Geometry of rank 2 distributions with nonzero Wilczynski invariants

In the famous 1910 “cinq variables” paper Cartan showed in particular that for maximally nonholonomic rank 2 distributions in ?⁵ with non-zero covariant binary biquadratic form the dimension of the pseudo-group of local symmetries does not exceed 7 and among such distributions he described the one-parametric family of distributions for which this pseudo-group is exactly 7-dimensional. Using the novel interpretation of the Cartan covariant binary biquadratic form via the classical Wilczynski invariant of curves in projective spaces associated with abnormal extremals of the distributions [4, 27, 28] one can generalize this Cartan result to rank 2 distributions in ?ⁿ satisfying certain genericity assumption, called maximality of class, for arbitrary n ≥ 5.

In the present paper for any rank 2 distribution of maximal class with at least one nonvanishing generalized Wilczynski invariants we construct the canonical frame on a (2n — 3)-dimensional bundle and describe explicitly the moduli spaces of the most symmetric models. The relation of our results to the divergence equivalence of Lagrangians of higher order is given as well.     

A perturbed martingale approach to global optimization

A new global stochastic search, guided mainly through derivative-free directional information computable from the sample statistical moments of the design variables within a Monte Carlo setup, is proposed. The search is aided by imparting to the directional update term additional layers of random perturbations referred to as ‘coalescence’ and ‘scrambling’. A selection step, constituting yet another avenue for random perturbation, completes the global search. The direction-driven nature of the search is manifest in the local extremization and coalescence components, which are posed as martingale problems that yield gain-like update terms upon discretization. As anticipated and numerically demonstrated, to a limited extent, against the problem of parameter recovery given the chaotic response histories of a couple of nonlinear oscillators, the proposed method appears to offer a more rational, more accurate and faster alternative to most available evolutionary schemes, prominently the particle swarm optimization.     

Measurement of the structure coefficient of refractive index fluctuations in a turbulent premixed butane-air flame by means of a laser-based interferometer technique

With a view to measuring the structure coefficient of refractive index fluctuations in a turbulent premixed butane-air flame, a thin laser beam is sent into the flame perpendicular to the flow direction. The laser beam generally undergoes fluctuations of direction, phase, and amplitude. Only the random deflections of the laser beam may be taken into account. After having traversed the flame, the perturbed laser beam enters into an interferometric system. Materials and experimental procedure are described. In the unperturbed interference pattern, the zones only sensitive to fluctuations of the angle-of-arrival of the laser beam are detected. From the random displacements of the central bright fringe, the structure coefficient of refractive index fluctuations in the flame is measured. To prove that the method of measurement is satisfactory, the result obtained is applied for computing the power spectral density of the angle-of-arrival of the laser beam from the formula of correlations of the laser beam deflection angles which we have demonstrated in previous works. This computed power spectral density is compared to that measured from the effective position of the detector. A good agreement is observed between the two results.     

Novikov algebras carrying an invariant Lorentzian symmetric bilinear form

In this note, we shall classify Novikov algebras that admit an invariant Lorentzian symmetric bilinear form.     

Assessment of different fixation protocols on the presence of membrane-bound vesicles in Caco-2 cells: A multidimensional view by means of correlative light and 3-D transmission electron microscopy

Herein, we present a comparative analysis of a variety of chemical and physical fixation protocols for the specific visualisation of the membrane-bound vesicles (MBVs) in the Caco-2 colorectal cancer (CRC) cell line. In so doing, we validated the applicability of specific specimen preparation protocols for the preservation and contrasting of membrane-associated vesicles. Next, by employing the best respective chemical (GOT) and physical (SHPF) fixation methods for the application of transmission electron tomography and modelling we were able to characterise MBVs in three-dimensions and at the nanometer scale. In the second part of this study, we employ a correlative light and electron microscopy (CLEM) approach in order to determine which vesicular compartments are implicated in the uptake of FITC-BSA as a model protein drug. In so doing, we provide a solid foundation for future studies investigating chemotherapeutic drug uptake, transport and fate in cancer cell lines.     

Detection on micro-Doppler effect based on 1550 nm laser coherent radar

A laser coherent detection system of 1550 nm wavelength was presented, and experimental research on detecting micro-Doppler effect in a dynamic target was developed. In this paper, the return signal in the time domain is decomposed into a set of components in different wavelet-scales by multi-resolution analysis, and the components are associated with the vibrational motions in a target. The micro-Doppler signatures are extracted by applying the reconstruction (inverse wavelet transform). During the course of the final data processing frequency analysis and time–frequency analysis are applied to analyze the vibrational signals and estimate the motion parameters successfully. The experimental results indicate that the micro-Doppler information in a moving can be effectively detected, and tiny vibrational signatures also can be acquired effectively by wavelet multi-resolution analysis and time–frequency analysis.     

Modeling and simulation of vibrational breathing-like modes in individual multiwalled carbon nanotubes

We study the collective vibrational breathing modes in the Raman spectrum of multiwalled carbon nanotubes (MCNTs). First, a bond polarization theory and the spectral moment's method (SMM) are used to calculate the non-resonant Raman frequencies of the breathing-like modes (BLMs) and the tangential-like ones (TLMs). Second, the Raman active modes of MCNTs are computed for different diameters and numbers of layers. The obtained low frequency modes in MCNTs can be identified to each single-walled carbon nanotubes. These modes that originate from the radial breathing ones of the individual walls are strongly coupled through the concentric tube–tube van der Waals interaction. The calculated BLMs in the low-frequency region are compared with the experimental Raman data obtained from other studies. Finally, special attention is given to the comparison with Raman data on MCNTs composed of six layers.     

电容温度传感器的实验研究

从液氮温度到水的沸点温度范围内,测量了介质分别为钽,涤纶,陶瓷,玻璃釉和陶瓷独石一体化结构的商用固体电容器的电容量-温度之间的关系.拟合测量结果表明,独石陶瓷电容器在正温度段具有较好的线性响应(-10pF/℃),灵敏度(0.1 ℃)和精确度(标准差为0.016);而涤纶电容器在负温度段的特性较好( 17pF/℃,0.06 ℃和0.01).此外,在约0.5特斯拉的恒定磁场作用下,无论在正或负温度段,上述测得的电容量-温度关系几乎不受影响.因此,本研究对开发抗强电磁场,自加热效应小或导热系数小的低温测温器具有较大的参考价值.