Search results for: Riemannian geometry

Authors: A. Benzian

Abstract:

The generalization of relativistic theory of gravity based essentially on the principle of equivalence stipulates that for all bodies, the grave mass is equal to the inert mass which leads us to believe that gravitation is not a property of the bodies themselves, but of space, and the conclusion that the gravitational field must curved space-time what allows the abandonment of Minkowski space (because Minkowski space-time being nonetheless null curvature) to adopt Riemannian geometry as a mathematical framework in order to determine the curvature. Therefore the work presented in this paper begins with the evolution of the concept of gravity then tensor field which manifests by Riemannian geometry to formulate the general equation of the gravitational field.

Keywords: inertia, principle of equivalence, tensors, Riemannian geometry

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Authors: Mancho Manev

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The concept of almost paracontact Riemannian manifolds (abbr., apcR manifolds) was introduced by I. Sato in 1976 as an analogue of almost contact Riemannian manifolds. The notion of an apcR manifold of type (p,q) was defined by S. Sasaki in 1980, where p and q are respectively the numbers of the multiplicity of the structure eigenvalues 1 and -1. It also has a simple eigenvalue of 0. In our work, we consider (2n+1)-dimensional apcR manifolds of type (n,n), i.e., the paracontact distribution of the studied manifold can be considered as a 2n-dimensional almost paracomplex Riemannian distribution with almost paracomplex structure and structure group O(n) × O(n). The aim of the present study is to introduce a new class of apcR manifolds. Such a manifold is obtained using the construction of a certain Riemannian cone over it, and the resulting manifold is a paraholomorphic paracomplex Riemannian manifold (abbr., phpcR manifold). We call it a para-Sasaki-like Riemannian manifold (abbr., pSlR manifold) and give some explicit examples. We study the structure of pSlR spaces and find that the paracontact form η is closed and each pSlR manifold locally can be considered as a certain product of the real line with a phpcR manifold, which is locally a Riemannian product of two equidimensional Riemannian spaces. We also obtain that the curvature of the pSlR manifolds is completely determined by the curvature of the underlying local phpcR manifold. Moreover, the ξ-directed Ricci curvature is equal to -2n, while in the Sasaki case, it is 2n. Accordingly, the pSlR manifolds can be interpreted as the counterpart of the Sasaki manifolds; the skew-symmetric part of ∇η vanishes, while in the Sasaki case, the symmetric part vanishes. We define a hyperbolic extension of a (complete) phpcR manifold that resembles a certain warped product, and we indicate that it is a (complete) pSlR manifold. In addition, we consider the hyperbolic extension of a phpcR manifold and prove that if the initial manifold is a complete Einstein manifold with negative scalar curvature, then the resulting manifold is a complete Einstein pSlR manifold with negative scalar curvature. In this way, we produce new examples of a complete Einstein Riemannian manifold with negative scalar curvature. Finally, we define and study para contact conformal/homothetic deformations by deriving a subclass that preserves the para-Sasaki-like condition. We then find that if we apply a paracontact homothetic deformation of a pSlR space, we obtain that the Ricci tensor is invariant.

Keywords: almost paracontact Riemannian manifolds, Einstein manifolds, holomorphic product manifold, warped product manifold

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Authors: Seyedehsomayeh Hosseini

Abstract:

Much attention has been paid over centuries to understanding and solving the problem of minimization of functions. Compared to linear programming and nonlinear unconstrained optimization problems, nonlinear constrained optimization problems are much more difficult. Since the procedure of finding an optimizer is a search based on the local information of the constraints and the objective function, it is very important to develop techniques using geometric properties of the constraints and the objective function. In fact, differential geometry provides a powerful tool to characterize and analyze these geometric properties. Thus, there is clearly a link between the techniques of optimization on manifolds and standard constrained optimization approaches. Furthermore, there are manifolds that are not defined as constrained sets in R^n an important example is the Grassmann manifolds. Hence, to solve optimization problems on these spaces, intrinsic methods are used. In a nondifferentiable problem, the gradient information of the objective function generally cannot be used to determine the direction in which the function is decreasing. Therefore, techniques of nonsmooth analysis are needed to deal with such a problem. As a manifold, in general, does not have a linear structure, the usual techniques, which are often used in nonsmooth analysis on linear spaces, cannot be applied and new techniques need to be developed. This paper presents necessary and sufficient conditions for a strict local minimum of extended real-valued, nonsmooth functions defined on Riemannian manifolds.

Keywords: Riemannian manifolds, nonsmooth optimization, lower semicontinuous functions, subdifferential

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Authors: Gabriel I. Loaiza Ossa, Carlos A. Cadavid Moreno, Juan C. Arango Parra

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It is known that the Riemannian manifold determined by the family of inverse Gaussian distributions endowed with the Fisher metric has negative constant curvature κ= -1/2, as does the family of usual Gaussian distributions. In the present paper, firstly, we arrive at this result by following a different path, much simpler than the previous ones. We first put the family in exponential form, thus endowing the family with a new set of parameters, or coordinates, θ₁, θ₂; then we determine the matrix of the Fisher metric in terms of these parameters; and finally we compute this matrix in the original parameters. Secondly, we define the inverse q-Gaussian distribution family (q < 3) as the family obtained by replacing the usual exponential function with the Tsallis q-exponential function in the expression for the inverse Gaussian distribution and observe that it supports two possible geometries, the Fisher and the q-Fisher geometry. And finally, we apply our strategy to obtain results about the Fisher and q-Fisher geometry of the inverse q-Gaussian distribution family, similar to the ones obtained in the case of the inverse Gaussian distribution family.

Keywords: base of changes, information geometry, inverse Gaussian distribution, inverse q-Gaussian distribution, statistical manifolds

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Authors: Ping Tan, Xiaomeng Su, Yi Shen

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The motion intention in the motor imagery braincomputer interface is identified by classifying the event-related desynchronization (ERD) and event-related synchronization ERS characteristics of sensorimotor rhythm (SMR) in EEG signals. When the subject imagines different limbs or different parts moving, the rhythm components and bandwidth will change, which varies from person to person. How to find the effective sensorimotor frequency band of subjects is directly related to the classification accuracy of brain-computer interface. To solve this problem, this paper proposes a Minimum Distance to Riemannian Mean Classification method based on Non-Uniform Filter Banks. During the training phase, the EEG signals are decomposed into multiple different bandwidt signals by using multiple band-pass filters firstly; Then the spatial covariance characteristics of each frequency band signal are computered to be as the feature vectors. these feature vectors will be classified by the MDRM (Minimum Distance to Riemannian Mean) method, and cross validation is employed to obtain the effective sensorimotor frequency bands. During the test phase, the test signals are filtered by the bandpass filter of the effective sensorimotor frequency bands, and the extracted spatial covariance feature vectors will be classified by using the MDRM. Experiments on the BCI competition IV 2a dataset show that the proposed method is superior to other classification methods.

Keywords: non-uniform filter banks, motor imagery, brain-computer interface, minimum distance to Riemannian mean

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Authors: Lina Wu, Ye Li, Jia Liu

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We are interested in solving Liouville-type problems to explore constancy properties for maps or differential forms on Riemannian manifolds. Geometric structures on manifolds, the existence of constancy properties for maps or differential forms, and energy growth for maps or differential forms are intertwined. In this article, we concentrate on discovery of solutions to Liouville-type problems where manifolds are Euclidean spaces (i.e. flat Riemannian manifolds) and maps become real-valued functions. Liouville-type results of vanishing properties for functions are obtained. The original work in our research findings is to extend the q-energy for a function from finite in L^q space to infinite in non-L^q space by applying p-balanced technique where q = p = 2. Calculation skills such as Hölder's Inequality and Tests for Series have been used to evaluate limits and integrations for function energy. Calculation ideas and computational techniques for solving Liouville-type problems shown in this article, which are utilized in Euclidean spaces, can be universalized as a successful algorithm, which works for both maps and differential forms on Riemannian manifolds. This innovative algorithm has a far-reaching impact on research work of solving Liouville-type problems in the general settings involved with infinite energy. The p-balanced technique in this algorithm provides a clue to success on the road of q-energy extension from finite to infinite.

Keywords: differential forms, holder inequality, Liouville-type problems, p-balanced growth, p-harmonic maps, q-energy growth, tests for series

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Authors: Ashkan Golgoon, Souhayl Sadik, Arash Yavari

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Eigenstrains in nonlinear solids are created due to anelastic effects such as non-uniform temperature distributions, growth, remodeling, and defects. Eigenstrains understanding is indispensable, as they can generate residual stresses and strongly affect the overall response of solids. Here, we study the residual stress and deformation fields of an incompressible isotropic infinite wedge with a circumferentially-symmetric distribution of finite eigenstrains. We construct a material manifold, whose Riemannian metric explicitly depends on the eigenstrain distribution, thereby we turn the problem into a classical nonlinear elasticity problem, where we find an embedding of the Riemannian material manifold into the ambient Euclidean space. In particular, we find exact solutions for the residual stress and deformation fields of a neo-Hookean wedge having a symmetric inclusion with finite radial and circumferential eigenstrains. Moreover, we numerically solve a similar problem when a symmetric Mooney-Rivlin inhomogeneity with finite eigenstrains is placed in a neo-Hookean wedge. Generalization of the eigenstrain problem to other geometries are also discussed.

Keywords: finite eigenstrains, geometric mechanics, inclusion, inhomogeneity, nonlinear elasticity

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Authors: Y. Lasbet, A. L. Boukhalkhal, K. Loubar

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The study of mixed convection is, usually, focused on the straight channels in which the onset of the mixed convection is well defined as function of the ratio between Grashof number and Reynolds number, Gr/Re. This is not the case for a complex channel wherein the mixed convection is not sufficiently examined in the literature. Our paper focuses on the study of the mixed convection in a complex geometry in which our main contribution reveals that the critical value of the ratio Gr/Re for the onset of the mixed convection increases highly in the type of geometry contrary to the straight channel. Furthermore, the accentuated secondary flow in this geometry prevents the thermal stratification in the flow and consequently the buoyancy driven becomes negligible. To perform these objectives, a numerical study in complex geometry for several values of the ratio Gr/Re with prescribed wall heat flux (H2), was realized by using the CFD code.

Keywords: complex geometry, heat transfer, laminar flow, mixed convection, Nusselt number

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Authors: Mohammadsadegh Zanganehfar

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Since the introduction of fractal geometry in 1970, numerous efforts have been made by architects and researchers to transfer this area of mathematical knowledge in the discipline of architecture and postmodernist discourse. The discourse of complexity and architecture is one of the most significant ongoing discourses in the discipline of architecture from the '70s until today and has generated significant styles such as deconstructivism and parametrism in architecture. During these years, several projects were designed and presented by designers and architects using fractal geometry, but due to the lack of sufficient knowledge and appropriate comprehension of the features and characteristics of this nonlinear geometry, none of the fractal-based designs have been successful and satisfying. Fractal geometry as a geometric technology has a long presence in the history of architecture. The current research attempts to identify and discover the characteristics, features, potentials, and functionality of fractals despite their aesthetic aspect by examining case studies of pre-modern architecture in Asia and investigating the function of fractals.

Keywords: Asian architecture, fractal geometry, fractal technique, geometric properties

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Authors: Morteza Faghfouri

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In this paper we establish a general inequality involving the Laplacian of the warping functions and the squared mean curvature of any doubly warped product isometrically immersed in a Riemannian manifold.

Keywords: integral submanifolds, S-space forms, doubly warped product, inequality

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Authors: Yuhei Kunihiro, Sorin V. Sabau, Kazuhiro Shibuya

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We study the molecular evolution of insulin from the metric geometry point of view. In mathematics, and particularly in geometry, distances and metrics between objects are of fundamental importance. Using a weaker notion than the classical distance, namely the weighted quasi-metrics, one can study the geometry of biological sequences (DNA, mRNA, or proteins) space. We analyze from the geometrical point of view a family of 60 insulin homologous sequences ranging on a large variety of living organisms from human to the nematode C. elegans. We show that the distances between sequences provide important information about the evolution and function of insulin.

Keywords: metric geometry, evolution, insulin, C. elegans

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Authors: Michel Wakim, Rodrigo Rivera Tinoco

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Supersonic ejector is an economical device that use high pressure vapor to compress a low pressure vapor without any rotating parts or external power sources. Entrainment ratio is a major characteristic of the ejector performance, so the ejector performance is highly dependent on its geometry. The aim of this paper is to design ejector geometry, based on pre-specified operating conditions, and to study the flow behavior inside the ejector by using computational fluid dynamics ‘CFD’ by using ‘ANSYS FLUENT 15.0’ software. In the first section; 1-D mathematical model is carried out to predict the ejector geometry. The second part describes the flow behavior inside the designed model. CFD is the most reliable tool to reveal the mixing process at different parts of the supersonic turbulent flow and to study the effect of the geometry on the effective ejector area. Finally, the results show the effect of the geometry on the entrainment ratio.

Keywords: computational fluids dynamics, ejector, entrainment ratio, geometry optimization, performance

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Authors: Soulef Amamria, Mohamed Sadok Bensalem, Mohamed Ghanmi

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The structural and sedimentological study of fault-related- folds in the Southern Tunisian Atlas is distinguished by a special geometry of the gravitational structures. This distinct geometry is observable in the example of a flap structure in Jebel Ben Zannouch with the formation of a stuck syncline. This geometry can be explained by the mechanism of major thrusting in Orbata anticline in the occidental extremity of Gafsa chains, with asymmetrical flank dips and hinge migration kinematics. These kinematics was originally controlled by the Breakthrough structure; the study of this special geometry of gravity flap structure depends on the sedimentation domain, shortening ratios, and erosion speed. This study constitutes one of the complete examples of kinematic model validation on a field scale.

Keywords: fault-related-folds, southern Tunisian Atlas, flap structure, breakthrough

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Authors: Seungyeong Choi, Namkyu Lee, Dong Il Shim, Young Mun Lee, Yong-Ki Park, Hyung Hee Cho

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Effect of the cross-sectional geometry on heat transfer and particle motion of circulating fluidized bed riser for CO₂ capture was investigated. Numerical simulation using Eulerian-eulerian method with kinetic theory of granular flow was adopted to analyze gas-solid flow consisting in circulating fluidized bed riser. Circular, square, and rectangular cross-sectional geometry cases of the same area were carried out. Rectangular cross-sectional geometries were analyzed having aspect ratios of 1: 2, 1: 4, 1: 8, and 1:16. The cross-sectional geometry significantly influenced the particle motion and heat transfer. The downward flow pattern of solid particles near the wall was changed. The gas-solid mixing degree of the riser with the rectangular cross section of the high aspect ratio was the lowest. There were differences in bed-to-wall heat transfer coefficient according to rectangular geometry with different aspect ratios.

Keywords: bed geometry, computational fluid dynamics, circulating fluidized bed riser, heat transfer

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Authors: Shannon Steinmetz, Ellen Gethner

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In this paper, a theoretical foundation is developed for patterned segmentation of audio using the geometry of music and statistical manifold. We demonstrate image content clustering using conic space sonification. The algorithm takes a geodesic curve as a model estimator of the three-parameter Gamma distribution. The random variable is parameterized by musical centricity and centric velocity. Model parameters predict audio segmentation in the form of duration and frame count based on the likelihood of musical geometry transition. We provide an example using a database of randomly selected images, resulting in statistically significant clusters of similar image content.

Keywords: sonification, musical information geometry, image, content extraction, automated quantification, audio segmentation, pattern recognition

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Authors: Cristina-Maria Păcurar

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The paper presents an original Python-based application that outlines the advantages of combining some elementary notions of mathematics with the study of a programming language. The application support refers to some of the first lessons of analytic geometry, meaning conics and quadrics and their reduction to a standard form, as well as some related notions. The chosen programming language is Python, not only for its closer to an everyday language syntax – and therefore, enhanced readability – but also for its highly reusable code, which is of utmost importance for a mathematician that is accustomed to exploit already known and used problems to solve new ones. The purpose of this paper is, on one hand, to support the idea that one of the most appropriate means to initiate one into programming is throughout mathematics, and reciprocal, one of the most facile and handy ways to assimilate some basic knowledge in the study of mathematics is to apply them in a personal project. On the other hand, besides being a mean of learning both programming and analytic geometry, the application subject to this paper is itself a useful tool for it can be seen as an independent original Python package for analytic geometry.

Keywords: analytic geometry, conics, python, quadrics

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Authors: Jacek Turski

Abstract:

The visual space geometries are constructed in the Riemannian geometry framework from simulated iso-disparity conics in the horizontalvisual plane of the binocular system with the asymmetric eyes (AEs). For the eyes fixating at the abathic distance, which depends on the AE’s parameters, the iso-disparity conics are frontal straight lines in physical space. For allother fixations, the iso-disparity conics consist of families of the ellipses or hyperbolas depending on both the AE’s parameters and the bifoveal fixation. However, the iso-disparity conic’s arcs are perceived in the gaze direction asthe frontal lines and are referred to as visual geodesics. Thus, geometriesof physical and visual spaces are different. A simple postulate that combines simulated iso-disparity conics with basic anatomy od the human visual system gives the relative depth for the fixation at the abathic distance that establishes the Riemann matric tensor. The resulting geodesics are incomplete in the gaze direction and, therefore, give thefinite distances to the horizon that depend on the AE’s parameters. Moreover, the curvature vanishes in this eyes posture such that visual space is flat. For all other fixations, only the sign of the curvature canbe inferred from the global behavior of the simulated iso-disparity conics: the curvature is positive for the elliptic iso-disparity curves and negative for the hyperbolic iso-disparity curves.

Keywords: asymmetric eye model, iso-disparity conics, metric tensor, geodesics, curvature

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Authors: Sachin Aggarwal, Sarah Kassinger, Nicholas Hoffman

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Geometry simplification is a key step in performing conjugate heat transfer analysis using CFD. This paper proposes a standard methodology for the geometry simplification of rotating machines, such as electrical generators and electrical motors (both air and liquid-cooled). These machines are extensively deployed throughout the aerospace and automotive industries, where optimization of weight, volume, and performance is paramount -especially given the current global transition to renewable energy sources and vehicle hybridization and electrification. Conjugate heat transfer analysis is an essential step in optimizing their complex design. This methodology will help in reducing convergence issues due to poor mesh quality, thus decreasing computational cost and overall analysis time.

Keywords: CFD, electrical machines, Geometry simplification, heat transfer

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Authors: A. K. Sethi, R. N. Patra, B. Nayak

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In this paper, we have considered Friedmann-Robertson-Walker (FRW) metric with generalized Chaplygin gas which has viscosity in the context of Lyra geometry. The viscosity is considered in two different ways (i.e. zero viscosity, non-constant r (rho)-dependent bulk viscosity) using constant deceleration parameter which concluded that, for a special case, the viscous generalized Chaplygin gas reduces to modified Chaplygin gas. The represented model indicates on the presence of Chaplygin gas in the Universe. Observational constraints are applied and discussed on the physical and geometrical nature of the Universe.

Keywords: bulk viscosity, lyra geometry, generalized chaplygin gas, cosmology

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Authors: Olivia Borgue, Massimo Panarotto, Ola Isaksson

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This article presents a neural networks-based strategy for reducing the need for support structures when designing for additive manufacturing (AM). Additive manufacturing is a relatively new and immature industrial technology, and the information to make confident decisions when designing for AM is limited. This lack of information impacts especially the early stages of engineering design, for instance, it is difficult to actively consider the support structures needed for manufacturing a part. This difficulty is related to the challenge of designing a product geometry accounting for customer requirements, manufacturing constraints and minimization of support structure. The approach presented in this article proposes an automatized geometry modification technique for reducing the use of the support structures while designing for AM. This strategy starts with a neural network-based strategy for shape recognition to achieve product classification, using an STL file of the product as input. Based on the classification, an automatic part geometry modification based on MATLAB© is implemented. At the end of the process, the strategy presents different geometry modification alternatives depending on the type of product to be designed. The geometry alternatives are then evaluated adopting a QFD-like decision support tool.

Keywords: additive manufacturing, engineering design, geometry modification optimization, neural networks

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Authors: Fuad M. Alkoot

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The main component of a machine learning system is the classifier. Classifiers are mathematical models that can perform classification tasks for a specific application area. Additionally, many classifiers are combined using any of the available methods to reduce the classifier error rate. The benefits gained from the combination of multiple classifier designs has motivated the development of diverse approaches to multiple classifiers. We aim to investigate using fractal geometry to develop an improved classifier combiner. Initially we experiment with measuring the fractal dimension of data and use the results in the development of a combiner strategy.

Keywords: fractal geometry, machine learning, classifier, fractal dimension

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Authors: Gebreegziabher Hailu Gebrecherkos

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This study examines the effectiveness of GeoGebra in developing the conceptual understanding of transformation geometry among Grade 11 students. Utilizing a quasi-experimental design, the research compares the learning outcomes of students who engaged with GeoGebra against those who received traditional instruction. Pre- and post-tests were administered to assess students' grasp of key transformation concepts, including translations, rotations, reflections, and dilations. Additionally, qualitative data were gathered through student interviews and classroom observations to explore their experiences and perceptions of using GeoGebra. Results indicate that students utilizing GeoGebra showed significantly greater improvement in their understanding of transformation geometry concepts. The interactive features of GeoGebra facilitated visualization and exploration, leading to enhanced engagement and deeper conceptual insights. The findings underscore the potential of GeoGebra as a powerful educational tool that not only fosters mathematical understanding but also accommodates diverse learning styles in the classroom. This study contributes valuable insights for educators seeking to improve the teaching and learning of transformation geometry in secondary education.

Keywords: calculus, conceptual understanding, GeoGebra, transformation geometry

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Authors: Prabhsharan Singh, Rahul Sindhu, Piyush Sikka

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The steering system is an integral part and medium through which the driver communicates with the vehicle and terrain, hence the most suitable steering geometry as per requirements must be chosen. The function of the chosen steering geometry of an All-Terrain Vehicle (ATV) is to provide the desired understeer gradient, minimum tire slippage, expected weight transfer during turning as these are requirements for a good steering geometry of a BAJA ATV. This research paper focuses on choosing the best suitable steering geometry for BAJA ATV tracks by reasoning the working principle and using fundamental trigonometric functions for obtaining these geometries on the same vehicle itself, namely Ackermann, Anti- Ackermann, Parallel Ackermann. Full vehicle analysis was carried out on Adams Car Analysis software, and graphical results were obtained for various parameters. Steering geometries were achieved by using a single versatile knuckle for frontward and rearward tie-rod placement and were practically tested with the help of data acquisition systems set up on the ATV. Each was having certain characteristics, setup, and parameters were observed for the BAJA ATV, and correlations were created between analytical and practical values.

Keywords: all-terrain vehicle, Ackermann, Adams car, Baja Sae, steering geometry, steering system, tire slip, traction, understeer gradient

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Authors: Valeriya Tyo, Serikbolat Yessengabulov

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Regions with extreme climate conditions such as Astana city require energy saving measures to increase the energy performance of buildings which are responsible for more than 40% of total energy consumption. Identification of optimal building geometry is one of the key factors to be considered. The architectural form of a building has the impact on space heating and cooling energy use, however, the interrelationship between the geometry and resultant energy use is not always readily apparent. This paper presents a comparative case study of two prototypical buildings with compact building shape to assess its impact on energy performance.

Keywords: building geometry, energy efficiency, heat gain, heat loss

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Authors: Ibtisam Masmali, Edwin Beggs

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In this paper, we take example of differential calculi, on the finite group A4. Then, we apply methods of non-commutative of non-commutative differential geometry to this example, and see how similar the results are to those of classical differential geometry.

Keywords: differential calculi, finite group A4, Christoffel symbols, covariant derivative, torsion compatible

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Authors: Toby Li, Julian Zhu

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In this paper, a model based on a simplified geometry is introduced to give a very conservative collision probability prediction for the Starlink satellite in its most densely clustered region. Under the model in this paper, the probability of collision for Starlink satellite where it clustered most densely is found to be 8.484 ∗ 10^−4. It is found that the predicted collision probability increased nonlinearly with the increased safety distance set. This simple model provides evidence that the continuous development of maneuver avoidance systems is necessary for the future of the orbital safety of satellites under the harsher Lower Earth Orbit environment.

Keywords: Starlink, collision probability, debris, geometry model

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Authors: Marc Diesse, Hochschule Heilbronn

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We address the question of identifying the configuration space singularities of linkages, i.e., points where the configuration space is not locally a submanifold of Euclidean space. Because the configuration space cannot be smoothly parameterized at such points, these singularity types have a significantly negative impact on the kinematics of the linkage. It is known that Jacobian methods do not provide sufficient conditions for the existence of CS-singularities. Herein, we present several additional algebraic criteria that provide the sufficient conditions. Further, we use those criteria to analyze certain classes of planar linkages. These examples will also show how the presented criteria can be checked using algorithmic methods.

Keywords: linkages, configuration space-singularities, real algebraic geometry, analytic geometry

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Authors: F. S. Irwansyah, I. Farida, Y. Maulana

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Studying chemistry requires the ability to understand three levels of understanding in the form of macroscopic, submicroscopic and symbolic, but the lack of emphasis on the submicroscopic level leads to the understanding of chemical concepts becoming incomplete, due to the limitations of the tools capable of providing visualization of submicroscopic concepts. The purpose of this study describes the stages of making augmented reality learning media on the concept of molecular geometry and analyze the feasibility test result of augmented reality learning media on the concept of molecular geometry. This research uses Research and Development (R & D) method which produces a product of AR learning media on molecular geometry concept and test the effectiveness of the product. Research stages include concept analysis and learning indicators, design development, validation, feasibility, and limited testing. The stages of validation and limited trial are aimed to get feedback in the form of assessment, suggestion and improvement on learning aspect, material substance aspect, visual communication aspect and software engineering aspects and media feasibility in terms of media creation purpose to be used in learning. The results of the overall feasibility test obtained r-calculation 0,7-0,9 with the interpretation of high feasibility value, whereas the result of limited trial got the percentage of eligibility with the average value equal to 70,83-92,5%. This percentage indicates that AR's learning media product on the concept of molecular geometry, deserves to be used as a learning resource.

Keywords: android, augmented reality, chemical learning, geometry

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Authors: Erkan Talay, Mustafa Yigit Yagci

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For the systems like sliding door, designers should predict not only strength but also dynamic behavior of the system and this prediction usually becomes more critical if design has radical changes refer to previous designs. Also, sometimes physical tests could cost more than expected, especially for rail geometry changes, since this geometry affects design of the body. The aim of the study is to observe and understand the dynamics of the sliding door in virtual environment. For this, multibody dynamic model of the sliding door was built and then affects of various parameters like rail geometry, roller diameters, or center of mass detected. Also, a design of experiment study was performed to observe interactions of these parameters.

Keywords: design of experiment, minimum closing effort, multibody simulation, sliding door

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Authors: Abdulrahman M. Homadi

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This study focuses on how to control the outlet temperature of a solar air heater in a way simpler than the existing methods. In this work, five cases have been studied by using ANSYS Fluent based on a CFD numerical method. All the cases have been simulated by utilizing the same criteria and conditions like the temperature, materials, areas except the geometry. The case studies are conducted in Little Rock (LR), AR, USA during the winter time supposedly on 15^th of December. A fresh air that is flowing with a velocity of 0.5 m/s and a flow rate of 0.009 m³/s. The results prove the possibility of achieving a controlled temperature just by changing the geometric shape of the heater. This geometry guarantees that the absorber plate always has a normal component of the solar radiation at any time during the day. The heater has a sectarian shape with a radius of 150 mm where the outlet temperature remains almost constant for six hours.

Keywords: solar energy, air heater, control of temperature, CFD

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