Articoli di riviste: "Transformation spectrale"

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DE LA RUE, THIERRY. "L'induction ne donne pas toutes les mesures spectrales". Ergodic Theory and Dynamical Systems 18, n. 6 (dicembre 1998): 1447–66. http://dx.doi.org/10.1017/s0143385798118059.

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We show here that some finite measure on $[-\pi,\pi]$ can never be obtained as a spectral measure of a transformation induced by a rotation. For this, we propose a new way to build a Kronecker set, which leads to a non loosely Bernoulli Gaussian–Kronecker automorphism.On montre ici qu'une certaine mesure finie sur $[-\pi,\pi]$ ne peut jamais être obtenue comme mesure spectrale d'une transformation induite par une rotation. On propose pour cela une nouvelle façon de construire un ensemble de Kronecker, qui permet de voir que certains systèmes dynamiques gaussiens–Kronecker ne sont pas lâchement Bernoulli.

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Baran, Mehmet. "Single and Multi-Soliton Solutions for a Spectrally Deformed Set of Maxwell-Bloch Equations". Symmetry 11, n. 3 (25 marzo 2019): 435. http://dx.doi.org/10.3390/sym11030435.

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A specific spectral deformation of the Maxwell-Bloch equations of nonlinear optics is investigated. The Darboux transformation formalism is adapted to this spectrally deformed system to construct its single and multi-soliton solutions. The Effects of spectral deformation on soliton behaviour is studied.

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TIAN, SHOU-FU, e HONG-QING ZHANG. "CONSTRUCTING 2N-SOLITON PERIODIC WAVE SOLUTIONS FOR GENERALIZED DERIVATIVE NONLINEAR SCHRÖDINGER EQUATION". International Journal of Modern Physics C 21, n. 09 (settembre 2010): 1149–68. http://dx.doi.org/10.1142/s0129183110015737.

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In this paper, three new kinds of N-fold Darboux transformations with multi-parameters for spectral problem associated with generalized Derivative Nonlinear Schrödinger equation (GDNS) are structured with the help of different gauge transformations. With these transformations, some new 2N-soliton periodic wave solutions for the GDNS equation are obtained by taking position spectral (λ > 0), negaton spectral (λ < 0) and complexiton spectral. When N = 1 we obtained two-soliton periodic wave solutions. In particular, when N = 2 we obtained some four-soliton periodic wave solutions. By using mathematical software, we show their profiles. In this method, we can give a Darboux transformation for a very systematic system of even-dimensional and odd-dimensional Lax integrable systems. This method can also be applied to other nonlinear evolution equations.

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Dooley, A. H., e S. J. Eigen. "A Family of Generalized Riesz Products". Canadian Journal of Mathematics 48, n. 2 (1 aprile 1996): 302–15. http://dx.doi.org/10.4153/cjm-1996-016-1.

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AbstractGeneralized Riesz products similar to the type which arise as the spectral measure for a rank-one transformation are studied. A condition for the mutual singularity of two such measures is given. As an application, a probability space of transformations is presented in which almost all transformations are singular with respect to Lebesgue measure.

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Deng, Y., e C. Wu. "EXAMINATION OF SPECTRAL TRANSFORMATIONS ON SPECTRAL MIXTURE ANALYSIS". ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XLII-3 (30 aprile 2018): 267–70. http://dx.doi.org/10.5194/isprs-archives-xlii-3-267-2018.

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While many spectral transformation techniques have been applied on spectral mixture analysis (SMA), few study examined their necessity and applicability. This paper focused on exploring the difference between spectrally transformed schemes and untransformed scheme to find out which transformed scheme performed better in SMA. In particular, nine spectrally transformed schemes as well as untransformed scheme were examined in two study areas. Each transformed scheme was tested 100 times using different endmember classes’ spectra under the endmember model of vegetation- high albedo impervious surface area-low albedo impervious surface area-soil (V-ISAh-ISAl-S). Performance of each scheme was assessed based on mean absolute error (MAE). Statistical analysis technique, Paired-Samples T test, was applied to test the significance of mean MAEs’ difference between transformed and untransformed schemes. Results demonstrated that only NSMA could exceed the untransformed scheme in all study areas. Some transformed schemes showed unstable performance since they outperformed the untransformed scheme in one area but weakened the SMA result in another region.

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Al-Dulaimi, Al-Waled, Todd K. Moon e Jacob H. Gunther. "Voice Transformation Using Two-Level Dynamic Warping and Neural Networks". Signals 2, n. 3 (14 luglio 2021): 456–74. http://dx.doi.org/10.3390/signals2030028.

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Voice transformation, for example, from a male speaker to a female speaker, is achieved here using a two-level dynamic warping algorithm in conjunction with an artificial neural network. An outer warping process which temporally aligns blocks of speech (dynamic time warp, DTW) invokes an inner warping process, which spectrally aligns based on magnitude spectra (dynamic frequency warp, DFW). The mapping function produced by inner dynamic frequency warp is used to move spectral information from a source speaker to a target speaker. Artifacts arising from this amplitude spectral mapping are reduced by reconstructing phase information. Information obtained by this process is used to train an artificial neural network to produce spectral warping information based on spectral input data. The performance of the speech mapping compared using Mel-Cepstral Distortion (MCD) with previous voice transformation research, and it is shown to perform better than other methods, based on their reported MCD scores.

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García-Ardila, Juan Carlos, e Francisco Marcellán. "Spectral Transformations and Associated Linear Functionals of the First Kind". Axioms 10, n. 2 (28 maggio 2021): 107. http://dx.doi.org/10.3390/axioms10020107.

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Given a quasi-definite linear functional u in the linear space of polynomials with complex coefficients, let us consider the corresponding sequence of monic orthogonal polynomials (SMOP in short) (Pn)n≥0. For a canonical Christoffel transformation u˜=(x−c)u with SMOP (P˜n)n≥0, we are interested to study the relation between u˜ and u(1)˜, where u(1) is the linear functional for the associated orthogonal polynomials of the first kind (Pn(1))n≥0, and u(1)˜=(x−c)u(1) is its Christoffel transformation. This problem is also studied for canonical Geronimus transformations.

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Garza, Luis, Javier Hernández e Francisco Marcellán. "Spectral transformations of measures supported on the unit circle and the Szegő transformation". Numerical Algorithms 49, n. 1-4 (31 gennaio 2008): 169–85. http://dx.doi.org/10.1007/s11075-008-9156-0.

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Albares, Paz, e Pilar Garcia Estévez. "Miura-Reciprocal Transformation and Symmetries for the Spectral Problems of KdV and mKdV". Mathematics 9, n. 9 (22 aprile 2021): 926. http://dx.doi.org/10.3390/math9090926.

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We present reciprocal transformations for the spectral problems of Korteveg de Vries (KdV) and modified Korteveg de Vries (mKdV) equations. The resulting equations, RKdV (reciprocal KdV) and RmKdV (reciprocal mKdV), are connected through a transformation that combines both Miura and reciprocal transformations. Lax pairs for RKdV and RmKdV are straightforwardly obtained by means of the aforementioned reciprocal transformations. We have also identified the classical Lie symmetries for the Lax pairs of RKdV and RmKdV. Non-trivial similarity reductions are computed and they yield non-autonomous ordinary differential equations (ODEs), whose Lax pairs are obtained as a consequence of the reductions.

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YANG, HONG-XIANG, DAO-LIN WANG e CHANG-SHENG LI. "THE GENERALIZED MULTI-COMPONENT AKNS HIERARCHY AND N-FOLD DARBOUX TRANSFORMATION". Modern Physics Letters B 20, n. 25 (30 ottobre 2006): 1575–89. http://dx.doi.org/10.1142/s0217984906011864.

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Starting from a 3×3 spectral problem, by using the Tu scheme, a hierarchy of generalized multi-component AKNS soliton equations are derived. It is shown that each equation in the resulting hierarchy is Liouville integrable. With the help of gauge transformations of the Lax pairs, an N-fold Darboux transformation (DT) with multi-parameters for the spectral problem is set up. For application, the soliton solutions of the first nonlinear soliton equation are explicitly given.

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Xue, Bo, Huiling Du e Ruomeng Li. "A Five-Component Generalized mKdV Equation and Its Exact Solutions". Mathematics 8, n. 7 (13 luglio 2020): 1145. http://dx.doi.org/10.3390/math8071145.

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In this paper, a 3 × 3 spectral problem is proposed and a five-component equation that consists of two different mKdV equations is derived. A Darboux transformation of the five-component equation is presented relating to the gauge transformations between the Lax pairs. As applications of the Darboux transformations, interesting exact solutions, including soliton-like solutions and a solution that consists of rational functions of e x and t, for the five-component equation are obtained.

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Tereshchenko, T. О., Y. S. Yamnenko, D. V. Kuzin e L. E. Klepach. "MULTILEVEL INVERTER TOPOLOGY AND CONTROL SIGNALS DEFINITION BASED ON ORTHOGONAL SPECTRAL TRANSFORMATIONS". Tekhnichna Elektrodynamika 2018, n. 4 (15 maggio 2018): 57–60. http://dx.doi.org/10.15407/techned2018.04.057.

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Chakraborty, Avijit, e David Okaya. "Frequency‐time decomposition of seismic data using wavelet‐based methods". GEOPHYSICS 60, n. 6 (novembre 1995): 1906–16. http://dx.doi.org/10.1190/1.1443922.

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Spectral analysis is an important signal processing tool for seismic data. The transformation of a seismogram into the frequency domain is the basis for a significant number of processing algorithms and interpretive methods. However, for seismograms whose frequency content vary with time, a simple 1-D (Fourier) frequency transformation is not sufficient. Improved spectral decomposition in frequency‐time (FT) space is provided by the sliding window (short time) Fourier transform, although this method suffers from the time‐ frequency resolution limitation. Recently developed transforms based on the new mathematical field of wavelet analysis bypass this resolution limitation and offer superior spectral decomposition. The continuous wavelet transform with its scale‐translation plane is conceptually best understood when contrasted to a short time Fourier transform. The discrete wavelet transform and matching pursuit algorithm are alternative wavelet transforms that map a seismogram into FT space. Decomposition into FT space of synthetic and calibrated explosive‐source seismic data suggest that the matching pursuit algorithm provides excellent spectral localization, and reflections, direct and surface waves, and artifact energy are clearly identifiable. Wavelet‐based transformations offer new opportunities for improved processing algorithms and spectral interpretation methods.

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VENEZIANO, DANIELE. "ITERATED RANDOM PULSE PROCESSES AND THEIR SPECTRAL PROPERTIES". Fractals 10, n. 01 (marzo 2002): 1–11. http://dx.doi.org/10.1142/s0218348x02000884.

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A new class of scaling random processes is introduced. The processes are obtained as sums of non-negative pulses and are generated through a recursive scheme that proceeds from coarser to finer scales. The representation at any given scale has the form of a filtered doubly-stochastic Poisson point process whose intensity depends linearly on the process at the immediately coarser scale. The filter functions (the pulses) at different scales are related through contractive affine transformations. If the transformations are isotropic in physical space, then the spectral density of the infinitely iterated process, [Formula: see text], is found to decay as [Formula: see text] along any radial direction, where the exponent c depends on the dimension of physical space and the parameters of the affine transformation. Various extensions of the basic scheme are considered, including pulses of random shape and anisotropic affine relations among the pulses at different scales. Processes of this type have several applications, including the representation of width functions in river basin hydrology.

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Wozniak, T. Z., Z. Ranachowski, P. Ranachowski, W. Ozgowicz e A. Trafarski. "The Application of Neural Networks for Studying Phase Transformation by the Method of Acoustic Emission in Bearing Steel/ Zastosowanie Sieci Neuronowych Do Badania Przemian Fazowych W Stali Łożyskowej Metodą Emisji Akustycznej". Archives of Metallurgy and Materials 59, n. 4 (1 dicembre 2014): 1705–12. http://dx.doi.org/10.2478/amm-2014-0288.

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Abstract The research was carried out on steel 100CrMnSi6-4 under isothermal austempering resulting in forming the duplex structure: martensitic and bainitic. The kinetics of transformation was controlled by the acoustic emission method. Complex phase transformations caused by segregation and carbide banding occur at the low-temperature heat treatment of bearing steel. At the temperature close to MS, a certain temperature range occurs where an effect of the first product of prior athermal martensite on the bainitic transformation can be observed. In the registered signal about 15 million various events were registered. There were considered three types of acoustic emission events (of high, medium and low energy), with relatively wide sections and with different spectral characteristics. It was found that the method of acoustic emission complemented by the application of neural networks is a sensitive tool to identify the kinetics of bainitic transformation and to show the interaction between martensitic and bainitic transformations.

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Jiang, Zhi Hao, Jeremy P. Turpin, Kennith Morgan, Bingqian Lu e Douglas H. Werner. "Spatial transformation-enabled electromagnetic devices: from radio frequencies to optical wavelengths". Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 373, n. 2049 (28 agosto 2015): 20140363. http://dx.doi.org/10.1098/rsta.2014.0363.

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Transformation optics provides scientists and engineers with a new powerful design paradigm to manipulate the flow of electromagnetic waves in a user-defined manner and with unprecedented flexibility, by controlling the spatial distribution of the electromagnetic properties of a medium. Using this approach, over the past decade, various previously undiscovered physical wave phenomena have been revealed and novel electromagnetic devices have been demonstrated throughout the electromagnetic spectrum. In this paper, we present versatile theoretical and experimental investigations on designing transformation optics-enabled devices for shaping electromagnetic wave radiation and guidance, at both radio frequencies and optical wavelengths. Different from conventional coordinate transformations, more advanced and versatile coordinate transformations are exploited here to benefit diverse applications, thereby providing expanded design flexibility, enhanced device performance, as well as reduced implementation complexity. These design examples demonstrate the comprehensive capability of transformation optics in controlling electromagnetic waves, while the associated novel devices will open up new paths towards future integrated electromagnetic component synthesis and design, from microwave to optical spectral regimes.

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Zapolsky, M. E., M. M. Lebediuk, Yu V. Tepliuk e N. B. Prokofyeva. "Features of interpretation of data of light and spectral dermatoscopy in patients with actinic keratosis". Ukrainian Journal of Dermatology, Venerology, Cosmetology, n. 2 (29 giugno 2021): 62–67. http://dx.doi.org/10.30978/ujdvk2021-2-62.

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Actinic keratosis (AK) is a common disease that is formed as a result of excessive insolation of exposed skin areas. One of the possible options for the development of the disease is the transformation of AK into squamous cell carcinoma. The timely diagnosis of suspicious areas of AK with their subsequent excision and histological examination has great importance in the prevention of neoplastic transformations of the skin.The aim of our study was to identify dermatoscopic patterns of the initial stages of neoplastic transformation of actinic keratosis and a comparative analysis of the diagnostic effectiveness of digital dermatoscopy, twocolor spectral dermatoscopy in relation to histological examination in a group of individuals suffering from actinic keratosis.There were 49 patients with AK under our supervision. All suspected cases of keratosis were additionally examined histologically. We analyzed the features of clinical forms and modified existing diagnostic methods. To expand the diagnostic capabilities of standard dermatoscopy, studies were performed in different ranges of light. Spectral dermatoscopy allowed estimating the potential foci of neoplastic transformation in blue and green light field (standard illumination range was suppressed). Particular attention was paid to areas of increased keratinization, areas of excessive vascularization with a predominance of superficial capillary network, microulcers with loose edges that contrast well with the green spectrum, as well as dynamic changes in color in one field of study for 30 days.It was found that the use of spectral dermatoscopy increases the diagnostic capabilities of AK and allows identifying more accurately the early signs of neoplastic transformations associated with both pathological neoangiogenesis («strawberry» pattern, glomerular network) and pathological proliferation (pseudogranulations, pathological keratinization, etc.).

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Hale, Michael T. "Spectral Density Matrix Transformations". Journal of the IEST 60, n. 1 (1 gennaio 2017): 21–30. http://dx.doi.org/10.17764/1098-4321.60.1.21.

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Abstract Reference criteria for a multiple degree-of-freedom (MDOF) random vibration test is generally provided in terms of an acceleration-based spectral density matrix (SDM). This SDM may be developed in terms of the auto-spectral densities (ASDs) and cross-spectral densities (CSDs) computed from the time histories acquired from an appropriately placed and oriented set of linear accelerometers. Such a direct measurement linear accelerometer based reference criteria will be denoted as SDMmeas. A second technique for defining a reference SDM is in terms of the accelerations associated with the six classical motion degrees-of-freedom as defined at an arbitrary point of origin. Such a reference will be denoted as SDMmotion. The objective at hand is to demonstrate the method of transforming between these two reference criteria spaces.

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Filipkovska, M. S., V. P. Kotlyarov, E. A. Melamedova e E. A. Moskovchenko. "Maxwell-Bloch Equations without Spectral Broadening: Gauge Equivalence, Transformation Operators and Matrix Riemann-Hilbert Problems". Zurnal matematiceskoj fiziki, analiza, geometrii 13, n. 2 (25 giugno 2017): 119–53. http://dx.doi.org/10.15407/mag13.02.119.

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Geng, Xianguo, Jiao Wei e Bo Xue. "A coupled nonlinear Schrödinger-type equation and its Darboux transformation". Modern Physics Letters B 32, n. 17 (18 giugno 2018): 1850192. http://dx.doi.org/10.1142/s0217984918501920.

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A new coupled nonlinear Schrödinger (NLS)-type equation is proposed by means of the negative power flow of a spectral problem. Resorting to the gauge transformation of the spectral problem and the reduction technique, Darboux transformations for the coupled NLS-type equation and its reduction are constructed, by which explicit solutions of the two coupled NLS-type equations can be engendered from their known solutions. This process can be done continually and will usually yield a series of solutions including multi-soliton solutions. As an illustrate example, one- and two-soliton solutions of the latter coupled NLS-type equation are obtained from a trivial solution.

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Luo, Lili, Qinrui Chang, Yifan Gao, Danyao Jiang e Fenling Li. "Combining Different Transformations of Ground Hyperspectral Data with Unmanned Aerial Vehicle (UAV) Images for Anthocyanin Estimation in Tree Peony Leaves". Remote Sensing 14, n. 9 (8 maggio 2022): 2271. http://dx.doi.org/10.3390/rs14092271.

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To explore rapid anthocyanin (Anth) detection technology based on remote sensing (RS) in tree peony leaves, we considered 30 species of tree peonies located in Shaanxi Province, China. We used an SVC HR~1024i portable ground object spectrometer and mini-unmanned aerial vehicle (UAV)-borne RS systems to obtain hyperspectral (HS) reflectance and images of canopy leaves. First, we performed principal component analysis (PCA), first-order differential (FD), and continuum removal (CR) transformations on the original ground-based spectra; commonly used spectral parameters were implemented to estimate Anth content using multiple stepwise regression (MSR), partial least squares (PLS), back-propagation neural network (BPNN), and random forest (RF) models. The spectral transformation highlighted the characteristics of spectral curves and improved the relationship between spectral reflectance and Anth, and the RF model based on the FD spectrum portrayed the best estimation accuracy (R2c = 0.91; R2v = 0.51). Then, the RGB (red-green-blue) gray vegetation index (VI) and the texture parameters were constructed using UAV images, and an Anth estimation model was constructed using UAV parameters. Finally, the UAV image was fused with the ground spectral data, and a multisource RS model of Anth estimation was constructed, based on PCA + UAV, FD + UAV, and CR + UAV, using MSR, PLS, BPNN, and RF methods. The RF model based on FD+UAV portrayed the best modeling and verification effect (R2c = 0.93; R2v = 0.76); compared with the FD-RF model, R2c increased only slightly, but R2v increased greatly from 0.51 to 0.76, indicating improved modeling and testing accuracy. The optimal spectral transformation for the Anth estimation of tree peony leaves was obtained, and a high-precision Anth multisource RS model was constructed. Our results can be used for the selection of ground-based HS transformation in future plant Anth estimation, and as a theoretical basis for plant growth monitoring based on ground and UAV multisource RS.

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Carron, Julien, e István Szapudi. "Optimal observables in galaxy surveys". Proceedings of the International Astronomical Union 10, S306 (maggio 2014): 235–38. http://dx.doi.org/10.1017/s1743921314010783.

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AbstractThe sufficient statistics of the one-point probability density function of the dark matter density field is worked out using cosmological perturbation theory and tested to the Millennium simulation density field. The logarithmic transformation is recovered for spectral index close to -1 as a special case of the family of power transformations. We then discuss how these transforms should be modified in the case of noisy tracers of the field and focus on the case of Poisson sampling. This gives us optimal local transformations to apply to galaxy survey data prior the extraction of the spectrum in order to capture most efficiently the information encoded in large scale structures.

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Kłosowski, Grzegorz, Tomasz Rymarczyk, Dariusz Wójcik, Stanisław Skowron, Tomasz Cieplak e Przemysław Adamkiewicz. "The Use of Time-Frequency Moments as Inputs of LSTM Network for ECG Signal Classification". Electronics 9, n. 9 (6 settembre 2020): 1452. http://dx.doi.org/10.3390/electronics9091452.

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This paper refers to the method of using the deep neural long-short-term memory (LSTM) network for the problem of electrocardiogram (ECG) signal classification. ECG signals contain a lot of subtle information analyzed by doctors to determine the type of heart dysfunction. Due to the large number of signal features that are difficult to identify, raw ECG data is usually not suitable for use in machine learning. The article presents how to transform individual ECG time series into spectral images for which two characteristics are determined, which are instantaneous frequency and spectral entropy. Feature extraction consists of converting the ECG signal into a series of spectral images using short-term Fourier transformation. Then the images were converted using Fourier transform again to two signals, which includes instantaneous frequency and spectral entropy. The data set transformed in this way was used to train the LSTM network. During the experiments, the LSTM networks were trained for both raw and spectrally transformed data. Then, the LSTM networks trained in this way were compared with each other. The obtained results prove that the transformation of input signals into images can be an effective method of improving the quality of classifiers based on deep learning.

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Chang, E. C., e K. Yoshimura. "A semi-Lagrangian advection scheme for radioactive tracers in the NCEP Regional Spectral Model (RSM)". Geoscientific Model Development 8, n. 10 (14 ottobre 2015): 3247–55. http://dx.doi.org/10.5194/gmd-8-3247-2015.

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Abstract. In this study, the non-iteration dimensional-split semi-Lagrangian (NDSL) advection scheme is applied to the National Centers for Environmental Prediction (NCEP) Regional Spectral Model (RSM) to alleviate the Gibbs phenomenon. The Gibbs phenomenon is a problem wherein negative values of positive-definite quantities (e.g., moisture and tracers) are generated by the spectral space transformation in a spectral model system. To solve this problem, the spectral prognostic specific humidity and radioactive tracer advection scheme is replaced by the NDSL advection scheme, which considers advection of tracers in a grid system without spectral space transformations. A regional version of the NDSL is developed in this study and is applied to the RSM. Idealized experiments show that the regional version of the NDSL is successful. The model runs for an actual case study suggest that the NDSL can successfully advect radioactive tracers (iodine-131 and cesium-137) without noise from the Gibbs phenomenon. The NDSL can also remove negative specific humidity values produced in spectral calculations without losing detailed features.

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Chang, E. C., e K. Yoshimura. "A semi-Lagrangian advection scheme for radioactive tracers in a regional spectral model". Geoscientific Model Development Discussions 8, n. 6 (2 giugno 2015): 4221–43. http://dx.doi.org/10.5194/gmdd-8-4221-2015.

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Abstract. In this study, the non-iteration dimensional-split semi-Lagrangian (NDSL) advection scheme is applied to the National Centers for Environmental Prediction (NCEP) regional spectral model (RSM) to alleviate the Gibbs phenomenon. The Gibbs phenomenon is a problem wherein negative values of positive-definite quantities (e.g., moisture and tracers) are generated by the spectral space transformation in a spectral model system. To solve this problem, the spectral prognostic specific humidity and radioactive tracer advection scheme is replaced by the NDSL advection scheme, which considers advection of tracers in a grid system without spectral space transformations. A regional version of the NDSL is developed in this study and is applied to the RSM. Idealized experiments show that the regional version of the NDSL is successful. The model runs for an actual case study suggest that the NDSL can successfully advect radioactive tracers (iodine-131 and cesium-137) without noise from the Gibbs phenomenon. The NDSL can also remove negative specific humidity values produced in spectral calculations without losing detailed features.

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Zhang, Ning, e Tiecheng Xia. "A Hierarchy of Lattice Soliton Equations Associated with a New Discrete Eigenvalue Problem and Darboux Transformations". International Journal of Nonlinear Sciences and Numerical Simulation 16, n. 7-8 (1 dicembre 2015): 301–6. http://dx.doi.org/10.1515/ijnsns-2014-0119.

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AbstractBy considering a new discrete isospectral eigenvalue problem, a hierarchy of integrable positive and negative lattice models is derived. It is shown that they correspond to positive and negative power expansions of Lax operators with respect to the spectral parameter, respectively. And the equation in the resulting hierarchy is integrable in Liouville sense. Further, a Darboux transformation is established for the typical equations by using gauge transformations of Lax pairs, from which the exact solutions are given.

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Carcione, José M. "The wave equation in generalized coordinates". GEOPHYSICS 59, n. 12 (dicembre 1994): 1911–19. http://dx.doi.org/10.1190/1.1443578.

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This work introduces a spectral collocation scheme for the viscoelastic wave equation transformed from Cartesian to generalized coordinates. Both the spatial derivatives of field variables and the metrics of the transformation are calculated by the Chebychev pseudospectral method. The technique requires a special treatment of the boundary conditions, which is based on 1-D characteristics normal to the boundaries. The numerical solution of Lamb’s problem requires two 1-D stretching transformations for each Cartesian direction. The results show excellent agreement between the elastic numerical and analytical solutions, demonstrating the effectiveness of the differential operator and boundary treatment. Another example, requiring 1-D transformations, tests the propagation of a Rayleigh wave around a corner of the numerical mesh. Two‐dimensional transformations adapt the grid to topographic features: a syncline, and an anticlinal structure formed with fine layers.

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Tang, Siyu, Chong Du e Tangzhe Nie. "Inversion Estimation of Soil Organic Matter in Songnen Plain Based on Multispectral Analysis". Land 11, n. 5 (21 aprile 2022): 608. http://dx.doi.org/10.3390/land11050608.

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Sentinel-2A multi-spectral remote sensing image data underwent high-efficiency differential processing to extract spectral information, which was then matched to soil organic matter (SOM) laboratory test values from field samples. From this, multiple-linear stepwise regression (MLSR) and partial least square (PLSR) models were established based on a differential algorithm for surface SOM modeling. The original spectra were subjected to basic transformations with first- and second-derivative processing. MLSR and PLSR models were established based on these methods and the measured values, respectively. The results show that Sentinel-2A remote sensing imagery and SOM content correlated in some bands. The correlation between the spectral value and SOM content was significantly improved after mathematical transformation, especially square-root transformation. After differential processing, the multi-band model had better predictive ability (based on fitting accuracy) than single-band and unprocessed multi-band models. The MLSR and PLSR models of SOM had good prediction functionality. The reciprocal logarithm first-order differential MLSR regression model had the best prediction and inversion results (i.e., most consistent with the real-world data). The MLSR model is more stable and reliable for monitoring SOM content, and provides a feasible method and reference for SOM content-mapping of the study area.

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NATH, MILAN, e SOMNATH PAUL. "GRAPH TRANSFORMATION AND DISTANCE SPECTRAL RADIUS". Discrete Mathematics, Algorithms and Applications 05, n. 03 (settembre 2013): 1350014. http://dx.doi.org/10.1142/s1793830913500146.

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Trees are very common in the theory and applications of combinatorics. In this paper, we consider graphs whose underlying structure is a tree and study the behavior of the distance spectral radius under a graph transformation. As an application, we find the corona tree that maximizes the distance spectral radius among all corona trees with a fixed maximum degree. We also find the graph with minimal (maximal) distance spectral radius among all corona trees. Finally, we determine the graph with minimal distance spectral radius in a special class of corona trees.

30

Kish, L. K., O. I. Lavrukhina, V. G. Amelin, A. V. Tretyakov, T. D. Pen’kov e D. Yu Nekrasov. "Non-target analysis of livestock products and feed for residues of drugs, pesticides, mycotoxins and their metabolites by high-resolution mass spectrometry (a review)". Industrial laboratory. Diagnostics of materials 89, n. 11 (21 novembre 2023): 5–13. http://dx.doi.org/10.26896/1028-6861-2023-89-11-5-13.

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A review of techniques of non-target analysis for simultaneous identification and determination of veterinary drugs, pesticides, mycotoxins, their metabolites, and substances of chemical transformation in livestock products using liquid chromatography and high-resolution mass spectrometry is presented. Some limitations of the approach are noted, such as the necessity of using common extraction conditions, the possibility of analyte transformations during the sample preparation, false positive results for isobaric and isomeric compounds, and the lack of spectral data for previously unexplored substances. However, the method is the most promising tool for the determination of pollutants not identified in the targeted analysis, as in the case of multicomponent screening of food and raw materials, and in the study of the parent compounds transformation.

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Huang, Zhaoqiang, Wenxuan Huang, Sheng Li, Bin Ni, Yalong Zhang, Mingwei Wang, Maolin Chen e Fuxiao Zhu. "Inversion Evaluation of Rare Earth Elements in Soil by Visible-Shortwave Infrared Spectroscopy". Remote Sensing 13, n. 23 (1 dicembre 2021): 4886. http://dx.doi.org/10.3390/rs13234886.

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According to historical information, more than 300 metal smelting enterprises have been in the southwest of Xiongan for 300 years; however, these polluting enterprises have been gradually closed with the increased intensity of environmental protection. In the paper, 264 soil samples were collected and analyzed in the range of 400 nm–2500 nm by the spectra vista corporation (SVC), and the spectral noise was smoothed by the Savitzky–Golay filter. In order to enhance the spectral differences and curve shapes, mathematical transformations, such as the standard normal variate (SNV), first-order differential (FD), second-order differential (SD), multiple scattering correction (MSC), and continuum removal (CR), were performed on the data, and the correlation between spectral transformation and contents of REEs was analyzed. Moreover, three machine learning models—partial least-squares (PLS), random forest (RF), back propagation neural network (BPNN)—were used to predict the contents of REEs. Experimental results prove that REEs are combined with spectral active substances, such as organic compounds, clay minerals, and iron oxide, and it is possible to determine the contents of REEs using the reflection spectrum. The R2 between the predicted values and measured contents reached 0.986 by using BPNN after FD transformation. More importantly, the predicted values basically agree with the actual situation for CASI/SASI airborne hyperspectral images, and this is an effective technique to obtain the contents of REEs in soil at the study area.

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Chalkia, Magdalene H., e Richard M. Warren. "Spectral fissioning in phonemic transformations". Perception & Psychophysics 55, n. 2 (marzo 1994): 218–26. http://dx.doi.org/10.3758/bf03211668.

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NADKARNI e ROBERTSON. "SPECTRAL RADIUS OF NONSINGULAR TRANSFORMATIONS". Real Analysis Exchange 15, n. 1 (1989): 275. http://dx.doi.org/10.2307/44152005.

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Mase, Hajime, e Yusuke Ozawa. "Transformation of Double Peak Spectral Waves." Doboku Gakkai Ronbunshu, n. 509 (1995): 183–91. http://dx.doi.org/10.2208/jscej.1995.509_183.

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Nour-Omid, Bahram, Beresford N. Parlett, Thomas Ericsson e Paul S. Jensen. "How to implement the spectral transformation". Mathematics of Computation 48, n. 178 (1 maggio 1987): 663. http://dx.doi.org/10.1090/s0025-5718-1987-0878698-5.

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Hall, R. L., e W. H. Zhou. "Spectral approximation by the polar transformation". Canadian Journal of Physics 76, n. 1 (1 gennaio 1998): 31–37. http://dx.doi.org/10.1139/p97-047.

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Abstract (sommario):

Central potentials V(r) are considered that admit the polar representation V(r) = g(h(r)), where h(r) = sgn (q)rq, q is fixed, and g is the polar transformation function. This representation allows the Schrödinger eigenvalues generated by V to be approximated in terms of those generated by the pure polar potential h(r). In many cases a pair of powers {q1, q2} can be chosen so that the corresponding polar functions {g1, g2} have definite and opposite convexity. For such cases, the spectral approximations provide both upper and lower bounds for the entire discrete spectrum. The example V(r) = ar2 + br2/(1 + cr2) is considered in detail. PACS No. 03.65Ge

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Abd El-Hamid, Hazem T., e Guan Hong. "Hyperspectral remote sensing for extraction of soil salinization in the northern region of Ningxia". Modeling Earth Systems and Environment 6, n. 4 (12 giugno 2020): 2487–93. http://dx.doi.org/10.1007/s40808-020-00829-3.

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Abstract Soil salinization affects negatively on agricultural productivity in the semiarid region of Ningxia. In this study, the performance of inversion model to determine soil salinization was assessed using some analysis and reflectance of wavelength. About 42 vegetation samples and 42 soil samples were collected for model extraction. Hyper-spectral data processing method was used to analyze spectral characteristics of different levels of salinization area vegetation. Spectral data were transformed in 16 different approaches, including root mean squares, logarithm, inversion logarithm, and first-order differentiation. After the transformation, the obtained soil and vegetation characteristics spectra correlate well with soil salt content, built soil index, and many vegetation indices. Nonlinear regression was employed to establish soil salinization remote sensing monitoring model. By comparing various spectral transformations, the first-order differential of soil spectral was the most sensitive to soil salinization degrees. The model of the current research was based on salinity index (SI) and improved soil-adjusted vegetation index (MSAVI). The correlation between simulated values and measured values was 0.758. Therefore, remote sensing monitoring derived from MSAVI–SI can greatly improve the dynamic and periodical monitoring of soil salinity in the study area.

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Zhluktova, Irina V., Vladimir A. Kamynin, Dmitry A. Korobko, Aleksei S. Abramov, Andrei A. Fotiadi, Alexej A. Sysoliatin e Vladimir B. Tsvetkov. "Broadband Supercontinuum Generation in Dispersion Decreasing Fibers in the Spectral Range 900–2400 nm". Photonics 9, n. 10 (18 ottobre 2022): 773. http://dx.doi.org/10.3390/photonics9100773.

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The spectrally flat supercontinuum generation in the wavelength range of 900–2400 nm is demonstrated in silica-based fibers of variable core diameter and dispersion. It is shown that, in comparison with standard optical fibers of the same length, supercontinuum spectra 200 nm wider can be realized in the samples under study. The significant difference between the spectral and temporal transformations of radiation depending on the direction of propagation is demonstrated in the researched fiber samples.

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Robinson, E. Arthur. "Mixing and spectral multiplicity". Ergodic Theory and Dynamical Systems 5, n. 4 (dicembre 1985): 617–24. http://dx.doi.org/10.1017/s0143385700003205.

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Abstract (sommario):

AbstractA mixing transformation is constructed which has non-simple spectrum of finite multiplicity. This example is based on a rank 1 mixing transformation and is constructed by cutting and stacking. It can be made to be mixing of all orders.

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Garza, L., e F. Marcellán. "Szegő transformations and rational spectral transformations for associated polynomials". Journal of Computational and Applied Mathematics 233, n. 3 (dicembre 2009): 730–38. http://dx.doi.org/10.1016/j.cam.2009.02.041.

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Rossi, T. M., e I. M. Warner. "Pattern Recognition of Two-Dimensional Fluorescence Data Using Cross-Correlation Analysis". Applied Spectroscopy 39, n. 6 (novembre 1985): 949–59. http://dx.doi.org/10.1366/0003702854249501.

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An algorithm for spectral matching of excitation-emission matrices (EEMs) is reported. The pattern-recognition method developed operates completely in the frequency domain after Fourier transformation of unknown and standard EEMs. Spectral matches are evaluated by correlation and intervector distances between Fourier spectra of EEMs. Application of this method to single-component EEMs demonstrates the utility of pattern recognition for the identification of spectrally similar anthracene derivatives. In a study of multicomponent EEMs, mixtures of polynuclear aromatics (PNAs) are identified by comparison to a standard set of mixtures, and eigenvector deconvolution is coupled with pattern recognition for the identification of individual components in two-component mixtures. In addition, the feasibility of applying automatic pattern recognition to the identification of bacteria based on their uptake of fluorescent dyes is explored.

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Laatikainen, Jyrki, Matias Koivurova, Jari Turunen, Tero Setälä e Ari T. Friberg. "Spectral scaling transformations of nonstationary light". EPJ Web of Conferences 266 (2022): 13020. http://dx.doi.org/10.1051/epjconf/202226613020.

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We present optical systems, which transform isodiffracting nonstationary beams into fields obeying either cross-spectral purity or spectral invariance. The designs are hybrid refractive-diffractive imaging systems, which are able to perform the desired transformations over a broad spectral bandwidth and irrespective of the state of spatial coherence of the input beam.

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Molina, P. C., M. P. Castro e C. S. Anjos. "ASSESSMENT OF PCA AND MNF INFLUENCE IN THE VHR SATELLITE IMAGE CLASSIFICATIONS". ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XLII-3/W12-2020 (4 novembre 2020): 55–60. http://dx.doi.org/10.5194/isprs-archives-xlii-3-w12-2020-55-2020.

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Abstract. Orbital images have been increasingly refined spatially as spectrally as that is the case with those provided by satellite Earth observation WorldView-3 used in this paper. However, the images are very susceptible to noise interference, so it is difficult to identify and characterize objects. Therefore, it is essential to use techniques to minimize them. Thus, through increasingly innovative processing, it is possible to carry out detailed characterization mainly of urban areas. This work aims to perform the classification of images Worldview-3 using the advanced methods of classification Random Forest and Deep Learning for the region of Botafogo in the municipality of Rio de Janeiro, Brazil. Such classifications were performed for four different data sets, including the spectral bands and transformations (MNF and PCA) resulting from the original images. The results demonstrate that the use of transformations resulting from the original images as input data for the extraction of attributes in conjunction with the spectral bands improves the accuracy of the classifications generated by the Random Forest and Deep Learning method.

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Chen, Hai, e Zi-Xiang Zhou. "Global explicit solutions with n double spectral parameters for the Myrzakulov-I equation". Modern Physics Letters B 30, n. 29 (28 ottobre 2016): 1650358. http://dx.doi.org/10.1142/s0217984916503589.

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Abstract (sommario):

The Darboux transformation with n double spectral parameters for the Myrzakulov-I equation is obtained by taking suitable limit of the spectral parameters. Global explicit solutions are obtained by using this Darboux transformation with n double spectral parameters.

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Vlaskina, S. I. "Peculiarities of photoluminescence spectra behavior in SiC crystals and films during phase transformations". Semiconductor Physics Quantum Electronics and Optoelectronics 19, n. 1 (8 aprile 2016): 62–66. http://dx.doi.org/10.15407/spqeo19.01.062.

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Karpov, Eduard G., Larry A. Danso e John T. Klein. "Anomalous strain energy transformation pathways in mechanical metamaterials". Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 475, n. 2226 (giugno 2019): 20190041. http://dx.doi.org/10.1098/rspa.2019.0041.

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This discussion starts with a mechanics version of Parseval's energy theorem applicable to any discrete lattice material with periodic internal structure: a microtruss, grid, frame, origami or tessellation. It provides a simple relationship between the strain energy volumetric/usual and spectral distributions in the reciprocal space. The spectral energy distribution leads directly to a spectral entropy of lattice deformation (Shannon's type), whose variance with a material coordinate represents the decrease of information about surface loads in the material interior. Spectral entropy is also a basic measure of complexity of mechanical responses of metamaterials to surface and body loads. Considering transformation of the energy volumetric and spectral distributions with a material coordinate pointed away from a surface load, several interesting anomalies are seen even for simple lattice materials, when compared to continuum materials. These anomalies include selective filtering of surface Raleigh waves (sinusoidal pressure patterns), Saint–Venant effect inversion illustrated by energy spectral distribution contours, occurrence of ‘hiding pockets’ of low deformation, and redirection of strain energy maximum away from axis of a concentrated surface load. The latter phenomenon can be significant for impact protection applications of mechanical metamaterials.

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Ariznabarreta, Gerardo, Juan C. García-Ardila, Manuel Mañas e Francisco Marcellán. "Matrix biorthogonal polynomials on the real line: Geronimus transformations". Bulletin of Mathematical Sciences 09, n. 02 (agosto 2019): 1950007. http://dx.doi.org/10.1142/s1664360719500073.

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In this paper, Geronimus transformations for matrix orthogonal polynomials in the real line are studied. The orthogonality is understood in a broad sense, and is given in terms of a nondegenerate continuous sesquilinear form, which in turn is determined by a quasi-definite matrix of bivariate generalized functions with a well-defined support. The discussion of the orthogonality for such a sesquilinear form includes, among others, matrix Hankel cases with linear functionals, general matrix Sobolev orthogonality and discrete orthogonal polynomials with an infinite support. The results are mainly concerned with the derivation of Christoffel-type formulas, which allow to express the perturbed matrix biorthogonal polynomials and its norms in terms of the original ones. The basic tool is the Gauss–Borel factorization of the Gram matrix, and particular attention is paid to the non-associative character, in general, of the product of semi-infinite matrices. The Geronimus transformation in which a right multiplication by the inverse of a matrix polynomial and an addition of adequate masses are performed, is considered. The resolvent matrix and connection formulas are given. Two different methods are developed. A spectral one, based on the spectral properties of the perturbing polynomial, and constructed in terms of the second kind functions. This approach requires the perturbing matrix polynomial to have a nonsingular leading term. Then, using spectral techniques and spectral jets, Christoffel–Geronimus formulas for the transformed polynomials and norms are presented. For this type of transformations, the paper also proposes an alternative method, which does not require of spectral techniques, that is valid also for singular leading coefficients. When the leading term is nonsingular, a comparison of between both methods is presented. The nonspectral method is applied to unimodular Christoffel perturbations, and a simple example for a degree one massless Geronimus perturbation is given.

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Heil, Kurt, e Urs Schmidhalter. "An Evaluation of Different NIR-Spectral Pre-Treatments to Derive the Soil Parameters C and N of a Humus-Clay-Rich Soil". Sensors 21, n. 4 (18 febbraio 2021): 1423. http://dx.doi.org/10.3390/s21041423.

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Near-infrared reflectance spectroscopy (NIRS) was successfully used in this study to measure soil properties, mainly C and N, requiring spectral pre-treatments. Calculations in this evaluation were carried out using multivariate statistical procedures with preceding pre-treatment procedures of the spectral data. Such transformations could remove noise, highlight features, and extract essential wavelengths for quantitative predictions. This frequently significantly improved the predictions. Since selecting the appropriate transformation was not straightforward due to the large numbers of available methods, more comprehensive insight into choosing appropriate and optimized pre-treatments was required. Therefore, the objectives of this study were (i) to compare various pre-processing transformations of spectral data to determine their suitability for modeling soil C and N using NIR spectra (55 pre-treatment procedures were tested), and (ii) to determine which wavelengths were most important for the prediction of C and N. The investigations were carried out on an arable field in South Germany with a soil type of Calcaric Fluvic Relictigleyic Phaeozem (Epigeoabruptic and Pantoclayic), created in the flooding area of the Isar River. The best fit and highest model accuracy for the C (Ct, Corg, and Ccarb) and N models in the calibration and validation modes were achieved using derivations with Savitzky–Golay (SG). This enabled us to calculate the Ct, Corg, and N with an R2 higher than 0.98/0.86 and an ratio of performance to the interquartile range (RPIQ) higher than 10.9/4.1 (calibration/validation).

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Kobasa, I. M., I. V. Kondratyeva e Yu V. Kropelnytska. "Sensitization of TiO2 by the symmetric cationic polymethine dye for the photocatalytic reduction of methylene blue". Functional Materials Letters 12, n. 03 (16 maggio 2019): 1950038. http://dx.doi.org/10.1142/s1793604719500383.

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Using the spectral, electrochemical and energy transformation characteristics of the cationic polymethine dye (D) 2-[(1E)-1,3-butadienyl-]-1-(phenylmethyl)-benindolium borfluoride, it has been found that the dye can be applied as a highly efficient sensitizer of TiO2. An intensity of the initially narrow light adsorption band becomes wider and embraces practically entire visible and near IR zones as a result of application of the dye to the surface of TiO2. Due to this effect, a wider array of light quanta can potentially be involved in the photocatalytic transformations. Some new heterostructures (HS) of the type D/TiO2 have been developed and their photocatalytic activities were determined in the test reaction of reduction of methylene blue by formaldehyde for different dye contents and under various modes of irradiation. The schemes of the energy transformation initiated by the light with different wavelengths are proposed and discussed.

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Lin, Yuanhang, Susan Meerdink e Paul Gader. "Spectral Transformations for Multitemporal Hyperspectral Classification". IEEE Geoscience and Remote Sensing Letters 19 (2022): 1–5. http://dx.doi.org/10.1109/lgrs.2021.3136569.

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