A data-driven analysis method known as dynamic mode decomposition (DMD) approximates the linear Koopman operator on projected space. In the spirit of Johnson-Lindenstrauss Lemma, we will use random projection to estimate the DMD modes in reduced dimensional space. In practical applications, snapshots are in high dimensional observable space and the DMD operator matrix is massive. Hence, computing DMD with the full spectrum is infeasible, so our main computational goal is estimating the eigenvalue and eigenvectors of the DMD operator in a projected domain. We will generalize the current algorithm to estimate a projected DMD operator. We focus on a powerful and simple random projection algorithm that will reduce the computational and storage cost. While clearly, a random projection simplifies the algorithmic complexity of a detailed optimal projection, as we will show, generally the results can be excellent nonetheless, and quality understood through a well-developed theory of random projections. We will demonstrate that modes can be calculated for a low cost by the projected data with sufficient dimension.

One of the most basic pieces of information gained from dynamic electromyography is accurately defining muscle action and phase timing within the gait cycle. The human gait relies on selective timing and the intensity of appropriate muscle activations for stability, loading, and progression over the supporting foot during stance, and further to advance the limb in the swing phase. A common clinical practice is utilizing a low-pass filter to denoise integrated electromyogram (EMG) signals and to determine onset and cessation events using a predefined threshold. However, the accuracy of the defining period of significant muscle activations via EMG varies with the temporal shift involved in filtering the signals; thus, the low-pass filtering method with a fixed order and cut-off frequency will introduce a time delay depending on the frequency of the signal. In order to precisely identify muscle activation and to determine the onset and cessation times of the muscles, we have explored here onset and cessation epochs with denoised EMG signals using different filter banks: the wavelet method, empirical mode decomposition (EMD) method, and ensemble empirical mode decomposition (EEMD) method. In this study, gastrocnemius muscle onset and cessation were determined in sixteen participants within two different age groups and under two different walking conditions. Low-pass filtering of integrated EMG (iEMG) signals resulted in premature onset (28% stance duration) in younger and delayed onset (38% stance duration) in older participants, showing the time-delay problem involved in this filtering method. Comparatively, the wavelet denoising approach detected onset for normal walking events most precisely, whereas the EEMD method showed the smallest onset deviation. In addition, EEMD denoised signals could further detect pre-activation onsets during a fast walking condition. A comprehensive comparison is discussed on denoising EMG signals using EMD, EEMD, and wavelet denoising in order to accurately define an onset of muscle under different walking conditions.

This work presents a novel approach to construct surrogate models of parametric Differential Algebraic Equations based on a tensor representation of the solutions. The procedure consists in building simultaneously, for every output of the reference model, an approximation given in tensor-train format. A parsimonious exploration of the parameter space coupled with a compact data representation allows to alleviate the curse of dimensionality. The approach is thus appropriate when many parameters with large domains of variation are involved. The numerical results obtained for a nonlinear elasto-viscoplastic constitutive law show that the constructed surrogate model is sufficiently accurate to enable parametric studies such as the calibration of material coefficients.

In this paper, we introduce the evolve-then-filter (EF) regularization method for reduced order modeling of convection-dominated stochastic systems. The standard Galerkin projection reduced order model (G-ROM) yield numerical oscillations in a convection-dominated regime. The evolve-then-filter reduced order model (EF-ROM) aims at the numerical stabilization of the standard G-ROM, which uses explicit ROM spatial filter to regularize various terms in the reduced order model (ROM). Our numerical results based on a stochastic Burgers equation with linear multiplicative noise. It shows that the EF-ROM is significantly better results than G-ROM.

We consider a general problem of optimal allocation of limited resources in a wireless telecommunication network. The users are divided into several different groups (or classes), which correspond to different levels of service. The network manager must satisfy these different users requirements. This approach leads to a convex optimization problem with balance and capacity constraints. We present several decomposition type methods to find a solution of this problem, which exploit its special features. We suggest to apply first the dual Lagrangian method with respect to the total capacity constraint, which gives the one-dimensional dual problem. However, calculation of the value of the dual cost function requires solution of several optimization problems. Our methods differ in approaches of solution of these auxiliary problems. We compare the performance of the suggested methods on several series of test problems. They show rather satisfactory convergence. Nevertheless, proper decomposition technique enhance the convergence essentially.

In order to solve the problem of feature extraction of underwater acoustic signals in complex ocean environment, a new method for feature extraction from ship radiated noise is presented based on empirical mode decomposition theory and permutation entropy. It analyzes the separability for permutation entropies of the intrinsic mode functions of three types of ship radiated noise signals, and discusses the permutation entropy of the intrinsic mode function with the highest energy. In this study, ship radiated noise signals measured from three types of ships are decomposed into a set of intrinsic mode functions with empirical mode decomposition method. Then, the permutation entropies of all intrinsic mode functions are calculated with appropriate parameters. The permutation entropies are obviously different in the intrinsic mode functions with the highest energy, thus, the permutation entropy of the intrinsic mode function with the highest energy is regarded as a new characteristic parameter to extract the feature of ship radiated noise. After that, the characteristic parameters, namely, the energy difference between high and low frequency, permutation entropy, and multi-scale permutation entropy, are compared with the permutation entropy of the intrinsic mode function with the highest energy. It is discovered that the four characteristic parameters are at the same level for similar ships, however, there are differences in the parameters for different types of ships. The results demonstrate that the permutation entropy of the intrinsic mode function with the highest energy is better in separability as the characteristic parameter than the other three parameters by comparing their fluctuation ranges and the average values of the four characteristic parameters. Hence, the feature of ship radiated noise can be extracted efficiently with the method.

Abstract In order to solve the problem that it is difficult to obtain the accurate trigger signal moment when using the time difference of UAV flight acoustic signals collected by acoustic sensors arranged in advance to locate the position of UAVs when they cannot be tracked by radar and are difficult to be observed by the human eye, an acoustic source localisation method with improved empirical modal decomposition (REMD) under an adaptive frequency window is proposed. Firstly, the collected UAV flight signals are smoothed and filtered, then the robust empirical modal decomposition (REMD) is used for IMF modal decomposition and spectral analysis of the collected signals, and a panning frequency window with variable bandwidth is introduced for corresponding frequency locking and extracting the IMFs; the GWO optimisation is used and the sliding metrics are set to determine the position of the panning frequency window automatically; finally, the extracted Finally, the extracted IMF components are reconstructed according to the criterion, and the trigger signal moments in the reconstructed IMF components are resolved and recorded, and the algorithm is used to calculate the difference between the reception moments of different sensors; for the traditional sound source localisation algorithms with a small detection range, which are prone to fall into the no-solution or false-solution, i.e., unable to achieve the localisation, a weighted least-squares-based Chan-Taylor algorithm is proposed for the localisation computation, and a weighted least-squares algorithm is proposed for the localisation computation, through the Inputting the sensor delay parameter and solving the linear equation system to get the target position information; finally, this paper verifies the robustness and performance of the design method with simulated and actual signals. The results show that the maximum positioning error is no more than 5% in an area with a side length of 15m in the measurement area. With the improved accuracy of time delay estimation, the positioning simulation results meet the positioning requirements even though the positioning error is further expanded when the measurement area is further expanded.

To predict the remaining useful life (RUL) of proton exchange membrane fuel cell (PEMFC) in advance, a prediction method based on the voltage recovery model and Bayesian optimization of a multi-kernel relevance vector machine (MK-RVM) is proposed in this paper. First, the empirical mode decomposition (EMD) method was used to preprocess the data, and then the MK-RVM was used to train the model. Then, the Bayesian optimization algorithm was used to optimize the weight coefficient of the kernel function to complete the parameter update of the prediction model, and the voltage recovery model was added to the prediction model to realize the rapid and accurate prediction of the RUL of PEMFC. Finally, the method proposed in this paper was applied to the open data set of PEMFC provided by FCLAB, and the prediction accuracy of the RUL of PEMFC was obtained by 95.35%, which showed that the method had good gen-eralization ability and verified the accuracy of the prediction for the RUL of PEMFC.

In this paper, we investigate the “statics and dynamics” return and volatility spillovers transmission across developed and developing countries. Quoted against the U.S. dollar, we study twenty-three global currencies over 2005 – 2016. Focusing on the spillover index methodology, the generalised VAR framework is employed. Our findings indicate no evidence of bi-directional return and volatility spillovers between developed and developing countries. However, a unidirectional volatility spillover from developed to developing countries is highlighted. Furthermore, our findings document significant bi-directional volatility spillovers within the European region (Eurozone and non-Eurozone currencies) with the British Pound (GBP) and the Euro (EUR) as the most significant transmitters of volatility. The findings reiterate the prominence of volatility spillovers to financial regulators.

The high dimensions and governing non linear dynamics in wind farm systems make the design of numerical optimal controllers computationally expensive. A possible pathway to circumvent this challenge lies in finding reduced order models which can accurately embed the existing non linearities. The work here presented applies the ideas motivated by non linear dynamical systems theory - the Koopman Operator - to an innovative algorithm in the context of wind farm systems - Input Output Dynamic Mode Decomposition - to improve on the ability to model the aerodynamic interaction between wind turbines in a wind farm and uncover insights into the existing dynamics. It is shown that a reduced order linear state space model can reproduce the downstream turbine generator power dynamics and reconstruct the upstream turbine wake. It is further shown that the fit can be improved by judiciously choosing the Koopman observables used in the IODMD algorithm without jeopardizing the models ability to rebuild the turbine wake. The extensions to the IODMD algorithm provide an important step towards the design of linear reduced order models which can accurately reproduce the dynamics in a wind farm.

Densimetric Froude (Fr) is the minimum velocity required to prevent sediment deposition in pipes. Prediction of Fr is of utmost importance in numerous applications in civil engineering. In this paper through using a new hybrid method. Genetic Algorithm (GA) is used for optimum selection of membership functions of Adaptive Neuro-Fuzzy Inference System (ANFIS), and Singular Value Decomposition (SVD) method is used to compute the linear parameters of ANFIS’s results section (ANFIS-GA/SVD). Also, two different target functions are known as training error (TE) and prediction error (PE) by Pareto curve, the trade-off between these functions is selected as the optimal modeling point. First, different models will be presented using the parameters affecting Fr prediction, classifying them in different groups; then the Fr parameter will be predicted for all the different models through utilizing three different sets of data and the ANFIS-GA/SVD technique. The results of the models indicate that the best Fr prediction is obtained when independent parameters such as volumetric sediment concentration (CV), ratio of median diameter of particle size to pipe diameter (d/D), ratio of median diameter of particle size to hydraulic radius (d/R) and overall friction factor of sediment (λs) use as input variables in prediction of Fr. A sensitivity analysis is also conducted for the purpose of examining the effect of each of the dimensionless parameters on Fr prediction accuracy. Comparing the results of the suggested models with the existing regression-based equations shows that ANFIS-GA/SVD (R²=0.986, MAPE=4.397, RMSE=0.206, SI=0.053, ρ=0.026, BIAS=-0.025) is more accurate than the rest of the models.

Information molecules of DNA and RNA should obey principles of quantum mechanics where unitary operators in form of unitary matrices have key meanings. Unitary matrices are the basis of calculations in quantum computers. This article presents some author's results, which show that matrix forms of the representation of structured systems of molecular-genetic alphabets can be considered as sets of sparse unitary matrices related with phenomenologic features of the degeneracy of the genetic code. These sparse unitary matrices have orthogonal systems of functions in their rows and columns. A complementarity exists among some unitary genetic matrices in relation each other. Decompositions of numeric genetic matrices into sets of sparse unitary matrices are connected with the logical operation of modulo-2 addition used in quantum computers as well. Tensor (or Kronecker) families of unitary genetic matrices with their fractal-like properties are also considered. The described results are discussed in the frame of development of quantum-information approaches for modeling genetic systems.

This article reports a novel and efficient method to synthesize graphene by thermal decomposition process. In this method, silicon carbide (SiC) thin films grown on Si(100) wafers with an AlN buffer layer were used as substrates. A CO₂ laser beam heating without vacuum or controlled atmosphere was applied for SiC thermal decomposition. The physical, chemical, morphological, and electrical properties of the laser-produced graphene were investigated for different laser energy densities. The results demonstrate that graphene was produced in form of small islands with quality, density and properties depending on the applied laser energy density. Furthermore, the produced graphene exhibits a sheet resistance characteristic similar to graphene grown on mono-crystalline SiC wafer, which indicates its potential for electronic device applications.

Iron-based materials are widely applied in Fenton chemistry and they have promising prospects in the processing of wastewater. The composition complexity and rich chemistry of iron and/or oxides, however, hamper the precise understanding on the active sites and the working mechanism which still remain highly controversial. Herein, iron oxides of four different model systems are designed through a conventional precipitation method plus H2 reduction treatment. These systems feature Fe@Fe3O4 with abundant oxygen vacancy, Fe0 and Fe3O4 particles with interface structures, and Fe3O4-dominated nanoparticles of different sizes. These materials are applied in the decomposition of methyl orange as a model reaction to assess the Fenton chemistry. The Fe@Fe3O4 with core-shell structures exhibited significantly higher decomposition activity than the other Fe3O4-rich nanoparticles. A thin Fe3O4 layer formed by auto-oxidation of iron particles when exposing to air can boost the activity as compared with the Fe0 and Fe3O4 particles with interface structures but poor oxygen vacancy. The unique hetero-structure with the co-existence of both metallic iron and oxygen vacancy displayed excellent redox propensity which might account for the superior Fenton activity. This finding provides a new perspective to understand and design highly efficient iron-based Fenton catalysts.

The processes of the sublimation and thermal decomposition of the 1‐ethyl‐3‐methylimidazolium hexafluorophosphate ionic liquid (EMImPF6) were studied by a complex approach including Knudsen effusion mass spectrometry, IR and NMR spectroscopy, and quantum chemical calculations. It was established that the vapor over liquid phase primarily consists of decomposition products under equilibrium conditions. Otherwise, the neutral ion pairs are the only vapor components under Langmuir conditions. To identify the nature of the decomposition products an experiment on the distillation of the ionic liquid was performed and the collected distillate was analyzed. It was revealed by the IR and NMR spectroscopy that EMImPF6 decomposes to substituted imidazole‐2‐ylidene (C6N2H10PF5) and HF. The measured vapor pressure of C6N2H10PF5 reveals a very low activity of the decomposition products (<10–4) in the liquid phase. The absence of significant accumulation of decomposition products in the condensed phase makes it possible to determine the enthalpy of sublimation of the ionic liquid assuming its unchanged activity. The thermodynamics of the EMImPF6 sublimation was studied by Knudsen effusion mass spectrometry. The formation enthalpy of EMImPF6 in ideal gas state was found from combination of the sublimation enthalpy and formation enthalpy of ionic liquid in the condensed state. The obtained value is in good agreement with those calculated by quantum chemical methods.

Radially polymerized dendritic compounds are nowadays an established polymer category next to their linear, branched and cross-linked counterparts. Their uncommon tree-like architecture is characterized by adjustable internal cavities and external groups. They are therefore exceptional absorbents and this attainment of high concentrations into their interior renders them ideal reac-tion media. In this framework they are applied in many environmentally benign implementa-tions. One of the most important among them is water purification though pollutant decomposi-tion. Simple and composite catalysts and photo-catalysts containing dendritic polymers and ap-plied in water remediation will be discussed jointly with some unconventional solutions and fu-ture prospects.

To better understand the genes with altered expression caused by infection with the novel coronavirus strain SARS-CoV-2 causing COVID-19 infectious disease, a tensor decomposition (TD)-based unsupervised feature extraction (FE) approach was applied to a gene expression profile dataset of the mouse liver and spleen with experimental infection of mouse hepatitis virus, which is regarded as a suitable model of human coronavirus infection. TD-based unsupervised FE selected 134 altered genes, which were enriched in protein-protein interactions with orf1ab, polyprotein, and 3C-like protease that are well known to play critical roles in coronavirus infection, suggesting that these 134 genes can represent the coronavirus infectious process. We then selected compounds targeting the expression of the 134 selected genes based on a public domain database. The identified drug compounds were mainly related to known antiviral drugs, several of which were also included in those previously screened with an in silico method to identify candidate drugs for treating COVID-19.

Plants are affected by soil environments to the same extent they affect soil functioning through interactions between environmental and genetic factors. Here, five plant species (broad bean, pea, cabbage, fennel, and olive) grown under controlled pot conditions were tested for their ability to differently stimulate the degradation of standard litter. Litter, soil C and N contents and soil microbial abundance were measured. The architecture and morphological traits of roots systems were also evaluated by using specific open-source software (SmartRoot). Soil chemical and microbiological characteristics were significantly influenced by the plant species. Variations in soil C/N dynamics were correlated with the diversity of root traits among species. Early-stage decomposition of the standard litter changed on the basis of the plant species. The results indicated that key soil processes are governed by interactions between plant roots, soil C and N, and the microbial metabolism that stimulate decomposition reactions. This, in turn, can have marked effects on soil chemical and microbiological fertility, both fundamental for sustaining crops, and can promote the development of new approaches for optimizing soil C and N cycling, managing nutrient transport, and sustaining and improving net primary production.

In this article, we prove an orthogonal decomposition theorem for real inner product gyrogroups, which unify some well-known gyrogroups in the literature: Einstein, M\"{o}bius, Proper Velocity, and Chen's gyrogroups. This leads to the study of left (right) coset partition of a real inner product gyrogroup induced from a subgyrogroup that is a finite-dimensional subspace. As a result, we obtain gyroprojectors onto the subgyrogroup and its orthogonal complement. We construct also quotient spaces and prove an associated isomorphism theorem. The left (right) cosets are characterized using gyrolines (cogyrolines) together with automorphisms of the subgyrogroup. With the algebraic structure of the decompositions, we study fiber bundles and sections inherited by the gyroprojectors. Finally, the general theory is exemplified for the aforementioned gyrogroups.

Empirical models help us understand the process of plant residue decomposition and nutrient release into the soil. The objective of this study was to determine an appropriate model to describe the decomposition of hairy vetch (Vicia villosa Roth) and cereal rye (Secale cereale L.) cover crop (CC) residue and nitrogen (N) release. Data pertaining to above and belowground CC residue mass loss and N release for up to 2633 cumulative decomposition degree days (112 d) after litterbag installation were obtained from two cropping system experiments, one conducted in 2015 and the other in 2017 and 2018 at the humid subtropical environment of southern IL, USA. Six exponential and two hyperbolic models were fit to percent mass and N remaining data to find the one with minimum Akaike Information Criterion (AIC) and residual sum of squares. Modified three-parameter single exponential and two- or three-parameter hyperbolic models best met the assumed criteria of selection for above and belowground CC residue, respectively. Fitting a double exponential model to a combined data for percent mass and N remaining, which identified two mass and N pools, a fast and a slow pool with different rate constants. A five-parameter double exponential with an asymptote met the preset criteria and passed all tests for normally distributed population, constant variance, and independence of residuals at α = 0.05 when fit to combined data of hairy vetch shoot mass and N remaining. However, a two-parameter hyperbolic and three-parameter asymptotic hyperbolic model provided the best fit to a combined data of cereal rye shoot mass and N remaining, respectively. Both hyperbolic decay models showed a good fit for belowground mass decomposition and N release for both CCs. Cereal rye had poorer fit than hairy vetch for mass and N remaining of both above and belowground mass. The best-selected decay models can be used to estimate the decomposition and N release rates of hairy vetch and cereal rye above and belowground residue in a similar environment.

Polarimetric features extracted from polarimetric synthetic aperture radar (PolSAR) images contain abundant scattering information of objects. Utilizing this information for PolSAR image classification can improve accuracy and enhance object monitoring. Although significant progress has been achieved in related research, there are still issues such as insufficient utilization of polarimetric information and features. In this paper, a deep learning classification method based on polarimetric channel power features for PolSAR is proposed. The distinctive characteristic of this method is that the polarimetric features inputted into the deep learning network are the power values of polarimetric channels, where these channels are treated equivalently and contain complete polarimetric information. In terms of experimental comparative study, besides polarimetric power combinations, three different data input schemes were employed as data for the input end of the convolutional neural network (CNN), taking into account existing research. The neural networks utilizes the extracted polarimetric features to classify images, and the classification accuracy analysis is employed to compare the strengths and weaknesses of different input schemes. It is worth mentioning that the polarized characteristics of the data input scheme mentioned in this article have been derived through rigorous mathematical deduction, and each polarimetric feature has clear physical meaning. By testing different data input schemes on the Gaofen-3 (GF-3) PolSAR image, the experimental results show that the method proposed in this article outperforms existing methods and can improve the accuracy of classification to a certain extent, validating the effectiveness of this method in large-scale area classification.

The goal of the current study is to analyse several nonlinear two-dimensional time-fractional Rosenau Hymanequations. The two-dimensional fractional Rosenau-Hyman equation has extensive use in engineering and applied sciences. The fractional view analysis of two-dimensional time-fractional Rosenau-Hyman equations is discussed using the homotopy perturbation approach, adomian decomposition method, and Yang transformation. Some examples involving two-dimensional time-fractional Rosenau-Hyman equations are provided in order to better understand the suggested approaches. The solutions appear as infinite series. We offer a comparison between the accurate solutions and those that are generated employing the proposed approaches in order to demonstrate the effectiveness and applicability of the proposed techniques. The results are graphically illustrated using 2D and 3D graphs. It has been noted that the obtained results and the targeted problems real solutions are quite similar. Calculated solutions at various fractional levels describe some of the problems useful dynamics. Other fractional problems that arise in other fields of science and engineering can be solved using a modified version of the current techniques.

The integration of renewable energy and hybrid energy storage system (HESS) into electrified railways to build electric railway smart microgrid system (ERSMS) is beneficial for reducing fossil fuel consumption and minimizing energy waste. However, the fluctuations of renewable energy generation and traction load challenge the energy management effectiveness for such a complex system. In this work, an energy management strategy is proposed which firstly decomposes the renewable energy into low-frequency and high-frequency components by an integrated empirical mode decomposition (IEMD). Then, a two-stage energy distribution approach is utilized to appropriately distribute the energy flow among the ERSMS. Finally, the feasibility and effectiveness of the proposed solution are validated through case study.

As one of the fastest-growing new energy sources, wind power technology has attracted widespread attention from all over the world. In order to improve the quality of wind power generation, wind speed prediction is an indispensable task. In this paper, an error correction based Variational Mode Decomposition and Broad Learning System (VMD-BLS) hybrid model is proposed for wind speed prediction. First, the wind speed is decomposed into multiple components by the VMD algorithm, and then an ARMA model is established for each component to find the optimal number of sequence divisions. Second, the BLS model is used to predict each component, and the prediction results are summed to obtain the wind speed forecast value. However, in some traditional methods, there is always time lag, which will reduce the forecast accuracy. To deal with this, a novel error correction technique is developed by utilizing BLS. Through verification experiment with actual data, it proves that the proposed method can reduce the phenomenon of prediction lag, and can achieve higher prediction accuracy than traditional approaches, which shows our method’s effectiveness in practice.

The deformation monitoring information of concrete dams contains some high-frequency com-ponents, and the high-frequency components are strongly nonlinear, which reduces the accuracy of dam deformation prediction. In order to solve such problems, this paper proposes a concrete dam deformation monitoring model based on empirical mode decomposition (EMD) combined with wavelet threshold noise reduction and sparrow search algorithm (SSA) optimization of long short-term memory network (LSTM). The model uses EMD combined with wavelet threshold to decompose and denoise the measured deformation data. On this basis, the LSTM model based on SSA optimization is used to mine the nonlinear function relationship between the reconstructed monitoring data and various influencing factors. The example analysis shows that the model has good calculation speed, fitting and prediction accuracy and it can effectively mine the date char-acteristics inherent in the measured deformation, and reduce the influence of noise components on the modeling accuracy.

This paper focuses on parametric model order reduction (PMOR) of guided ultrasonic wave propagation and its interaction with damage in a fiber metal laminate (FML). Structural health monitoring in FML seeks to detect, localize and characterize the damage with high accuracy and minimal use of sensors. This can be achieved by the inverse problem analysis approach which employs the signal measurement data recorded by the embedded sensors in the structure. The inverse analysis requires to solve the forward simulation of the underlying system several thousand times. These simulations are often exorbitantly expensive and triggered the need for improving their computational efficiency. A PMOR approach hinged on the proper orthogonal decomposition method is presented in this paper. An adaptive parameter sampling technique is established with the aid of a surrogate model to efficiently update the reduced-order basis in a greedy fashion. A numerical experiment is conducted to illustrate the parametric training of the reduced-order model. The results show that the reduced-order solution based on the PMOR approach is accurately complying with that of the high fidelity solution.

A transform approach based on a variable initial time (VIT) formulation is developed for discrete-time signals and linear time-varying discrete-time systems or digital filters. The VIT transform is a formal power series in z^(-1) which converts functions given by linear time-varying difference equations into left polynomial fractions with variable coefficients, and with initial conditions incorporated into the framework. It is shown that the transform satisfies a number of properties that are analogous to those of the ordinary z-transform, and that it is possible to do scaling of z^(- i) by time functions which results in left-fraction forms for the transform of a large class of functions including sinusoids with general time-varying amplitudes and frequencies. Using the extended right Euclidean algorithm in a skew polynomial ring with time-varying coefficients, it is shown that a sum of left polynomial fractions can be written as a single fraction, which results in linear time-varying recursions for the inverse transform of the combined fraction. The extraction of a first-order term from a given polynomial fraction is carried out in terms of the evaluation of z^(i) at time functions. In the application to linear time-varying systems, it is proved that the VIT transform of the system output is equal to the product of the VIT transform of the input and the VIT transform of the unit-pulse response function. For systems given by a time-varying moving average or an autoregressive model, the transform framework is used to determine the steady-state output response resulting from various signal inputs such as the step and cosine functions.

To date, Cartesian (x, y, z) coordinate system (CCS) has been the default approach to geometrically specify atomic spatial positions in protein structures since the launch of Protein Data Bank (PDB) in 1971. To this end, this paper proposes a local spherical coordinate system (SCS) approach as an alternative to the default approach and a previously reported global SCS approach. The local SCS approach here requires only two parameters (θ and φ), instead of x, y and z as required by the default CCS approach. Essentially, CCS and SCS are like the two sides of one coin, i.e., geometric coordinate system for three-dimensional position specification. Therefore, this paper furthermore argues that it is time to flip the coin over, and have a look at the other side of the coin, e.g., the local SCS approach, which possesses an intrinsically lower degree of descriptional complexity than that of the default CCS approach, and constitutes a potentially useful alternative perspective for all protein structural research field.

This study focuses on examining various approaches for Tensor Decompositions (TDs) and their potential applications in satellite imaging (SI) and deep learning (DL). The research highlights how these decompositions can contribute to the advancement of SI and DL, providing valuable insights for future utilization of TDs in research. It explores how these techniques contribute to the advancement of SI and DL methods, providing insights into their potential applications and suggesting future research directions. The study aims to enhance the use of TDs techniques to further advance research efforts in these fields. More importantly, the current investigation offers a thorough analysis of the potential advantages and reasons for employing TDs techniques in different domains, including satellite imaging and deep learning. The aim is to enhance research outcomes by utilizing TDs. The review also identifies unresolved issues and proposes future directions for further investigation in this field. Fundamentally, these proposed open problems will open new grounds to the research community to articulate, innovate, and provide more real-life applications to improve the current state of the art by delving into a wider vision for a higher-level performance of both satellite imaging (SI) and deep learning (DL). Looking at the bigger scenario, this also suggests that TDs could be potentially employed to revolutionize existing machine learning technologies as well as the current space AI industry.

A proposed interpretation of the characteristics and causes of the variation in science dynamics for technological evolution is described. The theoretical approach focuses on variability in research topics that guide scientific and technological evolution. Statistical method verifies the proposed approach by applying entropy, measures of dispersion and variance decomposition. The statistical evidence, using data of four main research fields in quantum technologies, suggests the following empirical properties: a) the growth of heterogeneity in research topics is inversely proportional to the age of research fields: recent research fields have a higher variability between topics with uncertainty in evolutionary dynamics, whereas older research fields have a lower variability and more concentration in specific research topics with stable evolution towards clear directions; b) the nature of research fields has a systematic effects in variability guiding the evolution of technologies. The theoretical approach and findings clarify main characteristics and causes of the evolution of science and technologies considering the underlying homogeneity or heterogeneity in research topics, providing main implications to improve the scientific and technological forecasting that may support appropriate R&D investments towards promising research fields and technologies

The aim of this work was to investigate a new, simple one-pot combustion synthesis technique for creating sulphur-based CuS/ZnS p-n heterojunction nanocomposite photocatalysts. The study examined the photocatalytic activity and reusability of these nanocomposites in removing rhodamine B (RhB) dye under visible light irradiation. Various methods of characterisation were employed to determine the properties of the materials, including particle morphology, crystalline phases and bandgap energy. The intrinsic reaction parameters, such as catalyst loading, pH level of the solution, and initial pollutant concentration, were varied to establish the optimal photo-degradation conditions. The results showed that a binary CuS/ZnS catalyst with a 10 gL-1 loading, at pH 5, degraded 97% of 5 ppm RhB dye after 270 minutes of visible light irradiation. Addition-ally, this composite catalyst exhibited excellent chemical stability and reusability, achieving 83% RhB dye removal after five recycling runs. Scavenger tests identified the photogenerated holes (h+) and superoxide free radicals (•O2) as the primary reactive species responsible for degradation. This study provides valuable insight into the design of highly efficient nanomaterials for removing organopollutants in wastewater, and a possible reaction mechanism is proposed.

The service conditions of underground coal mine equipment are poor, and it is difficult to accurately extract the fault characteristics of rolling bearings. In order to better improve the accuracy of fault identification of rolling bearings, a fault detection method based on multiscale permutation entropy and SOA-SVM is proposed. First, the whale optimization algorithm is used to select the modal analysis number K and the penalty factor α of the variational mode decomposition algorithm. Then, the vibration signal of rolling bearings is dissolved according to the optimized variational mode decomposition algorithm, and the multi-scale permutation entropy of the main intrinsic mode function is calculated. Finally, the feature values of the matrix are entered into the SVM algorithm optimized by the seagull optimization algorithm to obtain the classification result. The experimental results based on the published rolling bearing datasets of Western Reserve University show that the identification success rate of the proposed method can reach 98.75%. The fault detection of the rolling bearings can be completed accurately and efficiently.

Home-field advantage (HFA) encompasses all the processes leading to faster litter decomposition in the 'home' environment as compared to that of ‘away’ environments. To determine the occurrence of HFA in a forest and adjacent clear-cut, we set up a reciprocal litter decomposition experiment within the forest and clear-cut for two soil types (Cambisols and Gleysols) in temperate Germany. The forest was dominated by Norway spruce (Picea abies), whereas forest regeneration of European Beech (Fagus sylvatica) after clearcutting was encouraged. Our observation that Norway spruce decomposed faster than European beech in 70-yr-old spruce forest, was therefore most likely related to specialized litter-microbial interaction under existing spruce, and leading to a HFA. The ‘spruce’ microbial biome and soil conditions of original forest were then rapidly changed even after a short-term regeneration following clearcutting, resulting in faster beech decomposition also masking any HFA for spruce, particularly in moisture- and nutrient-deficient Cambisols. Divergence between forest and clear-cut in the Cambisol of their litter δ15N values beyond 9 months, implied litter N decomposition was only initially independent of soil and residual C status. We conclude that clearcutting modifies HFA and helps promote the establishment or regeneration of European beech in this and similar forest mountain upland areas.

Modeling fluid flow in three-dimensional (3D) Discrete Fracture Networks (DFNs) is of relevance in many engineering applications, such as hydraulic fracturing, oil/gas production, geothermal energy extraction, nuclear waste disposal and CO₂ sequestration. A new Boundary Element Method (BEM) technique with discontinuous quadratic elements and a parallel Domain Decomposition Method (DDM) is presented herein for the simulation of the steady-state fluid flow in 3D DFN systems with wellbores, consisting of planar fractures having arbitrary properties and wellbore trajectories. Numerical examples characterized by DFNs of increasing complexity are investigated to evaluate the accuracy and efficiency of the presented technique. The results show that accurate solutions can be obtained with less nodes than with mesh-based methods (e.g. Finite Element Method). In addition, the DDM algorithm used provides a quite fast convergence. The simulation results of the fluid flow around intersections among traces (linear intersections between fractures), intersections between traces and a fracture boundaries, and wellbore intersections is accurate. Source code is available at : https://github.com/BinWang0213/PyDFN3D.

The solution of structural problems with nonlinear material behaviour in a model order reduction framework is investigated in this paper. In such a framework, greedy algorithms or adaptive strategies are interesting as they adjust the reduced order basis (ROB) to the problem of interest. However, these greedy strategies may lead to an excessive increase in the size of the reduced basis, i.e. the solution is no more represented in its optimal low-dimensional expansion. Here, an optimised strategy is proposed to maintain, at each step of the greedy algorithm, the lowest dimension of the PGD basis using a randomised SVD algorithm. Comparing to conventional approaches such as Gram-Schmidt orthonormalisation or deterministic SVD, it is shown to be very efficient both in terms of numerical cost and optimality of the reduced basis. Examples with different mesh densities are investigated to demonstrate the numerical efficiency of the presented method.

The aim of this study is to propose and validate the state space mode decomposition technique for precise mode separation of non-classical damping systems and closely distributed modal systems. To assess the reliability and applicability of this technique, a 40-story building with a tuned mass damper is investigated, and acceleration responses measured by the building's health monitoring system are used for the verification of the technique. The mode separation results reveal that the separated modal power spectrum becomes distorted at neighboring natural frequency ranges when the performance index only considers the concentration of power spectral energy at the target natural frequency. However, by introducing an augmented performance index that includes a constraint condition to account for distortion, more accurate mode decomposition can be achieved.

In this paper a dynamic relationship between the CO2 emissions in Finland, Norway and Sweden is presented. With the help of a VAR(2) model, and using the Granger terminology, it is shown that the emissions in Finland are affecting those in Norway and Sweden. Other aspects of this dynamic relationship are presented as well.

This article deals with the conformable double Laplace transforms and their some properties with examples and also the existence Condition for the conformable double Laplace transform is studied. Finally, in order to obtain the solution of nonlinear fractional problems, we present a modified conformable double Laplace that we call conformable double Laplace decomposition methods (CDLDM). Then, we apply it to solve, Regular and singular conformable fractional coupled burgers equation illustrate the effectiveness of our method some examples are given.

The radar sensor described realizes healthcare monitoring capable of detecting subject chest-wall movement caused by cardiopulmonary activities, and wirelessly estimating the respiration and heartbeat rates of the subject without attaching any devices to the body. Conventional single-tone Doppler radar can only capture Doppler signatures because of a lack of bandwidth information with noncontact sensors. In contrast, we take full advantage of impulse radio ultra-wideband (IR-UWB) radar to achieve low power consumption and convenient portability, with a flexible detection range and desirable accuracy. A noise reduction method based on improved ensemble empirical mode decomposition (EEMD) and a vital sign separation method based on the continuous-wavelet transform (CWT) are proposed jointly to improve the signal-to-noise ratio (SNR) in order to acquire accurate respiration and heartbeat rates. Experimental results illustrate that respiration and heartbeat signals can be extracted accurately under different conditions. This noncontact healthcare sensor system proves the commercial feasibility and considerable accessibility of using compact IR-UWB radar for emerging biomedical applications.

This study employs the reflection symmetry decomposition (RSD) method to extract polarization scattering features from ground object images, aiming to determine the optimal data input scheme for deep learning networks in polarimetric synthetic aperture radar classification. Eight distinct polarizing feature combinations are designed, and the classification accuracy of various approaches is evaluated using the classic convolutional neural networks(CNNs) AlexNet and VGG16. The findings reveal that the commonly employed 6-parameter input scheme, favored by many researchers, lacks the comprehensive utilization of polarization information and warrants attention. Intriguingly, leveraging the complete 9-parameter input scheme based on the polarization coherence matrix results in improved classification accuracy. Furthermore, the input scheme incorporating all 21 parameters from the RSD and polarization coherence matrix notably enhances overall accuracy and the Kappa coefficient compared to the other 7 schemes. This comprehensive approach maximizes the utilization of polarization scattering information from ground objects, emerging as the most effective CNN input data scheme in this study. Additionally, the classification performance using the second and third component total power values (P2 and P3) from the RSD surpasses the approach utilizing surface scattering power value (PS) and secondary scattering power value (PD) from the same decomposition.

Ferrocenium (Fc+) inherits a number of molecular/electronic properties from the neutral counterparts’ ferrocene (Fc) including the high symmetry. Both Fc+ and Fc prefer the eclipsed structure (D5h) over the staggered structure (D5d) by an energy of 0.36 kcal·mol-1. The present study using the recently developed excess orbital energy spectrum (EOES) shows that the open shell Fc+ cation exhibits similar conformer dependent configurational changes to the neutral Fc conformer pair. A further energy decomposition analysis (EDA) discloses that the reasons for the preferred structures are different between Fc+ and Fc. The dominant differentiating energy between the Fc+ conformers is the electrostatic energy (EEstat), whereas in neutral Fc, it is the quantum mechanical Pauli repulsive energy (EPauli). Within the D5h conformer of Fc+, the EOES reveals that the -electrons of Fc+ experience more substantial conformer dependent energy changes than the -electrons (assumed the hole is in a β orbital).

The aim of this work is to broaden the theory of computation by making use of fuzzy sets and multisets, which are generalization of ordinary sets. We study fuzzy multiset finite automata (FMFA), which are characterized by the incorporation of vagueness when it comes to the choice of the next state and multiple occurrences of the same input symbol. The resulting automaton is a genaralization of both classical automata and fuzzy automata. We discuss the algebraic characteristics of FMFA sub-automata—separatedness, strongly connectedness, cyclic, directable, and triangular FMFA in terms of equivalence classes induced by an equivalence relation defined on state set of FMFA. Intrestingly, for a given FMFA, a new FMFA can be constructed that is a homomorphic image of the original FMFA. We define different posets structures that can be associated with a given FMFA and show that some of them are upper semilattices and discuss the inter-relationship of a given poset, a finite upper semilattice (FUSL), a FMFA and a posets/FUSL associated with a given FMFA. Finally, we introduce the concept of decomposition of a FMFA in two different ways and characterize the strongly connected, triangular and directable FMFA.

Louis de Broglie in the beginning 20th century voices his theory of a double solution, according to which a pilot wave accompanies a particle, simulated as a point singularity, along the most optimal path from its creation on a source up to the detection. The pilot wave is a real hidden wave, which is similar to the wave function resulting from the solution of the Schrödinger equation. This theory is in agreement with de Broglie’s postulate about the matter waves. In this article we are based on the Helmholtz decomposition theorem according to which any velocity may be represented as a sum of two velocities – irrotational and solenoidal ones. The first velocity stems from the gradient of the scalar field. The second occurs from a pseudo-vector field. We proclaim that the gradients of the scalar field define guiding paths of the pilot wave. While the pseudo-vector field defines a particle solenoidal filling. We give mathematical models of the irrotational and solenoidal flows simulating the position of a particle in a guiding wave. Modified Navier-Stokes equation in pair with the continuity equation resulting in the Schrödinger equation gives such solutions consisting of superposition of the irrotational and solenoidal flow. It is declared that the guiding wave forms from the irrotational flows. In turn, the solenoidal flows underlie forming particles that travel along optimal paths slave by the guiding wave. There are described mathematical solutions of the spherical particle washed by the superfluid representing the guiding wave along which it travels.

In this paper, the author utilizes Saddle Theorem and variational methods to deduce existence of at least six stationary solutions for reaction-diffusion Gilpin-Ayala competition model (RDGACM). To obtain the global stabilization of the positive stationary solution of the RDGACM, the author designs a suitable impulsive event triggered mechanism (IETM) to derive the global exponential stability of the the positive stationary solution. It is worth mentioning that the new mechanism can exclude Zeno behavior and effectively reduce the cost of impulse control through event triggering mechanism. Besides, compared with existing literature, the restrictions on the parameters of the RDGACM are relaxed so that the methods used in existing literature can not be applied to the relaxed case of this paper, and so the author makes comprehensive use of Saddle Theorem, orthogonal decomposition of Sobolev space $H_0^1(\Omega)$ and variational methods to overcome the mathematical difficulty. Numerical examples show the effectiveness of the methods proposed in this paper.

A reduced order model is developed to monitor aeroengines condition (defining their degradation from a baseline state) in real-time, by using data collected in specific sensors. This reduced model is constructed by applying higher order singular value decomposition plus interpolation to appropriate data, organized in tensor form. Such data are obtained using a detailed engine model that takes the engine physics into account. Thus, the method synergically combines the advantages of data-driven (fast online operation) and model-based (the engine physics is accounted for) condition monitoring methods. Using this reduced order model as surrogate of the engine model, two gradient-like condition monitoring tools are constructed. The first tool is extremely fast and able to precisely compute `on the fly’ the turbine inlet temperature, which is a paramount parameter for the engine performance, operation, and maintenance, and can only be roughly estimated by the engine instrumentation in civil aviation. The second tool is not so fast (but still reasonably inexpensive) and precisely computes both, the engine degradation and the turbine inlet temperature at which sensors data have been acquired. These tools are robust in connection with random noise added to the sensors data and can be straight forwardly applied to other mechanical systems.

This paper attempts to develop a Dynamic Mode Decomposition (DMD) based Reduced Order Model (ROMs) which can quickly but accurately predict the forces and moments experienced by a road vehicle such that they be used by an on-board controller to determine the vehicle's trajectory. DMD can linearize a large dataset of high-dimensional measurements by decomposing them into low-dimensional coherent structures and associated time-dynamics. This ROM then also can be applied to predict the future state of the fluid flow. Existing literature on DMD is limited to low Reynolds number applications. This paper presents DMD analyses of the flow around an idealized road vehicle, called the Ahmed body, at a Reynolds number of 2.7E6. The high dimensional dataset used in this paper was collected from a computational fluid dynamics (CFD) simulation performed using Menter's shear stress transport (SST) turbulence model within the context of Improved Delayed Detached Eddy Simulations (IDDES). The DMD algorithm, as available in literature, was found to suffer nonphysical dampening of the medium-to-high frequency modes. Enhancements to the existing algorithm were explored, and a modified DMD approach is presented in this paper which includes: (a) a requirement of higher sampling rate to obtain higher resolution of data, and (b) a custom filtration process to remove spurious modes. The modified DMD algorithm thus developed was applied to the high Reynolds number, separation dominated flow past the idealized ground vehicle. The effectiveness of the modified algorithm was tested by comparing future predictions of force and moment coefficients as predicted by the DMD-based ROM to the reference CFD simulation data, and found to offer significant improvement.

Deterministic-stochastic empirical mode decomposition (EMD) is used to obtain low-frequency (non-diffusive, i.e., background velocity) and high-frequency (diffusive, i.e., eddies) components from a Lagrangian drifter‘s trajectory. Eddy characteristics are determined from the time series of eddy trajectories from individual Lagrangian drifter such as the eddy radial scale, eddy velocity scale, eddy Rossby number, and eddy-background kinetic energy ratio. A long-term dataset of the SOund Fixing And Ranging float time series obtained near the California coast by the Naval Postgraduate School from 1992 to 2004 at depth between 150 and 600 m (http://www.oc.nps.edu/npsRAFOS/) is used as an example to demonstrate the capability of the deterministic-stochastic EMD.

This paper presents an approach to the application of the Model-Based Systems Engineering (MBSE) and Model-Based Systems Architecting (MBSA) principles to develop a Model-Based Pattern Language (MBPL). It takes too long for systems engineers and architects to develop a new system from scratch, particularly new space-based systems derived from the existing space systems architectures. A pattern language is a holistic view of reusable logical model artifacts; many are interdisciplinary and introductory, if at all. The results are mostly a combination of the application-specific logical solution, which further results in the best possible overall solution. The main benefit of the pattern language is reducing the time and validation required to generate a new space-based system architecture; this approach will develop top-level requirements in the initial phase of the system development. The rationale of the methodology proposed by the paper is as follows, collect, and decompose published literature and other open-source information available on space system architectures and system models; develop SysML models for systems, subsystems, products, assembly, subassembly level, and mission-specific requirements using CAMEO SysML software. Arrange these patterns to develop a functional ontology and construct a logical architecture pattern library. This approach created, updated, and managed SysML pattern language, which evaluated the expedited new model construction. Again, our objective is to develop a logical pattern language using public domain information and evaluate patterns by constructing a new space mission concept—for example, planetary surface habitat.

Quantum mechanics could be studied through polynomial algebra, as has been demonstrated by a work (“An approach to first-principles electronic structure calculation by symbolic-numeric computation” by A. Kikuchi). We carry forward the algebraic method of quantum mechanics through algebraic number theory; the basic equations are represented by the multivariate polynomial ideals; the symbolic computations process the ideal and disentangle the eigenstates as the algebraic variety; upon which one canbuild the Galois extension of the number field, in analogy with the univariate polynomial case, to investigate the hierarchy of solutions; the Galois extension is accompanied with the group operations, which permute the eigenstates from one to another, and furnish the quantum system with a non-apparent symmetry. Besides, this sort of algebraic quantum mechanics is an embodiment of the class field theory; some of the important consequences of the latter emerge in quantum mechanics. We shall demonstrate these points through simple models; we will see the use of computational algebra facilitates such sort of analysis, which might often be complicated if we try to solve them manually.

A new framework in quantum chemistry has been proposed recently ("An approach to first principles electronic structure calculation by symbolic-numeric computation'' by A. Kikuchi). It is based on the modern technique of computational algebraic geometry, viz. the symbolic computation of polynomial systems. Although this framework belongs to molecular orbital theory, it fully adopts the symbolic method. The analytic integrals in the secular equations are approximated by the polynomials. The indeterminate variables of polynomials represent the wave-functions and other parameters for the optimization, such as atomic positions and contraction coefficients of atomic orbitals. Then the symbolic computation digests and decomposes the polynomials into a tame form of the set of equations, to which numerical computations are easily applied. The key technique is Grröbner basis theory, by which one can investigate the electronic structure by unraveling the entangled relations of the involved variables. In this article, at first, we demonstrate the featured result of this new theory. Next, we expound the mathematical basics concerning computational algebraic geometry, which are necessitated in our study. We will see how highly abstract ideas of polynomial algebra would be applied to the solution of the definite problems in quantum mechanics. We solve simple problems in "quantum chemistry in algebraic variety'' by means of algebraic approach. Finally, we review several topics related to polynomial computation, whereby we shall have an outlook for the future direction of the research.

Synthetic Aperture RADAR (SAR) is a radar imaging technique in which the relative motion of the sensor is used to synthesize a very long antenna and obtain high spatial resolution. Standard SAR raw data processing techniques assume uniform motion of the satellite (or aerial vehicle) and a fixed antenna beam pointing sideway orthogonally to the motion path, assumed rectilinear. Despite SAR data processing is a well established imaging technology that has become fundamental in several fields and applications, in this paper a novel approach has been used to exploit coherent illumination, demonstrating the possibility of extracting a large part of the ancillary data information from the raw data itself, to be used in the focusing procedure. In this work an effort has been carried out to try to focus the raw SAR complex data matrix without the knowledge of anyof the parameters needed in standard focusing procedures as Range Doppler (RD) algorithm, ω - K algorithm and Chirp Scaling (CS) algorithm. All the literature references regarding the algorithms needed to obtain a precise image from raw data use such parameters that refer both to the SAR system acquisition geometry and its radiometric specific parameters. In [12], authors introduced a preliminary work dealing with this problem and able to obtain, in the presence of a strong point scatterer in the observed scene, good quality images, if compared to the standard processing techniques. In this work the proposed technique is described and performances parameters are extracted to compare the proposed approach to RD.