Search

In this paper, attention was focused on identifying the components of the amplitude-frequency spectrum of pressure pulsations in a hydraulic system in which an external low-frequency mechanical vibration was subjected to a proportional hydraulic directional control valve. It was observed that an operating machine or device equipped with hydraulic valves is a source of mechanical vibrations with a wide frequency spectrum. The influence of these vibrations on the pressure pulsation spectrum was analyzed, identifying the components resulting from the forcing of the directional control valve spool. In addition, it was noted that the pressure pulsation spectrum includes components resulting from the pulsation of the displacement pump output feeding the hydraulic system. A description of these spectrum components was also made and, using the solution superposition method, the components of the pressure pulsation spectrum over a wide frequency range were identified. [ABSTRACT FROM AUTHOR]

For a graph G with vertex set V G = { v 1 , v 2 , ... , v n } and edge set E G = { e 1 , e 2 , ... , e m } , let S G denotes the subdivision graph of G with vertex set V G ∪ E G . In S G , replace each vertex v i , i = 1 , 2 , ... , n , by n 1 vertices and join every vertex to the neighbors of v i . Then in the resulting graph, replace each vertex e j , j = 1 , 2 , ... , m , by m 1 vertices and join every vertex to the neighbors of e j . The resulting graph is denoted by S G (n 1 , m 1). This generalizes the construction of the subdivision graph S G to S G (n 1 , m 1) of a graph G. In this paper, we provide the complete information about the spectrum of S G (n 1 , m 1) using the spectrum of S G . Further, we determine the Laplacian spectrum of S G (n 1 , m 1) using the Laplacian spectrum of G , when G is a regular graph. Also, we find the Laplacian spectrum of S G (n 1 , m 1) using the Laplacian spectrum of S G when n 1 = m 1 . The energy of a graph G is defined as the sum of the absolute values of the eigenvalues of G. The incidence energy of a graph G is defined as the sum of the square roots of the signless Laplacian eigenvalues of G. Finally, as an application, we show that the energy of the graph S G (n 1 , m 1) is completely determined by the incidence energy of the graph G. [ABSTRACT FROM AUTHOR]

We introduce the zeta function of a signed graph and give a determinant expression for it in terms of the signed oriented line graph, and moreover, we obtain some properties of the zeta function of a signed graph. As applications we affirm the conjecture proposed by Sato [Weighted zeta functions of graph coverings, Electronic J. Combin. 13 (2006), #91] and give a method to construct a family of cospectral signed digraphs. Additionally, we show that two connected regular signed graphs have the same zeta function if and only if they are cospectral. [ABSTRACT FROM AUTHOR]

Given a graph G , consider the family of real symmetric matrices with the property that the pattern of their nonzero off-diagonal entries corresponds to the edges of G. For the past 30 years a central problem has been to determine which spectra are realizable in this matrix class. Using combinatorial methods, we identify a family of graphs and multiplicity lists whose realizable spectra are highly restricted. In particular, we construct trees with multiplicity lists that require a unique spectrum, up to shifting and scaling. This represents the most extreme possible failure of spectral arbitrariness for a multiplicity list, and greatly extends all previously known instances of this phenomenon, in which only single linear constraints on the eigenvalues were observed. [ABSTRACT FROM AUTHOR]

Given a rooted tree T with vertices u 1 , u 2 , ... , u n , the level matrix L (T) of T is the n × n matrix for which the (i , j) -th entry is the absolute difference of the distances from the root to v i and v j. This matrix was implicitly introduced by Balaji and Mahmoud (2017) as a way to capture the overall balance of a random class of rooted trees. In this paper, we present various bounds on the eigenvalues of L (T) in terms of other tree parameters, and also determine the extremal structures among trees with a given order. Moreover, we establish bounds on the multiplicity of any eigenvalue in the level spectrum and show that the bounds are best possible. Furthermore, we provide evidence that the level spectrum can characterise some trees. In particular, we provide an affirmative answer to a very recent conjecture on the level energy (sum of absolute values of eigenvalues). [ABSTRACT FROM AUTHOR]

A non-self-adjoint fourth-order differential operator with nonsmooth coefficients and periodic boundary conditions is considered. Results concerning the asymptotics of the spectrum of this operator are obtained. [ABSTRACT FROM AUTHOR]

What is the definition of Syndrome? Since the beginning of studies in genetics, certain terminologies have been created and used to define groups of diseases or alterations. With the advancement of knowledge and the emergence of new technologies, the use of basic concepts is being done in a mistaken or often confusing way. Because of this, revisiting and readjusting the old terms becomes imminent. Here, we explore these concepts and their use, through a literature compilation of an already well‐defined genetic alteration (16q11.2 microduplication). We bring comparisons in clinical and molecular scope of the alteration itself and its diagnostic methods, to improve the report of cases, rescuing terminologies and their applicability nowadays. Significance Statement: In the genomic era, where genetic tests and diagnostic technologies are advancing rapidly, the correct classification of certain pathologies is essential. For this, revisiting and readjustment of terms becomes imminent. Here, we analyze 16p11.2 microduplication cases and use the data to support a discussion about the use of some classic clinical terms, proposing a new point of view in descriptive care, related to both technological interpretation and expression. [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]

The results of the spectral observation analysis in the Hα line of a site of active region NOAA 11 024, which has been in the main phase of development given its sharply increased activity, are discussed. The studied site (its length is 10 Mm) has been located in the region of a new serpentine magnetic flow emergence. An arch filament system (AFS) has been formed on it, under which an Ellerman bomb (EB) emerged and developed, and a pore formed at a distance of approximately 7.2 Mm from the EB. The evolution of the AFS is studied, and the formation and development of all Hα-ejections that formed in its magnetic loops during the observations are investigated. Spectral data with high spatial (approximately 1″) and temporal (approximately 3 s) resolution were obtained with the THEMIS French–Italian solar telescope (Tenerife, Spain) on July 4, 2009. The observation time is 20 min (to 9:52–10:11 UT). We use the spectral region that contains the central part of the Hα chromospheric line. In all spectra, Hα ejections (surges) are visible both in the long wavelength and short wavelength wings of the absorption line. The changes in the Stokes I profiles shape are studied, which are very diverse and appreciably different from the profile for the undisturbed chromosphere. Depending on whether the ejection moved to the upward direction or to the downward one, the profile component corresponding to it is projected onto the blue or red line wing. Substantially broadened and dual lobed profiles appear close to the end of the observations, which indicates that both downward and upward plasma flows exist nearby. It is found that surges can be comprised of several jets that are formed during successive and periodic magnetic reconnections. Doppler shifts of the profile components are used to calculate the line-of-sight velocities (Vlos) of chromospheric matter in surges. The changes in the Vlos along the cross section of the surge jets at the place of their maximum intensity are analyzed. The Vlos of jets are different and probably depend on the magnetic field structure in the surge and the surrounding environment. The direction of jet movement is also different, since it depends on the phase of surge development. Most of the curves of Vlos changes consist of several segments. This indicates that the large jets are composed of several smaller jets, i.e., they had a fibrous structure. The flows of ascending and descending surges often occur simultaneously and coincide in time with the increase of the EB brightness. A vortex motion of the plasma is observed in one of the surges for approximately 3 min, as evidenced by the inclined dark streaks in the spectra. At the instant of the greatest brightness of the EB, there are seven surges in the studied site of AR, and the plasma moves downward with Vlos up to 77 km/s in three of them and upward with a much lower Vlos up to –35 km/s in five of them. During our observations, the maximum upward velocities of the chromospheric matter in the surges reach –110 km/s, and the downward velocities reach 90 km/s. In the upper part of the magnetic loops, the plasma velocities vary between –25 km/s and 22 km/s. The Vlos values in the site without active formations do not exceed ±2 km/s. It is also analyzed whether the processes of AFS evolution and EB development phases are related. The study is based on a detailed analysis of observational data obtained with high spatial and temporal resolutions, which allowed the authors to better understand the dynamics of the evolution of the arch filament system under which an Ellerman bomb has emerged and developed, and to reveal the features of the formation and development of surges that form in its magnetic loops. They are probably the result of successive and periodic magnetic reconnections, which are associated with the emergence of a new serpentine magnetic flux and occur when its loops interact with the preexisting magnetic field surrounding the active region or between the magnetic loops of the flux itself. [ABSTRACT FROM AUTHOR]

Let G be a directed graph with o r d e r n. The adjacency matrix of the directed graph G is a matrix A = [ a i j ] of order n × n , such that for i ≠ j , if there is an arc from i to j , then a i j = 1 , otherwise a i j = 0. Matrix B = J − A is called the antiadjacency matrix of the directed graph G , where J is the matrix of order n × n with all of those entries are one. In this paper, we provided several properties of the adjacency matrices of directed graphs, such as a determinant of a directed graphs, the characteristic polynomial of acyclic directed graphs, and regular directed graphs. Moreover, we discuss antiadjacency energy of acyclic directed graphs and give some examples of antiadjacency energy for several families of graphs. [ABSTRACT FROM AUTHOR]

Linear gravity anomalies (LGAs) on the Moon have been interpreted as ancient magmatic intrusions formed during the lunar expansion. The composition of such ancient subsurface intrusions may offer hints for the lunar thermodynamic state in the initial stage of lunar history. To pose a first compositional constraint on magmatism related to lunar expansion, this study analyzed the spectrum and gravity around craters on LGAs, such as Rowland, Roche, and Edison craters. Using reflectance spectra around the craters, we first surveyed non‐mare basaltic exposures. To test the LGA excavation scenario as a possible origin of the discovered exposures, we then compared the Gravity Recovery and Interior Laboratory data and post‐cratering gravity simulation with the iSALE shock physics code. Our spectral analysis reveals no basaltic exposure around the Rowland crater. Further, the observed termination of LGA at the crater rim contradicts the gravity simulation, which assumes that LGA predates the Rowland crater. These results suggest that LGA formation might postdate the Rowland formation and that lunar expansion lasted even after the Nectarian age. On the other hand, we found that both Roche and Edison craters possess basaltic exposures in their peripheries. Because the gravity reduction inside Roche crater can be reproduced in our simulation, the discovered basaltic exposures are possibly LGA materials ejected from these craters. The composition of those exposures shows that the LGA intrusions at the two locations are composed of low‐titanium magma, indicating that ancient magma during the expansion did not contain ilmenite‐rich melt, perhaps resulting from the low‐ilmenite content of the ancient upper mantle. Plain Language Summary: The Moon has positive, narrow, and long gravity anomalies, so‐called linear gravity anomalies (LGAs), which are thought to be magmatic intrusions formed during the ancient lunar expansion. The composition of these intrusions may provide insights into the early lunar thermal state. This study analyzed the reflectance spectra and gravity data around craters located on LGAs, specifically Rowland, Roche, and Edison craters, which are postulated to have ejected the LGA material. By analyzing the reflectance spectra, we first identified non‐mare basaltic exposures that likely originated from these subsurface formations. We next examine if these exposures are composed of the LGA materials by comparing the observed gravity with cratering simulation results. We found no basaltic exposures around Rowland and that gravity inside Rowland is not consistent with the excavation hypothesis, perhaps suggesting that LGA formation and lunar expansion occurred after the Rowland formation. On the other hand, we discovered basaltic exposures around both Roche and Edison craters, which can be interpreted as ejecta from the LGAs consistent with the gravity inside Roche crater. The composition of these exposures indicates that LGAs are composed of low‐titanium magma, which provides a new constraint on the ancient thermal state of the Moon. Key Points: High‐calcium pyroxene exposures and gravity reduction around Roche crater imply an excavation of lunar linear gravity anomaly materialsLunar subsurface dikes formed during the ancient expansion stage are estimated to be composed of low‐titanium magmaA linear gravity anomaly possibly postdates the Rowland crater, suggesting a potential prolongation of lunar expansion beyond the Nectarian age [ABSTRACT FROM AUTHOR]

Let { M k } k = 1 ∞ be a sequence of expansive matrices, and let { D k } k = 1 ∞ be a sequence of finite digit sets satisfying Z D k n = F q k n , where Z D k n = { x ∈ [ 0 , 1) n : ∑ d ∈ D k e 2 π i ⟨ d , x ⟩ = 0 } , F q k n = ( Z n q k ∩ [ 0 , 1) n) \ { 0 } and the sequence { q k } k = 1 ∞ is bounded with q k ≥ 2 . In this paper, we show that the associated integral Moran measure μ { M k } , { D k } is a spectral measure if and only if # D k = q k n for all k ≥ 1 and M k ∈ M n (q k Z) for all k ≥ 2 . [ABSTRACT FROM AUTHOR]

Let μ be a positive finite Borel measure on [0, 1). Cesàro-type operators C μ when acting on weighted spaces of holomorphic functions are investigated. In the case of bounded holomorphic functions on the unit disc we prove that C μ is continuous if and only if it is compact. In the case of weighted Banach spaces of holomorphic function defined by general weights, we give sufficient and necessary conditions for the continuity and compactness. For standard weights, we characterize the continuity and compactness on classical growth Banach spaces of holomorphic functions. We also study the point spectrum and the spectrum of C μ on the space of holomorphic functions on the disc, on the space of bounded holomorphic functions on the disc, and on the classical growth Banach spaces of holomorphic functions. All characterizations are given in terms of the sequence of moments (μ n) n ∈ N 0 . The continuity, compactness and spectrum of C μ acting on Fréchet and (LB) Korenblum type spaces are also considered. [ABSTRACT FROM AUTHOR]

Laser-induced fluorescence (LIF) is an established noninvasive measurement method to determine temperature distributions and local gas concentrations in combustion processes with high spatial and temporal resolution. This work presents high-precision LIF spectra of acetone and other tracers at ambient conditions. By using a large UV-sensitive sCMOS camera instead of an image intensified camera, many issues like nonlinearity, varying sensitivity, vignetting, limited resolution etc. could be minimized or eliminated. Particular care was taken to remove residual stray light and to calibrate the spectra with metrological traceability to the International System of Units SI. [ABSTRACT FROM AUTHOR]

This review explores the clinical presentation of similarities and differences in Attention-Deficit/Hyperactivity Disorder (ADHD) and Autism Spectrum Disorder (ASD). This paper investigates the deficits in executive function, social function, and emotional intelligence that are seen in both conditions and how the presence of both conditions can exacerbate these deficiencies. Understanding the clinical presentations in these domains is critical to refine diagnostic methods and treatments and improve outcomes for those affected by these neurodevelopmental disorders. The similarities in clinical presentation between ADHD and ASD present a significant diagnostic challenge, with individuals often exhibiting similar behaviors and difficulty navigating the complexities that encompass reacting to their environment. Further research is paramount in gaining more knowledge of the disorders and challenges faced by these individuals, especially those with the presence of both conditions. [ABSTRACT FROM AUTHOR]

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]

We investigate the existence of nodal solutions for the nonlinear Lidstone boundary value problem { (− 1) m (u (2 m) (t) + c u (2 m − 2) (t)) = λ a (t) f (u) , t ∈ (0 , r) , u (2 i) (0) = u (2 i) (r) = 0 , i = 0 , 1 , ⋯ , m − 1 , (P) where λ > 0 is a parameter, c is a constant, m ≥ 1 is an integer, a : [ 0 , r ] → [ 0 , ∞) is continuous with a ≢ 0 on the subinterval within [ 0 , r ] , and f : R → R is a continuous function. We analyze the spectrum structure of the corresponding linear eigenvalue problem via the disconjugacy theory and Elias's spectrum theory. As applications of our spectrum results, we show that problem (P) has nodal solutions under some suitable conditions. The bifurcation technique is used to obtain the main results of this paper. [ABSTRACT FROM AUTHOR]

The chordal ring (CR) graphs are a well-known family of graphs used to model some interconnection networks for computer systems in which all nodes are in a cycle. Generalizing the CR graphs, in this paper, we introduce the families of chordal multi-ring (CMR), chordal ring mixed (CRM), and chordal multi-ring mixed (CMRM) graphs. In the case of mixed graphs, we can have edges (without direction) and arcs (with direction). The chordal ring and chordal ring mixed graphs are bipartite and 3-regular. They consist of a number r (for r ≥ 1 ) of (undirected or directed) cycles with some edges (the chords) joining them. In particular, for CMR, when r = 1 , that is, with only one undirected cycle, we obtain the known families of chordal ring graphs. Here, we used plane tessellations to represent our chordal multi-ring graphs. This allowed us to obtain their maximum number of vertices for every given diameter. Additionally, we computationally obtained their minimum diameter for any value of the number of vertices. Moreover, when seen as a lift graph (also called voltage graph) of a base graph on Abelian groups, we obtained closed formulas for the spectrum, that is, the eigenvalue multi-set of its adjacency matrix. [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]

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]

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 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]

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]

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]

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]

Background: Differences/disorders of sex development (DSD) encompass a wide range of conditions. Their clinical spectrum and etiological diagnosis have not been reported in Moroccan patients. Aims: The study aims to highlight the clinical spectrum, etiological diagnosis, and management of patients with DSD. Subjects and methods: This is a retrospective study of all patients diagnosed with DSD under the age of 18 years, who were referred to the Pediatric Endocrinology Department and the Medical Genetics Laboratory at HASSAN II University Hospital of Fez between June 2018 and June 2023. Results: Out of 57 patients, 54.4% (n = 31) were diagnosed with 46,XX DSD, the most common type, while 45.6% (n = 26) had 46,XY DSD. Patients with 46,XX DSD presented earlier than those with 46,XY DSD, at a median age of 0.08 years and 0.96 years, respectively. The most commonly reported complaint was atypical genitalia. At the first presentation, the sex of rearing was already assigned to 26 males and 27 females. All patients with 46,XX DSD were diagnosed with congenital adrenal hyperplasia (CAH) at a median age of diagnosis of 0.92 years. Of these, 11 patients were raised as males. Disorders of androgen action or synthesis were more common in XY patients (69.2%). The consanguinity rate was 46.5%, and there were 19 cases with a positive family history, with 10 siblings having died. Conclusion: DSD are not rare in Morocco. Overall, CAH remains the most frequent DSD etiology. Molecular genetic analyses are needed to determine the accurate etiological distribution of DSD, especially in XY patients.

Efficient allocation of resources is crucial in wireless ad hoc networks (WANETs) as spectrum assets are costly. Cooperative communications were introduced as a solution to the problem of limited spectrum availability. In this approach, numerous nodes share their resources and increase the bandwidth available to end-users. This research investigates the practicality of a new algorithm that optimizes resources based on load for Cooperative Communications in 5 G WANETs. The algorithm consists of two components. Initially, a distributed algorithm for forming a topology is suggested. This algorithm employs a load-based approach to explore network conditions and efficiently choose the most suitable topology. An optimization algorithm that relies on a greedy strategy is suggested. In this approach, the chosen nodes send their bits to the receiver to maximize the attainable system throughput. A thorough simulation study is conducted to evaluate the overall performance of the proposed algorithm in assessing existing methods. The proposed model obtained 94.72 % energy efficiency, 91.69 % network throughput, 94.72 % spectrum utilization, 27.47 % network delay, 24.08 % packet loss rate, 94.38 % signal-to-noise ratio, 93.91 % data transfer rate, 95.87 % error detection rate, and 94.28 % link reliability rate. The results demonstrate that the suggested algorithm significantly enhances the system and the overall network performance compared to existing approaches. The proposed approach is feasible and environmentally friendly for optimizing bandwidth in 5 G wireless ad hoc Networks.

Let $ G $ be a directed graph with $ \mathrm{o}\mathrm{r}\mathrm{d}\mathrm{e}\mathrm{r}\; n. $ The adjacency matrix of the directed graph $ G $ is a matrix $ A = \left[{a}_{ij}\right] $ of order $ n\times n, $ such that for $ i\ne j $, if there is an arc from $ i $ to $ j, $ then $ {a}_{ij} = 1 $, otherwise $ {a}_{ij} = 0 $. Matrix $ B = J-A $ is called the antiadjacency matrix of the directed graph $ G, $ where $ J $ is the matrix of order $ n\times n $ with all of those entries are one. In this paper, we provided several properties of the adjacency matrices of directed graphs, such as a determinant of a directed graphs, the characteristic polynomial of acyclic directed graphs, and regular directed graphs. Moreover, we discuss antiadjacency energy of acyclic directed graphs and give some examples of antiadjacency energy for several families of graphs.

Let { R n } n = 1 ∞ ⊂ M 2 (Z) be a sequence of expanding matrices and let { B n } n = 1 ∞ ⊂ Z 2 be a sequence of p-element digit sets with R n = r n s n 0 r n a n d Z (δ ^ B n) = ⋃ j = 1 p - 1 j p ω n ρ n + Z 2 , where { ρ n , ω n } ⊂ { 1 , ⋯ , p - 1 } , gcd (ρ n , ω n) = 1 and p ≥ 3 is a prime number. The associated Moran measure is generated by the infinite convolution μ { R n , B n } : = δ R 1 - 1 B 1 ∗ δ R 1 - 1 R 2 - 1 B 2 ∗ ⋯. In the paper, we prove that μ { R n , B n } is a spectral measure if and only if r n , s n ∈ p Z under certain conditions on R n and B n . [ABSTRACT FROM AUTHOR]

For any square-summable commuting family (A i) i ∈ I of complex n × n matrices there is a normal commuting family (B i) i no farther from it, in squared normalized ℓ 2 distance, than the diameter of the numerical range of ∑ i A i ⁎ A i. Specializing in one direction (limiting case of the inequality for finite I) this recovers a result of M. Fraas: if ∑ i = 1 ℓ A i ⁎ A i is a multiple of the identity for commuting A i ∈ M n (C) then the A i are normal; specializing in another (singleton I) retrieves the well-known fact that close-to-isometric matrices are close to isometries. [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 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.

The concept of the covering energy of a poset is known. In this paper, we obtain a relation between the characteristic polynomials of the linear sum of two bounded posets and its components. Also, relations between covering energies of given posets and their linear sum as well as vertical sum are obtained. Eigenvalues and covering energies of some particular types of posets are also studied.

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.

Introduction. In the process of soil compaction it is important to have information about the current density of the layer, as it enables to quickly adjust the load on the compacted material. The field methods of compaction quality assessment do not cope with this task, as they make point estimation within the pavement area. Therefore, continuous compaction monitoring systems installed on vibratory road rollers are becoming increasingly common. The systems developed by BOMAG and AMMANN require, among other things, the phase angle between the exciter force and the roller movement to calculate the compaction quality index. The phase angle is determined by the unbalance position sensor, which is very labor-intensive. In addition, continuous compaction monitoring systems include an accelerometer. The purpose of this paper is to develop an indirect method for calculating the phase angle from accelerometer readings.The method of research. In order to achieve the purpose of the work, a roller-soil single-mass model in a typical mode for vibratory rollers (periodic loss of contact) has been studied. As a result of modeling it has been found that the reaction of the compacted material has the main influence on the vertical component of a roller acceleration and practically does not affect the horizontal component. This is confirmed by the experimental data.Results. The phase angle can be determined by mutual correlation of the horizontal and vertical acceleration signals of the roller obtained with the accelerometer.Conclusion. The study proposes a new method of calculating the phase angle between the exciter force and the roller displacement, which eliminates the direct measurement of this angle. The calculation of the angle is based on the readings of a two-axis accelerometer installed on the road roller. The proposed method enables to simplify the system of continuous compaction control and reduce the labor intensity of phase angle measurement.

We study the general properties, point spectrum and spectrum of a weighted composition operator Wm,φ{W}_{m,\varphi } with elliptic symbol φ\varphi on the unit ball BN{{\mathbb{B}}}_{N} of CN{{\mathbb{C}}}^{N}, and general weight m∈Hol(BN)m\in {\rm{Hol}}\left({{\mathbb{B}}}_{N}). We give a complete description of the spectra in the majority of cases, and we provide inclusions in general.

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]