Reciprocal Transformation Research Articles

Integrable Semi-Discretization for a Modified Camassa-Holm Equation with Cubic Nonlinearity

In the present paper, an integrable semi-discretization of the modified Camassa-Holm (mCH) equation with cubic nonlinearity is presented. The key points of the construction are based on the discrete Kadomtsev-Petviashvili (KP) equation and appropriate definition of discrete reciprocal transformations. First, we demonstrate that these bilinear equations and their determinant solutions can be derived from the discrete KP equation through Miwa transformation and some reductions. Then, by scrutinizing the reduction process, we obtain a set of semi-discrete bilinear equations and their general soliton solutions in the Gram-type determinant form. Finally, we obtain an integrable semi-discrete analog of the mCH equation by introducing dependent variables and discrete reciprocal transformation. It is also shown that the semi-discrete mCH equation converges to the continuous one in the continuum limit.

Reliable Prediction of Solar Photovoltaic Power and Module Efficiency using Bayesian Surrogate Assisted Explainable Data-Driven Model

This study proposes a Bayesian surrogate-driven explainable deep neural network model to predict and interpret the module efficiency and maximum output power of three commercially available photovoltaic modules: monocrystalline silicon, polycrystalline silicon, and amorphous silicon during the winter season. In addition, the influence of the photovoltaic material and ambient conditions on the predicted power and module efficiency is investigated. The model inputs include solar irradiance, module material (monocrystalline, polycrystalline, and amorphous silicon), season of the year (months), and time of day (morning to evening). Experiments were conducted on these three modules during the winter using data from Rawalpindi, Pakistan. These data were then fed into the deep neural network model to train and yield predictions. Several preprocessing techniques such as logarithmic transformation, square root, cube root, reciprocal, and exponential transformations are employed to improve the linearity of distributed data. For hyper-parameters optimization, Gaussian process, gradient boost regression trees, and random forest are used. The results show that the optimal deep neural network using random forest surrogate model along with square root and exponential transformation is able to predict the maximum power output and module efficiency of the considered photovoltaic modules for the entire investigated period with a correlation coefficient, R2 = 0.998. The least accurate model (R2=0.991) is a Gaussian process using simple data distribution. These results hold valuable insights for predicting and optimizing the performance of other solar photovoltaic modules in various climates and different seasons of the year.

Estimating Cadmium Concentration in Agricultural Soils with ZY1-02D Hyperspectral Data: A Comparative Analysis of Spectral Transformations and Machine Learning Models

The accumulation of cadmium (Cd) in agricultural soils presents a significant threat to crop safety, emphasizing the critical necessity for effective monitoring and management of soil Cd levels. Despite technological advancements, accurately monitoring soil Cd concentrations using satellite hyperspectral technology remains challenging, particularly in efficiently extracting spectral information. In this study, a total of 304 soil samples were collected from agricultural soils surrounding a tungsten mine located in the Xiancha River basin, Jiangxi Province, Southern China. Leveraging hyperspectral data from the ZY1-02D satellite, this research developed a comprehensive framework that evaluates the predictive accuracy of nine spectral transformations across four modeling approaches to estimate soil Cd concentrations. The spectral transformation methods included four logarithmic and reciprocal transformations, two derivative transformations, and three baseline correction and normalization transformations. The four models utilized for predicting soil Cd were partial least squares regression (PLSR), support vector machine (SVM), bidirectional recurrent neural networks (BRNN), and random forest (RF). The results indicated that these spectral transformations markedly enhanced the absorption and reflection features of the spectral curves, accentuating key peaks and troughs. Compared to the original spectral curves, the correlation analysis between the transformed spectra and soil Cd content showed a notable improvement, particularly with derivative transformations. The combination of the first derivative (FD) transformation with the RF model yielded the highest accuracy (R2 = 0.61, RMSE = 0.37 mg/kg, MAE = 0.21 mg/kg). Furthermore, the RF model in multiple spectral transformations exhibited higher suitability for modeling soil Cd content compared to other models. Overall, this research highlights the substantial applicative potential of the ZY1-02D satellite hyperspectral data for detecting soil heavy metals and provides a framework that integrates optimal spectral transformations and modeling techniques to estimate soil Cd contents.

Data transformations cause altered edaphic‐climatic controls and reduced predictability on soil carbon decomposition rates

AbstractData transformation of the reference soil organic matter (SOM) decomposition rates (kref), often derived as turnover times or in alternative formats, is commonly used to develop ecological models for projecting the persistence of SOM. However, the effects of reciprocal or logarithmic transformation of kref on model performance and edaphic‐climatic patterns remain uncertain. Here, we convert published kref values into reciprocal or logarithmic formats and establish machine learning models between the transformed kref and edaphic‐climatic predictors. We show that models trained with the transformed kref exhibit a 11.6%−68.4% reduction in performance upon re‐conversion to kref compared to those trained with the original kref. The variable importance analysis identifies distinct key predictors governing the original kref and its transformed counterparts. This suggests that data transformation alters the relative significance of predictors without necessarily improving kref prediction performance. Consequently, our study underscores the importance of directly focusing on the original values rather than alternative representations when dissecting a given variable's patterns and mechanisms in ecological modeling.

The multi-soliton solutions of another two-component Camassa–Holm equation with Darboux transformation approach

In this paper, we develop another approach to construct the multi-soliton solutions of a two-component Camassa–Holm equation in terms of Wronskians with help of a reciprocal transformation and a gauge transformation. Its kink solution, loop solution and smooth soliton solution are presented. Then with the non-trivial limiting procedure, the solution of Camassa–Holm equation is also derived from that of two-component Camassa–Holm equation.

Heritage as threshold: an autoethnographic exploration of the porticoes of Bologna (Italy)

The contents and aims of this paper derive from an autoethnographic exploration of the porticoes of Bologna, which in 2021 became part of the UNESCO World Heritage List. It was the difficulty of their candidacy process, which is not usual for Italian urban heritage, that shaped my concern with them. I conducted empirical research by walking under the porticoes in order to understand the reasons behind their otherness as official heritage and how these reasons can represent an interesting case for current geographical debates on heritage in its cultural dimension. Drawing first of all on the fact that my embodied experience of the porticoes was a liminal experience, I argue here that their otherness lies in being heritage as threshold by developing this idea in two ways. The first way consists of interpreting the spatiality of the porticoes in the light of the concept of threshold. To the extent that a threshold, as conceived here, is not a boundary but a zone of transition where binary terms are held together and interact with each other, the spatial nature of the porticoes as thresholds challenges the sedentary certainties and sharp boundaries of ‘authorized heritage discourse’. The second way in which I conceive and develop the idea of heritage as threshold consists of relating it, through the example of the porticoes, to the process of heritage-making. From this point of view, the idea of heritage as threshold is a spatial interpretation of the process of construction, deconstruction, reconstruction of heritage, whenever based on the interweaving of official discourses and everyday experiences, on their reciprocal influence and transformation. The construction of the narrative on the porticoes as heritage represents a perfect example of this process of transition and interchange between different perspectives – a process closely associated with the spatiality of thresholds.

Formation and local stability of a two-dimensional Prandtl boundary layer system in fluid dynamics

By the linearized method, Oleǐnik-Samokhin had constructed solutions to distinguish between two cases of the behavior of the fluid at the initial stage of its motion past the surface in Oleinǐk and Samokhin (1999). In this paper, we consider the development of the boundary layer about a body that gradually starts to move in a resting fluid. In the analytical frame, the formation of the layer shows that, when the layer starts to move, the local solutions of the Prandtl boundary layer system is positive. By the Crocco transformation, the Prandtl boundary layer system reduces a degenerate parabolic equation with a nonlinear boundary value condition. Then by the reciprocal transformation, we can obtain a divergence type parabolic equation. We quote a new kind of BV entropy solution matching up with this divergence type parabolic equation when t≥t0, where t0 is a small enough positive constant. By imposing some close connections between the velocity of the outflow and the geometric characteristic of the spatial domain, using Kružkov’s bi-variables method, the local stability of BV entropy solutions is proved. Thus, by the Crocco inverse transformation, in the analytical frame, we obtain the existence and the uniqueness of the global solution of the Prandtl boundary layer system for a regular spatial domain.

Endothelin-1, Extracellular Volume Overload, and Hemodynamics in Hemodialysis Patients.

Extracellular volume (ECV) overload and endothelial cell dysfunction are mortality risk factors in hemodialysis (HD) patients. Endothelin-1 (ET-1), an endothelium-derived vasoconstrictive peptide, is associated with poor outcomes in HD patients. We hypothesized there would be associations between ET-1 and ECV overload in hypertensive HD patients. We obtained pre-HD ET-1, ECV/weight (bioimpedance spectroscopy), pre-HD hemodynamics, and ambulatory blood pressure (BP) in an HD cohort. Following appropriate transformations, we conducted correlation and linear regression analyses idendifying associations between ET-1, ECV overload, total peripheral resistance index (TPRI), cardiac index (CI), and ambulatory BP. Among 66 patients, median ET-1 was 1.93 (1.49-2.56) pg/ml. Median pre-HD ECV/weight, median TPRI, mean CI, and mean systolic ambulatory BP were 0.25 (0.22-0.30) l/kg, 3,161 (2,711-3,642) dynes × s/cm-5/m2, 2.92 (0.6) l/min/m2, and 143 (14) mm Hg, respectively. After reciprocal-transformation, ET-1 correlated with reciprocal-transformed ECV/weight (r = 0.3, P = 0.01), log-transformed TPRI (r = -0.3, P = 0.006), CI (r = 0.3, P = 0.009), and ambulatory BP (r = -0.3, P = 0.02). These associations persisted in linear regression analysis (β = 0.15, P = 0.002; β = -0.8, P = 0.002; β = 0.2, P = 0.002; β = -19, P = 0.03). In hypertensive HD patients, ET-1 associates with ECV overload higher TPRI and ambulatory BP, and lower CI. Further research is necessary to determine if ECV reduction lowers ET-1 or if pharmacologic ET-1 antagonism can improve outcomes in HD patients with refractory ECV overload.

Embedding Municipal Green Bonds in Mexico City's hydrosocial cycle: 'Green' debt and climate action narratives

Mexico City's municipal "green" bonds (MGBs), issued in 2016 and 2018, financed two water infrastructure projects embedded in the city's hydrosocial cycle (the reciprocal transformation of water and society). The issuance of the MGBs created an entanglement of "green" debt and water circulation, which the city government touted as a successful "green" intervention for climate action. However, this article argues that the MGBs also masked climate injustices and colonial legacies that were already prevalent in Mexico City's water circulation infrastructure, affecting aspects including socio-economic and gender issues. To substantiate this claim, this article adopts climate coloniality and climate justice as analytical lenses and urban political ecology as a methodology to critically examine the "green" label epistemologies and climate action narratives that justify the issuance of MGBs linked to water infrastructure projects.

Iron complex regulated synergistic effect between the current and peroxymonosulfate enhanced ultrafast oxidation of perfluorooctanoic acid via free radical dominant electrochemical reaction

Iron complex regulated electrochemical reaction was triggered for revealing the reaction mechanism, degradation pathway, and applied potential of perfluorooctanoic acid (PFOA). The increased PMS concentrations, electrode spacing, and current density significantly enhanced PFOA elimination, with current density exhibiting a relatively strong interdependency to PFOA complete mineralization. The synergy between PMS and electrochemical reactions greatly accelerated PFOA decomposition by promoting the generation of key reaction sites, such as those for PMS activation and electrochemical processes, under various conditions. Furthermore, density functional theory calculations confirmed that the reciprocal transformation of Fe2+ and Fe3+ complexes was feasible under the electrochemical effect, further promoting the generation of active sites. The developed electrochemical oxidation with PMS reaction (EO/PMS) system can rapidly decompose and mineralize PFOA while maintaining strong tolerance to changing water matrices and organic and inorganic ions. Overall, it holds promise for use in treating and purifying wastewater containing PFOA.

Three defect types transformation of vertical graphene by elevating temperature

Clarifying the performance differences among sp3 hybrid, vacancy-like and boundary-like types of vertical graphene (VG) can enhance its extensive application. However, there is currently no systematic report on the reciprocal transformation of these defect types. Furthermore, it is crucial to investigate the growth characteristics of each defect type of VG and their transformation mechanisms. Herein, three defect types VG were successfully grown on copper foil by regulating the growth temperature. As the growth temperature increased, VG transitioned from sp3 hybrid type to vacancy-like type and then evolved into boundary-like type. This transformation can be primarily attributed to an increase in carbon nanosheets density at higher temperatures. Each type of VG defect offers distinct advantages for various applications: sp3 type VG exhibits excellent in-plane thermal conductivity, vacancy-like type VG shows good hydrophobicity, and boundary-like type VG has low reflectance in the near infrared region. Meanwhile, these applications are promising to redefine the defect type in the future. By analyzing the preparation and properties, this work deepen the insight to the different defect types of VG.

Study on the Rule of Change of Reservoir Rocks under Subcritical Steam Effect

This paper examines the lithology, pore throat, and fluid characteristics of the reservoir in Liaohe Oilfield Block 3624, using group V rocks as an example, combining a high-temperature and high-pressure reaction still with other equipment such as a rock mechanics tester and a scanning electron microscope. This study also designs and develops three controlled variable experiments, including the subcritical steam reservoir rock dissolution experiment, the subcritical steam reservoir rock mineral composition transformation experiment, and the subcritical steam reservoir rock mineral mechanical property experiment, also making clear the rule of change on the part of the rocks in the deep and heavy oil reservoirs after the injection of subcritical steam. Experimental results reveal the following: (1) Steam causes the dissolution of rocks, and when the steam temperature is in the subcritical region, dissolution is visible. After a 350 °C subcritical steam treatment, the relative melting temperatures of the components of rock materials are substantially greater than the melting point of the cement holding them together, causing the cement to significantly dissolve and a secondary crack network to emerge. (2) The mineral composition of the rocks changes as a result of elevated temperatures, with various mineral transformation trajectories being recorded after various steam treatments. Montmorillonite in reservoir rocks is converted into minerals like illite and chlorite in the subcritical steam temperature range. Another element influencing the creation of secondary cracks on rock surfaces is the reciprocal transformation of minerals, which alters the cohesiveness among mineral components. (3) Rocks suffer thermal damage and changes to their mechanical characteristics as a result of high-temperature steam dissolution and mineral transformations; the severity of these changes increases with the steam temperature.

A generalized super Camassa-Holm equation

We propose a generalized super Camassa-Holm equation, which is completely integrable in the sense of admitting of a Lax pair and a bi-Hamiltonian structure. Through Dirac reduction, we obtain a bi-Hamiltonian structure of the super Camassa-Holm equation introduced by Geng, Xue and Wu [Stud. Appl. Math. 130 (2013) 1-16]. By introducing an appropriate reciprocal transformation, we connect the generalized super Camassa-Holm equation with a negative generalized super KdV equation, which is also equipped with a Lax pair and a bi-Hamiltonian structure.

Assessing the value and sensitivity of ecosystem services based on land use in the middle and lower reaches of the Shiyang River

In response to increasing ecological and environmental challenges in arid areas, it is of great significance to investigate the ecosystem service value (ESV), accompanying the changes in ecological sensitivity for the protection of ecologically vulnerable areas. Our analysis seeks to elucidate the ESV and ecological sensitivity changes in the middle and lower reaches of the Shiyang River to determine the trends and influencing factors of ESV under changing land use patterns. The key findings include: (1) From 1995 to 2020, the ESV in the study area witnessed fluctuations, culminating in an overall decline of 1.249 × 108 yuan. (2) In 2020, sensitivity coefficients (CSs) for ESV were as follows: 0.4335 for grassland, 0.2586 for farmland, and 0.1170 for unused land within the study area. Furthermore, coefficients of improved cross-sensitivity (CICSs) for the reciprocal transformation of farmland, grassland, and unused land were 1.10, 1.18, and 1.54, respectively, indicating the pivotal role of the three land types in driving ESV fluctuations.

An Application of the Nonlinear Reciprocal Transformations in the Theory of DR Hierarchies

An Application of the Nonlinear Reciprocal Transformations in the Theory of DR Hierarchies

Reciprocal transformation based convex variational image restoration with multiplicative noise

Reciprocal transformation based convex variational image restoration with multiplicative noise

Impact of participation as a peer change agent on peer change agents themselves: a quantitative study of a peer-led, social media-based PrEP promotion intervention.

Despite the adoption of pre-exposure prophylaxis (PrEP) as a crucial HIV intervention, uptake remains suboptimal among men who have sex with men, a sexual minority group, due to barriers like cost and stigma. Peer change agents (PCAs) disseminate PrEP information within their social networks. This study explores the reciprocal effects of an online community-based participatory intervention on PCAs, focusing on their transformed PrEP uptake perceptions-leadership efficacy, social network dynamics, attitudes, perceived benefits and barriers and self-efficacy. Leveraging insights from the PrEP Chicago Study, our research addresses a key gap in community-based participatory interventions for PrEP uptake: the transformative experiences and perception shifts of PCAs involved in these interventions. We engaged 20 men who have sex with men, aged 18-45, as PCAs in a one-group pretest-posttest design intervention, which disseminated PrEP communications within their preferred online networks. We utilized the PrEP Chicago Study's 45 Likert items, tailored to reveal the PCAs' transformative potential. Data on PrEP uptake perceptions, sociodemographics and social media use were captured and analyzed using the Wilcoxon matched-pairs signed-rank test, a nonparametric method. PCAs demonstrated significant changes in their PrEP uptake perceptions, including leadership capacity, social network dynamics, attitudes toward PrEP, perceived benefits, barriers and self-efficacy. Our intervention highlights the reciprocal transformation PCAs undergo when disseminating PrEP information. This study adds a new dimension to community-based PrEP interventions and underscores the need for continued refinement of peer-led strategies to optimize the transformative potential of PCAs.

Higher-dimensional Chen–Lee–Liu equation and asymmetric peakon soliton

Integrable systems play a crucial role in physics and mathematics. In particular, the traditional (1+1)-dimensional and (2+1)-dimensional integrable systems have received significant attention due to the rarity of integrable systems in higher dimensions. Recent studies have shown that abundant higher-dimensional integrable systems can be constructed from (1+1)-dimensional integrable systems by using a deformation algorithm. Here we establish a new (2+1)-dimensional Chen–Lee–Liu (C–L–L) equation using the deformation algorithm from the (1+1)-dimensional C–L–L equation. The new system is integrable with its Lax pair obtained by applying the deformation algorithm to that of the (1+1)-dimension. It is challenging to obtain the exact solutions for the new integrable system because the new system combines both the original C–L–L equation and its reciprocal transformation. The traveling wave solutions are derived in implicit function expression, and some asymmetry peakon solutions are found.

Which range of streamflow data is most informative in the calibration of an hourly hydrological model?

ABSTRACT From which part of the streamflow time series does a hydrological model learn most about the behaviour of a catchment? How does this part change with the objective function used for model calibration? We calibrated the hourly model GR4H (Génie Rural à 4 paramètres au pas de temps Horaire) on data subsets selected based on the flow duration curve, which narrowed the range of streamflow that influenced the identification of model parameters the most. Using 658 catchments in the United States and France, we found that calibrating GR4H on the highest 50% of streamflow values of a given period provided similar parameters to calibration on the whole period, with the top 10% dominating the identification of parameters. The logarithmic transformation of streamflow balanced the contribution from high and low flows, but only the reciprocal transformation emphasized low flows. The proposed methodology identifies the informative ranges of streamflow data and allows anticipating potential model failures in nonstationary hydroclimatic conditions.

Synergetic management of the water-energy-food nexus for cropland ecosystems under climate change: Toward a multistakeholder-based systematic optimization approach

The optimal management of the water-energy-food (WEF) nexus in cropland ecosystems (CEs) can help promote food security and resource sustainability. However, the intrinsic interactions among multisource energy, water, the yield-formation process, and the economic-environmental effect have not been systematically quantified and determined. This paper constructs a WEF-based cooperative optimization model in CEs under climate-change conditions, which is capable of reflecting the reciprocal transformations and coordinated interactions among light energy, thermal energy and biomass energy in CEs and of balancing the energy/water use efficiency, economy and environmental factors considering the biomass residue potential. The method is tested and implemented on the Sanjiang Plain, Northeast China. The results show that (1) a cooperative relationship between energy utilization efficiencies and economic benefits was identified. For example, if the utilization efficiencies of light and heat energy increase by 1%, the economic benefits increase by 13.59%, and the biomass energy production potential increases by 10.82%. (2) The aboveground residue can be reused in power generation, carbonization, anaerobic fermentation, feed preparation and sales applications to increase the economic benefits by 3.38%–20.70%. This study contributes to a deeper understanding of multiple renewable energy management and the bound with water and food production, promoting the sustainable development of agroecosystems.