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For a general complex unital Banach algebraA, the spectrumalways commutes : for all a, b ∈ A, σ(ab) \ {0} = σ(ba) \ {0}. In this paper, we prove that the above commutative property is not true if we replace the usual spectrum by condition spectrum. Further we study the similar question for more general spec- trum called Ransford spectrum. [ABSTRACT FROM AUTHOR]

In this paper, we consider the M/G/1 stochastic clearing queueing model in a three-phase environment, which is described by integro-partial differential equations (IPDEs). Our first result is semigroup well-posedness for the dynamic system. Utilizing a C 0 —semigroup theory, we prove that the system has a unique positive time-dependent solution (TDS) that satisfies the probability condition. As our second result, we prove that the TDS of the system strongly converges to its steady-state solution (SSS) if the service rates of the servers are constants. For this asymptotic behavior, we analyze the spectrum of the system operator associated with the system. Additionally, the stability of the semigroup generated by the system operator is also discussed. [ABSTRACT FROM AUTHOR]

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Without optical and mechanical components, resolving information from composite light is challenging even from two dimensions. 3D (intensity, spectrum, and polarization state) reconstruction is extremely rare and only explored in the infrared region. Herein, the first polarization‐ and spectrum‐sensitive photodetector in the visible region is constructed, which relies on orientations of perovskite nanowire arrays and in situ voltage modulation. This detector can realize real‐time detection of spectral information and Stokes vector simultaneously. Such a design successfully obtains the information from three dimensions, and the multi‐dimensional imaging capability has also been demonstrated. This work provides a valid instance of multi‐dimensional photodetection and shows a development direction of extracting target features from miscellaneous information. [ABSTRACT FROM AUTHOR]

We consider bounded selfadjoint linear integral operators and in the Hilbert space which are usually called partial integral operators. We assume that acts on a function in the first argument and performs integration in , while acts on in the second argument and performs integration in . We assume further that and are bounded but not compact, whereas is compact and . Partial integral operators arise in various areas of mechanics, the theory of integro-differential equations, and the theory of Schrödinger operators. We study the spectral properties of , , and with nondegenerate kernels and established some formula for the essential spectra of and . Furthermore, we demonstrate that the discrete spectra of and are empty, and prove a theorem on the structure of the essential spectrum of . Also, under study is the problem of existence of countably many eigenvalues in the discrete spectrum of . [ABSTRACT FROM AUTHOR]

We prove an asymptotic expansion for the eigenvalues and eigenfunctions of Schrödinger-type operator with a confining potential and with the principle part of a periodic elliptic operator in divergence form. We compare the spectrum to the homogenized operator and characterize the corrections up to arbitrarily high order. [ABSTRACT FROM AUTHOR]

We consider the linear evolution system u ttt + α u tt + β Δ 2 u t + γ Δ 2 u = - η Δ θ θ t - κ Δ θ = η Δ u tt + α η Δ u t describing the dynamics of a thermoviscoelastic plate of MGT type with Fourier heat conduction. The focus is the analysis of the energy transfer between the two equations, particularly when the first one stands in the supercritical regime, and exhibits an antidissipative character. The principal actor becomes then the coupling constant η , ruling the competition between the Fourier damping and the MGT antidamping. Indeed, we will show that a sufficiently large η is always able to stabilize the system exponentially fast. One of the features of this model is the presence of the bilaplacian in the first equation. With respect to the analogous model with the Laplacian, this introduces some differences in the mathematical approach. From the one side, the energy estimate method does not seem to apply in a direct way, from the other side, there is a gain of regularity allowing to rely on analytic semigroup techniques. [ABSTRACT FROM AUTHOR]

Apple valsa canker has caused the bark rot, and even seriously suffered the growth of fruit trees. Timely and accurately detection of pathogenic infestation is of great significance for the early disease warning, diagnosis, prevention and control measures. Surface-enhanced Raman spectroscopy (SERS) is very feasible in the detection of plant diseases, due mainly to its simple operation, high detection efficiency, and signal strength far beyond the conventional Raman technology. In this research, an accurate and rapid detection was performed on the early infection of apple valsa canker pathogens using SERS technology. The research objects were taken as the rotten bacterial filaments, the healthy and infected apple branches. S-G smoothing and adaptive iterative re-weighted penalized least squares (Air-PLS) were combined to carry out the de-noising and baseline correction of Raman spectra. The characteristic bands of apple branches and pathogenic were identified. Specifically, the healthy apple branches shared the outstanding characteristic peaks near 1 286 and 1 587 cm-1, whereas, the characteristic peaks of infected apple branches were near 1 365, 1 595, and 2 925 cm-1. The hypha of pathogenic bacteria had the outstanding characteristic peaks near 731, 1 327, 1 598, and 2 930 cm-1. At the same time, 15 groups of healthy, infected, and hyphal samples were selected, and found that the peak values of the characteristic peaks near 1 286 and 1 587 cm-1 of healthy apple branches were less than 0.5 on average. Meanwhile, the peak ratio of the characteristic peaks near 1 365 and 1 595 cm-1 of infected apple branches was greater than 0.5 in most cases, while the peak ratio of the characteristic peaks near 1 327 and 1 598 cm-1 of hypha was greater than 1 on average. In the vicinity of 1 280-1 380 cm-1, the difference between 1 286 and 1 365 cm-1 was 79, corresponding to the Raman peak generated by healthy and infected samples, while the difference between 1 327 and 1 365 cm-1 was 38, corresponding to the Raman peak generated by hypha samples and infected samples. The displacement ratio was close to 2:1. The peak intensity of infected apple branches near 1 595 cm-1 was greater than that of healthy apple branches near 1 587 cm-1 and that of hypha near 1 598 cm-1. In general, there was the significant difference in the Raman spectra of healthy apple branches, infected apple branches, and hyphal samples. Back propagation artificial neural network (BP-ANN) was used to construct a qualitative discriminant model, while the BP binary classification model was constructed for the healthy and infected samples, where the recognition rate was up to 96.0%. The BP-four-classification model was also constructed for the healthy and samples with three degrees of infection, where the recognition rate reached 92.0%. In addition, the baseline prediction curve was contained the Raman spectral features in the process of baseline correction. BP-ANN binary and quadruple classification models were then constructed for the baseline prediction curve, where the accuracy was above 90%. Therefore, the SERS combined with BP-ANN can be expected to rapidly and accurately carry out the early diagnosis of apple valsa canker pathogen hypha infection. The finding can provide a technical idea for the early and rapid detection of plant diseases. [ABSTRACT FROM AUTHOR]

Background: Leprosy remains a significant public health concern in many regions, including India, with multibacillary forms posing unique challenges in diagnosis and management. This study aimed to comprehensively assess the spectrum of disease in multibacillary leprosy patients at a tertiary care center in Chennai. Methods: A prospective study was conducted over one and a half years, involving 38 newly diagnosed and untreated multibacillary leprosy patients. Clinical, bacteriological, and treatment response parameters were evaluated using standardized methods. Statistical analysis was performed using SPSS version 26. Results: The study analyzed 38 multibacillary leprosy patients. The study cohort exhibited a mean age of 40.2 years, with a notable male predominance (79%) aged 30-39. Coolies (28.9%) were the most affected occupation group. Borderline lepromatous leprosy (66%) was prevalent. Clinical assessments showed trophic ulcers (13%) and grade 2 deformities like claw hand (5.3%) and lagophthalmos (2.6%). Bacteriological evaluation post-MDT revealed significant BI reduction at 6 months (p < 0.001). While most patients attained negative smears, some remained positive at 12 months, warranting continued surveillance for sustained clearance. Conclusion: This study provides comprehensive insights into the epidemiological, clinical, and bacteriological characteristics of multibacillary leprosy, highlighting the efficacy of multidrug therapy in achieving favorable treatment outcomes. [ABSTRACT FROM AUTHOR]

Let { A n } n = 1 ∞ be a sequence of expanding matrices with A n ∈ M 2 ⁢ (ℤ) , and let { D n } n = 1 ∞ be a sequence of three-element digit sets with { x ∈ (0 , 1) 2 : ∑ d ∈ D n e 2 ⁢ π ⁢ i ⁢ 〈 d , x 〉 = 0 } = { ± 1 3 ⁢ (1 , i) t } , i ∈ { 1 , 2 } . The associated Moran measure generated by the infinite convolution μ { A n } , { D n } = δ A 1 - 1 ⁢ D 1 * δ A 1 - 1 ⁢ A 2 - 1 ⁢ D 2 * δ A 1 - 1 ⁢ A 2 - 1 ⁢ A 3 - 1 ⁢ D 3 * ⋯. In this paper, we give some necessary and sufficient conditions for μ { A n } , { D n } to be a spectral measure under some suitable conditions on A n and D n . [ABSTRACT FROM AUTHOR]

The radiation of signal by the plasma asymmetrical dipole antenna is studied for two methods of its excitation. Earlier, it was shown that the 2nd and 3rd harmonics of the input signal frequency in the radiation spectrum of the plasma antenna are 10–20 dB stronger than those of a metal antenna with the same geometry. In this work, we study experimentally and by computer simulations the effect of the method of excitation of the plasma asymmetrical dipole antenna on the spectral characteristics of the signal that it radiates. For the two excitation methods of the antenna, through an electrode and through a coaxial coupler, it was shown that the strength of the signal components at the frequency of the radiated signal and its multiple harmonics is different. The introduction of the coaxial coupler in the antenna excitation scheme allowed us to improve the coupling at the input signal frequency and decrease its components at the 2nd and 3rd harmonics. For the plasma antenna with the coaxial coupler, the difference between the 1st and 2nd harmonics was increased by almost 6 dB, and between the 1st and the 3rd ones by almost 20 dB compared to the antenna excitation scheme through the electrode. [ABSTRACT FROM AUTHOR]

Let A be an ordered Banach algebra and a, b ∈ A such that 0 ≤ a ≤ b. The domination problem involves finding natural conditions under which properties of b will be inherited by a. In [12] this problem was investigated for ergodic elements, where a ∈ A is ergodic if the sequence converges in A. In this paper we consider the more general problem where the assumption 0 ≤ a ≤ b is replaced by the weaker condition ±a ≤ b. [ABSTRACT FROM AUTHOR]

Purpose. To develop a hybrid method based on ICEEMDAN and OMEDA for high-fidelity detection of the diagnostic features of the technical condition of roller bearing. Methodology. Due to digital signal processing the search was made of the informative components on the broadband spectra, envelope spectra, squared envelope spectra. The usage of the methods of mathematical statistics for the selection of informative IMFs as a result of iterative calculate procedures. The introduction of blind deconvolution method with a proper objective function for the enhancement of impulse fault features. Findings. The use of traditional spectral methods provided an incomplete list of diagnostic features of bearing roller damage. The empirical mode decomposition (EMD) method and its minor versions provide the series of intrinsic mode functions (IMFs). On the broadband vibration spectra of the selected low-frequency IMFs, diagnostic features were not detected in a sufficient number. Further research focused on the development of a hybrid method that takes into account the demodulation procedure of the high-frequency components of those IMFs that were selected according to the complex evaluation index. The Fast Kurtogram technique determined an informative frequency band of 7.2–7.5 kHz for demodulation and construction of the squared envelope spectra, where harmonics of the roller spin frequency and some side bands with a width equal to the separator rotation frequency appeared. The use of OMEDA caused the reduction of residual noise on the squared envelope spectra and bilateral sidebands to appear around all harmonics of the roller spin frequency. Originality. For the first time, the whole list of the diagnostic features of roller faults of the axle-box bearing was identified using the developed hybrid method, which involves steps of noise reduction for enhancing a physical meaning of a proper frequency components, associated with faults. The usage of the optimal minimum entropy deconvolution adjusted method helped to eliminate noise and provide all diagnostic features of the technical condition on the squared envelope spectrum. Practical value. The results of the study help to control the quality of repair of the axle-box rolling bearings on the test rig at the workshop of the freight railway car depot. [ABSTRACT FROM AUTHOR]

A matrix model is considered related to a system describing two identical fermions and one particle of another nature on a lattice, interacting via annihilation and creation operators. The problem of the study of the spectrum of a block operator matrix is reduced to the investigation of the spectrum of block operator matrices of order three with a discrete variable, and the relations for the spectrum, essential spectrum, and point spectrum are established. Two-particle and three-particle branches of the essential spectrum of the block operator matrix are singled out. [ABSTRACT FROM AUTHOR]

In Ghana, most laboratory diagnoses of severe mycoses are based on histopathology findings due to inadequate availability of serology, culture, and molecular tests. The aim of this study was to evaluate the spectrum of mycoses diagnosed in Ghana. We retrospectively reviewed reports from 2012 to 2021 from three major pathology laboratories in Ghana to identify reports indicating the presence of fungal elements and diagnosis of a mycosis, then extracted demographic, clinical history, site of infection, stain(s), used and diagnosed mycosis details. Over the 10-year period, 107 cases were found. No apparent increasing and decreasing trend in the number of cases per year or in a period was observed. The age range of affected patients was from 4 to 86 years. Special stains for fungi were only used in 22 of 107 (20.6%) of cases. The most frequently affected site was the sino-nasal area (34%). Mycosis type was determined for 58 (54.2%) cases, comprising aspergillosis (21), candidiasis (14), dermatophytosis (6), mucormycosis (3), two cases each of chromoblastomycosis, histoplasmosis, eumycetoma, entomophthoromycosis, sporotrichosis, and Malassezia infection and a single case each of cryptococcosis and deep onychomycosis. Of the 53 (49.5%) cases with presumptive diagnosis data, only seven (13.2%) had a pre-biopsy suspicion of mycosis. There is a wide spectrum of mycoses in Ghana, including endemic mycoses not previously reported. Improving the use of special fungal stains could increase yield and mycoses identification. Laboratory diagnostic capacity needs enhancement to complement histopathology investigations with serology, culture, and molecular methods. [ABSTRACT FROM AUTHOR]

The paper considers the spectral problem associated with the study of local characteristics of weakly coupled systems in reactor physics. The method of associated invariant subspaces based on the matrix spectrum dichotomy method is described. With its help, distributions are found that reflect multiplicating properties of local areas in the system. [ABSTRACT FROM AUTHOR]

In this paper, it is investigated that necessary and sufficient conditions for a minimal operator defined by a degenerate first-order differential operator expression in the Hilbert space to be formally normal. Also, all normal extensions of the minimal operator are given with their domains. Moreover, the spectrum set of these normal extensions is given through the family of evolution operators. [ABSTRACT FROM AUTHOR]

The laws of interaction of electromagnetic wave radiation with pyridine molecules and atoms were studied using Raman light scattering spectra of light, and it was shown that the spectra appearing in the lower frequency range (0 ÷ 1031 cm−1) are related to the rotational-rocking movement of molecules. Based on quantum-chemical calculations, a structural model of the pyridine molecule was created. The possibility of determining the bond lengths and angles between the atoms in the pyridine molecule was suggested. Based on the obtained results, the frequency values of the Raman scattering spectra of light from the pyridine molecule were determined by theoretical calculations and compared with the experimental results. Based on the analysis of the results of the research, it was found that the intensity of the Raman scattering spectrum of the light generated by the rotational-rocking laws of the pyridine molecule is significantly smaller than the intensity of the spectra corresponding to other frequencies.

Single-bubble sonoluminescence spectra of the following samples were recorded in the modes of standing and moving bubble in liquid near the center of its levitation under the action of ultrasound: water contaminated with additives of commercial gasoline (1.5 – 38 mg·L−1), water with additives of individual gasoline components (hexane, benzene, toluene, p-xylene, naphthalene, anthracene, and p-terphenyl), and solutions of these gasoline components in hexane. Characteristic bands λmax of gasoline component emitters are recorded in the sonoluminescence spectra of a moving bubble for water samples contaminated with additives of commercial gasoline: 290 (p-xylene), 340 (p-terphenyl), 381, 399, 424, 449 (anthracene), and 438, 474, 516, 564 nm (C2, a hydrocarbon decomposition product during sonolysis).These bands are as a spectral portrait of gasoline contamination of water: they make it possible to identify gasoline in water in the above mentioned range of its content and to find a quantitative content of individual gasoline components.

The article proposes the improved method of spectral analysis of radio signals. The improvement is achieved due to the use of special operators in the signal conversion process. This allows you to distinguish the signal accurately and to determine its characteristics at the background of many airspace obstacles. The obtained graphical results fully confirm the advantages of the proposed method. The simulation results proved the advantage of the improved method of spectral analysis of radio signals; the advantage is achieved through the usage summing matrix functions in the process of signals conversion. The proposed improved method increases the accuracy of signals detection of secretly obtaining information means by 12%.

Isavuconazole is the newest of the clinically available advanced generation triazole antifungals and is active against a variety of yeasts, molds, and dimorphic fungi. Its current FDA-approved indications include the management of invasive aspergillosis as well as mucormycosis, though the latter indication is supported by limited clinical data. Isavuconazole did not achieve noninferiority to caspofungin for the treatment of invasive candidiasis and therefore lacks an FDA-approved indication for this invasive disease. Significant advantages of isavuconazole, primarily over voriconazole but in some circumstances posaconazole as well, make it an appealing option for the management of complex patients with invasive fungal infections. These potential advantages include lack of QTc interval prolongation, more predictable pharmacokinetics, a less complicated drug interaction profile, and improved tolerability, particularly when compared to voriconazole. This review discusses these topics in addition to addressing the in vitro activity of the compound against a variety of fungi and provides insight into other distinguishing factors among isavuconazole, voriconazole, and posaconazole. The review concludes with an opinion section in which the authors provide the reader with a framework for the current role of isavuconazole in the antifungal armamentarium and where further data are required.

Exploring the applications of Laplacian and signless Laplacian spectra extends beyond theoretical chemistry, computer science, electrical networks, and complex networks. These spectra, with their relevance, provide valuable insights into the structures of real-world networks and facilitate the prediction of their structural properties. The focal point of the study lies in the spectrum-based analysis of torus grid graphs. From these analyses, crucial network measures such as mean-first passage time, average path length, spanning trees, and spectral radius are derived. This research enriches our comprehension of the interplay between graph spectra and network characteristics, offering a holistic understanding of complex networks. Consequently, it contributes to the ability to make predictions and conduct analyses across diverse scientific disciplines.

A locale (frame) L has a largest spatial sublocale generated by the primes (spectrum points), the spatial part SpL. In this paper we discuss some of the properties of the embeddings SpL ⊆ L. First we analyze the behaviour of the spatial parts in the assembly: the points of L and of S(L)^op (∼=the congruence frame) are in a natural one-one correspondence while the topologies of SpL and Sp(S(L)^op) differ. Then we concentrate on some special types of embeddings of SpL into L, namely in the questions when SpL is complemented, closed, or open. While in the first part L was general, here we need some restrictions (weak separation axioms) to obtain suitable formulas

Abstract Nonparametric estimation of the covariance function and the power spectral density of uniformly spaced data from stationary stochastic processes with missing samples is investigated. Several common methods are tested for their systematic and random errors under the condition of variations in the distribution of the missing samples. In addition to random and independent outliers, the influence of longer and hence correlated data gaps on the performance of the various estimators is also investigated. The aim is to construct a bias-free estimation routine for the covariance function and the power spectral density from stationary stochastic processes under the condition of missing samples with an optimum use of the available information in terms of low estimation variance and mean square error, and that independent of the spectral composition of the data gaps. The proposed procedure is a combination of three methods that allow bias-free estimation of the desired statistical functions with efficient use of the available information: weighted averaging over valid samples, derivation of the covariance estimate for the entire data set and restriction of the domain of the covariance function in a post-processing step, and appropriate correction of the covariance estimate after removal of the estimated mean value. The procedures abstain from interpolation of missing samples as well as block subdivision. Spectral estimates are obtained from covariance functions and vice versa using Wiener–Khinchin’s theorem.

Abstract Objective To review the relationship between adiponectin levels and autism spectrum disorders (ASDs) in children. Background ASDs are associated with pervasive social interaction and communication abnormalities. Researchers have studied various pathophysiological mechanisms underlying ASDs to identify predictors for an early diagnosis to optimize treatment outcomes. Immune dysfunction, perhaps mediated by a decrease in anti-inflammatory adipokine, adiponectin, along with changes in other adipokines, may play a central role in increasing the risk for ASDs. However, other factors, such as low maternal vitamin D levels, atherosclerosis, diabetes, obesity, cardio-metabolic diseases, preterm delivery, and oxytocin gene polymorphism may also contribute to increased risk for ASDs. Methods Searches on the database; PubMed, Google Scholar, and Cochrane using keywords; adiponectin, adipokines, ASD, autism, autistic disorder, included English-language studies published till September 2022. Data were extracted on mean differences between adiponectin levels in children with and without ASDs. Results The search yielded six studies providing data on adiponectin levels in young patients with ASDs. As can be seen from Table 1, four of the six studies were positive for an inverse correlation between ASD and adiponectin levels. In addition, two of the four positive and one negative studies found low adiponectin levels associated with and the severity of autistic symptoms. However, results from one reviewed study were insignificant. Conclusion Most studies reviewed yielded lower adiponectin levels in children with ASDs as well as the severity of autistic symptoms.

Let $ T_{B} = \left[\begin{array}{ll} A & B \\ 0 & D \end{array}\right] $ be an unbounded upper operator matrix with diagonal domain, acting in $ \mathcal H \oplus\mathcal K $, where $ \mathcal H $ and $ \mathcal K $ are Hilbert spaces. In this paper, some sufficient and necessary conditions are characterized under which $ T_{B} $ is Browder (resp., invertible) for some closable operator $ B $ with $ \mathcal D(B)\supset \mathcal D(D) $. Further, a sufficient and necessary condition is given under which the Browder spectrum (resp., spectrum) of $ T_{B} $ coincides with the union of the Browder spectrum (resp., spectrum) of its diagonal entries.

BackgroundLuminescence dating technology has made significant advancements in determining the chronology of archaeological materials subjected to low firing temperatures. However, the luminescence dating of archaeological materials subjected to high firing temperatures remains challenging.PurposeThis study aims to explore the luminescence emission spectrum characteristics and luminescence properties of high-firing temperature quartz to verify the feasibility of thermoluminescence (TL) signals from different bands in luminescence dating.MethodsFirstly, the high-firing temperature (about 950 °C) quartz extracted from pottery unearthed at the Lingjiatan archaeological site was taken as a case study, spectral measurement platform was established using a Risø DA-20 luminescence dating instrument coupled with an Andor spectrometer and a charge-coupled device camera to analyze the luminescence spectral properties of archaeological quartz with high firing temperatures. Then, five filter combinations and two photomultiplier tubes (PMTs) were used to compare the TL and isothermal thermoluminescence (ITL) sensitivities of blue and red emissions. Kinetic parameters for Blue TL and Red TL were determined by deconvolving the glow curves with the general-order equation. Finally, exposure experiments were conducted on the Blue and Red TL using a solar simulator. The single aliquot regenerative dose (SAR) protocol was implemented to assess the applicability of the Blue TL-SAR, Blue ITL-SAR, Red TL-SAR, Red ITL-SAR, and optically stimulated luminescence (OSL)-SAR methods for dating archaeological quartz exposed to high temperatures during production or use.ConclusionsThe spectral analysis reveals that the archaeological quartz subjected to high firing temperature exhibits significant Red TL emissions at approximately 620 nm, which is correlated with the TL peak at 375 °C. This Red TL at 375 °C exhibits a marked insensitivity to light. The multi-wavelength TL, multiwavelength ITL, and conventional OSL dating results are consistent with the known radiocarbon age within the error range. This study demonstrates the potential feasibility of using luminescence signals of different wavelengths for chronological studies of archaeological materials subjected to high firing temperatures.

Hyperspectral Imaging (HSI) uses large portions of the electromagnetic spectrum to obtain information from images that would be very difficult to get otherwise. An important task in forensic analysis of documents is to extract signatures for authentication. Signatures in documents often overlap with other parts of a document such as typed text or stamps and hence it is difficult to retrieve them. In this work we present a novel algorithm for recovering signatures from hyperspectral images of documents where signatures overlap typed text, seals, stamps, or other images. We used pure pixel index approaches to analyze the hyper-pixels corresponding to regions where overlaps occur and spectral classification methods to analyze the extracted channels’ information and to separate the overlapping signatures. We used the structural similarity index to validate the extracted signatures. Our experimental results highlight the capability of the proposed algorithm to recover signatures with great precision in HSI document images.

A method is proposed for decomposing the integrated photoluminescence spectrum into components based on the analysis of an identifier, which is the ratio of the first and second derivatives of the experimental data. The question of the limits of applicability of this method of decomposition of a complex photoluminescence spectrum has been studied in this paper. The definition of the sensitivity of the method is given on the example of an integral spectrum formed by two Gaussians. The evolution of the dependence of the used identifier on the wavelength is shown with a change in the distance between the maxima of the elementary components. By means of a synthetic experiment, dependences of the sensitivity on the ratio of the half-widths and intensities of the components of the integral spectrum are plotted. The dependences obtained are non-linear and have local maxima and minima. The use of the calculated dependences makes it possible to estimate at what overlap of the bands the decomposition is still possible, and at what it is no longer possible to separate the elementary component from the integrated spectrum.

Abstract Background Congenital heart defects (CHDs) are the most common birth defects. Assessment of the incidence, distribution, disease spectrum, and genetic deficits of fetal CHDs in China is urgently needed. Methods A national echocardiography screening program for fetal CHDs was implemented in 92 prenatal screening–diagnostic centers in China. Findings A total of 18,171 fetal CHD cases were identified from 2,452,249 pregnancies, resulting in 7·4/1,000 as the national incidence rate of fetal CHD. The incidences of fetal CHD in the six geographical regions, the southern, central, eastern, southwestern, northern, and northwestern, were 7·647 (CI: 7·383–7·915), 7·839 (CI: 7·680–8·000), 7·647 (CI: 7·383–7·915), 7·562 (CI: 7·225–7·907), 5·618 (CI: 5·337–5·906), and 4·716 (CI: 4·341–5·108), respectively, per 1,000 pregnancies. Overall, ventricular septal defect was the most common fetal CHD, accounting for 17.04% of screened pregnancies nationwide, and tetralogy of Fallot, the most common anomaly in the major defect of fetal CHD, was the second most common, accounting for 9.72%. A total of 76.24% cases of fetal CHD were found to be an isolated intracardiac single defect. The remaining 23.76% of cases of fetal CHD had multiple heart defects. Among all extracardiac malformations, the central nervous system (CNS) was the most common tissue with extracardiac anomalies associated with CHD, accounting for 22.89% of fetal CHD cases. Chromosomal karyotyping identified trisomy 18 as the most common chromosomal abnormality in fetal CHD. We also documented that CHD-containing syndromes could be identified with a comprehensive approach integrating prenatal ultrasound, MRI, pathological autopsy, and cytogenetics and molecular genetics. Conclusion Implementation of prenatal echocardiography as a practically feasible platform to screen fetal CHD will reduce the financial and emotional burden of CHD, which may facilitate intrauterine and neonatal intervention of CHD.

The concept of covering energy of a poset is known and its McClelland type bounds are available in the literature. In this paper, we establish formulas for the covering energy of a crown with $2n$ elements and a fence with $n$ elements. A lower bound for the largest eigenvalue of a poset is established. Using this lower bound, we improve the McClelland type bounds for the covering energy for some special classes of posets.

Denote by I d c G the lattice of all principal ℓ -ideals of an Abelian ℓ -group G. Our main result is the following. Theorem For every countable Abelian ℓ-group G, every countable completely normal distributive 0 -lattice L, and every closed 0 -lattice homomorphism φ : I d c G → L , there are a countable Abelian ℓ-group H, an ℓ-homomorphism f : G → H , and a lattice isomorphism ι : I d c H → L such that φ = ι ∘ I d c f. We record the following consequences of that result: (1) A 0-lattice homomorphism φ : K → L , between countable completely normal distributive 0-lattices, can be represented, with respect to the functor I d c , by an ℓ -homomorphism of Abelian ℓ -groups iff it is closed. (2) A distributive 0-lattice D of cardinality at most ℵ 1 is isomorphic to some I d c G iff D is completely normal and for all a , b ∈ D the set { x ∈ D | a ≤ b ∨ x } has a countable coinitial subset. This solves Mundici's MV-spectrum Problem for cardinalities up to ℵ 1. The bound ℵ 1 is sharp. Item (1) is extended to commutative diagrams indexed by forests in which every node has countable height. All our results are stated in terms of vector lattices over any countable totally ordered division ring. [ABSTRACT FROM AUTHOR]

We analyze the spectrum of the operator $\Delta{-1} [\nabla \cdot (K\nabla u)]$ subject to homogeneous Dirichlet or Neumann boundary conditions, where $\Delta$ denotes the Laplacian and $K=K(x,y)$ is a symmetric tensor. Our main result shows that this spectrum can be derived from the spectral decomposition $K=Q \Lambda QT$, where $Q=Q(x,y)$ is an orthogonal matrix and $\Lambda=\Lambda(x,y)$ is a diagonal matrix. More precisely, provided that $K$ is continuous, the spectrum equals the convex hull of the ranges of the diagonal function entries of $\Lambda$. The domain involved is assumed to be bounded and Lipschitz. In addition to studying operators defined on infinite-dimensional Sobolev spaces, we also report on recent results concerning their discretized finite-dimensional counterparts. More specifically, even though $\Delta{-1} [\nabla \cdot (K\nabla u)]$ is not compact, it turns out that every point in the spectrum of this operator can, to an arbitrary accuracy, be approximated by eigenvalues of the associated generalized algebraic eigenvalue problems arising from discretizations. Our theoretical investigations are illuminated by numerical experiments. The results presented in this paper extend previous analyses which have addressed elliptic differential operators with scalar coefficient functions. Our investigation is motivated by both preconditioning issues (efficient numerical computations) and the need to further develop the spectral theory of second order PDEs (core analysis). [ABSTRACT FROM AUTHOR]

Light is essential for plant growth, although excessive light radiation may have negative effects on many plants, including soybeans. This study examined the influence of white (W), red (R), blue (B), and ultraviolet (UV-A) light on the key enzymes of Calvin cycle, key antioxidant enzymes and secondary metabolites, and also microbial and fungal communities of soybean plants (Glycine max (L.) Merr. To achieve this, fully expanded soybean leaves of 45-day-old plants were maintained in vitro for 7 days W, red R, blue B, or UV-A light. Soybean leaves under B treatment had enhanced Ribulose-1,5-bisphosphate carboxylase/oxygenase (Rubisco), fructose-1, 6-bisphosphatase (FBPase), glyceraldehyde 3-phosphate dehydrogenase (GAPDH), and fructose-1,6-bisphosphate aldolase (FBA) activities that improved photosynthesis and starch accumulation, compared to the W, R, and UV-A treatments. There were significant increases for B treatment in the activities of catalase (CAT), superoxide dismutase (SOD), and peroxidase (POD), and a reduction in the malondialdehyde (MDA) content. B treatment led to enrichment of secondary metabolites, such as phenols and flavonoids. Soybean leaves under R treatment had more plant growth-promoting bacteria than with B treatment. The relative abundances of Basidiomycota and Ascomycota fungi under B treatment were lower to avoid decomposition of substances than with the R and UV-A treatment. In summary, blue light improved soybean leaf growth and antioxidant capacity compared to red light. The wavelengths of B and UV-A are very close, although UV-A still reduced soybean leaf growth and accelerated leaf senescence. [ABSTRACT FROM AUTHOR]

By bifurcation and topological methods, we study the existence/nonexistence and multiplicity of one-sign or nodal solutions of the following k-th mean curvature problem in Minkowski spacetime r N − k v ′ 1 − v ′ 2 k ′ = λ N C N k r N − 1 H k (r , v) in (0 , R) , | v ′ | < 1 in (0 , R) , v ′ (0) = v (R) = 0. As a previous step, we investigate the spectral structure of its linearized problem at zero. Moreover, we also obtain a priori bounds and the asymptotic behaviors of solutions with respect to λ. [ABSTRACT FROM AUTHOR]

We consider a natural generalization of the concept of order of an element in a group G : an element g ∈ G is said to have order k in a subgroup H (respectively, in a coset H u) of G if k is the first strictly positive integer such that g k ∈ H (respectively, g k ∈ H u). We study this notion and its algorithmic properties in the realm of free groups and some related families. Both positive and negative (algorithmic) results emerge in this setting. On the positive side, among other results, we prove that the order of elements, the set of orders (called spectrum), and the set of preorders (i.e. the set of elements of a given order) with respect to finitely generated subgroups are always computable in free and free times free-abelian groups. On the negative side, we provide examples of groups and subgroups having essentially any subset of natural numbers as relative spectrum; in particular, non-recursive and even not computably enumerable sets of natural numbers. Also, we take advantage of Mikhailova's construction to see that the spectrum membership problem is unsolvable for direct products of nonabelian free groups. [ABSTRACT FROM AUTHOR]

We consider the spectral problem for the Dirac operator with arbitrary two-point boundary conditions and any square integrable potential . Necessary and sufficient conditions for an entire function to be the characteristic determinant of such an operator are established. In the case of irregular boundary conditions, conditions are found under which a set of complex numbers is the spectrum of the problem under consideration. [ABSTRACT FROM AUTHOR]

In this study, we engineered a sub-70 nm nanocomposite of ZnO/Zn2TiO4 using a low-temperature solution-phase method with titanium isopropoxide and zinc acetate as precursors, and isopropyl alcohol and water as solvents. The investigation focused on nanocomposite growth by varying precursor and surfactant concentrations and their efficiency within different pH ranges. All three ZnO/Zn2TiO4 nanocomposites exhibited hexagonal wurtzite ZnO and Zn2TiO4 structures. The crystallite size in these nanocomposites ranged from 39.50 nm to 62.67 nm for ZnO and 21.24 nm to 26.15 nm for Zn2TiO4. Morphological observations using FESEM revealed the formation of dispersed cotton packet-like nanocomposites with sizes ranging from 18 to 350 nm. FTIR analysis showed peaks indicative of Ti–O and Zn–O bond formation, and EDX spectrum confirmed the presence of Ti, O, and Zn. UV spectrums and photocatalytic investigations confirmed the successful formation of ZnO/Zn2TiO4 nanocomposites with notable photocatalytic degradation efficiency for methylene blue dye under various conditions. These findings suggest the potential applicability of the synthesized nanocomposites for environmental pollutant degradation. [ABSTRACT FROM AUTHOR]

Let n ≥ 2 be a natural number, denote by M n the space of all matrices of size n over an algebraically closed field F , and let K 1 , K 2 ⊆ F be two nonempty subsets, each having at most n elements. In the case when K 2 has at least the number of elements of K 1 , we characterize linear bijective maps φ on M n having the property that, for each n × n matrix T , we have that K 2 is a subset of the spectrum of φ (T) whenever K 1 is a subset of the spectrum of T. As an application, we characterize linear maps φ on M n having the property that, for each n × n matrix T , we have that K 1 is a subset of the spectrum of T if and only if K 2 is a subset of the spectrum of φ (T) , with no assumption on the cardinalities of K 1 and K 2. [ABSTRACT FROM AUTHOR]

Abstract—We have considered the interaction of an exciton mode with photonic modes in a GaN structure several pm in size. A technique for obtaining spectra from such structures has been demonstrated. The cavity shape and dimensions most optimal for efficient light/matter interaction have been selected. The theoretical spectrum for the selected cavity has been obtained and analyzed. [ABSTRACT FROM AUTHOR]

This paper investigates the general stabilization issues for continuous-time stochastic dynamics whose input delay and multiplicative noise in control variable exist simultaneously. On the one hand, we present a set of necessary and sufficient conditions for stabilizing the considered stochastic dynamics in mean-square sense. Different from many previous works, one significant innovation is that our control policy is designed as the feedback of an extended state that contains the current available state and some past control information. On the other hand, another important innovation is that we for the first time generalize the notions of critical stabilization and essential destabilization to stochastic time-delay model in terms of spectral analysis technique, while the related necessary and sufficient stabilization conditions are derived respectively. [ABSTRACT FROM AUTHOR]

We establish some Lie–Trotter formulae for unital complex Jordan–Banach algebras, showing that for any elements a, b, c in a unital complex Jordan–Banach algebra A the identities lim n → ∞ e a n ∘ e b n n = e a + b , lim n → ∞ U e a n e b n n = e 2 a + b , and lim n → ∞ U e a n , e c n e b n n = e a + b + c hold. These formulae are actually deduced from a more general result involving holomorphic functions with values in A . These formulae are employed in the study of spectral-valued (non-necessarily linear) functionals f : A → C satisfying f (U x (y)) = U f (x) f (y) , for all x , y ∈ A . We prove that for any such a functional f, there exists a unique continuous (Jordan-) multiplicative linear functional ψ : A → C such that f (x) = ψ (x) , for every x in the connected component of the set of all invertible elements of A containing the unit element. If we additionally assume that A is a JB ∗ -algebra and f is continuous, then f is a linear multiplicative functional on A . The new conclusions are appropriate Jordan versions of results by Maouche, Brits, Mabrouk, Schulz, and Touré. [ABSTRACT FROM AUTHOR]

This work presents a novel blue phosphor, Na2MgPO4F: Eu2+ (NMPF: Eu) for violet 405-nm light-emitting diode (LED) devices. The compound is synthesized via a simple one-step sintering process using readily available precursors. Notably, NMPF: Eu exhibits highly efficient and thermally stable blue emission when excited by violet light. The NMPF: Eu is applied to produce a white LED device driven by a 405 nm LED chip and Y3Al5O12: Ce3+ (YAG: Ce) yellow phosphor. The impacts of NMPF: Eu phosphors are investigated by varying their particle size while maintaining consistent doping concentrations. Impressively, the LED prototype displays a substantial reduction in blue light emission while generating white light with enhanced color rendering and luminous properties. These results highlight the suitability and potential of NMPF: Eu as a promising phosphor for widening violet LED applications, especially in generating white light perceptible to the human eyes. [ABSTRACT FROM AUTHOR]

Based on Thomson scattering classical theory and single electron model, numerical simulation of Thomson scattering X-ray source is completed with the help of MATLAB software. We discuss the influence of waist radius and initial phase of few-cycle laser pulse on maximum radiation energy, maximum radiation power, radiation angle distribution and spectrum when the collision center is at or away from the focus. It is found that the initial z-axis position of the electron has no effect on the overall change trend. The influence ability of waist radius appears a "watershed" phenomenon at b 0 = 4 λ 0 . When b 0 = 1 ∼ 3 λ 0 , with the increase in the waist radius, the maximum radiation energy and the maximum radiation power increase, and the collimation of laser and the monochromaticity of the spectrum become worse. When b 0 ≥ 4 λ 0 , the change in waist radius has no effect on these parameters. In addition, when the initial phase of few-cycle laser pulse increases in the range of 0–360°, the maximum radiation direction rotates counterclockwise, and the values of the maximum radiation energy and the instantaneous power of the maximum radiation energy and the peak value of the spectrum fluctuate only in a small range. [ABSTRACT FROM AUTHOR]

The asymptotic behavior of hyperbolic-parabolic coupled systems on some special networks (loop-type, chain-type, tree-type) are discussed. By a detailed spectral analysis, the asymptotic expressions of the spectrum of these three networks are obtained, and based on which, the lack of exponential decay is deduced for all these systems. Then using the frequency domain approach together with the asymptotic expressions of the spectrum, we derive the optimal polynomial decay rate of the systems under the smooth initial states. Moreover, some numerical simulations are given to support the results obtained. [ABSTRACT FROM AUTHOR]