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).

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.

Extremal problems on sum-free sets and coverings in tridimensional spaces

Given a prime power q, define c (q) as the minimum cardinality of a subset H of F 3 q which satisfies the following property: every vector in this space di ff ers in at most 1 coordinate from a multiple of a vector in H. In this work, we introduce two extremal problems in combinatorial number theory aiming to discuss a known connection between the corresponding coverings and sum-free sets. Also, we provide several bounds on these maps which yield new classes of coverings, improving the previous upper bound on c (q)

Study of partially encased composite beams with innovative position of stud bolts

In this article, static behavior of three partially encased composite beams under flexural condition is investigated in the context of studying some alternative positions for the headed studs. Shear resistance between the I-shaped beam and the concrete was provided by headed studs in two positions: vertically welded oil the bottom flange and horizontally welded on the faces of the web. Experimental results show that the headed studs provide the composite action and increase the bending strength. The most remarkable position seems to be the headed studs vertically welded oil the bottom flange. Ail analytical method to estimate the bending capacity of the encased beams is also proposed, giving a good prediction of the experimental results (C) 2008 Elsevier Ltd. All rights reserved.

Influence of the slice position on chloride migration tests for concrete in marine conditions

Chloride migration tests are used to measure the concrete capacity to inhibit chloride attack. Many researchers carry out this test in a slice of concrete extracted from the central part of cylindrical specimens, discarding about 75% of the concrete used to mold the specimens. This fact generated the question: would it be possible to extract more slices from a same specimen without losing the confidence in the results? The main purpose of this work is to answer this question. Moreover, another aim of this study was to show the difference of chloride penetration between finished faces and the formwork surfaces of concrete beams and slabs. The results indicated that it is possible to use more slices of a single specimen for a chloride migration test. Moreover, it was demonstrated that there is a significant difference of chloride penetration between the finished surface and the formwork surface of the specimens. (C) 2008 Elsevier Ltd. All rights reserved.

Hand position on the bunch and source-sink ratio influence the banana fruit susceptibility to crown rot disease

The postharvest development of crown rot of bananas depends notably on the fruit susceptibility to this disease at harvest. It has been shown that fruit susceptibility to crown rot is variable and it was suggested that this depends on environmental preharvest factors. However, little is known about the preharvest factors influencing this susceptibility. The aim of this work was to evaluate the extent to which fruit filling characteristics during growth and the fruit development stage influence the banana susceptibility to crown rot. This involved evaluating the influence of (a) the fruit position at different levels of the banana bunch (hands) and (b) changing the source-sink ratio (So-Si ratio), on the fruit susceptibility to crown rot. The fruit susceptibility was determined by measuring the internal necrotic surface (INS) after artificial inoculation of Colletotrichum musae. A linear correlation (r = -0.95) was found between the hand position on the bunch and the INS. The So-Si ratio was found to influence the pomological characteristics of the fruits and their susceptibility to crown rot. Fruits of bunches from which six hands were removed (two hands remaining on the bunch) proved to be significantly less susceptible to crown rot (INS = 138.3 mm 2) than those from bunches with eight hands (INS = 237.9 mm 2). The banana susceptibility to crown rot is thus likely to be influenced by the fruit development stage and filling characteristics. The present results highlight the importance of standardising hand sampling on a bunch when testing fruit susceptibility to crown rot. They also show that hand removal in the field has advantages in the context of integrated pest management, making it possible to reduce fruit susceptibility to crown rot while increasing fruit size.

Hamiltonian mappings and circle packing phase spaces.

We introduce three area preserving maps with phase space structures which resemble circle packings. Each mapping is derived from a kicked Hamiltonian system with one of the three different phase space geometries (planar, hyperbolic or spherical) and exhibits an infinite number of coexisting stable periodic orbits which appear to ‘pack’ the phase space with circular resonances.

The influence of joint position on the dynamics of perception-action coupling

Six right-handed subjects performed rhythmic flexion and extension movements of the index finger in time with an auditory metronome. On each block of trials, the wrist of the response hand was placed in a extended, neutral or flexed position. In the flex-on-the-beat condition, subjects were instructed to coordinate maximum excursion in the direction of finger flexion with each beat of the metronome. In the extend-on-the-beat condition, subjects were instructed to coordinate maximum excursion in the direction of finger extension with each beat of the metronome. The frequency of the metronome was increased from 2.00 Hz to 3.75 Hz in 8 steps (8 s epochs) of 0.25 Hz. During trials prepared in the extend-on-the-beat pattern, all subjects exhibited transitions to either a flex-on-the-beat pattern or to phase wandering as the frequency of pacing was increased. The time at which these transitions occurred was reliably influenced by the position of the wrist. Four subjects exhibited qualitative departures from the flex-on-the-beat pattern at pacing frequencies that were greater than those at which the extend-on-the-beat pattern could be maintained. The lime at which these departures occurred was not influenced by the position of the wrist. These results are discussed with reference to the constraints imposed on the coordination dynamics by the intrinsic properties of the neuromuscular-skeletal system.

Antipronation taping and temporary orthoses - Effects on tibial rotation position after exercise

Abnormal lower-limb biomechanics-in particular, abnormal pronation of the subtalar joint with concomitant increased internal rotation of the tibia-is one of the major causes of overuse injuries of the lower limb. A randomized, controlled, within-subjects research design (N = 14) was used to investigate the effect of a temporary felt orthosis and an antipronation taping technique to control the transverse tibial rotation position immediately after application and after each of two 10-minute periods of exercise. The results showed that the taping technique was superior to both the orthosis and no intervention in controlling tibial rotation position immediately after application and after 10 minutes of exercise. After 20 minutes of exercise, neither the tape nor the orthosis was significantly superior to the control; however, the trends suggested that some residual control was maintained. Future studies are needed to determine the amount of foot pronation control required to relieve symptoms in a symptomatic population in order to determine the clinical effectiveness of these treatment methods.

Phylogenetic position of Chitinophaga pinensis in the Flexibacter-Bacteroides-Cytophaga phylum

Comparison of the 16S rRNA gene sequence determined for Chitinophaga pinensis showed that this species is most closely related to Flexibacter filiformis in the Flexibacter-Bacteroides-Cytophaga phylum, These two chitinolytic bacteria, which are characterized by transformation into spherical bodies on ageing, belong to a strongly supported lineage that also includes Cytophaga arvensicola, Flavobacterium ferrugineum and Flexibacter sancti, The lineage is distinct from the microcyst-forming species Sporocytophaga myxococcoides.

On S-asymptotically omega-periodic functions on Banach spaces and applications

This paper is devoted to the study of the class of continuous and bounded functions f : [0, infinity] -> X for which exists omega > 0 such that lim(t ->infinity) (f (t + omega) - f (t)) = 0 (in the sequel called S-asymptotically omega-periodic functions). We discuss qualitative properties and establish some relationships between this type of functions and the class of asymptotically omega-periodic functions. We also study the existence of S-asymptotically omega-periodic mild solutions of the first-order abstract Cauchy problem in Banach spaces. (C) 2008 Elsevier Inc. All rights reserved.