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The method of least squares is developed for the optimum design of multi-section asymmetrical transdirectional (ATRD) couplers with arbitrary port impedance matching. Firstly, transmission matrix of a section of coupler is obtained, then the transmission matrix of whole multi-section coupler is determined, from which the scattering matrix of device is obtained. An error function is then constructed by scattering parameters. According to design specifications, error function depends on physical parameters of coupler (such as widths, spacings and lengths of transmission line sections and capacitor values), of which minimum point gives optimum values of it's dimensions and capacitors. Optimum design is carried out for a specified frequency response and bandwidth. Error minimization is implemented by the combination of genetic algorithm (GA) and conjugate gradient method (CGM). The design is verified by full-wave simulation software, fabrication and measurement. Several 3 dB, 6 dB and 10 dB couplers are designed with different bandwidths and port impedances. Compared to the proposed design method, design of asymmetrical multi-section couplers by full-wave simulation softwares is by trial and error and at best random and almost impossible because of extremely high CPU time due to the large number of parameters of coupler geometrical structure. [ABSTRACT FROM AUTHOR]

Polarization information can greatly improve the ability of detection, parameter retrieval, and classification for entomological radar. In recent, the instantaneous fully polarimetric measurement technique is used in entomological radar, so as to relax the restriction of invariant orientation during observation compared to the typical vertical-looking radar with linear-polarized rotation configuration. However, the fully polarimetric measurement is based on a multichannels’ radar system, and the imbalance and crosstalk between channels, namely, polarimetric errors, will severely affect the measurement of the polarimetric scattering matrix (PSM). Thus, polarimetric calibration is essential to obtain the accurate polarization information of targets. In contrast to inefficient and manual calibration methods, a data-driven polarimetric calibration method is proposed based on the assumption of reciprocity and bilateral symmetry of insects in this article. The polarimetric errors are elaborately decomposed into two components, which could be estimated by reciprocity and bilateral symmetry, respectively. In addition, because the proposed method is data-driven, the calibration process could be automatically executed to compensate for the temporal-variant polarimetric errors induced by temperature change and, thus, suitable for the long-term operation of entomological radar. Simulations and experiments are carried out to evaluate the performance of the proposed calibration method. Results show that it could achieve high accuracy when the number of insects used as calibrators is large enough. The proposed method has been applied in Ku-band high-resolution fully polarimetric entomological radars for cross-border migratory insect observation in Yunnan province, China. [ABSTRACT FROM AUTHOR]

Exploring polarimetric diversity of synthetic aperture radar (SAR) data is directly applicable to conventional monostatic cases. For this, the most used convention is the backscatter alignment. While establishing important advantages for the monostatic case (possibility to have equal values on the cross-polarimetric channels), it has been proven to introduce some difficulties for the bistatic case. This appears in relation to the so-called conjugate similarity operation, when (mathematically) asymmetric scattering matrices occur. In this article, we propose the detailed algorithm which provides a solution to the conjugate similarity operation, in the case of general scattering matrices. The proposed algorithm is based on the real representation (RR) matrix transformation. Furthermore, we investigate the characterization of canonical bistatic scatterers (three elementary targets). Raw bistatic polarimetric signals are obtained using simulations with a computationally electromagnetic (EM) software, capable of complete EM analysis. The eigenvalue classification illustrates the potential of additional information brought using the proposed RR scattering matrix (RRSM). The presence of complex eigenvalues is investigated in relation to the bistatic angle and one nonreciprocity parameter. [ABSTRACT FROM AUTHOR]

Ceramic additive manufacturing has been drawn massive attention as a novel processing for directly fabricating complex ceramic architectures. However, the uncured monomer causes defects in producing green body, debinding and sintering process in case of stereolithography. Therefore, high conversion of cured layer is required for the reliability and stability. Here, we report facilitation mechanisms of ceramic particles with acceleration and phase transition occuring in on-propagating matrix in suspension; scattering, free volume and micro-gel.. Scattering, lengthening the path of UV light, demonstrates higher efficiency of initiation confirmed with 1.6 times increased initial slope of heat flow. The free volume, securing the volumetric reaction site even in solidifying resin, indicates 0.45 times faster rate and two times rapider acceleration, respectively. Finally, micro-gel, generated as a result of steric hindrance between ceramic particles and glassified matrix with a prolonged diffusion, exhibits increase up to 26% in two phases systems. [ABSTRACT FROM AUTHOR]

Mining knowledge from imbalanced data is challenging due to the uneven distribution of classes and increasing dimensionality of data accumulated from real-life applications. Selecting informative features from imbalanced data is especially important for building an effective learning method. The global redundancy and the effect of imbalanced distribution need to be considered simultaneously. In this study, a feature selection method that considers the imbalanced distribution of classes in data is investigated by embedding the weighted constraint on the majority class into the global redundancy minimization GRM framework. Global redundancy minimization is acquired through an objective function that contains a feature redundancy matrix and feature scores. A new form of regularization to a within-class scatter matrix is first presented, which emphasizes the minority class and replaces the redundancy measurement approach. Then, after employing this new form of a within-class scatter matrix in GRM and taking the between-class distance as the GRM input score, a GRM-based discriminant feature selection algorithm (GRM-DFS) is proposed. Comparison studies on a within-class scatter matrix with different forms of regularization indicate that the proposed form of a within-class scatter matrix is effective when dealing with imbalanced data. Experiments on public imbalanced datasets are performed. The experimental results indicate that GRM-DFS is effective. [ABSTRACT FROM AUTHOR]

A method is developed for the analysis of an infinite cophased ultrawideband array consisting of TEM horns. The method is based on the theory of long lines. The methods of scattering matrices and conformal mapping are used for the determination of the characteristic impedance in each section of the infinite cophased array. The algorithm realizing the conformal mapping method is presented. The calculation results obtained with the use of the suggested technique and electromagnetic modeling in the ANSYS HFSS software environment are compared. [ABSTRACT FROM AUTHOR]

An adaptive beamforming method based on the polarimetric scattering matrix (PSM) of targets to suppress deceptive jamming located in the beam pattern main lobe is proposed in this study. For the netted radar system, the true/false mixed targets of different/same range ambiguity region are distinguished by the range-PSM dimension; the flexible allocation of antenna resource is realised by the number of estimated targets; the main-lobe deceptive jamming is also suppressed by the adaptive beamforming method. First, a polarimetric multiple-input multiple-output (MIMO) radar with a frequency diverse array (FDA) was considered as the initial antenna configuration. Subsequently, the performance of the transmit–receive spatial frequency was analysed, and the characteristics of false targets in the polarimetric FDA-MIMO radar were discussed. We then considered the optimisation problem between the transmit polarisation and the frequency increment, as well as the allocation of antenna resources. Finally, an adaptive beamforming method was utilised to achieve deceptive jamming suppression in the main lobe. The effectiveness of PSM was verified with respect to identifying true/false targets, and the jamming suppression performance was evaluated in the main lobe by comparing it with existing systems via simulation results. [ABSTRACT FROM AUTHOR]

This paper investigates the impact of interface angles on the coupling efficiency of a fiber Fabry-Perot interferometer (FFPI) sensor using both simulation and experimental methods. The FFPI sensor, which consists of a single-mode fiber (SMF), hollow-core fiber (HCF), and diaphragm, has its coupling efficiency determined by the generalized scattering matrix of the cascaded fiber system. To obtain the interface angles of the FFPI sensor, a new on-line monitoring system is developed based on microscopic images of the FFPI cavity and an image processing algorithm using OpenCV. By combining the eigenmode expansion method (EME) model and the online interface angle measurement technique, the coupling efficiency and spectral contrast of the FFPI cavity are evaluated and improved. Additionally, the corresponding working point in the intensity demodulation based FFPI sensor can be quickly identified. Using this method, an FFPI sensor with a spectral contrast of over 35 dB is achieved, which is significantly higher than existing similar sensors, and its sensitivity also reaches 50.80 mV/MPa. This work also holds significance for controlling and enhancing the spectral characteristics of other cascaded fiber optic sensors. • Advances FFPI fiber optic sensing to >35 dB spectral contrast & 50.80 mV/MPa pressure sensitivity. [ABSTRACT FROM AUTHOR]

Ultrasonic scattering matrices contain rich defect information and have great potential for characterising small crack-like defects. However, experimentally measured scattering matrices often exhibit some level of distortions compared to those of the idealised defects, posing challenges for accurate defect characterisation. In this paper, defect characterisation was performed by adopting a nearest neighbour approach based on a scattering matrix database of reference defects, and the test data were contaminated by coherent measurement noise of varying amplitudes. The performance of different similarity metrics on characterisation accuracy was studied, including the Euclidean similarity, cosine similarity, Pearson correlation coefficient, and the structural similarity index. Based on a comprehensive analysis of the strengths and weaknesses of different similarity metrics, we propose a defect characterisation framework by constructing similarity graphs and leveraging advanced graph neural networks. Within the proposed approach, multiple metrics were adopted to quantify the similarity between the scattering matrices of different defects, and an improved dynamic graph attention network was developed based on a customised neighbour sampling strategy to learn the optimal metric from the graph-structured data. Experimental results show that compared to the conventional approach which adopted a globally optimal similarity metric, the proposed method can reduce the root mean squared error for the length and angle predictions by 60.5% and 67.1%, respectively. • The scattering matrix was used for characterisation of small, inclined cracks. • Performance of various similarity metrics on characterisation accuracy was studied. • An improved graph attention network was developed to optimise the similarity metric. • A customised neighbour sampling strategy was adopted to process unseen data. [ABSTRACT FROM AUTHOR]

A three dimensional (3D) dual-band phase gradient metamaterial (PGM) is proposed based on the Pancharatnam-Berry phase approach in this work. First, a 3D dual-band co-polarization reflection metamaterial under circularly polarized (CP) wave incidence was achieved by a vertical metallic Split-Ring Resonator (SRR). The co-polarization reflection efficiency is more than 90% over the spectra 4.78 GHz–4.92 GHz and 11.2 GHz–12.8 GHz. The underlying physical mechanism for copolarization reflection is analyzed by using the scattering matrix approach. Then, the dual-band PGM is constructed by utilizing the vertical metallic SRR with different rotation angles. The PGM can achieve surface wave coupling and efficiently anomalous reflection, respectively, in the two spectra under CP wave incidence. Due to the opposite phase gradients for left-handed circularly polarized and right-handed circularly polarized wave incidence, the incidence linearly polarized wave was divided into two beams of CP waves and coupled into surface waves or anomalously reflected along opposite directions. Both the simulated and measured results demonstrated the great performances of dual-band PGMs. [ABSTRACT FROM AUTHOR]

We apply the spectral element method to the determination of scattering and bound states of the multichannel Schrodinger equation. In our approach, the reaction coordinate is discretized on a grid of points whereas the internal coordinates are described by either purely diabatic or locally diabatic (diabatic-by-sector) bases. Bound levels and scattering matrix elements are determined with spectral accuracy using relatively small number of points. The scattering problem is cast as a linear system solved using state-of-the-art sparse matrix non-iterative packages. Boundary conditions can be imposed so as to compute a single column of the matrix solution. A comparison with log-derivative propagators customarily used in molecular physics is performed. The same discretization scheme can also be applied to bound levels that are computed using direct scalable sparse-matrix solvers. [ABSTRACT FROM AUTHOR]

Experimental data on the narrowing of fluorescence spectra of laser-pumped random media are interpreted within the framework of a probabilistic model of incoherent amplification of the stimulated component of fluorescence. R6G- and DCM-doped layers of dense-packed anatase and anatase-rutile particles and suspensions of DCM crystallites were examined under pulse-periodic laser pumping with various pump intensities at the wavelength of 532 nm. It was shown that, in the case of quasi-stationary fluorescence response at high pump intensities, amplification of stochastically propagating partial components of fluorescence field at various wavelengths is governed by the pump-independent factor of fluorescence amplification and the average number of stimulated emission acts in the pumped system. Analysis of the experimental data has shown that, despite certain simplifying assumptions, the considered model reasonably describes evolution of the fluorescence spectra of random fluorescent media with the increase in the pump intensity. A procedure of recovery of the fluorescence amplification factor from the sets of fluorescence spectra obtained at various pump intensities is considered. Features of the spectral shapes of the recovered amplification factors caused by the influence of the scattering matrices in pumped media are discussed. • Fluorescence enhancement in random media is analyzed applying a probabilistic model. • The key model parameter is the wavelength-dependent fluorescence amplification factor. • The amplification factor is highly sensitive to fluorophore-matrix interactions. • Enhancement is limited by the saturated average number of stimulated emission acts. [ABSTRACT FROM AUTHOR]

We investigate the spectral properties of photonic crystals, lacking parity-time (PT) symmetry, using scattering matrix formalism. We show using the symmetry properties of matrices that a defective photonic crystal, doped with three-level atoms, breaks PT symmetry. For the two defect modes lying in the band gap region, both the reflection and the absorption become nonreciprocal, while the transmission remains reciprocal. We show that the relevant energy spectra do not exhibit exceptional points, thereby invalidating its necessity to achieve non-reciprocity in reflection and absorption. We further demonstrate how this non-reciprocity can be coherently controlled using the driving field and dissipation rates of the atoms. • Broken PT symmetry due to atomic doping of defect layer in photonic crystal system. • Reciprocal transmission while nonreciprocity in reflection and absorption. • Exceptional points, not necessary to exhibit nonreciprocity. • Energy spectra of the system exhibit phase transitions. • Control of optical properties of crystal, from nearly reciprocal to nonreciprocal. [ABSTRACT FROM AUTHOR]

In this paper, we present the class of linear models with errors belonging to the family of scale mixture of normal distributions, considering the reparameterization of the scatter matrix based on the Modified Cholesky Decomposition approach and that the mixing parameters of the model are deterministic but unknown and vary from each observation. Scoring functions and Hessian matrices are derived for the parameters of interest and an iterative process is proposed for parameter estimation. Some aspects of predicting new observations and robustness of maximum likelihood estimates are discussed, as well as the performance of different models with different structures for one of the parameters of the family of distributions used. The methodology is applied in an extensive comparative approach with synthetic and real data. Performance results and prediction of new observations show that the proposed model performs better compared to recent models based on Normal, Student-t and Laplace distributions. • A new approach to regression modeling for longitudinal data is presented using a class of linear models. • The scatter matrix parameterization is based on the Modified Cholesky Decomposition approach. • Deterministic and unknown mixing parameters are considered, which vary for each observation, for the distribution considered. • Some aspects of predicting new observations and robustness of maximum likelihood estimates are discussed • The performance and prediction results from new observations show that the proposed model performs better compared to recent models. [ABSTRACT FROM AUTHOR]

The erratum clarifies that the scattering matrix provided in Eq. 29 is valid only for a nonreciprocal system. It also corrects the matrix in Eq. 32(b) in the Appendix of the article. [ABSTRACT FROM AUTHOR]

Consistency and complementarity are two important principles in multiview feature extraction. However, most current multiview feature extraction methods only explore the former but neglect the latter. To alleviate this limitation, in this article we propose a relaxed multiview discriminant analysis (RMDA) model. Firstly, a relaxed loss function is formulated to make the projection matrices have more degrees of freedom. Then two scatter matrices are utilized to preserve cross-view between-class and within-class discriminative information. The proposed RMDA explores the complementarity of multiple views while maintaining the consistency across different views. To solve the RMDA problem efficiently, an iteration strategy is proposed. Theoretical analysis demonstrates the effectiveness and quadratic convergence rate of the RMDA algorithm. To further deal with nonlinearities present in the data, a relaxed kernel multiview discriminant analysis (RKMDA) is put forward too. Several corroborating numerical tests using artificial dataset and real datasets are provided to showcase the merits of the RMDA and RKMDA relative to several competing methods. [ABSTRACT FROM AUTHOR]

Oil spills on the ocean surface are a serious threat to the marine ecosystem. Automation of oil spill detection through full/dual polarimetric Synthetic Aperture Radar (SAR) images is considered a good aid for oil spill disaster management. This paper uses the power of log transformation to discern the scattering behavior more effectively from the coherency matrix (T3). The proposed coherency matrix is tested on patches of the clean sea surface and four different classes of oil spills, viz. heavy sedimented oil, thick oil, oil-water emulsion, fresh oil; by analyzing the entropy (H), anisotropy (A), and mean scattering angle alpha (α), following the H/A/ α decomposition. Experimental results show that not only does the proposed T3 matrix differentiate between Bragg scattering of the clean sea surface from a random scattering of thick oil spills but is also able to distinguish between different emulsions of oil spills with water and sediments. Moreover, unlike classical T3, the proposed method distinguishes concrete-like structures and heavy sedimented oil even though both exhibit similar scattering behavior. The proposed algorithm is developed and validated on the data acquired by the UAVSAR full polarimetric L band SAR sensor over the Gulf of Mexico (GOM) region during the Deepwater Horizon (DWH) oil spill accident in June 2010. [ABSTRACT FROM AUTHOR]

Data are distributed between different parties. Collecting data from multiple parties for analysis and mining will serve people better. However, it also brings unprecedented privacy threats to the participants. Therefore, safe and reliable data publishing among multiple data owners is an urgent problem to be solved. We mainly study the problem of privacy protection in data publishing. For a centralized scenario, we propose the LDA-DP algorithm. First, the within-class mean vectors and the pooled within-class scatter matrix are perturbed by the Gaussian noise. Second, the optimal projection direction vector with differential privacy is obtained by the Fisher criterion. Finally, the low-dimensional projection data of the original data are obtained. For distributed scenarios, we propose the Mul-LDA-DP algorithm based on a blockchain and differential privacy technology. First, the within-class mean vectors and within-class scatter matrices of local data are perturbed by the Gaussian noise and uploaded to the blockchain network. Second, the projection direction vector is calculated in the blockchain network and returned to the data owner. Finally, the data owner uses the projection direction vector to generate low-dimensional projection data of the original data and upload it to the blockchain network for publishing. Furthermore, in a distributed scenario, we propose a correlated noise generation scheme that uses the additivity of the Gaussian distribution to mitigate the effects of noise and can achieve the same noise level as the centralized scenario. We measure the utility of the published data by the SVM misclassification rate. We conduct comparative experiments with similar algorithms on different real data sets. The experimental results show that the data released by the two algorithms can maintain good utility in SVM classification. [ABSTRACT FROM AUTHOR]

We present a detailed study of the scattering system given by the Neumann Laplacian on the discrete half‐space perturbed by a periodic potential at the boundary. We derive asymptotic resolvent expansions at thresholds and eigenvalues, we prove the continuity of the scattering matrix, and we establish new formulas for the wave operators. Along the way, our analysis puts into evidence a surprising relation between some properties of the potential, like the parity of its period, and the behaviour of the integral kernel of the wave operators. [ABSTRACT FROM AUTHOR]

We construct a distorted Fourier transformation associated with the multi-dimensional quantum walk. In order to avoid the complication of notations, almost all of our arguments are restricted to two-dimensional quantum walks (2DQWs) without loss of generality. The distorted Fourier transformation characterizes generalized eigenfunctions of the time evolution operator of the QW. The 2DQW which will be considered in this paper has an anisotropy due to the definition of the shift operator for the free QW. Then, we define an anisotropic Banach space as a modified Agmon-Hörmander's B ∗ space, and we derive the asymptotic behavior at infinity of generalized eigenfunctions in these spaces. The scattering matrix appears in the asymptotic expansion of generalized eigenfunctions. [ABSTRACT FROM AUTHOR]

In this paper we study in detail the deformations introduced in [1] of the integrable structures of the AdS2,3 integrable models. We do this by embedding the corresponding scattering matrices into the most general solutions of the Yang-Baxter equation. We show that there are several non-trivial embeddings and corresponding deformations. We work out crossing symmetry for these models and study their symmetry algebras and representations. In particular, we identify a new elliptic deformation of the AdS3× S3× M4 string sigma model. [ABSTRACT FROM AUTHOR]

Despite its long history, a double-concave (DC) Fabry-Perot open resonator (FPOR) has recently gained popularity in the characterization of dielectrics in the 20–110 GHz range, mainly due to such novel accomplishments as full automation of the measurement process and the development of even more accurate and computationally efficient electromagnetic model. However, it has been discovered that such a DC resonator suffers from unwanted mode coupling present for electrically thick samples. Such limitations are missing in a plano-concave (PC) FPOR. For those reasons, the aim in this article is to apply the newly proposed scattering matrix method in the study of major properties of that kind of a resonator and, subsequently, to propose a new tool dedicated to the measurement of dielectrics without the aforementioned limits. For the first time in the literature, major properties of the PC FPOR with and without the sample, such as resonance frequencies, geometric factors, energy filling factors, and the resulting quality factor, are rigorously computed. Moreover, their impact on the accuracy of the loss tangent extraction is investigated. Such a study, which opens the way for accurate microwave characterization of electrically thick dielectric sheets above 20 GHz, has never been performed before. The whole complex permittivity extraction algorithm presented in this article is validated experimentally by measuring well-known materials, namely, C-plane sapphire, silicon, and Z-cut monocrystalline quartz. [ABSTRACT FROM AUTHOR]

The electrons associated with molecules and other small quantum structures exist in states that are bound or quasibound to the molecule. The quasibound states, which can significantly affect chemical reaction dynamics, have finite lifetimes and are associated with complex energy poles of the scattering matrix. Using Wigner–Eisenbud (R-matrix) scattering theory, we examine the symmetry properties of the quasibound states of a molecule-size tetrahedral system, and we examine the relation of quasibound states to the scattering properties. In addition, using R-matrix theory, we construct a non-Hermitian Hamiltonian whose complex energy eigenvalues coincide with the bound and quasi-bound states of the molecule. We show that each bound state and quasibound state of the tetrahedral system belongs to a distinct irreducible representation of the tetrahedral group, and that an incident electron belonging to one irreducible representation can only scatter within the same irreducible representation. [ABSTRACT FROM AUTHOR]

In this work we demonstrate the extended and generalized methodology for the design of Quad-Furcated Profiled Horns (Q-FPHs). Based on a design case of a 4λ0 x 4λ0 Q-FPH, we extract the Generalized Scattering Matrix (GSM) of the enlarged quad-furcated discontinuity and provide analytical expressions for its multimode feeding. Next, the four feeding and the upper common waveguide sections are optimized accordingly through Mode-Matching (MM). The high aperture efficiency levels delivered by the methodology are verified by full-wave simulations of the optimized design case and compared to the state-of-the-art which is thereby redefined. [ABSTRACT FROM AUTHOR]

The aim of the paper is to analyse acoustic reflective muffler applying the scattering matrix method. In general, the method is based on dividing the muffler/system into separate subsystems and apply the acoustic multi-ports theory to calculate the scattering matrix of each element to finally combine the results and obtain the scattering matrix of the entire system/muffler. The multi-port procedure is derived from the theory of electric networks and allows to analyse acoustic devises of complex geometry with prescribed accuracy. Based on the scattering matrix, the transmission loss was determined. [ABSTRACT FROM AUTHOR]

We derive dispersion estimates for solutions of a one‐dimensional discrete Dirac equations with a potential. In particular, we improve our previous result, weakening the conditions on the potential. To this end we also provide new results concerning scattering for the corresponding perturbed Dirac operators which are of independent interest. Most notably, we show that the reflection and transmission coefficients belong to the Wiener algebra. [ABSTRACT FROM AUTHOR]

Duct silencers provide effective noise reduction for heating, ventilation and air conditioning systems. These silencers can achieve an excellent sound attenuation through the attributes of their design. The reactive silencer works on the principle of high reflection of sound waves at low frequencies. On the other hand, the dissipative silencer works on the principle of sound absorption, which is very effective at high-frequencies. Combining these two kinds of silencers allowed covering the whole frequency range. In this paper, the effect of liner characteristics composed of a perforated plate backed by a porous material and geometry discontinuities on the acoustic power attenuation of lined ducts is evaluated. This objective is achieved by using a numerical model to compute the multimodal scattering matrix, thus allowing deducing the acoustic power attenuation. The numerical results are obtained for six configurations, including cases of narrowing and widening of a radius duct with sudden or progressive discontinuities. Numerical acoustic power attenuation shows the relative influence of the variation in the values of each parameter of the liner, and of each type of radius discontinuities of ducts. [ABSTRACT FROM AUTHOR]

Problems of difference equations with jump (discontinuity) conditions have an important role for many branches of sciences. They can be used to model a wide range of real-world applications such as heating, massing in physics, bursting rhythm models in medicine, optimal control models in economics, and so on. In this paper, we consider some spectral and scattering properties of matrix difference equations with jump conditions and hyperbolic eigenparameter. Using the asymptotic behavior of Jost function, we find eigenvalues, spectral singularities, resolvent operator, and spectrum of this problem. Also, we investigate scattering matrix and get some properties of scattering matrix. Finally, we present an example about the scattering matrix and the existence of eigenvalues in special cases. [ABSTRACT FROM AUTHOR]

We provide new insight into the analysis of N-body problems by studying a compactification M N of R 3 N that is compatible with the analytic properties of the N-body Hamiltonian H N . We show that our compactification coincides with a compactification introduced by Vasy using blow-ups in order to study the scattering theory of N-body Hamiltonians and with a compactification introduced by Georgescu using C ∗ -algebras. In particular, the compactifications introduced by Georgescu and by Vasy coincide (up to a homeomorphism that is the identity on R 3 N ). Our result has applications to the spectral theory of N-body problems and to some related approximation properties. For instance, results about the essential spectrum, the resolvents, and the scattering matrices of H N (when they exist) may be related to the behavior near M N \ R 3 N (i.e., "at infinity") of their distribution kernels, which can be efficiently studied using our methods. The compactification M N is compatible with the action of the permutation group S N , which allows to implement bosonic and fermionic (anti-)symmetry relations. We also indicate how our results lead to a regularity result for the eigenfunctions of H N . [ABSTRACT FROM AUTHOR]

Fully polarimetric (FP) SAR systems offer parameters that describe and quantify the scattering mechanisms from the surface cover. These are usually derived from decomposition of matrices derived from the original scattering matrix from observations at each pixel. Power from scattering mechanisms have potential for retrieval of sea ice information, which cannot be derived using traditional backscatter (magnitude or phase) measured by single- or dual-polarization SAR systems. This study investigates the potential of selected FP parameters that represent the power of three scattering mechanisms, in addition to the total power, in identifying ice types and surface features for operational use. Parameters were obtained from a set of 62 RADARSAT-2 Quad-pol data over Resolute Passage, central Arctic, during the period September-December 2017. A scattering-based color-composite scheme was developed. Analysis of the examined color images was supported by information from regional ice charts and SAR image interpretations from the Canadian Ice Service. Case studies are presented to demonstrate the potential of the proposed color-composite tool. Open water, new ice, multi-year ice and a few surface features including rafted, ridged and smooth/rough surfaces can be identified better in the color images. Physical interpretation of the relative power from the given scattering mechanisms is explained for the relevant ice types and surfaces. [ABSTRACT FROM AUTHOR]

For entomological radar, the polarization information of the target is usually used to estimate the biological parameters, such as orientation, body length, and mass, of the insect. Thus, the accuracy of polarization measurement directly affects the performance of the biological parameters' estimation. The polarization measurement error is mainly caused by the imbalance of amplitude and phase between two polarization channels and the crosstalk of the dual-polarization antenna. In order to obtain the correct polarization information of the target, the polarimetric calibration of the entomological radar is required. This paper proposes a new polarimetric calibration technique based on antenna rotation, which does not require the calibrator to have a specific polarization scattering matrix (PSM). Compared with the currently existing calibration techniques, no prior knowledge of the calibrator PSM is required (in fact, any fixed-point target can be used as a calibrator); thus, the errors introduced by the mechanical process can be avoided. Simulations and data measured by radar verify the effectiveness of the method. This method has the potential to be extended to other fully polarimetric radar systems in the future, such as fully polarimetric weather radar, fully polarimetric synthetic aperture radar (SAR), and so on. [ABSTRACT FROM AUTHOR]

Pollen is nowadays recognized as one of the main atmospheric particles affecting public human health as well as the Earth's climate. In this context, an important issue concerns our ability to detect and differentiate among the existing pollen taxa. In this paper, the potential differences that may exist in light scattering by four of the most common pollen taxa, namely ragweed, birch, pine and ash, are analysed in the framework of the scattering matrix formalism at two wavelengths simultaneously (532 and 1064 nm). Interestingly, our laboratory experimental error bars are precise enough to show that these four pollen taxa, when embedded in ambient air, exhibit different spectral and polarimetric light-scattering characteristics, in the form of 10 scattering matrix elements (5 per wavelength), which allow each to be identified separately. To end with, a simpler light-scattering criterion is proposed for classification among the four considered pollen taxa by performing a principal component (PC) analysis, which still accounts for more than 99 % of the observed variance. We thus believe this work may open new insights for future atmospheric pollen detection. [ABSTRACT FROM AUTHOR]

The scattering matrices of e + N+ with JĎ€ = 1.5+ in discrete energy regions are calculated using the eigenchannel R-matrix method. We obtain good parameters of multichannel quantum defect theory (MQDT) that vary smoothly as the function of the energy resulting from the analytical continuation property of the scattering matrices. By employing the MQDT, all discrete energy levels for N could be calculated accurately without missing anyone. The MQDT parameters (i.e., scattering matrices) can be calibrated with the available precise spectroscopy values. In this work, the optical oscillator strengths for the transition between the ground state and Rydberg series are obtained, which provide rich data for the diagnostic analysis of plasma. [ABSTRACT FROM AUTHOR]

Unstable particles rarely feature in conjunction with integrability in 1+1D quantum field theory. However, the family of homogenous sine-Gordon models provides a rare example where both stable and unstable bound states are present in the spectrum whilst the scattering matrix is diagonal and solves the usual bootstrap equations. In the standard scattering picture, unstable particles result from complex poles of the S-matrix located in the unphysical sheet of rapidity space. Since they are not part of the asymptotic spectrum, their presence is only felt through the effect they have on physical quantities associated either to the theory as a whole (i.e. scaling functions, correlation functions) or to the stable particles themselves (i.e. energy/particle density). In two recent publications, the effect of unstable particles in different out-of-equilibrium settings has been studied. It has been shown that their presence is associated with specific signatures in many quantities of physical interest. A good way to select those quantities is to adopt the generalised hydrodynamic approach and to consider the effective velocities and particle densities of the stable particles in the theory. For an initial state given by a spacial gaussian profile of temperatures peaked at the origin, time evolution gives rise to particle and spectral particle densities that exhibit hallmarks of the creation and decay of unstable particles. While these signatures have been observed numerically elsewhere, this paper explores their quantitative and qualitative dependence on the parameters of the problem. We also consider other initial states characterised by "inverted gaussian" and "double gaussian" temperature profiles. [ABSTRACT FROM AUTHOR]

In this paper, a generalized nonlinear Schrödinger (gNLS) equation with time-varying coefficients is analytically studied using its Lax representation and the associated Riemann-Hilbert (RH) problem equipped with a symmetric scattering matrix in the Hermitian sense. First, Lax representation and the associated RH problem of the considered gNLS equation are established so that solution of the gNLS equation can be transformed into the associated RH problem. Secondly, using the solvability of unique solution of the established RH problem, time evolution laws of the scattering data reconstructing potential of the gNLS equation are determined. Finally, based on the determined time evolution laws of scattering data, the long-time asymptotic solution and N-soliton solution of the gNLS equation are obtained. In addition, some local spatial structures of the obtained one-soliton solution and two-soliton solution are shown in the figures. This paper shows that the RH method can be extended to nonlinear evolution models with variable coefficients, and the curve propagation of the obtained N-soliton solution in inhomogeneous media is controlled by the selection of variable–coefficient functions contained in the models. [ABSTRACT FROM AUTHOR]

The polarimetric distortions present in the polarimetric SAR (PolSAR) data sets leads to unexpected results from the polarimetric decomposition and classification models, which in turn result in the ground target misinterpretation. The most important polarimetric distortions in airborne PolSAR data sets are the channel imbalance and crosstalk. The minimization of these polarimetric distortions using polarimetric calibration techniques is very important to carry out the quantitative analysis using PolSAR data and time series analysis and to compare results between different sensors. In the current state of the art, the spatial variability of the polarimetric distortions at different slant‐range positions in the data set was not completely analyzed and also the temporal variability of the polarimetric distortions using multiple data sets needs to be more investigated. Therefore, the main objectives of this study were to develop an operational processor to perform the external polarimetric calibration of the L‐band Uninhibited Aerial Vehicle Synthetic Aperture Radar system and to analyze the spatio‐temporal behavior of the polarimetric distortions. The polarimetric distortion matrix (PDM) was formulated after considering the crosstalk and channel imbalance polarimetric distortions to derive the scattering matrix free from all kinds of polarimetric distortions from the observed scattering matrix. The Quegan, improved Quegan, and Ainsworth methods for polarimetric calibration were implemented to solve the PDM. The residual channel imbalance and crosstalk after polarimetric calibration were estimated to compare the calibration efficiency of these methods. After that, a spatio‐temporal analysis was carried out with several data sets to assess the spatio‐temporal behavior of these polarimetric distortions. The polarimetric signatures and the coherency matrix behavior of the trihedral corner reflectors were used to analyze the ground target characterization improvement after polarimetric calibration. The results obtained from this study revealed that the crosstalk is the major cause for the polarimetric distortions and the channel imbalance and phase bias present in the data sets were not high. From the spatio‐temporal analysis, it was found that the variability of these polarimetric distortions both in spatial and temporal domains was minimum and can be discarded without causing any considerable error in the polarimetric calibration process. Key Points: The major cause for the polarimetric distortions in the UAVSAR data sets was due to the crosstalkThe channel imbalance and phase bias distortions were not high for all the data setsPolSAR calibration involves the use of Quegan, Improved Quegan, and Ainsworth methods in this study [ABSTRACT FROM AUTHOR]

This article presents the results of numerical simulation and optimization of electromagnetic characteristics of a new waveguide polarizer design containing a conducting diaphragm and pins. The theoretical model of a waveguide polarizer with one diaphragm and four pins is developed and applied for the optimization. The main electromagnetic characteristics of the polarizer were obtained based on the elements of general scattering matrix of the designed device. In order to check the performance of the developed mathematical model it was simulated in a software using the finite difference time domain (FDTD) technique. The proposed design of a waveguide polarizer has the ability of fine tuning of its characteristics by mechanical change of the heights of applied pins. Developed theoretical approach and obtained numerical results can be used to develop new tunable waveguide polarizers and filters with diaphragms and pins. [ABSTRACT FROM AUTHOR]

With the development of remote sensing technology, hyperspectral sensors can record reflectance of ground objects in hundreds of bands, which undoubtedly brings great benefits for hyperspectral remote sensing image that contains abundant information of the land covers. At present, some hyperspectral images are contaminated by the noise and a lack of spatial information, this phenomenon hinders the improvement of classification accuracy. To further mine the spatial features of hyperspectral image, we propose an effective feature extraction method based on Spectral-Gabor space discriminant analysis (SGDA). The framework of SGDA is roughly divided into four steps: firstly, we obtain p i { p i | 1 ≤ i < d } principal components by PCA, where d denotes the number of features; secondly, we filter the p i principal components with Gabor filter on five different scales and eight different orientations and obtain Gabor spatial features; thirdly, incorporating the spectral features of original hyperspectral data into the Gabor spatial features to form the Spectral-Gabor space features F; finally, we project the fusion features to a low-dimensional subspace, and then maximize the Spectral-Gabor space between-class scatter matrix ( S b SG ) and minimize the Spectral-Gabor space within-class scatter matrix ( S w SG ) at the same time inspired by the idea of Fisher line discriminant analysis. Also, in the above fusion process, the proportion of spectral and spatial information can be controlled by using a penalty factor α . Experimental results on three hyperspectral datasets show the better classification performance of the SGDA method than the state-of-art methods on the condition of small sample size by Maximum Likelihood Classifier (MLC). [ABSTRACT FROM AUTHOR]

We prove that the wave operators for nxn matrix Schrödinger equations on the half line, with general selfadjoint boundary condition, are bounded in the spaces Lp(R+,Cn),1

0∞(1+x)|V(x)|dx < ∞. Moreover, assuming that ∫0∞(1+xγ)|V(x)|dx < ∞,γ > 5/2, and that the scattering matrix is the identity at zero and infinite energy, we prove that the wave operators are bounded in L¹(R+, Cn), and in L∞(R+, Cn). We also prove that the wave operators for nxn matrix Schrödinger equations on the line are bounded in the spaces Lp(R, Cn), 1 < p < ∞, assuming that the perturbation consists of a point interaction at the origin and of a potential, V, that satisfies the condition ∫-∞∞(1+|x|)/V(x)/dx<∞. Further, assuming that ∫-∞∞(1+|x|γ)|V(x)|dx < ∞, γ > 52, and that the scattering matrix is the identity at zero and infinite energy, we prove that the wave operators are bounded in L¹(R, Cn), and in L∞ (R+, Cn). We obtain our results for n x n matrix Schrödinger equations on the line from the results for 2n x 2n matrix Schrödinger equations on the half line. [ABSTRACT FROM AUTHOR]

We consider diffraction of waves on a product cone. We first show that diffractive waves enjoy a one-step polyhomogeneous asymptotic expansion, which is an improvement of Cheeger and Taylor's classical result of half-step polyhomogeneity of diffractive waves [Comm. Pure Appl. Math. 35 (1982), 275-331 and 487-529]. We also conclude that on product cones, the scatteringmatrix is the diffraction coefficient,which is the principal symbol of the diffractive half wave kernel, for strictly diffractively related points on the cross section. This generalize the result of Ford, Hassell and Hillairet in 2-dimensional flat cone settings (Ford, Hassell, and Hillairet, 2018). In the last section, we also give a radiation field interpretation of the relationship between the scattering matrix and the diffraction coefficient. [ABSTRACT FROM AUTHOR]

We propose a realizable device design for an all-electrical robust valley filter that utilizes spin protected topological interface states hosted on monolayer 2D-Xene materials with large intrinsic spin–orbit coupling. In contrast with conventional quantum spin-Hall edge states localized around the X-points, the interface states appearing at the domain wall between topologically distinct phases are either from the K or K ′ points, making them suitable prospects for serving as valley-polarized channels. We show that the presence of a large band-gap quantum spin-Hall effect enables the spatial separation of the spin–valley locked helical interface states with the valley states being protected by spin conservation, leading to robustness against short-range nonmagnetic disorder. By adopting the scattering matrix formalism on a suitably designed device structure, valley-resolved transport in the presence of nonmagnetic short-range disorder for different 2D-Xene materials is also analyzed in detail. Our numerical simulations confirm the role of spin–orbit coupling in achieving an improved valley filter performance with a perfect quantum of conductance attributed to the topologically protected interface states. Our analysis further elaborates clearly the right choice of material, device geometry and other factors that need to be considered while designing an optimized valleytronic filter device. [ABSTRACT FROM AUTHOR]

A spectral shift function (SSF) is an important object in the scattering theory which is related both to the spectral density and to the scattering matrix. In the paper, it is shown how to employ the SSF formalism to solve scattering problems when the continuum is discretized, e.g. when solving a scattering problem in a finite volume or in the representation of some finite square-integrable basis. A new algorithm is proposed for reconstructing integrated densities of states and the SSF using a union of discretized spectra corresponding to a set of Gaussian bases with the shifted scale parameters. The examples given show that knowledge of the discretized spectra of the total and asymptotic Hamiltonians is sufficient to find the scattering partial phase shifts at any required energy, as well as the resonances parameters. [ABSTRACT FROM AUTHOR]

This article presents a novel method to design the decoupling and matching network (DMN) for dual-band multi-input–multioutput (MIMO) antennas. The DMN consists of a grid of metallic microstrip stubs, some of which are connected while others are not. The connecting condition in the DMN is the only unknown variable for realizing high antenna isolation. It is determined by rigorous design formulas upon scattering matrix and optimized by the binary optimization algorithm, e.g., genetic algorithm (GA). Thus, high isolation among antennas can be achieved without requiring the optimization process in the electromagnetic simulation tool. Three decoupling examples of two two-element symmetric and asymmetric arrays and a four-element array are presented to elaborate the design procedure and verify the advance of the proposed decoupling method. Results show that the adoption of DMN offers enhancement in impedance matching, isolation, and efficiency, as well as the reduction of envelop correlation coefficient within two desired frequency bands for all cases, validating the proposed decoupling method. [ABSTRACT FROM AUTHOR]

The waveguide occupies a domain having several cylindrical outlets to infinity and is described by the non-stationary Maxwell system with perfectly conductive boundary conditions. For the corresponding stationary problem with spectral parameter, the continuous spectrum eigenfunctions and the scattering matrix are defined. We calculate the wave operators, introduce the scattering operator and describe its connection with the scattering matrix. The proof is based on extending the Maxwell system to an equation of the form with elliptic operator . We associate to the equation an initial boundary value problem and develop the scattering theory for the problem. The information on the Maxwell system is derived from the results obtained for the extended problem. [ABSTRACT FROM AUTHOR]

In this work, the double and triple pole soliton solutions for the Gerdjikov–Ivanov type of the derivative nonlinear Schrödinger equation with zero boundary conditions (ZBCs) and nonzero boundary conditions (NZBCs) are studied via the Riemann–Hilbert (RH) method. With spectral problem analysis, we first obtain the Jost function and scattering matrix under ZBCs and NZBCs. Then, according to the analyticity, symmetry, and asymptotic behavior of the Jost function and scattering matrix, the RH problem (RHP) with ZBCs and NZBCs is constructed. Furthermore, the obtained RHP with ZBCs and NZBCs can be solved in the case that reflection coefficients have double or triple poles. Finally, we derive the general precise formulas of N-double and N-triple pole solutions corresponding to ZBCs and NZBCs, respectively. In addition, the asymptotic states of the one-double pole soliton solution and the one-triple pole soliton solution are analyzed when t tends to infinity. The dynamical behaviors for these solutions are further discussed by image simulation. [ABSTRACT FROM AUTHOR]

Simultaneous polarimetric radars can measure the polarization scattering matrix (PSM) of moving targets within one pulse. The key point is the orthogonal waveform design to reduce the interference caused by the simultaneous transmission and reception. Meanwhile, to ensure the measurement accuracy of moving targets, the Doppler tolerance of the transmitted waveforms is also important. In this article, first, a matched filter (MF) at the receiver is considered and a unified framework with a newly proposed objective function to design Doppler resilient sequences under several constraints is described. The proposed objective function contains the widely used peak sidelobe level (PSL) and the integrated sidelobe level (ISL) as special cases. Meanwhile, a series of constraint conditions, including the unimodular constraint, the uncertainty modulus constraint, and the PAR constraint, is considered. Thereafter, a mismatched filter is considered for further improving the correlation properties and a similar framework for designing the optimal receiving filter at the expense of a controllable signal-to-noise ratio (SNR) loss is proposed. Numerical results are presented to verify the performance of the proposed methods. The designed sequence pair is also implemented on a fully polarimetric system to measure the PSM of a canonical target in the anechoic chamber, and the effectiveness of the proposed framework is verified by using the simultaneous polarimetric radar. It is predicted that the framework has the potential to be applied for other multichannel systems. [ABSTRACT FROM AUTHOR]

In this article, a highly efficient approach is presented for obtaining scattering parameters from the coupling matrix of a microwave filter and duplexer whether they are lossless of lossy. By analyzing and making the application of eigenvalue decomposition theory to calculate the inversion of the coupling matrix, a new set of formulas are generated to calculate the scattering parameters. The example of a 14‐cavity crossing coupled filter and a 17‐order duplexer are calculated and fabricated for illustrating the capabilities of the new proposed approach. Compared with the traditional method in textbook, the time consumed on computing is shortened by 80%, which validates that the method in this article has a huge advantage in handling S‐parameter calculation of filter and duplexer with multiple couplings. [ABSTRACT FROM AUTHOR]

We choose the Reduction Formula, PCAC and Low Energy Theory to reduce the S matrix of a OZI allowed two-body strong decay involving a light pseudoscalar, the covariant transition amplitude formula with relativistic wave functions as input is derived. After confirm this method by the decay D ∗ (2010) → D π , we study the newly observed D s 0 (2590) + with supposing it to be the state D s (2 1 S 0) + , we find its decay width Γ is highly sensitive to the D s 0 (2590) + mass, which result in the meaningless comparison of widths by different models with various input masses. Instead of width, we studied the overlap integral over the wave functions of initial and final states, here we parameterized it as X which is model-independent, and the ratio Γ / | P f | 3 , both are almost mass independent, to give us useful information. The results show that, all the existing theoretical predictions X D s (2 S) → D ∗ K = 0.25 ∼ 0.41 and Γ / | P f | 3 = 0.81 ∼ 1.77 MeV - 2 are smaller than experimental data 0. 585 - 0.035 + 0.015 and 4. 54 - 0.52 + 0.25 MeV - 2 . Further compared with X D ∗ (2010) → D π ex = 0.540 ± 0.009 , the current data X D s (2 S) → D ∗ K ex = 0. 585 - 0.035 + 0.015 is too big to be an reasonable value, so it is early to say D s 0 (2590) + is the conventional D s (2 1 S 0) + meson. [ABSTRACT FROM AUTHOR]