über die Striktionslinien von einparametrigen Scharen linearer Räume

A generalisation of a ruled surface in n-dimensional euclidean space may be generated by euclidean motion of a s-plane A_s. For this one-parametric family {A_s} the curve of striction is defined and the following theorems are proved:

1. The generators A_s are parallel along the curve of striction, i.e. the multivectors representing A_s form a parallel vector field along the curve of striction.
2. If the curve of striction is geodesic on {A_s}, it is also an isogonal trajectory of the family of generators {A_s}.

     

A sub-nanosecond Synchronized MAC – PHY cross-layer design for Wireless Sensor Networks

In this paper, we present a Wireless Sensor node implementation which aims at solving two major issues in Wireless Sensor Networks. This solution provides nanosecond-scale synchronization between nodes and high data-rate transmission thanks to cross-layer design and the time-domain properties of UltraWide Band (UWB) modulation schemes. The high data rate is achieved through a specific implementation of a IR-UWB physical layer. Specific algorithms are also implanted into the MAC and physical layers and form a cross-layered synchronization protocol for deterministic Wireless Sensor Networks named WiDeCS (Wireless Deterministic Clock Synchronization). This protocol propagates master time reference to nodes of a cluster tree network. WiDeCS Cross layered scheme is possible thanks to flag signals rising in the physical layer. These signals, owing to the UWB time domain properties, capture precise timestamps of transmission and reception. Hardware level simulations show a clock synchronization precision of 2 ns with a 2 GHz bandwidth signal, and an ASIC demonstrator shows 374 ps synchronization precision and 677 ps of standard deviation with the same bandwidth. In this paper, the physical layer implementation is detailed, and the cross-layered WiDeCS scheme is demonstrated.     

Meromorphic Traveling Wave Solutions of the Complex Cubic-Quintic Ginzburg-Landau Equation

We look for singlevalued solutions of the squared modulus M of the traveling wave reduction of the complex cubic-quintic Ginzburg-Landau equation. Using Clunie??s lemma, we first prove that any meromorphic solution M is necessarily elliptic or degenerate elliptic. We then give the two canonical decompositions of the new elliptic solution recently obtained by the subequation method.     

Separable geodesic action slicing in stationary spacetimes

A simple observation about the action for geodesics in a stationary spacetime with separable geodesic equations leads to a natural class of slicings of that spacetime whose orthogonal geodesic trajectories represent the world lines of freely falling fiducial observers. The time coordinate function can then be taken to be the observer proper time, leading to a unit lapse function, although the time coordinate lines still follow Killing trajectories to retain the explicitly stationary nature of the coordinate grid. This explains some of the properties of the original Painlevé-Gullstrand coordinates on the Schwarzschild spacetime and their generalization to the Kerr-Newman family of spacetimes, reproducible also locally for the Gödel spacetime. For the static spherically symmetric case the slicing can be chosen to be intrinsically flat with spherically symmetric geodesic observers, leaving all the gravitational field information in the shift vector field.     

Suppressing one‐bond homonuclear 13C,13C scalar couplings in the J‐HMBC NMR experiment: application to 13C site‐specifically labeled oligosaccharides

Site‐specific ¹³C isotope labeling is a useful approach that allows for the measurement of homonuclear ¹³C,¹³C coupling constants. For three site‐specifically labeled oligosaccharides, it is demonstrated that using the J‐HMBC experiment for measuring heteronuclear long‐range coupling constants is problematical for the carbons adjacent to the spin label. By incorporating either a selective inversion pulse or a constant‐time element in the pulse sequence, the interference from one‐bond ¹³C,¹³C scalar couplings is suppressed, allowing the coupling constants of interest to be measured without complications. Experimental spectra are compared with spectra of a nonlabeled compound as well as with simulated spectra. The work extends the use of the J‐HMBC experiments to site‐specifically labeled molecules, thereby increasing the number of coupling constants that can be obtained from a single preparation of a molecule. Copyright © 2014 John Wiley & Sons, Ltd.