Global Geometry of 3-Body Motions with Vanishing Angular Momentum Ⅰ

Following Jacobi's geometrization of Lagrange's least action principle, trajectories of classical mechanics can be characterized as geodesics on the configuration space M with respect to a suitable metric which is the conformal modification of the kinematic metric by the factor (U h), where U and h are the potential function and the total energy, respectively.In the special case of 3-body motions with zero angular momentum, the global geometry of such trajectories can be reduced to that of their moduli curves, which record the change of size and shape, in the moduli space of oriented m-triangles, whose kinematic metric is, in fact, a Riemannian cone over the shape space M* ～- S2 (1/2).In this paper, it is shown that the moduli curve of such a motion is uniquely determined by its shape curve (which only records the change of shape) in the case of h ≠ 0, while in the special case of h = 0 it is uniquely determined up to scaling. Thus, the study of the global geometry of such motions can be further reduced to that of the shape curves, which are time-parametrized curves on the 2-sphere characterized by a third order ODE. Moreover,these curves have two remarkable properties, namely the uniqueness of parametrization and the monotonicity, that constitute a solid foundation for a systematic study of their global geometry and naturally lead to the formulation of some pertinent problems.     

The projected GSURE for automatic parameter tuning in iterative shrinkage methods

Linear inverse problems are very common in signal and image processing. Many algorithms that aim at solving such problems include unknown parameters that need tuning. In this work we focus on optimally selecting such parameters in iterative shrinkage methods for image deblurring and image zooming. Our work uses the projected Generalized Stein Unbiased Risk Estimator (GSURE) for determining the threshold value λ and the iterations number K in these algorithms. The proposed parameter selection is shown to handle any degradation operator, including ill-posed and even rectangular ones. This is achieved by using GSURE on the projected expected error. We further propose an efficient greedy parameter setting scheme, that tunes the parameter while iterating without impairing the resulting deblurring performance. Finally, we provide extensive comparisons to conventional methods for parameter selection, showing the superiority of the use of the projected GSURE.     

Optimization of a quarter-car suspension model coupled with the driver biomechanical effects

In this paper a Human-Vehicle-Road (HVR) model, comprising a quarter-car and a biomechanical representation of the driver, is employed for the analysis. Differential equations are provided to describe the motions of various masses under the influence of a harmonic road excitation. These equations are, subsequently, solved to obtain a closed form mathematical expression for the steady-state vertical acceleration measurable at the vehicle-human interface. The solution makes it possible to find optimal parameters for the vehicle suspension system with respect to a specified ride comfort level. The quantitative definition given in the ISO 2631 standard for the ride comfort level is adopted in this paper for the optimization procedure. Numerical examples, based on actually measured road profiles, are presented to prove the validity of the proposed approach and its suitability for the problem at hand.     

Line-laser-based yarn shadow sensing break sensor

In this paper, a line-laser-based yarn break sensor is proposed. In the proposed sensor, yarns are illuminated by a line laser placed on one side of the yarn plane. A screen is placed on the other side and the image formed on the screen is detected by a camera. The total number of yarns is compared with the total number of shadows formed by the yarns or the total number of light spots formed due to the distances between yarns. If the total number of yarns to be detected is greater than the total number of shadows or light spots formed due to the distances between the yarns, the sensor warns of breaking. In the proposed method, evaluation is made using only light spots or shadows formed by the yarns. Consequently, the yarn type, structure, color, or dimensions do not affect the results.Design principles of the line-laser-based yarn break sensor, which consists of a screen and a Charged Coupled Device (CCD) camera, are presented. The screen displays the shadows formed by the yarns and the light spots formed due to the distances between them. The CCD camera detects the image on the screen. Formation of the shadows by the yarns is explained and an analytical formula that expresses the dimensions of the shadows is obtained. The detection area of the sensor is expressed relative to the total number of yarns, yarn thickness, and distances between the yarns. Line laser radiation angle and light spot intensity equations are obtained relative to the width of the detection area and the height of the line laser placement. The screen length is obtained relative to the number of yarns and the placement of the laser, the yarn plane, and the screen.Different placement situations of the line laser (transmitter), the screen, and the CCD camera (receiver) relative to the yarn plane are discussed. An experimental setup is developed to test the system. The image formed on the screen is studied.     

Syntheses,Structures, and Comprehensive NMR Spectroscopic Investigations of Hetero‐Chalcogenidometallates: The Right Mix toward Multinary Complexes

Library of semiconductors : Mixtures of binary chalcogenidostannate anions in protic solution show statistic chalcogenide exchange (see scheme), which is examined by comprehensive NMR investigations, DFT calculations and chemical reactions. A simple approach is provided to generate a library of semiconductor compounds with finely tuned opto‐electronic properties.

     

Radical scavenging efficiency of different fullerenes C60-C70 and fullerene soot

This investigation was undertaken to determine the antioxidant activity of a range of fullerenes C₆₀ and C₇₀ in order to rank them according to their comparative efficiency. The model reaction of initiated (2,2′- azobisisobutyronitrile, AIBN) cumene oxidation was used to determine rate constants for addition of radicals to fullerenes. Measurements of oxidation rates in the presence of different fullerenes showed that the antioxidant activity as well as the mechanism and mode of inhibition were different for fullerenes C₆₀ and C₇₀ and fullerene soot. All fullerenes - C₆₀ of gold grade, C₆₀/C₇₀ (93/7, mix 1), C₆₀/C₇₀ (80 ± 5/20 ± 5, mix 2) and C₇₀ operated as alkyl radical acceptora, whereas fullerene soot surprisingly retarded the model reaction by a dual mode similar to that for the fullerenes and with an induction period like many of the sterically hindered phenolic and amine antioxidants. For the C₆₀ and C₇₀ the oxidation rates were found to depend linearly on the reciprocal square root of the concentration over a sufficiently wide range thereby fitting the mechanism for the addition of cumylalkyl radicals to the fullerene core. This is consistent with literature data on the more ready and rapid addition of alkyl and alkoxy radicals to the fullerenes compared with peroxy radicals. Rate constants for the addition of cumyl radicals to the fullerenes were determined to be k_(333K) = (1.9 ± 0.2) × 10⁸ (C₆₀); (2.3 ± 0.2) × 10⁸ (C₆₀/C₇₀, mix 1); (2.7 ± 0.2) × 10⁸ (C₆₀/C₇₀, mix 2); (3.0 ± 0.3) × 10⁸ (C₇₀), M⁻¹ s⁻¹. The increasing C₇₀ constituent in the fullerenes leads to a corresponding increase in the rate constant.The fullerene soot inhibits the model reaction according to the mechanism of trapping of peroxy radicals; the oxidation proceeds with a pronounced induction period and kinetic curves are linear in semi-logarithmic coordinates.For the first time the effective concentration of inhibiting centres and inhibition rate constants for the fullerene soot have been determined to be fn[C₆₀−soot] = (2.0 ± 0.1) × 10⁻⁴ mol g⁻¹ and k_inh = (6.5 ± 1.5) × 10³ M⁻¹ s⁻¹ respectively.The kinetic data obtained specify the level of antioxidant activity for the commercial fullerenes and scope for their rational use in different composites. The results may be helpful for designing an optimal profile of composites containing fullerenes.     

The composite sorption material for radioiodine trapping from air stream and the method for its preparation

Journal of Radioanalytical and Nuclear Chemistry - Samples of a composite sorption material based on a highly porous polyurethane foam matrix with various pore sizes were obtained. Activated...     

GPS signal acquisition via compressive multichannel sampling

In this paper, we propose an efficient acquisition scheme for GPS receivers. It is shown that GPS signals can be effectively sampled and detected using a bank of randomized correlators with much fewer chip-matched filters than those used in existing GPS signal acquisition algorithms. The latter use correlations with all possible shifted replicas of the satellite-specific C/A code and an exhaustive search for peaking signals over the delay-Doppler space. Our scheme is based on the recently proposed analog compressed sensing framework, and consists of a multichannel sampling structure with far fewer correlators.The compressive multichannel sampler outputs are linear combinations of a vector whose support tends to be sparse; by detecting its support one can identify the strongest satellite signals in the field of view and pinpoint the correct code-phase and Doppler shifts for finer resolution during tracking. The analysis in this paper demonstrates that GPS signals can be detected and acquired via the proposed structure at a lower cost in terms of number of correlations that need to be computed in the coarse acquisition phase, which in current GPS technology scales like the product of the number of all possible delays and Doppler shifts. In contrast, the required number of correlators in our compressive multichannel scheme scales as the number of satellites in the field of view of the device times the logarithm of number of delay-Doppler bins explored, as is typical for compressed sensing methods.