Compact operators without extended eigenvalues

A complex number lambda is called an extended eigenvalue of a bounded linear operator T on a Banach space B if there exists a non-zero bounded linear operator X acting on B such that XT = lambda TX. We show that there are compact quasinilpotent operators on a separable Hilbert space, for which the set of extended eigenvalues is the one-point set {1}.

Decay measures on locally compact abelian topological groups

Source: PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS Volume: 131 Pages: 1257-1273 Part: Part 6 Published: 2001 Times Cited: 5 References: 23 Citation MapCitation Map beta Abstract: We show that the Banach space M of regular sigma-additive finite Borel complex-valued measures on a non-discrete locally compact Hausdorff topological Abelian group is the direct sum of two linear closed subspaces M-D and M-ND, where M-D is the set of measures mu is an element of M whose Fourier transform vanishes at infinity and M-ND is the set of measures mu is an element of M such that nu is not an element of MD for any nu is an element of M \ {0} absolutely continuous with respect to the variation \mu\. For any corresponding decomposition mu = mu(D) + mu(ND) (mu(D) is an element of M-D and mu(ND) is an element of M-ND) there exist a Borel set A = A(mu) such that mu(D) is the restriction of mu to A, therefore the measures mu(D) and mu(ND) are singular with respect to each other. The measures mu(D) and mu(ND) are real if mu is real and positive if mu is positive. In the case of singular continuous measures we have a refinement of Jordan's decomposition theorem. We provide series of examples of different behaviour of convolutions of measures from M-D and M-ND.

On effective linearly ordered sets of comparison functions

Both the existence and the non-existence of a linearly ordered (by certain natural order relations) effective set of comparison functions (=dense comparison classes) are compatible with the ZFC axioms of set theory.

Mechanically tunable multiband compact quadrifilar helix antenna with dual mode operation

We show that by introducing a gap at the center of the helical sections (where the current is minimum) of a lambda/2 quadrifilar helix antenna (QHA) and varying the axial length and radial gap between the overlapping volutes, the antenna gives a 28% impedance bandwidth which is nine times the bandwidth of a conventional QHA. A 16% bandwidth with a front to back ratio of >= 14 dB is achievable with 5-14% reduction in the size of the QHA. The structure can yield a monopole radiation pattern suitable for terrestrial applications or a hemispherical pattern suitable for satellite use. The simulation results are validated by measurements at L-band.

Dual-mode compact structure comprising of side-fed bifilar and quadrifilar helix antenna

A side-fed bifilar helix antenna can be integrated with a quadrifilar helix antenna in a piggy back configuration in order to achieve a dual-mode radiating structure. The overall length of the structure is 0.44 lambda at the resonant frequency (1.54 GHz) of the space mode antenna and 0.39 lambda at the resonant frequency (1.34 GHz) of the terrestrial mode antenna. The computed results are validated by experimental data.

Compact quadrifilar helix antenna

Introduction: The quadrifilar helix antenna (QHA) is used widely for terrestrial [1] and space communication systems [2], where it is necessary to generate a circularly polarised cardioid-shaped radiation pattern with a high front-to-back ratio and low cross-polarisation. The radiating structure comprises four helical conductors which are excited in phase quadrature at the feed point, which is usually located at the centre of the top radials. The physical size of the quadrifilar antenna can be reduced by dielectric loading [3] or by meandering the printed linear elements [4]. However, in the former arrangement dielectric absorption reduces the radiation efficiency of the antenna, and the latter technique is not suitable for constructing free standing wire structures, which are normally used for spacecraft payloads in the VHF and UHF bands [2]. This Letter shows that a significant reduction in the axial length of a 1/2 turn half-wavelength QHA can be achieved by modifying the geometry of the helices in the region around the midpoint where a current null exists. Simulated and experimental results at L band are used to show that a size reduction of up to 15% is possible without significantly degrading the pattern shape and the bandwidth.

Support vector machine classification for large data sets via minimum enclosing ball clustering

Support vector machine (SVM) is a powerful technique for data classification. Despite of its good theoretic foundations and high classification accuracy, normal SVM is not suitable for classification of large data sets, because the training complexity of SVM is highly dependent on the size of data set. This paper presents a novel SVM classification approach for large data sets by using minimum enclosing ball clustering. After the training data are partitioned by the proposed clustering method, the centers of the clusters are used for the first time SVM classification. Then we use the clusters whose centers are support vectors or those clusters which have different classes to perform the second time SVM classification. In this stage most data are removed. Several experimental results show that the approach proposed in this paper has good classification accuracy compared with classic SVM while the training is significantly faster than several other SVM classifiers.

The rotational broadening of V395 Carinae. Implications on the compact object's mass

Context: The masses previously obtained for the X-ray binary 2S 0921-630 inferred a compact object that was either a high-mass neutron star or low-mass black-hole, but used a previously published value for the rotational broadening (v sin i) with large uncertainties. Aims: We aim to determine an accurate mass for the compact object through an improved measurement of the secondary star's projected equatorial rotational velocity. Methods: We have used UVES echelle spectroscopy to determine the v sin i of the secondary star (V395 Car) in the low-mass X-ray binary 2S 0921-630 by comparison to an artificially broadened spectral-type template star. In addition, we have also measured v sin i from a single high signal-to-noise ratio absorption line profile calculated using the method of Least-Squares Deconvolution (LSD). Results: We determine v sin i to lie between 31.3±0.5 km s-1 to 34.7±0.5 km s-1 (assuming zero and continuum limb darkening, respectively) in disagreement with previous results based on intermediate resolution spectroscopy obtained with the 3.6 m NTT. Using our revised v sin i value in combination with the secondary star's radial velocity gives a binary mass ratio of 0.281±0.034. Furthermore, assuming a binary inclination angle of 75° gives a compact object mass of 1.37±0.13 M_?. Conclusions: We find that using relatively low-resolution spectroscopy can result in systemic uncertainties in the measured v sin i values obtained using standard methods. We suggest the use of LSD as a secondary, reliable check of the results as LSD allows one to directly discern the shape of the absorption line profile. In the light of the new v sin i measurement, we have revised down the compact object's mass, such that it is now compatible with a canonical neutron star mass.

Compact ridge waveguide filter with parallel and series-coupled resonators

A novel 3rd-order compact E-plane ridge waveguide filter is presented. Miniaturization is achieved upon introducing a configuration of parallel-coupled E-plane ridge waveguide resonators. Furthermore, the proposed filter allows for transmission zeros at finite frequencies. Fabrication simplicity and mass producibility of standard E-plane filters is maintained. The numerical and experimental results are presented to validate the proposed configuration. A miniaturisation factor of 2 and very sharp upper cutoff are achieved. 2005 Wiley Periodicals, Inc.