The authors undertook pilot studies to assess the accuracy of the reverse engineering process of worn nonstandard spur gears (non-standardized modulus value, unusual profile/pressure angle, high or low teeth), using conventional techniques and measuring instruments. Eight gears were tested, the module of which ranges from 1.020 to 4.98 mm and the number of teeth from 13 to 42. The key parameter, the basic pitch, was selected to estimate the accuracy of the process. The goal is to determine the value of the profile angle. Eleven models were proposed to estimate the nominal tolerance field, using various types of random data distribution. The tested gears were made in IT grade: 6, 7, 8 and 9 according to DIN 3961. Vernier disc micrometers with various measurement ranges were used for research. It has been shown that the nominal module does not have to be treated as a random variable in the population. EIG (Equation of Identity) was developed, allowing conversion of any gear with specific values of geometric parameters into an identical gear with alternative values of these parameters. The directions and degrees of shifts of the estimated tolerance fields relative to the nominal field were determined. The most effective estimating model was selected in the context of the percentage filling of the nominal tolerance field, taking into account the symmetric Student-Fisher distribution with a confidence level of 60%. Further directions of the research activities were described.

Precise monitoring of individual crop growth and health status is crucial for precision agriculture practices. However, traditional manual inspection methods are time-consuming, labor-intensive, and often lack the spatial resolution required for detailed analysis. 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 objective was to develop a methodology for precise identification, extraction, and monitoring of individual corn crops throughout their growth cycle. This was achieved by integrating UAV-derived data with image processing, computational geometry, and machine learning techniques. UAV imagery was ac-quired bi-weekly at altitudes of 40m and 70m, capturing the entire growth cycle of a 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. Local spatial analysis and image processing techniques were em-ployed 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. For enhanced accuracy in canopy size delineation, vegetation indices were incorporated into the Voronoi model segmentation, refining the initial canopy area esti-mates by eliminating interference from soil and shadows. The proposed methodology enables precise estimation and monitoring of crop canopy size, height, biomass reduction, lodging, and stunted growth over time, providing valuable insights for precision agriculture practices. 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 mon-itoring at the individual plant level.

A cyclic antipodal points of a circle is a pair of points that are the intersection of the circle with a diameter of the circle. A recent proof of Ptolemy’s Theorem, simultaneously in both (i) Euclidean geometry; and (ii) the relativistic model of hyperbolic geometry (which is identified with the Klein model of hyperbolic geometry), motivates in this article the study of four cyclic antipodal points of a circle, ordered arbitrarily counterclockwise. The translation of results from Euclidean geometry into hyperbolic geometry is obtained by means of hyperbolic trigonometry, called gyrotrigonometry, to which Einstein addition gives rise. Formulas that extend the Pythagorean formula in both Euclidean and hyperbolic geometry are obtained as byproducts

SARS-CoV-2 Omicron variant spike RBD epitopes in complex with spike (S) -protein D614G mutations now predominate globally and increase infectivity by assembling more functional S proteins into the virion. On average, homeopathic medicine contains less than one molecule per dose on average. Single variable SphericalHarmonicY, LaguerreL, WhittakerM, SphericalBesselJ, LegendreP, LegendreQ, LaguerreL, ChebyshevT, and Hypergeometric1F1 Functions pFqarise in connection with the power series solution of the Schrodinger equation or in the summation of perturbation expansions in quantum mechanics. A quantum interpretation of the homeopathic method is presented here through a novel algebraic topology approach to supersymmetry and symmetry breaking in quantum fields and quantum gravity theory with the aim of developing a wide range of physical-based drug design applications in a Small Molecule Quantized Water Memory Network suggesting that the Hidden Black Hole Paradox of Information Loss might be solved under suitable conditions.

This study presents a novel approach for quantifying the dynamics of monthly hydraulic geometry relationships in the Jingjiang reach of the Yangtze River by integrating leaf area index (LAI) data as an indicator of riparian vegetation. A comprehensive system of ordinary differential equations (ODEs) couples traditional power-law hydraulic geometry equations with LAI, capturing the influence of erosion control on channel morphology. The periodic delayed response theory and automatic differentiation techniques are employed to enhance the modeling framework's capabilities. Calibration and verification demonstrate the models' effectiveness in capturing overall trends in discharge, width, and depth dynamics, outperforming traditional constant-parameter approaches. However, model predictive abilities are limited under extreme climate conditions due to training on normal climate data. Key assumptions, including the periodic delayed response theory's neglect of peak discharges, simplified representation of artificial cut-offs, and reliance on remotely sensed data with limited local validation, introduce uncertainties. The proposed modeling framework shows potential for broader application to other river systems with appropriate adjustments. Future research could incorporate additional environmental factors, integrate models across scales, couple with advanced simulation techniques, and expand stability assessments beyond the riverbed index. By addressing related challenges, this integrated approach lays a foundation for enhancing understanding of river morphodynamics and channel stability.

Matrices and their inverses allow accurate calculations to be produced quickly and compactly and can be used to control any process represented by a system of equations. Singular matrices require extensive workarounds (costing time and money) to solve these systems of equations because they have no inverse. Finding their inverse involves division by zero. Nevertheless, recently a new number set called semi-structured complex numbers was developed to enable division by zero in algebraic equations. The aim of this research was to demonstrate that the inverse of a singular matrix can be found using semi-structured complex numbers. This research reveals (1) Singular matrices and their inverses can be used to find a unique solution to a pair of simultaneous equations that appear to have infinitely many solutions or appear to have no solution; (2) Singular matrices map coordinates in projective space to coordinates in Euclidean space and their inverse maps coordinates in Euclidean space to coordinates in projective space; (3) the inverse of a singular matrix proves that parallel lines in Euclidean space do not intersect but in projective space intersect at a “point at infinity” and (4) collinear lines that intersect at infinitely many points in Euclidean space only intersect at one point in projective space.

This study aims to reveal the revolutionary Gamma Distribution Manifold (GDM) info-geometric analysis combined with potential Gamma distribution (GD) applications to advance Satellite Earth Observations (SEOs). An exposition of the GDM Fisher Information Matrix (FIM) was undertaken, together with the analytic investigation of the existence of FIM’s inverse. The derivation of GDM’s Geodesic Equations (GEs) is undertaken. The solution of the obtained Geodesic Equations is optimally complicated, and it provides more extensions to numerous open problems. Notably, the current paper provides a first-time unification between three multi-interdisciplinary fields, namely, information geometry theory, probability theory, and Satellite earth observations. Looking at the other side of the coin, the provided revolutionary approach in this current work reports the significant impact of info-geometric analysis on the probabilistic dynamics as well as the influential role of information geometry on satellite and space industry. This poses numerous open issues that initiates a new form of contemporary unification between these inter-disciplinaries to discover another visionary thinking out of traditional statistical frames. In other words, refraining ourselves from using classical statistical frames of thinking and delving into a new info-geometric vision of statistical distributions as well as examining real life applications of information geometry to advance satellite earth observations. The curtain is drawn on this paper by providing several challenging open problems in combination with a concluding remark and the next phase of research.

This study delves into the intricate interplay between cosmology and gravity in dilaton-based models, enhancing our understanding. Exploring boundary theories coupled to gravity, we derive a four-dimensional effective theory from the cosmological constant. Dilaton gravity is then scrutinized, revealing elegant solutions and insights into brane embedding. The analysis extends to probe scalar fields, employing the WKB approximation in both conformal and non-conformal cases. In summary, this work contributes to a nuanced understanding of the complex relationship between cosmology and gravity in dilaton-based frameworks.

The dimethylaminophenyl-substituted silver phthalocyanine [dmaphPcAg] can be used as a UV-vis photoinitiator for in situ preparation of a silver/polymer nanocomposite. To verify early steps of the supposed mechanism of radical polymerization, we performed quantum chemical calculations of m[dmaphPcAg]q complexes with charges q = +1 to -2 in the two lowest spin states m, of a free ligand and its dehydrogenated/deprotonated products m[dmaphPcHn]q, n = 2 to 0, q= 0, -1 or -2, in the lowest spin states m. The calculated electronic structures and electron transitions of all the optimized structures in CHCl3 solutions are compared with experimental EPR and UV-vis spectra, respectively. The unstable 3[dmaphPcAg]+ species deduced only from previous EPR spin trap experiments was identified. In addition to 2[dmaphPcAg]0, our results suggest the coexistence of both reaction intermediates 1[dmaphPcAg]- and 3[dmaphPcAg]- in reaction solutions. Silver nanoparticle formation is a weak point of the supposed reaction mechanism from the energetic, stereochemistry, and electronic structure points of view.

The current letter complements my info-geometric discoveries, especially those provided from two papers of mine. Fundamentally, the statistical relativization of the Generalized Brownian Motion Manifold. Following this innovative and unprecedented track of research will open a plethora of numerous info-geometric investigations to many unexplored related phenomena in the hope to uncover more new interpretations for the Generalized Brownian Motion Manifold from an info-geometric perspective.

Using the potent tools of information geometry (IG), the current research analyses the information geometrics of the five-dimensional HTBFC Manifold. By enabling a unique revolutionary analysis for the performance of Human-Trust Based Feedback Control (HTBFC), the integration of information geometry into HTBFC facilitates the relativistic analysis of the five-dimensional HTBFC manifold. Both the two- and three-dimensional manifold subcases are investigated. This work provides a ground-breaking approach to IG unification of Human- Machine Interactions (HMIs). Some potential applications of HTBFC to robotics are presented.Conclusions are provided, along with some emerging open problems and recommendations for future research.

The current study characterizes the transient M/M/1 queue manifold info-geometrically, through devising Fisher Information matrix(FIM) and its inverse(IFIM). Additionally, the impact of stability on the existence of IFIM and explore the geodesic equations of motion has been revealed. More potentially, the paper discusses some info-geometric applications to Machine Learning are highlighted. Closing remarks with some challenging open problems combined with the next phase of research are given.

From a differential geometric perspective, information geometry (IG) aims to characterise the structure of statistical geodesic models. The research done for this paper offers a novel method for modelling the information geometry of a queuing system. From the perspective of IG, the manifold of the transient M/M/infinity queue is described in this context. The Fisher Information matrix (FIM) as well as the inverse of (FIM), (IFIM) of transient M/M/infinity QM are devised. In addition to that, new results that uncovered the significant impact of stability of QM on the existence of (IFIM) are obtained. Moreover, the Geodesic equations of motion of the coordinates of the underlying transient are obtained. Also, it is revealed that stable QM is developable (i.e., has a zero Gaussian curvature) and has a non-zero Ricci Curvature Tensor (RCT). Novel stability dynamics of transient M/M/iInfinity queue manifold is revealed by discovering the mutual dual impact between the behaviour of (RCT) and the stability(instability) phases of M/M/Infinity QM. Furthermore, a new discovery that presents the significant impact of stability of queue manifold and the continuity of the unique representation between M/G/1 queue manifold and Ricci Curvature Tensor (RCT). The information matrix exponential (IME) is devised. Also, it is shown that stability of the devised (IME) enforces the instability of M/M/ Infinity QM. More interestingly, novel relativistic info-geometric queueing theoretic links are revealed .

This research delves into the intricate challenges confronting the agricultural sector, with a specialized focus on mitigating infections in tomato crops, particularly powdery mildew induced by the Leveillula Taurica pathogen. Tomatoes, renowned for their nutritional richness, are vital to global food security. However, conventional methodologies for disease detection exhibit both laborious processes and limited accuracy. In response to these challenges, this study advocates for an innovative fusion of hyperspectral imaging and deep learning methodologies to detect crop disease and its severity. The systematic workflow commenced with the curation of a dataset, involving the acquisition of live images through OpenCV, followed by conversion to RGB format and subsequent feature extraction utilizing a pre-trained visual geometry group (VGG-16) model for enhanced analysis. Sequentially, RGB images were transformed into simulated hyperspectral images (SHSI) leveraging a Neural Network generator model, offering a distinctive viewpoint on spectral information. This novel approach transcends conventional constraints by delivering a three-dimensional perspective, seamlessly integrating spatial and spectral dimensions for holistic data acquisition. The SHSI is further transmuted into a 3D visualization cube comprehensive grasp of spatial and spectral aspects encompassing spectral, spatial, and Haralick features. The research concludes with severity detection, categorized as low, moderate, or high, employing a Gaussian Mixture Model (GMM) and K-means for visualization.

In this study, the unsteady Reynolds-averaged Navier-Stokes (URANS) equations are employed in conjunction with the Menter Shear Stress Transport (SST)-Scale-Adaptive Simulation (SAS) turbulence model in compressible flow, unstructured mesh and complex geometry. Whereas, other scale-resolving approaches in space and time, such as Direct Numerical Simulation (DNS) and Large-Eddy Simulation (LES), supply more comprehensive information about the turbulent energy spectra of the fluctuating component of the flow; however, previously mentioned avenues imply computationally intensive situations, usually performed over structured meshes and relatively simply geometries. In contrast, the SAS approach is designed according to “physically” prescribed length scales of the flow. More precisely, it operates by locally comparing the length scale of the modelled turbulence to the von Karman length scale (which is prescribed according to local fluid velocity derivatives and depends on the grid point distribution in the computational domain). This length scale ratio allows the flow to dynamically adjust the local eddy viscosity in order to better capture the large scale motions (LSM) in unsteady regions of URANS simulations. While SAS may be constrained to model only low flow frequencies or waivenumbers (i.e., LSM), its versatility and computational low-cost make it attractive to obtain a quick first insight of the flow physics; particularly, in those situations dominated by strong flow unsteadiness. The selected numerical application is the well-known M219 three-dimensional rectangular acoustic cavity from the literature at two different freestream Mach numbers, M∞ (0.85 and 1.35) and a length-to-depth ratio of 5:1. Thus, we consider the “deep configuration" in experiments by Henshaw. The SST-SAS model has demonstrated a satisfactory compromise between simplicity, accuracy and flow physics description.

This paper offers a novel geometric and visual approach to the renowned Four Color Map Theorem and K5 non-planarity problem while unveiling their profound connection to the "kissing number" problem in 2D. We represent planar graphs through circles and tangents, simplifying complex structures and shedding light on these classic problems. Our proofs by contradiction, rooted in the kissing number concept, reveal that both the Four Color Map Theorem and K5 non-planarity are fundamentally linked, as they pivot around the concept of coloring. This study bridges the realms of geometry and graph theory, providing fresh insights and emphasizing the significance of the kissing number problem in various fields.

Advanced methods of treatment are needed to fight the threats of virus-transmitted deseases and pandemics. Often they are based on an improved biophysical understanding of virus replication strategies and processes in their host cells. For instance, an essential component of the replication of the Hepatitis C virus (HCV) proceeds under the influence of non-structural HCV proteins (NSPs) that are anchored to the endoplasmatic reticulum (ER), such as the NS5a protein. The diffusion of NSPs has been studied by in-vitro fluorescence recovery after photobleaching (FRAP) experiments. The diffusive evolution of the concentration field of NSPs on the ER can be described by means of surface partial differential equations (sufPDE). Knodel et al, Viruses 2018, 10, 28 estimated the diffusion coefficient of the NS5a protein by minimizing the discrepancy of an extended set of sufPDE simulations and experimental FRAP time series data. Here, we provide a scaling analysis of the sufPDEs that describe the diffusive evolution of the concentration field of NSPs on the ER. This analysis provides an estimate of the diffusion coefficient that is based only on the ratio of the membrane surface area in the FRAP region and its contour length. The quality of this estimate is explored by comparison to numerical solutions of the sufPDE for a flat geometry and for ten different 3D embedded 2D ER grids that are derived from fluorescence z-stack data of the ER. Finally, we apply the new data analysis to the experimental FRAP time-series data analyzed in our previous paper, and we discuss the opportunities of the new approach.

Having garnered significant attention in the scientific community over the past decade, Wire Arc Directed Energy Deposition (arc-DED) technology is at the heart of this investigation into additive manufacturing parameters. Singularly focused on invar as the selected material, the primary objective revolves around devising an indirect cord height measurement approach. This innovative methodology involves the seamless integration of internal signals and sensors, enabling the derivation of crucial measurements sans the requirement for direct physical interaction or conventional measurement methodologies. Through the course of this research, meticulous alteration of deposition parameters is undertaken to thoroughly scrutinize their influence on the ultimate cord dimensions. The fusion of cutting-edge manufacturing techniques with advanced sensor technology constitutes the essence of this endeavor, offering substantial potential to augment precision and efficiency in additive manufacturing processes. Remarkably cost-effective, this solution circumvents the need for intricate measurements and significantly contributes to the proper layer-by-layer growth process.

(3+1)D quantum mechanics is a four-dimensional quantum formalism, which is developed neither in a Minkowski spacetime, nor in a purely Hilbert space and not its metric is Lorentzian. This quantum mechanics also yields the quantum Einstein field equation in (3+1)D quantum spacetime. Every observable (3+1)D quantum spacetime can be found to contain internally hidden opposite spin quantum state, that results Supersymmetry. Closed continuous mappings of this hidden quantum state immediately yield more extra hidden dimensions including string. This string is found to be fundamentally eleven-dimensional (rather than lower dimensional) by nature within this quantum spacetime, which is necessarily a natural phenomenon of (3+1)D Quantum Mechanics.

The extreme environmental issues and the resulting needs to save energy have turned the attention to electrification of energy applications. One of the key components involved in energy efficiency improvements is the appropriate conception and manufacturing of electric machines. This paper overviews the electromagnetic analysis governing the behavior of permanent magnets that enabled substantial efficiency gains in recent electric machine developments. Particular emphasis is given to model the properties and losses developed in permanent magnets in the emerging high speed applications. In addition, the investigation of properties and harmonic losses related to ferromagnetic materials constituting the machine magnetic circuits are equally analyzed and discussed. The experimental validation of the implemented methodologies and developed models with respect to the obtained precision is reported. The introduction of mixed numerical techniques based on the finite element method intended to appropriately represent the different physical phenomena encountered is outlined and discussed. Finally, fast and accurate simulation techniques including aggregated lumped parameter models considering harmonic losses associated with inverter supplies are commented.

Effective development of digital twins of real-world objects requires sophisticated data collection techniques and algorithms for automated modeling of individual objects. In City Information Modeling (CIM) systems, individual buildings can be modeled automatically at the second Level Of Detail or LOD 2. Similarly, automated solutions for 3D modeling of individual trees at different levels of details are required for Tree Information Modeling (TIM) and building Forest Digital Twins (FDT). The existing algorithms support the automated modeling of trees by generating models of the canopy and the lower part of the trunk. Our work in this paper is based on the assumption that, similar to the canopy shape, the structure of tree trunk and branches is also an important consideration. An algorithm for automated modeling of tree trunks is proposed. Aiming to generate 3D models of tree trunks, the suggested approach starts by extracting the trunk point cloud, which is then segmented into single stems. Finally, the individual stems are modeled by dividing them into slices. The geometry of the developed tree models is represented in a matrix format. This solution enables automatic comparisons of tree elements over time, which is necessary for monitoring changes in forest stands and promoting sustainable forest management. Despite the huge variation of trunk geometric forms, the proposed modeling approach can gain an accuracy of better than 4 cm in the constructed tree trunk models.

The dynamic factors in the environment violate the static environment assumption of the SLAM algorithm, leading to a decrease in the accuracy of camera positioning. In recent years, many studies have attempted to address dynamic objects by combining semantic constraints and geometric constraints, but issues such as poor real-time performance, the potential for mistakenly treating humans as rigid objects, and subpar performance in high-dynamic scenes still persist. This paper proposes a dynamic scene visual SLAM algorithm called Dynamic SLAM based on target tracking and multi-view geometry (TKG-SLAM), based on object detection, Kalman filters, and multi-view geometry. This algorithm takes into consideration both real-time performance and algorithm accuracy. It combines semantic constraints and multi-view geometry constraints, selectively running the algorithm in different scenarios, filtering and preserving static points for camera pose estimation. Experimental results demonstrate that, compared to current state-of-the-art dynamic SLAM methods, our approach achieves optimal performance in some scenarios and exhibits stronger real-time capabilities.

We present a summary of the main results within the Scale Invariant Vacuum (SIV) paradigm based on the Weyl Integrable Geometry (WIG) as an extension to the standard Einstein General Relativity (EGR). After a brief review of the mathematical framework, where we also highlight the connection between the weak-field SIV equations and the notion of un-proper time parametrization within the reparametrization paradigm, we continue with the main results related to early Universe; that is, applications to inflation, Big Bang Nucleosynthesis, and the growth of the density fluctuations within the SIV. In the late time Universe the applications of the SIV paradigm are related to scale-invariant dynamics of galaxies, MOND, dark matter, and the dwarf spheroidals where one can find MOND to be a peculiar case of the SIV theory. Finally, within the recent time epoch, we highlight that some of the change in the length-of-the-day (LOD), about 0.92 cm/yr, can be accounted for by SIV effects in the Earth-Moon system.

Robot workpiece machining is interesting in industry since it offers some advantages, such as higher flexibility in comparison with the conventional approach based on the CNC technology. However, in recent years we have been facing a strong progressive shift to custom based manufacturing and low volume/high mix production, which require a novel approach to automation by the employment of collaborative robotics. However, collaborative robots feature only limited motion capability, to provide safety in cooperation with human workers. Thus, it is highly necessary to perform more detailed robot task planning to ensure its feasibility and optimal performance. In this paper, we deal with the problem of studying kinematic robot performance in the case of such manufacturing tasks, where the robot tool is constrained to follow the machining path embedded on the workpiece surface at a prescribed orientation. The presented approach is based on the well-known concept of manipulability, although the latter suffers from physical inconsistency due to mixing different units of linear and angular velocity in a general 6 DOF task case. Therefore, we introduce the characteristics of the workpiece surface constraint in the robot kinematic analysis, that enables evaluation of its available velocity capability in a reduced dimension space. Such constrained robot kinematics transform the robot`s task space to a two-dimensional surface tangent plane, and the manipulability analysis may be limited to the space of linear velocity only. Thus, the problem of physical inconsistency is avoided effectively. We show the theoretical derivation of the proposed method, which was verified by numerical experiments.

This article investigates on the radial and non-radial geodesic structures of the generalized K-essence Vaidya spacetime. Within the framework of K-essence geometry, it is important to note that the metric does not possess conformal equivalence to the conventional gravitational metric. This study employs a non-canonical action of the Dirac-Born-Infeld kind. In this work, we categorize the generalized K-essence Vaidya mass function into two distinct forms. Both the forms of the mass functions have been extensively utilized to analyze the radial and non-radial time-like or null geodesics in great details inside the comoving plane. Indications of the existence of wormhole can be noted during the extreme phases of spacetime, particularly in relation to black holes and white holes, which resemble the Einstein-Rosen bridge. In addition, we have also detected the distinctive indication of the quantum tunneling phenomenon around the central singularity.

Knowledge is a property that measures the degree of awareness of an agent about a target in an environment. The goal in conventional intelligent and cognitive agent development is to build agents that can be trained to gain knowledge about a target. The definition and operations of this knowledge associated to the agent is not clear, whereas these are required for developing a reliable, scalable and flexible agent. In this paper, we provide a concise theoretical framework for the description and quantification of the knowledge property needed for an efficient design of cognitive and rational intelligent agents. We relate the quantification scheme to the epistemological description of knowledge and present many illustrative examples on the usefulness of the quantification scheme.

Despite the successful reconciliation of special relativity and quantum mechanics (QM), a good century ago, general relativity (GR) in its current classical formulation still does not compile with QM. While GR gives precise sensical predictions at large scales, QM is obviously dominated at small scales! We think that the everlasting battle for exploring and understanding the Universe and for privileging a consistent perception of reality is therefore awaiting a consolidator rather than a conqueror. This should be capable of either unifying the two different benchmarks or at least bringing one closer to the other! The latter describes the consolidating approach, which is based on extending QM to relativistic energies and gravitational fields and generalizing Riemann to discretized Finsler geometry. Some properties of the additional geometric structures and curvatures which are disclosed by the proposed quantization and apparently overlooked in Einstein's GR, are analytically and numerically characterized. The analytical analyses introduce dynamics with possible nonlinear connections. We conclude that i) additional geometric structures and curvatures are intrinsic essential and ii) the spacetime at the quantum scale is no longer smooth or continuous. A maximal proper force is predicted, which maximally gravitationally accelerates a test particle and importantly manifests the quantum geometric nature of the generalized spacetime curvature.

Recently, historians have discussed the relevance of the nineteenth-century mathematical discipline of projective geometry for early modern classical logic in relation to possible solutions to semantic problems facing it. In this paper I consider Hegel’s Science of Logic as an attempt to provide a projective geometrical alternative to the implicit Euclidean underpinnings of Aristotle’s syllogistic logic. While this proceeds via Hegel’s acceptance of the role of the three means of Pythagorean music theory in Plato’s cosmology, the relevance of this can be separated from any fanciful “music of the spheres” approach by the fact that common mathematical structures underpin both music theory and projective geometry, as suggested in the name of projective geometry’s principal invariant, the “harmonic cross-ratio”. Here I demonstrate this common structure in terms of the phenomenon of “inverse foreshortening”. As with recent suggestions concerning the relevance of projective geometry for logic, Hegel’s modifications of Aristotle respond to semantic problems of his logic.

This paper presents a novel real time control strategy on four-wheel independent steering system for electric vehicle with stepper motors using neural networks combined with fuzzy logic. The control of the four wheels is based on a variation of Hopfield Neural Network (VHNN) method, in which the input is the error of each steering motor and the output is processed by a hyperbolic tangent function (HTF) feeding the fuzzy logic controller (FLC), which ultimately drives the stepper motor. The whole system is made up of the four aforementioned blocks where they work in sync and inseparable from each other with the common goal of driving all the steering stepper motors at the same time. Simulation results demonstrate that the proposed control method has strong robustness and practicability under different angles and speeds.

We review the main features of the non-local gauge, named the contour gauge. The contour gauge belongs to the axial type of gauges and extends the local gauge used in the most of approaches. The geometry of gluon fields and the path-dependent formalism are the essential tools for the description of non-local gauges. The principle feature of the contour gauge is that there are no the residual gauges which are left in the finite domain of space. In the review, we present the useful correspondence between the contour gauge conception and the Hamiltonian (Lagrangian) formalism. The Hamiltonian formalism is turned out to be a very convenient framework for the understanding of contour gauges. The comprehensive comparison analysis of the local and non-local gauges advocates the advantage of the contour gauge use. As an example of practical worth, we consider the Drell-Yan process and discuss the gauge invariance of the corresponding hadron tensor. We show that the appropriate use the contour gauge leads to the existence of extra diagram contributions. These additional contributions, first, restore the gauge invariance of the hadron tensor and, second, give the important terms for the observable quantities. We also demonstrate the significant role of the additional diagrams to form the relevant contour in the Wilson path-ordered exponential. Ultimately, it leads to the spurious singularity fixing. Moreover, in the present review, we discuss in detail the problem of spin and orbital angular momentum separation. We show that in SU(3) gauge theories the gluon decomposition on the physical and pure gauge components has a strong mathematical evidence provided the contour gauge conception has been used. In addition, we prove that the contour gauge possesses the special kind of residual gauge that manifests at the boundary of space. Besides, the boundary field configurations can be associated with the pure gauge fields.

Gravitation is interpreted to be an “ontomathematical” force or interaction rather than an only physical one. That approach restores Newton’s original design of universal gravitation in the framework of “The Mathematical Principles of Natural Philosophy”, which allows for Einstein’s special and general relativity to be also reinterpreted ontomathematically. The entanglement theory of quantum gravitation is inherently involved also ontomathematically by virtue of the consideration of the qubit Hilbert space after entanglement as the Fourier counterpart of pseudo-Riemannian space. Gravitation can be also interpreted as purely mathematical or logical “force” or “interaction” as a corollary from its ontomathematical (rather than physical) realization. The ontomathematical approach to gravitation is implicit in general relativity equating it to operators in pseudo-Riemannian space obeying the Einstein field equation and also well-known by the “geometrization of physics”. Quantum mechanics shares the same by the separable complex Hilbert space and defining “physical quantity” by the Hermitian operators.

This research endeavors to illuminate the path toward efficient and optimized propeller design by delving into the realm of aerodynamics. Propellers, as vital mechanical marvels, constitute the core of numerous propulsion systems, spanning from aircraft and marine vessels to wind turbines. The pursuit of enhanced propeller efficiency and performance holds paramount importance in industries where propulsion assumes a critical role, underscoring the indispensable need for a profound understanding of aerodynamics. Through meticulously crafted theoretical insights and their practical applications, this study embarks on a journey into the fascinating realm of propeller aerodynamics. While the paper primarily addresses the aerodynamic aspects of propeller design and optimization, it serves as a foundational guide for those seeking to comprehend the intricacies of propeller engineering.The research journey commences with an in-depth exploration of the fundamental principles governing propeller performance. It unveils the intricate dynamics of airflow surrounding propeller blades, shedding light on their proficiency in generating thrust, lift, and torque. The bedrock of the theoretical insights is a comprehensive analysis encompassing airfoil profiles, blade geometry, and the underlying principles of blade element theory. In navigating the ensuing pages, the study embarks on the task of demystifying the intricate methods and calculations that propel the design and optimization of propellers. Leveraging cutting-edge methodologies, the research systematically assesses the aerodynamic characteristics of propellers across various operational conditions. These invaluable insights empower the tailoring of propeller designs with precision, aligning them seamlessly with specific performance objectives. The aim is not only to impart a comprehensive understanding of propeller aerodynamics but also to provide actionable insights for engineers and researchers striving to enhance propeller efficiency. This research endeavor serves as a guiding light for both propeller enthusiasts and professionals alike. It not only enriches the broader discourse on propeller technology but also equips readers with the requisite knowledge and tools to embark on their own quests for optimized propeller design. As propulsion technologies continue their evolution, the steadfast principles elucidated herein will persist, guiding future innovations and advancements in the realm of propeller engineering. This paper serves as a profound resource, offering new researchers a comprehensive understanding of propellers and their intricate design processes.

A mixture of nonlabeled (14N2H4) and 15N labeled hydrazine (15N2H4) in an aqueous solution is oxidized to 15N2, 14N2, and 14N15N molecules, indicating the intermediate existence of the 14NH2-14NH-15NH-15NH2 with subsequent hydrogen transfers and splitting of side N-N bonds. Structures, thermodynamics, and electron characteristics of various N4H6 molecules in aqueous solutions are investigated using theoretical treatment at the CCSD/cc-pVTZ level of theory to explain the crucial part of the hydrazine oxidation reaction. Most N4H6 structures in aqueous solutions are decomposed during geometry optimization. Splitting the bond between central nitrogen atoms is the most frequent, but the breakaway of the side nitrogen is energetically the most preferred. The N-N fissions are enabled by suitable hydrogen rearrangements. Gibbs free energy data indicate the dominant abundance of NH3... N2... NH3 species. The side N atoms have very high negative charges, which should support hydrogen transfers in aqueous solutions. The only stable cyclo-(NH)4…H2 structure has a too high Gibbs energy and breaks the H2 molecule. The remaining initial cyclic structures are split into hydrazine and HN≡NH or H2N≡N species, and their relative abundance in aqueous solutions is vanishing.

Triangles are an ever present feature in nature, which the building construction industry duly echoes. However, an exact expression intended to offer the radiant field due to any triangle in an upright or inclined position had not been identified by previous research. In this case, the author has been able to solve by direct integration, the canonical expression of radiative transfer. This result alone confers a myriad of possibilities that had been inconceivable before, for studying in detail the three-dimensional heat transfer behavior of volumes and figures in which triangles do manifest, such as fins, windows, roof-gables and louvers of various kinds. Typically, shading devices, when tilted, give rise in their extremes to rhomboidal shapes which were difficult to take into account or had to be subject to discretization and subsequent Monte Carlo methods in order to perform an approximate calculation of their emission. This implied a lengthy and inexact procedure that induced many errors and consumed computing time. We can now avoid all the former downsides due to the advances hereby presented. As the novel expression can be converted into an algorithm it will be advantageously employed for simulation. This significant finding dovetails in the intricate puzzle of radiated heat and we believe that their consequences will greatly affect the conception and design of HVAC devices, aircraft manufacturing and specifically building or lighting industries among others.

This paper considers the possibility that abstract thinking and advanced synthesis skills might be selection criteria for extraterrestrial civilizations to accept communication with mankind on Earth. For this purpose, a notation not relying upon the use of alphabet and numbers is proposed, in order to denote just some basic structures of current physical theories: vector fields, 1-form fields, and tensor fields of arbitrary order. An advanced civilization might appreciate the way here proposed to achieve a concise description of electromagnetism and general relativity, and hence it might accept the challenge of responding to our signals. The abstract symbols introduced in this paper to describe the basic structures of physical theories are encoded into black and white bitmap images that can be easily converted into short bit sequences and modulated on a carrier wave for radio transmission.

The purpose of the investigation was to determine the relationship between rotary kiln liner loss and steel structure ovality. As measurement apparatus, a terrestrial laser scanner was used. The interior and exterior of the rotary kiln were measured. The primary focus object was inner-lining loss and the geometric characteristics of cylindrical shells. The research uncovered significant disparities in inner lining loss between sections. A correlation was found between ovality and elimination of inner lining. Due to the hypothesis of constant inner linig loss from the middle of the rotary kiln, the investigation found that the loss of brick lining was less than the value reported from the boreholes. The study offers significant information on maintenance and repair strategies for rotary kilns, which have the potential to increase their efficiency and useful life.

We examine here the conductance changes associated with the change in spin state in a variety of different structures, using the example of the spin crossover complex [Fe(H2B(pz)2)2(bipy)] (pz= (pyrazol-1-yl)-borate and bipy = 2,2’-bipyridine) and [Fe(Htrz)2(trz)](BF4)] (Htrz = 1H-1,2,4-triazole) thin films . This conductance change is highly variable depending on the mechanism driving the change in spin state, the substrate and the device geometry. Simply stated, the choice of spin crossover complex used to build a device is not the only factor in determining the change in conductance with the change in spin state.

Deep neural networks with powerful auto-optimization tools have been widely applied in various research fields, e.g., NLP and computer vision. However, existing neural network architectures typically are constructed using different inductive biases, e.g., preconceptions, expecting to decrease parameter search space during training, reduce computational cost or introduce expert knowledge in the neural network design. As an alternative, Multilayer Perceptron (MLP) provides much better freedom for exploration, has a lower inductive bias than convolutional neural networks (CNNs), and offers good flexibility in learning complex patterns. Even though, such neural architectures are commonly built in a flat Euclidean space, which is not necessarily the optimal space for any data, and is especially not good for modeling hierarchical correlations. Hyperbolic neural networks (HNNs) have gained attention for their ability to capture hierarchical structures present in complex data types like graphs. Recently, there has been an increasing interest to extend HNNs to computer vision tasks, motivated by the observations that images possess rich hierarchical relations. However, this is generally applied by employing a Euclidean backbone for learning higher-level semantic representations and only incorporating a hyperbolic classifier for classification, which, we argue, does not make full use of the advantage of hyperbolic space. Considering the recovery of the attention-free Multilayer Perceptron(MLP), in this paper, we extend it to non-Euclidean space and propose a novel architecture, named Hyperbolic Res-MLP (HR-MLP), that leverages fully hyperbolic layers to learn feature embeddings and perform image classification in an end-to-end fashion. With the help of the proposed Lorentz cross-patch and cross-channel layers, we can directly perform operations in the hyperbolic domain with fewer parameters, making it faster to train and providing comparatively better performance than its Euclidean counterpart. Experiments on CIFAR10, CIFAR100, and MiniImageNet demonstrate a comparable and superior performance when compared to Euclidean baselines. Our code is available at (https://github.com/Ahmad-Omar-Ahsan/HR-MLP)

As a radiant light source within the dynamic range of most spacecraft payloads, the moon pro-vides an excellent reference for on-orbit radiometric calibration. This research hinges on the pre-cise simulation of lunar spectral irradiances and the Earth-based Moon observation geometry. The paper leverages the Hapke model to simulate the temporal changes in lunar spectral irradi-ances, utilizing datasets obtained from Lunar Reconnaissance Orbiter Camera (LROC). The re-search also details the transformation process from the lunar geographic coordinate system to the instantaneous projection coordinate system, thereby delineating the necessary observational geometry. The insights offered by this study have the potential to enhance future in-orbit space-craft calibration procedures, thereby boosting the fidelity of data gathered from satellite obser-vations.

The present paper provides a new definition for dual spline curves in a geometric intuitive way based on adaptive curve refinement techniques. The dual spline is an implementation of the interpolatory subdivision scheme for curve modeling, which is comprised of polynomial segments of different degrees. Specially, the dual spline curves are mainly aims to solve the difficult geometry defeaturing problems in the existing computer-aided technology. Dual spline curves maintain various desirable properties of conventional curve modeling methods, such as local adaptive subdivision, high interpolation accuracy and convergence, continuous and discontinuous boundary approximation. By adding fictitious and intrinsic nodes inside or at the vertices of interpolation elements, the dual spline is flexible and convenient for approximating a set of ordered points or discrete segments. Combined with the Lagrange interpolation polynomial and meshless method, the proposed approach is capable of approximating the non-smooth boundary for geometry defeaturing. Experimental results are given to verify the validity, robustness, and accuracy of the proposed method.

Recently, federated learning (FL) has been receiving great attention as an effective machine learning method to avoid the security issue in raw data collection as well as to distribute the computing load to edge devices. However, even though wireless communications is a essential part for implementing FL in edge networks, there have been a few works that analyze the effect of wireless networks on FL. In this paper, we investigate FL in small-cell networks where multiple base stations (BSs) and users are located according to homogeneous Poisson point process (PPP) with different densities. We comprehensively analyze the effects of geographic node deployment on the model aggregation in FL on the basis of stochastic geometry-based analysis. We derive the closed-form expressions of coverage probability with tractable approximations and discuss the minimum required BS density for achieving a target model aggregation rate in small-cell networks. Our analysis and simulation results provide insightful information for understanding the behaviors of FL in small-cell networks, and it can be exploited as a guideline for designing the network facilitating the wireless FL.

Ditching-rotary tiller was widely used in tillage and ditching furrow during rapeseed sowing. As its ditching furrow system (consist of four identical ditching plows) would bear great drag resistance from the soil during operation, the ditching plow was optimized based on differential geometry analysis and EDEM simulation. Resistance-velocity simulation indicated the plow with parabolic type guide curve had better reduce-drag characteristics. Differential geometry analysis indicated decay rate of E and growth rate of G could represent the variable regularity of drag resistance with the increase of velocity. The L value could represent the magnitude of drag resistance. The smaller L value, decay rate of E and growth rate of G, the better drag-reduce characteristics. Quadratic rotation orthogonal combination design shown the optimal structural parameter values were: Δθ=15°, θmin=45°, h=250mm, l=100mm. The minimum average drag resistance was 230.1N. The differential geometry analysis of optimal ditching plow shown |dE/dκ| and |dG/dκ| could obtain minimum value, indicating growth rate of drag resistance for optimal plow was the lowest within the experimental level. Field experiment indicated the operation effect of optimized ditching furrow system could met the requirements of rapeseed sowing. The research provided in-depth theoretical guidance for Drag-reduce design of plow.

Electrically conductive adhesives (ECA’s) are used widely to replace or reinforce lead soldering or conductive metal components in electronic packaging applications such as die attachment, solderless interconnections, component repair, display interconnections, and heat dissipation. Their conductive behavior as well as the associated behaviors such as heat conduction and mechanical behavior (strength, rigidity, deformation and viscoelastic behavior, which may be affected by moisture ingression) are affected by adhesive film thickness, volume fraction, size and shape of the conductive filler, as well as uncured base adhesive viscosity, substrate and filler surface treatment and the applied pressure (during bonding and during conduction). The adhesive resistivity decreases precipitously above a characteristic filler volume fraction called the percolation threshold. In general, micron-sized metal fillers mixed in an adhesive (often an epoxy) resulting with different film thicknesses exhibit thickness thresholds for transition from three-dimensional conductivity to two-dimensional conductivity with considerable increases in thickness-direction (z-axis) resistivity when the film thicknesses are smaller than these threshold values. Recently, the use of conductive nanoparticles allowed decreases in percolation threshold levels as well as increases in mechanical strength and durability of ECA’s. Most ECA’s are supplied in liquid or paste form in varying viscosities and therefore, the method of their application also affects their performance. This work intends to provide an understanding of these effects on conduction behavior in (usually high-priced) equipment in which they are used.

Ptolemy’s Theorem in Euclidean geometry, named after the Greek astronomer and mathematician Claudius Ptolemy, is well known. We translate Ptolemy’s Theorem from analytic Euclidean geometry into the Poincar´e ball model of analytic hyperbolic geometry, which is based on M¨obius addition. The translation of Ptolemy’s Theorem from Euclidean geometry into hyperbolic geometry is achieved by means of the hyperbolic trigonometry, called gyrotrigonometry, to which the Poincar´e ball model gives rise, and by means of the duality of trigonometry and gyrotrigonometry.

The objective of this research is to conduct a comparative analysis between rectangular-shaped ASTM D3039 specimens with different angles (0°, 15°, and 90°) and various tensile test specimens based on ASTM and ISO standards, all 3D-printed using polyethylene terephthalate glycol (PETG) material through FDM. The study aimed to assesses the weak spot commonly found at the neck of the specimens. Two different printing orientations, namely flat and on-edge, were investigated, and a comprehensive examination and comparison were made regarding the variations in tensile strength, E-modulus, strain, and elongation at break among the tested samples. Additionally, the broken areas was evaluated, and a numerical study utilizing the finite element method (FEM) was conducted to identify stress risers' locations in each specimen type. The experimental results demonstrated that the ASTM D3039-0° specimen exhibited the best tensile properties when printed in the on-edge orientation, while the flat orientation yielded the best results in terms of the broken area. On the other hand, the ISO 527-2 specimens displayed the lowest tensile properties, regardless of the printing orientation. The study highlighted the enhanced tensile properties achieved with the rectangular shape. Specifically, the tensile strength of ASTM D3039-0° was 17.87% and 21% higher than that of the ISO 527 geometry shape for the flat and on-edge orientations, respectively. The numerical analysis indicated that the ISO 527-2 specimen had either no or minimal stress raisers, and the higher stresses observed in the narrow section were isolated from the gripping location.

When generalized noncommutative Heisenberg algebra accommodating impacts of finite gravitational fields as specified by loop quantum gravity, doubly–special relativity, and string theory, for instance, is thoughtfully applied to the eight-dimensional manifold (M8), the generalization of the Riemannian manifold becomes imminent. By constructing the deformed affine connections on a four-dimensional Riemannian manifold, we have determined the minimal length deformation of Riemann curvature tensor and its contractions, the Ricci curvature tensor, and Ricci scalar. Consequently, we have been able to construct the deformed Einstein tensor. As in Einstein’s classical theory of general relativity, we have proved that the covariant derivative of the deformed Einstein tensor vanishes, as well. We conclude that the minimal length correction suggests a correction to the spacetime curvature which is manifest in the additional curvature terms of the corrected Riemann tensor and its contractions. Accordingly, the spacetime curvature endows additional curvature and geometrical structure.

When the minimal length approach emerging from noncommutative Heisenberg algebra, generalized uncertainty principle (GUP), and thereby integrating gravitational fields to this fundamental theory of quantum mechanics (QM) is thoughtfully extended to Einstein field equations, the possible deformation of the metric tensor could be suggested. This is a complementary term combining the effects of QM and general relativity (GR) and comprising noncommutative algebra together with maximal spacelike four–acceleration. This deformation compiles with GR as curvature in relativistic eight–dimensional spacetime tangent bundle, generalization of Riemannian spacetime, is the recipe applied to derive the deformed metric tensor. This dictates how the affine connection on Riemannian manifold is straightforwardly deformed. We have discussed the symmetric property of deformed metric tensor and affine connection. Also, we have evaluated the dependence of a parallel transported tangent vector on the spacelike four–acceleration given in units of L, where L = rℏcG3 is a universal constant, c is speed of light, and ℏ is Planck constant, and G is Newton’s gravitational constant.

In this paper, we introduce the notions of nearly Sasakian and nearly Kähler statistical structures with a non-trivial example. The conditions for a real hypersurface in a nearly Kähler statistical manifold to admit a nearly Sasakian statistical structure are given. We also study Invariant and anti-invariant statistical submanifolds of nearly Sasakian statistical manifolds. At the end, some conditions under which such a submanifold of a nearly Sasakian statistical manifold is itself a nearly Sasakian statistical manifold are given.

We propose a promising model of discrete spacetime based on nonassociative geometry and complex networks. Our approach treats space as a simplicial 3-complex (or complex network), built from "atoms" of spacetime and entangled states forming n-dimensional simplices (n=1,2,3). At large scales, a highly connected network is a coarse, discrete representation of a smooth spacetime. We show that for high temperatures, the network describes disconnected discrete space. At the Planck temperature, the system experiences the phase transition, and for low temperatures, the space becomes a triangulated discrete space. We show that the cosmological constant depends on the universe’s topology. The "foamy" structure, analogous to Wheeler’s "spacetime foam," significantly contributes to the effective cosmological constant, which is determined by the Euler characteristic of the universe.

As a first step a unification of the gravitational with the electromagnetic interaction within a classical framework is proposed. It is based on a V₅-geometry, with x₅ = q/m. The sole source term is mechanical stress energy, positioned along x₅. The trajectories of test-bodies are placed in V₄ (x₅ = const)-slices. The resulting field equation couples a geometric G-tensor to mechanical stress energy, its momentum with respect to V₅ and the change of this momentum with proper time τ. The following step proceeds to the quantization of space-time to enable the formalization of elementary particles und strong interaction. This is complimented by the inclusion of spin and the weak force, leading finally to a grand total equation, the stationary version of which corresponds to Schroedinger´s equation, the instationary version to the Einstein equation of General Relativity.

Physics-informed neural networks are a promising method to yield surrogate models of flow fields. We present a metamodeling technique for variable geometries based on physics-informed neural networks. The method was applied to the DU99W350 airfoil at a Reynolds number of 1×10⁵. The model predicted the Reynolds-averaged velocity and pressure field around the airfoil for arbitrary angles of attack between 10.0° and 17.5°. The model was trained with data from CFD simulations for a limited set of angles of attack. Additionally, satisfaction of the a priori known boundary conditions as well as the Reynolds-averaged Navier-Stokes equations were trained. A sensitivity analysis concerning the Reynolds number, the amount and distribution of training data, and the turbulence model was conducted showing the superiority of the pseudo-Reynolds stress method and the demand of labeled training data in the domain. The trained network was capable of predicting the developing flow separation on the suction surface and exhibited excellent agreement with CFD results even in the proximity to the wall for interpolations as well as extrapolations from the labeled data set.

Creating self-learning algorithms, developing deep neural networks and improving other methods that "learn" for various areas of human activity is the main goal of the theory of machine learning. It helps to replace the human with a machine, aiming to increase the quality of production. The theory of artificial neural networks, which already have replaced the humans in problems of detection of moving objects, recognition of images or sounds, time series prediction, big data analysis and numerical methods remains the most dispersed branch of the theory of machine learning. Certainly, for each area of human activity it is necessary to select appropriate neural network architectures, methods of data processing and some novel tools from applied mathematics. But the universal problem for all these neural networks with specific data is the achieving the highest accuracy in short time. Such problem can be resolved by increasing sizes of architectures and improving data preprocessing, where the accuracy rises with the training time. But there is a possibility to increase the accuracy without time growing, applying optimization methods. In this survey we demonstrate existing optimization algorithms of all types, which can be used in neural networks. There are presented modifications of basic optimization algorithms, such as stochastic gradient descent, adaptive moment estimation, Newton and quasi-Newton optimization methods. But the most recent optimization algorithms are related to information geometry, for Fisher-Rao and Bregman metrics. This approach in optimization extended the theory of classic neural networks to quantum and complex-valued neural networks, due to geometric and probabilistic tools. There are provided applications of all introduced optimization algorithms, what delighted many kinds of neural networks, which can be improved by including any advanced approaches in minimization of the loss function. Afterwards, we demonstrated ways of developing optimization algorithms in further researches, engaging neural networks with progressive architectures. Classical gradient based optimizers can be replaced by fractional order, bilevel and, even, gradient free optimization methods. There is a possibility to add such analogues in graph, spiking, complex-valued, quantum and wavelet neural networks. Besides the usual problems of image recognition, time series prediction, object detection, there are many are other tasks for modern theory of machine learning, such as solving problem of quantum computations, partial differential and integro-differential equations, stochastic processes and Brownian motion, making decisions and computer algebra.

During few last years, climate change including global warming which is attributed to human activities and also its long-term adverse effects on the planet’s functions have been identified as the most challenging discussion topics which have arisen many concerns and efforts to find the possible solutions. Since the warmth arising from Earth’s landscapes affects the world’s weather and climate patterns, we decided to study the changes in the Land Surface Temperature (LST) patterns in different seasons through non-linear methods. Here, we particularly want to estimate the non-integer dimension and fractal structure of the land surface temperature. For this study, the (LST) data has been obtained during the daytime by the Moderate Resolution Imaging Spectroradiometer (MODIS) on NASA’s Terra satellite. Depending on what time of the year data has been collected, temperatures change in different ranges. Since equatorial regions remain warm, and Antarctica and Greenland remain cold, and also because altitude affects temperature, we selected Riley County in the U.S. state of Kansas, which does not belong to any of this type locations and we are interested to observe the seasonal changes in temperature in this county. The results of the present study show that the Land Surface Temperature (LST) belongs to the class of fractal process with non-integer dimension.

Fractals offer the ability to generate fascinating geometric shapes with all sorts of unique characteristics (for instance, fractal geometry provides a basis for modelling infinite detail found in nature). While fractals are non-euclidean mathematical objects which possess an assortment of properties (e.g., attractivity and symmetry), they are also able to be scaled down, rotated, skewed and replicated in embedded contexts. Hence, many different types of fractals have come into limelight since their origin discovery. One particularly popular method for generating fractal geometry is using Julia sets. Julia sets provide a straightforward and innovative method for generating fractal geometry using an iterative computational modelling algorithm. In this paper, we present a method that combines Julia sets with dual-quaternion algebra. Dual-quaternions are an alluring principal with a whole range interesting mathematical possibilities. Extending fractal Julia sets to encompass dual-quaternions algebra provides us with a novel visualize solution. We explain the method of fractals using the dual-quaternions in combination with Julia sets. Our prototype implementation demonstrate an efficient methods for rendering fractal geometry using dual-quaternion Julia sets based upon an uncomplicated ray tracing algorithm. We show a number of different experimental isosurface examples to demonstrate the viability of our approach.

We employed the Riemannian Face Manifold (RFM) as an alternative approach to the conventional linear Euclidean space for explaining the atypicality bias in face likeliness judgments. The RFM posits that the mental representation of faces is better captured as a manifold of stable states, accounting for the nonlinearity in the physical properties of faces. To examine the relationship between physical and psychological distance of morph and typical/atypical faces, we manipulated the parameter k and incorporated a weight function in the Riemannian metric. Our results indicate that the psychological distance between the morph and typical face was longer than that between the morph and atypical face, consistent with prior research on the atypicality bias in perceptual similarity. The RFM approach provides mathematical support and is a powerful tool for studying face perception and recognition, offering potential implications for explaining the other-race effect. Future research can utilize the RFM to investigate individual differences in face recognition abilities and expertise, and how they impact psychological distance and face processing.

Computer extended Descriptive Geometry (CeDG) is a new approach to solve and build computer models of three dimensional (3D) geometrical systems through descriptive geometry procedures that have demonstrated reliability and accuracy. CeDG may calculate a parametric algebraic exact form for the spatial curves generated in the intersection of two surfaces, as well as of the flattened pattern of any developable surface involved in those encounters. This study presents first the theoretical foundations and methodology to calculate those parametric algebraic curves. Secondly, a compound hopper is defined and modelled through CeDG (implemented in GeoGebra) and CAD (Solid Edge 2023) approaches to evaluate the advantages of CeDG against CAD. The results demonstrate the robustness and accuracy of the CeDG technique for surfaces intersection and flattening and the advantages of CeDG against Solid Edge 2023 in solving the hopper case study.

The research paper proposes an algorithm to find congruence criteria between two convex polygons in Euclidean Geometry. It begins with a review of triangles, then extends to quadrilaterals and eventually gener- alizes the case to n-sided polygons. It attempts to prove said algorithm using a method of induction and a case-by-case analysis. It also states a corollary to said algorithm

We exploit the properties of complex time to obtain an analytical relationship based on considerations of causality between the two conserved quantities of a system’s Hamiltonian and its Entropy Production. In natural units, when complexified, the one is simply the Wick-rotated complex-conjugate of the other. A Hilbert transform relation is constructed in the formalism of Quantitative Geometrical Thermodynamics which enables system irreversibility to be handled analytically within a framework that unifies both the microscopic and macroscopic scales, and which also unifies the treatment of both reversibility and irreversibility as complementary parts of a single physical description. In particular the thermodynamics of two unitary entities are considered: the alpha particle which is absolutely stable (that is, trivially reversible with zero entropy production), and a black hole whose absolute disequilibrium (unconditional irreversibility) is characterized by a non-zero entropy production for which we show an alternate derivation confirming our previous one (Universe 7, 2021, 325). The thermodynamics of a canonical decaying harmonic oscillator are also considered. In this treatment the complexification of time also enables a meaningful physical interpretation of both “imaginary time” and “imaginary energy”.

Central to an understanding of the physical nature of biosystems is an apprehension of their ability to control entropy dynamics in their environment.  To achieve ongoing stability and survival, living systems must adaptively respond to incoming information signals concerning matter and energy perturbations in their biological continuum (biocontinuum).  Entropy dynamics for the living system are then determined by the natural drive for reconciliation of these information divergences in the context of the constraints formed by the geometry of the biocontinuum information space.  The configuration of this information geometry is determined by the inherent biological structure, processes and adaptive controls that are necessary for the stable functioning of the organism.  The trajectory of this adaptive reconciliation process can be described by an information-theoretic formulation of the living system’s procedure for actionable knowledge acquisition that incorporates the axiomatic inference of the Kullback Principle of Minimum Information Discrimination (a derivative of Jaynes’ principle of maximal entropy). Utilizing relative information for entropic inference provides for the incorporation of a background of the adaptive constraints in biosystems within the operations of Fisher biologic replicator dynamics.  This mathematical expression for entropic dynamics within the biocontinuum may then serve as a theoretical framework for the general analysis of biological phenomena.

We have shown that according to the predictions of the standard quantum theory, signaling is possible using a postponed compensation Hong-Ou-Mandel interferometer, although it violates Lorentz invariance. We argue that new physics is required to deal with such a paradox. Either quantum principles or relativity needs reassessment. We propose an experiment that can decide whether relativity rules over quantum or vice versa.

There must exist a reformulation of quantum field theory, even at low energies, which does not depend on classical time. The octonionic theory proposes such a reformulation, leading to a pre-quantum pre-spacetime theory. The ingredients for constructing such a theory, which is also a unification of the standard model with gravitation, are : (i) the pre-quantum theory of trace dynamics – a matrix-valued Lagrangian dynamics, (ii) the spectral action principle of non-commutative geometry, (iii) the number system known as the octonions, for constructing a non-commutative manifold and for defining elementary particles via Clifford algebras, (iv) a Lagrangian with $E_8 \times E_8$ symmetry. The split bioctonions define a sixteen dimensional space (with left-right symmetry) whose geometry (evolving in Connes time) relates to the four known fundamental forces, while predicting two new forces, $SU(3)_{grav}$ and $U(1)_{grav}$. This latter interaction is possibly the theoretical origin of MOND. Coupling constants of the standard model result from left-right symmetry breaking, and their values are theoretically determined by the characteristic equation of the exceptional Jordan algebra of the octonions. The quantum-to-classical transition, precipitated by the entanglement of a critical number of fermions, is responsible for the emergence of classical spacetime, and also for the familiar formulation of quantum theory on a spacetime background.

Hydraulic relationships are important for water resource management, hazard prediction, and modelling. Since Leopold first identified power law expressions that could relate streamflow to top-width, depth, and velocity, hydrologists have been estimating ‘At-a-station Hydraulic Geometries’ (AHG) to describe average flow hydraulics. As the amount of data, data sources, and application needs increase, the ability to apply, integrate and compare disparate and often noisy data is critical for applications ranging from reach to continental scales. However, even with quality data, the standard practice of solving each AHG relationship independently can lead to solutions that fail to conserve mass. The challenge addressed here is how to extend the physical properties of the AHG relations, while improving the way they are hydrologically addressed and fit. We present a framework for minimizing error while ensuring mass conservation at reach - or hydrologic Feature - scale geometries’(FHG) that complies with current state-of-the-practice conceptual and logical models. Through this framework, FHG relations are fit for the United States Geological Survey’s (USGS) Rating Curve database, the USGS HYDRoacoustic dataset in support of the Surface Water Oceanographic Topography satellite mission (HYDRoSWOT), and the hydraulic property tables produced as part of the NOAA/Oakridge Continental Flood Inundation Mapping framework. The paper describes and demonstrates the accuracy, interoperability, and application of these relationships to flood modelling and presents this framework in an R package.

A high-voltage transmission tower consists of structures to avoid the risk of electric shock and to prevent the risk of collapse. Hence, towers are generally designed to be high-rise for efficiency. The main posts of the tower are primary structural members that resist loads under various load conditions. Therefore, the contribution of the secondary member to securing the stiffness and strength of the main posts by reducing the effective buckling length is important. However, there are no detailed design criteria for secondary members. In this study, the structural effects of horizontal members and braces on the torsional stiffness, elastic buckling strength, and load-carrying capacity of transmission towers were observed through various structural analysis methods including linear-elastic, eigenvalue, and geometric nonlinear and inelastic analyses under governing load combinations. According to the analytical study, rather than the horizontal members, the brace spacing significantly affects the structural performance. Therefore, the number of horizontal members can be minimized if sufficient brace members are erected. If the brace spacing is wide, it is recommended that the horizontal members be erected to create K bracing, and the buckling resistance of the main posts can be thus enhanced.

The main purpose of this study was to develop a model for predicting the quality of holes drilled in the root part of a spar of helicopter main rotor blades made of the Glass Fiber Reinforced Plastic (GFRP)-Ti multilayer polymer composite. As the main quality criterion, delaminations at the entry and exit of the drill from the hole were taken. In the experimental study a conventional drill and two modified geometry drills: a double-point angle drill and a dagger drill were used. Preliminary experiments showed the best hole quality when using modified drills, which allowed further detailed study only with both modified drills at different drilling speeds and feed rates. Its results in the form of training sets were used to build the Artificial Neural Networks (ANNs) to predict delamination at the entry and exit of drilled holes. The analysis of the fitted response functions, presented as 3D surfaces plots and superimposed contour plots, made it possible to choose the better tool - a double-point angle drill and determine the optimal area for drilling speed and feed rates, confirming that the prediction of the quality and productivity of machining composites based on ANN is an effective tool to search and quantify the quality criteria of such technologies.

Coronary artery disease (CAD) represents a modern pandemic associated with significant morbidity and mortality. The multi-faceted pathogenesis of this entity has long been investigated, highlighting the contribution of systemic factors such as hyperlipidemia and hypertension. Nevertheless, recent research has drawn light to the importance of geometrical features of coronary vasculature on the complexity and vulnerability of coronary atherosclerosis. Various parameters have been investigated so far, including vessel-length, cross-sectional area, curvature, and tortuosity, using primarily invasive angiography and recently non-invasive cardiac computed tomography angiography (CCTA). It is clear that there is correlation between geometrical parameters and both the haemodynamic alterations augmenting the atherosclerosis-prone environment and the extent of plaque burden. The purpose of this review is to discuss the currently available literature regarding this issue and propose a potential non-invasive imaging biomarker, the geometric risk score, which could be of importance to allow early detection of individuals at increased risk of developing CAD.

Purpose – Extend the Blade Element Momentum Theory (BEMT) such that rotors with pronounced cone and axis angle (tilt or yaw) can be calculated. Derive an equation for the speed ratio (lambda) as a function of Tip Speed Ratio (TSR), radius, blade, cone and axis angle. This converts the BEMT into an Unsteady BEMT or UBEMT. Present the Wagner rotor as one such rotor geometry. --- Methodology – Literature review and calculations. --- Findings – The UBEMT can be used to calculate highly unconventional rotor geometries. --- Research Limitations – Although the aerodynamic coefficients used in the UBEMT are from measurements in steady flow conditions, they can be used with success. --- Practical Implications – Also conventional Horizontal Axis Wind Turbines (HAWT) with noticeable cone and axis angle should be calculated with the UBEMT. The accuracy of power calculations of these HAWTs can be slightly improved. --- Originality – Analytic equations for rotors with cone and axis angle have barely been discussed.

When gravity is quantum, the point structure of space-time should be replaced by a non-commutative geometry. This is true even for quantum gravity in the infra-red. Using the octonions as space-time coordinates, we construct a pre-spacetime, pre-quantum Lagrangian dynamics. We show that the symmetries of this non-commutative space unify the standard model of particle physics with $SU(2)_R$ chiral gravity. The algebra of the octonionic space yields spinor states which can be identified with three generations of quarks and leptons. The geometry of the space implies quantisation of electric charge, and leads to a theoretical derivation of the mysterious mass ratios of quarks and the charged leptons. Quantum gravity is quantisation not only of the gravitational field, but also of the point structure of space-time.

Eric Lord has observed: “In nature, helical structures arise when identical structural subunits combine sequentially, the orientational and translational relation between each unit and its predecessor remaining constant.” This paper proves Lord’s Observation. Constant-time algorithms are given for the segmented helix generated from the intrinsic properties of a stacked object and its conjoining rule. Standard results from screw theory and previous work are combined with corollaries of Lord’s observation to allow calculations of segmented helices from either transformation matrices or four known consecutive points. The construction of these from the intrinsic properties of the rule for conjoining repeated subunits of arbitrary shape is provided, allowing the complete parameters describing the unique segmented helix generated by arbitrary stackings to be easily calculated. Free-libre open-source interactive software and a website is provided which performs this computation for arbitrary prisms along with interactive 3D visualization . We prove that any subunit can produce a toroid-like helix or a maximally-extended helix, forming a continuous spectrum based on joint-face normal twist. This software, website and paper, taken together, compute, render, and catalog an exhaustive “zoo” of 28 uniquely-shaped platonic helices, such as the Boerdijk-Coxeter tetrahelix and various species of helices formed from dodecahedra.

There is no formal difference between particles and black holes. This formal similarity lies in the intersection of gravity and quantum theory; quantum gravity. Motivated by this similarity, `wave-black hole duality' is proposed, which requires having a proper energy-momentum tensor of spacetime itself. Such a tensor is then found as a consequence of `principle of minimum gravitational potential'; a principle that corrects the Schwarzschild metric and predicts extra periods in orbits of the planets. In search of the equation that governs changes of observables of spacetime, a novel Hamiltonian dynamics of a Pseudo-Riemannian manifold based on a vector Hamiltonian is adumbrated. The new Hamiltonian dynamics is then seen to be characterized by a new `tensor bracket' which enables one to finally find the analogue of Heisenberg equation for a `tensor observable' of spacetime.

This short reading is an extraction from our previous work (Nyambuya 2020), the purpose of which is to make clear that it is very much possible to use Weyl (1918)'s idea of a conformal metric to achieve tensorial affinities. We are of the strong view that this is very important as it is predominantly assumed that this not possible. We want to dispel this myth once and for al-time.

We present a summary of the main results within the Scale Invariant Vacuum (SIV) paradigm as related to the Weyl Integrable Geometry. After a brief review of the mathematical framework, we will highlight the main results related to inflation within the SIV [9], the growth of the density fluctuations [8], and the application of the SIV to scale-invariant dynamics of Galaxies, MOND, Dark Matter, and the Dwarf Spheroidals [7]. The connection of the weak-field SIV results to the un-proper time parametrization within the reparametrization paradigm is also discussed [14].

A theoretical description of quantum jumps at the level of elementary particles is proposed, based on a micro-cosmological interpretation of their de Broglie phase. The third quantization formalism proposed in current literature for the description of baby universes in quantum cosmology is used here to describe the breakdown of unitarity in the transition from the pre-jump to the post-jump wave function. The corpuscular aspect manifested by the particle in the micro-interaction that originates the jump is represented by a pair of evanescent "micro-universes", respectively pre- and post-jump, connected by a wormhole. The latter represents the actual implementation of the interaction that leads to the projection on the outgoing state; this interaction is always local, even when the selected outgoing state is entangled. Therefore, the decoherence which leads to the emergence of classicality is originated by the same fundamental interactions of the Standard Model involved in the unitary evolution of the wave function. The objective nature of the reduction process admits implications on the possibility of using the formalism in the cosmological context, which are briefly discussed.

Snap fit is a common mechanical mechanism. It uses the physical asymmetry that is easy to assemble but difficult to disassemble to provide a simple and fast link between objects. The ingenious combination of geometric shape, bending elasticity and friction of the snap fit is the mechanism behind the easy to assemble but difficult to disassemble disassemble. Yoshida and Wada (2020) has done a groundbreaking work in the analysis of the elastic snap fit. During our study of their paper, while we really enjoyed their research, unfortunately we detected several questioning formulations. After careful checking, we found that those formulations are not typographical, therefore it is necessary to make corrections. This paper reformulates the linear elasticity of a cylindrical snap fit, obtains an exact solution and proposes an accurate relation between the opening angle and bending tangent angle. Under the first order approximation, our formulations can reduced to the results of Yoshida and Wada and hence confirms the scientific correctness of Yoshida and Wada's work. Furthermore, this paper also derives a correct vertical displacement expression, and propose a new way of disassembly by bending for the first time and formulate a scaling law by data fitting. All formulations are validated by finite element simulation and experiment. The research here is helpful to the design of elastic snap fit or adjustable mechanical mechanism and metamaterial cell.

We developed a novel approach in the field of spatiotemporal modelling, based on the spatialisation of time: the Timescape algorithm. It is especially aimed at sparsely distributed datasets in ecological research, whose spatial and temporal variability is strongly entangled. The algorithm is based on the definition of a spatiotemporal distance that incorporates a causality constraint and that is capable of accommodating the seasonal behaviour of the modelled variable as well. The actual modelling is conducted exploiting any established spatial interpolation technique, substituting the ordinary spatial distance with our Timescape distance, thus sorting, from the same input set of observations, those causally related to each estimated value at a given site and time. The notion of causality is expressed topologically and it has to be tuned for each particular case. The Timescape algorithm originates from the field of stable isotopes spatial modelling (isoscapes), but in principle it can be used to model any real scalar random field distribution.

Radiation Fireballs are singular phenomena which involve severe thermal radiation and consequently, they need to be duly assessed and prevented. Although the radiative heat transfer produced by a sphere is relatively well known, the shadowing measures implemented to control the fireball’s devastating effects have frequently posed a difficult analytical instance, mainly due to its specific configuration. In this article, since the usual solving equations for the said cases are impractical, the authors propose a novel graphic-algorithm method that sorts the problem efficiently for different kinds of obstructions and relative positions of the fireball and the defenses. Adequate application of this method may improve the safety of a significant number of facilities exposed to such risks.

Acid fracturing simulation is used widely to optimize carbonate reservoirs and improve acid fracturing treatment performance. In this study, a method was used to minimize the risk of the acid fracturing treatment. First, optimal fracture geometry parameters with UFD methods are calculated. After that, design components change as long as fracture geometry parameters reach their optimal values. The results showed a high flow rate needed to achieve optimal fracture geometry parameters with increasing acid volume. Sensitivity analysis was performed on controllable and reservoir parameters. It observed that a high flow rate should be applied for a low fluid viscosity to achieve the optimization goals. Straight acid reaches optimal conditions at a high flow rate and low volume. These conditions for retarded acids appear only at a low flow rate and high volume. The study of the acid concentration for gelled acid showed that as it increased, the flow rate and volume increased. Besides, for low permeability formation, a large fracture half-length and small fracture width are desirable. In this case, a higher flow rate will be required. The sensitivity analysis showed that the optimum flow rate and acid volume increase and decrease for the high Young's modulus. The effect of closure stress was also investigated and observed for a sample with high closure stress, low flow rate, and high acid volume are required.

We propose a non-invasive approach to control the quality of spheroids and their fusion into a complex bioconstruct. The proposed method is based on the union of the nutrient concentration change calculated using Fick's law and the "reaction-diffusion" equations, taking into account absorption coefficient with specifying the exact fusion geometry using implicit Function Repre-sentation (FRep) functions. The proposed approach allows us to analyze the viability of cells within the spheroid, predict the fusion of spheroids, and accurately model complex heteroge-neous biostructures as a future task for our research. These results will significantly accelerate the development of such a promising field of additive biotechnologies as 3D bioprinting.

Here we studied Bianchi type-III string cosmological models generated by means of a cloud of strings with particles connected to them in the framework of Lyra geometry considering five-dimensional space-time. To obtain the exact solutions of field equations we consider that the shear scalar and the scalar expansion are proportional, σ∞θ which leads to D=cn and secondly we adopt the assumption considering the Reddy String Condition, ρ+λ=0. From the two different cases obtained here, first case leads to the Bianchi type-III string cosmological model in Lyra geometry in five-dimensional space-time and the second case leads to the five-dimensional vacuum universe in general relativity. The Geometrical and physical properties of the model universe are studied comparing with the present day’s observational findings. The model universe obtained here starts with the big bang and as time progresses both particle density ρp and energy density ρ decreases with expansion of our Universe.

Every biological image contains quantitative data that can be used to test hypotheses about how patterns were formed, what entities are associated with one another, and whether standard mathematical methods inform our understanding of biological phenomena. In particular, spatial point distributions and polygonal tessellations are particularly amendable to analysis with a variety of graph theoretic, computational geometric, and spatial statistical tools such as: Voronoi Polygons; Delaunay Triangulations; Perpendicular Bisectors; Circumcenters; Convex Hulls; Minimal Spanning Trees; Ulam Trees; Pitteway Violations; Circularity; Clark-Evans spatial statistics; Variance to Mean Ratios; Gabriel Graphs; and, Minimal Spanning Trees. Furthermore, biologists have developed a number of empirically related correlations for polygonal tessellations such as: Lewis’s Law (the number of edges of convex polygons are positively correlated with the areas of these polygons): Desch’s Law (the number of edges of convex polygons are positively correlated with the perimeters of these polygons); and Errara’s Law (daughter cell areas should be roughly half that of their parent cells’ areas). We introduce a new Pitteway Law that the number of sides of the convex polygons in a Voronoi tessellation of biological epithelia is proportional to the minimal interior angle of the convex polygons as angles less than 90 degrees result in Pitteway violations of the Delaunay dual of the Voronoi tessellation.

Elliptic scator algebra is possible in 1+n dimensions, n∈N. It is isomorphic to complex algebra in 1+1 dimensions, when the real part and any one hypercomplex component are considered. It is endowed with two representations: an additive one, where the scator components are represented as a sum; and a polar representation, where the scator components are represented as products of exponentials. Within the scator framework, De Moivre’s formula is generalized to 1+n dimensions in the so called victoria equation. This novel formula is then used to obtain compact expressions for the integer powers of scator elements. A scator in S1+n can be factored into a product of n scators that are geometrically represented as its projections onto n two dimensional planes. A geometric interpretation of scator multiplication in terms of rotations with respect to the scalar axis is expounded. The powers of scators, when the ratio of their director components is a rational number, lie on closed curves. For 1+2 dimensional scators, twisted curves in a three dimensional space are obtained. Collecting previous results, it is possible to evaluate the exponential of a scator element in 1+2 dimensions.

Currently, various industrial processes are carried out in fluidized bed reactors, such as fermentation, water treatment, and algae growth. Knowing its internal dynamics is fundamental for the intensification of these processes. This work assesses the motion of fluidized calcium alginate spheres under the influence of an upward fluid flow within a 1.2 m high and 0.1 m inner diameter acrylic column. The Radioactive Particle Tracking technique is a proper methodology to study the internal dynamics of these kinds of equipment. Liquid-Solid Fluidized Bed is compared with the Gas-Liquid-Solid Fluidized Bed operation mode in terms of mixing behavior. Data gathered is analyzed in view of Shannon entropy as a dynamic mixing measure. Mixing times are found to be of the same order of magnitude. However, the Liquid-Solid Fluidized Bed achieves a lower homogenization degree. Also, we found good agreement between two criteria for assessing stability for the mixed state: the Shannon Entropy time-series plateau and the Glansdorff-Prigogine criterion based on Fisher information.

A way of systematizing different geometries by geometrical transformations is presented by using Klein’s perspective. Symmetry is considered the basic precedent, and different groups of transformations are introduced by using Erlangen program ideas. So, to focus on the importance of geometric transformations, two purposes are shown: first, the classification of geometries is based on the invariants of geometric transformations; and second, the construction of geometry unlike the theory of deduction can be done by means of geometric transformations.

According to Swiss-American Doctor of Sciences and Agricultural Engineer Jean-Pierre Jost, "plants communicate with each other by the quality of light emitted by their leaves or by means of stress hormones and other volatile chemicals. They also make use of cocktails of chemicals, pheromones, shape and colors to attract pollinators whereas other signals repel unwanted organisms. Insects are able to decode such messages and respond accordingly. Plants are apparently also communicating by sounds and electric signals." (1) How do plants do these things? Of course, it's easy to imagine it's all purely mechanical. But at the risk of sounding like a mysticism fanatic, I wonder if plants' activities are part of a spectrum of consciousness that pervades the entire universe. This spectrum would result from everything in the universe having the BITS or BInary digiTS of electronics as their ultimate composition. As explained in this hypothesis, something I call vector-tensor-scalar geometry is essential to my hypothesis. VTS geometry produces the particles of chemicals and pheromones, and refers to communication via electric signals when it speaks of electromagnetic-gravitational interaction. There's another consequence if everything in the universe is ultimately composed of electronic BITS and the cosmos is a spectrum of consciousness/artificial intelligence. It's impossible for an absence of consciousness to exist, either after death or before conception.

This hypothesis is the result of my conviction that science will oneday prove everything in space and time is part of a unification. In "A Brief History of Time", Stephen Hawking wrote, "If everything in the universe depends on everything else in a fundamental way, it might be impossible to get close to a full solution (of the universe's puzzles) by investigating parts of the problem (such as general relativity and quantum mechanics) in isolation." The goal: to establish a “proof of concept” to which equations can be added. It’s concluded the Steady State, Big Bang, Inflation and Multiverse theories all ultimately fail and a topological model including bits (binary digits), Mobius strips, figure-8 Klein bottles and Wick rotation works better. The failed cosmologies have impressive points leading to the idea that they’re all necessary stepping-stones. For example, the Big Bang is seen here as violation of the 1st Law of Thermodynamics but its supposed origin from quantum fluctuations is reminiscent of bits switching between 1 and 0. The topological hypothesis has potential to explain dark matter, dark energy, and electromagnetic-gravitational union. Finally, the article introduces what is called vector-tensor-scalar geometry - and extensions of Einstein's Gravity and Maxwell's Electromagnetism.

The part of this article dealing with topological insulators and topological superconductors was first written about two years ago - the ideas in the part about the topological universe originated six years ago or more. It’s rather strange that I never put the two parts together in writing before. My belief in unification is unshakeable - I’ve been convinced for years that the universe must be composed of topology. Since Earth is part of the cosmos, entanglement means it must have topological materials. The reverse is also true: topological materials on Earth are well known to science - so in a unification, space and time inevitably possess topological composition. Topological materials (topological insulators, topological superconductors) can be less mystifying if they’re related to the paradigm-shifting deterministic view of quantum mechanics which is described in the universal topology (the “rubber-sheet geometry” of the cosmos): see my previous submission “Hypothesis of Quantum Gravity - Resulting from a Static, Topological Universe Resulting from the Positives and Negatives of the Steady State and Big Bang Theories" at https://www.preprints.org/manuscript/202105.0239/v1 (the first section of this present article is a quick summary of the relevant parts).

There must exist a reformulation of quantum field theory which does not refer to classical time. We propose a pre-quantum, pre-spacetime theory, which is a matrix-valued Lagrangian dynamics for gravity, Yang-Mills fields, and fermions. The definition of spin in this theory leads us to an eight dimensional octonionic space-time. The algebra of the octonions reveals the standard model; model parameters are determined by roots of the cubic characteristic equation of the exceptional Jordan algebra. We derive the asymptotic low energy value 1/137 of the fine structure constant, and predict the existence of universally interacting spin one Lorentz bosons, which replace the hypothesised graviton. Gravity is not to be quantized, but is an emergent four-dimensional classical phenomenon, precipitated by the spontaneous localisation of highly entangled fermions.

The novel coronavirus has presented specimen-access challenges to geoscientific researchers, including paleobiologists interested in fossil ammonoids. Ammonoid sutures are geometric patterns formed by the intersection of the septa and the shell wall, and have long been a diagnostic tool for ammonite researchers for such applications as species identification, taxonomic relationships, ontogenetic change, functional and evolutionary morphology, and other aspects of ammonoid paleobiology. Without access to specimens in museum and institutional collections, researchers must rely on previously published illustrations and photographs of ammonoid sutures. However, many of these illustrations were published decades ago without an index of scale. Suture tracings lacking a scale bar are not usable by researchers interested in applying the quantitativeness of fractal geometry to the interpretation of septal complexity. Additonally, distortion of the marginal elements of suture geometry occurs due to shell curvature near the venter and umbilicus. The revised approach described here eliminates the problem of missing scale information in fractal analysis of ammonite sutures, making use of just the lateral lobe and adjacent saddle. Our revised method’s non-requirement of a full hemisuture also facilitates comparisons among sutures within an ontogenetic sequence, or sutures from multiple ammonite taxa.

The asymmetric skew divergence smooths one of the distributions by mixing it, to a degree determined by the parameter $\lambda$, with the other distribution. Such divergence is an approximation of the KL divergence that does not require the target distribution to be absolutely continuous with respect to the source distribution. In this paper, an information geometric generalization of the skew divergence called the $\alpha$-geodesical skew divergence is proposed, and its properties are studied.

The present paper investigates the influence of the specimen size of EN-AW6082 wrought aluminium alloy subjected to very high cycle fatigue (VHCF) tests. The hourglass specimens were tested under fully reversed loading condition, up to 10^9 cycles, by means of the ultrasonic fatigue testing machine developed by Italsigma® (Italy). Three specimens groups were considered, with a diameter in the middle cross-section ranging from 3 mm up to 12 mm. The stress field in the specimens was determined numerically and by strain gauge measurements in correspondence of the cross-section surface. The dispersion of experimental results has been accounted for, and data are reported in P-S-N diagrams. The decrease in fatigue resistance with increasing specimen size is evident. Theoretical explanation for the observed specimen-size effect is provided, based on Fractal Geometry concepts, allowing to obtain scale independent P-S*-N curves. The fatigue life expectation in the VHCF regime of the EN-AW6082 aluminium alloy full-scale components is rather overestimated if it is assessed only from standard small specimens of 3 mm in diameter. Experimental tests carried out on larger specimen, and a proper extrapolation, are required to assure safe structural design.

Ampelography, the botanical discipline dedicated to the identification and classification of grapevine cultivars, was grounded on the description of morphological characters and more recently is based on the application of DNA polymorphisms. New methods of image analysis may help to optimize morphological approaches in ampelography. The objective of this study was the classification of representative cultivars of Vitis vinifera conserved in the Spanish collection of IMIDRA according to seed shape. Thirty eight cultivars representing the diversity of this collection were analyzed. A consensus seed silhouette was defined for each cultivar representing the geometric figure that better adjusted to their seed shape. All the cultivars tested were classified in ten morphological groups, each corresponding to a new model. The models are geometric figures defined by equations and similarity to each model is evaluated by quantification of percent of the area shared by the two figures, the seed and the model (J index). The comparison of seed images with geometric models is a rapid and convenient method to classify cultivars. A large proportion of the collection may be classified according to the new models described and the method permits to find new models according to seed shape in other cultivars.

In this work, generalized geometry of second-order tangent groups and affine configuration complexes is proposed. Initially, geometry for higher weights n=4 and weights n=5 is presented through some interesting and suitable homomorphisms, finally, this geometry is extended and generalized for any weight n.

New class of conserved quantities is constructed. These quantities find direct application in mechanics of dissipative (generally non-conservative) dynamical systems. Approach demands formulation in the language of geometric mechanics, providing theoretical framework for situations with energy flow in and out of the system. As a by product, we suggest possibility of existence of Hamiltonian form for every autonomous ODE system, evolution of which is governed by non-potential generator of motion. Various examples are provided, ranging from physics and mathematics, to chemical kinetics and population dynamics in biology. Applications of these ideas in geometric integration techniques (GNI) of numerical analysis are discussed, and as an example of such, new discrete gradient-based numerical method is introduced.

Several problems of radiative transfer are yet unsolved because of the difficulties of the calculations involved in them, especially if the intervening shapes are geometrically complex. The main goal of our investigation in this domain is to convert the formulas that were previously derived, into a graphical interface based on the projected solid-angle principle. Such procedure is now feasible by virtue of several widely diffused programs for Algorithms Aided Design (AAD). Accuracy and reliability of the process is controlled by means of the analytical software DianaX developed at an earlier stage by the authors. With this new approach the often cumbersome procedure of lighting and thermal exchange calculations can be simplified and made available for the neophyte, with the undeniable advantage of reduced computer time.

The goal of this work is to show that the underlying symmetries of effective field theory can be traced to the onset of self-similarity. In particular, we argue that the scale-free structure of fractal geometry lies at the heart of invariance principles in classical and Quantum Field Theory.

We investigate a possible reduction mechanism from (bosonic) Quantum Field Theory (QFT) to Quantum Mechanics (QM), in a way that could explain the apparent loss of degrees of freedom of the original theory in terms of quantum information in the reduced one. This reduction mechanism consists mainly in performing an ansatz on the boson field operator, which takes into account quantum foam and non-commutative geometry. Through the reduction mechanism, QFT reveals its hidden internal structure, which is a quantum network of maximally entangled multipartite states. In the end, a new approach to the quantum simulation of QFT is proposed through the use of QFT's internal quantum network

Quantum mechanics could be studied through polynomial algebra, as has been demonstrated by a work (“An approach to first-principles electronic structure calculation by symbolic-numeric computation” by A. Kikuchi). We carry forward the algebraic method of quantum mechanics through algebraic number theory; the basic equations are represented by the multivariate polynomial ideals; the symbolic computations process the ideal and disentangle the eigenstates as the algebraic variety; upon which one canbuild the Galois extension of the number field, in analogy with the univariate polynomial case, to investigate the hierarchy of solutions; the Galois extension is accompanied with the group operations, which permute the eigenstates from one to another, and furnish the quantum system with a non-apparent symmetry. Besides, this sort of algebraic quantum mechanics is an embodiment of the class field theory; some of the important consequences of the latter emerge in quantum mechanics. We shall demonstrate these points through simple models; we will see the use of computational algebra facilitates such sort of analysis, which might often be complicated if we try to solve them manually.

The interlaminar strength of mechanically interlocked polymer-metal-interfaces is strongly dependent on the surface structure of the metal component. Therefore, this contribution assesses the suitability of the fractal dimension for quantification of the surface structure as well as interlaminar strength prediction of aluminum/polyamide 6 polymer-metal-hybrids. Seven different surface structures, manufactured by blasting, combined blasting and etching, thermal spraying and laser ablation, are investigated. The experiments are carried out on a novel butt-bonded hollow cylinder testing method that allows shear and tensile strength determination with one specific specimen geometry. The fractal dimension of the metal surfaces is derived from cross-sectional images. For comparison, the surface roughness slope is determined and related to the interlaminar strength. Finally, a fracture analysis is conducted. For the investigated material combination, the experimental results indicate that the fractal dimension is an appropriate measure for predicting the interlaminar strength

As people grow a custom to effortless outdoor navigation there is a rising demand for similar possibility indoors as well. Unfortunately, indoor localization, being one of the necessary requirements for navigation, continues to be problem without a clear solution. In this article we are proposing a method for an indoor positioning system using a single image. This is made possible using small preprocessed database of images with known control points as the only preprocessing needed. Using feature detection with SIFT algorithm we can look through the database and find image which is the most similar to the image taken by user. Pair of images is then used to find coordinates of database image using PnP problem. Furthermore, projection and essential matrices are determined allowing for the user image localization ~ determining the position of the user in indoor environment. Benefits of this approach lies in the single image being the only input from user and no requirements for new onsite infrastructure and thus enables a simpler realization for the building management.

The world is moving to the next phase of the energy transition with high penetrations of renewable energy. Flexible and scalable redox flow battery (RFB) technology is expected to play an important role in ensuring electricity network security and reliability. Continuous performance improvements will further enhance their value by reducing parasitic losses and maximizing available energy conversion over broader operating conditions. Concentration overpotentials from poor internal reactant distribution at high and low states of charge (SOC) limit power densities and are thus an important area of investigation. However, efforts to address these coupled electrochemical phenomena can compromise mechanical performance. Modelling and simulation of cell design innovations have shown it is possible to reduce losses from pump energy while increasing the availability of active species where required. The combination of wedge-shaped cells with static mixers investigated in this paper can reduce pressure drop and improve energy efficiency. Toroidal vanadium redox flow battery (VRB/VRFB) designs incorporating this innovation are presented for further development to improve community engagement with the technology.

The authors previously found a model of universal quantum computation by making use of the coset structure of subgroups of a free group $G$ with relations. A valid subgroup $H$ of index $d$ in $G$ leads to a \lq magic' state $\left|\psi\right\rangle$ in $d$-dimensional Hilbert space that encodes a minimal informationally complete quantum measurement (or MIC), possibly carrying a finite \lq contextual' geometry. In the present work, we choose $G$ as the fundamental group $\pi_1(V)$ of an exotic $4$-manifold $V$, more precisely a \lq small exotic' (space-time) $R^4$ (that is homeomorphic and isometric, but not diffeomorphic to the Euclidean $\mathbb{R}^4$). Our selected example, due to to S. Akbulut and R.~E. Gompf, has two remarkable properties: (a) it shows the occurence of standard contextual geometries such as the Fano plane (at index $7$), Mermin's pentagram (at index $10$), the two-qubit commutation picture $GQ(2,2)$ (at index $15$) as well as the combinatorial Grassmannian Gr$(2,8)$ (at index $28$) , (b) it allows the interpretation of MICs measurements as arising from such exotic (space-time) $R^4$'s. Our new picture relating a topological quantum computing and exotic space-time is also intended to become an approach of \lq quantum gravity'.