Floquet multipliers and the stability of periodic linear differential equations: a unified algorithm and its computer realization

Floquet multipliers (characteristic multipliers) play significant role in the stability of the periodic equations. Based on the iterative method, we provide a unified algorithm to compute the Floquet multipliers (characteristic multipliers) and determine the stability of the periodic linear differential equations on time scales unifying discrete, continuous, and hybrid dynamics. Our approach is based on calculating the value of A and B (see Theorem 3.1), which are the sum and product of all Floquet multipliers (characteristic multipliers) of the system, respectively. We obtain an explicit expression of A (see Theorem 4.1) by the method of variation and approximation theory and an explicit expression of B by Liouville's formula. Furthermore, a computer program is designed to realize our algorithm. Specifically, you can determine the stability of a second order periodic linear system, whether they are discrete, continuous or hybrid, as long as you enter the program codes associated with the parameters of the equation. In fact, few literatures have dealt with the algorithm to compute the Floquet multipliers, not mention to design the program for its computer realization. Our algorithm gives the explicit expressions of all Floquet multipliers and our computer program is based on the approximations of these explicit expressions. In particular, on an arbitrary discrete periodic time scale, we can do a finite number of calculations to get the explicit value of Floquet multipliers (see Theorem 4.2). Therefore, for any discrete periodic system, we can accurately determine the stability of the system even without computer! Finally, in Section 6, several examples are presented to illustrate the effectiveness of our algorithm

Techniques d'imagerie radar pour la caractérisation et le diagnostic des chaussées

This work concerns 3-D tomographic imaging with Ground-Based Synthetic Aperture Radar (GB-SAR) for in situ pavement defect detection. A side-looking bistatic GB-SAR operated in forward-scattering (FSC) mode characterized by a high Signal-to-Noise Ratio (SNR) and constant vertical resolution is proposed. Tomographic focusing is introduced to solve the ground-range ambiguity and improve the resolution by using an additional vertical aperture. A Constant Offset Sliding Bistatic (COSBis) SAR configuration operated in the FSC mode is proposed, which reduces the system complexity to a minimal level by using a single pair of Tx and Rx antennas, leading to an improved ground-range resolution, through focusing along an angular aperture created by the horizontal motion. Experimental results demonstrate the capability of the proposed mode for detecting artificial defects, and characterizing detailed features by employing polarimetric diversity. High-resolution techniques are applied to COSBis approach to refine roadway diagnosis. The innovative GB-SAR configuration, coupled with high-resolution imaging techniques, proves a good potential for roadway inspection and maintenance.Ce travail concerne l'imagerie tomographique 3-D par Radar à Synthèse d'Ouverture de terrain (GB-SAR) pour la détection in situ des défauts de chaussée.Un GB-SAR bistatique à visée latérale, fonctionnant en mode de propagation vers l'avant (FSC), caractérisé par un rapport Signal sur Bruit (SNR) élevé et une résolution verticale constante, est proposé. Une focalisation tomographique utilisant une ouverture dans la direction verticale est introduite pour résoudre l'ambiguïté et améliorer la résolution en distance au sol. Une configuration SAR bistatique FSC à déplacement horizontal et à décalage constant (COSBis), est proposée afin de réduire la complexité du système à un niveau minimal, en utilisant une seule paire d'antennes Tx et Rx, et qui permet d'obtenir une résolution en distance au sol améliorée par focalisation sur une ouverture angulaire générée par le mouvement horizontal. Les résultats expérimentaux démontrent la capacité du mode proposé à détecter des défauts artificiels et à caractériser des détails fins en utilisant une diversité de polarisation. Des techniques d'analyse spectrale à haute résolution sont appliquées à l'approche COSBis pour affiner le diagnostic routier. Cette configuration innovante de GB-SAR, associée à des techniques d'imagerie à haute résolution, démontre un fort potentiel pour l'inspection et la maintenance des chaussées

The eigenvector-eigenvalue identity for the quaternion matrix with its algorithm and computer program

Peter Denton, Stephen Parke, Terence Tao and Xining Zhang [arxiv 2019] presented a basic and important identity in linear commutative algebra, so-called {\bf the eigenvector-eigenvalue identity} (formally named in [BAMS, 2021]), which is a convenient and powerful tool to succinctly determine eigenvectors from eigenvalues. The identity relates the eigenvector component to the eigenvalues of $A$ and the minor $M_j$, which is formulated in an elegant form as $$\lvert v_{i,j} \rvert^2\prod_{k=1;k\ne i}^{n-1}({\lambda_i}(A)-{\lambda_k}(A))=\prod_{k=1}^{n-1}({\lambda_i}(A)-{\lambda_k}(M_j)). \,\,\,$$ In fact, it has been widely applied in various fields such as numerical linear algebra, random matrix theory, inverse eigenvalue problem, graph theory, neutrino physics and so on. In this paper, we extend the eigenvector-eigenvalue identity to the quaternion division ring, which is non-commutative. A version of eigenvector-eigenvalue identity for the quaternion matrix is established. Furthermore, we give a new method and algorithm to compute the eigenvectors from the right eigenvalues for the quaternion Hermitian matrix. A program is designed to realize the algorithm to compute the eigenvectors. An open problem ends the paper. Some examples show a good performance of the algorithm and the program

Comparison of Imaging Radar Configurations for Roadway Inspection and Characterization

This paper investigates the performance of a wide variety of radar imaging modes, such as nadir-looking B-scan, or side-looking synthetic aperture radar tomographic acquisitions, performed in both back- and forward-scattering geometries, for the inspection and characterization of roadways. Nadir-looking B-scan corresponds to a low-complexity mode exploiting the direct return from the response, whereas side-looking configurations allow the utilization of angular and polarimetric diversity in order to analyze advanced features. The main objective of this paper is to evaluate the ability of each configuration, independently of aspects related to operational implementation, to discriminate and localize shallow underground defects in the wearing course of roadways, and to estimate key geophysical parameters, such as roughness and dielectric permittivity. Campaign measurements are conducted using short-range radar stepped-frequency continuous-waveform (SFCW) devices operated in the C and X bands, at the pavement fatigue carousel of Université Gustave Eiffel, over debonded areas with artificial defects. The results indicate the great potential of the newly proposed forward-scattering tomographic configuration for detecting slight defects and characterizing roadways. Case studies, performed in the presence of narrow horizontal heterogeneities which cannot be detected using classical B-scan, show that both the coherent integration along an aperture using the back-projection algorithm, and the exploitation of scattering mechanisms specific to the forward-looking bistatic geometry, allows anomalous echoes to be detected and further characterized, confirming the efficacy of radar imaging techniques in such applications

3D SAR imaging using bistatic opposite side acquisitions, the bizona concept

International audienceThis paper proposes a new three dimensional imaging mode, called Bizona, based on acquisitions performed in a forward-looking bistatic configuration,. It is shown that spatial diversity using several transmitting, or receiving, positions permit to overcome some ambiguities and lack of sensitivity in the horizontal direction of such geometrical configurations, and that the Bizona mode is characterized by a higher power budget and a natural ability to discriminate scatterers located at different heights. The performance of this imaging principle is assessed using both simulated and measured signal

Evaluation of PHBHHx and PHBV/PLA fibers used as medical sutures

Two types of fibers were prepared by using bio-based materials: a mono-filament made from poly(3-hydroxybutyrate-co-3-hydroxyhexanoate) (PHBHHx) and a multi-filament made from poly(3-hydroxybutyrate-co-3-hydroxyvalerate) (PHBV) and polylactic acid (PLA) blend. The two fibers were evaluated for mechanical properties, biocompatibility and degradability for the potential application as medical sutures. The PHBHHx fiber showed remarkable biocompatibility by H.E. Stainning, with very little impact to the surrounding tissues. The degradation of the fiber was observed by SEM after implantation for 36 weeks, and the major degradation product was detected after 96 weeks. Consistently, the PHBHHx fiber maintained more than half of the mechanical properties after 96 weeks. The other fiber was prepared by twisting PHBV/PLA blend strands to a bunch, and showed high biocompatibility and relatively high degradability. The bunched structure loosed after 36 weeks of implantation. These low-cost and easily prepared fibers have great potential in medical applications, since they could avoid the formation of fibrous capsule, reduce the size of scar, and degrade into non-toxic and even beneficial products

Thermal phonon modulation of III-nitride semiconductors under strong electric fields

Self-heating effects in high-power III-nitride semiconductor electronics and optoelectronic devices limit their practical applications, while phonon modulation can be used to alleviate heat dissipation problems. In this paper, we report our efforts to suppress macroscopic polarization fields when applying strong electric fields, which affect the phonon frequency. We investigate alterations in phonon frequencies for two materials, 2H-GaN and 2H-AlN, for various electric field strengths ranging from 0.00 V/Å to 0.07 V/Å and 0.00 V/Å to 0.18 V/Å, respectively. We also analyze the changes in the macroscopic dielectric tensor and the BORN effective charge tensor. The calculation results reveal that the vibration frequencies of the longitudinal-optical (LO) A1(LO) mode are decreased by approximately 2 cm−1 for 2H-GaN and 3 cm−1 for 2H-AlN. Our simulation results are consistent with the Raman spectroscopy results of Si-doped 2H-GaN specimens illuminated with 325 nm excitation for a variety of carrier concentrations. This study contributes to a better understanding of the factors influencing phonon behavior, thus offering new methods for optimizing the thermal regulation and dissipation patterns of III-nitride semiconductor materials and devices

Determination of Narrow Coal Pillar Width and Roadway Surrounding Rock Support Technology in Gob Driving Roadway

In order to determine the rational width of coal pillars and study the surrounding rock control technology of gob side entry driving with a narrow coal pillar, this paper first calculates the width of narrow coal pillar according to limit equilibrium theory; after that, the lateral support pressure and plastic zone development of the goaf is analyzed by numerical simulation to determine the rational width of reserved coal pillar; finally, through the ring breaking deformation regulation of surrounding rock of the gob side entry, the deformation and failure characteristics of the gob-side roadway during excavation and the influence of mining on the deformation and failure of the gob-side roadway are analyzed. The research results show that, combined with theoretical analysis and numerical simulation, the width of narrow coal pillar is decided to be 10 m; the deformation of the coal pillar side of the gob side roadway is much bigger than the roof subsidence, the deformation of the solid coal wall and the floor deformation; after the bolt support design of the gob side roadway, the deformation and damage of the gob side roadway during the driving period is small; during mining, the deformation of the narrow coal pillar wall is the key factor to determine the stability of the gob roadway; under the bolt support scheme, the overall deformation and failure of surrounding rock of the goaf roadway is small, and the control effect of the surrounding rock of the goaf roadway is good

Impact of inner ear malformation and cochlear nerve deficiency on the development of auditory-language network in children with profound sensorineural hearing loss

Profound congenital sensorineural hearing loss (SNHL) prevents children from developing spoken language. Cochlear implantation and auditory brainstem implantation can provide partial hearing sensation, but language development outcomes can vary, particularly for patients with inner ear malformations and/or cochlear nerve deficiency (IEM&CND). Currently, the peripheral auditory structure is evaluated through visual inspection of clinical imaging, but this method is insufficient for surgical planning and prognosis. The central auditory pathway is also challenging to examine in vivo due to its delicate subcortical structures. Previous attempts to locate subcortical auditory nuclei using fMRI responses to sounds are not applicable to patients with profound hearing loss as no auditory brainstem responses can be detected in these individuals, making it impossible to capture corresponding blood oxygen signals in fMRI. In this study, we developed a new pipeline for mapping the auditory pathway using structural and diffusional MRI. We used a fixel-based approach to investigate the structural development of the auditory-language network for profound SNHL children with normal peripheral structure and those with IEM&CND under 6 years old. Our findings indicate that the language pathway is more sensitive to peripheral auditory condition than the central auditory pathway, highlighting the importance of early intervention for profound SNHL children to provide timely speech inputs. We also propose a comprehensive pre-surgical evaluation extending from the cochlea to the auditory-language network, showing significant correlations between age, gender, Cn.VIII median contrast value, and the language network with post-implant qualitative outcomes