Search Results (97)

We introduce a BiHom-type skew-symmetric bracket on general linear Lie algebra $GL\left(V\right)$ built from two commuting inner automorphisms $\alpha =A{d}_{\psi }$ and $\beta =A{d}_{\varphi }$, with $\psi ,\varphi \in GL\left(V\right)$ and integers $i,j$. We prove that $(GL\left(V\right),{[·,·]}_{(\psi ,\varphi )}^{(i,j)},\alpha ,\beta )$ is a BiHom–Lie algebra, and we study the Lax equation obtained by replacing the commutator in the finite nonperiodic Toda lattice by this bracket. For the symmetric choice $\varphi =\psi$ with $(i,j)=(0,0)$, the deformed flow is equivariant under conjugation and becomes gauge-equivalent, via $\tilde{L}={\psi }^{-1}L\psi$, to a Toda-type Lax equation with a conjugated triangular projection. In particular, scalar deformations amount to a constant rescaling of time. On embedded $2\times 2$ blocks, we derive explicit trigonometric and hyperbolic formulae that make symmetry constraints (e.g., tracelessness) transparent. In the asymmetric hyperbolic case, we exhibit a trace obstruction showing that the right-hand side is generically not a commutator, which amounts to symmetry breaking of the isospectral property. We further extend the construction to the weakly coupled Toda lattice with an indefinite metric and provide explicit $2\times 2$ solutions via an inverse-scattering calculation, clarifying and correcting certain formulas in the literature. The classical Toda dynamics are recovered at special parameter values. Full article

Non-contact heart rate estimation technology based on frequency-modulated continuous wave (FMCW) radar has garnered extensive attention in single-target scenarios, yet it remains underexplored in multi-target environments. Accurate discrimination of multiple targets and precise estimation of their heart rates constitute key challenges in the multi-target domain. To address these issues, we propose a novel scheme for multi-target heart rate estimation. First, a high-precision distance-bin selection (HDBS) method is proposed for target localization in the range domain. Next, multiple-input multiple-output (MIMO) array processing is combined with the Root-multiple signal classification (Root-MUSIC) algorithm for angular domain estimation, enabling accurate discrimination of multiple targets. Subsequently, we propose an efficient method for interference suppression and vital sign extraction that cascades variational mode decomposition (VMD), local mean decomposition (LMD), and wavelet thresholding (WT) termed as VLW, which enables high-quality heartbeat signal extraction. Finally, to achieve high-precision and super-resolution heart rate estimation with low computational burden, an improved fast iterative interpolated beamforming (FIIB) algorithm is proposed. Specifically, by leveraging the conjugate symmetry of real-valued signals, the improved FIIB algorithm reduces the execution time by approximately 60% compared to the standard version. In addition, the proposed scheme provides sufficient signal-to-noise ratio (SNR) gain through low-complexity accumulation in both distance and angle estimation. Six experimental scenarios are designed, incorporating densely arranged targets and front-back occlusion, and extensive experiments are conducted. Results show this scheme effectively discriminates multiple targets in all tested scenarios with a mean absolute error (MAE) below 2.6 beats per minute (bpm), demonstrating its viability as a robust multi-target heart rate estimation scheme in various engineering fields. Full article

The canonical quantization of gravity in general relativity is greatly simplified by the artificial decomposition of space time into a 3 + 1 formalism. Such a simplification appears to come at the cost of general covariance. This quantization procedure requires tangential and perpendicular infinitesimal diffeomorphisms generated by the symmetry group under the Legendre transformation of the given action. This gauge generator, along with the fact that Weyl curvature scalars may act as “intrinsic coordinates” (or a dynamical reference frame) that depend only on the spatial metric ($g_{ab}$) and the conjugate momenta ($p^{cd}$), allows for an alternative approach to canonical quantization of gravity. In this paper, we present the tensorial solution of the set of Weyl scalars in terms of canonical phase-space variables. Full article

Ultrafast laser processing can produce micro/nanostructures, which is of great interest in advanced manufacturing. Ultrafast laser-induced events include non-equilibrium dynamic phenomena, occurring on the femtosecond to picosecond time scale and nanometer to micron space scale. Single-shot ultrafast imaging can provide multiple time-correlated evolution frames in one non-repeatable event with a temporal resolution of sub-picoseconds. However, previous approaches suffer from degraded spatial resolution, which is a bottleneck in microscopic imaging. For the spatial-frequency multiplexing methods based on structured illumination, a reconstruction strategy was proposed utilizing the frames’ conjugate symmetry in the Fourier domain. The spatial resolution is double that of the traditional algorithm by evaluating with synthetic data, revealing that the reconstruction resolution can reach the diffraction limitation. A two-frame microscopic system was constructed with a frame interval of 300 fs and a maximum spatial resolution of 1.4 μm. The interaction between a femtosecond laser and a fused silica glass plate was captured in a single shot and the dynamic evolution of the induced plasma was observed, verifying the application feasibility in ultrafast laser processing, providing experimental observations for interaction mechanism research and theoretical model optimization. Full article

This study employs molecular orbital (MO) analysis, density of states (DOS) analysis, and advanced techniques such as charge density difference (CDD), transition density matrix (TDM), transition electric dipole moment density (TEDM), and transition magnetic dipole moment density (TMDM) to systematically investigate the electronic structure characteristics of Fc-[8]CPP and Fc-[11]CPP. Using density functional theory (DFT) and time-dependent DFT (TD-DFT), the π-electron delocalization properties and optical behaviors of these molecules were analyzed. Furthermore, their responses to external electromagnetic fields were explored through electronic circular dichroism (ECD) and Raman spectroscopy, comparing chiral optical responses and electron–vibration coupling effects to elucidate their photophysical properties. The results reveal that the HOMO-LUMO energy gaps of Fc-[8]CPP and Fc-[11]CPP are 5.81 eV and 5.95 eV, respectively, with a slight increase as ring size grows; Fc-[8]CPP exhibits a stronger chiral response, while Fc-[11]CPP shows reduced chirality due to enhanced symmetry. Finally, TD-DFT calculations demonstrate that their optical absorption is dominated by localized excitations with partial charge transfer contributions. These findings provide a theoretical foundation for designing conjugated macrocyclic materials with superior optoelectronic performance. Full article

In this study we explored the chiral behavior of a honeycomb-like chiral metamaterial with a negative Poisson’s ratio. This type of structure is widely used in sectors such as construction and packaging, but is not as common in electromagnetics/electrical engineering. Moreover, in contrast with typical layer-by-layer chiral metamaterial structures, which are usually formed by metallic patterns with C4 symmetry, this hexachiral structure presents C6 symmetry. The aim of this paper is analyzing the electromagnetic behavior of this kind of auxetic metamaterial with special attention to its chiral behavior. This structure is analyzed by means of measurements and simulations of its reflection and transmission responses (scattering parameters) in different configurations, showing that a dual-layer configuration with conjugated faces provides high electromagnetic activity (gyrotropy) with low losses. Full article

In this article, an improved real-valued dimension-reduction MUSIC (IRDR-MUSIC) algorithm is proposed for a crossed-dipole array. Initially, conjugate symmetry of the spatial component in the manifold vector is derived such that two real-valued matrices for the sum and difference covariance are constructed, which consist of the real and imaginary parts of the complex covariance matrix respectively. However, sum and difference covariance matrices with information loss would deteriorate the performance. Thus, given that the sum and difference covariance matrices have an identical null space, a joint sum–difference covariance matrix combining both the sum and difference covariance matrices is constructed, which includes the complete information of a complex covariance matrix. Accordingly, a computationally efficient IRDR-MUSIC algorithm with an enhanced performance is proposed. Compared with the existing dimension-reduction MUSIC algorithm, the proposed IRDR-MUSIC algorithm greatly reduce the complexity reduction almost without any performance loss since singular-value decomposition of the joint sum–difference covariance matrix operates in the real-valued domain, and only half of the range of the spatial spectrum search is required. Furthermore, the proposed IRDR-MUSIC algorithm outperforms the state-of-art complex-valued, symmetry-compressed, dimension-reduction MUSIC algorithm in both its multi-target resolution and computational efficiency. Numerical simulations and analyses verify the superiority of the proposed IRDR-MUSIC algorithm. Full article

High-precision direction of arrival (DOA) of wideband signals is a very important technology in the field of radar and communication. In this work, we propose an efficient support vector regression (SVR) architecture via a genetic algorithm (GA) for wideband DOA estimation, which exhibits high estimation performance and generalization performance. By adopting the two-sided correlation transformation (TCT) algorithm, the network is trained only from reference frequency data to increase the training efficiency. In order to reduce the redundant information in the array covariance matrix and lower the dimensionality of the input features, the array covariance matrix at a single frequency point is preprocessed according to its conjugate symmetry and elemental characteristics, and the dimensionality-reduced input features are obtained. Specifically, the dimensionality of the input features does not increase with the number of sub-bands when dealing with broadband signals or ultra-broadband signals, which can significantly reduce the training time of the model and the storage capacity of the system. The increased performance of the proposed algorithm is highly desirable in resource-constrained scenarios, and the experimental results demonstrate the efficiency and superiority of the proposed network compared with existing methods. Full article

The one-dimensional quaternion fractional Fourier transform (1DQFRFT) introduces a fractional-order parameter that extends traditional Fourier transform techniques, providing new insights into the analysis of quaternion-valued signals. This paper presents a rigorous theoretical foundation for the 1DQFRFT, examining essential properties such as linearity, the Plancherel theorem, conjugate symmetry, convolution, and a generalized Parseval’s theorem that collectively demonstrate the transform’s analytical power. We further explore the 1DQFRFT’s unique applications to probabilistic methods, particularly for modeling and analyzing stochastic processes within a quaternionic framework. By bridging quaternionic theory with probability, our study opens avenues for advanced applications in signal processing, communications, and applied mathematics, potentially driving significant advancements in these fields. Full article

Based on the idea of a surface moving frame in differential geometry, a surface envelopment approximation method is proposed for the integrated design of point-contact tooth surfaces. This method utilizes the envelopment characteristic curve of the first tooth surface as the spline curve and adopts the local structure of the second tooth surface along a predesigned contact path as the surface interpolation condition. Through motion transformation described by the motion invariants of the first tooth surface, a conjugate motion space for the second tooth surface is fully defined by the motion invariants of the first tooth surface. This constitutes the basis of the integrated optimization design space and ensures the global optimization and machinability of the tooth surface design method. Using the experimental data of the point meshing tooth surface loading contact, the gap between the two tooth surfaces during no-load meshing is used as the design target parameter to predict and control the shape and size of the contact area under heavy load and further the symmetry requirements of the tooth surface design. Consequently, a variational inequality model for the global optimal design of the point meshing tooth surface is established. Full article

This study develops a mathematical model for soil moisture diffusion, addressing the inverse problem of determining both the diffusion coefficient and the variation coefficient in a nonlinear moisture transfer equation. The model incorporates specific boundary and initial conditions and utilizes experimentally measured moisture values at a boundary point as input data. An iterative method, based on an explicit gradient scheme, is introduced to estimate the soil parameters. The initial boundary value problem is discretized, leading to a difference analog and the formulation of a conjugate difference problem. Iterative formulas for calculating the unknown parameters are derived, with a priori estimates ensuring the convergence of the iterative process. Additionally, the research establishes the convergence of the numerical model itself, providing a rigorous foundation for the proposed approach. The study also emphasizes symmetry in moisture calculations, ensuring consistency regardless of the calculation direction (from right to left or left to right) and confirming that moisture distribution remains symmetric within specified intervals. This preservation of symmetry enhances the model’s robustness and accuracy in parameter estimation. The numerical simulations were successfully conducted over a 7-day period, demonstrating the model’s reliability. The discrepancy between the numerical predictions and experimental observations remained within the margin of measurement error, confirming the model’s accuracy. Full article

The recently developed iterative Wiener filter using a fourth-order tensorial (FOT) decomposition owns appealing performance in the identification of long length impulse responses. It relies on the nearest Kronecker product representation (with particular intrinsic symmetry features), together with low-rank approximations. Nevertheless, this new iterative filter requires matrix inversion operations when solving the Wiener–Hopf equations associated with the component filters. In this communication, we propose a computationally efficient version that relies on the conjugate gradient (CG) method for solving these sets of equations. The proposed solution involves a specific initialization of the component filters and sequential connections between the CG cycles. Different FOT-based decomposition setups are also analyzed from the point of view of the resulting parameter space. Experimental results obtained in the context of echo cancellation confirm the good behavior of the proposed approach and its superiority in comparison to the conventional Wiener filter and other decomposition-based versions. Full article

A major challenge for massive multiple-input multiple-output (MIMO) technology is designing an efficient signal detector. The conventional linear minimum mean square error (MMSE) detector is capable of achieving good performance in large antenna systems but requires computing the matrix inverse, which has very high complexity. To address this problem, several iterative signal detection methods have recently been introduced. Existing iterative detectors perform poorly, especially as the system dimensions increase. This paper proposes two detection schemes aimed at reducing computational complexity in massive MIMO systems. The first method leverages the symmetric accelerated over-relaxation (SAOR) technique, which enhances convergence speed by judiciously selecting the relaxation and acceleration parameters. The SAOR technique offers a significant advantage over conventional accelerated over-relaxation methods due to its symmetric iteration. This symmetry enables the use of the conjugate gradient (CG) acceleration approach. Based on this foundation, we propose a novel accelerated SAOR method named CGA-SAOR, where CG acceleration is applied to further enhance the convergence rate. This combined approach significantly enhances performance compared to the SAOR method. In addition, a detailed analysis of the complexity and numerical results is provided to demonstrate the effectiveness of the proposed algorithms. The results illustrate that our algorithms achieve near-MMSE detection performance while reducing computations by an order of magnitude and significantly outperform recently introduced iterative detectors. Full article

We numerically demonstrate the dispersion map configured by random-based residual dispersion per span (RDPS) applied into the mid-span spectral inversion (MSSI) system to mitigate the impact of chromatic dispersion and the fiber nonlinearity in wavelength division multiplexed (WDM) signals. The dispersion map proposed was a scheme in which the RDPS of all optical fiber spans in the front section of the midway optical phase conjugator (OPC) are randomly selected, and the arrangement order of the RDPS in the rear section is inverted from that of the front section. Numerical simulations were performed by evaluating the compensation of the distorted 960 Gb/s WDM signal as a function of the variation of the DCF length and the SMF length, which are involved in determining RDPS. It was confirmed that the compensation effect of the proposed dispersion maps has improved compared to the conventional dispersion map since the dispersion maps examined in this paper have antipodal symmetry around the midway OPC. In particular, it was confirmed that the method of randomly determining the RDPSs by varying the DCF length slightly improved system performance compared to the variation of SMF lengths. We also found that the feature of the RDPS random distribution patterns can achieve excellent compensation for the distorted WDM signal through 50 iterations. Full article

For all integers $n\ge 1$ and $k\ge 2$, the Hadamard product $v_1★\cdots ★v_k$ of k elements of $K^{n+1}$ (with K being the complex numbers or real numbers) is the element $v\in K^{n+1}$ which is the coordinate-wise product of $v_1,\dots ,v_k$ (introduced by Cueto, Morton, and Sturmfels for a model in Algebraic Statistics). This product induces a rational map $h:{\mathbb{P}}^n{\left(K\right)}^k⤏{\mathbb{P}}^n\left(K\right)$. When $K=\mathbb{C}$, $k=2$ and $X_i\left(\mathbb{C}\right)\subset {\mathbb{P}}^n\left(\mathbb{C}\right)$, $i=1,2$ are irreducible, we prove four theorems for the case $dim{X}_2\left(\mathbb{C}\right)=1$, three of them with $X_2\left(\mathbb{C}\right)$ as a line. We discuss the existence (non-existence) of a cancellation law for ★-products and use the symmetry group of the Hadamard product. In the second part, we work over $\mathbb{R}$. Under mild assumptions, we prove that by knowing $X_1\left(\mathbb{R}\right)★\cdots ★X_k\left(\mathbb{R}\right)$, we know $X_1\left(\mathbb{C}\right)★\cdots ★X_k\left(\mathbb{C}\right)$. The opposite, i.e., taking and multiplying a set of complex entries that are invariant for the complex conjugation and then seeing what appears in the screen ${\mathbb{P}}^n\left(\mathbb{R}\right)$, very often provides real ghosts, i.e., images that do not come from a point of $X_1\left(\mathbb{R}\right)\times \cdots \times X_k\left(\mathbb{R}\right)$. We discuss a case in which we certify the existence of real ghosts as well as a few cases in which we certify the non-existence of these ghosts, and ask several open questions. We also provide a scenario in which ghosts are not a problem, where the Hadamard data are used to test whether the images cover the full screen. Full article