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Studies assessing the use of ground‐penetrating radar (GPR) for locating unmarked human graves commonly use pigs as proxies, with recent concerns about the adequacy of pigs as substitutes for humans. Also, there is little agreement on how to identify and describe GPR signals associated with graves. Hence, this project's aim is to compare GPR signals acquired over simulated clandestine graves with pig and human remains. We established human, pig, and control graves at the REST[ES] human decomposition facility in May 2022 and monitored the graves over 17 months using a 250 MHz antenna GPR system. Our results showed the presence of perturbed and V‐shaped reflectors, diffraction hyperbolas, and reflectors with amplitude loss at depth between 0.6 and 0.75 m in the radargram for graves with human and pig remains. We corroborate recent studies which concluded that the use of proxies is a viable alternative to human cadavers. The observed radar signatures were classified into five key patterns, which are characteristic of similar data collected with 250 MHz above graves reported in the literature. These classes are: V‐shaped dipping reflections from grave walls (class A), small hyperbolic reflections superimposed onto a near‐linear reflector (class B), hyperbolic reflections from remains within the grave (class C), new high‐amplitude reflection patterns (class D) and significant loss or interruption of reflections (class E). Our proposed classification can help streamline future investigations where the goal is to interpret burials within large GPR datasets and provide language to communicate these results to the broader scientific community. [ABSTRACT FROM AUTHOR]

Tolerance to high‐intensity constant power exercise can be characterized by the hyperbolic power‐duration (or velocity–duration) relationship. The hyperbola is defined by the asymptote (critical power or velocity) and the curvature constant (W′ or D′). The effects of thermoregulatory stress on middle‐distance running performance are equivocal—possibly due to the complexities of the hyperbolic velocity–duration relationship for these relatively short duration events. We aimed to measure the effects of heat stress on the velocity–duration relationship in amateur runners. Fifteen participants (23 ± 6 years) completed a series of constant‐velocity running bouts to intolerance in three heat indices (MILD: 20°C, VERY HOT: 38°C, EXTREME: 55°C). Critical velocity (CV) in MILD (3.52 ± 0.86 m/s) was higher than VERY HOT (3.39 ± 0.82 m/s) and EXTREME (3.29 ± 1.05 m/s; F[2.28] = 3.80, p < 0.035) with no effect of thermal stress on D′ (F[2.28] = 2.48, p = 0.11). In amateur competitive/recreational runners, heat stress of ≥38°C heat index negatively affected CV. Thus, even during relatively short events, such as middle‐distance running where fluid loss is not a primary concern, heat stress may negatively impact performance. [ABSTRACT FROM AUTHOR]

Switchgrass (Panicum virgatum L.) is a prominent bioenergy crop with robust resilience to environmental stresses. However, our knowledge regarding how precipitation changes affect switchgrass photosynthesis and its responses to light and CO2 remains limited. To address this knowledge gap, we conducted a field precipitation experiment with five different treatments, including −50%, −33%, 0%, +33%, and +50% of ambient precipitation. To determine the responses of leaf photosynthesis to CO2 concentration and light, we measured leaf net photosynthesis of switchgrass under different CO2 concentrations and light levels in 2020 and 2021 for each of the five precipitation treatments. We first evaluated four light and CO2 response models (i.e., rectangular hyperbola model, nonrectangular hyperbola model, exponential model, and the modified rectangular hyperbola model) using the measurements in the ambient precipitation treatment. Based on the fitting criteria, we selected the nonrectangular hyperbola model as the optimal model and applied it to all precipitation treatments, and estimated model parameters. Overall, the model fit field measurements well for the light and CO2 response curves. Precipitation change did not influence the maximum net photosynthetic rate (Pmax) but influenced other model parameters including quantum yield (α), convexity (θ), dark respiration (Rd), light compensation point (LCP), and saturated light point (LSP). Specifically, the mean Pmax of five precipitation treatments was 17.6 μmol CO2 m−2 s−1, and the ambient treatment tended to have a higher Pmax. The +33% treatment had the highest α, and the ambient treatment had lower θ and LCP, higher Rd, and relatively lower LSP. Furthermore, precipitation significantly influenced all model parameters of CO2 response. The ambient treatment had the highest Pmax, largest α, and lowest θ, Rd, and CO2 compensation point LCP. Overall, this study improved our understanding of how switchgrass leaf photosynthesis responds to diverse environmental factors, providing valuable insights for accurately modeling switchgrass ecophysiology and productivity. [ABSTRACT FROM AUTHOR]

By the circle method, an asymptotic formula is established for the number of integer points on certain hypersurfaces within multiprojective space. Using Möbius inversion and the modified hyperbola method, we prove the Manin–Peyre conjecture on the asymptotic behavior of the number of rational points of bounded anticanonical height for certain smooth hypersurfaces in the multiprojective space of sufficiently large dimension. [ABSTRACT FROM AUTHOR]

We study anti-symmetric solutions about the hyperplane $\{x_n=0\}$ for the following fractional Hardy–Hénon system: \[ \left\{\begin{array}{@{}ll} (-\Delta)^{s_1}u(x)=|x|^\alpha v^p(x), & x\in\mathbb{R}_+^n, \\ (-\Delta)^{s_2}v(x)=|x|^\beta u^q(x), & x\in\mathbb{R}_+^n, \\ u(x)\geq 0, & v(x)\geq 0,\ x\in\mathbb{R}_+^n, \end{array}\right. \] where $0 , $n>2\max \{s_1,s_2\}$. Nonexistence of anti-symmetric solutions are obtained in some appropriate domains of $(p,q)$ under some corresponding assumptions of $\alpha,\beta$ via the methods of moving spheres and moving planes. Particularly, for the case $s_1=s_2$ , one of our results shows that one domain of $(p,q)$ , where nonexistence of anti-symmetric solutions with appropriate decay conditions at infinity hold true, locates at above the fractional Sobolev's hyperbola under appropriate condition of $\alpha, \beta$. [ABSTRACT FROM AUTHOR]

The paper presents a set of equations that stands to the basis of a computer program and to the software themselves, that offers to the user the possibility to automatic draw the arcs used to approximate the representation of a chamfer hexagonal prism. Also, the authors present the way to use software that generates the arcs that approximate hyperbolas resulting on a chamfered hexagonal prism. [ABSTRACT FROM AUTHOR]

In this paper, we consider the following elliptic system of Hamiltonian type on a bounded domain: (0.1) { − Δ u = K 1 (| y |) | v | p − 1 v , in B 1 (0) , − Δ v = K 2 (| y |) | u | q − 1 u , in B 1 (0) , u = v = 0 on ∂ B 1 (0) , where K 1 (r) and K 2 (r) are positive bounded functions, B 1 (0) is the unit ball in R N , (p , q) is a pair of positive numbers lying on the critical hyperbola: 1 p + 1 + 1 q + 1 = N − 2 N. We investigate the local uniqueness and the nondegeneracy of the bubbling solution for problem (0.1). Our proof is based on the local Pohozaev identities, blow-up analysis, and the properties of Greens function. Our results are quite different from single equation, which is mainly caused by the non-cooperative nonlinear terms and (p , q) lying on the critical hyperbola. We believe that the various new ideas and technique computations that we used in this paper would be very useful to deal with other related problems of Hamiltonian type with interact critical exponents. [ABSTRACT FROM AUTHOR]

In this paper, we consider the following elliptic system - Δ u = | v | p - 1 v + ϵ (α u + β 1 v) , in Ω , - Δ v = | u | q - 1 u + ϵ (β 2 u + α v) , in Ω , u = v = 0 , on ∂ Ω , where Ω is a smooth bounded domain in R N , N ≥ 3 , ϵ is a small parameter, α , β 1 and β 2 are real numbers, (p, q) is a pair of positive numbers lying on the critical hyperbola 1 p + 1 + 1 q + 1 = N - 2 N. We first revisited the blowing-up solutions constructed in Kim and Pistoia (J Funct Anal 281(2):58, 2021) and then we proved its non-degeneracy. We believe that the various new ideas and technique computations that we used in this paper would be very useful to deal with other related problems involving critical Halmitonian system and the construction of new solutions. [ABSTRACT FROM AUTHOR]

Respiratory drive is defined as the intensity of respiratory centers output during the breath and is primarily affected by cortical and chemical feedback mechanisms. During the involuntary act of breathing, chemical feedback, primarily mediated through CO2, is the main determinant of respiratory drive. Respiratory drive travels through neural pathways to respiratory muscles, which execute the breathing process and generate inspiratory flow (inspiratory flow-generation pathway). In a healthy state, inspiratory flow-generation pathway is intact, and thus respiratory drive is satisfied by the rate of volume increase, expressed by mean inspiratory flow, which in turn determines tidal volume. In this review, we will explain the pathophysiology of altered respiratory drive by analyzing the respiratory centers response to arterial partial pressure of CO2 (PaCO2) changes. Both high and low respiratory drive have been associated with several adverse effects in critically ill patients. Hence, it is crucial to understand what alters the respiratory drive. Changes in respiratory drive can be explained by simultaneously considering the (1) ventilatory demands, as dictated by respiratory centers activity to CO2 (brain curve); (2) actual ventilatory response to CO2 (ventilation curve); and (3) metabolic hyperbola. During critical illness, multiple mechanisms affect the brain and ventilation curves, as well as metabolic hyperbola, leading to considerable alterations in respiratory drive. In critically ill patients the inspiratory flow-generation pathway is invariably compromised at various levels. Consequently, mean inspiratory flow and tidal volume do not correspond to respiratory drive, and at a given PaCO2, the actual ventilation is less than ventilatory demands, creating a dissociation between brain and ventilation curves. Since the metabolic hyperbola is one of the two variables that determine PaCO2 (the other being the ventilation curve), its upward or downward movements increase or decrease respiratory drive, respectively. Mechanical ventilation indirectly influences respiratory drive by modifying PaCO2 levels through alterations in various parameters of the ventilation curve and metabolic hyperbola. Understanding the diverse factors that modulate respiratory drive at the bedside could enhance clinical assessment and the management of both the patient and the ventilator. [ABSTRACT FROM AUTHOR]

In finite-volume methods, monotonic upstream-centered schemes for conservation laws (MUSCL) offer second-order spatial accuracy but tend to produce highly dissipative solutions for density discontinuity and weak shock waves. To address this limitation within a second-order framework, a novel strategy for hybridizing MUSCL with the tangent of the hyperbola interface capturing technique for both steady and unsteady compressible flows is presented. This hybridization optimizes the process based on the degree of nonlinearity and discontinuity around the target cells, providing a novel method to sharply resolve weak shock waves and robustly compute strong shock waves within the hybrid scheme. The proposed scheme sharply captures exceedingly weak shock waves that conventional MUSCL fails to resolve accurately due to excessive numerical dissipation. Furthermore, for resolving small vortices induced by instability at slip lines, computational results demonstrate high-resolution surpassing fifth-order spatial accuracy schemes within this second-order spatial accuracy framework with less computational cost. Moreover, the scheme exhibits commendable convergence and robustness when applied to steady-state problems featuring strong shock waves. This scheme offers a more precise and high-resolution alternative to conventional MUSCL for compressible flow computations, as it requires no additional stencil for reconstruction, unlike conventional fifth-order schemes. [ABSTRACT FROM AUTHOR]

Let OP1,OP2,OP3 be three non-parallel segments in a plane ω. In this and the next article [9] we find the necessary and sufficient conditions for the existence of the common inscribed ellipse EI and the common circumscribing hyperbola HC (both with center O) of the three ellipses having as conjugate semi-diameters the pairs (OP1,OP2), (OP2,OP3) and (OP3,OP1). To this end we introduce a parallel projection (hyperbolic Pohlke's projection) such that EI and HC are the outline of the image into ω of a suitable hyperboloid. [ABSTRACT FROM AUTHOR]

To explore the effect of Vitis amurensis Rupr. leaf on CO2 response characteristics, 4 varieties of 5 a Vitis amurensis Rupr. were as materials, including 'Beibinghong' 'Beiguohong' 'Shuanghong' and 'Xuelanhong'. The intercellular CO2 concentration (Ci), stomatal conductance (Gs), water utilization rate (WUE), transpiration rate (r) were determined including using Li-6400 portable photosynthesis system. The photosynthetic CO2 response curve (Pn-Ci) of Vitis amurensis Rupr. leaf was fitted by rectangular hyperbola model, Michaelis-Menten model, modified rectangular hyperbola model. The results showed that, the fitting values of photosynthetic parameters were close to measured values by the modified rectangular hyperbola models, which could directly calculate the CO2 saturation point (CSP). With the increase of atmospheric CO2 concentration (Ca), Ci of 4 varieties showed a linear increasing trend, Gs and Tr generally increased first and then decreased, WUE decreased first and then increased with 'U' trend. The principal component analysis extracted 2 principal components, which the cumulative variance contribution rate reached 84.613%. The score of 'Xuelanhong' was the highest in the comprehensive evaluation, which had the best adaptability in low Ca environment, and conversion rate of light energy was the highest. 'Shuanghong' was second, which could maintain high photosynthetic efficiency at different concentrations of Ca. In conclusion, the modified rectangular hyperbola models was the best on fitted the Pn-Ci response curve of Vitis amurensis Rupr. [ABSTRACT FROM AUTHOR]

The aim of this work is to analyze the applicability of a convex hyperbola chart's methodology to determine how many pumps should be working in a pumping station of a real case study to consume the least amount of energy. The applicability of the convex hyperbola charts is demonstrated, its effectiveness is shown, and a step-by-step exemplification is presented. Moreover, the order in which pumps should be activated is analyzed and discussed. The pumping station of the optimization is located in Tres Cantos, Madrid, Spain; it consists of a pumping station of four (+1 reserved) hydraulic pumps that take water from a reservoir and distribute it through a branched pipeline. The geometric height difference Hg of the case study is variable. This article also shows how the variability of Hg plays a major role in the optimal configuration of the pumping station. This paper also proves how the number of pumps to activate or disactivate does not necessarily need to be consecutive, meaning that activating or disactivating pumps one by one may not be the best solution. The convex hyperbola charts show how there can be circumstances in which skipping a certain number of pumps is the best solution. How the pump efficiency is distributed along the commercial pump plays a major role in determining which is the best configuration of active pumps. A straightforward and inexpensive optimization methodology for the optimization of the energy in a water supply system was proved and exemplified. This simple methodology can be applied by engineers in the operation of a water supply system when pumping is required, e.g., in agricultural systems or in underdeveloped areas where energy expenses need to be considered. [ABSTRACT FROM AUTHOR]

In this study, we introduce a novel approach to determine root orientation from Ground Penetrating Radar (GPR) data, employing a dual-fitting strategy involving hyperbola fitting and polynomial regression surface fitting. The initial hyperbola fitting serves to capture essential parameters, while the subsequent polynomial regression surface fitting seeks to unveil nuanced relationships between root orientation angles and hyperbola characteristics. This dual-fitting framework represents a significant advancement in root analysis methodologies, offering a more refined and comprehensive understanding of root orientation derived from GPR data. [ABSTRACT FROM AUTHOR]

In the last 20 years, the localization of Mobile Station (MS) in cellular networks has become an exciting topic of the multitude of applications related to location information. The localization of MSs below the US Federal Communications Commission is considered the primary driving force to investigate and supply optimum solutions. A new Mobile Station localization technique is proposed, and its efficiency is evaluated in this paper. The proposed technique, hybrid SADOA/AOA, combines the signal attenuation difference of arrival (SADOA), which generates a circle on which the MS may lie, and the angle of arrival (AOA) techniques, which uses trigonometry laws of sine and cosine to locate the MS. This technique uses Taylor series expansion to solve the hyperbolas and Line of Bearings derived by the two techniques individually. Then it proceeds to use the linear least squares algorithm iteratively to find the location. Simulation results showed that the hybrid SADOA/AOA outperforms the conventional SADOA technique without hardware modification, and it can overcome the shadowing effect of the environment. [ABSTRACT FROM AUTHOR]

We study the motion of a test particle in a conservative force field. In the framework of the 2D inverse problem of Newtonian dynamics, we find 2D potentials that produce a preassigned monoparametric family of regular orbits f (x , y) = c on the x y -plane (where c is the parameter of the family of orbits). This family of orbits can be represented by the "slope function" γ = f y f x uniquely. A new methodology is applied to the basic equation of the planar inverse problem in order to find potentials of a special form, i.e., V = F (x + y) + G (x − y) , V = F (x + i y) + G (x − i y) and V = P (x) + Q (y) , and polynomial ones. According to this methodology, we impose differential conditions on the family of orbits f (x , y) = c. If they are satisfied, such a potential exists and it is found analytically. For known families of curves, e.g., circles, parabolas, hyperbolas, etc., we find potentials that are compatible with them. We offer pertinent examples that cover all the cases. The case of families of straight lines is referred to. [ABSTRACT FROM AUTHOR]

We study the following Lane–Emden system: $$\begin{align*} & -\Delta u=|v|^{q-1}v \quad \ \textrm{in}\ \Omega, \qquad -\Delta v=|u|^{p-1}u \quad \ \textrm{in}\ \Omega, \qquad u_{\nu}=v_{\nu}=0 \quad \ \textrm{on}\ \partial \Omega, \end{align*}$$ with |$\Omega $| a bounded regular domain of |${\mathbb{R}}^{N}$|⁠ , |$N \ge 4$|⁠ , and exponents |$p, q$| belonging to the so-called critical hyperbola |$1/(p+1)+1/(q+1)=(N-2)/N$|⁠. We show that, under suitable conditions on |$p, q$|⁠ , least-energy (sign-changing) solutions exist, and they are classical. In the proof we exploit a dual variational formulation, which allows to deal with the strong indefinite character of the problem. We establish a compactness condition which is based on a new Cherrier-type inequality. We then prove such condition by using as test functions the solutions to the system in the whole space and performing delicate asymptotic estimates. If |$N \ge 5$|⁠ , |$p=1$|⁠ , the system above reduces to a biharmonic equation, for which we also prove existence of least-energy solutions. Finally, we prove some partial symmetry and symmetry-breaking results in the case |$\Omega $| is a ball or an annulus. [ABSTRACT FROM AUTHOR]

A design approach to multimode resonant, backfire dipole antenna with nearly equal E‐/H‐plane patterns is proposed in this letter. The antenna is comprised by a 1.5‐wavelength sectorial dipole, a hyperbola‐intersected elliptical primary reflector, and an elliptical subreflector. By adjusting the size and shape of the intersected‐hyperbola elliptical reflector and the position of the tangentially loaded stubs, the nearly equal E‐/H‐plane bandwidth (i.e., equal‐beamwidth bandwidth) of the antenna can be manipulated to coincide with its impedance bandwidth. As has been validated, the antenna exhibits an octave impedance bandwidth from 1.61 to 3.26 GHz (67.8% for |S11| < −10 dB), which is identical to its equal‐beamwidth bandwidth. The average half‐power beam width is around 63°/65° in E‐/H‐plane, and the average backfire gain is 8.8 dBi. [ABSTRACT FROM AUTHOR]

In this article we study conics inscribed in a triangle, which appear always in a group of related four. We find conditions that such a group contains simultaneously a rectangular hyperbola and a parabola. These conditions involve the de Longchamps circle of the triangle of reference, which necessarily it is obtuse. [ABSTRACT FROM AUTHOR]

This work outlines a new multi-physics-compatible immersed rigid body method for Eulerian finite-volume simulations. To achieve this, rigid bodies are represented as a diffuse scalar field, and an interface seeding method is employed to mediate the interface boundary conditions. The method is based on an existing multi-material diffuse interface method that is capable of handling an arbitrary mixture of fluids and elastoplastic solids. The underlying method is general and can be extended to a range of different applications including high-strain rate deformation in elastoplastic solids and reactive fluid mixtures. As such, the new method presented here is thoroughly tested through a variety of problems, including fluid–rigid body interaction, elastoplastic–rigid body interaction, and detonation–structure interaction. Comparison is drawn between both experimental work and previous numerical results, with excellent agreement in both cases. The new method is straightforward to implement, highly local, and parallelizable. This allows the method to be employed in three dimensions with multiple levels of adaptive mesh refinement using complex immersed geometries. The rigid body field can be static or dynamic, with the tangent of hyperbola interface capturing reconstruction method being used to keep the interface sharp in the dynamic case. [ABSTRACT FROM AUTHOR]

Plateau surfaces have excellent sliding properties because only the high peaks of surface asperity are smoothed. Therefore, they form the sliding surfaces for automobile engines and machine tools, contributing to their high performance and low environmental impact. As the development and production of these machines require the evaluation of their plateau surface components, methods for plateau surface evaluation have been proposed by the International Organization for Standardization (ISO) and in previous research. These evaluation methods include a processing procedure for fitting a hyperbola to the material probability curve (MPC) of a plateau surface. However, the ISO standard does not clearly state the rationale for restricting the fitting curve to a hyperbola. As shown in a previous study, another curve that can fit the shape of the MPC of a plateau surface is expected to be a parabola in addition to a hyperbola. Parabolas and hyperbolas are curves known as conic sections. In this research, we examine the validity of hyperbolic curve fitting and explore the fitting of a conic curve by utilizing information on conjugate diameters. Approximations using a curve better suited to the shape of the MPCs of the plateau surface can anticipate to the realization of higher-quality evaluations of the surface. Through this research, we aim to contribute to the development of industry as well as improve the performance and mitigate the environmental impact of automobile engines and machine tools. [ABSTRACT FROM AUTHOR]

In this paper we give necessary conditions for quadratic functions f : R → R that satisfy the additional equation y 2 f (x) = x 2 f (y) under the condition x y = 1 . [ABSTRACT FROM AUTHOR]

In this paper we study a complete quadrangle in the Euclidean plane that has a rectangular hyperbola circumscribed to it. Hereby, the approach is based on the rectangular coordinates and we prove the following main result: Let ABCD be a complete quadrangle and l a , l b , l c , l d mutually parallel lines through the circumcenters of BCD, ACD, ABD, ABC, respectively. Orthopoles of the lines l a , l b , l c , l d with respect to the triangles BCD, ACD, ABD, ABC lie on a line which passes through the center of the rectangular hyperbola H circumscribed to ABCD, and it is antiparallel to the given lines with respect to the axes of the hyperbola H . [ABSTRACT FROM AUTHOR]

Developable degree-4 (DD4) vertices have four facets and four creases and can be unfolded flat. The rigid-folding kinematics of DD4 vertices is rich in that it generally has two folding modes and can get stuck when two facets bind together. To study the full spectrum of the kinematics of DD4 vertices, parametric solutions for fold angles in terms of the cotangents of half-angles are derived from the opposite and adjacent fold angle relationships. It is shown that any two fold angles of a general DD4 vertex are related by the equation of a hyperbola. When the vertex has collinear creases or is flat-foldable, the pertinent hyperbola equations degenerate into linear relationships. Meanwhile, when DD4 vertices are classified into three categories according to Grashof's criterion, both unique and binding folds can be readily located from the facet with the largest or smallest sector angle. The rigid-folding kinematics of typical vertices is then investigated. In addition to the flat state, the two folding modes can also be switched at the binding states if self-intersection is permitted. The results provide new formulae and clear geometric views on the rigid-folding kinematics of DD4 vertices, which are fundamental for constructing larger origami patterns. [ABSTRACT FROM AUTHOR]

Luminex single antigen bead (SAB) kits from One Lambda (OL) and Lifecodes (LC) are widely used for HLA antibody detection but have substantial differences in design and assay protocol resulting in different mean fluorescence intensity (MFI) values. Here, we present a non‐linear modeling approach to accurately convert MFI values between two vendors and to establish user‐independent MFI cutoffs when analyzing big datasets. HLA antibody data from a total of 47 EDTA‐treated sera tested using both OL and LC SAB kits were analyzed. MFI comparisons were made for the common 84 HLA class I and 63 class II beads. In the exploration set (n = 24), a non‐linear hyperbola model on raw MFI corrected by locus‐specific highest self MFI subtraction yielded the highest correlation (class I r2: 0.946, class II r2: 0.898). Performance of the model was verified in an independent validation set (n = 12) (class I r2: 0.952, class II r2: 0.911). Furthermore, in an independent cohort of post‐transplant serum samples (n = 11) using the vendor‐specific MFI cutoffs dictated by the current model, we found 94% accuracy in bead‐specific reactivity assignments by the two vendors. We recommend using the non‐linear hyperbola modeling approach with self HLA correction and locus‐specific analyzes to harmonize MFI values between two vendors in particular research datasets. As there are considerable variations between the two assays, using MFI conversion for individual patient samples is not recommended. [ABSTRACT FROM AUTHOR]

In this paper, we present a concise and efficient interface capturing scheme on polyhedral unstructured mesh with its numerical implementation for incompressible fluid simulation with surface tension. The so-called coupled Level-Set and Tangent of Hyperbola INterface Capturing scheme with a Consistent Single-step time integration (THINC/CSLS) updates both the volume-of-fluid (VOF) and level-set function simultaneously from a THINC reconstruction function. The proposed scheme has the potential to integrate the positive aspects of mass conservation from the VOF method and the accurate geometric representation from the level-set method. Other innovative and noteworthy aspects of the present scheme are listed as (1) an adaptive THINC reconstruction strategy is applied to ensure the boundness of the VOF function for various Courant–Friedrichs–Lewy (CFL) numbers and the high quality of the level-set function for surface tension; (2) a single-step update procedure for both VOF and level-set function is implemented for better algorithmic consistency and efficiency; (3) a well-adapted numerical model is developed for incompressible simulation with free surface for both structured and unstructured grids. A comprehensive numerical procedure is introduced and validated by various well-received benchmark tests. Convincing evidence suggests that the present scheme is both accurate and efficient compared with other most advanced methods. [ABSTRACT FROM AUTHOR]

The spatiotemporal organization of networks of dynamical units can break down resulting in diseases (e.g., in the brain) or large-scale malfunctions (e.g., power grid blackouts). Re-establishment of function then requires identification of the optimal intervention site from which the network behavior is most efficiently re-stabilized. Here, we consider one such scenario with a network of units with oscillatory dynamics, which can be suppressed by sufficiently strong coupling and stabilizing a single unit, i.e., pinning control. We analyze the stability of the network with hyperbolas in the control gain vs coupling strength state space and identify the most influential node (MIN) as the node that requires the weakest coupling to stabilize the network in the limit of very strong control gain. A computationally efficient method, based on the Moore–Penrose pseudoinverse of the network Laplacian matrix, was found to be efficient in identifying the MIN. In addition, we have found that in some networks, the MIN relocates when the control gain is changed, and thus, different nodes are the most influential ones for weakly and strongly coupled networks. A control theoretic measure is proposed to identify networks with unique or relocating MINs. We have identified real-world networks with relocating MINs, such as social and power grid networks. The results were confirmed in experiments with networks of chemical reactions, where oscillations in the networks were effectively suppressed through the pinning of a single reaction site determined by the computational method. [ABSTRACT FROM AUTHOR]

In this study, a high-robustness hybrid scheme of weighted essentially non-oscillatory (WENO) scheme with a modified tangent of hyperbola for interface capturing (THINC) algorithm is developed for compressible multicomponent flow on general curvilinear grids. Numerical errors induced by mesh deformation bring loss of numerical accuracy and simulation instability, resulting in inaccurate results such as interface distortion, numerical oscillations or even simulation failure. To address this issue, the WENO scheme combined with an improved THINC strategy is designed to alleviate these errors and maintain the high resolution of interfaces. A modified THINC algorithm is developed for the non-uniform grids, in which the steepness parameter is scaled adaptively according to varying grid spacings. This approach is capable of reducing numerical dissipations for interface reconstruction. The overestimated quasi-conservative WENO formulation are employed to hold the equilibriums of velocity, pressure, and temperature at the material interface. Numerical validations are tested on non-uniform grids with various randomness amplitudes to verify the effectiveness in one- and two-dimensional benchmark problems showing the better performances in shock- and interface-capturing capabilities. [ABSTRACT FROM AUTHOR]

The Piatetski-Shapiro sequence associated with c > 1 and c ∉ N is given by N c = (⌊ n c ⌋) n ∈ N. Let p be an odd prime and let g (x) , h (x) ∈ F p [ x ] be coprime polynomials. We estimate exponential sums with Piatetski-Shapiro sequences of the shape ∑ m ≤ M m ∈ N c , (h (m) , p) = 1 e p (g (m) h (m)) , where e p (y) = exp ⁡ (2 π i y / p). In particular, when g (x) / h (x) = r x + s x ¯ and 1 < c < 6 / 5 , our results improve the bound for Kloosterman sums with Piatetski-Shapiro sequences which was given by Shparlinski and Technau. Furthermore, bounds for max ⁡ { m , m ˜ } subject to m , m ˜ ∈ Z ∩ [ 1 , p) , z indivisible by p , g (m) m ˜ ≡ z (mod p) and m belonging to some fixed Piatetski-Shapiro sequence are also obtained. [ABSTRACT FROM AUTHOR]

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In this paper, we deal with the existence of nontrivial solutions to the following class of strongly coupled Hamiltonian systems: where , , and the nonlinearities and possess exponential growth ranges above the exponential critical hyperbola. Our approach is based on Trudinger-Moser type inequalities for weighted Sobolev spaces and variational methods. In this paper, we deal with the existence of nontrivial solutions to the following class of strongly coupled Hamiltonian systems: where , , and the nonlinearities and possess exponential growth ranges above the exponential critical hyperbola. Our approach is based on Trudinger-Moser type inequalities for weighted Sobolev spaces and variational methods. [ABSTRACT FROM AUTHOR]

At present, the demand for accurate indoor positioning at a low cost is increasing. Based on the architecture of networking passive radio frequency identification (RFID) systems, research into passive location algorithms is important for finding a location solution with ultra-low cost, easy implementation, and no required maintenance. In this paper, TDACC (time difference of arrival with conic curves) based on signal propagation time is proposed, which breaks down the positioning problem into solving the intersection of an ellipse and a hyperbola. The results indicate that this method has a positioning error of 0 m in the absence of signal interference. When the time delay fluctuates to 1 ns and 2 ns, the average errors of TDACC are 0.19 m and 0.33 m, respectively. Different from other time-based localization methods, the proposed method only requires two distribution nodes without time synchronization, which reduces the system cost. These results will help to promote the deeper semantic communication level fusion of passive RFID. By improving the coordinate positioning in the semantic prior knowledge base, this method will lead to more efficient and accurate industry applications. [ABSTRACT FROM AUTHOR]

Currently Information and Communication Technologies (ICT) have become relevant in the practices of mathematics teachers, national guidelines have demanded that this be an integrated competence in graduates. However, given the flexibility in the country that any professional with training for a degree in Mathematics can work as a teacher, it prevents teachers from using technological resources effectively and according to today's educational needs. day. Thus, the objective of this research is to characterize the specialized knowledge of the mathematics teacher who teaches the modeling of the hyperbola and its parts through ICT. The approach of this research is qualitative, with an instrumental type case study design, the questionnaire and non-participant observation are used as information collection techniques to a teacher who teaches mathematics in tenth of secondary school using ICT, especially the GeoGebra software. Among the relationships found in this research is the knowledge of the practices and teaching of mathematics as an approximation to the graphic modeling of the hyperbola through GeoGebra. [ABSTRACT FROM AUTHOR]

This paper reports on the findings of a baseline study that fed on to a broader investigation exploring ICT integration in the teaching of functions. The baseline study was premised on the observation that the notion of function, despite being a fundamental and central idea in the mathematics school curriculum, presents pedagogical challenges to both teachers and learners. The study used the qualitative case study design to investigate Grade 11 mathematics learners' errors and misconceptions under hyperbolic functions at a rural high school in the Limpopo province of South Africa. Informed by the constructivist APOS theory conception levels, learners' errors were detected from their written responses in a diagnostic test. The learners were then individually interviewed during task-based interviews to infer on the misconceptions underlying their errors. Qualitative analysis of the data revealed the following categories of misconceptions: algebraic, conceptual, asymptotic, graphical, and notational misconceptions. The study established that errors, if diagnosed and corrected, are springboards and milestones to the formulation and construction of proper mathematical ideas. To resolve learners' misconceptions, this study recommends that teachers should use explorative and discovery pedagogical strategies to enable learners realize their own misconceptions and self-correct. Based on the findings of this study, the integration of Information and Communication Technologies (ICTs) in teaching functions as an intervention strategy will be explored. [ABSTRACT FROM AUTHOR]

In this paper, we investigate an uncertainty diagram and Kirkwood–Dirac (KD) nonclassicality based on discrete Fourier transform (DFT) in a d-dimensional system. We first consider the uncertainty diagram of the DFT matrix, which is a transition matrix from basis A to basis B. Here, the bases A ,   B are not necessarily completely incompatible. We show that for the uncertainty diagram of the DFT matrix, there is no "hole" in the region of the (n A , n B) plane above and on the line n A + n B = d + 1 . Then, we present where the holes are in the region strictly below the line and above the hyperbola n A n B = d . Finally, we provide an alternative proof of the conjecture about KD nonclassicality based on DFT. [ABSTRACT FROM AUTHOR]

This paper first defines a bi-parameter ellipse and then place it together with the rectangular hyperbola xy = N to study their intersections. The study reveals several new properties of the intersections that are merely dependent on the two parameters that determine the ellipse. It is also shown that the new properties are available for studying integers and are helpful to develop new method to factorizing integers. Mathematical reasoning is presented in detail for each conclusion and each conclusion is demonstrated with Geogebra software. [ABSTRACT FROM AUTHOR]

Anisotropic Self-Complementary Metasurfaces (SC-MTSs) are structures constituted by an alternation of complementary inductive and capacitive strips, which are "self-dual" according to Babinet's duality principle. They support the propagation of two orthogonally polarized surface-wave modes with the same phase velocity along the principal directions (i.e., along the strips and normal to them). The isofrequency dispersion curves of these modes are hyperbolas, and therefore, these MTSs fall in the category of hyperbolic MTSs. It is shown here that the hyperbolic dispersion curves may degenerate in same cases into almost straight lines, which implies that the velocity of energy transport is constantly directed along the same direction for any possible phasing orthogonal to the strips. In this circumstance, the SC-MTS can be conveniently used to design dual-polarized leaky-wave antennas by modulating the impedances of the complementary strips. [ABSTRACT FROM AUTHOR]

We know that circular shapes we encounter in daily life may appear to be elliptical from some viewing points. It is reasonable to expect that an ellipse may appear to be circular from certain viewpoints. In this paper, we investigate the locus of viewpoints from which an ellipse appears circular. It will be shown that the locus of viewpoints is a hyperbola passing through the two foci of the ellipse. Conversely, the locus of viewpoints from which a hyperbola looks circular is an ellipse passing through the two foci of the hyperbola. Further, the locus of viewpoints from which a parabola looks circular is itself a parabola, passing through the focus of the original parabola. There is a simple duality between the object to be observed and the observer. [ABSTRACT FROM AUTHOR]

As a non-destructive examination tool, ground penetrating radar (GPR) is essential for locating subsurface items and illuminating the underground environment. Unfortunately, there is still work to be done in the practical application of automatic detection of subsurface objects in the radargram. The most frequent targets for their detection are those that resemble cylinders. A buried cylinder is known to produce a hyperbolic signature in GPR images. For the purpose of recognizing subsurface cylinders using GPR data, a novel approach is proposed. The approach makes use of both the strengths of the ResNet model and the characteristics of the hyperbolic curve. Specifically, by introducing priori knowledge and inception modules into the ResNet framework, the suggested method obtains a significant improvement in terms of object recognition at a very low computation cost. At the same time, a hyperparameter optimization strategy is also provided for model training. The evaluations by comparison with other modules demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The widely used tool, ground penetrating radar (GPR), has proven to be an excellent research method for glaciological studies. The total ice thickness and englacial structures can be studied, and the method can give information on the temperature regime within the ice. Good velocity profiles are needed to convert measured two‐way travel time to depth information. In addition, a good velocity analysis can be used to improve data processing. A number of methods can be used to find the GPR wave velocity, which are briefly described. This study used hyperbola fitting to estimate the velocity in a glaciological study. In addition, Kirchhoff's migration was used to fine‐tune this velocity estimate. Within the Longyearbreen glacier, situated next to Longyearbyen on Spitsbergen, Svalbard archipelago, objects in the ice act as scattering points that create hyperbolas. Using the hyperbola‐fitting method, a GPR wave velocity equal to 0.170 ± 0.005 m/ns was estimated. By doing Kirchhoff's migration and studying the collapse of hyperbolas with variations of the migration velocity, a more accurate velocity estimate can be achieved; 0.172 ± 0.002 m/ns. A more accurate velocity estimate like this opens possibilities for better characterization of the ice body and ice thickness variations, as well as the variation of these as a function of time. In March 2022, the maximum ice thickness in the investigated area was calculated to be 88 ± 1 m. [ABSTRACT FROM AUTHOR]

Two‐dimensional (2D) images of light beams reflected off the objects in space impinge on the retinal photoreceptors of our two laterally separated eyes. Nevertheless, we experience our visual percept as a single 3D entity—our visual world that we tend to identify with the physical world. However, experiments point to different geometries in these two worlds. Using the binocular system with asymmetric eyes (AEs), this article studies the global geometric aspects of visual space in the Riemannian geometry framework. The constant‐depth curves in the horizontal field of binocular fixations consist of families of arcs of ellipses or hyperbolas depending on the AE parameters and the eyes' fixation point. For a single set of AE parameters, there is a unique symmetric fixation at the abathic distance such that the constant‐depth conics are straight frontal lines. Critically, the distribution of these constant‐depth lines is independent of such fixations. In these cases, a two‐parameter family of the Riemann metrics is proposed to account for the retinotopy of the brain's visual pathways and simulated constant‐depth lines. The obtained geodesics for a subset of metric parameters include incomplete geodesics that give finite distances to the horizon. The Gaussian curvature of the phenomenal horizontal field is analyzed for all the metric parameters. The sign of the curvature can be inferred from the global behavior of the constant‐depth ellipses and hyperbolas only when for the metric parameters for which the constant‐depth frontal lines at the abathic distance fixations are geodesics. [ABSTRACT FROM AUTHOR]