Search Results (4,771)

The article considers nonlinear fractional differential equations with cotangent derivative. The boundary conditions are multipoint and integral specified, and the nonlinear terms are in Orlicz function spaces. Several existence theorems for solutions of such boundary value problems are obtained by different fixed-point methods. Illustrative examples serve to illustrate the theoretical parts. Full article

In this study, we investigate a class of mixed fractional partial integro-differential equations (FrPI-DE) involving symmetric singular kernels. The considered model problem involves Caputo fractional derivatives and integral operators that describe spatial interactions in a bounded domain. For the purpose of analysis, the original problem is reformulated in the form of a nonlinear Volterra–Fredholm integral equation (NV-FIE). The existence and uniqueness of the solution are established by the Banach fixed point theorem. To compute numerical solutions, a modified Toeplitz matrix method (TMM) is proposed to handle the singular kernel efficiently. The method transforms the integral equation to a system of nonlinear algebraic equations, which can be solved numerically. The convergence properties of the resulting numerical scheme are analyzed and illustrate the effectiveness of the method by providing numerical examples involving logarithmic, Cauchy-type, and weakly singular kernels. Numerical results indicate that the proposed method provides highly accurate approximations and exhibits stable convergence behavior for different parameter values. Furthermore, these results confirm the effectiveness and reliability of the proposed method for solving fractional integro-differential equations that include symmetric singular kernels. Full article

In this paper, we revisit the recent result of Luo, Xu, and Raina on an Erdélyi-type integral for Saran’s three-variable hypergeometric function $F_K$. We provide a new proof of this integral and derive an attractive new integral related to Appell’s function $F_2$. A further extension on the L-variable $F_K$ function, which appears in physics, is also discussed. Furthermore, we prove various q-Erdélyi-type integrals for the q-analogue of the $F_K$-function. An interesting discrete analogue is also included. We also provide a valuable compilation of the sources for known Erdélyi-type integrals of many different hypergeometric functions. Full article

Canopy fractional vegetation cover (FVCc) is a critical indicator for evaluating the effectiveness of ecological restoration, and its accurate estimation provides valuable data for regional ecological management. In this study, Sentinel-2 and MODIS data were integrated to develop an angular relationship model for MODIS reflectance, which was then used to estimate Sentinel-2 reflectance at a 45° viewing angle. Background reflectance at a 10 m spatial resolution was derived using a four-scale model, and total and shrub-herb fractional vegetation cover were estimated using a pixel dichotomy model. Finally, an empirical model tailored to the characteristics of the study area was developed to retrieve FVCc. Cross-validation results demonstrated that the multi-angle retrieval method proposed in this study achieved higher accuracy than the single-angle approach. The spatial distribution of FVCc in Changting County is characterized by higher values in peripheral areas and lower values in the central region. Temporal transitions among fractional vegetation cover classes were predominantly upward, indicating an overall trend of continuous improvement. These findings provide important technical support and a scientific basis for estimating and monitoring dynamic changes in forest canopy fractional vegetation cover. Full article

Under dynamic loading conditions, the output voltage of proton exchange membrane fuel cells (PEMFCs) exhibits nonlinear degradation characterized by non-Gaussian fluctuations, abrupt changes, and long-range temporal dependence, which are difficult to model using conventional short-correlation or remaining useful life (RUL) prediction approaches. To capture both historical dependency and stochastic jump behavior, this study proposes a SHAP-driven mechanism–data fusion fractional stochastic degradation model based on fractional Brownian motion (fBm) and fractional Poisson process (fPp) for degradation trend forecasting. A terminal voltage mechanism model considering activation, ohmic, and concentration polarization losses is first established, and SHapley Additive exPlanations (SHAP) analysis is employed to quantify the contributions of multi-source operational variables and enhance interpretability. The Hurst exponent is then used to verify long-range dependence and jump characteristics in the voltage sequence. Subsequently, fBm is integrated with a fPp to construct a unified stochastic degradation framework capable of jointly describing continuous decay and discrete abrupt variations, enabling multi-step probabilistic prediction with confidence intervals. Validation on the publicly available FCLAB FC1 and FC2 datasets shows that the proposed model achieves superior overall performance under both steady and dynamic conditions, with MAPE/RMSE/R² of 0.027%/0.00178/0.9895 and 0.056%/0.00259/0.9896, respectively, outperforming fBm, Wiener, WTD-RS-LSTM, and CNN-LSTM methods. The proposed approach provides accurate and interpretable degradation forecasting for PEMFC health management and maintenance decision support. Full article

Glass fiber-reinforced epoxy composites were modified with carbon nanotubes (CNTs), Al₂O₃, and TiO₂ nanoparticles to comparatively evaluate their influence on tensile, flexural, and low-velocity impact performance within an integrated experimental–numerical framework. Nanoparticles were incorporated at controlled weight fractions to identify dispersion-controlled reinforcement regimes and the onset of heterogeneity-driven mechanical transitions. Among all formulations, 0.5 wt% CNTs provided the most pronounced static mechanical enhancement, increasing tensile strength to 419.50 MPa (≈21% improvement over the reference GF laminate) and flexural strength to 230.23 MPa (≈26% increase). In contrast, impact performance exhibited a non-monotonic evolution; the highest absorbed energy (9.64 J) was observed at 2 wt% CNTs, indicating that dynamic energy dissipation mechanisms do not necessarily scale proportionally with static strength gains. Oxide-filled systems demonstrated stiffness-dominated behavior, where increasing filler content amplified elastic mismatch and progressively reduced strength despite modulus enhancement. Finite element simulations conducted in ANSYS LS-DYNA (MAT_022) reproduced global stiffness trends within the dispersion-controlled regime. Tensile strength predictions agreed within 0–9% at optimal CNT loading, whereas larger deviations (up to ~33%) emerged under bending-dominated loading in oxide-rich systems, reflecting amplified sensitivity to microstructural heterogeneity. The coupled evolution of stiffness–strength decoupling (SSDI) and FEM deviation (η) enabled identification of a Composite Heterogeneity Threshold (CHT), defined as the nanoparticle concentration beyond which stiffness enhancement no longer translates into proportional strength or toughness improvement. Beyond this threshold, dispersion-induced heterogeneity not only reduces mechanical efficiency but also marks the boundary of homogenized continuum model adequacy across static and dynamic loading conditions. Full article

Although satellite sensors provide global observations, factors such as cloud interference and narrow swath widths frequently result in partial data gaps which constrain the continuous spatiotemporal analysis of the column-averaged dry air mole fraction of CO₂ (XCO₂). To address this challenge, this study develops a novel multi-stage fusion framework that integrates GOSAT and OCO-2 data using inverse error variance weighting and a dynamic bias correction technique, generating a seamless monthly XCO₂ dataset for East Asia (2016–2024). Validation against TCCON measurements (RMSE = 1.22 ppm; R² = 0.96) and WDCGG data (RMSE = 2.85 ppm; R² = 0.76) demonstrates the high accuracy of the product. The results show that the growth rate consistently exceeds 2.2 ppm/year, with clear seasonal patterns characterized by spring maxima and summer minima. Spatially, the locus of rapid growth has shifted toward central and western China, reflecting patterns of regional economic development, while substantial concentrations still persist in the industrialized regions of eastern China, Japan, and South Korea. This study provides new insights into regional atmospheric CO₂ dynamics and emphasizes the efficacy of dynamic bias correction in data fusion. Full article

The development of stable and high-yielding fodder pearl millet genotypes with improved quality traits is crucial for enhancing livestock productivity under diverse environments. In this study, twenty-six elite genotypes, including brown midrib (bmr) lines and two check cultivars, were evaluated across four locations, which fall broadly under two agro-climatic zones of India, during the summer season of 2024 to assess their stability for yield and fodder quality traits. Significant genotypic differences and genotype × environment interactions (GEIs) were observed for all traits, indicating substantial genetic variability and environmental influence on trait expression. Additive Main Effects and Multiplicative Interaction (AMMI) and Weighted Average of Absolute Scores (WAAS) analyses identified IGPM 100 as a high-yielding and stable genotype across environments, whereas Baif Bajra 1 and IGBV 97 exhibited specific adaptation. Among quality traits, ICMbmr 2401, ICMbmr 2402, and ICMbmr 2404 recorded consistently low lignin content, confirming their potential for improving forage digestibility. Further, ICFPM 05 recorded high tillering and longer leaves, while ICMFV 2308 exhibited late flowering across locations, indicating their potential for use in developing leafy, late-flowering genotypes. The multi-trait stability index (MTSI) efficiently identified IGPM 100, ICFPM 02, ICMbmr 2404, and IGBV 9 as superior and stable genotypes across multiple traits. High selection differentials for green fodder yield and negative differentials for lignin and fibre fractions highlight the possibility of a simultaneous improvement in yield and quality traits. Overall, the integration of AMMI, WAAS, and MTSI models facilitated the identification of broadly adapted and trait-specific genotypes, which, after evaluating their combining ability, can be used for developing fodder pearl millet composites and hybrids. Full article

Sea-surface reflections and wind–wave motion render maritime channels strongly time-varying and statistically non-stationary, while nearshore deployments face sparse infrastructure and co-channel multiuser interference. This study integrates reconfigurable intelligent surfaces (RISs) with rate-splitting multiple access (RSMA) for joint online resource allocation. A physics-inspired time-varying channel model is established by embedding fractional Brownian motion-driven slow statistical drift and reflection-phase perturbations. With imperfect, delayed channel state information (CSI) and discrete RIS phase quantization, a proportional-fairness utility maximization problem is formulated to jointly optimize shore base-station precoding, RIS phase shifts, and RSMA common-rate allocation. To cope with strong non-convexity, high dimensionality, mixed continuous–discrete coupling, and partial observability, a fractal-aware recurrent robust Actor–Critic (FRRAC) algorithm is developed. FRRAC encodes short observation histories using a gated recurrent unit and incorporates a lightweight Hurst-proxy estimator to capture slow channel statistics for robust value evaluation and policy learning. Truncated quantile critics and mixed prioritized–uniform replay further improve value robustness, training stability, and sample efficiency. Simulation results show that FRRAC converges faster and more stably under both conventional and fractal non-stationary channel modeling, and outperforms representative baselines across the objective and multiple statistical metrics, validating its effectiveness for joint resource optimization in maritime RIS–RSMA systems. Full article

Ischemic cardiomyopathy is defined as coronary artery disease accompanied by left ventricular dysfunction with an ejection fraction equal to or less than 40%. The substrate of ischemic cardiomyopathy is heterogeneous, characterized by the coexistence of normal, stunned, hibernating, and scarred myocardium within the same myocardial region. Altogether, these components may represent different phases of a single pathological process. It is well-established that the assessment of isolated myocardial viability and ischemia alone has failed to reliably guide the indication for coronary artery bypass grafting (CABG). CABG in patients with low ejection fraction carries a significant risk of perioperative mortality and morbidity, largely related to the development of postcardiotomy shock. Preoperative optimization with pharmacologic or mechanical circulatory support (MCS) is often essential; the decision requires integrating multiple complex factors, including clinical presentation, response to optimization therapy, myocardial viability, the presence of hibernating or scarred myocardium, left ventricular end-systolic volume index, coronary angiography findings, hemodynamic assessment, and the Pulmonary Arterial Pressure Index score. A preoperative evaluation that incorporates anatomical, morphological, functional, and hemodynamic domains enables more precise selection and timing of MCS. Preemptive left ventricular unloading mitigates the physiological impact of cardiopulmonary bypass, preserves end-organ perfusion, and reduces the need for high-dose vasopressors. However, the risk–benefit ratio remains uncertain and may be associated with serious complications. Careful judgment regarding the indications for MCS has the potential to enhance the safety of CABG in high-risk patients, but robust, long-term, prospective studies are needed to determine its true impact on clinical outcomes. In this review, we will examine the indications and criteria for the use of MCS in patients with advanced ischemic cardiomyopathy, as well as the various devices available for preoperative or intraoperative support, including technical considerations, advantages and disadvantages, and associated complications. Full article

Sorghum (Sorghum bicolor L. Moench) is one of the most important cereal crops in Mexico due to its extensive cultivation and use in human nutrition, livestock production, and the biofuel industry. However, its productivity is severely affected by the sorghum aphid, Melanaphis sorghi Theobald, 1904 (Hemiptera: Aphididae), a major pest of this crop. Its control relies primarily on synthetic chemical insecticides, whose intensive use has led to environmental impacts and health risks, prompting the search for more sustainable alternatives. In this study, the insecticidal activity of root extracts from Bessera elegans was evaluated against apterous adults of M. sorghi using artificial diet bioassays at different concentrations and exposure times. Chemical characterization of the extracts and the active fraction was carried out using high-performance liquid chromatography (HPLC) and gas chromatography coupled to mass spectrometry (GC–MS). The methanolic extract exhibited the lowest LC₅₀ value (2562 ppm), indicating the highest insecticidal potency, while the acetone extract achieved the highest maximum mortality (98%) at the highest tested concentration. Fractionation of the methanolic extract allowed the identification of fraction BeF1 as the most active, with 94% mortality at 1000 ppm. Chemical characterization indicated a predominance of polyphenolic secondary metabolites, mainly flavonoids and lignans. These results highlight the potential of B. elegans as a natural alternative for the integrated management of the sorghum aphid. Full article

Plant growth-promoting rhizobacteria (PGPR) are considered promising bio-inoculants for poplar production, but their effects can vary depending on bacterial strain, host genotype, and growth environment. In this study, we evaluated the responses of ten poplar clones representing three taxonomic groups to five indigenous PGPR strains under greenhouse and open-field nursery conditions. Under greenhouse conditions, Priestia aryabhattai GJRr2, Variovorax boronicumulans HNRr1, and a mixed inoculum (Mix) showed the most consistent positive effects. Plant height increased from 86.1 ± 5.6 cm in the control to 156.0 ± 9.4 cm in the GJRr2 treatment, whereas HNRr1 produced the greatest stem diameter (9.01 ± 0.26 mm) and total fresh weight (94.0 ± 6.0 g). Clone identity explained a larger independent fraction of growth variation than bacterial strain, and the strongest integrated responses were observed in I-476, Dorskamp, and Eco28. Field responses were generally weaker, but GJRr2 and Mix still increased height, DBH, and stem volume, whereas ORa was associated with negative responses in these traits. These results demonstrate that PGPR effects in poplar are strain-specific, clone-dependent, and environmentally contingent, indicating that inoculant selection should account for both host genotype and performance stability across growth conditions. Full article

Oligometastatic prostate cancer represents a distinct biological state between localized and widely metastatic disease, characterized by a limited number of lesions. Stereotactic body radiotherapy (SBRT) has emerged as a key metastasis-directed therapy (MDT), enabling precise ablation of metastatic lesions with minimal toxicity. Prospective clinical trials such as SABR-COMET, STOMP, ORIOLE, RADIOSA, and EXTEND have shown that SBRT delays disease progression, prolongs progression-free survival, and postpones the need for systemic therapy, while maintaining a favorable safety profile. Nevertheless, methodological limitations persist, including heterogeneity in defining oligometastatic disease, variability in dosing and fractionation, and the lack of predictive biomarkers. Ongoing phase III trials aim to validate the integration of SBRT with modern systemic therapies, including next-generation androgen receptor pathway inhibitors, to optimize clinical outcomes in hormone-sensitive and castration-resistant oligometastatic prostate cancer. This review summarizes current evidence, clinical applications, and future directions for SBRT in this patient population. Full article

Flotation circuits typically incorporate grinding stages, yet mathematical models for these processes often operate on different principles, leading to misalignment in circuit design. Building on a previously established grinding model for flotation performance, this research introduces significant advances to develop a more comprehensive and industrially relevant framework. The primary innovation is the integration of mechanical entrainment and gangue recovery into the kinetic model, distinguishing between species captured by true flotation and those carried to the surface despite being non-hydrophobic. We developed a robust set of grinding-mill equations based on first-order kinetics to describe the mass-fraction transformation of both true-flotation and entrainment species. To ensure practical applicability, a systematic experimental and modeling methodology for parameter adjustment is introduced, providing a clear sequence for identifying breakage rate constants and flotation kinetic parameters. The proposed strategy was validated using two distinct case studies: an expanded analysis of a copper sulfide ore (ore A) and a new case involving significant gangue entrainment (ore B). The results demonstrate that the model accurately predicts species kinetics, providing a high-fidelity, cost-effective tool to optimize mineral recovery and prevent economic losses from overgrinding in industrial processing plants. Full article

This work aims to introduce the concept of graphic rational contractions in the framework of extended $\mathcal{F}$-metric spaces and to establish fixed point theorems related to these mappings. In addition, we define and examine the class of interpolative Ćirić–Reich–Rus-type cyclic contractions in the same setting, deriving several new fixed point results that broaden existing theories. To illustrate the validity and originality of the obtained results, appropriate examples are presented. Furthermore, the developed theoretical results are applied to study the existence of solutions for fractional differential equations and nonlinear mixed Volterra–Fredholm integral equations, highlighting their effectiveness and practical importance. Full article