Search Results (189)

For the splitting iterative scheme to solve the system of linear equations, an equivalent form in terms of descent and residual vectors is formulated. We propose an extrapolation technique using the new formulation, such that a new splitting iterative scheme (NSIS) can be simply generated from the original one by inserting an acceleration parameter preceding the descent vector. The spectral radius of the NSIS is proven to be smaller than the original one, and so has a faster convergence speed. The orthogonality of consecutive residual vectors is coined into the second NSIS, from which a stepwise varying orthogonalization factor can be derived explicitly. Multiplying the descent vector by the factor, the second NSIS is proven to be absolutely convergent. The modification is based on the maximal reduction of residual vector norm. Two-parameter and three-parameter NSIS are investigated, wherein the optimal value of one parameter is obtained by using the maximization technique. The splitting iterative schemes are unified to have the same iterative form, but endowed with different governing equations for the descent vector. Some examples are examined to exhibit the performance of the proposed extrapolation techniques used in the NSIS. Full article

This work aims to assess the droplets produced by a novel evaporation process, proposed as an alternative for managing tequila vinasses, using a spectral camera with three spectral bands and a thermal camera mounted on an unmanned aerial vehicle (UAV). High-resolution satellite images with seven spectral bands complemented this characterization. The spectral characterization was conducted by comparing three experimental conditions: the background of the study area without droplets, the droplets generated from purified water, and the droplets produced from tequila vinasses. Two monitoring campaigns, conducted in November 2024 and January 2025, revealed that the tequila vinasse droplets exhibited a maximum influence radius of 16 m, primarily regulated by wind speed conditions (6–16 km/h). Thermal analysis identified the droplet plume as a zone with a lower temperature, creating a thermal contrast of up to 6.6 °C against the average background temperature of 36.6 °C. No significant difference was observed in the influence radius between the droplets generated from vinasse and those from potable water. Spectral analysis of the UAV and satellite images showed significant (p < 0.05) differences in reflectance when the droplets were present (e.g., the coastal blue band increased from an average of 14.43 to 95.59 when vinasse droplets were present). This suggests that the presence of chemical compounds altered light absorption and reflection. However, the instrument’s sensitivity limited the detection of organic compounds at concentrations below its detection limit. The monitoring data presented in this manuscript is crucial for developing strategies to mitigate the potential environmental impacts of the droplets emitted by this novel process. Full article

The galaxy NGC 7469 is a bright infrared source with an active galactic nucleus (AGN) and an intense star-forming region with a radius of approximately 500 parsecs, where the star formation rate is estimated to be 20–50 $M_{\odot }{\mathrm{yr}}^{-1}$. This study presents the results of spectral and photometric observations carried out during the period from 2020 to 2024 at the Fesenkov Astrophysical Institute (Almaty, Kazakhstan) and the Nasreddin Tusi Shamakhy Astrophysical Observatory (Shamakhy, Azerbaijan). Photometric data were obtained using B, V, and Rc filters, while spectroscopic observations covered the wavelength range of $\lambda$ 4000–7000 Å. Data reduction was performed using the IRAF and MaxIm DL Pro6 software packages. An analysis of the light curves revealed that after the 2019–2020 outburst, the luminosity level of NGC 7469 remained relatively stable until the end of 2024. In November–December 2024, an increase in brightness (∼0.3–0.5 magnitudes) was recorded. Spectral data show variations in the Ha fluxes and an enhancement of them at the end of 2024. On BPT diagrams, the emission line flux ratios [OIII]/H $\beta$ and [NII]/H $\alpha$ place NGC 7469 on the boundary between regions dominated by different ionization sources: AGN and star-forming regions. The electron density of the gas, estimated from the intensity ratios of the [SII] 6717, 6731 Ålines, is about $900–1000{\mathrm{cm}}^{-3}$. Continued observations will help to determine whether the trend of increasing brightness and emission line fluxes recorded at the end of 2024 will persist. Full article

LiTaO₃ crystals doped with Cr³⁺ and Nd³⁺ ions are promising for developing active nonlinear laser media. In this work, the defect structure of LiTaO₃ crystals, including those doped with Cr³⁺ and Nd³⁺, is examined. X-ray patterns of all six investigated LiTaO₃:Cr:Nd crystals are identical and correspond to a highly perfect structure. Using optical microscopy, the presence of defects of various shapes, microinhomogeneities, and lacunae was revealed. The optical absorption and Raman scattering spectra of a series of nonlinear, optical, double-doped LiTaO₃:Cr³⁺:Nd³⁺ (0.06 ≤ [Cr³⁺] ≤ 0.2; 0.2 ≤ [Nd³⁺] ≤ 0.45 wt%) crystals showed that at concentrations of doping Cr³⁺ ions less than 0.09 wt% and Nd³⁺ ions less than 0.25 wt%, the crystal structure is characterized by a low level of defects, and the optical transmission spectra characterized by narrow lines corresponding to electron transitions in Nd³⁺ ions. In this case, for the radiative transition in the cation sublattice, the existence of three nonequivalent neodymium centers is observed, and for the radiative transition, two nonequivalent centers are observed. IR absorption spectroscopy in the OH⁻-stretching vibration range revealed two main spectral regions: 3463–3465 cm⁻¹, associated with stoichiometry changes, and 3486–3490 cm⁻¹, linked to complex defects such as (V^-_Li)-OH and (Ta⁴⁺_Li)-OH. A distinct low-intensity line at ~3504 cm⁻¹ was observed only in doped crystals, attributed to (Nd²⁺_Li)-OH defects that significantly distort the oxygen-octahedral clusters due to the larger ionic radius of Nd³⁺ compared to Ta⁵⁺. In contrast, Cr-related defects cause only minor distortions. The Klauer method indicated that the highest concentration of OH⁻-groups occurs in the LiTaO₃:Cr³⁺ (0.09 wt%):Nd³⁺ (0.25 wt%) crystal, where multiple complex defects are present. Full article

While the adjacency tensor of a bipartite 2-graph is a nonnegative biquadratic tensor, it is inherently reducible. To address this limitation, we introduce the concept of quasi-irreducibility in this paper. The adjacency tensor of a bipartite 2-graph is quasi-irreducible if that bipartite 2-graph is not bi-separable. This new concept reveals important spectral properties: although all M⁺-eigenvalues are M⁺⁺-eigenvalues for irreducible nonnegative biquadratic tensors, the M⁺-eigenvalues of a quasi-irreducible nonnegative biquadratic tensor can be either M⁰-eigenvalues or M⁺⁺-eigenvalues. Furthermore, we establish a max-min theorem for the M-spectral radius of a nonnegative biquadratic tensor. Full article

Let G be a graph with n vertices, and let $d_G\left(u\right)$ denote the degree of vertex u in $G.$ The maximum degree matrix ${\mathcal{M}}_G$ of G is the square matrix of order n whose $(u,v)$-entry is equal to $max{d}_G\left(u\right),d_G\left(v\right)$ if vertices u and v are adjacent in G, and zero otherwise. Let $B_{p,q,r}$ be the graph obtained from the complete graph $K_p$ by removing an edge $uv$, and identifying vertices u and v with the end vertices $u\prime$ and $v\prime$ of the paths $P_q$ and $P_r$, respectively. Let $\mathbb{G}n,d$ denote the set of simple, connected graphs with n vertices and diameter d. A graph in $\mathbb{G}n,d$ that attains the largest spectral radius of the maximum degree matrix is called a maximizing graph. In this paper, we first characterize the spectrum of the maximum degree matrix for graphs of the form $B_{n-i+2,i,d-i}$, where $1\le i\le \lfloor \frac{d}{2}\rfloor$. Furthermore, for $d\ge 2,$ we prove that the maximizing graph in $\mathbb{G}n,d$ is $Bn-d+2,\lfloor \frac{d}{2}\rfloor ,\lceil \frac{d}{2}\rceil .$ Finally, if $d\ge 4$ is an even integer, then the spectral radius of the maximum degree matrix in $B_{n-d+2,\lfloor \frac{d}{2}\rfloor ,\lceil \frac{d}{2}\rceil }$ can be computed as the largest eigenvalue of a symmetric tridiagonal matrix of order ${\displaystyle \frac{d}{2}}+1$. Full article

In this work, we address the solvability of a Riemann–Liouville-type fractional-impulsive integral boundary value problem. Under some conditions on the spectral radius corresponding to the related linear operator, we use fixed-point methods to obtain several existence theorems for our problem. In particular, we obtain the existence of multiple positive solutions via the Avery–Peterson fixed-point theorem. Note that our linear operator depends on the impulsive term and the integral boundary condition. Full article

LetGbe a graph. An odd $[1,k]$-factor of a graph G is a spanning subgraph H of G such that $de{g}_H(v)$ is odd and $1⩽de{g}_H(v)⩽k$ for every $v\in V(G)$ where k is a positive odd integer. We call a spanning subgraph H of a graph G a strong star factor if every component of H is isomorphic to an element of the stars $K_{1,1},K_{1,2},\cdots ,K_{1,r}$ and is an induced subgraph of G where $r⩾2$ is an integer. In a $\{K_{1,1},K_{1,2},C_m:m⩾3\}$-factor of G, each component is isomorphic to a member in $\{K_{1,1},K_{1,2},C_3,C_4\cdots ,C_m\}$. A graph G is a strong star factor deleted graph if $G-e$ has a strong star factor for each edge e of G. In this paper, through the typical spectral techniques, we obtain the respective necessary and sufficient conditions defining a strong star factor deleted graph, an odd $[1,k]$-factor deleted graph, and a $\{K_{1,1},K_{1,2},C_m:m⩾3\}$-factor deleted graph. We determine a lower bound on the size to guarantee that G is a $\{K_{1,1},K_{1,2},C_m:m⩾3\}$-factor deleted graph. We establish the upper bound of the signless Laplacian spectral radius (resp. the spectral radius) and the lower bound of the distance signless Laplacian spectral radius (resp. the distance spectral radius) to determine whether G admits a strong star factor. Furthermore, by constructing extremal graphs, we show that all the bounds obtained in this contribution are the best possible. Full article

Micro-racetrack resonators have become one of the key components for realizing signal processing, generation, and integration in microwave photonics, owing to their high Q factor, compact footprint, and tunability. However, most of the reported micro-racetrack resonators are confined to the single-mode regime. In this paper, we designed an ultra-compact multimode micro-racetrack resonator (MMRR) based on shape-optimized multimode waveguide bends (MWBs). Cubic spline curves were used to represent the MWB boundary and adjoint methods were utilized for inverse optimization, achieving an effective radius of 8 μm. Asymmetric directional couplers (ADCs) were designed to independently couple three modes into a multimode micro-racetrack, according to phase-matching conditions and transmission analysis. The MMRR was successfully fabricated on a commercial platform using a 193 nm dry lithography process. The device exhibited high loaded Q factors of 2.3 × 10⁵, 4.1 × 10⁴, and 2.9 × 10⁴, and large free spectral ranges (FSRs) of 5.4, 4.7, and 4.2 nm for ${\mathrm{TE}}_0$, ${\mathrm{TE}}_1$, and ${\mathrm{TE}}_2$ modes, with about a 19 × 55 μm² footprint. Full article

Eigenvalue decomposition (EVD) of covariance matrices or coherence matrices has been employed to suppress noise in phase information, and this approach has shown some effectiveness in data processing. However, while this method helps attenuate noisy phase components, it also tends to significantly degrade the true deformation phase information, which can be detrimental in certain applications. To address this issue, this paper proposes an optimal eigenvalue decomposition phase optimization method, incorporating a spectral radius-constrained covariance matrix construction, named SREVD. This method constructs a covariance matrix using spectral radius constraints and then selects optimal eigenvectors from the covariance matrix for weighted combination, yielding the final optimized phase. The advantages of this approach (1) include the use of spectral radius constraints to obtain a stable covariance matrix, and (2) rather than using the eigenvector associated with the maximum eigenvalue for phase optimization, the interferometric phase is reconstructed by a weighted combination of eigenvectors selected through eigenvalue-based optimization. Experimental analysis conducted in a mining area in Datong, Shanxi Province, China, yields the following conclusions: compared to the original interferogram and the traditional EVD-optimized interferogram, the proposed SREVD method demonstrates superior noise suppression. After optimization with SREVD, the density of monitoring points has been significantly improved. The final number of selected points is 9.06 times that of StaMPS and 1.3 times that of EVD optimization, which can better reflect the topographic changes in the study area. Full article

The tunable CO₂ laser is a common pump source for optically pumped terahertz lasers. In this paper, based on a sealed-off CO₂ laser tube and a grating-tuned cavity, we reported an efficient, high-power, low-cost, simple structure and tunable continuous-wave CO₂ laser. A sealed-off CO₂ laser tube was designed and customized, and its plasma discharge characteristics were experimentally analyzed. The influence of output coupler transmittance and discharge current on the laser’s tunability and output power was systematically studied using grating tuning. A total of 78 spectral lines were achieved within the wavelength range of 9.17–10.86 μm. The maximum output power of 55.5 W was recorded on the 10P20 line when the output coupler transmittance was approximately 22%. The laser exhibited a beam spot radius of about 3.8 mm and a beam quality factor (M²) of 1.74. Full article

In this article, we study singular fractional-order differential equations with a variable coefficient, namely the linear operator of the differential equation containing a linear term with a variable coefficient. The coefficient $a\left(s\right)$ permits singularity at $s=0, 1$, and the nonlinearity $\mathfrak{f}(s,\chi )$ may be singular at $s=0, 1$ and $\chi =0$. By utilizing the fixed-point index theory, the existence of positive solutions are derived under sharp conditions concerning spectral radius. Full article

Optical fiber-based acoustic detectors for ultrasound imaging in medical field feature plano-concave Fabry–Perot cavities integrated on fiber tips, realized via dip-coating. This technique imposes constraints on sensor geometry, potentially limiting performance. Lab-on-Fiber technology enables complex three-dimensional structures with precise control over geometric parameters, such as the curvature radius. A careful investigation of the optical and mechanical aspects involved in the sensors’ performances is crucial for determining the design rules of such probes. In this study, we numerically analyzed the impact of curvature on the optical and acoustic properties of a plano-concave cavity using the Finite Element Method. Performance metrics, including sensitivity, bandwidth, and directivity, were compared to planar Fabry–Perot configurations. The results suggest that introducing curvature significantly enhances sensitivity by improving light confinement, especially for cavity thicknesses exceeding half the Rayleigh zone (∼45 μm), reaching an enhancement of 2.5 a L = 60 μm compared to planar designs. The curved structure maintains high spectral quality (FOM) despite 2% fabrication perturbations. A mechanical analysis confirms no disadvantages in acoustic response and bandwidth (∼40 MHz). These findings establish curved plano-concave structures as robust and reliable for high-sensitivity polymeric lab-on-fiber ultrasound detectors, offering improved performance and fabrication tolerance for MHz-scale bandwidth applications. Full article

Abundant and diverse urban bird communities promote ecosystem and human health in cities. However, the estimation of bird community structure requires large amounts of resources. On the other hand, calculating remotely sensed spectral indices is cheap and easy. Such indices are directly related to vegetation cover, built-up cover, and temperature, factors that also affect the presence and abundance of bird species in urban areas. Therefore, spectral indices can be used as proxies of the structure of urban bird communities. We estimated the abundance, taxonomic, functional, and phylogenetic diversity of the bird community at each of 18 50 m radius survey stations in the urban core area of Kavala, Greece. We also calculated eight spectral indices (means and standard deviations, SDs) around survey stations at 50 m, 200 m, and 500 m spatial scales. The land surface temperature SD (LST) was the most important proxy, positively related to bird abundance at the 50 m and 200 m spatial scales. At the same time, the mean green normalized difference vegetation index (GNDVI) was the most important proxy, negatively related to abundance at the 500 m spatial scale. Means and SDs of vegetation indices, such as the normalized difference vegetation index (NDVI), enhanced vegetation index (EVI2), soil-adjusted vegetation index (SAVI), and atmospherically resistant vegetation index (ARVI), were the most important proxies, positively related to taxonomic and functional diversity at all the spatial scales. The mean and SDs of LST, normalized difference moisture index (NDMI), and normalized difference built-up index (NDBI) variously affected taxonomic and functional diversity. The mean and SDs of LST were the best proxies of phylogenetic diversity at the 50 m and 500 m spatial scales, while the SDs of NDBI and NDMI were the best proxies at the 200 m spatial scale. The results suggest that several spectral indices can be used as reliable proxies of various facets of urban bird diversity. Using such proxies is an easy and efficient way of informing successful urban planning and management. Full article

A wavelength-swept laser (WSL) demodulation system offers a unique time-domain analysis solution for high-sensitivity optical fiber sensors, providing a high-resolution and high-speed method compared to optical spectrum analysis. However, most traditional WSL-demodulated sensing systems require a synchronous trigger signal or an additional optical dispersion link for sensing analysis and typically use a fiber Bragg grating (FBG) as the sensing unit, which limits displacement sensitivity and increases fabrication costs. We present a novel displacement sensing system that combines a trigger-free WSL demodulation method with a cascaded balloon-like interferometer, featuring a simple structure, high sensitivity, and low temperature cross-sensitivity. The sensor is implemented by bending a short length of single-mode fiber with an optimal radius of around 4 mm to excite cladding modes, which form an interference spectral response with the core mode. Experimental findings reveal that the system achieves a high sensitivity of 397.6 pm/μm for displacement variation, corresponding to 19.88 ms/μm when demodulated using a WSL with a sweeping speed of 20 nm/s. At the same time, the temperature cross-sensitivity is as low as 5 pm/°C or 0.25 ms/°C, making it a strong candidate for displacement sensing in harsh environments with significant temperature interference. Full article