and denoting by X(xi), omega(alpha) <= xi < omega(alpha+1), the Banach space of all X-valued continuous functions defined in the interval of ordinals [0,xi] and equipped with the supremum, we provide complete isomorphic classifications of some Banach spaces K(X(xi),Y(eta)) of compact operators from X(xi) to Y(eta), eta >= omega. It is relatively consistent with ZFC (Zermelo-Fraenkel set theory with the axiom of choice) that these results include the following cases: 1.X* contains no copy of c(0) and has the Mazur property, and Y = c(0)(J) for every set J. 2. X = c(0)(I) and Y = l(q)(J) for any infinite sets I and J and 1 <= q < infinity. 3. X = l(p)(I) and Y = l(q)(J) for any infinite sets I and J and 1 <= q < p < infinity.

ON ISOMORPHIC CLASSIFICATIONS OF SPACES OF COMPACT OPERATORS

We prove an extension of the classical isomorphic classification of Banach spaces of continuous functions on ordinals. As a consequence, we give complete isomorphic classifications of some Banach spaces K(X,Y(n)), eta >= omega, of compact operators from X to Y(eta), the space of all continuous Y-valued functions defined in the interval of ordinals [1, eta] and equipped with the supremum norm. In particular, under the Continuum Hypothesis, we extend a recent result of C. Samuel by classifying, up to isomorphism, the spaces K(X(xi), c(0)(Gamma)(eta)), where omega <= xi < omega(1,) eta >= omega, Gamma is a countable set, X contains no complemented copy of l(1), X* has the Mazur property and the density character of X** is less than or equal to N(1).

Equifocality of a singular Riemannian foliation

A singular foliation on a complete Riemannian manifold M is said to be Riemannian if each geodesic that is perpendicular to a leaf at one point remains perpendicular to every leaf it meets. We prove that the regular leaves are equifocal, i.e., the end point map of a normal foliated vector field has constant rank. This implies that we can reconstruct the singular foliation by taking all parallel submanifolds of a regular leaf with trivial holonomy. In addition, the end point map of a normal foliated vector field on a leaf with trivial holonomy is a covering map. These results generalize previous results of the authors on singular Riemannian foliations with sections.

ON SPACES OF COMPACT OPERATORS ON C(K, X) SPACES

This paper concerns the spaces of compact operators kappa(E,F), where E and F are Banach spaces C([1, xi], X) of all continuous X-valued functions defined on the interval of ordinals [1, xi] and equipped with the supremun norm. We provide sufficient conditions on X, Y, alpha, beta, xi and eta, with omega <= alpha <= beta < omega 1 for the following equivalence: (a) kappa(C([1, xi], X), C([1, alpha], Y)) is isomorphic to kappa(C([1,eta], X), C([1, beta], Y)), (b) beta < alpha(omega). In this way, we unify and extend results due to Bessaga and Pelczynski (1960) and C. Samuel (2009). Our result covers the case of the classical spaces X = l(p) and Y = l(q) with 1 < p, q < infinity.

COUNTABLE GROUPS OF ISOMETRIES ON BANACH SPACES

A group G is representable in a Banach space X if G is isomorphic to the group of isometrics on X in some equivalent norm. We prove that a countable group G is representable in a separable real Banach space X in several general cases, including when G similar or equal to {-1,1} x H, H finite and dim X >= vertical bar H vertical bar or when G contains a normal subgroup with two elements and X is of the form c(0)(Y) or l(p)(Y), 1 <= p < +infinity. This is a consequence of a result inspired by methods of S. Bellenot (1986) and stating that under rather general conditions on a separable real Banach space X and a countable bounded group G of isomorphisms on X containing -Id, there exists an equivalent norm on X for which G is equal to the group of isometrics on X. We also extend methods of K. Jarosz (1988) to prove that any complex Banach space of dimension at least 2 may be renormed with an equivalent complex norm to admit only trivial real isometries, and that any complexification of a Banach space may be renormed with an equivalent complex norm to admit only trivial and conjugation real isometrics. It follows that every real Banach space of dimension at least 4 and with a complex structure may be renormed to admit exactly two complex structures up to isometry, and that every real Cartesian square may be renormed to admit a unique complex structure up to isometry.

POLAR ACTIONS ON CERTAIN PRINCIPAL BUNDLES OVER SYMMETRIC SPACES OF COMPACT TYPE

We study polar actions with horizontal sections on the total space of certain principal bundles G/K -> G/H with base a symmetric space of compact type. We classify such actions up to orbit equivalence in many cases. In particular, we exhibit examples of hyperpolar actions with cohomogeneity greater than one on locally irreducible homogeneous spaces with nonnegative curvature which are not homeomorphic to symmetric spaces.

Influence of Poly(Vinyl Alcohol) (PVA) on the Cyclic-Voltammetry Behavior of Single-Crystal Pt Surfaces in Aqueous H(2)SO(4)

In the present work we investigated the electrochemical behavior of PVA on polycrystalline Pt and single-crystal Pt electrodes. PVA hampered the characteristic hydrogen UPD and anion adsorption on all investigated surfaces, with the processes on Pt(110) being the most affected by the PVA presence. Several oxidation waves appeared as the potential was swept in the positive direction and the Pt(111) was found to be the most active for the oxidation processes. (C) 2011 The Electrochemical Society. [DOI: 10.1149/1.3615965] All rights reserved.

Support vector machines for detecting age-related changes in running kinematics

Age-related changes in running kinematics have been reported in the literature using classical inferential statistics. However, this approach has been hampered by the increased number of biomechanical gait variables reported and subsequently the lack of differences presented in these studies. Data mining techniques have been applied in recent biomedical studies to solve this problem using a more general approach. In the present work, we re-analyzed lower extremity running kinematic data of 17 young and 17 elderly male runners using the Support Vector Machine (SVM) classification approach. In total, 31 kinematic variables were extracted to train the classification algorithm and test the generalized performance. The results revealed different accuracy rates across three different kernel methods adopted in the classifier, with the linear kernel performing the best. A subsequent forward feature selection algorithm demonstrated that with only six features, the linear kernel SVM achieved 100% classification performance rate, showing that these features provided powerful combined information to distinguish age groups. The results of the present work demonstrate potential in applying this approach to improve knowledge about the age-related differences in running gait biomechanics and encourages the use of the SVM in other clinical contexts. (C) 2010 Elsevier Ltd. All rights reserved.

Selection of new glass-forming compositions in Al-La system using a combination of topological instability and thermodynamic criteria

A combination of an extension of the topological instability ""lambda criterion"" and a thermodynamic criterion were applied to the Al-La system, indicating the best range of compositions for glass formation. Alloy compositions in this range were prepared by melt-spinning and casting in an arc-melting furnace with a wedge-section copper mold. The GFA of these samples was evaluated by X-ray diffraction, differential scanning calorimetry and scanning electron microscopy. The results indicated that the gamma* parameter of compositions with high GFA is higher, corresponding to a range in which the lambda parameter is greater than 0.1, which are compositions far from Al solid solution. A new alloy was identified with the best GFA reported so far for this system, showing a maximum thickness of 286 mu m in a wedge-section copper mold. Crown Copyright (C) 2009 Published by Elsevier B.V. All rights reserved.

Normal Versus Pathological Voice Signals Using Wavelet Analysis and Least Squares Support-Vector Machines

State of Sao Paulo Research Foundation (FAPESP)

Optimization of modal filters based on arrays of piezoelectric sensors

Modal filters may be obtained by a properly designed weighted sum of the output signals of an array of sensors distributed on the host structure. Although several research groups have been interested in techniques for designing and implementing modal filters based on a given array of sensors, the effect of the array topology on the effectiveness of the modal filter has received much less attention. In particular, it is known that some parameters, such as size, shape and location of a sensor, are very important in determining the observability of a vibration mode. Hence, this paper presents a methodology for the topological optimization of an array of sensors in order to maximize the effectiveness of a set of selected modal filters. This is done using a genetic algorithm optimization technique for the selection of 12 piezoceramic sensors from an array of 36 piezoceramic sensors regularly distributed on an aluminum plate, which maximize the filtering performance, over a given frequency range, of a set of modal filters, each one aiming to isolate one of the first vibration modes. The vectors of the weighting coefficients for each modal filter are evaluated using QR decomposition of the complex frequency response function matrix. Results show that the array topology is not very important for lower frequencies but it greatly affects the filter effectiveness for higher frequencies. Therefore, it is possible to improve the effectiveness and frequency range of a set of modal filters by optimizing the topology of an array of sensors. Indeed, using 12 properly located piezoceramic sensors bonded on an aluminum plate it is shown that the frequency range of a set of modal filters may be enlarged by 25-50%.

The influence of crystallographic orientation on the generation of multiple structural phases generation in Silicon by cyclic microindentation

A Raman scattering study on multiple phase generation in silicon submitted to successive Vickers microindentation cycles, in different crystallographic orientations, was performed. The microindentations were perfon-ned in a virgin single crystal (100)-oriented surface, in the [001] and [011] directions. The results indicated that the formation of multiple phases by cyclic microindentation may depend on the crystallographic direction and number of successive cycles: the onset of several different structural phases was detected after the third cycle for the [001] direction and only after 15 cycles for the [011] direction, indicating that there is a crystallographic orientation dependence for multiple phase generation. (C) 2007 Elsevier B.V. All rights reserved.

Crystallisation behaviours of Al-based metallic glasses: Compositional and topological aspects

The different types of thermal crystallisation behaviours observed during continuous heating of M-based metallic glasses have been successfully associated with the topological instability. criterion, which is simply calculated from the alloy composition and metallic radii of the alloying elements and aluminium. In the present work, we report on new results evidencing the correlation between the values of X and the crystallisation behaviours in Al-based alloys of the Al-Ni-Ce system and we compare the glass-forming abilities of alloys designed with compositions corresponding to the same topological instability condition. The results are discussed in terms of compositional and topological aspects emphasizing the relevance of the different types of clusters in the amorphous phase in defining the stability of the glass and the types of thermal crystallisation. (C) 2008 Elsevier B.V. All rights reserved.

Topological instability, average electronegativity difference and glass forming ability of amorphous alloys

In this paper, we report the remarkable agreement of the glass forming ability of binary alloys with a new criterion that combines the topological instability parameter (lambda) and the average electronegativity difference among the elements of an alloy, assuming both exert a synergetic effect. The best glass forming compositions for Zr-Cu and Ti-Ni systems are well predicted by this new approach. Although the new criterion needs further refinement, it is concluded that the proposed approach is a promising and simple tool to guide and reduce the tedious and labour intensive work to find good glass former compositions in metallic systems. (C) 2008 Elsevier Ltd. All rights reserved.

Thermodynamic and topological instability approaches for forecasting glass-forming ability in the ternary Al-Ni-Y system

A thermodynamic approach to predict bulk glass-forming compositions in binary metallic systems was recently proposed. In this approach. the parameter gamma* = Delta H-amor/(Delta H-inter - Delta H-amor) indicates the glass-forming ability (GFA) from the standpoint of the driving force to form different competing phases, and Delta H-amor and Delta H-inter are the enthalpies for-lass and intermetallic formation, respectively. Good glass-forming compositions should have a large negative enthalpy for glass formation and a very small difference for intermetallic formation, thus making the glassy phase easily reachable even under low cooling rates. The gamma* parameter showed a good correlation with GFA experimental data in the Ni-Nb binary system. In this work, a simple extension of the gamma* parameter is applied in the ternary Al-Ni-Y system. The calculated gamma* isocontours in the ternary diagram are compared with experimental results of glass formation in that system. Despite sonic misfitting, the best glass formers are found quite close to the highest gamma* values, leading to the conclusion that this thermodynamic approach can lie extended to ternary systems, serving as a useful tool for the development of new glass-forming compositions. Finally the thermodynamic approach is compared with the topological instability criteria used to predict the thermal behavior of glassy Al alloys. (C) 2007 Elsevier B. V. All rights reserved.