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In the open literature, there are numerous studies on the normal and extreme (flood and drought) behavior of wet and dry periods based on the understanding of the standard precipitation index (SPI), which provides a series of categorizations by considering the standard normal (Gaussian) probability distribution function (PDF). The numerical meaning of each categorization assessment is quite lacking in terms of future predictions of wet and dry period duration based on historical records. This paper presents a new approach for calculating possible formations of future wet and dry period durations based on historical records through an effective fractal geometric forecasting approach. The essence of the proposed methodology is based on the number of dry periods (steps) of non-overlapping monthly duration along consecutive broken line paths in the SPI classification for wet and dry period durations. It has been observed that the plot of periods on double logarithmic paper falls along a straight line against the number of such periods, implying a power function, which is the essence of fractal geometry. Extending the empirically derived straight line provides the number of periods that may occur in the future over a range of SPI levels. This methodology is referred to as SPI fractal (SPIF), and the classic SPI classification is converted into SPIF wet and dry polygons, which provide additional information about the drought period number within a valid polygonal area, compared to the classic SPI results. The wet and dry period features of any hydro-meteorology time series are constrained in SPIF polygons. The application of the methodology was carried out on monthly rainfall records on the European side of the Istanbul Florya meteorological station in Turkey. [ABSTRACT FROM AUTHOR]

It is essential to establish a digital twin scene, which helps to depict the dynamically changing geographical environment accurately. Digital twins could improve the refined management level of intelligent tunnel construction; however, research on geographical twin models primarily focuses on modeling and visual description, which has low analysis efficiency. This paper proposes a knowledge-guided intelligent analysis method for the geometric deformation of tunnel excavation profile twins. Firstly, a dynamic data-driven knowledge graph of tunnel excavation twin scenes was constructed to describe tunnel excavation profile twin scenes accurately. Secondly, an intelligent diagnosis algorithm for geometric deformation of tunnel excavation contour twins was designed by knowledge guidance. Thirdly, multiple visual variables were jointly used to support scene fusion visualization of tunnel excavation profile twin scenes. Finally, a case was selected to implement the experimental analysis. The experimental results demonstrate that the method in this article can achieve an accurate description of objects and their relationships in tunnel excavation twin scenes, which supports rapid geometric deformation analysis of the tunnel excavation profile twin. The speed of geometric deformation diagnosis is increased by more than 90% and the cognitive efficiency is improved by 70%. The complexity and difficulty of the deformation analysis operation are reduced, and the diagnostic analysis ability and standardization of the geographic digital twin model are effectively improved. [ABSTRACT FROM AUTHOR]

In the approach of metric-based geometric parameterization, the concept of database filtration and proper orthogonal decomposition manipulation quantitatively enhances the generation of new geometric parameters so that the problem-oriented information is reflected in aerodynamic design. Compared with the conventional approach that applies only geometric filtration, this paper incorporates performance filtration so that the problem-oriented information is no longer limited to geometric constraints, thereby enabling the guidance of optimization direction in a more informed manner. This paper focuses on the pressure distribution of samples and their relationship with geometric variations. A variational autoencoder is employed to extract the dominant features of the aerodynamic potentials that an initial geometry can attain in optimization. The authors believe that the aerodynamic potential is reflected in how the pressure distribution differs from that of the initial geometry. Then, samples have to meet the performance filtration criterion based on pressure distribution proposed by designers according to their aerodynamic understanding of the optimization problem. Finally, the remaining collection of qualified samples generates new geometric parameters via proper orthogonal decomposition. The conventional and new approaches were validated in a two-dimensional airfoil case of drag coefficient optimization; the lift-to-drag ratio improved by 17.07% using the traditional method, and by 38.20% using the new approach. The pressure distribution shows that the performance filtration approach produces more supercritical properties than the geometric filtration approach. This implies that the performance filtration approach can capture more intricate details related to the aerodynamic performance of the airfoil. [ABSTRACT FROM AUTHOR]

Multi-packer completion strings have played a pivotal role in secure exploitation of oil and gas, increasing production and mitigating greenhouse gas emissions. While the integration of multi-packer structures has proven advantageous in oil and gas exploration, it has introduced complexities in load distribution, consequently giving rise to safety concerns. This study undertakes a thorough examination of the mechanical analysis pertaining to multi-packer completion strings. We present an analytical model for predicting the axial forces acting on the multi-packer string, utilizing the geometric constraint arising from the immobility of packers. It is demonstrated that the pressure differentials at the packers exhibit uniqueness in relation to both initial and boundary conditions, as well as the geometrical constraint. This paper provides an analytical solution for these pressure differentials. Novel concepts regarding the eigen-matrix of an N-packer completion string, influenced solely by Poisson's ratio, a virtual (N + 1) th packer and the eigen-depth and eigen-ratio of two adjacent packers, are proposed and their applications are discussed. Furthermore, this paper delves into a deeper examination of the multi-packer string's underlying mechanism. A consistent algorithm grounded in geometric analysis is developed based on the analytical model. Validation of our model is performed using three practical cases across various operation conditions, and the results demonstrate the efficacy of this methodology in accurately predicting failure occurrences. Sensitivity analysis results further substantiate the robustness of this method in practical applications. Additionally, it has been shown that strategically positioning the packers in areas where the string is highly prone to fractures significantly enhances the safety of the multi-packer string system. The findings presented in this paper offer a foundational framework for analyzing the mechanical behavior of constrained strings. Furthermore, there is potential for the development of the analytical model to incorporate additional factors, such as string system with packers of semi-free or free movement. The proposed method is also of fundamental significance for safety evaluation of string systems in carbon storage projects, which is obtaining increasing attention in the context of carbon neutralization. [ABSTRACT FROM AUTHOR]

In the context of extremely uneven sources and loads in China, several large‐scale power transmission systems have been established. Affected by the small equivalent impedance of the system, the increase of negative sequence currents during open‐phase operation has seriously threatened the stable operation of synchronous generators. The necessity of negative sequence current suppression is particularly prominent. To address the above issues, this paper analyzes the feasible negative sequence suppression capacity of the grid‐connected inverter under the principle of positive sequence priority. Using the geometric analysis method to determine the optimal suppression capacity. The none‐phase‐locked loop (PLL) control method is used to improve the response speed and form the negative sequence current suppression strategy adapted to the open‐phase operation period. A simulation model was built in PSCAD to verify the effectiveness of the proposed strategy. The result shows that the suppression strategy has a faster response than the conventional PLL control. In scenarios with large negative sequence currents to be suppressed, a maximum suppression effect of approximately 63% can be achieved. Compared with the traditional suppression capacity selection, the strategy in this paper can reduce the residual of negative sequence current by about 10% at most. The negative sequence currents intruding into the generator can be effectively suppressed without additional devices. [ABSTRACT FROM AUTHOR]

This paper provides another proof of Fermat's theorem. As in the previous work, a geometric approach is used, namely: instead of integers a, b, c, a triangle with side lengths a, b, c is considered. To preserve the completeness of the proof of the theorem in this work, the proof is repeated for the cases of right and obtuse triangles. In this case, the Fermat equation ap+bp = cp has no solutions for any natural number p > 2 and arbitrary numbers a, b, c. When considering the case when the numbers a, b, c are sides of an acute triangle, it is proven that Fermat's equation has no solutions for any natural number p > 2 and non-zero integer numbers a, b, c. Numbers a = k, b = k+m, c = k+n, where k, m, n are natural numbers that satisfy the inequalities n > m, n < k+m, exhaust all possible variants of natural numbers a, b, c, which are the sides of the triangle. In an acute triangle, the following condition is additionally satisfied: k > n -m + √2n(n - m). To study the Fermat equation, an auxiliary function f(k,p) = kp+(k+m)p-(k+n)p, is introduced, which is a polynomial of natural degree p in the variable k. The equation f(k, p) = 0 has a single positive root for any natural p = 2. A recurrent formula connecting the functions f(k,p+1) and f(k,p) has been proven: f(k,p+1) = kf(k, p)-[n(k+n)p-m(k+m)p]. The proof of the main proposition 2 is based on considering all possible relationships between the assumed integer solution of the equation f(k, p+1) = 0 and the number (ñ -m) corresponding to this solution k. The proof was carried out using the mathematical apparatus of number theory, elements of higher algebra and the foundations of mathematical analysis. These studies are a continuation of the author's works, in which some special cases of Fermat's theorem were proved. [ABSTRACT FROM AUTHOR]

Fault detection and isolation (FDI) problems for linear parameter-varying (LPV) systems with state time-delays are studied in this paper. By defining the concept of unobservability subspace and designing its calculation algorithm, the geometric approach is introduced to the time-delay LPV systems. Utilizing Wirtinger-based integral inequality, we obtain a sufficient condition to solve the so-called H∞-based residual generation problem for the LPV systems. In this paper, we consider two cases: the time delay is known and the time delay is unknown but its estimated value can be obtained. Corresponding observers are proposed for both cases based on the geometric approach and H∞ techniques. Lyapunov-Krasovskii functional is utilized to handle the time-delays and Wirtinger’s inequality is employed to reduce conservatism. Numerical examples are presented to demonstrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

The corrugated board is a versatile and durable material that is widely used in the packaging industry. Its unique structure provides strength and cushioning, while its recyclability and bio-degradability make it an environmentally friendly option. The strength of the corrugated board depends on many factors, including the type of individual papers on flat and corrugated layers, the geometry of the flute, temperature, humidity, etc. This paper presents a new approach to the analysis of the geometric features of corrugated boards. The experimental set used in the work and the created software are characterized by high reliability and precision of measurement thanks to the use of an identification procedure based on image analysis and a genetic algorithm. In the applied procedure, the thickness of each layer, corrugated cardboard thickness, flute height and center line are calculated. In most cases, the proposed algorithm successfully approximated these parameters. [ABSTRACT FROM AUTHOR]

Approximating Bézier curve by polygon is a traditional technique in computer-aided geometric design, and there are several methods for constructing such polygons. In this paper, we propose to approximate Bézier curve by the least square polygon (LSP). LSP was derived by least square fitting which minimizes the integral of approximating errors. We provide a closed formula for the vertices of LSP. Because of its optimization method, LSP has lower approximation errors than existing approximating polygons. This observation is verified by many numerical examples we tested and several typical examples are included in this paper. [ABSTRACT FROM AUTHOR]

This paper reports results on the classification of traveling wave solutions, including nonnegative traveling wave solutions in a weak sense, in the spatial 1D degenerate parabolic equation. These are obtained through dynamical systems theory and geometric approaches (in particular, Poincaré compactification). Classification of traveling wave solutions means enumerating those that exist and presenting properties of each solution, such as its profile and asymptotic behavior. The results examine a different range of parameters included in the equation, using the same techniques as discussed in the earlier work [Y. Ichida, Discrete Contin. Dyn. Syst., Ser. B, 28 (2023), no. 2, 1116-1132]. In a clear departure from this previous work, the classification results obtained in this paper and the successful application of the known transformation also yield results for the classification of (weak) nonnegative traveling wave solutions for spatial 1D porous medium equations with special nonlinear terms. Finally, the bifurcations at infinity occur in the two-dimensional ordinary differential equations that characterize these traveling wave solutions are shown. [ABSTRACT FROM AUTHOR]

The intrusion detection system is responsible for revealing different intrusion activities, including the denial of service, man-in-middle, Mirai, Scan, and other types of intrusion activities. It is used in many applications, including the smart home Internet of Things networks, where security risks threaten the privacy of individuals. In this context, many works were proposed for detecting and classifying the different types of attacks. However, many challenges are identified for this type of problem, such as the large amount of data available, the imbalanced nature of the data, and the quality of detection and classification outcomes. This paper aims to address these challenges by proposing an approach that considers a metaheuristic-based random weight neural network to detect intrusion activities and classify the different types and subtypes of activities. The following points summarize the contribution of this paper. First, the automatic tuning of the neural network parameters where the weights, biases, regularization value, the number of neurons, and the type of activation function are optimized by different metaheuristic algorithms to produce high-quality results. Second, the proposed approach adopts a clustering with reduction technique to tackle the challenge of processing large volumes of data. Third, oversampling the dataset is also embedded in the proposed approach to avoid a biased classification of the majority class. The experiments are conducted based on a large dataset with more than half a million instances. The results show that the proposed approach outperforms the other classification approaches in geometric mean (G-Mean) and has promising results. [ABSTRACT FROM AUTHOR]

In this paper we investigate a model for quantum gravity on finite noncommutative spaces using the theory of blobbed topological recursion. The model is based on a particular class of random finite real spectral triples (A,H,D,γ,J), called random matrix geometries of type (1,0), with a fixed fermion space (A,H,γ,J), and a distribution of the form e-S(D)dD over the moduli space of Dirac operators. The action functional S(D) is considered to be a sum of terms of the form ∏si=1Tr(Dni) for arbitrary s⩾1. The Schwinger-Dyson equations satisfied by the connected correlators Wn of the corresponding multi-trace formal 1-Hermitian matrix model are derived by a differential geometric approach. It is shown that the coefficients Wg,n of the large N expansion of Wn's enumerate discrete surfaces, called stuffed maps, whose building blocks are of particular topologies. The spectral curve (Σ,ω0,1,ω0,2) of the model is investigated in detail. In particular, we derive an explicit expression for the fundamental symmetric bidifferential ω0,2 in terms of the formal parameters of the model. [ABSTRACT FROM AUTHOR]

In this paper we present and provide a proof for a set of non-recursive formulae arising in the computation of the largest output-nulling and the smallest input-containing subspaces which have been used in a variety of contexts in the framework of the geometric approach. These expressions have been used in the literature both in the strictly proper and in the non-strictly proper case, but, to the best of our knowledge, a proof is still missing. These formulae are established here in the general possibly non-strictly proper case. Some ancillary side results of independent interest are also proposed. [ABSTRACT FROM AUTHOR]

Although deep learning has been proven to significantly outperform most traditional methods in the classification of large-scale balanced image datasets, collecting enough samples for defect classification is extremely time-consuming and costly. In this paper, we propose a lightweight defect classification method based on few-shot image generation and self-attention fused convolution features. We constructed a 4-class dataset using welding seam images collected from a solar cell module packaging production line. To address the issue of limited defect samples, especially for classes with less than 10 images, we implemented two strategies. Geometric enhancement techniques were first used to extend the defective images. Secondly, multi-scale feature fusion Generative Adversarial Networks (GANs) were utilized to further enhance the dataset. We then performed the feature-level fusion of convolution neural networks and self-attention networks, achieving a classification accuracy of 98.19%. Our experimental results demonstrate that the proposed model performs well in small sample defect classification tasks. And, it can be effectively applied to product quality inspection tasks in industrial production lines. [ABSTRACT FROM AUTHOR]

This paper reports results on the existence and characterization of nonnegative stationary solutions (including the weak sense) of a spatial one-dimensional degenerate parabolic equations. The characterization of stationary solutions given in this paper refers to the enumeration of those that exist and the presentation of solution information such as the profile and asymptotic behavior of each of them. Due to the influence of terms derived from the degeneracy of the equations, it is not easy to classify and characterize the existence of stationary solutions of the equations considered in this paper. These results are obtained by using dynamical systems theory and geometric approaches (in particular, Poincaré compactification). In addition, an application of the results obtained in this paper is given. The results of the characterization of nonnegative weak stationary solutions of the spatial one-dimensional porous medium equation with special nonlinear terms are shown. These can be obtained by carefully using transformations known from previous studies. [ABSTRACT FROM AUTHOR]

Because they are safe and easy to use, collaborative robots are revolutionizing many sectors, including industry, medicine, and agriculture. Controlling their dynamics, movements, and postures are key points in this evolution. Inverse kinematics is then crucial for robot motion planning. In 6R serial robots, achieving a desired pose is possible with different joint combinations. In this paper, our focus lies in studying forward and, mainly, inverse kinematics of the FANUC CRX-10iA cobot, a 6R cobotic arm with a non-spherical wrist. Its specific structural parameters implies that no analytical solutions exist except for some particular situations. FANUC does not provide the complete set of inverse kinematic solutions, even when 16 solutions are possible, only 8 of them are provided in Roboguide software. Furthermore, the existing literature on joints-to-workspace mapping for CRX cobots is currently very limited. It either lacks or provides partial or inconsistent inverse kinematics analysis. We present and detail a novel fully geometric method for numerically solving inverse kinematics meeting the requirement of high precision and a fast response. This approach provides both the exact number of inverse kinematics solutions and the sets of joint angles even for singular configuration. Its effectiveness was verified through simulations using the Roboguide Software and experimentation on the actual CRX-10iA cobot. Several examples (8, 12, or 16 inverse kinematic solutions) have enabled us to validate and prove the robustness and reliability of this geometric approach. [ABSTRACT FROM AUTHOR]

Masonry domes have always represented one of the most fascinating and daring architectural structures, with great symbolic relevance. However, their structural behaviour under environmental actions, such as earthquakes, has not yet been thoroughly investigated. This paper defines an interdisciplinary methodological approach, based on advanced digital survey techniques to evaluate constructive, geometrical, and structural aspects of historical domes. The applied procedure comprises the study of archival documents and diagnostic reports, in-situ analyses and advanced three-dimensional surveys, the development of simplified discrete-element-based structural models, and the performing of pushover analyses. The procedure is applied to a case study represented by the dome of the 'Badia di Sant'Agata' church in Catania, an earthquake-prone town located in Eastern Sicily. This church was built after the devastating 1693 earthquake and its dome represents one of the most significant examples among hundreds of masonry domes built in Sicily. The historical and constructive investigation showed that the dome was built without supporting formworks, by laying 21 concentric courses of limestone voussoirs on a peculiar springing ring made of mortared rubble stones. The numerical simulations highlighted that this peculiar ring affects the dome's failure mechanism and limits its displacement capacity and the maximum shear transferred to the substructure. [ABSTRACT FROM AUTHOR]

This paper provides a comprehensive analysis of recent advancements in additive manufacturing, a transformative approach to industrial production that allows for the layer-by-layer construction of complex parts directly from digital models. Focusing specifically on Directed Energy Deposition, it begins by clarifying the fundamental principles of metal additive manufacturing as defined by International Organization of Standardization and American Society for Testing and Materials standards, with an emphasis on laser- and powder-based methods that are pivotal to Directed Energy Deposition. It explores the critical process mechanisms that can lead to defect formation in the manufactured parts, offering in-depth insights into the factors that influence these outcomes. Additionally, the unique mechanisms of defect formation inherent to Directed Energy Deposition are examined in detail. The review also covers the current landscape of process evaluation and non-destructive testing methods essential for quality assurance, including both traditional and contemporary in situ monitoring techniques, with a particular focus given to advanced machine-vision-based methods for geometric analysis. Furthermore, the integration of process monitoring, multiphysics simulation models, and data analytics is discussed, charting a forward-looking roadmap for the development of Digital Twins in Laser–Powder-based Directed Energy Deposition. Finally, this review highlights critical research gaps and proposes directions for future research to enhance the accuracy and efficiency of Directed Energy Deposition systems. [ABSTRACT FROM AUTHOR]

The applications and understanding of Land-use Regulations (LuR) are more communicable when they are linked to the digital representation of the physical world. In order to support issuing a planning permit and move towards the establishment of automated planning permit checks, this paper investigates how LuRs related to a planning permit process can be modelled in 3D called 3D CityLuR. 3D CityLuR serves as a 3D model for representing LuRs' legal extents on a city scale. It is formed based on multiple geometric modelling approaches representing LuRs, which can provide a better cognitive understanding of LuRs and subsequently facilitate LuR automatic checks. To this purpose, according to LuRs' descriptions and characteristics explained in related planning documents, key parameters representing LuRs' extent are identified (e.g. maximum distance in overlooking or maximum allowed height in building height regulations). Accordingly, to automatically model each LuR, a geometric modelling approach (e.g. Boundary Representation (B-Rep), CSG, and extrusion) that best fits with the identified key parameters is proposed. In addition, to combine 3D CityLuR with an integrated BIM-GIS environment, the level of information need in terms of geometries and semantics is specified. Finally, the paper results in a showcase for five LuRs including building height, energy efficiency protection, overshadowing open space, overlooking, and noise impacts regulations. The showcase is a proof of concept for determining how these LuRs can be modelled in 3D and combined with 3D city models based on the selected geometric modelling approaches, identified parameters, and level of information need. [ABSTRACT FROM AUTHOR]

This paper considers the problem of finding maximum volume (axis-aligned) inscribed boxes in a compact convex set, defined by a finite number of convex inequalities, and presents optimization and geometric approaches for solving them. Several optimization models are developed that can be easily generalized to find other inscribed geometric shapes such as triangles, rhombi, and squares. To find the largest volume axis-aligned inscribed rectangles in the higher dimensions, an interior-point method algorithm is presented and analyzed. For two-dimensional space, a parametrized optimization approach is developed to find the largest area (axis-aligned) inscribed rectangles in convex sets. The optimization approach provides a uniform framework for solving a wide variety of relevant problems. Finally, two computational geometric (1−ε) –approximation algorithms with sublinear running times are presented that improve the previous results. History: Accepted by Antonio Frangioni, Area Editor for Design & Analysis of Algorithms—Continuous. Funding: The author is grateful for the support of Northeastern University for this research. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information (https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0239) as well as from the IJOC GitHub software repository (https://github.com/INFORMSJoC/2022.0239). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/. [ABSTRACT FROM AUTHOR]

The selection of the optimal methodology for the 3D geometric documentation of cultural heritage is a subject of high concern in contemporary scientific research. As a matter of fact, it requires a multi-source data acquisition process and the fusion of datasets from different sensors. This paper aims to demonstrate the workflow for the proper implementation and integration of geodetic, photogrammetric and laser scanning techniques so that high-quality photorealistic 3D models and other documentation products can be generated for a complicated, large-dimensional architectural monument and its surroundings. As a case study, we present the monitoring of the Mehmet Bey Mosque, which is a landmark in the city of Serres and a significant remaining sample of the Ottoman architecture in Greece. The surveying campaign was conducted in the context of the 2022–2023 annual workshop of the Interdepartmental Program of Postgraduate Studies "Protection Conservation and Restoration of Cultural Monuments" of the Aristotle University of Thessaloniki, and it served as a geometric background for interdisciplinary cooperation and decision-making on the monument restoration process. The results of our study encourage the fusion of terrestrial laser scanning and photogrammetric datasets for the 3D modeling of the mosque, as they supplement each other as regards geometry and texture. [ABSTRACT FROM AUTHOR]

The precision of workpiece machining is critically influenced by the geometric errors in the kinematics of grind robots, which directly affect their absolute positioning accuracy. To tackle this challenge, this paper introduces a logistic-tent chaotic mapping Levenberg Marquardt algorithm designed to accurately identify and compensate for this geometric error. the approach begins with the construction of a forward kinematic model and an error model specific to the robot. Then the algorithm is adopted to identify and compensate for the geometric error. The method establishes a mapping interval around the initial candidate solutions derived from iterative applications of the Levenberg Marquardt algorithm. Within this interval, the logistic-tent chaotic mapping method generates a diverse set of candidate solutions. These candidates are evaluated based on their fitness values, with the optimal solution selected for subsequent iterations. Empirical compensation experiments have validated the proposed method's precision and effectiveness, demonstrating a 6% increase in compensation accuracy and a 47.68% improvement in efficiency compared to existing state-of-the-art approaches. This process not only minimizes the truncation error inherent in the Levenberg Marquardt algorithm but also significantly enhances solution efficiency. Moreover, simulation experiments on grind processes further validate the method's ability to significantly improve the quality of workpiece machining. [ABSTRACT FROM AUTHOR]

Compared with large enterprises, the development scale and organizational structure of small and medium-sized enterprises are insufficient, which brings certain limitations to the development of small and medium-sized enterprises in China. In order to promote the long-term development of small and medium-sized enterprises in the new era, it is necessary to require enterprise leaders to innovate marketing plans, strengthen risk management of enterprises, and enhance their strength in market competition. The market risk evaluation of small and medium sized enterprises (SMSEs) in the new era is a multiple-attribute decision-making (MADM). The IVIFSs are employed as the tool for portraying uncertain information during the market risk evaluation of SMSEs in the new era. In this paper, the interval-valued intuitionistic fuzzy (IVIF) Hamacher interactive power geometric (IVIFHIPG) technique is addressed based on IVIF Hamacher interactive weighted geometric (IVIFHIWG) technique and power geometric (PG) technique. Some properties of IVIFHIPG technique were addressed. Then, the IVIFHIPG technique is employed to manage MADM under IVIFSs. Finally, an example for market risk evaluation of SMSEs in the new era is employed to verify the IVIFHIPG technique. Thus, the main contributions of this paper are addressed: (1) the IVIFHIPG technique is addressed based on IVIFHIWG technique and PG technique; (2) the IVIFHIPG technique is came up with to manage the MADM under IVIFSs; (3) a numerical example for market risk evaluation of SMSEs in the new era has been came up with to show the IVIFHIPG technique; and (4) some comparative analysis is addressed to verify the I IVIFHIPG technique. [ABSTRACT FROM AUTHOR]

This paper presents a comprehensive review of mitigation approaches, with a specific focus on geometric modifications, to mitigate shaft voltage and bearing current in electric drives. While existing literature extensively covers inverter-based and coupling path-based methods, the potential of geometric modifications has been relatively underexplored. The geometric modification approach offers a cost-effective and weight-saving solution that can be incorporated during the early design phase of the machine. The review begins by outlining various mitigation techniques applied at the victim machine, including bearing insulation, ceramic ball bearings, shaft grounding, and more. Subsequently, it delves into the machine geometric modification approach, examining methods related to winding design, stator and rotor iron geometry, rotor surface insulation, and stator slot wedge modifications. The paper highlights the practical relevance of geometric modifications, emphasizing their advantages over conventional methods. The review paper aims to shed new light on the potential of geometric modifications in mitigating shaft voltage and bearing current in electric drives. By providing valuable insights into this approach, researchers and engineers can develop robust and efficient electric drive systems, advancing the field of electrical machine design and operation. [ABSTRACT FROM AUTHOR]

The application of contemporary artificial intelligence techniques to address geometric problems and automated deductive proofs has always been a grand challenge to the interdisciplinary field of mathematics and artificial intelligence. This is the fourth article in a series of our works, in our previous work, we established a geometric formalized system known as FormalGeo. Moreover, we annotated approximately 7000 geometric problems, forming the FormalGeo7k dataset. Despite the fact that FGPS (Formal Geometry Problem Solver) can achieve interpretable algebraic equation solving and human-like deductive reasoning, it often experiences timeouts due to the complexity of the search strategy. In this paper, we introduced FGeo-TP (theorem predictor), which utilizes the language model to predict the theorem sequences for solving geometry problems. The encoder and decoder components in the transformer architecture naturally establish a mapping between the sequences and embedding vectors, exhibiting inherent symmetry. We compare the effectiveness of various transformer architectures, such as BART or T5, in theorem prediction, and implement pruning in the search process of FGPS, thereby improving its performance when solving geometry problems. Our results demonstrate a significant increase in the problem-solving rate of the language model-enhanced FGeo-TP on the FormalGeo7k dataset, rising from 39.7% to 80.86%. Furthermore, FGeo-TP exhibits notable reductions in solution times and search steps across problems of varying difficulty levels. [ABSTRACT FROM AUTHOR]

This paper introduces an efficient numerical method for approximating solutions to geometric boundary value problems. We propose the multiplicative sinc–Galerkin method, tailored specifically for solving multiplicative differential equations. The method utilizes the geometric Whittaker cardinal function to approximate functions and their geometric derivatives. By reducing the geometric differential equation to a system of algebraic equations, we achieve computational efficiency. The method not only proves to be computationally efficient but also showcases a valuable symmetric property, aligning with inherent patterns in geometric structures. This symmetry enhances the method's compatibility with the often-present symmetries in geometric boundary value problems, offering both computational advantages and a deeper understanding of geometric calculus. To demonstrate the reliability and efficiency of the proposed method, we present several examples with both homogeneous and non-homogeneous boundary conditions. These examples serve to validate the method's performance in practice. [ABSTRACT FROM AUTHOR]

The connection between contextuality and graph theory has paved the way for numerous advancements in the field. One notable development is the realization that sets of probability distributions in many contextuality scenarios can be effectively described using well-established convex sets from graph theory. This geometric approach allows for a beautiful characterization of these sets. The application of geometry is not limited to the description of contextuality sets alone; it also plays a crucial role in defining contextuality quantifiers based on geometric distances. These quantifiers are particularly significant in the context of the resource theory of contextuality, which emerged following the recognition of contextuality as a valuable resource for quantum computation. In this paper, we provide a comprehensive review of the geometric aspects of contextuality. Additionally, we use this geometry to define several quantifiers, offering the advantage of applicability to other approaches to contextuality where previously defined quantifiers may not be suitable. This article is part of the theme issue 'Quantum contextuality, causality and freedom of choice'. [ABSTRACT FROM AUTHOR]

The United Nations' Human Development Index remains a widely used and accepted measure of human development. Although it has been revised over the years to address various critiques, a remaining concern is the way the three dimensions are aggregated into the single index. A deterioration in one dimension can be compensated for by an improvement in another. Since compensability is inextricably linked with trade-offs and intensity of preferences, a non-compensatory (i.e., Condorcet) approach to aggregation is employed in this paper. Although non-compensatory approaches have been employed previously, this paper adds to the literature by undertaking an application of the Condorcet approach to the entire HDI. This approach, which does not use intensities of preferences, ensures that the degree of compensability connected with the aggregation model is at the minimum possible level. To achieve this, country level rankings are then compared to those for the 2020 Human Development Index which aggregates dimensions using a geometric mean. The findings demonstrated substantial changes in rank-order between the HDI and Condorcet approach. This outcome provides empirical evidence which demonstrates that the non-compensatory Condorcet approach can mitigate issues of compensation present within the geometric aggregation technique currently employed by the HDI. These findings have potential implications in aiding the identification and employment of potential policy priorities—specifically, the notion that policy should emphasise the development of a country as opposed to economic growth alone. [ABSTRACT FROM AUTHOR]

This paper analyses a general qualitative depiction of changes in the configuration of the non-linear model of a tractor-semitrailer with excessive turnability under stationary circular motions within a broad range of control parameters, such as the longitudinal velocity of motion and angle of rotation of the wheels of the controlled unit. It allows us to foresee the jackknifing effect and to estimate the conditions necessary for safe travel. The proposed analysis combines the transparent geometric approach to analyse the configuration of a tractor-semitrailer, which was developed earlier by J.P. Pauwelussen, and the ability to investigate real bifurcations of the non-linear equation of handling and the non-linear equation of folding angle tractor-semitrailer analytically. Based on this approach, we obtain new analytical dependencies that determine the boundaries of divergent loss of stability of the entire manifold of stationary states of a tractor-semitrailer model and estimates of the maximum values of the angle of folding under different values of the vehicle's longitudinal velocity. This is achieved without the prior determination of the manifold of stationary states itself. [ABSTRACT FROM AUTHOR]

Recent days point clouds have become one of the most common 3D sources of information which is provides accurate geometry features of the object. 3D point clouds can be derived from either photogrammetry, Lidar or SAR in some cases depending upon the application. These point clouds consisting of 3D geospatial location of an object in form of XYZ coordinates which can be used in various ways to deduct information related to that object either based on visualisation or geometrical interpretation. Quality assessment standards for these point clouds are still very much in nascent stage with optimum accuracy in relative terms only. In this paper, multiple scale of point cloud has been used to understand the level of information these clouds consist on these multiple scales. Based on the 3D spatial information of these point cloud in local neighbourhood, some of invariant geometric properties can be computed for each 3D point with respective covariance matrix. These can be used to describe the local 3D structure using eigenvalues for these matrices. Using these Geometric features an approach is developed to understand the point cloud quality assessment. The proposed methodology exploits these special geometric properties to evaluate the 3D scene structure. Further, the point cloud is classified using shape detection algorithm which evaluates the geometric features to detect the mathematical shapes in the point cloud. This paper also enlightens on different geometric features that can be extracted from a point cloud and the importance of it. [ABSTRACT FROM AUTHOR]

In this paper, we consider the power allocation problem for 5 G wireless networks using massive multiple input multiple output technologies. Two non-linear optimization models are considered to maximize the worst user signal-to-interference noise ratio and the total capacity of the network subject to power constraints. In particular, we transform the first one into a geometric programming (GP) problem. Whereas the second one leads to a signomial programming formulation. The main contributions of the paper are first to propose novel formulations for power allocation in wireless networks while using stochastic, geometric, and signomial programming frameworks altogether. We derive stochastic formulations for each GP model to deal with the uncertainty of wireless channels. Secondly, since solving optimally the stochastic models represents a challenging task, we obtain tight bounds using approximation solution methods. In particular, the piece-wise linear programming and the sequential approximation methods allow us to obtain tight intervals for the objective function values of the stochastic models. Notice that these intervals contain the optimal solutions. In particular, we propose an approximated GP model that allows obtaining lower bounds for the signomial problem. This is achieved by using the arithmetic–geometric mean inequality. Finally, we compare the deterministic and stochastic models and prove the robustness of the stochastic models. Notice that we solve all the instances and obtain near-optimal solutions for most of them. [ABSTRACT FROM AUTHOR]

This paper considers the problem of understanding the exit time for trajectories of gradient-related first-order methods from saddle neighborhoods under some initial boundary conditions. Given the 'flat' geometry around saddle points, first-order methods can struggle to escape these regions in a fast manner due to the small magnitudes of gradients encountered. In particular, while it is known that gradient-related first-order methods escape strict-saddle neighborhoods, existing analytic techniques do not explicitly leverage the local geometry around saddle points in order to control behavior of gradient trajectories. It is in this context that this paper puts forth a rigorous geometric analysis of the gradient-descent method around strict-saddle neighborhoods using matrix perturbation theory. In doing so, it provides a key result that can be used to generate an approximate gradient trajectory for any given initial conditions. In addition, the analysis leads to a linear exit-time solution for gradient-descent method under certain necessary initial conditions, which explicitly bring out the dependence on problem dimension, conditioning of the saddle neighborhood, and more, for a class of strict-saddle functions. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of quantifying parametric uncertainty in classical empirical interatomic potentials (IPs) using both Bayesian (Markov Chain Monte Carlo) and frequentist (profile likelihood) methods. We interface these tools with the Open Knowledgebase of Interatomic Models and study three models based on the Lennard-Jones, Morse, and Stillinger–Weber potentials. We confirm that IPs are typically sloppy, i.e., insensitive to coordinated changes in some parameter combinations. Because the inverse problem in such models is ill-conditioned, parameters are unidentifiable. This presents challenges for traditional statistical methods, as we demonstrate and interpret within both Bayesian and frequentist frameworks. We use information geometry to illuminate the underlying cause of this phenomenon and show that IPs have global properties similar to those of sloppy models from fields, such as systems biology, power systems, and critical phenomena. IPs correspond to bounded manifolds with a hierarchy of widths, leading to low effective dimensionality in the model. We show how information geometry can motivate new, natural parameterizations that improve the stability and interpretation of uncertainty quantification analysis and further suggest simplified, less-sloppy models. [ABSTRACT FROM AUTHOR]

Accurate identification and segmentation of individual tree points are crucial for assessing forest spatial distribution, understanding tree growth and structure, and managing forest resources. Traditional methods based on Canopy Height Models (CHM) are simple yet prone to over- and/or under-segmentation. To deal with this problem, this paper introduces a novel approach that combines marker-controlled watershed segmentation with a spectral clustering algorithm. Initially, we determined the local maxima within a series of variable windows according to the lower bound of the prediction interval of the regression equation between tree crown radius and tree height to preliminarily segment individual trees. Subsequently, using this geometric shape analysis method, the under-segmented trees were identified. For these trees, vertical tree crown profile analysis was performed in multiple directions to detect potential treetops which were then considered as inputs for spectral clustering optimization. Our experiments across six plots showed that our method markedly surpasses traditional approaches, achieving an average Recall of 0.854, a Precision of 0.937, and an F1-score of 0.892. [ABSTRACT FROM AUTHOR]

Structural deformation is ubiquitous throughout geological history. For a mineral deposit that underwent structural deformation after its formation, its geological architecture may have been severely distorted from its original geometry. Due to lack of concern for this fact, the effectiveness of existing mineral prospectivity methods could be limited in areas that experienced structural deformation. This paper proposes a three-dimensional (3D) mineral prospectivity modeling method with geometric restoration. An energy-based geometric restoration approach is presented to restore the existing geometry of geological architecture to the original one according to a series of prior constraints. To represent the original ore-forming environment, the original mineralization distribution and the predictor variables are estimated from the restored 3D geological models. Then, Random Forest is applied to build the mineral prospectivity model that associates predictor variables with the original mineralization distribution. The proposed method was applied to the world-class Jinchuan Ni–Cu–(PGE) sulfide deposit, which underwent significant off-fault deformation after its formation. It was found that, by restoration of the geometry of geological objects and the mineralization distribution, the predictor variables are more reasonable and significant to indicate spatial associations to the mineralization at Jinchuan. This led to a more accurate prospectivity model with superior evaluation metrics (AUCs, F1 scores, kappa coefficients, and PR curves, etc.) compared with the prospectivity model built without geometric restoration. Therefore, 3D mineral prospectivity modeling with geometric restoration is probably much more effective and reliable in quantifying spatial associations with mineralization and in targeting subsurface orebodies in areas that underwent structural deformation. [ABSTRACT FROM AUTHOR]

In this paper, we propose the application of a new geometric procedure in order to calculate a set of transmission zeros of a propagation environment. Since the transmission zeros play a crucial role in modern communication systems, there is a need to apply the efficient solutions characterized by a maximum speed operation. It turns out that the classical method based on the Smith–McMillan factorization is time-consuming, so its contribution to the detection of transmission zeros could be unsatisfactory. Therefore, in order to fill the gap, we present a new algorithm strictly dedicated to the multivariable telecommunications systems described by the transfer-function approach. Consequently, a set of new achievements resulted, particularly in terms of computational efforts. Indeed, the proposed procedure allows us to overcome obstacles derived from technological limitations. The representative simulation examples confirm the great potential of this new method. Finally, it has been pointed out that the newly introduced geometric-originated approach has significantly reduced the computational burden. Indeed, for the randomly selected matrix of the 5 × 5 dimension describing the sensor-related propagation environment, two representative scenarios were performed in order to manifest the crucial properties. In the first scenario, the sets of multiple transmission zeros were analyzed, ultimately leading to intriguing results. The Smith–McMillan solution took three times longer to discover the mentioned sets. On the other hand, the second instance brought us the same result. Naturally, the discussed difference has increased as a function of the number of matrix elements. For the square matrices involving 100 components, we have observed the respective differences, both over Q I = 100 and Q I I = 60 . It should be emphasized that the finding derived from the Smith–McMillan factorization corresponds to the geometric-related approach in the context of some mechanisms. This is particularly visible when appointing the greatest common divisors. [ABSTRACT FROM AUTHOR]

This paper proposes and analyzes a novel efficient high-order finite volume method for the ideal magnetohydrodynamics (MHD). As a distinctive feature, the method simultaneously preserves two critical physical constraints: a discretely divergence-free (DDF) constraint on the magnetic field and the positivity-preserving (PP) property, which ensures the positivity of density, pressure, and internal energy. To enforce the DDF condition in each cell, we design a new discrete projection approach that projects the reconstructed point values at the cell interface into a DDF space, without using any approximation polynomials. This projection method is highly efficient, easy to implement, and particularly suitable for the high-order finite volume methods that return only the point values (no explicit approximation polynomials) in the reconstruction. Moreover, we also develop a new finite volume framework for constructing provably PP schemes for the ideal MHD system. The framework comprises the discrete projection technique, a suitable approximation to the Godunov--Powell source terms, and a simple PP limiter. We provide rigorous analysis of the PP property of the proposed finite volume method, demonstrating that the DDF condition and the proper approximation to the source terms eliminate the impact of magnetic divergence terms on the PP property. The analysis is challenging due to the internal energy function's nonlinearity and the intricate relationship between the DDF and PP properties. To address these challenges, we adopt the recently developed geometric quasilinearization approach [K. Wu and C.-W. Shu, SIAM Rev., 65 (2023), pp. 1031--1073], which transforms a nonlinear constraint into a family of linear constraints. Finally, we validate the effectiveness of the proposed method through several benchmark and demanding numerical examples. The results demonstrate that the proposed method is robust, accurate, and highly effective, confirming the significance of the proposed DDF projection and PP techniques. [ABSTRACT FROM AUTHOR]

This paper presents a geometric approach to solve the inverse kinematics for an anthropomorphic robotic arm with seven degrees of freedom (DoF). The proposal is based on conformal geometric algebra (CGA), by which many geometric primitives can be operated naturally and directly. CGA allows for the intersection of geometric entities such as two or more spheres or a plane's projection over a sphere. Rigid transformations of such geometric entities are performed using only one operation through another geometric entity called a motor. CGA imposes geometric restrictions on the inverse kinematics solution, which avoids computation of the forward kinematics or other numerical solutions, unlike traditional approaches. Comparisons with state-of-the-art algorithms are included to prove our algorithm's superior performance: such as decreased execution time and errors of the end-effector for a series of desired poses. [ABSTRACT FROM AUTHOR]

The complete and accurate acquisition of geometric information forms the bedrock of maintaining high-end instrument performance and monitoring product quality. It is also a prerequisite for achieving the 'precision' and 'intelligence' that the manufacturing industry aspires to achieve. Industrial microscopes, known for their high accuracy and resolution, have become invaluable tools in the precision measurement of small components. However, these industrial microscopes often struggle to demonstrate their advantages when dealing with complex shapes or large tilt angles. This paper introduces a ray-tracing model for point autofocus microscopy, and it provides the quantified relationship formula between the maximum acceptable tilt angle and the beam offset accepted in point autofocus microscopy, then analyzing the maximum acceptable tilt angle of the objects being measured. This novel approach uses the geometric features of a high-precision reference sphere to simulate the tilt angle and displacement of the surface under investigation. The research findings show that the maximum acceptable tilt angles of a point autofocus microscope vary across different measured directions. Additionally, the extent to which the maximum acceptable tilt angles are affected by the distances of the beam offset also varies. Finally, the difference between the experiment results and the theoretical results is less than 0.5°. [ABSTRACT FROM AUTHOR]

Geometric numerical integration has recently been exploited to design symplectic accelerated optimization algorithms by simulating the Bregman Lagrangian and Hamiltonian systems from the variational framework introduced by Wibisono et al. In this paper, we discuss practical considerations which can significantly boost the computational performance of these optimization algorithms and considerably simplify the tuning process. In particular, we investigate how momentum restarting schemes ameliorate computational efficiency and robustness by reducing the undesirable effect of oscillations and ease the tuning process by making time-adaptivity superfluous. We also discuss how temporal looping helps avoiding instability issues caused by numerical precision, without harming the computational efficiency of the algorithms. Finally, we compare the efficiency and robustness of different geometric integration techniques and study the effects of the different parameters in the algorithms to inform and simplify tuning in practice. From this paper emerge symplectic accelerated optimization algorithms whose computational efficiency, stability and robustness have been improved, and which are now much simpler to use and tune for practical applications. [ABSTRACT FROM AUTHOR]

Summary: A general, rectangular kernel matrix may be defined as Kij=κ(xi,yj)$$ {K}_{ij}=\kappa \left({x}_i,{y}_j\right) $$ where κ(x,y)$$ \kappa \left(x,y\right) $$ is a kernel function and where X={xi}i=1m$$ X={\left\{{x}_i\right\}}_{i=1}^m $$ and Y={yi}i=1n$$ Y={\left\{{y}_i\right\}}_{i=1}^n $$ are two sets of points. In this paper, we seek a low‐rank approximation to a kernel matrix where the sets of points X$$ X $$ and Y$$ Y $$ are large and are arbitrarily distributed, such as away from each other, "intermingled", identical, and so forth. Such rectangular kernel matrices may arise, for example, in Gaussian process regression where X$$ X $$ corresponds to the training data and Y$$ Y $$ corresponds to the test data. In this case, the points are often high‐dimensional. Since the point sets are large, we must exploit the fact that the matrix arises from a kernel function, and avoid forming the matrix, and thus ruling out most algebraic techniques. In particular, we seek methods that can scale linearly or nearly linearly with respect to the size of data for a fixed approximation rank. The main idea in this paper is to geometrically select appropriate subsets of points to construct a low rank approximation. An analysis in this paper guides how this selection should be performed. [ABSTRACT FROM AUTHOR]

In the geomatics domain the use of deep learning, a subset of machine learning, is becoming more and more widespread. In this context, the 3D semantic segmentation of heritage point clouds presents an interesting and promising approach for modelling automation, in light of the heterogeneous nature of historical building styles and features. However, this heterogeneity also presents an obstacle in terms of generating the training data for use in deep learning, hitherto performed largely manually. The current generally low availability of labelled data also presents a motivation to aid the process of training data generation. In this paper, we propose the use of approaches based on geometric rules to automate to a certain degree this task. One object class will be discussed in this paper, namely the pillars class. Results show that the approach managed to extract pillars with satisfactory quality (98.5% of correctly detected pillars with the proposed algorithm). Tests were also performed to use the outputs in a deep learning segmentation setting, with a favourable outcome in terms of reducing the overall labelling time (−66.5%). Certain particularities were nevertheless observed, which also influence the result of the deep learning segmentation. [ABSTRACT FROM AUTHOR]

This paper reports results on the existence, shapes, and asymptotic behavior of positive radially symmetric stationary solutions for several models of chemotaxis in higher dimensions. The systems treated in this paper are the simplest parabolic-elliptic Keller-Segel model and the simplest attraction-repulsion chemotaxis system, in which a positive-valued (resp. negative-valued) solution of one is a negative-valued (resp. positive-valued) solution of the other from symmetry. In particular, the construction of functions satisfying equations that diverge at the endpoints of finite intervals is an interesting result. The key to the discussion is to derive a scalar equation by using a transformation on the averaged mass for the equation satisfied by the radially symmetric stationary solution and to investigate the infinity dynamics as geometric information for the two-dimensional ordinary differential equations derived from it. To achieve this, we use a method that combines classical results from the continuous dynamical systems theory and Poincaré-Lyapunov compactification. In addition, the results for singular solutions are discussed in light of the results of previous studies. [ABSTRACT FROM AUTHOR]

This paper presents a geometric approach to pitch estimation (PE) – an important problem in music information retrieval (MIR), and a precursor to a variety of other problems in the field. Though there exist a number of highly accurate methods, both mono-pitch estimation and multi-pitch estimation (particularly with unspecified polyphonic timbre) prove computationally and conceptually challenging. A number of current techniques, while incredibly effective, are not targeted towards eliciting the underlying mathematical structures that underpin the complex musical patterns exhibited by acoustic musical signals. Tackling the approach from both theoretical and experimental perspectives, we present a novel framework, a basis for further work in the area, and results that (while not state of the art) demonstrate relative efficacy. The framework presented in this paper opens up a completely new way to tackle PE problems and may have uses both in traditional analytical approaches as well as in the emerging machine learning (ML) methods that currently dominate the literature. [ABSTRACT FROM AUTHOR]

We present an approach to extend the functionality and the use of kernel machines in image processing applications. We introduce a novel way to design spatial kernel machines with spatial properties and demonstrate how those newly introduced spatial properties enhance the possibilities of the use of kernel machines in image processing applications as a proof of concept. In this paper, we demonstrate four particular extensions: 1) how to model shapes efficiently with spatially computed kernel parameters in a geometrically scalable way; 2) how to visualize the kernel parameters precisely and intuitively on binary 2D shapes; 3) how to construct a one-class classifier from the binary classifier in a straightforward manner without re-training; and 4) how to use the computed kernel parameters for filtering. The existing literature on kernel machines mostly focuses on estimating the optimal kernel parameters via additional cost function(s). In this paper, instead of employing an additional cost function to estimate the kernel-related parameters, we investigate on an analytical solution to predict the actual kernel parameters locally and show how to build a spatial kernel machine with our analytical approach. Classical kernel machines do not perform well on precise shape modeling with a low number of support vectors as demonstrated in this paper. However, we demonstrate and visualize that our analytical approach provides a natural means to relate the kernel parameters to the 2D shapes for sparse shape modeling, where the shape boundary represents the decision boundary. For that, we incorporate the selected kernel function’s geometric properties as an additional constraint into the classifier’s optimization problem by defining an easy-to-explain and intuitive concept: similarity domains. In our experiments, we study and demonstrate how the resulting new kernel machine enhances the capabilities of the classical kernel machines with applications on shape modeling, (geometrically) scaling the non-linear decision boundary at various scales and precise visualization of the kernel parameters in 2D images. [ABSTRACT FROM AUTHOR]

In the conventional practice of producing noncentrifugal sugar (NCS), many technologies are available for juice evaporation, all of which may not be sustainable. The sustainability of these units is dependent on multiple criteria belonging to resources, technical, economic, process‐output, and environmental parameters. This paper presents the work undertaken to identify the most sustainable juice evaporation unit (to produce NCS) among 10 alternatives using three multicriteria evaluation (MCE) techniques, namely TOPSIS, PROMETHEE II, and VIKOR. The analyses were based on 11 evaluation criteria covering four sustainability elements. Analytic hierarchy process (AHP) and entropy weight approaches were used to assess the importance of each criterion for the ranking of evaporation units. The necessary data were obtained from three different decision‐maker groups, namely academics and sustainability promoters, NCS manufacturers, and NCS plant suppliers. The resulting criteria weights indicate that capital cost (with AHP analysis based weights as 16.81, 12.51, 15.30% for decision‐makers groups I, II, III, and a weight of 23.28% from entropy method) is found to be the most crucial criterion. With assessment values of 0.741, 0.186, and 0.048 in TOPSIS, PROMETHEE II, and VIKOR, respectively, "single pan with the improved furnace" emerged to be the most sustainable option. This result is also substantiated by a group priority index of 1.08 obtained through the geometric mean method of analysis. This suggests that "single pan with the improved furnace" is the most sustainable one for NCS production. Furthermore, sensitivity analyses undertaken indicate that "single pan with the improved furnace" is most and least sensitive to "greenhouse emissions" and "process time," respectively. With these outcomes, this paper demonstrates that the methodology adopted herein could be considered for assessing the sustainability of other process units involved in NCS production. Practical Applications: In the conventional practice of producing NCS, there are various technologies available for the evaporation of juice. This paper narrates the MCE‐based work to identify a sustainable juice evaporation unit. It can be suggested that the most sustainable unit is "single pan with improved furnace" and the least sustainable is "multi‐effect evaporator." The results of the present analysis suggested that the use of the other nine units for the production of NCS is to be subjected to thorough scrutiny, specifically regarding their sustainability. The methodology taken up for this analysis could be extended for other subprocesses in the NCS production process line to get the most sustainable process line. [ABSTRACT FROM AUTHOR]

Following on our earlier single‐station, 2‐dimensional (2D) broadband interferometric mapping and polarization (BIMAP) observations of lightning discharges, we recently deployed two BIMAP stations at Los Alamos National Laboratory to map the lightning sources and their polarization in full 3‐dimensional (3D) space (BIMAP‐3D). The two stations are separated by 11.5‐km and each station consists of four antenna sets (instead of three for the original BIMAP) that form a Y‐shaped array for improved interferometric performance. In this paper, we report the BIMAP‐3D system design, a generalized and analytical 2D interferometry technique for noncoplanar antenna array, a two‐stage 3D mapping technique based on geometric triangulation and baseline‐based differential time of arrival, and a technique to reconstruct the polarization orientation in 3D space by combining the 2D polarization results from the two‐station observations. Along with description of the techniques, we demonstrate and discuss the initial lightning results, including 3D maps for a hybrid intracloud and cloud‐to‐ground flash and for a normal intracloud flash, development of abnormal K‐change leaders, and polarization signatures for a K‐change leader. We find that with the two‐stage 3D mapping techniques, the sources can be located to meters accuracy for a favorable event that occurs between the two stations. We also find the polarization vectors for the example K leader are mostly orthogonal to the leader channel after the full 3D polarization analysis. The main purpose of this paper is to report the BIMAP‐3D techniques and capabilities. Detailed analysis of more specific discharge processes will be reported in later studies. Plain Language Summary: A new 3‐dimensional broadband radio frequency interferometric mapping and polarization system (BIMAP‐3D) is developed and deployed at Los Alamos National Laboratory for lightning research. BIMAP‐3D provides an unprecedented capability in high‐resolution, time‐evolving 3D lightning source mapping and 3D source polarization detection for detailed study of lightning discharge physics. In this research, we described the BIMAP‐3D system, introduced a suite of advanced data processing techniques, and demonstrated BIMAP‐3D's capabilities with actual lightning observations. This new capability is expected to lead to a range of new understandings and discoveries for a variety of lightning discharge processes. Key Points: A new 3D broadband interferometric mapping and polarization system for lightning study is introducedA suite of new data process algorithms is reported, and 3D lightning results for overall flashes and K‐change leaders are demonstratedPolarization orientations for a K‐change leader are found mostly orthogonal to the leader channel [ABSTRACT FROM AUTHOR]

In the past 20 years, Lebai gully (Linzhi, Tibet, China) has been affected by several debris flow events. These debris flow events caused the blockage of three-quarters of the river channel at the mouth of the Lebai gully, threatening thousands of acres of cultivated land, houses, and residents' property in the upper reaches of the Yarlung Tsangpo River. However, few investigations have been carried out on the debris flows in the Lebai gully, and the triggering mechanism of Lebai debris flows remains elusive. In this paper, we presented a detailed demonstration of the geological environment and geomorphological features of the Lebai Basin, and a detailed geohazard history of the Lebai gully was collected and presented based on interviews with local villagers. To provide information on the lithological, hydrological, and geotechnical characteristics of the terrain in Lebai gully, the electrical resistivity tomography (ERT) method was carried out to research the subsurface characteristics of debris flow fans. The ERT results illustrated the two-layered vertical strata of the debris fan, and the shallow layer of relatively low resistivity, which has thicknesses of 5–18 m, could be described as Quaternary colluvial deposits, while the deep layer of relatively high resistivity could be considered Precambrian bedrock. Taking a relatively large-scale debris flow on August 20, 2003, as an example, a detailed discussion was carried out on the possible factors triggering this event, and it was found that the Lebai debris flows were closely related to pre-event rainfall, air temperature, and antecedent earthquakes. Moreover, with the intention of evaluating the future risk of river blockage and helping to make rational decisions on developing suitable mitigation measures, the unstable deposits found in field investigations were generalized to geometric models according to their geometric characteristics, and the volumes of these unstable materials in each location were estimated using digital elevation models and geometric spatial analysis methods. A dynamic model named RAMMS was used to predict these unstable materials' dynamic processes and final deposit characteristics. The simulation results revealed a great possibility that the Yarlung Tsangpo River will be blocked at the mouth of Lebai gully in the future, and it is necessary to take further mitigation measures. The research in this paper contributes to a better understanding of the debris flows in the Lebai Basin and provides meaningful and valuable information for debris flow hazard mitigation in the future. [ABSTRACT FROM AUTHOR]

Indoor localization has recently and significantly attracted the interest of the research community mainly due to the fact that Global Navigation Satellite Systems (GNSSs) typically fail in indoor environments. In the last couple of decades, there have been several works reported in the literature that attempt to tackle the indoor localization problem. However, most of this work is focused solely on two-dimensional (2D) localization, while very few papers consider three dimensions (3D). There is also a noticeable lack of survey papers focusing on 3D indoor localization; hence, in this paper, we aim to carry out a survey and provide a detailed critical review of the current state of the art concerning 3D indoor localization including geometric approaches such as angle of arrival (AoA), time of arrival (ToA), time difference of arrival (TDoA), fingerprinting approaches based on Received Signal Strength (RSS), Channel State Information (CSI), Magnetic Field (MF) and Fine Time Measurement (FTM), as well as fusion-based and hybrid-positioning techniques. We provide a variety of technologies, with a focus on wireless technologies that may be utilized for 3D indoor localization such as WiFi, Bluetooth, UWB, mmWave, visible light and sound-based technologies. We critically analyze the advantages and disadvantages of each approach/technology in 3D localization. [ABSTRACT FROM AUTHOR]