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[en] Highlights: • We discuss two-dimensional superintegrable systems of Thompson's type separable in Cartesian coordinates. • Using the Chebyshev theorem on binomial differentials we express angle variables via elementary function of Cartesian coordinates. • Using addition of polynomial and rational functions we construct first integral of N-th order in momenta. • We present integrable deformation of the Fokas–Lagerstrom system with polynomial integral of motion of the sixth order in momenta. - Abstract: We continue the study of superintegrable systems of Thompson's type separable in Cartesian coordinates. An additional integral of motion for these systems is the polynomial in momenta of N-th order which is a linear function of angle variables and the polynomial in action variables. Existence of such superintegrable systems is naturally related to the famous Chebyshev theorem on binomial differentials.
[en] We have extended our analytically derived PDB-NMA formulation, Atomic Torsional Modal Analysis or ATMAN (Tirion and ben-Avraham 2015 Phys. Rev. E 91 032712), to include protein dimers using mixed internal and Cartesian coordinates. A test case on a 1.3 resolution model of a small homodimer, ActVA-ORF6, consisting of two 112-residue subunits identically folded in a compact 50 sphere, reproduces the distinct experimental Debye–Waller motility asymmetry for the two chains, demonstrating that structure sensitively selects vibrational signatures. The vibrational analysis of this PDB entry, together with biochemical and crystallographic data, demonstrates the cooperative nature of the dimeric interaction of the two subunits and suggests a mechanical model for subunit interconversion during the catalytic cycle. (paper)
[en] The sytem consists of an inverted U-shaped frame with right angled corners, so mounted that it can be adjusted verically, antero-posteriorly and made to rotate on an axis ('the axis of the frame') formed by its free ends. The frame carries an arc probe carrier whose probe holder slides on an arc which is centred on the axis of the frame. The centre of the probe holder and axis of fram lie in one plane 'The plane of probe'. After positioning the patient in the frame on the CT table, using either table indexing or laser positioning light, the plane of the probe is brought in the CT plane of the target. Once in this CT plane, direct measurements can be obtained so as to bring the axis of the frame passing through the target and centring the arc on the target. The frame can then be rotated to any desired angle and the probe holder can be moved to any position on the arc without altering the direction of the probe with respect to the target. As the structures in the probe plane are constructed of plastic, it can be used within the scanner with praactically no artifacts, and direct measurements can be obtained without any calculations. This system can be used in any total body scanner with standard features and no special computer programming is necessary. This is a simple and truly CT-oriented stereotactic system with a high degree of accuracy. (Author)
[en] An X-Y gas proportional counter has been built to measure the QDDD focal surface image size. It consists of two crossed independent stages with delay line cathode readout. Its intrinsic resolution for 8.8 MeV alphas is 0.3 mm FWHM in both directions
[fr]On a construit un compteur X-Y proportionnel a gaz pour mesurer la taille de l'image sur la surface focale du spectrometre QDDD. Il se compose de deux etages independants croises avec lecteur de cathode a ligne a retard. La resolution intrinseque pour des alphas de 8,8MeV est de 0,3mm a mi-hauteur dans les deux directions
[en] We analyze the concept of a nondegenerate superintegrable system in n-dimensional Euclidean space. Attached to this idea is the notion that every such system affords a separation of variables in one of the various types of generic elliptical coordinates that are possible in complex Euclidean space. An analysis of how these coordinates are arrived at in terms of their expression in terms of Cartesian coordinates is presented in detail. The use of well-defined limiting processes illustrates just how all these systems can be obtained from the most general nondegenerate superintegrable system in n-dimensional Euclidean space. Two examples help with the understanding of how the general results are obtained
[en] We study analytically and numerically ‘accessible’ spatiotemporal solitons in a three-dimensional strongly nonlocal nonlinear medium. A general localized soliton solution of the ‘acceptable’ type is obtained in the Cartesian coordinates, using even and odd parabolic-cylinder functions. Characteristics of these accessible spatiotemporal solitons are discussed. The validity of the analytical solutions and their stability is verified by means of direct numerical simulations. (paper)
[en] Trajectory planning schemes generally interpolate or approximate the desired path by a class of polynomial functions and generate a sequence of time based control set points for the control of the manipulator movement from certain initial configuration to final configuration. Schemes for trajectory generation can be implemented in Joint space and in Cartesian space. This paper describes Joint Space trajectory schemes and Cartesian Space trajectory schemes and their implementation for Infomate, a six degrees of freedom serial link robot manipulator. LSPBs and cubic Spline are chosen as interpolating functions of time for each type of schemes. Modules developed have been incorporated in an OLP system for Infomate. Trajectory planning Schemes discussed in this paper incorporate the constraints of velocities and accelerations of the actuators. comparison with respect to computation and motion time is presented for above mentioned trajectory schemes. Algorithms have been developed that enable the end effector to follow a straight line; other paths like circle, ellipse, etc. can be approximated by straight line segments. (author)
[en] A method for implementing cylindrical coordinates in the Athena magnetohydrodynamics (MHD) code is described. The extension follows the approach of Athena's original developers and has been designed to alter the existing Cartesian-coordinates code as minimally and transparently as possible. The numerical equations in cylindrical coordinates are formulated to maintain consistency with constrained transport (CT), a central feature of the Athena algorithm, while making use of previously implemented code modules such as the Riemann solvers. Angular momentum transport, which is critical in astrophysical disk systems dominated by rotation, is treated carefully. We describe modifications for cylindrical coordinates of the higher-order spatial reconstruction and characteristic evolution steps as well as the finite-volume and CT updates. Finally, we present a test suite of standard and novel problems in one, two, and three dimensions designed to validate our algorithms and implementation and to be of use to other code developers. The code is suitable for use in a wide variety of astrophysical applications and is freely available for download on the Web.