Search

We introduce a notion of regular separation for solutions of systems of ODEs y' = F(x, y), where F is definable in a polynomially bounded o-minimal structure and y = (y1, y2). Given a pair of solutions with flat contact, we prove that, if one of them has the property of regular separation, the pair is either interlaced or generates a Hardy field. We adapt this result to trajectories of three-dimensional vector fields with definable coefficients. In the particular case of real analytic vector fields, it improves the dichotomy interlaced/separated of certain integral pencils, obtained by F. Cano, R. Moussu and the third author. In this context, we show that the set of trajectories with the regular separation property and asymptotic to a formal invariant curve is never empty and it is represented by a subanalytic set of minimal dimension containing the curve. Finally, we show how to construct examples of formal invariant curves which are transcendental with respect to subanalytic sets, using the so-called (SAT) property, introduced by J.-P. Rolin, R. Shaefke and the third author. [ABSTRACT FROM AUTHOR]

Given a collection |$\mathcal {A}$| of holomorphic functions, we consider how to describe all the holomorphic functions locally definable from |$\mathcal {A}$|⁠. The notion of local definability of holomorphic functions was introduced by Wilkie, who gave a complete description of all functions locally definable from |$\mathcal {A}$| in the neighbourhood of a generic point. We prove that this description is no longer complete in the neighbourhood of non-generic points. More precisely, we produce three examples of holomorphic functions that suggest that at least three new operations need to be added to Wilkie's description in order to capture local definability in its entirety. The constructions illustrate the interaction between resolution of singularities and definability in the o-minimal setting. [ABSTRACT FROM AUTHOR]

Let ξ be an analytic vector field at (ℝ³, 0) and I be an analytically non-oscillatory integral pencil of ξ; i.e., I is a maximal family of analytically non-oscillatory trajectories of ξ at 0 all sharing the same iterated tangents. We prove that if I is interlaced, then for any trajectory Γ ∈ I, the expansion ℝan,Γ of the structure ℝan by Γ is model-complete, o-minimal and polynomially bounded. [ABSTRACT FROM AUTHOR]

Decreasing turnaround time is a paramount objective in clinical diagnosis. We evaluated the discrimination power of Raman spectroscopy when analyzing colonies from 80 strains belonging to nine bacterial and one yeast species directly on solid culture medium after 24-h (macrocolonies) and 6-h (microcolonies) incubation. This approach, that minimizes sample preparation and culture time, would allow resuming culture after identification to perform downstream antibiotic susceptibility testing. Correct identification rates measured for macrocolonies and microcolonies reached 94.1% and 91.5%, respectively, in a leave-one-strain-out cross-validation mode without any correction for possible medium interference. Large spectral differences were observed between macrocolonies and microcolonies, that were attributed to true biological differences. Our results, conducted on a very diversified panel of species and strains, were obtained by using simple and robust sample preparation and preprocessing procedures, while still confirming published results obtained by using more complex elaborated protocols. Instrumentation is simplified by the use of 532-nm laser excitation yielding a Raman signal in the visible range. It is, to our knowledge, the first side-by-side full classification study of microorganisms in the exponential and stationary phases confirming the excellent performance of Raman spectroscopy for early species-level identification of microorganisms directly from an agar culture. [ABSTRACT FROM AUTHOR]

We give a version of the Łojasiewicz inequality for the real polynomials on non-compact domains. The inequality takes in account not only distance to a fiber, but also distance to a polar set. It improves the recent results of [D. S. Tiep, H. H. Vui and N. T. Thao, Łojasiewicz inequality for polynomial functions on non-compact domains, Int. J. Math. 23(4) (2012), Article ID: 1250033, 28 pp., doi:10.1142/S0129167X12500334], since we consider a distance to a smaller set. Then we use this new version of the inequality to obtain a sufficient condition for the existence of a vanishing component at infinity for real polynomials in several variables. [ABSTRACT FROM AUTHOR]

Introduces the CARTOGAM portable gamma camera, a detector used for gamma-imaging applications in nuclear facilities. Information on the design of the device; Description of a mode to improve the sensitivity of the camera; Illustration of the CARTOGAM gamma-imaging system.