Articles published on Complex plane
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- Research Article
- 10.1016/j.aprim.2025.103440
- Jul 1, 2026
- Atencion primaria
- Ane Fernández San Juan + 5 more
Patient with pluripathology-centered care: The patients' voice and the professionals' vision
- Research Article
- 10.1093/jxb/erag134
- Jun 24, 2026
- Journal of experimental botany
- Yichun Qiu + 1 more
Angiosperms represent the most abundant and diverse lineage of land plants, and their evolutionary success is closely linked to major reproductive innovations, including the origin of flowers and the embryo-nourishing endosperm. Many of the genes underlying these innovations belong to the MADS-box transcription factor family. While the functions of MIKCC-type MADS-box genes in floral development are well established, this review focuses on the other two lineages, M-type and MIKC*-type genes, and synthesizes recent advances in the understanding of their functional roles and evolutionary histories. M-type genes are key regulators of female gametophyte and endosperm development, indicating that two hallmark features of angiosperms were promoted by distinct MADS-box gene classes. MIKC*-type genes govern pollen development and are phylogenetically more closely related to M-type genes; together, they form the plant-specific Type I clade, which primarily regulates gametophytic programmes. This contrasts with the Type II clade, comprising MIKCC-type genes that diversified to control sporophytic development. Both Type I and Type II clades originated from plant-specific duplications of ancestral MEF2-like genes. Through extensive lineage-specific expansion and diversification, these MADS-box transcription factors have played a central role in plant terrestrialization by integrating stress responses with reproductive development and the patterning of progressively complex body plans.
- Research Article
- 10.1080/17476933.2026.2685094
- Jun 20, 2026
- Complex Variables and Elliptic Equations
- Heinrich Begehr
For a planar domain of the complex plane, the area integral operator with harmonic Green function as kernel provides a particular solution to the Poisson equation. This operator serves to convoluting harmonic Green functions with itself resulting in a variety of hybrid polyharmonic Green functions. Besides Green also Neumann and Robin functions are involved as other polyharmonic Green functions of lower order, e.g. the polaharmonic Green-Almansi function, could be incorporated. A broad class of polyharmonic Green functions of different kinds is attained by convoluting harmonic Robin functions, because Robin functions depend on two real parameters. As they are themselves interpolations between Green and Neumann functions, many particular cases are covered. They are useful to solve polyharmoic Robin boundary value problems for higher order Poisson equations under proper solvability conditions, Dirichlet, Requier, and Neumann problems included.
- Research Article
- 10.1080/17476933.2026.2682927
- Jun 18, 2026
- Complex Variables and Elliptic Equations
- Vasudevarao Allu + 1 more
In this paper, we first obtain an estimate of the coefficients for α-harmonic mappings. The Landau type theorem for α-harmonic mappings defined on the unit disc D of the complex plane is then obtained by applying these estimates.
- Research Article
- 10.3390/biomimetics11060413
- Jun 11, 2026
- Biomimetics (Basel, Switzerland)
- Yubao Xu + 2 more
The greater cane rat algorithm (GCRA) draws inspiration from the seasonal behavioral patterns of the greater cane rats: extensive roaming during the non-breeding period for global exploration, and aggregative foraging during the reproductive period for local exploitation. The GCRA leverages independent movement and population aggregation to iteratively update positions in pursuit of the optimal solution, which exhibits inherent structural deficiencies: precipitous population diversity collapse, lethargic convergence dynamics, suboptimal computational precision, high susceptibility to local optima, and severe dimensional scalability. This paper proposes a modified complex-valued encoding GCRA (CGCRA) that exploits the mathematical structure of complex numbers to construct a two-dimensional search domain on the complex plane and facilitate collaborative optimization. The CGCRA maps the decision variables onto the complex domain, the real part executes the native foraging mechanism for local fine-grained exploitation, and the imaginary part exploits phase rotation to generate global exploratory perturbations. The CGCRA leverages a dual-encoding redundancy mechanism with inherent error tolerance to attenuate result volatility, augment information capacity and population heterogeneity, elevate search adaptability and disturbance rejection, accelerate parallel computation and exploration efficiency, and facilitate spatial transformation and multi-dimensional data manipulation. Twenty-three benchmark functions and twelve real-world engineering designs are employed to assess the CGCRA's stability and practical feasibility rigorously. The CGCRA delivers comprehensive spatial mapping and adaptive coordination to facilitate population collaboration and bolster resilience, expedite exhaustive research, and advance optimization efficiency. The experimental results demonstrate that the CGCRA emphasizes instructive superiority and practical utility to regulate exploration and exploitation, reduce result dispersion, mitigate search stagnation, accelerate convergence efficiency, elevate solution precision, and fortify stability and robustness.
- Research Article
- 10.1080/09537287.2026.2683319
- Jun 10, 2026
- Production Planning & Control
- Sandeep Kumar + 1 more
The development of sustainable agricultural supply chains is critical for improving operational efficiency, coordination, and resilience under increasing demand uncertainty, climate variability, and resource constraints. These supply chains involve complex planning and control decisions across interconnected stages, including pre-production, production, post-harvest processing, and distribution. However, existing research on artificial intelligence (AI) and machine learning (ML) remains fragmented and lacks an integrated planning and control perspective. This study addresses this gap by developing a conceptual decision-support framework that positions ML as a decision-intelligence layer embedded within planning, coordination, and control processes. Using a structured literature synthesis, the study maps ML techniques to key operational decision contexts across the supply chain. The framework demonstrates how ML-enabled decision support can enhance yield planning, resource allocation, logistics coordination, quality control, and waste reduction, while linking these decisions to sustainability outcomes such as environmental efficiency, economic resilience, and transparency. The study also identifies key implementation challenges, including data availability, interoperability, infrastructure constraints, and organizational readiness. The study contributes a decision-centric framework that integrates ML with supply chain planning and control, providing actionable insights for improving performance and sustainability in agricultural supply chains.
- Research Article
1
- 10.1016/j.mex.2025.103778
- Jun 1, 2026
- MethodsX
- Farooq Ahmed Shah + 4 more
Construction and applications of iterative methods for finding approximate solutions of nonlinear equations having unknown zeros of multiplicity with fractal geometry and dynamical behavior.
- Research Article
- 10.1080/10652469.2026.2674837
- May 22, 2026
- Integral Transforms and Special Functions
- Daniyal Israfilov
Let G be a finite Jordan domain in the complex plane C , bounded by a Dini-smooth curve Γ. In this paper, we establish several direct and inverse approximation theorems in the variable exponent Smirnov classes E p ( ⋅ ) ( G ) . The results describe the relationship between the degree of polynomial approximation and the smoothness properties of analytic functions, belonging to these spaces. Our approach relies on Faber polynomials and Faber series associated with the domain G, together with tools from variable exponent Lebesgue space theory.
- Research Article
- 10.3390/s26113303
- May 22, 2026
- Sensors (Basel, Switzerland)
- Xu Wang + 2 more
In ubiquitous Wi-Fi sensing, human motion interval segmentation is crucial for applications ranging from basic intrusion detection to advanced activity understanding. Existing methods often treat the Channel State Information (CSI) primarily as time series, overlooking its rich information in the spatial and frequency domains. To address this, we propose a training-free motion segmentation method that exploits the spatiotemporal features of CSI. We first analyze the discriminative spatial distributions of the CSI Ratio on the complex plane and construct a spatiotemporally dual-constrained local density estimator to characterize motion-induced perturbations. To overcome subcarrier selection challenges, we introduce a packet-level asymmetric truncation-based fusion algorithm, which yields a feature representation with a pronounced bimodal histogram. This enables the automatic determination of the optimal segmentation threshold based on the distribution characteristics of the truncated density image. Experiments in typical indoor environments demonstrate that the proposed method achieves high accuracy in both motion event detection and interval localization.
- Research Article
- 10.1080/10589759.2026.2677049
- May 22, 2026
- Nondestructive Testing and Evaluation
- Qiongbin Lin + 4 more
ABSTRACT Eddy current testing is critical for industrial pipeline safety. The measurement of defect depth on curved surfaces is influenced by both defect orientations and lengths. In this paper, a novel characteristic slope-based defect depth estimation method is proposed using the designed flexible honeycomb-shaped sensor. The designed flexible honeycomb-shaped sensor with the adjacent anti-phase excitation strategy can enhance magnetic field strength and suppress lift-off noise. From the detected signals, the signal trajectories in the complex plane exhibit a slope invariance with respect to defect orientations and lengths, while maintaining a distinct monotonic dependency on defect depth. Based on this slope feature, a defect depth inversion model is constructed employing the Natural Gradient Boosting algorithm. Experiments have been conducted on aluminium alloy pipes containing defects of varying lengths and orientations. The results demonstrate that the method effectively overcomes the interference of defect orientations and lengths. It achieves high precision depth assessment with an average prediction accuracy reaching 98.8%.
- Research Article
- 10.1186/s12957-026-04415-2
- May 21, 2026
- World journal of surgical oncology
- Clara Fernández Fernández + 9 more
This report describes a critical complication following the first stage of an unplanned ALPPS procedure (Associating Liver Partition and Portal vein Ligation for Staged hepatectomy). While ALPPS is designed to induce rapid hypertrophy of the future liver remnant (FLR), the development of portal vein thrombosis (PVT) in the remnant liver can be catastrophic, jeopardizing the success of the second stage. This report highlights the novelty of using a rescue transsplenic mechanical thrombectomy and balloon dilation to restore flow, demonstrating a successful interventional radiology approach to salvage a complex surgical plan. A 68-year-old male with a history of rectal adenocarcinoma was diagnosed with a 6cm hepatic lesion (pancreatobiliary origin) infiltrating the right portal vein. During an intended right hepatectomy, intraoperative tumor progression prompted conversion to the first stage of a tourniquet ALPPS procedure. Ten days post-surgery, CT imaging revealed a partially occlusive thrombosis of the main portal vein and insufficient FLR growth. A transsplenic portography was performed, confirming stenosis at the left portal branch. The medical team intervened using Alteplase instillation followed by mechanical thrombectomy and balloon dilation of the stenotic area and embolization of the splenic tract. This approach restored portal flow and allowed completion of hepatectomy after adequate hypertrophy. Transsplenic mechanical thrombectomy performed by interventional radiology represents an effective option for the treatment of portal vein thrombosis following the first stage of an ALPPS procedure. In our case, it enabled portal recanalization and promoted the growth of the future liver remnant.
- Research Article
- 10.1038/s41598-026-51905-0
- May 14, 2026
- Scientific reports
- Tzahi Golan + 2 more
The production of bifaces is a central feature of the Acheulian culture, reflecting complex planning, material selectivity, and skilled execution. At Gesher Benot Ya'aqov (GBY), a key early Middle Pleistocene site situated within the tectonically active northern segment of the Dead Sea Transform, basalt served as a significant raw material used for the manufacture of giant cores, bifaces (handaxes and cleavers), and associated debris. However, the geological instability of the region, together with the burial and erosion of basalt flows, complicates the identification of the sources exploited by GBY hominins. Here we apply a set of geochemical analyses including major elements, trace elements, rare earth elements, and multivariate statistical approaches to basalt artifacts and regional geological samples, including subsurface drill cores. These data reveal the compositional range of basalts available around GBY and allow the mapping of archaeological specimens onto this geochemical landscape. The results demonstrate that most artifacts were produced from basalt flows immediately surrounding the site, while a subset of tools particularly some cleavers reflect the use of additional flows not currently exposed at the surface. Together, these findings clarify the raw-material procurement strategies employed by GBY hominins and highlight a selective, structured approach to basalt exploitation within a dynamically changing landscape. The integration of geological and archaeological evidence offers new insights into the planning depth, technological behavior, and adaptive strategies of Acheulian populations in the Jordan Valley.
- Research Article
- 10.1186/s41205-026-00324-y
- May 6, 2026
- 3D Printing in Medicine
- Jose Carlos Villalobos-Lizardi + 11 more
BackgroundGiven the established and reproducible benefit of 3D-printed models in complex congenital heart disease (CHD) surgical planning, the focus has shifted from validating their utility to refining anatomical fidelity through enhanced imaging integration. The purpose of this study is to evaluate the perceived clinical utility of multimodality fusion 3D-printed cardiac models and to determine whether inclusion of valve structures confers incremental benefit over conventional single-modality 3D models in enhancing anatomical understanding and preoperative surgical planning among pediatric cardiac surgeons and imaging cardiologists in complex CHD.MethodsIn this feasibility study, multimodality fusion 3D models were successfully generated by integrating cross-sectional imaging (cardiac computed tomography and magnetic resonance) with 3D echocardiographic datasets to reproduce atrioventricular valve apparatus and subvalvular structures in 10 pediatric patients with complex CHD. Ten faculty members (7 pediatric cardiologists with advanced imaging expertise and 3 pediatric cardiothoracic surgeons) evaluated 10 patient-specific models using a structured Likert questionnaire.ResultsSurgeons assigned significantly higher ratings than imagers for anatomical understanding (median 5 vs 4; p = 0.002) and surgical planning (p < 0.001). Participants agreed that multimodality models are most valuable in complex congenital heart disease, particularly in cases requiring ventricular septal defect patching or intraventricular baffle repair involving the subvalvular apparatus.ConclusionMultimodality imaging fusion for 3D printing is technically feasible and produces high-quality models with strong intraoperative correlation. Incorporation of atrioventricular valve anatomy provides meaningful incremental benefit—particularly for surgeons—enhancing operative planning in complex CHD.Graphical Supplementary informationThe online version contains supplementary material available at 10.1186/s41205-026-00324-y.
- Research Article
- 10.18623/rvd.v23.6344
- May 5, 2026
- Veredas do Direito
- Nataliya Ulyanova
The article examines the residential architectural environment of modern Moscow. The aim of the work is to analyze decorative elements in architecture with the specifics of planning coloristic principles and their influence on the modern construction of urban complexes, which is necessary for the modern development of the city. The article examines the planning and organization of color perception of the socio-cultural space using the example of modern residential architecture in Moscow. By analyzing the architectural complexes of the modern city and its developing surroundings, a model for organizing the color space of urban developments is proposed. The article examines modern residential architectural complexes of the Russian Federation in the city of Moscow, the North-Eastern Administrative District, as well as various types of planning of decorative elements and architectural details of facades in the territories of modern urban developments. To achieve the stated goal, the work examined contemporary opinions and assessments of the planning of residential complex territories bordering historical architectural monuments and protected zones using various research methods. The obtained results make it possible to develop a model of a socially sustainable architectural ensemble that includes the functions of socio-cultural, artistic and educational significance.
- Research Article
- 10.1016/j.isatra.2026.03.026
- May 1, 2026
- ISA transactions
- Xuefeng Zhang + 1 more
Alternative LMI formulations for the stability of LTI fractional-order systems.
- Research Article
- 10.1002/adts.202501861
- May 1, 2026
- Advanced Theory and Simulations
- Avradip Ghosh + 2 more
ABSTRACT Understanding the behavior of wave propagation in viscoelastic materials is essential across numerous scientific and engineering fields. It improves our ability to predict and interpret the dynamics of viscoelastic materials and wave interactions in complex environments. This paper presents a tensor‐based framework for analyzing and visualizing frequency‐dependent wave propagation in three‐dimensional linear viscoelastic media. Fractional‐order damping is incorporated through combining elastic and viscous tensors, leading to complex stiffness models governed by fractional calculus. These models are integrated into the frequency‐wavenumber domain formulation of the Green's function, which captures anisotropic elasticity and directional attenuation. While it is well established that damping shifts wave poles into the complex plane, the present framework embeds this effect directly into a frequency‐dependent Green's function formulation extended to fractional viscoelasticity. It demonstrates that viscoelastic damping regularizes the Green‐Christoffel operator by removing real‐direction singularities. Furthermore, polar decomposition is applied to the Green's function tensors, uniquely separating them into stretch (amplitude, damping) and rotation (phase, direction) components. This dual spectral‐geometric representation separates amplitude (stretch) from direction‐dependent phase evolution encoded in the unitary rotation tensor that reflects complex polarization. Overall, this framework offers a structured method for visualizing viscoelastic wave propagation and supports anisotropic material characterization.
- Research Article
- 10.1111/sapm.70228
- May 1, 2026
- Studies in Applied Mathematics
- Yuri Latushkin + 1 more
ABSTRACT We study the resonances of (generally, non‐self‐adjoint) Schrödinger operators with matrix‐valued square‐well potentials. We compute explicitly the Jost function and derive complex transcendental equations for the resonances. We prove several results concerning the distribution of resonances in the complex plane. We compute the multiplicity of resonances and prove a version of the Weyl Law for the number of resonances.
- Research Article
- 10.1016/j.jtocrr.2026.100984
- May 1, 2026
- JTO clinical and research reports
- Rob G Stirling + 33 more
Lung cancer is a heterogeneous and complex disease requiring multidisciplinary input for optimal management planning, with guidelines recommending that all patients be discussed in a multidisciplinary setting. Multidisciplinary meeting (MDM) discussion aims to enhance evidence-based management, improve treatment access, and optimize complex management plans. We aimed to assess the extent and impacts of MDM discussion in patients with lung cancer described by the Victorian Lung Cancer Registry from 2011 to 2023 in Victoria, Australia. We identified MDM-presented and nonpresented patients and assessed the impacts of MDM presentation. OR and survival hazard ratios were assessed using Cox proportional regression analysis. Survival analysis was determined using the Kaplan-Meier product-limit method. Sensitivity analyses were conducted using landmark analysis and propensity score matching methods. A total of 18,597 patients were included, of whom 67% had evidence of presentation to a lung cancer MDM, with MDM presentation increasing from 59.1% to 80.6% during the study period. MDM presentation was associated with higher levels of provision of guideline-concordant treatment in NSCLC (56.2% versus 44.5%, p < 0.001), and lower levels of no treatment (10.0% versus 21.4%, p < 0.001). Modifiable factors that could increase MDM presentation include referral of patients of older age, stage IV disease, SCLC, and diagnosis at a private or regional hospital. Propensity-matched survival analysis in NSCLC revealed a median survival of 1.1 years for MDM-presented versus 0.86 years for nonpresented individuals, providing a 12% reduction in mortality hazard (hazard ratio 0.88 [0.82-0.95], p < 0.001). During the period of activity of the Victorian Lung Cancer Registry, MDM presentation increased from 59.1% to 80.6%. Management outcomes in MDM-presented patients identified multiple underserved cohorts and revealed considerable increases in treatment modalities and guideline-concordant treatment in NSCLC in this observational study, with an associated 12% improvement in survival advantage overall.
- Research Article
- 10.1088/1572-9494/ae5802
- May 1, 2026
- Communications in Theoretical Physics
- Feng Zhang + 2 more
Abstract In this study, we develop the inverse scattering transform of the focusing Lakshmanan-Porsezian-Daniel equation with a one-sided nonzero boundary condition, where the asymptotic amplitude tends to zero on one side at spatial infinity while remaining nonzero on the other. For the direct scattering problem, single-valued eigenfunctions are rigorously defined, and their analyticity, symmetries, and asymptotic behavior are rigorously analyzed. Furthermore, the Marchenko integral equations and the Riemann-Hilbert problems (both right and left) on a single sheet of scattering variable are constructed and utilized to formulate the inverse problem. Additionally, a proper uniformization variable is defined to formulate both the direct and inverse scattering problems, which maps the two-sheeted Riemann surface of the spectral parameter onto a single complex plane. Ultimately, the time evolutions of the eigenfunctions are derived, revealing the nontrivial time dependence of the scattering data.
- Research Article
- 10.1061/jsendh.steng-14906
- May 1, 2026
- Journal of Structural Engineering
- Manuel Matus + 1 more
Extreme wind events are responsible for significant human and economic losses, with low-rise buildings particularly affected during such events. The current wind load provisions are based on wind tunnel tests of rectangular building models conducted over the past four decades. However, modern buildings have evolved into complex plan shapes that are often hardly represented by simplified shapes in existing provisions. This study investigated the pressure distribution around buildings with nonrectangular plans. Seven models were constructed and tested in a large wind tunnel under simulated atmospheric boundary-layer conditions. The results indicate that the wall and roof pressure distributions can vary significantly from those of rectangular buildings. Owing to the increased number and complexity of corners, more separation zones are formed, leading to a higher likelihood of multiple simultaneous suction zones. A comparison with current wind provisions also revealed that, in several cases, the local and area-averaged pressures exceeded the recommended design guidelines. Further research is essential to develop a wind load database that encompasses a wider variety of building shapes and ultimately establishes nonrectangular building wind design guidelines.