Half Sphere Research Articles

An Efficient Procedure to Compensate for the Errors Due to the Probe Mispositioning in a Cylindrical Near-Field Facility.

This paper deals with the compensation of the probe mispositioning errors occurring in a cylindrical near-field (NF) facility due to the imprecise control of the linear and azimuthal positioners allowing the cylindrical scanning and/or to their limited resolution and to defects in the rails guiding the linear motion. As a result, 3-D errors in the positioning of the probe at any sampling point, as prescribed by the adopted non-redundant representation, affect the accuracy of the NF measurements. An efficient procedure is here proposed to properly compensate for these errors. It involves two steps. The former allows one to correct the mispositioning errors due to the deviation of each actual sampling point from the nominal measurement cylinder. The latter makes use of an iterative technique to restore the NF samples at any sampling point fixed by the used non-redundant representation from the ones obtained at the previous step and affected by 2-D mispositioning errors. Once these steps have been fruitfully applied, the so-compensated NF samples are effectively interpolated through a 2-D optimal sampling interpolation (OSI) formula to accurately reconstruct the input data required to perform the traditional cylindrical near-to-far-field transformation. The OSI representation is here developed by considering an elongated antenna under test as enclosed either in a prolate spheroid or in a cylinder terminated by two half spheres (rounded cylinder) in order to make the representation effectively non-redundant. Numerical test results, which thoroughly prove the efficacy of the devised procedure in correcting even severe 3-D mispositioning errors, are reported.

Internal temperature measurement of ablating bodies in high-speed flows

A novel pyranine-based luminescent temperature sensor was embedded within water ice to study heat transfer dynamics of blunt-nosed ablating bodies in supersonic and hypersonic flows. A circular half cylinder and sphere test article were created out of water ice with an embedded temperature sensitive layer to observe cross-sectional temperature profiles. The half cylinder and sphere were exposed to flow with stagnation temperatures of 700 K and 800 K at Mach 2 and Mach 7 respectively. The luminescent sensor successfully measured the amount of ablated material and the temperature profiles inside of the test articles during convective heating. The cumulative heat absorbed by the test articles as a function of time was calculated from the ablated material and the temperature rise measured from the luminescent sensor. The calculated cumulative heat was then compared to analytical estimates for convective heating of blunt-nosed bodies in high-speed flows and shown to be in good agreement.

Estimation of the Needed Regolith for Covering Lunar Habitat by Protective Layer

Abstract The article deals with estimation of the amount of regolith to be mined with respect to the preparation of lunar habitat. Estimation of the size of the pit is related to the overlay of regolith for habitat made of a composite concrete-like structure. The evaluation is based on the number of inhabitants, necessary floor area, and the considered structure that is made of three segments. The first segment is a linear vault with a half cylinder cross section ending with a half sphere on both sides of the vault. Elementary formulas for the computation of volume of cylinder and sphere are applied.

Evaluasi Efisensi Riser Untuk Bentuk Riser Samping yang Berbeda Menggunakan Metode Simulasi Casting

As the solidification reaches the hot spot area, no molten metal remains and shrinkage is formed. To anticipate the shrinkage, a riser is added to the casting system. An optimal riser design would produce free shrinkage components. One of the factors that affect riser efficiency is the riser shape. This study aims to find the most efficient side riser shape by using simulation software. The riser shape of tubes, tubes with a half sphere on top, hemispheres, conical tubes, tubes with an oval cross-section, and cubes are used in this experiment, with the volume of all risers kept constant. The most efficient shape of the riser is the tube. The tube riser produces a larger modulus. The tube riser generated directional solidification. The same pattern can be seen in the niyama criteria and solidification temperature, where the tube riser has a more continuous pattern compared to other riser shapes.

Potential-flow computations in infinite or zero gravity limits via a weakly singular boundary integral equation

Potential flow computations, based on a weakly singular integral equation, are considered in the infinite-gravity limit g=∞ and the zero-gravity limit g=0. The weakly singular integral equation, obtained via a straightforward and rigorous application of Green’s basic identity, involves a distribution of weak dipoles that is continuous across the body surface. The integral equation is solved via a low-order panel method, which is validated for a half sphere and applied to the S60 ship model in translation along the x, y or z-axis. A systematic numerical analysis of the convergence of numerical predictions shows that the number of panels that is required to obtain a 0.1% accuracy is significantly different for the infinite-gravity or zero-gravity flows, and for translation of the S60 hull along the x, y or z-axis. In particular, a very large number of panels is required for translation of the S60 ship model along the horizontal x or y-axis in the zero-gravity limit.

Identification of acoustic point sources in a two-layered medium from multi-frequency sparse far field patterns

We consider the reconstruction of point sources in a two layered medium from the multi-frequency sparse far field patterns taken on the upper half sphere. The point sources are located in both the upper half space and the lower half space, and consequently bring difficulty for the inverse problem because of the combination of two different types of far field patterns. After establishing the uniqueness of the point sources by the multi-frequency far field patterns at properly chosen sparse observation directions, we introduce a multi-step numerical scheme for identifying all the points sources. Numerical examples show that the proposed sampling methods work very well for locating the positions and the formulas for determining the corresponding scattering strengths are valid and stable with respect to the noises.

Placental development in the early stages of red-rumped agouti pregnancy (Dasyprocta leporina Linnaeus, 1758).

Hystricomorpha rodents display a similar placentation model to humans. The present study was carried out considering the scarcity of information concerning the placental development in agouti. Describe the microscopy of the placenta, subplacenta and yolk sac of agoutis in early pregnancy and report on the inversion of the yolk sac. Fifteen females between the 14th-32nd day of gestation were used following euthanasia. Gestational buttons were collected, fixed, processed, stained to optical microscopy or immunohistochemistry. Chorioallantoic placenta (CP) ranged from conical to a half-sphere, as follows: from the 14th to 17th day, the CP displays an inverted "V" shape, predominantly formed by cytotrophoblasts; from 20 to 22 days, formed almost entirely by cytotrophoblasts; at 28 days, a half sphere, with distinct lobes and interlobular area, numerous maternal gaps delimited by syncytiotrophoblasts and trophoblast giant cells; at 32 days, globose and undergoing the maturation process. Subplacenta, located between decidua and CP, initially presents septa consisting of simple columnar epithelium and after 17 days, comprising stratified epithelium. Visceral yolk sac (VYS) is attached to two CP projections between 14 and 17 days, formed by a simple cubic epithelium and inverted. Between 20 and 22 days, the epithelium displays apical villous projections with cytoplasmic vacuoles and a vascularized mesoderm. After the 24th day, the VYS near the placenta is pleated, very vascularized and villous, with decreased villi sizes further away from the placenta. The agouti CP displays similar characteristics to other hystricomorpha, including placenta lobulation, a subplacenta and an inverted vitelline placenta.

Half sphere and single clip-bar retained implant supported silicone auricular prosthesis.

Implant supported auricular prosthesis can be retained by several mechanical means, one of them being the Hader bar and clip system. Conventionally two or more rider clips are used. This technique describes a modified Hader bar design to maintain retention while eliminating the requirement of a second clip, significantly bringing down cost.

Experimental Performance Analysis of a Hybrid Wave Energy Harvesting System Combining E-Motions with Triboelectric Nanogenerators

This paper discusses a disruptive approach to wave energy conversion, based on a hybrid solution: the E-Motions wave energy converter with integrated triboelectric nanogenerators. To demonstrate it, a physical modelling study was carried out with nine E-Motions sub-variants, which were based on three original hull designs (half-cylinder (HC), half-sphere (HS) and trapezoidal prism (TP)). A unidirectional lateral tribo-device was incorporated within the E-Motions’ hull during the experiments. The physical models were subjected to eight irregular sea-states from a reference study on the Portuguese coastline. Results point towards a significant hydrodynamic roll response, with peaks of up to 40 °/m. Three peaks were observed for the surge motions, associated with slow drifting at low frequencies. The response bandwidth of the HC sub-variants was affected by the varying PTO mass-damping values. By comparison, such response was generally maintained for all HS sub-variants and improved for the TP sub-variants, due to ballast positioning adjustments. Maximum power ratios ranged between 0.015 kW/m3 and 0.030 kW/m3. The TENGs demonstrated an average open-circuit voltage and power per kilogram ratio of up to 85 V and 18 mW/kg, respectively, whilst exhibiting an evolution highly dependent upon wave excitation, surge excursions and roll oscillations. Thus, TENGs enable redundant dual-mode wave energy conversion alongside E-Motions, which can power supporting equipment with negligible influence on platform hydrodynamics.

The Nirenberg Problem on Half Spheres: A Bubbling-off Analysis

Abstract In this paper, we perform a refined blow-up analysis of finite energy approximated solutions to a Nirenberg-type problem on half spheres. The latter consists of prescribing, under minimal boundary conditions, the scalar curvature to be a given function. In particular, we give a precise location of blow-up points and blow-up rates. Such an analysis shows that the blow-up picture of the Nirenberg problem on half spheres is far more complicated that in the case of closed spheres. Indeed, besides the combination of interior and boundary blow ups, there are nonsimple blow-up points for subcritical solutions having zero or nonzero weak limit. The formation of such nonsimple blowups is governed by a vortex problem, unveiling an unexpected connection with Euler equations in fluid dynamic and mean fields type equations in mathematical physics.

Three-Dimensional Morphology and Watershed-Algorithm-Based Method for Pitting Corrosion Evaluation

Pitting corrosion and stress concentration at rust pits are the principal reasons for severe degradation in fatigue performance of corroded steel structures. The accurate evaluation of rust pits on rough and uneven corrosion surfaces is the foundation of fatigue life estimation for corroded steel structures. In this paper, a new method for the identification, extraction, and evaluation of rust pits on the surface of corroded steel structures was proposed based on a three-dimensional morphology and watershed algorithm. An accelerated corrosion experiment was first executed to acquire corroded steel plates, and then surface profile measurements were conducted to obtain the three-dimensional morphology of the corroded steel surfaces. Furthermore, the surface topography data of the corroded steel surfaces were written into a gray matrix through coordinate transformation. Then, the gray matrix was successively filtered and gradient-mapped, and the watershed was calculated to obtain the pit mark matrix and pit depth matrix. A calculation method for the size and shape of rust pits was consequently developed, and a statistical analysis of the extraction results of the rust pits was also conducted. The results showed that rust pit density had a peak value at the corrosion duration of 3 months, and rust pit density showed a fluctuating process with corrosion duration that continued to increase until 15 months. The values of the depth diameter ratios of rust pits were concentrated in the range of 0.1~0.8. With corrosion duration increasing from 3 months to 4, 6, 8, 12, and 15 months, the distribution range of the depth diameter ratios of rust pits decreased at first and then increased, followed by decrease and, finally, increase. The width distribution of the rust pits was independent of the depth distribution of the rust pits. The values of the volume ratios were mostly distributed between π/12 and π/4, and the shapes of most rust pits were similar to half (ellipsoidal) spheres.

KONSEP MATEMATIKA PADA TRADISI PERNIKAHAN SUKU TIDUNG

In today's modern era, preserving culture is very important. One effort that can be made is to integrate culture into learning mathematics . This research is conducted to identify the mathematical concepts of the Tidung wedding ritual in Nunukan Regency, North Kalimantan. The mathematical concepts found can be used as material to integrate culture in learning mathematics. The concept of the program is known as ethnomathematics. This research is ethnographic. Mathematical concepts in the Tidung wedding tradition will be identified in the tools and activities of the wedding ritual. The data were obtained through direct observation, interviews, and documentation analysis. Data analysis was carried out in four stages: data reduction, data presentation, concluding, and checking the validity of the data using triangulation methods. The results showed that there were mathematical concepts in the tools used in the wedding procession. Tools that can be used in learning mathematics include bagas silow, dian, busak dian, nasi rasul, nasi pengantin, sirih pinang, selapah, pelujan, raja besila, gandur, batu asa, padaw, and panggaw. The identified mathematical concepts are cylinders, circles, cuboids, geometric transformations, regular polygons, half spheres, integrals, quadrilaterals, arithmetic sequences and series, congruences, number patterns, and triangles. Then, there are counting activities in the ritual activities of bepupur/pupuran and bejiu pengantin (bridal bath). TRANSLATE with x English Arabic Hebrew Polish Bulgarian Hindi Portuguese Catalan Hmong Daw Romanian Chinese Simplified Hungarian Russian Chinese Traditional Indonesian Slovak Czech Italian Slovenian Danish Japanese Spanish Dutch Klingon Swedish English Korean Thai Estonian Latvian Turkish Finnish Lithuanian Ukrainian French Malay Urdu German Maltese Vietnamese Greek Norwegian Welsh Haitian Creole Persian // TRANSLATE with COPY THE URL BELOW Back EMBED THE SNIPPET BELOW IN YOUR SITE Enable collaborative features and customize widget: Bing Webmaster Portal Back // ORIGINAL: "; langMenu.appendChild(origLangDiv); LanguageMenu.Init('LanguageMenu', LanguageMenu_keys, LanguageMenu_values, LanguageMenu_callback, LanguageMenu_popupid); window["LanguageMenu"] = LanguageMenu; clearInterval(intervalId); } }, 1); // ]]>

Printed 3D Gesture Recognition Thermoformed Half Sphere Compatible with In‐Mold Electronic Applications

The development of conformable electronic systems’ focuses on the multifunctional smart materials transform areas from the automotive industry to biomedicine, based on improved integration and advanced functionalities. In‐mold electronics (IME) combines thermoforming, injection molding, and printed electronics, resulting in sensing structural parts integrated into smart surfaces, communicating with computer systems, and enabling advanced experiences in terms of human‐machine interaction. Contrary to flexible electronics, designed as bend conductors around a single axis, thermoformed electronics allow deformations in the three‐axial directions for different geometries. Herein, a 2D screen‐printed pattern using conductive silver ink thermoformed into a spherical surface suitable for 3D gesture recognition is reported. The mechanical deformation of the high‐impact polystyrene sheet (HIPS) and polyethylene terephthalate‐glycol (PETG) substrates during the thermoforming process of the electrical circuit is characterized experimentally. The electrical resistance changes through the circuit in the stages of the fabrication process due the thickness decrease and the propagation of the small cracks. Both evaluations contribute to a better understanding of the performance of the materials when subject to the IME process. Validation of the 3D gesture recognition operation is carried out, demonstrating their full operability, as well as the possibilities that the combination of technologies allows.

Reconstruction of polytopes from the modulus of the Fourier transform with small wave length

Abstract Let 𝒫 {\mathcal{P}} be an n-dimensional convex polytope and let 𝒮 {\mathcal{S}} be a hypersurface in ℝ n {\mathbb{R}^{n}} . This paper investigates potentials to reconstruct 𝒫 {\mathcal{P}} , or at least to compute significant properties of 𝒫 {\mathcal{P}} , if the modulus of the Fourier transform of 𝒫 {\mathcal{P}} on 𝒮 {\mathcal{S}} with wave length λ, i.e., | ∫ 𝒫 e - i ⁢ 1 λ ⁢ 𝐬 ⋅ 𝐱 ⁢ 𝐝𝐱 | for ⁢ 𝐬 ∈ 𝒮 , \biggl{\lvert}\int_{\mathcal{P}}e^{-i\frac{1}{\lambda}\mathbf{s}\cdot\mathbf{x% }}\,\mathbf{dx}\biggr{\rvert}\quad\text{for }\mathbf{s}\in\mathcal{S}, is given, λ is sufficiently small and 𝒫 {\mathcal{P}} and 𝒮 {\mathcal{S}} have some well-defined properties. The main tool is an asymptotic formula for the Fourier transform of 𝒫 {\mathcal{P}} with wave length λ when λ → 0 {\lambda\rightarrow 0} . The theory of X-ray scattering of nanoparticles motivates this study, since the modulus of the Fourier transform of the reflected beam wave vectors is approximately measurable on a half sphere in experiments.

Non simple blow ups for the Nirenberg problem on half spheres

<p style='text-indent:20px;'>In this paper we study a Nirenberg type problem on standard half spheres <inline-formula><tex-math id="M1">\begin{document}$ (\mathbb{S}^n_+,g_0) $\end{document}</tex-math></inline-formula> consisting of finding conformal metrics of prescribed scalar curvature and zero boundary mean curvature. This problem amounts to solve the following boundary value problem involving the critical Sobolev exponent:</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{equation*} (\mathcal{P}) \quad \begin{cases} - \Delta_{g_0} u \, + \, \frac{n(n-2)}{4} u \, = K \, u^{\frac{n+2}{n-2}},\, u > 0 \quad \mbox{in } \mathbb{S}^n_+, \\ \frac{\partial u}{\partial \nu }\, = \, 0 \quad \mbox{on } \partial \mathbb{S}^n_+, \end{cases} \end{equation*} $\end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>where <inline-formula><tex-math id="M2">\begin{document}$ K \in C^3(\mathbb{S}^n_+) $\end{document}</tex-math></inline-formula> is a positive function. We construct, under generic conditions on the function <inline-formula><tex-math id="M3">\begin{document}$ K $\end{document}</tex-math></inline-formula>, finite energy solutions of a subcritical approximation of <inline-formula><tex-math id="M4">\begin{document}$ (\mathcal{P}) $\end{document}</tex-math></inline-formula> on half spheres of dimension <inline-formula><tex-math id="M5">\begin{document}$ n \geq 5 $\end{document}</tex-math></inline-formula>, which exhibit multiple blow up of <i>cluster-type</i> at the same boundary point. These solutions may have zero or non zero weak limit and may develop clusters at different boundary points. Such a blow up phenomena on half spheres drastically contrast with the case of the Nirenberg problem on spheres, where non simple blow up for finite energy solutions cannot occur and unveils an unexpected connection with vortex type problems arising in Euler equations in fluid dynamic and mean fields type equations in mathematical physics. We construct also, under suitable conditions on the restriction of <inline-formula><tex-math id="M6">\begin{document}$ K $\end{document}</tex-math></inline-formula> on <inline-formula><tex-math id="M7">\begin{document}$ \partial \mathbb{S}^n_+ $\end{document}</tex-math></inline-formula>, approximate solutions of arbitrarily large energy and Morse index.</p>

Analytical and numerical calculation of the detachment of particle structures from fibers

Not much research has been done on the detachment of deposit structures from fibers in gas flow. This study presents two approaches to determine the fluid velocities uc required for detachment. The first is an analytical model based on the imbalance of drag and adhesive forces. With the help of available models in literature two curves for uc as a function of deposit diameter were calculated. The two curves represent the different conditions present in a deposited structure, consisting of a mixture of reactive and inert matter, before and after reaction. It approximates the structure by one sphere, that consists of two identical half spheres, of which one detaches due to drag. The second approach is a CFD model, in which the deposited particle structure is represented through an immersed boundary method (IBM). It calculates adhesive forces based on the van der Waals force between two half-spaces, while drag is directly evaluated from flow properties at the structure’s surface. To be comparable with the analytical approach, it also approximates the deposit with two half spheres. The models are capable of describing detachment velocity behavior as a function of deposit structure size and porosity as reported in literature.Copyright © 2021 American Association for Aerosol Research

Precise estimation of residue relative solvent accessible area from Cα atom distance matrix using a deep learning method.

The solvent accessible surface is an essential structural property measure related to the protein structure and protein function. Relative solvent accessible area (RSA) is a standard measure to describe the degree of residue exposure in the protein surface or inside of protein. However, this computation will fail when the residues information is missing. In this article, we proposed a novel method for estimation RSA using the Cα atom distance matrix with the deep learning method (EAGERER). The new method, EAGERER, achieves Pearson correlation coefficients of 0.921-0.928 on two independent test datasets. We empirically demonstrate that EAGERER can yield better Pearson correlation coefficients than existing RSA estimators, such as coordination number, half sphere exposure and SphereCon. To the best of our knowledge, EAGERER represents the first method to estimate the solvent accessible area using limited information with a deep learning model. It could be useful to the protein structure and protein function prediction. The method is free available at https://github.com/cliffgao/EAGERER. Supplementary data are available at Bioinformatics online.

The Nirenberg problem on high dimensional half spheres: the effect of pinching conditions

In this paper we study the Nirenberg problem on standard half spheres (mathbb {S}^n_+,g), , n ge 5, which consists of finding conformal metrics of prescribed scalar curvature and zero boundary mean curvature on the boundary. This problem amounts to solve the following boundary value problem involving the critical Sobolev exponent: (P)-Δgu+n(n-2)4u=Kun+2n-2,u>0inS+n,∂u∂ν=0on∂S+n.\\documentclass[12pt]{minimal}\t\t\t\t\\usepackage{amsmath}\t\t\t\t\\usepackage{wasysym}\t\t\t\t\\usepackage{amsfonts}\t\t\t\t\\usepackage{amssymb}\t\t\t\t\\usepackage{amsbsy}\t\t\t\t\\usepackage{mathrsfs}\t\t\t\t\\usepackage{upgreek}\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\t\t\t\t\\begin{document}$$\\begin{aligned} (\\mathcal {P}) \\quad {\\left\\{ \\begin{array}{ll} -\\Delta _{g} u \\, + \\, \\frac{n(n-2)}{4} u \\, = K \\, u^{\\frac{n+2}{n-2}},\\, u > 0 &{}\\quad \\text{ in } \\mathbb {S}^n_+, \\\\ \\frac{\\partial u}{\\partial \\nu }\\, =\\, 0 &{}\\quad \\text{ on } \\partial \\mathbb {S}^n_+. \\end{array}\\right. } \\end{aligned}$$\\end{document}where K in C^3(mathbb {S}^n_+) is a positive function. This problem has a variational structure but the related Euler–Lagrange functional J_K lacks compactness. Indeed it admits critical points at infinity, which are limits of non compact orbits of the (negative) gradient flow. Through the construction of an appropriate pseudogradient in the neighborhood at infinity, we characterize these critical points at infinity, associate to them an index, perform a Morse type reduction of the functional J_K in their neighborhood and compute their contribution to the difference of topology between the level sets of J_K, hence extending the full Morse theoretical approach to this non compact variational problem. Such an approach is used to prove, under various pinching conditions, some existence results for (mathcal {P}) on half spheres of dimension n ge 5.

BUGINESE ETHNOMATHEMATICS: BARONGKO CAKE EXPLORATIONS AS MATHEMATICS LEARNING RESOURCES

Mathematics is still viewed as a culture-free subject. This forms a negative perception for students on mathematics. Most students assume that mathematics and culture are not related. This may occur because mathematics taught in school is not contextual and far from the reality of everyday life. Historically, mathematics has become a part of everyday life. As a maritime nation, Indonesia has a diverse culture. But many teachers are not yet aware of the integration of the culture into mathematics learning. Barongko cake is one of the Buginese cultural heritages. Buginese people have unconsciously been practicing mathematics in making these cakes. Therefore, this research aims to explore activities in making Barongko cakes in the Buginese community that involves mathematical concepts. This research is a qualitative descriptive with an ethnographic approach. The data collection methods are carried out through observation, documentation, interview with an expert in making Barongko cake. This research found that Barongko making process involves mathematics in the concept of division, congruence, and similarity, as well as a triangular prism, and half sphere. This cake has the potential to be used as a source of contextual mathematics learning in schools.

A nomogram for estimating intracranial pressure using acute subdural hematoma thickness and midline shift

Although criteria for surgical treatment of acute subdural hematoma (SDH) have been proposed, interaction exists between SDH, midline shift (MLS), and intracranial pressure (ICP). Based on our half sphere finite-element model (FEM) of the supratentorial brain parenchyma, tools for ICP estimation using SDH thickness (SDHx) and MLS were developed. We performed 60 single load step, structural static analyses, simulating a left-sided SDH compressing the cerebral hemispheres. The Young's modulus was taken as 10,000 Pa. The ICP loads ranged from 10 to 80 mmHg with Poisson's ratios between 0.25 and 0.49. The SDHx and the MLS results were stored in a lookup table. An ICP estimation equation was derived from these data and then was converted into a nomogram. Numerical convergence was achieved in 49 model analyses. Their SDHx ranged from 0.79 to 28.3 mm, and the MLS ranged from 1.5 to 16.9 mm. The estimation formula was log(ICP) = 0.614–0.520 log(SDHx) + 1.584 log(MLS). Good correlations were observed between invasive ICP measurements and those estimated from preoperative SDHx and MLS data on images using our model. These tools can be used to estimate ICP noninvasively, providing additional information for selecting the treatment strategy in patients with SDH.