Two explicit guard functions Kj = Kj(δz), j = 1, 2, are obtained, which depend on the distance δz between z and the nearest point of the integer lattice in the complex plane, such that δzK1(δz) ≤ |σ(z)|e−π|z|2/2 ≤ δzK2(δz), z ∈ C, where σ(z) stands for the Weierstraß σ-function. This result is used to improve the circular truncation error upper bound in the qth order Whittaker-type derivative s...

We explicitly determine the skew-symmetric eigenvectors and corresponding eigenvalues of the real symmetric Toeplitz matrices T = T (a, b, n) := (a+ b|j − k|)1≤j,k≤n of order n ≥ 3 where a, b ∈ R, b 6= 0. The matrix T is singular if and only if c := a b = −n−1 2 . In this case we also explicitly determine the symmetric eigenvectors and corresponding eigenvalues of T . If T is regular, we explic...

We study the vibrational properties near a free surface of disordered spring networks derived from jammed sphere packings. In bulk systems, without surfaces, it is well understood that such systems have a plateau in the density of vibrational modes extending down to a frequency scale ω*. This frequency is controlled by ΔZ = 〈Z〉 - 2d, the difference between the average coordination of the sphere...

The completeness of normal rational curves, considered as (q + 1)-arcs in PG(n, q), is investigated. Previous results of Storme and Thas are improved by using a result by Kovacs. This solves the problem completely for large prime numbers q and odd nonsquare prime powers q = p2h+l with p prime, p > po(h), h>\,1where po(h) is an odd prime number which depends on h.

We study nonlocal effects associated with particle collisions in dense suspension flows, in the context of the Affine Solvent Model, known to capture various aspects of the jamming transition. We show that an individual collision changes significantly the velocity field on a characteristic volume Ω_{c}∼1/δz that diverges as jamming is approached, where δz is the deficit in coordination number r...

We present a comparison between the published optical, IR and CO spectroscopic redshifts of 15 (sub-)mm galaxies and their photometric redshifts as derived from longwavelength (radio–mm–FIR) photometric data. The redshift accuracy measured for 12 sub-mm galaxies with at least one robustly-determined colour in the radio–mm–FIR regime is δz ≈ 0.30 (r.m.s.). Despite the wide range of spectral ener...

Acousto-optical coherence tomography (AOCT) is a variant of acousto-optic imaging (also called ultrasound modulated optical tomography) that makes possible to get resolution along the ultrasound propagation axis z. We present here AOCT experimental results, and we study how the z resolution depends on time step between phase jumps T(φ), or on the correlation length Δz. By working at low resolut...

Electrical impedance tomography (EIT) could provide images of fast neural activity in the adult human brain with a resolution of 1 ms and 1 mm by imaging impedance changes which occur as ion channels open during neuronal depolarization. The largest changes occur at dc and decrease rapidly over 100 Hz. Evoked potentials occur in this bandwidth and may cause artefactual apparent impedance changes...