Spectrum Method Research Articles

Thermodynamic analysis and equilibration response time prediction of recuperator in the SCO2 Brayton cycle

The recuperator of supercritical carbon dioxide (SCO2) Brayton cycle significantly affects the system's flexible control due to its thermal inertia. In this study, the structural parameters and operating parameters of recuperator are considered to quantitatively analyze the law of their influence on equilibration response time. Chebyshev spectrum method has been innovatively applied to the one-dimensional dynamic response model of recuperator. The dynamic response time of recuperator under the condition of temperature variation on the hot side is analyzed. The results show that reducing the thermal inertia of solid wall (by increasing the specific surface area of recuperator) can effectively decrease the equilibrium time. Additionally, the rate of inlet temperature variation should not be too large to reduce the thermal inertia of fluid. The zigzag channel demonstrates better dynamic response characteristic than straight channel. A novel dimensionless formula, based on structure and operating parameters, is proposed to quantitatively characterize and predict the equilibrium time for both straight and zigzag channel, the error is within ±20 %. Moreover, a high-precision neural network is trained to predict the equilibrium time directly. The results provide significant theoretical and application support for alleviating the thermal inertia of PCHE and improving the flexibility of SCO2 system.

Bandgap tuning in ZnxCd1-xTe superlattices through variable atomic ordering.

We explore the entire search space of 32-layer ZnxCd1-xTe superlattices to find the structures that minimize and maximize the bandgap at each possible zinc concentration. The searching is accomplished through an accurate and efficient combination of valence force field dynamics, the empirical pseudopotential method, and the folded spectrum method. We also describe the use of an alternate preconditioner that improves the robustness and efficiency of the locally optimal preconditioned conjugate gradient's solutions to the folded spectrum method. The physical properties of these superlattices, such as their formation energies, bandgaps, densities of states, effective masses, and optical response functions, are investigated with density functional theory paired with hybrid functionals and compare well to available experimental measurements. It is revealed that the bandgap of ZnxCd1-xTe may change by up to 0.2eV depending on how the layers in the superlattice are ordered. Stacking order has a large, irregular effect on the effective masses, but optical response functions seem insensitive to it.

High-Efficiency Simulation of Coherent Beam Combining Using Scaled Angular Spectrum Method with GPU Acceleration

High-Efficiency Simulation of Coherent Beam Combining Using Scaled Angular Spectrum Method with GPU Acceleration

Schiff base derived from 2-hydroxy napthaldehyde as anti-corrosive for mild steel in acid media: experimental investigation and theoretical modelling

Schiff bases (SBs) have the fundamental characteristics of substances that are mostly eligible for testing as inhibitors of corrosion for various metal/electrolyte systems. Through their electron-rich centres, such as the > C = N– (imine) moiety, SBs adsorb and create a surface coating that mitigates corrosion. Because of its π-acceptor characteristics, the > C = N– (imine) moiety provides a strong bonding with the metallic ions. It's vital to note that SBs with polar substituents at the right locations can form chelates with the central metal ions; as a result, these SBs are anticipated to function better as corrosion inhibitors than SBs without substituents. Two distinct Schiff bases, NL1 and NL2, with naphthalene rings have been synthesised, and their structures have been confirmed by the use of 1H and 13C NMR spectrum methods. The anticorrosion potential of the NL1 and NL2 was further confirmed by quantum chemical calculations such as DFT studies and ESP diagrams. The corrosion inhibition potential of the NL1 and NL2 was investigated using the electrochemical method, demonstrating maximum corrosion inhibition efficiency up to 89.2% and 89.5%, respectively on mild steel in 1 M HCl media. The results are further supported by Scanning Electron microscopic (SEM) images and EDAX studies.

Bayesian peak identification method for low count rate gamma spectrum under short-time measurement based on physical priors

A Bayesian peak identification method based on physical model had been proposed in this study to perform qualitative analysis for the low count rate gamma spectrum under short-time measurement. Based on the prior knowledge about gamma detection, the distribution of energy deposited in the detector near the region of interest of a target peak through photoelectric effect, Compton scattering and multiple scattering had been analyzed and approximated using three elementary components, then, the distribution of each component after convolution had been studied, and at last, a probabilistic mixture model had been proposed to directly describe the distribution of measured energy within region of interest. When the data measurement has been completed, a Gibbs sampler was used to estimate the posterior distribution of model parameters to discriminate the existence of target peaks. The numerical and physical experiments were performed to verify the effectiveness of the parameter estimation algorithm and the performance of the proposed identification method. The numerical experiments showed the identification precision is proportional to counts and peak-to-total ratio, when the peak-to-total ratio is greater than 0.5, the proposed method could identify the peak with a probability greater than 50% given 50 observations. The physical experiment used a NaI(Tl) detector to measure 137Cs, 60Co and 152Eu sources in a laboratory environment at different equivalent distances, the peak identification precision had been tested for the proposed method, and the experiments proved that the probabilistic model is a good approximation to the physical process, and the proposed identification method outperformed the conventional method under short-time measurement conditions.

Controlled growth of MPA-capped ZnS quantum dots through concentration-modulated single injection hydrothermal method

This study presents the controlled growth of 3-Mercaptopropionic acid (MPA)-capped ZnS quantum dots (QDs) using a concentration-modulated single injection hydrothermal method. Employing the Concentration optimization by optical spectra (COOS) method, we optimized the MPA:Zn:S ratios to investigate the influence of the capping agent, cation, and anion for exceptional properties suitable for optoelectronic and sensor applications. CMSIH operates as a single-step synthesis process, reducing processing time and complexity. This streamlined approach not only enhances efficiency but also minimizes the risk of contamination and ensures batch-to-batch consistency in QD production. Its moderate operating conditions, compared to other high-energy methods, also contribute to reduced energy consumption and environmental impact, aligning with sustainable manufacturing practices. Further, X-ray diffraction (XRD) confirmed the Zinc blend (cubic) phase of ZnS, and Fourier-transform infrared spectroscopy (FTIR) validated MPA capping. The QDs exhibited strong quantum confinement, causing a blue shift in absorption peaks compared to bulk ZnS. Higher MPA concentrations ranging from 0.02 M to 0.1 M induced a red shift in the absorption edge due to prolonged reaction times and strong cation binding by MPA. Variations in cation Zn and anion S ratios from 0.02 M to 0.1 M caused blue and red shifts in the absorption edge, respectively. For instance, Zn:S = 0.04:0.01 M increased cation concentrations, reducing QD size up to 0.67 nm, while enhanced anion concentrations Zn:S = 0.04:0.04 M enlarged the QDs size up to 2.35 nm. Remarkably, calculated QD sizes using Brus’ equation were smaller than the Bohr radius, even at an elevated temperature of 95 °C, indicating significant quantum confinement. Luminescence studies revealed reduced luminescence with higher MPA concentrations, increased luminescence intensity with higher cation Zn+ concentrations, and a red shift in the luminescence peak with higher anion S concentrations. As the temperature rises, there is an observable decrease in luminescence intensity. Furthermore, the investigation into the relationship between chemical composition and optical properties of MPA-capped ZnS QDs at elevated temperatures expands understanding of quantum confinement effects. The synthesised unique ultra small ZnS QDs can be used in advanced quantum sensors mainly as radiation detectors.

A Practice-Oriented Approach for Seismic and Energy Performance Upgrading of Existing Buildings

ABSTRACT Recent studies have focused on identifying the optimal seismic and energy upgrading interventions, among different alternatives, for poorly performing existing buildings. Most of such studies use detailed methodologies to assess the seismic and energy performance of buildings, which are time and computationally demanding, making it nearly unfeasible for practitioners and decision-makers to use them, rendering practice-oriented approaches extremely needed. To overcome the current limitations of more research-oriented methods, this study employs different available simplified approaches, namely SPO2FRAG, cloud-based capacity spectrum method and the Italian seismic risk classification guidelines (Sismabonus), to estimate some of the variables considered when using a multi-criteria decision-making (MCDM) framework to select the optimal combined retrofitting strategy, among a set of different options. To this end, a case-study school building was selected and four seismic retrofitting solutions, combined with three energy-based interventions, were identified. The performance of the building, in its as-built and retrofitted conditions, was analysed considering both simplified and detailed approaches for the estimation of two of the seismic-related variables, namely annual probability of failure and expected annual losses. Such simplified and refined estimates were used as MCDM input, comparing the ranking of retrofitting combined alternatives obtained in both cases, demonstrating the suitability of the proposed simplified methodology for engineering practice.

A Critical Evaluation of the Coefficient Method, Capacity Spectrum Method and Modal Pushover Analysis for Irregular Steel Buildings in Seismic Zones

A Critical Evaluation of the Coefficient Method, Capacity Spectrum Method and Modal Pushover Analysis for Irregular Steel Buildings in Seismic Zones

Generalizing the moments method for primary neutron spectra

Motivated by recent experimental results Hartouni et al. (2023); Mannion et al. (2023) which identified the presence of non-Maxwellian ion velocity distributions in ICF plasmas, we revisit the moments method for analysing the shapes of primary neutron spectra emitted by plasmas undergoing thermonuclear burn. We assume that the ion distribution functions are of an arbitrary form and develop a set of “generalized” moments, that are ordered in terms of increasing powers of centre of mass velocity, but for which the effects of shifts of centre of mass velocity (equivalent to fluid velocity in the case of Maxwellian ion distributions) are suppressed. This set of generalized moments provides the most sensitive measure of relative velocity contributions to the shape of the neutron spectrum (an effect that has been colloquially referred to as “viso”). We also demonstrate that pairs of antipodal neutron spectral detectors are most suitable for measuring these contributions.

Extended legality of curved boundary integral method

The angular spectrum method is an efficient approach for synthesizing electromagnetic beams from planar electric field distributions. The electric field definition is restricted to a plane, which can introduce inaccuracy when applying the synthesized beam to curved surface features. The angular spectrum method can also be interpreted as a pure source method defining the field symmetrically with respect to the creation plane. Recently, we generalized that symmetric field method to arbitrary source distributions, which are valid at any point on compact, regular surface Ω in R3. We call this approach the Curved Boundary Integral method. The electromagnetic fields synthesized with this method satisfy the Helmholtz equation and are adjusted via amplitude and phase at the desired surface. The fields are obtained as a relatively simple integral. However, restrictions on where in space the synthesized field is valid were included in the mathematical proof length to avoid obscuring the main points. These restrictions can be significant depending on the shape and degree of curvature of surface Ω. In this article, we remove these restrictions so that the integral representation of the electromagnetic beam becomes valid at all points r∈R3∖Ω, with a minor restriction. Its modification can work even on Ω. We demonstrate the importance of this extended legality with a source field parametrized into the torus surface. The electromagnetic radiation of this structure would not be valid at any point in space without this extension. Finally, we show that by changing the order of integration, the field singularity at each source point is eliminated.

Seismic Isolation Layout Optimized of Mid-Rise Reinforced Concrete Building Frame Structure

Seismic isolation technology plays a crucial role in enhancing earthquake resistance and mitigating disasters for building structures. In this study, the ETABS analysis software V21.0.1 is utilized to establish a numerical model of a six-story steel reinforced concrete frame structure. Both the time-history analysis method and response spectrum method are employed to calculate the seismic response of the model under earthquake actions. The placement of an isolation layer on the foundation and from the first to fifth floor is considered, with separate calculations conducted for each scenario. Subsequently, a comprehensive comparison and analysis of the dynamic response characteristics among different design schemes are performed. The results demonstrate that the most favorable isolation effect is achieved when the isolation layer is implemented on the foundation or first floor. Compared to non-isolated structures, the natural period of the structure can be extended by 2.2 times and 2 times under the base isolation and first-floor top isolation schemes, respectively. The damping coefficients can reach 0.35 and 0.36, respectively, while the inter-story drift angles can be reduced by 66% and 67%, respectively.

SEISMIC ANALYSIS OF RC FRAMED STRUCTURE CONSIDERING L-SHAPED SHEAR WALL AND HOLLOW CORE SHEAR WALL USING ETABS

This paper conducts a seismic analysis of a 20- story RCC residential building with integrated shear walls, aiming to optimize their placement. Seven structural models were evaluated, exploring different placements of shear walls inside and outside the building envelope. Using the response spectrum method in ETABS software, the study analyzed the structure located in Zone III, with medium to stiff soil conditions. Key parameter assessed is story displacement. The findings reveal significant performance differences between conventional RCC structures and those with shear walls, showing enhanced resistance to shear forces and overall structural performance. Placing shear walls at interior center edges was found most effective, with corners also proving effective compared to interior placements. Optimal placement near the building core enhances resilience against seismic forces, emphasizing the critical role of strategic shear wall placement in fortifying buildings in earthquake-prone areas. Key Words: Shear wall, RC Framed Building, Dynamic Analysis, Response Spectrum Analysis, Comparative Analysis, ETABS Software.

Dynamic spectral extraction method with approximately the same optical path length of non-invasive quantitative analysis of human blood components

The non-invasive quantitative analysis of blood components using spectroscopic methods based on Beer-Lambert law, and dynamic spectroscopic theory needs to meet the four applicable conditions of this law. However, in practical applications, due to the scattering characteristics of human tissue, it is difficult to meet the two conditions (parallel monochromatic light and non-scattering homogeneous system of absorbing substances), which will reduce the accuracy of quantitative analysis. To reduce the principle error caused by scattering, this paper proposes an extraction method for dynamic spectra with approximately the same optical path length. This method extracts approximately the same absorbance values from photoplethysmographic (PPG) spectral signals. A smaller absorbance value corresponds to a thinner blood layer, in which light can be approximated as parallel light, thus maximizing the satisfaction of the conditions of Beer-Lambert law. In the experimental, compared with the traditional single-edge extraction method, the proposed method has higher prediction accuracy. The correlation coefficients of the total cholesterol and triglycerides increased by 31.22% and 38.05%, and the root mean square errors decreased by 29.63% and 37.14%. The results show that the methods can significantly enhance the robustness of non-invasive quantitative analysis of blood components based on dynamic spectral theory.

Novel automatic de-scattering method for three-dimensional fluorescence spectra based on deep learning

Three-dimensional excitation–emission matrix fluorescence spectroscopy is often plagued by scattering effects, mainly Rayleigh and Raman scattering, and thus must be pre-processed for de-scattering before spectral analysis. In this study, a new method based on deep learning was proposed to automaticly remove the scattering from fluorescence spectra. First, the semantic segmentation model Deeplabv3+ was used to realize the segmentation of the scattering region in the original fluorescence spectrum and compared with other segmentation models. The results show that the mean intersection over union (mIoU) of this model is 89.58 % and its Accuracy is 95.40 %, which are better than those of the other models. Then, the Globally and Locally Consistent Image Completion (GLCIC) network was used to repair the spectral energy of the scattering areas. Model effectiveness in scattering removal is evaluated using metrics such as mean absolute error, mean relative error, structural similarity, and peak signal-to-noise ratio. Furthermore, this study employs PARAFAC for component analysis of the spectra after scattering removal by the model, comparing them with actual components, all yielding correlation coefficients greater than 0.99. The results show that compared with the traditional scattering-removal method based on the mathematical model, the proposed method can automatically remove scattering areas in batch samples’ fluorescence spectra, without the need for manual parameter setting or other processes. This improves scattering removal efficiency, enhances the simplicity, and speed of fluorescence detection technology.

Analysis of Land-Use/Cover-Type Extraction Results of Tamarix Shrub Forest of China Based on Remote Sensing Technology

The endmember spectrum method can improve image classification quality based on the spectral features of pure pixels in remote sensing images. The CART (Classification and Regression Tree) is a powerful machine learning algorithm that can also be used for remote sensing image classification. In this study, the Tamarix chinensis forest in the Changyi National Marine Ecological Special Reserve in Shandong Province was taken as the research object, and the endmember spectrum method and the CART decision tree method were used to compare and analyze the results of land-use/cover-type classification extraction. In the extraction process, the land use/cover types of the Tamarix forest in the study area were first divided into forested land types such as high-density forest land, medium-density forest land, and low-density forest land, as well as non-forested land types such as water bodies, roads, dams, buildings, and bare soil. Through analysis, the following conclusions could be drawn: while the overall forest cover of the Tamarix forest is high, there is still some room for further afforestation and ecological restoration in the protection area; from the results of land-use/cover extraction results based on the endmember spectrum method in the study area, it can be seen that this method has better results when extracting well-grown forested land, such as high-density Tamarix chinensis forests and medium-density Tamarix chinensis forests, and poorer results when extracting non-forested land, such as low-density tamarisk forests, roads, buildings, dams, and water bodies; from the results of land use/cover extraction based on a CART decision tree in the study area, it can be seen that this method is more effective when extracting non-forested land, such as roads, buildings, dams, and water bodies, but less effective when extracting forested land, such as high-density Tamarix chinensis forests, medium-density Tamarix chinensis forests, and low-density Tamarix chinensis forests. The relevant research results and conclusions of this study can provide some reference for the classification and extraction of large-scale shrub forest cover types based on remote sensing images.

Hong Guo Ginseng Guo (HGGG) protects against kidney injury in diabetic nephropathy by inhibiting NLRP3 inflammasome and regulating intestinal flora

BackgroundDiabetic nephropathy (DN) is one of the most serious complications of diabetes which leads to end-stage renal failure and approximately one-third of patients need dialysis. There is still a lack of effective and specific treatment for DN. Searching new drugs from natural foods is an alternative approach to treat diabetes and its complications. Hong Guo Ginseng Guo (HGGG), a berry with palatability and nutritional benefits, has exhibited medicinal properties to mitigate the progression of DN. PurposeThis study investigates the effects of HGGG on streptozotocin (STZ)-induced diabetic nephropathy (DN) in rats and elucidates the mechanisms underlying its reno-protective and diabetes management benefits. MethodsThe LC-MS spectra method identified the primary ingredients in HGGG. To induce DN, male Sprague-Dawley (SD) rats received a single intraperitoneal injection of 75 mg/kg STZ. Over an eight-week treatment period, we assessed biochemical parameters including blood glucose, urine albumin-to-creatinine ratio (UACR), blood urea nitrogen (BUN), and urine N-acetyl-beta-d-glucosaminidase (NAG). Tissue pathology was examined using Masson's trichrome, Periodic Acid-Schiff (PAS), and Hematoxylin-Eosin (H&E) stains. We analyzed pro-inflammatory mediators and tissue fibrosis extent using Western blotting and immunohistochemistry. Gut microbiota composition was characterized via 16S rDNA sequencing. ResultsSeventeen chemical compounds were identified, with lobetyolin, luteolin, and rutin highlighted as the primary active elements. HGGG extract appeared to confer renal protection, demonstrated by improvements in UACR, BUN, and urine NAG levels. The reno protective effects in HGGG-treated DN rats were linked to reduced renal fibrosis and inhibition of the NLRP3 inflammasome. Additionally, HGGG administration improved gut barrier integrity and altered the gut microbiota in DN rats, increasing the relative abundance of beneficial bacteria known for regulating polyamines and producing short-chain fatty acids (SCFAs), including Ruminococcus, Barnesiella_sp, Anaerovoracaceae, and Prevotellaceae_NK3B31. Meanwhile, treatment with HGGG decreasing the presence of Oscillospira, potential pathogens responsible for producing lipopolysaccharide (LPS). ConclusionHGGG has potential as a beneficial fruit for managing diabetes and its associated complications through modulation of the gut microbiota.

Similarity measure method of near-infrared spectrum combined with multi-attribute information

Due to the high-dimensionality, redundancy, and non-linearity of the near-infrared (NIR) spectra data, as well as the influence of attributes such as producing area and grade of the sample, which can all affect the similarity measure between samples. This paper proposed a t-distributed stochastic neighbor embedding algorithm based on Sinkhorn distance (St-SNE) combined with multi-attribute data information. Firstly, the Sinkhorn distance was introduced which can solve problems such as KL divergence asymmetry and sparse data distribution in high-dimensional space, thereby constructing probability distributions that make low-dimensional space similar to high-dimensional space. In addition, to address the impact of multi-attribute features of samples on similarity measure, a multi-attribute distance matrix was constructed using information entropy, and then combined with the numerical matrix of spectral data to obtain a mixed data matrix. In order to validate the effectiveness of the St-SNE algorithm, dimensionality reduction projection was performed on NIR spectral data and compared with PCA, LPP, and t-SNE algorithms. The results demonstrated that the St-SNE algorithm effectively distinguishes samples with different attribute information, and produced more distinct projection boundaries of sample category in low-dimensional space. Then we tested the classification performance of St-SNE for different attributes by using the tobacco and mango datasets, and compared it with LPP, t-SNE, UMAP, and Fisher t-SNE algorithms. The results showed that St-SNE algorithm had the highest classification accuracy for different attributes. Finally, we compared the results of searching the most similar sample with the target tobacco for cigarette formulas, and experiments showed that the St-SNE had the highest consistency with the recommendation of the experts than that of the other algorithms. It can provide strong support for the maintenance and design of the product formula.

Spectral library and method for sparse unmixing of hyperspectral images in fluorescence guided resection of brain tumors.

Through spectral unmixing, hyperspectral imaging (HSI) in fluorescence-guided brain tumor surgery has enabled the detection and classification of tumor regions invisible to the human eye. Prior unmixing work has focused on determining a minimal set of viable fluorophore spectra known to be present in the brain and effectively reconstructing human data without overfitting. With these endmembers, non-negative least squares regression (NNLS) was commonly used to compute the abundances. However, HSI images are heterogeneous, so one small set of endmember spectra may not fit all pixels well. Additionally, NNLS is the maximum likelihood estimator only if the measurement is normally distributed, and it does not enforce sparsity, which leads to overfitting and unphysical results. In this paper, we analyzed 555666 HSI fluorescence spectra from 891 ex vivo measurements of patients with various brain tumors to show that a Poisson distribution indeed models the measured data 82% better than a Gaussian in terms of the Kullback-Leibler divergence, and that the endmember abundance vectors are sparse. With this knowledge, we introduce (1) a library of 9 endmember spectra, including PpIX (620 nm and 634 nm photostates), NADH, FAD, flavins, lipofuscin, melanin, elastin, and collagen, (2) a sparse, non-negative Poisson regression algorithm to perform physics-informed unmixing with this library without overfitting, and (3) a highly realistic spectral measurement simulation with known endmember abundances. The new unmixing method was then tested on the human and simulated data and compared to four other candidate methods. It outperforms previous methods with 25% lower error in the computed abundances on the simulated data than NNLS, lower reconstruction error on human data, better sparsity, and 31 times faster runtime than state-of-the-art Poisson regression. This method and library of endmember spectra can enable more accurate spectral unmixing to aid the surgeon better during brain tumor resection.

Single-beam digital holographic reconstruction: a phase-support enhanced complex wavefront on phase-only function for twin-image elimination.

In in-line digital holographic microscopy (DHM), twin-image artifacts pose a significant challenge, and reduction or complete elimination is essential for object reconstruction. To facilitate object reconstruction using a single hologram, significantly reduce inaccuracies, and avoid iterative processing, a digital holographic reconstruction algorithm called phase-support constraint on phase-only function (PCOF) is presented. In-line DHM simulations and tabletop experiments employing the sliding-window approach are used to compute the arithmetic mean and variance of the phase values in the reconstructed image. A support constraint mask, through variance thresholding, effectively enabled twin-image artifacts. Quantitative evaluations using metrics such as mean squared error, peak signal-to-noise ratio, and mean structural similarity index show PCOF's superior capability in eliminating twin-image artifacts and achieving high-fidelity reconstructions compared with conventional methods such as angular spectrum and iterative phase retrieval methods. PCOF stands as a promising approach to in-line digital holographic reconstruction, offering a robust solution to mitigate twin-image artifacts and enhance the fidelity of reconstructed objects.

A new method for fluid identification and saturation calculation of low contrast tight sandstone reservoir

The resistivity difference between oil and gas layers and the water layers in low contrast tight sandstone reservoirs is subtle. Fluid identification and saturation calculation based on conventional logging methods are facing challenges in such reservoirs. In this paper, a new method is proposed for fluid identification and saturation calculation in low contrast tight sandstone reservoirs. First, a model for calculating apparent formation water resistivity is constructed, which takes into account the influence of shale on the resistivity calculation and avoids apparent formation water resistivity abnormal values. Based on the distribution of the apparent formation water resistivity obtained by the new model, the water spectrum is determined for fluid identification in low contrast tight sandstone reservoirs. Following this, according to the average, standard deviation, and endpoints of the water spectrum, a new four-parameter model for calculating reservoir oil and gas saturation is built. The methods proposed in this paper are applied to the low contrast tight sandstone reservoirs in the Q4 formation of the X53 block and X70 block in the south of Songliao Basin, China. The results show that the water spectrum method can effectively distinguish oil-water layers and water layers in the study area. The standard deviation of the water spectrum in the oil-water layer is generally greater than that in the water layer. The new four-parameter model yields more accurate oil and gas saturation. These findings verify the effectiveness of the proposed methods.