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1
Akkiraju, Nataraj. "Approximating spheres and sphere patches." Computer Aided Geometric Design 15, no. 7 (July 1998): 739–56. http://dx.doi.org/10.1016/s0167-8396(98)00017-x.
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Laird, Edgar. "Heaven and the Sphaera Mundi in the Middle Ages." Culture and Cosmos 04, no. 01 (June 2000): 10–35. http://dx.doi.org/10.46472/cc.0104.0205.
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This paper examines the development of the idea of heaven in relation to the sphaera mundi - the sphere of the world - in medieval literature. The sphaera mundi is a model of the cosmos that at its most elementary is very simple indeed. At the centre of it is the earth, so small as to be virtually a dot in comparison to the whole or even to the smallest star. Earth is surrounded by the sea, which in turn is surrounded by air, as also air is surrounded by fire. Surrounding the fire is a sphere that 'bears' the moon, and around that sphere are others, like layers of an onion, bearing the other planets: Mercury, then Venus, the sun, Mars, Jupiter and Saturn. Then come the sphere bearing the fixed stars and, beyond it, one or more others. All these spheres together constitute the sphere of the world.
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Farkas, Zoltán. "A társadalmi élet alszférái." Belvedere Meridionale 35, no. 4 (2023): 101–23. http://dx.doi.org/10.14232/belv.2023.4.7.
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According to my conception, we can distinguish the four main spheres of modern human life: the spheres of private life, community life, social life, and coercive life. The modern state (or national) society is a heterogeneous society in which the main life spheres mentioned have been developed, and in which the sphere of social life is of fundamental importance. In this paper, the focus of inquiry is that the sphere of social life is also complex, from the point of view that it is differentiated into social sub-spheres. First, I point out the main conceptions regarding the differentiation of society into subsystems, fields, or spheres, especially Bourdieu’s field theory, and then I define the concept of social sub-sphere. After that, I distinguish the sphere of everyday social life on the one hand, and the sphere of political life on the other; and within the former sphere (or partly in the area of other life spheres) I make a distinction between further sub-spheres: the relatively pure social sub-sphere, the semi-social sub-sphere, and the mixed life sphere.
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Nasyrova, S. I. "Inter-Component Relations in a Human-Centered Economy (Part 2)." Economics and Management 27, no. 9 (October 21, 2021): 687–96. http://dx.doi.org/10.35854/1998-1627-2021-9-687-696.
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Aim. The presented study aims to identify and describe the relations of mutual restriction between the fundamental spheres of a human-oriented economy.Tasks. The author describes problems associated with the need to study the human-oriented economy; establishes horizontal and vertical economic relations in the economic system; discovers the specific aspects of horizontal economic relations through the interaction between the spheres of a human-oriented economy; identifies normal and pathological restriction relations.Methods. This study uses scientific methods of cognition, namely content analysis and the Wuxing Pentagram.Results. Horizontal relations between the defining spheres of a human-oriented economy are determined. The resource (human needs) that ensures interaction between the spheres of the economic system under consideration is identified. Normal restriction relations are described: natural-material sphere — information-digital sphere, information-digital sphere — cognitive sphere, cognitive sphere — social-service sphere, social-service sphere — creatosphere, creatosphere — natural-material sphere. Pathological restriction relations are detected: informationdigital sphere — natural-material sphere, cognitive sphere — information-digital sphere, socialservice sphere — cognitive sphere, creatosphere — social-service sphere, natural-material sphere — creatosphere.Conclusions. Examination of restriction relations in a human-oriented economy provides insight into the directions for the regulation of the corresponding economic system, which, according to the author, will ensure not only personal, but also economic growth.
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Wie, Chu-Ryang. "Two-Qubit Bloch Sphere." Physics 2, no. 3 (August 2, 2020): 383–96. http://dx.doi.org/10.3390/physics2030021.
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Three unit spheres were used to represent the two-qubit pure states. The three spheres are named the base sphere, entanglement sphere, and fiber sphere. The base sphere and entanglement sphere represent the reduced density matrix of the base qubit and the non-local entanglement measure, concurrence, while the fiber sphere represents the fiber qubit via a simple rotation under a local single-qubit unitary operation; however, in an entangled bipartite state, the fiber sphere has no information on the reduced density matrix of the fiber qubit. When the bipartite state becomes separable, the base and fiber spheres seamlessly become the single-qubit Bloch spheres of each qubit. Since either qubit can be chosen as the base qubit, two alternative sets of these three spheres are available, where each set fully represents the bipartite pure state, and each set has information of the reduced density matrix of its base qubit. Comparing this model to the two Bloch balls representing the reduced density matrices of the two qubits, each Bloch ball corresponds to two unit spheres in our model, namely, the base and entanglement spheres. The concurrence–coherence complementarity is explicitly shown on the entanglement sphere via a single angle.
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Gorodski, Claudio. "Minimal sphere bundles in Euclidean spheres." Geometriae Dedicata 53, no. 1 (November 1994): 75–102. http://dx.doi.org/10.1007/bf01264046.
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Ajala, Samuel Omoloye. "Smooth structures on sphere bundles over spheres." International Journal of Mathematics and Mathematical Sciences 11, no. 4 (1988): 701–11. http://dx.doi.org/10.1155/s0161171288000857.
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In [1] R. De Sapio gave a classification of smooth structures of ap-sphere bundle over aq-sphere with one cross-section andp<q. In [2] J. Munkres also gave a classification up to concordance of differential structures in the case where the bundle has at least two cross-sections. In [3] R. Schultz gave a classification in the casep≥q. Here we will give a classification of thep-sphere bundle over aq-sphere without any cross-section andp<q.
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Liu, Shuang, Peng Chen, and Keqiu Li. "Multiple sub-hyper-spheres support vector machine for multi-class classification." International Journal of Wavelets, Multiresolution and Information Processing 12, no. 03 (May 2014): 1450035. http://dx.doi.org/10.1142/s0219691314500350.
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Support vector machine (SVM) is originally proposed to solve binary classification problem. Multi-class classification is solved by combining multiple binary classifiers, which leads to high computation cost by introducing many quadratic programming (QP) problems. To decrease computation cost, hyper-sphere SVM is put forward to compute class-specific hyper-sphere for each class. If all resulting hyper-spheres are independent, all training and test samples can be correctly classified. When some of hyper-spheres intersect, new decision rules should be adopted. To solve this problem, a multiple sub-hyper-sphere SVM is put forward in this paper. New algorithm computed hyper-spheres by SMO algorithm for all classes first, and then obtained position relationships between hyper-spheres. If hyper-spheres belong to the intersection set, overlap coefficient is computed based on map of key value index and mother hyper-spheres are partitioned into a series of sub-hyper-spheres. For the new intersecting hyper-spheres, one similarity function or same error sub-hyper-sphere or different error sub-hyper-sphere are used as decision rule. If hyper-spheres belong to the inclusion set, the hyper-sphere with larger radius is partitioned into sub-hyper-spheres. If hyper-spheres belong to the independence set, a decision function is defined for classification. With experimental results compared to other hyper-sphere SVMs, our new proposed algorithm improves the performance of the resulting classifier and decreases computation complexity for decision on both artificial and benchmark data set.
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Uniawati, Uniawati. "ELONG UGI: KAJIAN ESTETIKA DALAM PANDANGAN VLADIMIR BRAGINSKY." Seshiski: Southeast Journal of Language and Literary Studies 1, no. 1 (June 10, 2021): 34–46. http://dx.doi.org/10.53922/seshiski.v1i1.13.
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This paper describes the aesthetic values of elong ugi "Ala Masea-Sea" by using the concept of beauty in Vladimir Braginsky's view. There are three levels of beauty according to Braginsky, namely; the beauty sphere, the utility sphere, and the functional sphere (refinement). These three levels of spheres are the basis for analysis to answer the three main problems that are formulated in this article. The results of the analysis showed that the elong ugi "Ala Masea-Sea" fulfills two spheres, namely the beauty spheres and the faedah spheres. The functional sphere or the highest sphere in terms of the beauty of a work is not contained in elong ugi "Ala Masea-Sea". However, elong ugi "Ala Masea-Sea" as a classical Bugis literature shows a strong aesthetic value.
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Montiel, Sebastián. "Willmore two-spheres in the four-sphere." Transactions of the American Mathematical Society 352, no. 10 (June 13, 2000): 4469–86. http://dx.doi.org/10.1090/s0002-9947-00-02571-x.
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Cardim, Nancy de Souza, Kee Y. Lam, Maria Hermínia de P. L. Mello, Duane Randall, and Mário Olivero Marques da Silva. "Span of orthogonal sphere bundles over spheres." Topology and its Applications 202 (April 2016): 325–36. http://dx.doi.org/10.1016/j.topol.2016.01.004.
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Heller, Sebastian. "Willmore spheres in the $3$-sphere revisited." Communications in Analysis and Geometry 31, no. 4 (2023): 793–98. http://dx.doi.org/10.4310/cag.2023.v31.n4.a1.
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Riedl, Thomas, and Jörg K. N. Lindner. "Automated SEM Image Analysis of the Sphere Diameter, Sphere-Sphere Separation, and Opening Size Distributions of Nanosphere Lithography Masks." Microscopy and Microanalysis 28, no. 1 (December 27, 2021): 185–95. http://dx.doi.org/10.1017/s1431927621013866.
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AbstractColloidal nanosphere monolayers—used as a lithography mask for site-controlled material deposition or removal—offer the possibility of cost-effective patterning of large surface areas. In the present study, an automated analysis of scanning electron microscopy (SEM) images is described, which enables the recognition of the individual nanospheres in densely packed monolayers in order to perform a statistical quantification of the sphere size, mask opening size, and sphere-sphere separation distributions. Search algorithms based on Fourier transformation, cross-correlation, multiple-angle intensity profiling, and sphere edge point detection techniques allow for a sphere detection efficiency of at least 99.8%, even in the case of considerable sphere size variations. While the sphere positions and diameters are determined by fitting circles to the spheres edge points, the openings between sphere triples are detected by intensity thresholding. For the analyzed polystyrene sphere monolayers with sphere sizes between 220 and 600 nm and a diameter spread of around 3% coefficients of variation of 6.8–8.1% for the opening size are found. By correlating the mentioned size distributions, it is shown that, in this case, the dominant contribution to the opening size variation stems from nanometer-scale positional variations of the spheres.
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MICHELAT, Alexis, and Tristan RIVIÈRE. "The Classification of Branched Willmore Spheres in the 3-Sphere and the 4-Sphere." Annales scientifiques de l'École Normale Supérieure 55, no. 5 (2022): 1199–288. http://dx.doi.org/10.24033/asens.2515.
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Szymanek, Ewa, and Artur Tyliszczak. "Numerical Analysis of a Flow over Spheres Embedded on a Flat Wall." Processes 9, no. 2 (February 1, 2021): 277. http://dx.doi.org/10.3390/pr9020277.
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This paper presents the results of numerical simulations of flow in a periodic channel with the walls covered in the central part by spherical elements that have the same overall surface areas but different radii. Two distributions of the sphere are considered, with the subsequent rows placed one after another or shifted. The computations are performed using the high-order code, whereas the solid elements are modelled with the help of the immersed boundary method. For selected cases, the results are validated by comparison with the solutions obtained using the ANSYS Fluent code on a very dense body-fitted mesh. It was found that the increase in the sphere diameter slows down the flow, which is attributed to the larger blockage of the channel cross-section caused by larger spheres and the occurrence of intense mixing (recirculation) between the spheres. The velocity profiles in the vicinity of the sphere are largely dependent on sphere diameter and rise when it increases. It was found that the distribution of the spheres plays an important role only when the spheres are large. In the part of the channel far from the sphere, the velocity profiles are significantly influenced by the sphere diameter but seem to be independent of the sphere distributions.
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Nasyrova, S. I. "Inter-Component Relations in a Human-Centered Economy (Part 1)." Economics and Management 27, no. 8 (September 21, 2021): 612–21. http://dx.doi.org/10.35854/1998-1627-2021-8-612-621.
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Aim. The presented study aims to identify and interpret mutual support relationships between the key areas of a human-oriented economy.Tasks. The authors formulate the problems of the relevance of examining economic relationships within the framework of various economic systems; substantiate the existence of economic support relationships and restrictions in the context of a human-centered economy; identify and structure normal and pathological economic support relationships between the spheres of a human-oriented economy.Methods. The theoretical and methodological basis of this study is based on the Wuxing Pentagram.Results. The authors present their view of economic support relationships in a human-centered economy as a result of interaction between its spheres: natural-material, social-service, information-digital, creatosphere and cognitive sphere. The resource (human needs) that ensures the interaction between the components of the economic system is identified. Normal support relationships are determined: natural-material sphere — social-service sphere; social-service sphere –information-digital sphere; information-digital sphere — creatosphere; creatosphere — cognitive sphere; cognitive sphere — natural-material sphere. Pathological support relationships are detected: social-service sphere — natural-material sphere; information-digital sphere — socialservice sphere; creatosphere — information-digital sphere; cognitive sphere — creatosphere; natural-material sphere — cognitive sphere.Conclusions. By defining and understanding inter-component support relationships in the context of a human-oriented economy, it becomes possible to determine directions for their regulation to ensure productive development of the economic system as a whole and each person in particular.
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Hagino, Takeshi, Yuichiro Yokoyama, Yutaka Kuriyama, and Han Haitjema. "Sphericity Measurement Using Stitching Interferometry." Key Engineering Materials 523-524 (November 2012): 883–88. http://dx.doi.org/10.4028/www.scientific.net/kem.523-524.883.
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A newly developed practical sphericity measurement system by means of stitching interferometry is described in this paper. Spheres are widely used in industry. In particular, spheres with stem are usually used in metrological applications such as reference sphere for Coordinate Measuring Machines. It is common to calibrate form of spheres with tactile roundness measurement, however a comprehensive form measurement is desired for evolving high precision applications. The developed system consists of commercial base Fizeau type interferometer to capture partial surface areas of sphere and five axes stages to handle sphere with stem. Hence the system is very suitable for measurement of such stemmed spheres. This system yields three dimensional form maps of stitched sphere and peak to valley sphericity. Standard deviation of sphericity value yielded using this system is less than 5 nm in 8 times repetition. Finally, an equatorial profile clipped from stitched sphere shows good agreement with a result of tactile roundness measuring method within 10 nm typically.
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UN, ANTONIUS STEVEN. "Sphere Sovereignty according to Kuyper." Unio Cum Christo 6, no. 2 (October 1, 2020): 97. http://dx.doi.org/10.35285/ucc6.2.2020.art5.
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This article systematically describes the principle of sphere sovereignty according to Abraham Kuyper. Four themes are critically examined: the sovereignty of Christ as the main basis of Kuyper’s principle and its relation to creation, fall, and redemption; structural pluralism as the way of understanding social structure; the notion of religious and confessional pluralism; finally, the role of the state as the sphere of spheres. A positive critique of Kuyper’s principle is given in conclusion. KEYWORDS: Sphere sovereignty, sphere of spheres, structural pluralism, confessional pluralism, creation, fall, redemption, faith, public justice
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Wilson, Holly, and Matthew Scobie. "Fiscal Accountability to te Tiriti o Waitangi." Policy Quarterly 20, no. 3 (August 19, 2024): 32–38. http://dx.doi.org/10.26686/pq.v20i3.9555.
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This article investigates possible models for strengthening fiscal accountability to te Tiriti o Waitangi. We utilise the spheres of influence framework set out by Matike Mai Aotearoa (2016), with a rangatiratanga sphere, a kāwanatanga sphere and a relational sphere. We outline tax-like practices in the rangatiratanga sphere and how the kāwanatanga sphere resources itself. We then explore expectations and protocols for accountability within the respective spheres, before proposing three possible models to strengthen fiscal accountability in line with te Tiriti o Waitangi. These models include a Māori tax commissioner, a Waitangi Tribunal kaupapa inquiry into or including fiscal authority, and an independent Māori tax authority.
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Stoyan, Dietrich. "SURFACES OF HARD-SPHERE SYSTEMS." Image Analysis & Stereology 33, no. 3 (July 25, 2014): 225. http://dx.doi.org/10.5566/ias.1134.
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In various situations surfaces appear that are formed by systems of hard spheres. Examples are porous layers as surfaces of sand heaps and biofilms or fracture surfaces of concrete. The present paper considers models where a statistically homogeneous system of hard spheres with random radii is intersected by a plane and the surface is formed by the spheres with centers close to this plane. Formulae are derived for various characteristics of such surfaces: for the porosity profile, i.e. the local porosity in dependence on the distance from the section plane and for the geometry of the sphere caps that look above the section plane.It turns out that these characteristics only depend on the first-order characteristics of the sphere system, its sphere density and the sphere radius distribution.Comparison with empirically studied biofilms shows that the model is realistic.
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Bender, Darrell. "Classical Quantum Hidden Variable Gravitation." Advances in Image and Video Processing 12, no. 6 (June 12, 2024): 635–79. https://doi.org/10.14738/aivp.126.18064.
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Years ago, just by thinking about it, we discovered the rate of a unit clock in a gravitational field, and, after that, because of the slower clock rate in a gravitational field, that the energy that an energy wave sphere loses becomes its energy of motion. We calculated the radius of a proton energy wave sphere contained in an electron energy wave sphere. We extend the concept of energy wave spheres to imaginary energy wave spheres to explain the change in frequency of the wave in an energy wave sphere. We show that a black hole is an imaginary energy wave sphere with radius alpha and wave velocity ic, which gives the nature of the kernel with radius alpha of a mass M. We show that the radial component of the velocity of a light ray, perpendicular to a radius in a gravitational field, has the velocity of an imaginary energy wave sphere inside the photon. We did not come here to offer a false theory, but, rather, a look through the veil of gravitation. We are the looking glass. A light ray with constant velocity -c moving toward the imaginary kernel of a mass M along a radius has a real energy wave sphere with wave velocity 0 always. In the face of imaginary energy wave spheres along its path, the wave velocity of the energy wave sphere never becomes imaginary assuming any energy lost by the wave goes into the velocity of the energy wave sphere. Taking this non-imaginary wave velocity clue amounts to assuming it holds for all real energy wave spheres and, as a consequence, that the absolute velocity of a real energy wave sphere cannot exceed c. Knowing that the source of this velocity is the energy wave sphere itself, we should have already concluded this anyway. As for a real kernel for the mass M for some radius less than alpha, no real energy wave sphere has an imaginary energy wave sphere to hold it together for such a radius. The only conceivable place to match the wave velocity of the real kernel of a mass M, where the wave velocity of the kernel is c and the velocity of the energy wave sphere, not its wave velocity, is -c, is at the radius alpha, thus extending the notion of a black hole to include this real energy wave sphere.
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Rodgers, R. P. C., and A. J. Baddeley. "Nested Monte Carlo study of random packing on the sphere." Journal of Applied Probability 28, no. 03 (September 1991): 539–52. http://dx.doi.org/10.1017/s0021900200042406.
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We consider two random sequential packing processes in which spheres of unit radius are randomly attached to the surface of a fixed unit sphere. Independent random spheres are generated and added successively, provided there is no overlap with previous spheres. In model 1, the process stops when a trial sphere intersects one of the previously-accepted spheres. In model 2, random sequential packing, any such overlapping trial sphere is discarded and the next random sphere is tried, until it is impossible to add any further spheres. Previous workers have conjectured convincingly that no exact analytical solution is possible for this type of problem. We use Monte Carlo simulation methods to estimate transition probabilities for the two models. Because some probabilities are extremely small, a simulation using independent repetitions of the model would be inefficient. We designed a branching process of conditionally binomial trials, and performed over 108 trials on a supercomputer.
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Tee, Y. H., and E. K. Longmire. "Understanding The Effect Of Turbulent Structures On Three-Dimensional Sphere Motions In Boundary Layers." Proceedings of the International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics 20 (July 11, 2022): 1–16. http://dx.doi.org/10.55037/lxlaser.20th.211.
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This paper investigates the effect of turbulent activity on the wall-normal motion of spheres with specific gravities of 1.006 (P1) and 1.152 (P3) a t Re_x = 670 and 1300. These spheres extend into the logarithmic region with d+ = 56 and 116. Both sphere and fluid motions were tracked simultaneously using separate techniques; 3D particle tracking was used to track the individual spheres over a streamwise distance of 5 boundary layer thicknesses while stereoscopic particle image velocimetry was implemented to track the fluid motion surrounding the spheres over streamwise-spanwise planes at multiple streamwise and wallnormal locations. Upon release, sphere P1 accelerated strongly and lifted off of the wall due to strong mean shear before descending back towards the wall at both Re_x. Then, the sphere either ascended again without returning to the wall or else contacted the wall and slid before lifting off again. This sphere did not develop any significant rotations throughout its trajectory. The subsequent lift-offs observed, which were of similar or larger magnitude to the initial lift-offs, were prompted by fluid upwash and/or temporary increases in shear l ift due to passing high momentum zones. While ejection events were found to be important to sphere lift-offs, we did not observe any distinct fluid structures or sweep motions associated with sphere descents. These descents were likely dominated by gravity after the positive lift on the sphere decreased following its detachment from the wall. The upward impulse from Q2 type events was limited, and once the sphere moved away from the wall, the upward shearing lift was insufficient to keep the sphere suspended. The denser sphere P3, by contrast, did not lift off upon release and initially slid along the wall while lagging the fluid significantly. After it had propagated approximately 1.5𝛿 downstream, it began rolling forward (while slipping) and accelerated again. The forward rotation induced sufficient Magnus lift to generate small lift-off events of magnitude ≤ 0.2d repeating at relatively high frequency independent of the larger turbulence structures around the sphere.
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DERKSEN, J. J., and R. A. LARSEN. "Drag and lift forces on random assemblies of wall-attached spheres in low-Reynolds-number shear flow." Journal of Fluid Mechanics 673 (March 4, 2011): 548–73. http://dx.doi.org/10.1017/s0022112010006403.
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Direct numerical simulations of the shear flow over assemblies of uniformly sized, solid spheres attached to a flat wall have been performed using the lattice-Boltzmann method. The random sphere assemblies comprised monolayers, double layers and triple layers. The Reynolds number based on the sphere radius and the overall shear rate was much smaller than 1. The results were interpreted in terms of the drag force (the force in the streamwise direction) and lift force (the force in the wall-normal direction) experienced by the spheres as a function of the denseness of the bed and the depth of the spheres in the bed. The average drag and lift forces decay monotonically as a function of the surface coverage of the spheres in the top layer of the bed. The sphere-to-sphere variation of the drag and lift forces is significant due to interactions between spheres via the interstitial fluid flow.
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Peñaherrera-Pazmiño, Ana Belén, Ramiro Fernando Isa-Jara, Elsa Hincapié-Arias, Silvia Gómez, Denise Belgorosky, Eduardo Imanol Agüero, Matías Tellado, Ana María Eiján, Betiana Lerner, and Maximiliano Pérez. "AQSA—Algorithm for Automatic Quantification of Spheres Derived from Cancer Cells in Microfluidic Devices." Journal of Imaging 10, no. 11 (November 20, 2024): 295. http://dx.doi.org/10.3390/jimaging10110295.
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Sphere formation assay is an accepted cancer stem cell (CSC) enrichment method. CSCs play a crucial role in chemoresistance and cancer recurrence. Therefore, CSC growth is studied in plates and microdevices to develop prediction chemotherapy assays in cancer. As counting spheres cultured in devices is laborious, time-consuming, and operator-dependent, a computational program called the Automatic Quantification of Spheres Algorithm (ASQA) that detects, identifies, counts, and measures spheres automatically was developed. The algorithm and manual counts were compared, and there was no statistically significant difference (p = 0.167). The performance of the AQSA is better when the input image has a uniform background, whereas, with a nonuniform background, artifacts can be interpreted as spheres according to image characteristics. The areas of spheres derived from LN229 cells and CSCs from primary cultures were measured. For images with one sphere, area measurements obtained with the AQSA and SpheroidJ were compared, and there was no statistically significant difference between them (p = 0.173). Notably, the AQSA detects more than one sphere, compared to other approaches available in the literature, and computes the sphere area automatically, which enables the observation of treatment response in the sphere derived from the human glioblastoma LN229 cell line. In addition, the algorithm identifies spheres with numbers to identify each one over time. The AQSA analyzes many images in 0.3 s per image with a low computational cost, enabling laboratories from developing countries to perform sphere counts and area measurements without needing a powerful computer. Consequently, it can be a useful tool for automated CSC quantification from cancer cell lines, and it can be adjusted to quantify CSCs from primary culture cells. CSC-derived sphere detection is highly relevant as it avoids expensive treatments and unnecessary toxicity.
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Lu, Liangyu, Jian Li, Hongwei Li, Chengtao Gao, Haibo Xie, Yuzhu Xiong, Zhu Luo, Qi Sun, and Fuping Dong. "Controllable synthesis of hierarchical polysilsesquioxane surfaces: from spheres-on-sphere to bowls-on-sphere structure." Applied Surface Science 481 (July 2019): 75–82. http://dx.doi.org/10.1016/j.apsusc.2019.03.044.
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Rodgers, R. P. C., and A. J. Baddeley. "Nested Monte Carlo study of random packing on the sphere." Journal of Applied Probability 28, no. 3 (September 1991): 539–52. http://dx.doi.org/10.2307/3214490.
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We consider two random sequential packing processes in which spheres of unit radius are randomly attached to the surface of a fixed unit sphere. Independent random spheres are generated and added successively, provided there is no overlap with previous spheres. In model 1, the process stops when a trial sphere intersects one of the previously-accepted spheres. In model 2, random sequential packing, any such overlapping trial sphere is discarded and the next random sphere is tried, until it is impossible to add any further spheres.Previous workers have conjectured convincingly that no exact analytical solution is possible for this type of problem. We use Monte Carlo simulation methods to estimate transition probabilities for the two models. Because some probabilities are extremely small, a simulation using independent repetitions of the model would be inefficient. We designed a branching process of conditionally binomial trials, and performed over 108 trials on a supercomputer.
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Tuma, RS, JA Stolk, and MB Roth. "Identification and characterization of a sphere organelle protein." Journal of Cell Biology 122, no. 4 (August 15, 1993): 767–73. http://dx.doi.org/10.1083/jcb.122.4.767.
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Sphere organelles are nuclear structures in amphibian oocytes that are easily visible by light microscopy. These structures are up to 10 microns in diameter and have been described morphologically for decades, yet their function remains obscure. The present study defines a protein component of the sphere organelle, named SPH-1, which is recognized by a mAb raised against purified Xenopus laevis oocyte nucleoplasm. SPH-1 is an 80-kD protein which is localized specifically to spheres and is undetectable elsewhere on lampbrush chromosomes or in nucleoli. We show using confocal microscopy that SPH-1 is localized to the cortex of sphere organelles. Furthermore, we have isolated a cDNA that can encode SPH-1. When epitope-tagged forms of SPH-1 are expressed in X. laevis oocytes the protein specifically localizes to spheres, demonstrating that the cloned cDNA encodes the sphere antigen. Comparison of the predicted amino acid sequence with sequence databases shows SPH-1 is related to p80-coilin, a protein associated with coiled bodies; coiled bodies are nuclear structures found in plant and animal cells. The sphere-specific mAb stains X. laevis tissue culture cells in a punctate nuclear pattern, showing that spheres or sphere antigens are present in somatic cells as well as germ cells and suggesting a general and essential function for spheres in all nuclei.
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Al-Dayel, Ibrahim, Sharief Deshmukh, and Olga Belova. "Characterizing non-totally geodesic spheres in a unit sphere." AIMS Mathematics 8, no. 9 (2023): 21359–70. http://dx.doi.org/10.3934/math.20231088.
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<abstract><p>A concircular vector field $ \mathbf{u} $ on the unit sphere $ \mathbf{S}^{n+1} $ induces a vector field $ \mathbf{w} $ on an orientable hypersurface $ M $ of the unit sphere $ \mathbf{S}^{n+1} $, simply called the induced vector field on the hypersurface $ M $. Moreover, there are two smooth functions, $ f $ and $ \sigma $, defined on the hypersurface $ M $, where $ f $ is the restriction of the potential function $ \overline{f} $ of the concircural vector field $ \mathbf{u} $ on the unit sphere $ \mathbf{S}^{n+1} $ to $ M $ and $ \sigma $ is defined as $ g\left(\mathbf{u}, N\right) $, where $ N $ is the unit normal to the hypersurface. In this paper, we show that if function $ f $ on the compact hypersurface satisfies the Fischer–Marsden equation and the integral of the squared length of the vector field $ \mathbf{w} $ has a certain lower bound, then a characterization of a small sphere in the unit sphere $ \mathbf{S}^{n+1} $ is produced. Additionally, we find another characterization of a small sphere using a lower bound on the integral of the Ricci curvature of the compact hypersurface $ M $ in the direction of the vector field $ \mathbf{w} $ with a non-zero function $ \sigma $.</p></abstract>
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Sugár, István P. "Density of electric field energy around two surface-charged spheres surrounded by electrolyte II. The smaller sphere is inside the larger one." AIMS Biophysics 9, no. 1 (2022): 61–71. http://dx.doi.org/10.3934/biophy.2022006.
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<abstract> <p>Based on the generalized version of Newton's Shell Theorem <xref ref-type="bibr" rid="b7">[7]</xref> the electric field energy density, <italic>u<sub>F</sub></italic> around two surface-charged spheres surrounded by electrolyte where the smaller sphere is inside the larger one is analytically calculated. According to the calculations when the surfaces of the spheres are farther from each other than four times of the Debye length the field energy density around and inside the smaller sphere is basically independent from the presence of the larger sphere. The electric field energy density is maximal when the smaller sphere touches the inner surface of the larger sphere and the maximum of <italic>u<sub>F</sub></italic> is located at the touching point on the outer surface of the larger sphere.</p> </abstract>
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KIM, SOON-CHUL. "SEGREGATION OF FLUIDIZED BINARY HARD-SPHERE SYSTEMS UNDER GRAVITY." International Journal of Modern Physics B 19, no. 04 (February 10, 2005): 763–74. http://dx.doi.org/10.1142/s0217979205027809.
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We have derived an analytic expression for the contact value of the local density of binary hard-sphere systems under gravity. We have obtained the crossover conditions for the Brazil-nut type segregation of binary hard-sphere mixtures and binary hard-sphere chain mixtures from the segregation criterion, where the segregation occurs when the density (or the pressure) of the small spheres at the bottom is higher than that of the large spheres, or vice versa. For the binary hard-sphere chain mixtures, the crossover condition for the segregation depends on the number of monomers composed of hard-sphere chains as well as the mass and the diameter of each species. The fundamental-measure theories (FMTs) and local density approximation (LDA) are employed to examine the crossover condition for the segregation of the gravity-induced hard-sphere mixtures. The calculated results show that the LDA does not explain the density oscillation near the bottom, whereas the modified fundamental-measure theory (MFMT) compares with molecular dynamics simulations.
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VARSAIE, S. "ν-SPHERES, ν-DEGREES AND ν-ALGEBRAS." International Journal of Geometric Methods in Modern Physics 06, no. 07 (November 2009): 1089–95. http://dx.doi.org/10.1142/s0219887809004090.
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A novel supergeometric generalization of common n-sphere, called ν-sphere, is introduced. It is shown that a canonical volume form exists on a ν-sphere. Then a concept of degree is developed for the maps between them. Finally, a semigroup action on ν-spheres is discussed.
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Krüger, M., T. Emig, G. Bimonte, and M. Kardar. "Non-equilibrium Casimir forces: Spheres and sphere-plate." EPL (Europhysics Letters) 95, no. 2 (June 27, 2011): 21002. http://dx.doi.org/10.1209/0295-5075/95/21002.
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Ferus, Dirk, and Ulrich Pinkall. "Constant curvature 2-spheres in the 4-sphere." Mathematische Zeitschrift 200, no. 2 (June 1989): 265–71. http://dx.doi.org/10.1007/bf01230286.
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Ruan, H. H., Z. Y. Gao, and T. X. Yu. "Crushing of thin-walled spheres and sphere arrays." International Journal of Mechanical Sciences 48, no. 2 (February 2006): 117–33. http://dx.doi.org/10.1016/j.ijmecsci.2005.08.006.
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Kahl, G. "Hard-sphere yukawa reference system for soft spheres." Journal of Non-Crystalline Solids 117-118 (February 1990): 104–7. http://dx.doi.org/10.1016/0022-3093(90)90889-t.
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Lei, Ya-Wen. "Publics, Scientists and the State: Mapping the Global Human Genome Editing Controversy." China Quarterly 246 (May 4, 2021): 400–427. http://dx.doi.org/10.1017/s0305741021000229.
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AbstractLiterature on scientific controversies has inadequately attended to the impact of globalization and, more specifically, the emergence of China as a leader in scientific research. To bridge this gap in the literature, this article develops a theoretical framework to analyse global scientific controversies surrounding research in China. The framework highlights the existence of four overlapping discursive arenas: China's national public sphere and national expert sphere, the transnational public sphere and the transnational expert sphere. It then examines the struggles over inclusion/exclusion and publicity within these spheres as well as the within- and across-sphere effects of such struggles. Empirically, the article analyses the human genome editing controversy surrounding research conducted by scientists in China between 2015 and 2019. It shows how elite scientists negotiated expert–public relationships within and across the national and transnational expert spheres, how unexpected disruption at the nexus of the four spheres disrupted expert–public relationships as envisioned by elite experts, and how the Chinese state intervened to redraw the boundary between openness and secrecy at both national and transnational levels.
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Davis, Robert H., and N. A. Hill. "Hydrodynamic diffusion of a sphere sedimenting through a dilute suspension of neutrally buoyant spheres." Journal of Fluid Mechanics 236 (March 1992): 513–33. http://dx.doi.org/10.1017/s0022112092001514.
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The motion of a heavy sphere sedimenting through a dilute background suspension of neutrally buoyant spheres is analysed for small Reynolds number and large Péclet number. For this particular problem, it is possible not only to calculate the mean velocity of the heavy particle, but also the variance of the velocity and the coefficient of hydrodynamic diffusivity. Pairwise, hydrodynamic interactions between the heavy sphere and the background sphere are considered exactly using volume integrals and a trajectory analysis. Explicit formulae are given for the two limiting cases when the radius of the heavy sphere is much greater and much less than that of the background spheres, and numerical results are given for moderate size ratios. The mean velocity is relatively insensitive to the ratio of the radius of the background spheres to that of the heavy sphere, unless this ratio is very large, whereas the hydrodynamic diffusivity increases rapidly as the radius ratio is increased. The predictions are in reasonable agreement with the results of falling-ball rheometry experiments.
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Ma, Hongru. "Theory and calculation of colloidal depletion interaction." International Journal of Modern Physics B 32, no. 18 (July 15, 2018): 1840005. http://dx.doi.org/10.1142/s0217979218400052.
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Colloidal dispersion is composed of particles with size ranging from 1 nm to [Formula: see text]m dispersed in solvents. There are the volume exclusion interaction and other interactions between colloidal particles, of which the former interaction causes the depletion effect. When a big sphere is immersed in the colloidal system of small spheres, there is a depletion layer around the big sphere where the center of small sphere cannot enter. The depletion layers of two big spheres overlap if they are close to each other, increasing the free volume accessed by small spheres and thereby enlarging the entropy of the system. As a result, an effective interaction between the two big spheres is resulted from the change of entropy as a function of their distance, which is referred to as the depletion interaction. This paper first introduces the concept and scenario of the depletion interaction in colloidal systems. Then we briefly introduce various numerical or simulations methods of the depletion interaction of hard sphere systems, such as the acceptance ratio method, Wang–Landau method, and the density functional theory method. Taking the Asakura–Oosawa model as an example, we introduce a useful approximation method, Derjaguin approximation as well as the derivation of some approximate formula for the depletion interaction of different hardcore colloidal systems, such as between a pair of spheres in mono-disperse small spheres, between a hard sphere and a hard wall in a liquid of small spheres, and between a pair of hard spheres in a liquid of thin rods and thin disks.
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Petri, Dennis P., and Frans Visscher. "Revisiting Sphere Sovereignty to Interpret Restrictions on Religious Freedom." Philosophia Reformata 80, no. 1 (May 26, 2015): 99–122. http://dx.doi.org/10.1163/23528230-08001007.
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In this article, the Kuyperian concept of sphere sovereignty will be revisited in order to describe the multidimensionality of religious freedom. This article will show that true religious freedom requires not only a sovereign church sphere – the respect of church autonomy –, but also the freedom for religious expression in all other spheres of society. The first section will try to show that restrictions on religious expression in any sphere of society are restrictions on religious freedom. The second and third sections will provide examples of two global dynamics which in very distinct ways go against sphere sovereignty and specifically restrict religious expression in different spheres of society: “Islamic extremism” and “secular intolerance”. The article will conclude with a reflection about the virtues of sphere sovereignty as a guarantee against tyranny, and therefore also as a safeguard of religious freedom.
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Chen, Zhuo, Zhou Zhou, and Bing Yan Jiang. "Effect of Wall Thickness of Hollow Sphere on the Stress Distribution of Random Hollow Sphere Syntactic Foam." Applied Mechanics and Materials 670-671 (October 2014): 630–33. http://dx.doi.org/10.4028/www.scientific.net/amm.670-671.630.
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This paper addresses elastic analysis based on 3D finite element model for hollow sphere structures. In finite element models, which were analyzed under pressure of 1MPa, volume fraction of hollow spheres is kept at 30%, and hollow spheres are randomly located in the matrix. Five types of hollow sphere are used to form the model. All the types of hollow spheres have 60μm particle sizes, but different wall thicknesses. A comparison in stress distribution between the hollow sphere and matrix is made, which shows that in composites containing thin-walled hollow particles the maximum stress is located in the inner surface of particle wall, whereas increasing the wall thickness of hollow spheres results in getting some part of matrix around hollow spheres involved in energy absorption. Moreover, the location of the maximum stress in matrix related closely to the spatial arrangement of the particles. The study provides an insight into the micro structural performance of syntactic foam under load.
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Sukhorukova, Yuliya Aleksandrovna. "Features of the functioning of deverbal nouns with the prefix 'пред-' (based on the Russian National Corpus)." Philology. Issues of Theory and Practice 17, no. 4 (April 18, 2024): 1185–91. http://dx.doi.org/10.30853/phil20240172.
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The aim of the study is to demonstrate the potential influence of the prefix 'пред-' on the realization of deverbal nouns with this prefix in texts from specific functional spheres presented in the Russian National Corpus. The paper analyzed deverbal nouns with the prefix 'пред-' and unprefixed deverbatives across 9 functional spheres of the Russian National Corpus (ecclesiastical-theological sphere, everyday life, literary sphere, business official sphere, journalism, educational-scientific sphere, industrial-technical sphere, advertising, electronic communication). The data obtained allowed the researcher to identify the significance of the prefix 'пред-' in the functioning of units with the prefix and differences in their realization compared to unprefixed deverbal nouns. The scientific novelty of the study lies in the first-ever analysis of deverbal nouns with the prefix 'пред-' across the functional spheres of the Russian National Corpus. The work describes the characteristics of deverbatives with 'пред-' in these functional spheres and identifies the potential influence of the prefix 'пред-' on the functioning of deverbal nouns with the prefix. The results of the study indicated that among deverbatives with the prefix 'пред-', the most frequent functional spheres are mainly the ecclesiastical-theological one, the industrial-technical one (compared to unprefixed deverbal nouns), and the educational-scientific one, leading to the conclusion about the influence of the prefix 'пред-' on the functioning of the analyzed deverbatives.
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Han, Jianye. "The three grand cultural spheres of the Holocene Eurasian Continent." Chinese Archaeology 24, no. 1 (December 1, 2024): 143–50. https://doi.org/10.1515/char-2024-0009.
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Abstract Based on the typology of ceramic wares and analysis of the spatial distribution, origin, and dispersal of other categories of archaeological remains, it can be determined that three grand cultural spheres existed on the Holocene Eurasian Continent prior to the rise of the Silk Road. These were the Early Eastern Cultural Sphere, centered around the Yellow River valley and the Yangtze River valley; the Early Western Cultural Sphere, centered around the Tigris-Euphrates River valley (Mesopotamia); the Early Northern Cultural Sphere, located to the north of the Eastern and Western Cultural Spheres. Due to cultural interactions, collisions, and exchanges, there were large intersection zones between the three grand cultural spheres.
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Sugár, István P. "Density of electric field energy around two surface-charged spheres surrounded by electrolyte I. The spheres are separated from each other." AIMS Biophysics 9, no. 2 (2022): 86–95. http://dx.doi.org/10.3934/biophy.2022008.
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<abstract> <p>Based on the generalized version of Newton's Shell Theorem the electric field energy density, <italic>u<sub>F</sub></italic> around two separated surface-charged spheres surrounded by electrolyte is calculated. According to the calculations when the surfaces of the charged spheres are farther from each other than four times of the Debye length the field energy density around one of the charged sphere is basically independent from the presence of the other sphere. In this case at low electrolyte ion concentration <italic>u<sub>F</sub></italic> = 0 within the spheres and outside the sphere <italic>u<sub>F</sub></italic> decreases with increasing distance from the surface of the sphere, while at high electrolyte ion concentration <italic>u<sub>F</sub></italic> fast decreases with increasing inner and outer distance from the surface of the sphere. When the charged sheres are close to each other their electric interaction affects the field energy density especially where the surfaces of the spheres are close to each other. Also to model electrophoresis analytical equations are derived for the interaction energy between and the density of electric field energy around a charged flat surface and a charged sphere surrounded by neutral electrolyte.</p> </abstract>
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Faeedfar, Ziba, and Yasin Lotfata. "Public Sphere as Democratic Sphere." Issues in Social Science 6, no. 2 (December 21, 2018): 90. http://dx.doi.org/10.5296/iss.v6i2.14082.
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Political public space is more conflicted and stressed. Process of black-balling other actors is dominant here. Other civilian public spaces mean mutual learning and opinion improvement. These two spaces try to affect each other. Civilian public spaces try to affect political public space with political discourses. The only way to determine the willpower of the society is participation. Planning is conducted through this participation which brings democracy concept with. Planning is the participation of the folk in the decision phase. It puts communicative rationality instead of instrumental rationality in decisions to be taken for the community. This newly existing planning concept is based on the principle of consensus creating. All these let the planning turn into a democracy project. Handling the planning in such a concept and bringing together new spatial representation form in transmitting information by regarding spatial changings must be concept of planning of today. This study conducted a brief review on constructing democratic public space.
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Srivastava, Deepak Kumar. "Slow Rotation of Concentric Spheres with Source at Their Centre in a Viscous Fluid." Journal of Applied Mathematics 2009 (2009): 1–13. http://dx.doi.org/10.1155/2009/740172.
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The problem of concentric pervious spheres carrying a fluid source at their centre and rotating slowly with different uniform angular velocities , about a diameter has been studied. The analysis reveals that only azimuthal component of velocity exists, and the couple, rate of dissipated energy is found analytically in the present situation. The expression of couple on inner sphere rotating slowly with uniform angular velocity , while outer sphere also rotates slowly with uniform angular velocity , is evaluated. The special cases, like (i) inner sphere is fixed (i.e., ), while outer sphere rotates with uniform angular velocity , (ii) outer sphere is fixed (i.e., ), while inner sphere rotates with uniform angular velocity , and (iii) inner sphere rotates with uniform angular velocity , while outer sphere rotates at infinity with angular velocity , have been deduced.
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Feng, J., and D. D. Joseph. "The motion of a solid sphere suspended by a Newtonian or viscoelastic jet." Journal of Fluid Mechanics 315 (May 25, 1996): 367–85. http://dx.doi.org/10.1017/s0022112096002467.
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This paper describes experimental observations of a solid sphere suspended by a vertical or inclined jet. A laminar Newtonian jet is able to suspend a sphere only through viscous entrainment at low Reynolds numbers (Re ~ 10). A turbulent Newtonian jet (Re ~ 104) attracts a sphere that is sufficiently large but rejects smaller ones. The Coanda effect is responsible for steady suspension of solid spheres even in highly slanted jets. Anomalous rotation, opposite to the direction of the local shear, occurs under certain conditions, and its physical mechanism cannot be explained based on available information. A viscoelastic laminar jet is narrower than a comparable Newtonian one and it can suspend spheres at Reynolds numbers in the hundreds, precisely the Re range in which a Newtonian jet fails to suspend a sphere. It is suggested that the contrast between laminar Newtonian and viscoelastic jets may be related to a reversal in the pressure distribution on the surface of the sphere caused by non-Newtonian normal stresses. Flow visualization provides insights into the flow field in the jet and around the solid sphere.
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Kravets, Taras. "SOCIO-GEOGRAPHICAL ESSENCE OF THE MILITARY SPHERE OF UKRAINE." GEOGRAPHY AND TOURISM, no. 57 (2020): 50–57. http://dx.doi.org/10.17721/2308-135x.2020.57.50-57.
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The purpose of the article is to analyze the existing approaches to understanding the terms military sphere, military-industrial complex, defense-industrial complex, security and defense sector, military sector, determining the positioning of the military sphere and its position relative to other natural-geographical areas, joints and overlaps, identification of its functions and problems that interfere with proper functioning. Development of directions and prospects for the development of the military sphere and the Armed Forces of Ukraine in general. Method. The research was conducted on the basis of the analysis of available literature sources on this topic and the application of a spherical approach to the analysis of the positioning of the military sphere and the definition of its components. The available domestic and foreign literary sources and the ratio of these concepts within this literature are studied. Results. Theoretical and methodological problems of comparing concepts related to the military sphere and their interchangeability and interconnectedness are studied. The scheme of correlation of concepts of military sphere, defense-industrial complex and military-industrial complex is offered. Based on the spherical approach, we propose a scheme of the military sphere, which we consider as a sphere formed within the geosphere at the junction of social and natural spheres, at the intersection of demographic, informational, spiritual, environmental, technical, economic, political and social spheres. Within each oblast forming the sphere, three main sectors with the greatest influence on the military sphere are singled out. Six main functions of the sphere are singled out and arranged in order of importance on the basis of the proposed scheme. Scientific novelty. The need for this study is due to the fact that despite the fact that since 2014 and to date, fighting has been going on in the east of our country, in many universities the discipline of military geography and related disciplines is being stolen, the term military sphere has not been proposed. clear positioning of the military sphere among other social spheres. To date, the functions performed by the military sphere and the factors contributing to the improvement and development of this sphere have not been determined, which is what led to the implementation of this study. Practical meaning. Based on modeling and analysis, the main areas that affect the military sphere as such and to what extent are identified, the areas of greatest influence and sectors of influence within the regions are identified. The functions of the military sphere and the main factors influencing its development and transformation are highlighted, as well as what measures need to be implemented to improve the situation. The results of the research are developed for planning by the state structures of the program of development of the military sphere and for teaching the discipline "Military Geography". The geographical features of the military sphere are singled out, to which the greatest attention should be paid when analyzing the transformation of the military sphere.
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Liu, Longfei, Zhangang Zhang, Hong Zhang, Hui Li, Zhifeng Lei, Junyang Luo, Chao Peng, Changhao Sun, and Yujuan He. "Characterization of Surface α-Particle Radiation, Internal Traceability and Simulation of Typical Tin Spheres." Applied Sciences 14, no. 10 (May 17, 2024): 4257. http://dx.doi.org/10.3390/app14104257.
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Surface α-particle emissivity testing and spectral characterization of two leaded tin spheres (Sn10%Pb90%, Sn63%Pb37%) and one lead-free tin sphere (Sn96.5%Ag3.0%Cu0.5%, SAC305) were carried out. The results show that Sn10%Pb90% Sn spheres have the highest α-particle emissivity; Sn63%Pb37% Sn spheres are the next highest, which is an order of magnitude lower than the α-particle emissivity of Sn10%Pb90% Sn spheres; and SAC305 Sn spheres have the lowest emissivity, which is reduced by about 55.6% compared to the emissivity of Sn63%Pb37% Sn spheres. All three types of tin spheres, after purification treatment, achieved the grade of ultra-low alpha particle emissivity (<0.002 α/(cm2·h)). The internal radionuclide traceability of the tin sphere, combined with the energy spectrum, reveals that the emission spectrum of the tin sphere exhibits an obvious “single peak” characteristic, with the peak energy in the interval of 5 MeV~5.5 MeV. Comparative analyses revealed that 210Po is the main nuclide that produces alpha particles, and 210Po originates from the decay of 210Pb. Further Monte Carlo simulations show that α-particles with energies greater than 4.1 MeV in the measured energy spectrum all come from the contribution of radionuclides within 5 μm of the surface layer of the tin sphere, which accounts for 60% of the total radioactivity. Combining the experimental and simulation results, it is found that the internal radionuclides of the tin sphere are characterized by more surface layer and less internal layer. The above results are of great significance for the establishment of α-particle mitigation methods for tin spheres.
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Yu, Wei, Hui Jian Li, Xi Liang, and Chang Jun He. "Studies on Mechanical Properties of Thin-Walled MHS Structure." Advanced Materials Research 189-193 (February 2011): 1321–24. http://dx.doi.org/10.4028/www.scientific.net/amr.189-193.1321.
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Metallic hollow sphere structure cellular material is a type of super-light cellular metallic material. Its basic cell is thin-walled metallic hollow sphere. A series of quasi-static uniaxial compression experiments of two spheres array, three spheres array and tetrahedral packing structure were conducted. It is found that one sphere produces deformation at the contact place of two spheres, and the deformation is larger than that at the contact place of plates. The three spheres array and tetrahedral packing structure have the same phenomenon. Then, the Young’s moduli of these three models had been studied, and it is found that the tetrahedral packing structure has a larger value than the others. The compressive deformation behaviors of two and three spheres with the spheres glued together were studied too. These research findings can be the basis of the design of MHS structure cellular material.