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Electrochemiluminescence resonance energy transfer (ECL-RET) is a versatile signal transduction strategy widely used in the fabrication of chem/biosensors. However, this technique has not yet been applied in visualized imaging analysis of intracellular species due to the insulating nature of the cell membrane. Here, we construct a ratiometric ECL-RET analytical method for hypochlorite ions (ClO−) by ECL luminophore, with a luminol derivative (L-012) as the donor and a fluorescence probe (fluorescein hydrazide) as the acceptor. L-012 can emit a strong blue ECL signal and fluorescein hydrazide has negligible absorbance and fluorescence signal in the absence of ClO−. Thus, the ECL-RET process is turned off at this time. In the presence of ClO−, however, the closed-loop hydrazide structure in fluorescein hydrazide is opened via specific recognition with ClO−, accompanied with intensified absorbance and fluorescence signal. Thanks to the spectral overlap between the ECL spectrum of L-012 and the absorption spectrum of fluorescein, the ECL-RET effect is gradually recovered with the addition of ClO−. Furthermore, the ECL-RET system has been successfully applied to image intracellular ClO−. Although the insulating nature of the cell itself can generate a shadow ECL pattern in the cellular region, extracellular ECL emission penetrates the cell membrane and excites intracellular fluorescein generated by the reactions between fluorescein hydrazide and ClO−. The cell imaging strategy via ECL-RET circumvents the blocking of the cell membrane and enables assays of intracellular species. The importance of the ECL-RET platform lies in calibrating the fluctuation from the external environment and improving the selectivity by using fluorescent probes. Therefore, this ratiometric ECL sensor has shown broad application prospects in the identification of targets in clinical diagnosis and environmental monitoring. [ABSTRACT FROM AUTHOR]

Numerous works have been dedicated to the topic of m -isometries, including [2–6,14,18–20,27,47,48]. In this article, we introduce the concept of (m , N A) -isometry, where A is a non-zero operator and m is a positive integer, as an extension of the m -isometry class created by J. Alger and M. Stankus in the 1980s. We present some algebraic and spectral characteristics of (m , N A) -isometries. Additionally, we investigate the product of an (m , N A) -isometry by an (n , N B) -isometry, which enhances and broadens the previous work of Gu et al. on m -isometries [40]. Finally, we apply our main findings to elementary operators defined on the Hilbert-Schmidt class, which can be identified with a tensor product. This provides a new, less complicated, and non-combinatorial proof of Theorem 2.10 of [30]. [ABSTRACT FROM AUTHOR]

The non-commuting graph of a non-abelian group G with center Z(G) is a simple undirected graph whose vertex set is G∖Z(G) and two vertices x,y are adjacent if xy≠yx. In this paper, we compute Signless Laplacian spectrum and Signless Laplacian energy of non-commuting graphs of certain finite non-abelian groups. We obtain several conditions such that the non-commuting graph of G is Q-integral and observe relations between energy, Signless Laplacian energy and Laplacian energy. In addition, we look into the hyperenergetic and hypoenergetic properties of non-commuting graphs of finite groups. We also assess whether the same graphs are Q-hyperenergetic and L-hyperenergetic. [ABSTRACT FROM AUTHOR]

Optical remote sensing imagery can serve as a crucial data source in numerous fields. However, the susceptibility to weather conditions (like clouds and rain) can render the cloud contamination, leading to the significant influence on optical images. The image quality can be required to restore the spectral information in cloud-contaminated regions. In this study, the spectral information was reconstructed in the cloud-contaminated regions using an object-oriented approach. Synthetic aperture radar (SAR) data was integrated with the radar signals and land cover information, in order to serve as the constraints for the reconstruction. The distance matrix was calculated on the SAR images, and then transplant onto the optical images for the replacement. The pixel-level matching accuracy was enhanced to maximize the retention of spectral information from the original images. A solid foundation was provided for the accurate extraction of subsequent land surface information. The performance was also evaluated to verify the improved model. The comparative experiments were conducted with the traditional pixel replacement, weighted linear regression, and curvature-driven. Visual inspection was carried out over various scenes. The results revealed that the superior quality was achieved in the imagery reconstruction in the thick cloud areas and cloud shadows. Particularly, the consistency was maintained among various land cover pixels in the reconstructed areas by the object-oriented method. The boundaries and areas were accurately delineated in the various types of fine-grained land cover. Quantitative analysis was conducted to validate using some metrics, such as correlation coefficient, root mean square error (RMSE), peak signal-to-noise ratio (PSNR), and structural similarity index (SSIM). The spectral characteristic curves of the pixels were reconstructed to closely match those of the reference images, with the correlation coefficients exceeding 0.99. Notably, significant improvement was observed in the spectral curve recovery of vegetation pixels with the enhanced relative to the rest. The radar vegetation indices were optimized to employ an object-oriented matching mechanism during pixel reconstruction. The traditional pixel replacement model was optimized effectively. Furthermore, the band reflectance was closely resembled that of the reference images. Among the five bands of cloud-contaminated images after reconstruction, the highest correlation coefficients were observed with Band 2 and Band 3 reaching 0.925 and 0.922, respectively, and RMSE values of 0.009 and 0.007, respectively. The reconstructed images shared the minimal quality loss and high similarity to the reference images, with the highest PSNR and SSIM values across all bands. Specifically, the structural similarity values of the reconstructed Band 2 and Band 3 images were 0.902 and 0.910, respectively, with the PSNR values reaching 31.978 and 33.173, respectively. The superior image quality was obtained similar to reference images, which was consistence with spectral characteristics. The experimental results were used to the qualitatively and quantitatively validated the effectiveness of the reconstruction. The object-oriented approach can be expected to reconstruct the spectral information in the cloud-contaminated regions. The remotely sensed images were consistently produced with the higher spectral reconstruction accuracy in the different types of land cover and spectral bands. However, the replacing pixel spectral information was relied primarily on from single-image data. Some limitations was matched the effectiveness between cloudy and cloud-free regions, when reconstructing the large-scale, thick cloud areas in single remote sensing images. Additionally, the global searching can fail to the optimal reconstruction for the locally contaminated cloud pixels. Therefore, further investigation is required to determine the optimal local search range for the pixel matching using different extents of cloud contamination. [ABSTRACT FROM AUTHOR]

The infinite-dimensional hypercube (IDH) is an infinite connected graph with infinite degree at each its vertex, and can be viewed as an infinite-dimensional analog of finite-dimensional hypercubes. In this paper, we investigate a self-adjoint operator determined by the topology of the IDH and a function on the nonnegative integers, which can be interpreted as the Hamiltonian of a free fermion field. We prove that, under some mild conditions, the operator has only pure point spectrum and its spectrum is even a compact interval of the real line. We also obtain some commutation relations concerning the operator, which are of physical interest. [ABSTRACT FROM AUTHOR]

As the availability and importance of high energy X-ray sources grows, accurate source characterizations provide critical information for field flatness corrections, beam hardening corrections, detector response corrections, and radiation shielding assessments. This study uses MCNP6.2 to create accurate high definition angular and energy dependent X-ray source definitions for the most common high energy industrial X-ray sources at 450 kVp, 3 MVp, 6 MVp, 9 MVp, and 15 MVp. [ABSTRACT FROM AUTHOR]

We consider two spectral problems on an equilateral rooted tree with the standard (continuity and Kirchhoff's type) conditions at the interior vertices (except of the root if it is interior) and Dirichlet conditions at the pendant vertices (except of the root if it is pendant). For the first (Neumann) problem we impose the standard conditions (if the root is an interior vertex) or Neumann condition (if the root is a pendant vertex) at the root, while for the second (Dirichlet) problem we impose the Dirichlet condition at the root. We show that for caterpillar trees the spectra of the Neumann problem and of the Dirichlet problem uniquely determine the shape of the tree. Also, we present an example of co-spectral snowflake graphs. [ABSTRACT FROM AUTHOR]

In this paper, we prove an interpolation inequality on Riemann–Liouville fractional integrals and then use it to study the strong stability and semi-uniform stability of fractional resolvent families of order 0 < α < 2 . Let A denote the generator of a bounded fractional resolvent family. We show that if σ (A) ∩ (i R) α is countable and σ r (A) ∩ (i R) α = ∅ , then the bounded fractional resolvent family is strongly stable. And the semi-uniform stability of the fractional resolvent family is equivalent to σ (A) ∩ (i R) α = ∅ . Moreover, the relation between decay rates of semi-uniform stability and growth of the resolvent of A along (i R) α is given. [ABSTRACT FROM AUTHOR]

We investigate the spectrum and the essential spectra of weighted automorphisms of the polydisc algebra A n . In the case n = 2 we provide a detailed and, in most cases, complete description of these spectra. [ABSTRACT FROM AUTHOR]

The Cayley sum graph is a graph whose vertex comprises elements of an abelian group G, and edges are the sum of these vertices belonging to a subset of G, namely, S. We introduce the Cayley sum signed graph by giving the sign to these edges. An edge receives a positive sign if any of the incident vertices belong to S. Otherwise, it receives a negative sign. We discuss the properties of the Cayley sum signed graph. [ABSTRACT FROM AUTHOR]

In this paper, we consider the wreath product of two graphs that yields much more larger graphs than other graph products. We drive a formula for the adjacency spectrum of the wreath product of a complete graph and a circulant graph. As its applications, we obtain their (normalized) Laplacian spectra and further compute the adjacency spectra when the circulant graphs are respectively the Möbius ladder graph, the crown graph and the Andrásfai graph. Moreover, some known results are generalized and a problem is posed for further study. [ABSTRACT FROM AUTHOR]

Let G be a connected graph with adjacency matrix A(G) and distance matrix D(G). Let dist (u , v) denote the distance between the pair of vertices u , v ∈ V (G) , then the transmission trs (u) of vertex u is defined as ∑ v ∈ V (G) dist (u , v) . Let trs (G) be the diagonal matrix whose diagonal elements are the transmissions of the vertices of G. And, let deg (G) be the diagonal matrix whose diagonal elements are the degrees of the vertices of G. In this paper we investigate the Smith normal form (SNF) and the spectrum of the matrices D + deg (G) : = deg (G) + D (G) , D deg (G) : = deg (G) - D (G) , A + trs (G) : = trs (G) + A (G) and A trs (G) : = trs (G) - A (G) . In particular, we explore how good the SNF and the spectrum of these matrices are for determining graphs up to isomorphism. We found that the SNF of A trs has an interesting behaviour when compared with other classical matrices. We note that the SNF of A trs can be used to compute the structure of the sandpile group of certain graphs. We compute the SNF of D + deg , D deg , A + trs and A trs for several graph families. We prove that the SNF of D + deg , D deg , A + trs and A trs determine complete graphs. Finally, we derive some results about the spectrum of D deg and A trs . [ABSTRACT FROM AUTHOR]

We consider a special class of generalized Paley graphs over finite fields, namely the Cayley graphs with vertex set 픽qm and connection set the nonzero (qℓ + 1)th powers in 픽qm, as well as their complements. We explicitly compute the spectrum and the energy of these graphs. As a consequence, the graphs turn out to be (with trivial exceptions) simple, connected, non-bipartite, integral and strongly regular, of pseudo or negative Latin square type. Using the spectral information we compute several invariants of these graphs. We exhibit infinitely many pairs of integral equienergetic non-isospectral graphs. As applications, on the one hand we solve Waring’s problem over 픽qm for the exponents qℓ + 1, for each q and for infinitely many values of ℓ and m. We obtain that the Waring number g(qℓ + 1,qm) = 1 or 2, depending on m and ℓ, thus solving some open cases. On the other hand, we construct infinite towers of integral Ramanujan graphs in all characteristics. Finally, we give the Ihara zeta functions of these graphs. [ABSTRACT FROM AUTHOR]

A strong and fast-moving electrical storm occurred in the Southwest Florida region overnight, from 01:00 UTC on 17 April to 07:00 UTC on 17 April 2023. Video recordings were conducted in the region at Latitude N 26.34° and Longitude W 81.79° for 5 h and 15 min, from 01:45 UTC to 07:00 UTC. The camera captured the flashes transforming from pinkish, violet, blue, and then emerald green in the sky twice: the first colored flash lasted 2.0 s, and the second one lasted 0.5 s. The characteristics of the flashes were analyzed using video images integrated with lightning flash data from the Geostationary Lightning Mapper (GLM). To gain deeper insights into the associated atmospheric conditions, the Advanced Baseline Imager (ABI) was also used to help understand the spectral anomalies. Both events had similarities: the same pattern of changing luminous colors in the optical images and the trajectory of the lightning discharges, showing clusters and horizontal distributions. Event 1 occurred mainly over the ocean and featured more intense storms, heavier rain, and denser, higher cloud-tops compared to Event 2, which occurred inland and involved dissipating storms. Moreover, the group energy detected in Event 1 was an order of magnitude higher than in Event 2. We attribute the wavelength of the recorded colored luminosity to varying atmospheric molecular concentrations, which ultimately contributed to the unique spectral line. In this study, we explore the correlation between colored flashes and specific atmospheric concentrations. [ABSTRACT FROM AUTHOR]

High spectral resolution imaging spectroscopy plays a crucial role in solar observation, regularly serving as a backend instrument for solar telescopes. These instruments find direct application in deriving Doppler velocity from hyperspectral images, offering insights into the dynamic motion of matter on the solar surface. In this study, we present the development of a Fabry–Pérot interferometer (FPI) based imaging spectrometer operating at the Fe I (617.3 nm) wavelength for precise Doppler velocity measurements. The spectrometer features a moderate spectral resolution of λ / Δ λ ≈ 60 , 000 , aiming to balance the imaging signal-to-noise ratio (SNR). The instrument underwent successful observational experiments on the 65-cm Educational Adaptive-Optics Solar Telescope (EAST) at the Shanghai Astronomy Museum. Obtained Doppler velocities were compared with data from the Helioseismic and Magnetic Imager (HMI), the maximum column and row correlation coefficients are 0.9261 and 0.9603, respectively. The estimated cut-off normalized frequency of the power spectral density (PSD) curve for velocity map is approximately 0.4/0.21 times higher than that observed in the HMI data, with potentially higher spatial resolution achievable under better seeing conditions. Based on the estimated imaging SNR levels, the accuracy of velocity measurements is approximately 50 m s−1. [ABSTRACT FROM AUTHOR]

The Sun is a major source of energy for the planetary system in our solar system. The solar output shows variations in timescales from a few days (Bartel's 27-day solar rotation cycle) to several years (the 11-year solar cycle and longer timescales). This variability can be seen in the magnetic field, particle flux, and electromagnetic radiation flux behavior. Several indicators, such as the sunspot number and the Mg II index, have been used as solar activity proxies. Further, direct measurements in radio at centimeter wavelengths have been conducted since 1947 (the F10.7 index). This work uses multiscale techniques to study the relations between these solar indexes and their long-term variations through multiscale techniques. The monthly averages of these indexes from 1979 to 2022 are analyzed using wavelet scalogram, global wavelet spectrum, wavelet cross-correlation, and wavelet entropy techniques. As a result, some nonlinear multiscale aspects in the long-term variations of these solar indexes are identified. The major scales at which these indexes vary are found to be, in order of decreasing energy: sunspots (130.1, 253.9, 11.7, 5.0, and 2.0 months); F10.7 (130.1, 253.9, 39.1, 10.9, 9.9, and 5.4 months), and Mg II (132.9, 39.0, and 10.3 months). Thus, all three indexes present the nearly 11-year solar cycle period as the strongest signal. The three indexes are correlated with a coefficient higher than 0.85 and vary in phase for scales near the 11-year solar cycle, with slight and large deviations from it for longer and shorter scales, respectively. The wavelet entropy analysis shows that the F10.7 and sunspot number values are comparable, while Mg II entropy values are much lower. The entropy also indicates that the minimum values for all the indexes occur close to the solar minimum. However, after the last solar maximum in 2014, the entropy increased even in the declining phase of the cycle, during the 2015 – 2020. [ABSTRACT FROM AUTHOR]

Let R = ϱ I n and D = 0 , e 1 , ... , e n , where ϱ > 1 and e i is the i-th coordinate vector in R n . The spectral properties of the n - dimensional Sierpinski measure μ R , D has been studied over two decades. In this paper, a special type of spectrum called a typical spectrum for μ R , D is considered. We show that ϱ ∈ (n + 1) N is necessary and sufficient for μ R , D to admit a typical spectrum if n + 1 is prime. And some necessary conditions for μ R , D to admit a typical spectrum are provided when n + 1 is not a prime number. Furthermore, under the condition on real Hadamard matrix, we prove that μ R , D admits a quasi-typical spectrum if and only if ϱ ∈ 2 N . These results show that the spectral properties of the Sierpinski measure μ R , D are really different between n + 1 is prime and non-prime. As a corollary, we prove that ϱ ∈ 2 N are the only integers such that μ R , D becomes a spectral measure when n = 3 . [ABSTRACT FROM AUTHOR]

When analyzing a narrowband signal, the Hilbert transform is often used, which makes it possible to describe the process through slowly changing functions: the envelope (amplitude) and, weakly dependent on time, the characteristic signal frequency—the "instantaneous" frequency. Based on the smoothness of these characteristics, one can evaluate the process and compare it at different periods. This approach was used to analyze the spectral components of a series of average monthly Wolf numbers. This description of the main and second harmonics, supplemented by the properties of the long-period component, gives a fairly complete picture of the entire series of monthly averages. The work examines the correspondence of the characteristics of reliable data, with this approach, to the accepted description in terms of the parameters of cycles (maximum of the cycle, duration of the cycle, and its growth branches) and constructs an "envelope" of the maxima of the cycles. The time dynamics of the instantaneous frequencies of the fundamental and second harmonics of the entire series are also presented, and significant differences in their behavior are noted in the intervals corresponding to the reconstructed and reliable parts. [ABSTRACT FROM AUTHOR]

Quantifying the effect of maize tassel on canopy reflectance is essential for creating a tasseling progress monitoring index, aiding precision agriculture monitoring, and understanding vegetation canopy radiative transfer. Traditional field measurements often struggle to detect the subtle reflectance differences caused by tassels due to complex environmental factors and challenges in controlling variables. The three-dimensional (3D) radiative transfer model offers a reliable method to study this relationship by accurately simulating interactions between solar radiation and canopy structure. This study used the LESS (large-scale remote sensing data and image simulation framework) model to analyze the impact of maize tassels on visible and near-infrared reflectance in heterogeneous 3D scenes by modifying the structural and optical properties of canopy components. We also examined the anisotropic characteristics of tassel effects on canopy reflectance and explored the mechanisms behind these effects based on the quantified contributions of the optical properties of canopy components. The results showed that (1) the effect of tassels under different planting densities mainly manifests in the near-infrared band of the canopy spectrum, with a variation magnitude of ±0.04. In contrast, the impact of tassels on different leaf area index (LAI) shows a smaller response difference, with a magnitude of ±0.01. As tassels change from green to gray during growth, their effect on reducing canopy reflectance increases. (2) The effect of maize tassel on canopy reflectance varied with spectral bands and showed an obvious directional effect. In the red band at the same sun position, the difference in tassel effect caused by the observed zenith angle on canopy reflectance reaches 200%, while in the near-infrared band, the difference is as high as 400%. The hotspot effect of the canopy has a significant weakening effect on the shadow effect of the tassel. (3) The non-transmittance optical properties of maize tassels reduce canopy reflectance, while their high reflectance increases it. Thus, the dual effects of tassels create a game in canopy reflectance, with the final outcome mainly depending on the sensitivity of the canopy spectrum to transmittance. This study demonstrates the potential of using 3D radiative transfer models to quantify the effects of crop fine structure on canopy reflectance and provides some insights for optimizing crop structure and implementing precision agriculture management (such as selective breeding of crop optimal plant type). [ABSTRACT FROM AUTHOR]

Roughly speaking, the spectrum of multiplicative functions is the set of all possible mean values. In this paper, we are interested in the spectra of multiplicative functions supported over powerfull numbers. We prove that its real logarithmic spectrum takes values from − 2 / (4 + 2) = − 0.26160... to 1 while it is known that the logarithmic spectrum of real multiplicative functions over all natural numbers takes values from 0 to 1. In the course of this study, we correct and complete the proof of Granville and Soundararajan on the spectrum of all multiplicative functions. • Correct a proof of Granville and Soundararajan on the spectrum of multiplicative functions. • Extend the study of spectrum to multiplicative functions supported over powerfull / squarefull numbers. • The key idea of proof is the construction of accurate auxiliary multiplicative functions to decompose the original ones via Dirichlet convolution. [ABSTRACT FROM AUTHOR]

The hyperspectral camera for auroral imaging (HySCAI), which can provide a two-dimensional (2D) aurora image with full spectrum, was developed to study auroral physics. HySCAI consists of an all-sky lens, monitor camera, galvanometer scanner, grating spectrograph, and electron multiplying charge coupled device (EM-CCD). The galvanometer scanner can scan a slit image of the spectrograph on the all-sky image plane in the direction perpendicular to the slit. HySCAI has two gratings; one is 500 grooves/mm for a wide spectral coverage of 400–800 nm with a spectral resolution (FWHM) of 2.1 nm, and the other is 1500 grooves/mm for a higher spectral resolution of 0.73 nm with a narrower spectral coverage of 123 nm. The absolute sensitivity is 2.1 count/s/R with 4 × 4 binning (256 × 340 image) at 557.7 nm. The exposure time depends on the brightness of the aurora emission and is typically 64 s for a 2D image (0.2 s per line scan). This system has been installed at the KEOPS (Kiruna Esrange Optical Platform Site) of the SSC (Swedish Space Corporation) in Kiruna, Sweden. All-sky images with a liquid crystal filter and a sky color camera have also been installed to compensate for the poor time resolution of HySCAI. 2D aurora monochromatic images for given wavelength are obtained by reconstructing the EM-CCD image over the scan period. HySCAI has the advantage of providing a 2D image of intensity for a weak emission line, which appears on top of a high background emission without the contamination from other emissions, which is usually difficult in a system with a bandpass filter. As the first light results, monochromatic images of N 2 + 1NG (0, 1) (427.8 nm), N 2 + 1NG (0, 2) (470.9 nm), H β (486.1 nm), N II (500.1 nm), N I ( 2 D) (520.0 nm), O I ( 1 S) (557.7 nm,), NaD (589.3 nm), O I ( 1 D) (630.0 nm), and N 2 + 1NG (670.5 nm) emission intensity were measured. We estimated the precipitating electron energy from a ratio of I(630.0 nm)/I(427.8 nm) to be 1.6 keV. [ABSTRACT FROM AUTHOR]

It is a common postulate that spectral properties of operators describing physical systems are independent of the underlying reference frames. For the Laplace operator on topological crystals, we prove such a statement from a deeper analysis of the behavior of spectral properties with respect to arbitrary choices. In particular, we investigate the impact of the choice of a unit cell, and of the choice of a family of generators for the transformation group. [ABSTRACT FROM AUTHOR]

This article presents a new proof of a theorem concerning bounds of the spectrum of the product of unitary operators and a generalization for differentiable curves of this theorem. The proofs involve metric geometric arguments in the group of unitary operators and the sphere where these operators act. [ABSTRACT FROM AUTHOR]

The largely binary nature of biological sex and its conflation with the socially constructed concept of gender has created much strife in the last few years. The notion of gender identity and its differences and similarities with sex have fostered much scientific and legal confusion and disagreement. Settling the debate can have significant repercussions for science, medicine, legislation, and people's lives. The present review addresses this debate though different levels of analysis (i.e., genetic, anatomical, physiological, behavioral, and sociocultural), and their implications and interactions. We propose a rationale where both perspectives coexist, where diversity is the default, establishing a delimitation to the conflation between sex and gender, while acknowledging their interaction. Whereas sex in humans and other mammals is a biological reality that is largely binary and based on genes, chromosomes, anatomy, and physiology, gender is a sociocultural construct that is often, but not always, concordant with a person' sex, and can span a multitude of expressions. [ABSTRACT FROM AUTHOR]

Let $ \mathcal {G}_R $ G R denote a unitary one-matching bi-Cayley graph over a finite commutative ring R. In this paper, we give a necessary and sufficient condition for $ \mathcal {G}_R $ G R (respectively, the complement of $ \mathcal {G}_R $ G R and the line graph of $ \mathcal {G}_R $ G R ) to be Ramanujan. [ABSTRACT FROM AUTHOR]

This paper mainly deals with the Sturm–Liouville operator H = 1 w (x) - d d x p (x) d d x + q (x) , x ∈ Γ acting in L w 2 Γ , where Γ is a metric graph. We establish a relationship between the bottom of the spectrum and the positive solutions of quantum graphs, which is a generalization of the classical Allegretto–Piepenbrink theorem. Moreover, we prove the Persson-type theorem, which characterizes the infimum of the essential spectrum. [ABSTRACT FROM AUTHOR]

The maximum length binary sequence (MLBS) is widely used as a broadband pseudo-random noise excitation signal, for example, for system identification. Although its properties have been known for decades, misleading or inaccurate statements can be found in many references. For example, it is sometimes stated that the spectrum of the MLBS is white, whereas in other references a sinc behavior is stated. In this paper, we therefore analyze the MLBS properties based on precise definitions for the given context (time-discrete vs. time-continuous, periodic vs. non-periodic, etc.), especially with respect to Fourier analysis. Another difficulty arises from the fact that in the literature the mathematical definitions are often simplified by means of normalizations which makes the physical interpretation difficult. Therefore, special emphasis is put on scaling factors which allow such a physical interpretation. [ABSTRACT FROM AUTHOR]

We obtain a complete description of the spectrum of the Fréchet algebra of symmetric analytic functions bounded on balls on the sequence space ℓ1$\ell _1$. This is achieved after proving that on the analogous algebra for ℓp$\ell _p$, 1≤p<∞$1\le p <\infty$, the radius function of any evaluation homomorphism δx,x∈ℓp$\delta _x, \nobreakspace x \in \ell _p$, coincides with the norm of x$x$. [ABSTRACT FROM AUTHOR]

Almost Moore mixed graphs appear in the context of the degree/diameter problem as a class of extremal mixed graphs, in the sense that their order is one unit less than the Moore bound for such graphs. The problem of their existence has been considered just for diameter 2. In this paper, we give a complete characterization of these extremal mixed graphs for diameters 2 and 3. We also derive some optimal constructions for other diameters. [ABSTRACT FROM AUTHOR]

Background: Rapidly progressive dementia (RPD), characterized by a rapid cognitive decline leading to dementia, comprises a diverse range of disorders. Despite advancements in diagnosis and treatment, research on RPD primarily focuses on Western populations. Objective: This study aims to explore the etiology and demographics of RPD in Chinese patients. Methods: We retrospectively analyzed 323 RPD inpatients at Huashan Hospital from May 2019 to March 2023. Data on sociodemographic factors, epidemiology, clinical presentation, and etiology were collected and analyzed. Results: The median onset age of RPD patients was 60.7 years. Two-thirds received a diagnosis within 6 months of symptom onset. Memory impairment was the most common initial symptom, followed by behavioral changes. Neurodegenerative diseases accounted for 47.4% of cases, with central nervous system inflammatory diseases at 30.96%. Autoimmune encephalitis was the leading cause (16.7%), followed by Alzheimer's disease (16.1%), neurosyphilis (11.8%), and Creutzfeldt-Jakob disease (9.0%). Alzheimer's disease, Creutzfeldt-Jakob disease, and frontotemporal dementia were the primary neurodegenerative causes, while autoimmune encephalitis, neurosyphilis, and vascular cognitive impairment were the main non-neurodegenerative causes. Conclusions: The etiology of RPD in Chinese patients is complex, with neurodegenerative and non-neurodegenerative diseases equally prevalent. Recognizing treatable conditions like autoimmune encephalitis and neurosyphilis requires careful consideration and differentiation. [ABSTRACT FROM AUTHOR]

The Π‐operator, also known as Ahlfors–Beurling transform, plays an important role in solving the existence of locally quasiconformal solutions of Beltrami equations. In this paper, we first construct the Π‐operator on a general Clifford–Hilbert space. This Π‐operator is also an L2 isometry. Further, it can also be used for solving certain Beltrami equations when the Hilbert space is the L2 space of a measure space. Then, we show that this technique can be applied to construct the classical Π‐operator in the complex plane and some other examples on some conformally flat manifolds, which are constructed by U/Γ, where U is a simply connected subdomain of either ℝn+1 or 핊n−1, and Γ is a Kleinian group acting discontinuously on U. The Π‐operators on those manifolds also preserve the isometry property in certain L2 spaces, and their Lp norms are bounded by the Lp norms of the Π‐operators on ℝn+1 or 핊n−1, depending on where U lies. The applications of the Π‐operator to solutions of the Beltrami equations on those conformally flat manifolds are also discussed. At the end, we investigate the Π‐operator theory in the upper‐half space with the hyperbolic metric. [ABSTRACT FROM AUTHOR]

In this paper, we have computed the spectrum and the q -index of the super q -deformed Ginsparg–Wilson Dirac operator in the different cases (fuzzy, non-fuzzy, gauged, and non-gauged) on the superquantum fuzzy two-sphere S q μ (2 | 2) . We also presented the appropriate spin structure that this operator acts on the superquantum (Dirac) spinor bundle. Finally, it was shown that in the non-quantum limit, when q tends to 1, in each case, there is a correct commutative limit for the spectrum and the q -index. [ABSTRACT FROM AUTHOR]

Let A be a unital Hermitian Banach algebra with the spectrum of a ∈ A denoted by σ A (a) . We show that if a continuous and multiplicative function ϕ : A → C satisfies ϕ (a) ∈ σ (a) for all a ∈ A , then ϕ is linear and hence a character of A . [ABSTRACT FROM AUTHOR]

We consider the Wiener–Hopf integral operator in a countably-normed space of measurable functions of rapid decay on the real axis and show that the class of bounded Wiener–Hopf operators contains those with discontinuous symbol of a special form. Under study are the problems of boundedness, noetherianity, and invertibility of such operators. In particular, we obtain some criteria for invertibility in terms of a symbol by introducing the concept of canonical smooth degenerate factorization and establishing that the invertibility of the Wiener–Hopf operator is equivalent to the presence of a canonical smooth degenerate factorization of the symbol of the operator. We describe the canonical smooth degenerate factorization by some functional called the singular index as well as the spectrum of the Wiener–Hopf operator and some relations connecting the spectra of the Wiener–Hopf integral operators. [ABSTRACT FROM AUTHOR]

Green function of a 2n-th order differential equation with normal coefficients on the half-axis is studied. We first consider the Green function of our equation with “frozen” coefficients. Using Levi’s method, we obtain a Fredholm-type integral equation for the Green function of our problem, whose kernel is a Green function of a problem with constant coefficients. We prove an existence and uniqueness theorem for this integral equation in some Banach spaces of operator-valued functions. The main result of this paper is a theorem stating that the solution of the obtained integral equation is a Green function of our problem. [ABSTRACT FROM AUTHOR]

The linear Diophantine fuzzy graph (LDFG) notion serves as a new mathematical approach for the ambiguity and uncertainty modeling in decision-making issues. An LDFG eliminates the strict limitations of various existing graphs. The energy concept in graph theory is one of the most attractive topics that is very important in biological and chemical sciences. The article aims at developing the notion of fuzzy graphs (FG) towards LDFGs, and, also, we extend the energy notion of an FG to the energy of an LDFG and use the concept of energy to model problems linked to the LDFG. To fulfill such a purpose, we make an LDFG and investigate the effectiveness of that part by calculating the concept of energy on this LDFG. We define the LDFG adjacency matrix (AM) concept and the energy of an LDFG. Also, we introduce the new Laplacian energy (LE) concept of an LDFG and investigate its properties. Finally, an application of the LDFG energy to find the most effective component in the hospital information system has been presented. [ABSTRACT FROM AUTHOR]

In the laboratory analysis of geological data, a number of problems arise due to the insufficient accuracy of the results. For example, different laboratories may provide different end results for the same samples, which creates a problem. This can lead to unreliable results, which can ultimately reduce the quality of the assessment. Machine learning allows to speed up the processing of radar data, as well as avoid the above-mentioned «misunderstandings». The problem of conducting scientific research at specialized landfills for a comprehensive assessment of the possibilities of using computer technology in the interpretation of georadar profiles is urgent. This makes it possible to objectively evaluate the result of automatic interpretation of georadar data. The several machine-learning algorithms described in the article are designing to improve the analysis and interpretation of data by incorporating various methods for optimizing georadar data processing processes. These methods include regression, classification and clustering. By incorporating these methods of optimizing the processing of georadar data into several machine-learning algorithms, the software can provide a comprehensive analysis and interpretation of the data obtained. This allows for a better understanding of the relationships, patterns and trends in the data, which ultimately leads to more informed decision-making and improved understanding. To improve the understanding of the results, the following quantitative indicators were obtained: correlation coefficient - 0.7072, determination coefficient - 0.5001, all these indicators correspond to these models. The deviation from the regression line is on average 22.37 units. Based on the classification results, the soil was determined to be wet. Errors in the sets do not exceed 1 %. [ABSTRACT FROM AUTHOR]

We show that, in general, the characteristic polynomial of a hypergraph is not determined by its "polynomial deck", the multiset of characteristic polynomials of its vertex-deleted subgraphs, thus settling the "polynomial reconstruction problem" for hypergraphs in the negative. The proof proceeds by showing that a construction due to Kocay of an infinite family of pairs of 3-uniform hypergraphs which are non-isomorphic but share the same hypergraph deck, in fact, have different characteristic polynomials. The question remains unresolved for ordinary graphs. [ABSTRACT FROM AUTHOR]

Let $ n \geq ~2 $ n ≥ 2 be a natural number, and denote by $ \mathcal {M}_{n} $ M n the algebra of all $ n \times n $ n × n matrices over an algebraically closed field $ \mathbb {F} $ F of zero characteristic. Let also $ K_{1} $ K 1 and $ K_{2} $ K 2 be two non-empty proper subsets of $ \mathbb {F} $ F . In this paper, we characterize linear maps φ on $ \mathcal {M}_{n} $ M n having the property that, for every $ T \in \mathcal {M}_{n} $ T ∈ M n , the spectrum of T is a subset of $ K_1 $ K 1 if and only if the spectrum of $ \varphi (T) $ φ (T) is a subset of $ K_2 $ K 2 . We obtain a similar caracterization for the case when $ K_{1} $ K 1 and $ K_{2} $ K 2 have both at most n elements, working with the equality of the spectrum to the fixed subsets instead of the inclusion. [ABSTRACT FROM AUTHOR]

The Boidol group is the smallest non- ∗ -regular exponential Lie group. It is of dimension 4 and its Lie algebra is an extension of the Heisenberg Lie algebra by the reals with the roots 1 and -1. We describe the C*-algebra of the Boidol group as an algebra of operator fields defined over the spectrum of the group. It is the only connected solvable Lie group of dimension less than or equal to 4 whose group C*-algebra had not yet been determined. [ABSTRACT FROM AUTHOR]

Condition spectrum is an essential generalization of the spectrum. This article considers the condition spectrum of bounded linear operators on Banach space and develops certain topological properties. It is observed that the condition spectrum is useful than the spectrum and pseudospectrum for identifying the norm behavior of non-normal matrices. For a bounded linear operator A on a Banach space, we find upper and lower bounds for ‖ e tA ‖ , t ≥ 0 and ‖ A n ‖ , n = 1 , 2 , ... using the condition spectrum of A. These bounds are used to identify the transient effect of the quantities appearing in the time dependent linear dynamical system. [ABSTRACT FROM AUTHOR]

In this paper, we introduce inductive limits of the Fréchet spaces ℓ (p +) , ces (p +) , and d (p +) ( 1 ≤ p < ∞ ) and projective limits of the (LB)-spaces ℓ (p -) , ces (p -) , and d (p -) ( 1 < p ≤ ∞ ). After having established some topological properties of such spaces as acyclicity and ultrabornologicity, we prove that the generalized Cesàro operators C t ( 0 ≤ t ≤ 1 ) act continuously in these sequence spaces, and we determine the spectra. Finally, we study the ergodic properties, that is, power boundedness, (uniform) mean ergodicity, and supercyclicity, of the operators C t acting in the (LF)-spaces and in the (PLB)-spaces mentioned above. [ABSTRACT FROM AUTHOR]

We consider the Neumann–Poincaré operator on a three-dimensional axially symmetric domain which is generated by rotating a planar domain around an axis which does not intersect the planar domain. We investigate its spectral structure when it is restricted to axially symmetric functions. If the boundary of the domain is smooth, we show that there are infinitely many axially symmetric eigenfunctions and derive Weyl-type asymptotics of the corresponding eigenvalues. We also derive the leading order terms of the asymptotic limits of positive and negative eigenvalues. The coefficients of the leading order terms are related to the convexity and concavity of the domain. If the boundary of the domain is less regular, we derive decay estimates of the eigenvalues. The decay rate depends on the regularity of the boundary. We also consider the domains with corners and prove that the essential spectrum of the Neumann–Poincaré operator on the axially symmetric three-dimensional domain is non-trivial and contains that of the planar domain. [ABSTRACT FROM AUTHOR]

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K2 is a new generation of GLONASS satellites that provides code division multiple access (CDMA) signals in the L1, L2 and L3 frequency bands in addition to legacy L1 and L2 signals based on frequency division multiple access (FDMA) modulation. The first GLONASS-K2 satellite was launched in August 2023 and started signal transmission in early September 2023. Based on measurements with a 30-m high-gain antenna, spectral characteristics of the various signal components are described and relative power levels are identified. A 3 dB (L1) to 4 dB (L2) higher total power is determined for the CDMA signal compared to the legacy FDMA signal and an equal power of the open service and secured CDMA signal components is found. The ranging code of the L2 channel for service information, which has not been publicly disclosed so far, is identified as a Gold code sequence consistent with the data channel of the L1 open service CDMA signal. The high-gain antenna measurements are complemented by tracking data from terrestrial receivers that enable a first assessment of user performance. An up to 50% improvement in terms of noise and multipath performance is demonstrated for the new L1 and L2 CDMA signals in comparison with their legacy counterpart, but no obvious differences between the different binary phase-shift keying and binary offset carrier modulations of the data and pilot components of these signals could be identified for the test stations. Triple-frequency carrier phase observations from L1, L2, and L3 CDMA signals exhibit good consistency at the noise and multipath level, except for small variations that can be attributed to slightly different antenna phase patterns on the individual frequencies. Overall, the new CDMA signals are expected to notably improve and facilitate precise point positioning applications once fully deployed across the GLONASS constellation. [ABSTRACT FROM AUTHOR]

This research paper covers a comprehensive investigation into the design, analysis, and performance evaluation of frequency reconfigurable antennas. The relentless advancement of wireless communication technology has necessitated the development of antennas that can adapt seamlessly to a wide range of operating frequencies. The proposed antenna design incorporates a circular ring configuration with a PIN diode for dynamic frequency tuning. The reconfigurable element allows for versatile operation across multiple frequency bands, avoiding the requirement for separate antennas and simplifying system integration. The performance evaluation encompasses key parameters such as radiation pattern, gain, bandwidth, and efficiency, assuring optimal performance across the specified frequency range. The measured and simulated results validate the accuracy and effectiveness of the recommended structure. The research findings contribute to the state-of-the-art advancements in frequency reconfigurable antenna engineering, enabling efficient wireless communication systems for several applications, such as cellular networks, WLANs, satellite communication systems, and cognitive radio networks. [ABSTRACT FROM AUTHOR]

The present paper explores the spectral cocycle defined in [9] in the special case of bijective substitutions on two letters, the most prominent example being the Thue-Morse substitution. We derive an explicit subexponential behaviour of the deviations from the expected exponential behavior. Moreover, these sharp bounds will be exploited to prove that the top Lyapunov exponent is greater or equal to the top exponent of the subshift topological factors after a renormalization. In order to obtain such results for the substitutive subshift factors, we define a special kind of sum, which is a multiple version of the twisted Birkhoff sum. For the particular case of the Thue-Morse substitution, we derive that the exponent is zero, we give an explicit subexponential bound for the twisted Birkhoff sums and we do the same for subshift topological factors. [ABSTRACT FROM AUTHOR]

We have developed new methods for constructing exponential Riesz bases by combining existing ones. These methods involve taking unions of frequency sets and domains respectively, offering easier construction compared to known techniques. Along with examples illustrating our methods, we also provide several examples that highlight the intricate nature of exponential Riesz bases.

Abstract The hyperspectral camera for auroral imaging (HySCAI), which can provide a two-dimensional (2D) aurora image with full spectrum, was developed to study auroral physics. HySCAI consists of an all-sky lens, monitor camera, galvanometer scanner, grating spectrograph, and electron multiplying charge coupled device (EM-CCD). The galvanometer scanner can scan a slit image of the spectrograph on the all-sky image plane in the direction perpendicular to the slit. HySCAI has two gratings; one is 500 grooves/mm for a wide spectral coverage of 400–800 nm with a spectral resolution (FWHM) of 2.1 nm, and the other is 1500 grooves/mm for a higher spectral resolution of 0.73 nm with a narrower spectral coverage of 123 nm. The absolute sensitivity is 2.1 count/s/R with 4 × 4 binning (256 × 340 image) at 557.7 nm. The exposure time depends on the brightness of the aurora emission and is typically 64 s for a 2D image (0.2 s per line scan). This system has been installed at the KEOPS (Kiruna Esrange Optical Platform Site) of the SSC (Swedish Space Corporation) in Kiruna, Sweden. All-sky images with a liquid crystal filter and a sky color camera have also been installed to compensate for the poor time resolution of HySCAI. 2D aurora monochromatic images for given wavelength are obtained by reconstructing the EM-CCD image over the scan period. HySCAI has the advantage of providing a 2D image of intensity for a weak emission line, which appears on top of a high background emission without the contamination from other emissions, which is usually difficult in a system with a bandpass filter. As the first light results, monochromatic images of $$\hbox {N}_2^+$$ N 2 + 1NG (0, 1) (427.8 nm), $$\hbox {N}_2^+$$ N 2 + 1NG (0, 2) (470.9 nm), $$\hbox {H}_{\beta }$$ H β (486.1 nm), N II (500.1 nm), N I ( $$^2$$ 2 D) (520.0 nm), O I ( $$^1$$ 1 S) (557.7 nm,), NaD (589.3 nm), O I ( $$^1$$ 1 D) (630.0 nm), and $$\hbox {N}_2^+$$ N 2 + 1NG (670.5 nm) emission intensity were measured. We estimated the precipitating electron energy from a ratio of I(630.0 nm)/I(427.8 nm) to be 1.6 keV. Graphical Abstract

We find the spectrum and eigenvectors of an arbitrary irreducible complex tridiagonal matrix with two-periodic main diagonal. This is expressed in terms of the spectrum and eigenvectors of the matrix with the same sub- and superdiagonals and zero main diagonal. Our result generalises some recent results where the latter matrix stemmed from certain discrete orthogonal polynomials including specific cases of the classical Krawtchouk and Hahn polynomials.