Geometry Techniques Research Articles

ROCK SLOPE STABILITY ASSESSMENT WITH PROPOSAL OF GEOTECHNICAL SOLUTIONS FOR UNSTABLE PARTS

In recent years, the lack of construction land in attractive locations, especially in urban areas, has posed increasing challenges to designers and builders. That is why projects for the construction pit protection and ensuring the permanent slopes stability are increasingly present in geotechnical engineering. This paper presents a practical example from the initial phase of the commercial building construction in a rock cut at the entrance to Vrbnik, island of Krk. Due to the lack of construction space, and the floor plan placement of the building itself and accompanying contents, the construction project planned the implementation of an almost vertical rock slope in the background of the main object. To be able to propose a conceptual solution that would ensure the permanent stability of the mentioned rock slope, during the excavation phase of the construction pit (cut), a geodetic survey of the found condition and a geotechnical-geological prospecting of the rock mass were performed. The purpose of the investigation was to determine the condition of the slope, along with detecting the quality zones of the rock mass according to different engineering classifications, and with the aim of proposing techniques that need to protect certain parts of the slope. As proof of the permanent stability of the slope, for the established parameters of the rock mass and the proposed geometry and protection techniques, a stability analysis was carried out for characteristic cross-sections.

Clustering Molecules at a Large Scale: Integrating Spectral Geometry with Deep Learning.

This study conducts an in-depth analysis of clustering small molecules using spectral geometry and deep learning techniques. We applied a spectral geometric approach to convert molecular structures into triangulated meshes and used the Laplace-Beltrami operator to derive significant geometric features. By examining the eigenvectors of these operators, we captured the intrinsic geometric properties of the molecules, aiding their classification and clustering. The research utilized four deep learning methods: Deep Belief Network, Convolutional Autoencoder, Variational Autoencoder, and Adversarial Autoencoder, each paired with k-means clustering at different cluster sizes. Clustering quality was evaluated using the Calinski-Harabasz and Davies-Bouldin indices, Silhouette Score, and standard deviation. Nonparametric tests were used to assess the impact of topological descriptors on clustering outcomes. Our results show that the DBN + k-means combination is the most effective, particularly at lower cluster counts, demonstrating significant sensitivity to structural variations. This study highlights the potential of integrating spectral geometry with deep learning for precise and efficient molecular clustering.

Detection of Individual Corn Crop and Canopy Delineation from Unmanned Aerial Vehicle Imagery

Precise monitoring of individual crop growth and health status is crucial for precision agriculture practices. However, traditional inspection methods are time-consuming, labor-intensive, prone to human error, and may not provide the comprehensive coverage required for the detailed analysis of crop variability across an entire field. This research addresses the need for efficient and high-resolution crop monitoring by leveraging Unmanned Aerial Vehicle (UAV) imagery and advanced computational techniques. The primary goal was to develop a methodology for the precise identification, extraction, and monitoring of individual corn crops throughout their growth cycle. This involved integrating UAV-derived data with image processing, computational geometry, and machine learning techniques. Bi-weekly UAV imagery was captured at altitudes of 40 m and 70 m from 30 April to 11 August, covering the entire growth cycle of the corn crop from planting to harvest. A time-series Canopy Height Model (CHM) was generated by analyzing the differences between the Digital Terrain Model (DTM) and the Digital Surface Model (DSM) derived from the UAV data. To ensure the accuracy of the elevation data, the DSM was validated against Ground Control Points (GCPs), adhering to standard practices in remote sensing data verification. Local spatial analysis and image processing techniques were employed to determine the local maximum height of each crop. Subsequently, a Voronoi data model was developed to delineate individual crop canopies, successfully identifying 13,000 out of 13,050 corn crops in the study area. To enhance accuracy in canopy size delineation, vegetation indices were incorporated into the Voronoi model segmentation, refining the initial canopy area estimates by eliminating interference from soil and shadows. The proposed methodology enables the precise estimation and monitoring of crop canopy size, height, biomass reduction, lodging, and stunted growth over time by incorporating advanced image processing techniques and integrating metrics for quantitative assessment of fields. Additionally, machine learning models were employed to determine relationships between the canopy sizes, crop height, and normalized difference vegetation index, with Polynomial Regression recording an R-squared of 11% compared to other models. This work contributes to the scientific community by demonstrating the potential of integrating UAV technology, computational geometry, and machine learning for accurate and efficient crop monitoring at the individual plant level.

A Comprehensive study on the γ-ray shielding performance of Al–Cu–PbO alloy: Experimental and simulation studies

The importance of radiation shielding is increasing due to the expanding areas exposed to radiation emissions. As a result, there is a crucial need to develop metal alloys and composites that demonstrate exceptional capabilities in absorbing neutron and gamma rays for effective radiation protection. The major purpose of this study is to determine the gamma photon attenuation coefficients of several Al–Cu–PbO alloys for radiation detection applications. The transmission geometry technique was used to calculate experimental mass attenuation coefficients at photon energies ranging from 0.662 to 1.33 MeV. To corroborate the experimental results, the mass attenuation coefficients for the alloys under consideration were calculated and confirmed by simulation using the MCNP5 method. The study analyzes the possibility of these alloys as alternative materials for nuclear radiation shielding applications.

Tropological sigma models

With the use of mathematical techniques of tropical geometry, it was shown by Mikhalkin some twenty years ago that certain Gromov-Witten invariants associated with topological quantum field theories of pseudoholomorphic maps can be computed by going to the tropical limit of the geometries in question. Here we examine this phenomenon from the physics perspective of topological quantum field theory in the path integral representation, beginning with the case of the topological sigma model before coupling it to topological gravity. We identify the tropicalization of the localization equations, investigate its geometry and symmetries, and study the theory and its observables using the standard cohomological BRST methods. We find that the worldsheet theory exhibits a nonrelativistic structure, similar to theories of the Lifshitz type. Its path-integral formulation does not require a worldsheet complex structure; instead, it is based on a worldsheet foliation structure.

INTERDISCIPLINARY OUTLOOKS ON SHILPASHASTRAS: INTEGRATING ART, AESTHETICS AND SPIRITUALITY

This paper aims to explore the multidimensional possibilities of Shilpashastras, an ancient Indian recognised tradition about various disciplines - Shilpashastras, the ancient Indian texts on art, architecture, aesthetics and craftsmanship, represent an insightful source of knowledge that has significantly formed the cultural and artistic backdrop of the ancient India. Among these, Sangramansutradhara, Manasollas, Aparajitpreccha, Kashyapshilpshastra, shilpratnakar, 'Manasara Shilpa Shastra'etc. As an inclusive guide, investigating into the elaborate details of architectural and sculptural components found in temples and other structures. It precisely outlines philosophies of design, spatial geometry, and construction techniques, providing a complete view of temple architecture. The 'Vastu Shastra' additional covers the discourse by focusing on the main beliefs of design, layout, and three-dimensional prearrangement, offering an insightful considerate of how spaces can be organized to harmonize with cosmic dynamisms. This concise study aims to lighten the elaborate links between artistic expression, aesthetic principles, and spiritual symbolism essential in ancient Indian texts. Themes to be addressed include historical perspectives on the development of Shilpashastras, philosophical insights into their aesthetic foundations, the spiritual significance of symbols and iconography, contemporary applications in art and design, and strategies for cultural heritage preservation. It seeks to expedite dialogue and collaboration among scholars, artists, practitioners, and enthusiasts, enriching our understanding of ancient Indian iconography, approach to reflect a all-inclusive understanding of the relationship between art, architecture, and spirituality in ancient India, providing invaluable insights into the symbolic language and visual culture of the time.

Counting \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{N}$$\\end{document} = 8 black holes as algebraic varieties

We calculate the helicity trace index B14 for \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{N}$$\\end{document} = 8 pure D-brane black holes using various techniques of computational algebraic geometry and find perfect agreement with the existing results in the literature. For these black holes, microstate counting is equivalent to finding the number of supersymmetric vacua of a multi-variable supersymmetric quantum mechanics which in turn is equivalent to solving a set of multi-variable polynomial equations modulo gauge symmetries. We explore four different techniques to solve a set of polynomial equations, namely Newton Polytopes, Homotopy continuation, Monodromy and Hilbert series. The first three methods rely on a mixture of symbolic and high precision numerics whereas the Hilbert series is symbolic and admit a gauge invariant analysis. Furthermore, exploiting various exchange symmetries, we show that quartic and higher order terms are absent in the potential, which if present would have spoiled the counting. Incorporating recent developments in algebraic geometry focusing on computational algorithms, we have extended the scope of one of the authors previous works [1, 2] and presented a new perspective for the black hole microstate counting problem. This further establishes the pure D-brane system as a consistent model, bringing us a step closer to \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{N}$$\\end{document} = 2 black hole microstate counting.

Human-Trust Based Feedback Control (HTBFC) Five-Dimensional Manifold Info-Geometric Analysis and how HTBEC Impacts Robotics

This work examines the five-dimensional HTBFC Manifold’s info-geometrics using effective information geometry (IG) techniques. The performance of HTBFC can be analysed from a novel relativistic approach by merging IG framework. Subcases of manifolds in two and three dimensions are studied. Human-machine interactions (HMIs) can now be unified through IG in a novel way because to this study. The presentation includes the essential robotic applications of HTBFC. A few newly identified unsolved issues and suggestions for additional study are included in the conclusions.

ALGEBRA ENVIRONMENTS I.

Algebra environments capture properties of non–commutative conditional expectations in a general algebraic setting. Their study relies on algebraic geometry, topology, and differential geometry techniques. The structure algebraic and Banach manifolds of algebra environments and their Zariski and smooth tangent vector bundles are particular objects of interest. A description of derivations on algebra environments compatible with geometric structures is an additional issue. Grassmann and flag manifolds of unital involutive algebras and spaces of projective compact group representations in C∗–algebras are analyzed as structure manifolds of associated algebra environments.

Genuinely nonabelian partial difference sets

AbstractStrongly regular graphs (SRGs) provide a fertile area of exploration in algebraic combinatorics, integrating techniques in graph theory, linear algebra, group theory, finite fields, finite geometry, and number theory. Of particular interest are those SRGs with a large automorphism group. If an automorphism group acts regularly (sharply transitively) on the vertices of the graph, then we may identify the graph with a subset of the group, a partial difference set (PDS), which allows us to apply techniques from group theory to examine the graph. Much of the work over the past four decades has concentrated on abelian PDSs using the powerful techniques of character theory. However, little work has been done on nonabelian PDSs. In this paper we point out the existence of genuinely nonabelian PDSs, that is, PDSs for parameter sets where a nonabelian group is the only possible regular automorphism group. We include methods for demonstrating that abelian PDSs are not possible for a particular set of parameters or for a particular SRG. Four infinite families of genuinely nonabelian PDSs are described, two of which—one arising from triangular graphs and one arising from Krein covers of complete graphs constructed by Godsil—are new. We also include a new nonabelian PDS found by computer search and present some possible future directions of research.

Model manifold of transmission loss from a Pekeris waveguide using VGS parameters

In geoacoustic inversion, selecting an appropriate seabed parametrization, especially with an unknown number of sediment layers, is a challenge that is compounded by potential bias when establishing bounds in the parameter search space. One approach to addressing these issues is rooted in the techniques of Information Geometry. Information Geometry informs model selection and parameterization by quantifying which model parameters are informed by observational data. This paper provides an information geometric analysis of the Pekeris waveguide, where the acoustic properties of the lower half-space are derived from the viscous grain-shearing (VGS) model. Specifically, we consider single frequency transmission loss (TL) across a wide range of VGS parameters. By exploring the limits and boundaries of the geometric manifolds, particularly as parameters approach both low and high extremes, this approach provides indications of parameter hierarchies and correlations. Results will include slices of the model manifold and an evaluation of the boundary structure, providing insight into the relative impact of VGS parameters and the delineation of limiting regions. In doing so, this paper seeks to inform model selection and parameterization in geoacoustic inversion studies. [Work supported by the Office of Naval Research. Grant N00014-21-S-B001.]

A Comprehensive Overview of Photon-Proton Scattering and QCD Methodology

The AdS/CFT correspondence is used as a helpful reference in the light front hyperbolic geometry technique, which solves this issue by mapping a confining gauge theory parameterized on the light front to a greater anti-de Sitter space. Three different interaction processes exist Direct or angular the target photon quark and the photon pair directly. When a lepton-antilepton pair is produced, only quantum electrodynamics (QED) is used; however, when a quark-antiquark pair is produced, both QED and perturbative quantum chromodynamics (QCD) are used. A deep-inelastic electron-photon scattering experiment was used to study the photon structure function, which describes the photon inherent quark composition: Single resolved: the desired spectroscopy quark combination creates the vector meson, one of the constituents of relationships to the investigating photon. The main focus of the current study was on photon-proton and QCD methodology. The main theoretical conclusion resulting from the work carried out can be used in the development of the conceptual concept of further researchers and this work also will be a guideline for future researchers.

Instability Phenomena in Centrifugal Compressors and Strategies to Extend the Operating Range: A Review

Centrifugal compressors are widely used in different fields. Their design requires high performance and a wide operating range, where, at lower mass flow rates, unstable flow dynamic phenomena occur, which are extremely harmful and, at the same time, complex to fully understand. This review paper presents the main research from the last 40 years on the subject of instability in centrifugal compressors, aiming to clarify the main (sometimes contradictory) causes, classifying them according to the component in which they are triggered or the interaction between them. Importance is given to works that develop criteria for the identification of the stability limit with simplified models. The main techniques used to extend the stability limit are also presented by distinguishing between passive and active fixed-flow control methods; moreover, the main works on variable geometry techniques are reported, showing the advantages and disadvantages of their use. Finally, an overview of the innovative applications of centrifugal compressors, such as fuel cells, is presented. The aim of this review is to highlight the continued interest in this field of study and provide the tools to understand the different unstable mechanisms and techniques used to extend the operating limit.

The Application of Nature-Based Solutions for Urban Heat Island Mitigation in Asia: Progress, Challenges, and Recommendations.

Unprecedented urbanization in Asia affects the net radiation and energy flux of urban areas in the form of urban heat islands (UHI). The application of nature-based solutions (NbS) via urban green and blue infrastructures is a promising approach to mitigate UHI via urban boundary condition modifications, which affect the energy balance. This narrative review discusses the application of green and blue infrastructures in the Asian context by highlighting its progress, challenges, and recommendations. This review is descriptive in nature and includes perspectives on the discussed topics. Studies on the application of green and blue infrastructures in UHI mitigation are still scant in Asia. Their cooling performance is greatly influenced by their types, size, geometry, surface roughness, spread (threshold distance), temporal scales, topography, pollution levels, prevailing climate, and assessment techniques. Distinct urban characteristics, climatic conditions, environmental risks, lack of awareness and expertise, lack of policy and government incentives, and limited scientific studies are the major challenges in their implementation of UHI mitigation in Asia. Although green and blue infrastructures are associated with urban cooling, more in-depth experimental work and multidisciplinary research collaboration are paramount to exploring its implementation potential in Asia and other countries that share similar urban and environmental characteristics.

Constructing a straight line intersecting four lines

In this paper, we determine the set S of straight lines L0 that have intersections with four given distinct lines L1,…,L4 in R3. If any two of the four given lines are skew, i.e., not co-planar, Bielinski and Lapinska used techniques in projective geometry to show that there are either zero, one, or two elements in the set S. Using linear algebra techniques, we determine S and show that there are no, one, two or infinitely many elements L0 in S, where the last case was overlooked in the earlier paper. For the sake of completeness, we provide a comprehensive determination of all the elements L0 in S if at least two of the four given lines are co-planar. In this scenario, there may also be zero, one, two, or infinitely many solutions.

Voronoi discretization to improve the meshless local Petrov–Galerkin method in 3D-computational fracture mechanics

Purpose1) The OE-MLPG penalty meshfree method is developed to solve cracked structure.(2) Smartening the numerical meshfree method by combining the particle swarm optimization (PSO) optimization algorithms and Voronoi computational geometric algorithm. (3). Selection of base functions, finding optimal penalty factor and distribution of appropriate nodal points to the accuracy of calculation in the meshless local Petrov–Galekrin (MLPG) meshless method.Design/methodology/approachUsing appropriate shape functions and distribution of nodal points in local domains and sub-domains and choosing an approximation or interpolation method has an effective role in the application of meshless methods for the analysis of computational fracture mechanics problems, especially problems with geometric discontinuity and cracks. In this research, computational geometry technique, based on the Voronoi diagram (VD) and Delaunay triangulation and PSO algorithm, are used to distribute nodal points in the sub-domain of analysis (crack line and around it on the crack plane).FindingsBy doing this process, the problems caused by too closeness of nodal points in computationally sensitive areas that exist in general methods of nodal point distribution are also solved. Comparing the effect of the number of sentences of basic functions and their order in the definition of shape functions, performing the mono-objective PSO algorithm to find the penalty factor, the coefficient, convergence, arrangement of nodal points during the three stages of VD implementation and the accuracy of the answers found indicates, the efficiency of V-E-MLPG method with Ns = 7 and ß = 0.0037–0.0075 to estimation of 3D-stress intensity factors (3D-SIFs) in computational fracture mechanics.Originality/valueThe present manuscript is a continuation of the studies (Ref. [33]) carried out by the authors, about; feasibility assessment, improvement and solution of challenges, introduction of more capacities and capabilities of the numerical MLPG method have been used. In order to validate the modeling and accuracy of calculations, the results have been compared with the findings of reference article [34] and [35].

Nonlocal correlations of a fully entangled qubit-qutrit Bell scenario

With the aim of understanding the role that entanglement plays in the generation of EPR correlations, in this paper we address the study of a Bell scenario involving qubit-qutrit entangled pairs with only two measurement options per side. The key feature of our setup is the proposition of two non-projective POVMs to describe the Bob's measurement operators, preserving orthogonal and projective measurements for Alice. Despite the eigenvalues of the CHSH operator indicate that the correlations generated cannot exceed the local bound, their eigenvectors are used to define two families of maximally entangled states (negativity one). A consequence of the above is that in this scenario entanglement can be fully understood in terms of local resources and shared randomness. This fact is used later to design, using techniques of convex geometry, a device that reproduces the correlations generated by these families of maximally entangled states for the considered setup.

An Examination of the Effects of Different Transplanting Dates, Planting Geometry and Training Techniques on the Yield Traits, Productivity and Quality of Cucumber (Cucumis sativus L.) under Naturally Ventilated Polyhouse

An experiment was conducted to investigate the effect of date of transplanting, planting geometry and training system on the fruit yield and quality of cucumber (Cucumis sativus L.) under naturally ventilated polyhouse at the Research Farm of Department of Agricultural Engineering, College of Agriculture, CSK Himachal Pradesh Krishi Vishvavidyalaya, Palampur, The experiment was laid out in Factorial Randomized Block Design with three replications and eighteen treatments, comprised of three date of transplanting (1st fortnight of March, 2nd fortnight of March and 1st fortnight of April), two planting geometry viz., 60 cm x 30 cm, 75 cm x 30 cm and three training systems viz., two shoots, three shoots and four shoots. Results revealed that plants transplanted earlier (1st fortnight of March) at a wider spacing of (75 cm x 30 cm) recorded significantly higher number of fruits per plant, fruit length, fruit weight and total soluble solids, while maximum fruit yield was recorded under closer spacing of 60 cm x 30 cm. With regards to the number of shoots per plant, plants with three shoots recorded significantly higher fruit yield. So it can be concluded that plants transplanted in the 1st fortnight of March, trained to three shoots and spaced at 60 cm x 30 cm apart were found to be the best for higher fruit yield and better quality of the produce.

Comprehensive Quality of Life Report from a Prospective Clinical Trial of 4DCT-Ventilation Functional Lung Avoidance Radiation Therapy

Functional imaging has been developed that uses 4DCT images and image processing to generate lung ventilation maps (4DCT-ventilation). 4DCT-ventilation functional avoidance uses 4DCT-images to generate plans that avoid functional regions of the lung with the goal of reducing pulmonary toxicity. A 4DCT-ventilation functional avoidance, phase II, multi-center clinical trial was completed, and patient reported outcomes (PRO) measured. PROs are an essential measure of quality-of-life following radiotherapy. The purpose of this work is to quantify PRO changes for lung cancer patients treated with functional avoidance and to compare PROs against clinical pneumonitis. Patients with locally advanced lung cancer receiving curative intent radiotherapy (prescriptions of 45-75 Gy) and chemotherapy were accrued. Each patient had a 4DCT-ventilation image generated using 4DCT data. Favorable arc geometry and optimization techniques were used to generate functional avoidance plans. PRO instruments included the Functional Assessment of Cancer Therapy Lung (FACT-L) questionnaire and the Visual Analog Scale (VAS) administered pre-treatment and 3-, 6-, and 12-months post-treatment to gather data on physical, social, emotional, functional, and pulmonary well-being. The percentage of patients with clinically significant decline was calculated using the FACT-TOI (Trial Outcome Index), FACT-LCS (Lung Cancer Subscale), and VAS instruments. To evaluate the correlation between PROs and clinical toxicity, the percentage of clinically significant FACT-LCS decline was compared (Chi-square test) for patients who did or did not experience grade 2+ pneumonitis. Fifty-nine patients completed baseline PRO surveys. Median age was 65, 83% of patients had non-small-cell lung cancer, with 75% having stage III disease. Clinically significant FACT-TOI decline at, 3, 6, and 12 months was 46.3%, 38.5%, and 26.8%, respectively. The percentage of patients with clinically significant FACT-LCS decline was 33.3%, 33.3%, and 29.3%, at 3 months, 6 months, and 12 months, respectively. The percentage of patients with clinically significant VAS decline at 3, 6, and 12 months was 18.9%, 20.0%, and 18.6%, respectively. Patients who experienced grade 2+ pneumonitis had a greater percentage of clinically significant decline at all time-points with the results reaching significance (p = 0.045) at 6 months. The study presents the first comprehensive evaluation of PROs for patients treated with 4DCT-ventilation functional avoidance. The data show that 20-40% of patients had clinically significant decline and that PROs had a strong correlation with pneumonitis. The PRO data demonstrate that functional avoidance results in low rates of patient reported outcome clinical decline and provide seminal results to be used in phase III studies.

Local orthogonal maps and rigidity of holomorphic mappings between real hyperquadrics

We propose a coordinate-free approach to study the holomorphic maps between the real hyperquadrics in complex projective spaces. It is based on a notion of orthogonality on the projective spaces induced by the Hermitian structures that define the hyperquadrics. There are various kinds of special linear subspaces associated to this orthogonality which are well respected by the relevant holomorphic maps and we obtain rigidity theorems by analyzing the images of these linear subspaces, together with techniques in projective geometry. Our method allows us to recover and generalize a number of well-known results in the field with simpler arguments.