Spherical Polyhedron Research Articles

Se-incorporated polycaprolactone spherical polyhedron enhanced vitamin B2 loading and prolonged release for potential application in proliferative skin disorders

Development of novel drug vehicles for vitamin B2 (VitB2) delivery is very important for designing controllable release system to improve epidermal growth and bone metabolism. In this work, selenium (Se)-incorporated polycaprolactone (PCL) spherical polyhedrons are successfully synthesized via a single emulsion solvent evaporation method which is utilized to load VitB2 to fabricate cell-responsive Se-PCL@VitB2 delivery systems. Their physicochemical properties are characterized by DLS, SEM, XRD, FTIR, and TGA-DSC. The release kinetics of VitB2 or Se from the samples are investigated in PBS solution (pH = 2.0, 5.0, 7.4, 8.0 and 12.0). The cytocompatibilities are also evaluated with normal BMSC and epidermal HaCat cells. Results exhibit that Se-PCL@VitB2 particles presents spherical polyhedral morphology (approximately (3.25 ± 0.46) μm), negative surface charge (-(54.03 ± 2.94) mV), reduced crystallinity and good degradability. Stability experiments imply that both VitB2 and Se might be uniformly dispersed in PCL matrix. And the incorporation of Se facilely promotes the loading of VitB2. The encapsulation efficiency and loading capacity are (98.42 ± 1.06)% and (76.25 ± 1.27) for Se-PCL@VitB2 sample. Importantly, it exhibits more prolonged release of both VitB2 and Se in neutral PBS solution (pH = 7.4) than other pH conditions. Presumably, the electrostatic interaction between Se, VitB2 and PCL contribute to its release mode. Cell experiments show that Se-PCL@VitB2 presents strong cytotoxicity to HaCat cells mainly due to the cytotoxic effect of Se anions and PCL degradation products. However, it exhibits weak inhibitory effect on BMSC cells. These note that the synthesized Se-PCL@VitB2 particles can be promising drug vehicles for potential application in epidermal proliferative disorders.

Visualization of Escher‐like Kaleidoscopic Spherical Patterns of Regular Polyhedron Symmetry

AbstractIn this paper, we present a method for creating Escher‐like spherical patterns with regular polyhedron symmetries. Using the generators of the symmetry groups associated with regular polyhedra, we first provide fast algorithms to construct spherical tilings. Then, to obtain Escher‐like patterns, we specify texturing techniques to decorate the resulting tilings. Moreover, we present a strategy to create a novel dynamic effect of Escher‐like kaleidoscopes in which the motifs have a complete body. The method has the advantages of simple implementation, fast calculation, good graphics, and artistic effects, which can be used to create rich elegant spherical patterns.

Effect of praseodymium valence change on the structure, magnetic, and microwave absorbing properties of M-type strontium ferrite: the mechanism of influence of citric acid dosage and calcination temperature

SrFe12-xPrxO19(x = 0–0.5) powders were synthesized and the effects of praseodymium doping amount, citric acid dosage, and calcination temperature on its structure, magnetic properties, and microwave absorbing properties were studied. The results of X-ray diffraction, scanning electron microscopy, and transmission electron microscopy show that praseodymium doping leads to the lattice expansion and makes strontium ferrite easier to form spherical polyhedron in microscopic morphology. The Fe2O3 impurity phase disappears and FePr1-ySryO3-δ impurity phase appears with the increase of the calcination temperature. It was inferred from Raman spectra and X-ray photoelectron spectroscopy that some Pr3+ ions form Pr4+ ions and the latter may occupy iron or strontium sites, and the transition from the Fe3+ to Fe2+ may occur at 4f2 site. The vibrating sample magnetometer results show that the saturation magnetization decreases first and then increases; the coercivity increases and the anisotropy field decreases after doping praseodymium. Praseodymium-doped strontium ferrite has strong absorption in low frequency band (C-band) or medium frequency band (X-band), while the matching thickness corresponding to high frequency band (Ku-band) is small. The maximum reflection loss reaches −50.95 dB and the effective absorption bandwidth (RL < −10 dB) is 4.76 GHz. Increasing the calcination temperature or doping amount will reduce the matching thickness, while increasing the amount of citric acid will disperse the grains and reduce the dielectric loss. It can be concluded that praseodymium valence change leads to the increase of Fe2+ ions and oxygen defects and there is also interface polarization between M-phase and heterogeneous phase, which together increases the dielectric loss of the material. Meanwhile, praseodymium doping can significantly increase the magnetic loss caused by natural resonance. These show that praseodymium doping improves the impedance matching of the material, increases the attenuation constant, and significantly improves the wave absorption performance.

The planar tilt-detector array for wide view radiation pattern parallel measurement

Based on planar-positioned detector array with deflection angles, this paper presents a non or less rotation method for parallel obtaining large view-angle radiation patterns. The method theoretically relies on the cosine negative quadratic relationship, on which two layouts are proposed. The first rotation-free polar layout can provide results compatible with traditional goniometers for narrow-view sources. The experiments on 1D systems demonstrate the two have good consistency with the normalized square root errors ranging from 0.56% to 0.68%. Furthermore, a 73-channel parallel system is constructed for 3D wireframe radiation patterns. Particularly, the second Cartesian layout is proposed based on the spherical polyhedron segmentation, and a 144-channel less-rotation system is constructed for large view-angle patterns with uncertainty ranging from 0.40% to 0.43%. Therefore, the method can be employed to construct radiation pattern measurement systems with attributes of parallel, large view-angle, and rotation-free or less-rotation.

Nucleation and growth of Al3Sc precipitates during isothermal aging of Al-0.55 wt% Sc alloy

The nucleation and growth process of Al 3 Sc precipitates in Al-0.55 wt% Sc alloy during isothermal aging was studied by transmission electron microscopy (TEM) and high-resolution transmission electron microscopy (HRTEM). It is found at the early aging stage that the solute Sc atoms are enriched on the stacking fault in the matrix then rapidly converted to L1 2 -ordered Al 3 Sc precipitates without the formation of other transition phases. The matrix and precipitates form a sharp interface at the beginning of phase transition and maintain a completely coherent crystallographic orientation relationship. Due to the influence of the anisotropy of interface energy, the equilibrium shape of the precipitated phase is similar to the spherical polyhedron. In the coarsening stage of precipitates, the interface of α-Al/Al 3 Sc gradually changes from coherent to semi-coherent, resulting in the gradual loss of symmetry of the non-contrast line, and finally the stress field contrast on the surface of particles and interface dislocations gradually appear. • The solute Sc atoms are enriched on the SF in the matrix. • The precipitate sequence of Al-0.55wt.%Sc alloy at 523K is SSSS → Solute clusters → Al 3 Sc.

On the Bieri–Neumann–Strebel–Renz Σ1-invariant of even Artin groups

We calculate the Bieri-Neumann-Strebel-Renz invariant $\Sigma^1(G)$ for even Artin groups $G$ with underlying graph $\Gamma$ such that if there is a closed reduced path in $\Gamma$ with all labels bigger than 2 then the length of such path is always odd. We show that $\Sigma^1(G)^c$ is a rationally defined spherical polyhedron.

Newtonian Event-Chain Monte Carlo and Collision Prediction with Polyhedral Particles.

Polyhedral nanocrystals are building blocks for nanostructured materials that find applications in catalysis and plasmonics. Synthesis efforts and self-assembly experiments have been assisted by computer simulations that predict phase equilibria. Most current simulations employ Monte Carlo methods, which generate stochastic dynamics. Collective and correlated configuration updates are alternatives that promise higher computational efficiency and generate trajectories with realistic dynamics. One such alternative involves event-chain updates and has recently been proposed for spherical particles. In this contribution, we develop and apply event-chain Monte Carlo for hard convex polyhedra. Our simulation makes use of an improved computational geometry algorithm XenoSweep, which predicts sweep collision in a particularly simple way. We implement Newtonian event chains in the open-source general-purpose particle simulation toolkit HOOMD-blue for serial and parallel simulation. The speedup over state-of-the-art Monte Carlo is between a factor of 10 for nearly spherical polyhedra and a factor of 2 for highly aspherical polyhedra. Finally, we validate the Newtonian event-chain algorithm by applying it to a current research problem, the multistep nucleation of two classes of hard polyhedra.

Isotropic enhancement of the thermal conductivity of polymer composites by dispersion of equiaxed polyhedral boron nitride fillers

Recently, hexagonal boron nitride (h-BN) has attracted attention as a high-thermal-conductivity filler for insulating polymers used in electronic devices. However, since the crystal structure of h-BN is analogous to that of graphite, h-BN exhibits a platelet crystalline shape with the anisotropy of high thermal conductivity for the in-planar direction and an extremely low thermal conductivity for the trans-planar direction. Consequently, the composites dispersed by conventional h-BN platelets indicated considerably low thermal conductivity in the trans-planar direction owing to the orientation of h-BN platelets. In this study, the anisotropic thermal conductivity was improved by dispersion of equiaxed h-BN fillers. Equiaxed h-BN fillers with spherical polyhedron shape were successfully synthesized through liquid-phase crystal growth by heating an h-BN powder with a rare-earth oxide. The common low thermal conductivity observed for the trans-planar direction was improved in the epoxy composites including equiaxed h-BN fillers, which attained 21.4 Wm−1K−1 corresponding to a six-times-higher thermal conductivity than platelet h-BN filler.

EFFECTIVE STRUCTURE OF A WOODEN RESIDENTIAL BUILDING IN THE FORM OF A GEODESIC DOME WITH A UNIVERSAL CONNECTOR

Abstract. Since the middle of the twentieth century, a new architectural solution has been spherical shells broken down into elements by geodesic lines – circles with radii equal to the radius of the sphere. A geodesic dome is a dome made of a spherical polyhedron with an optimally distributed arrangement of vertices and edges tending to a perfect sphere. Using the technical capabilities of computer design, digital models of the layout and calculation of geodesic domes became available. It is possible not only to calculate multi-mesh network layouts with high accuracy, but also to automate the design. At the same time, it cannot be said that the optimal system has already been obtained and studied. The issues of optimal shaping, taking into account a simple universal connector and confirmation of theoretical results by field tests, remain not fully studied. Development of the design of a mesh wooden house in the form of a geo dome with optimal parameters of the geodetic network and nodal connections of the frame elements using a universal connector is the theme of this publication. The proposed form of division is a fullerene polyhedron describing a sphere and consisting of five and hexagonal faces. The dome polyhedron is built on the basis of the icosahedron. The number of partitions of vertices and edges that make up the split edge ‒ the frequency, is chosen equal to 3. The first class of partitioning by the "equal chords" method is adopted. The proposed universal connector for connecting parts of building structures at any angle and a method of mounting building structures using a universal connector. As a result of introduction of new technical decisions we receive essential simplification of a design, reduction of quantity of its components, at the same time increase of its manufacturability and providing an opportunity to connect details of building designs in an end face at any angle.

Polygon Based Topology Formation and Information Gathering in Satellite Based Wireless Sensor Network

The satellite network is one of the major source of information and these days small satellites are gaining lot of focus. The group of small satellites form a distributed network that work collaboratively to accomplish the mission task. These networks are very similar to the terrestrial wireless sensor network in terms of restricted resources and constrained capabilities. Sometimes, network of small satellites is also called as space based wireless sensor network (SBWSN). In any distributed network, topology formation and its control plays a significant role. This is true for SBWSN also. The topology in SBWSN decides the area of coverage (field of view), time of coverage, data gathered and data transmitted to ground station. The proposed topology is a distributed network of small satellites formed by trivalent, toroidal and spherical polyhedron graph forming a fullerene, which is called as polygon based network topology (PBNT). It comprises of both pentagonal (Fp) and hexagonal (Fh) faces with K regular graphs such that K ≥ 3 with genus equal to 1. It also satisfies Eulers formula with n vertices. The fullerene comprises of simple rings and each of this ring forms the cluster. Each cluster is further represented as a triangular grid, that is linearly convex or non-linear, with K-connected graph along with Hamiltonian extendible cycle. The nodes/satellites on the triangular grid represent sensing nodes (low capability nodes/satellites), while the vertices of the ring are sink nodes (higher capability nodes/satellites). In this work, the topology is formed by small satellites (pico or nano satellites). In the proposed topology formation, the network is considered as virtual network with logical neighbours forming the cluster. Each node in the cluster covers a particular swath for a particular time interval based on the mission payload and on the p3 tiling. In the simulation, we consider n small satellites being placed in low earth orbit (LEO), (where n ranges from 3 to 150). The performance enhancements are seen during simulation in the following parameters, (1) Coverage Area: The coverage area increases as multiple satellites have different field of view at different times. (2) Reduces Gaps:The proposed distributed network also minimises uncovered areas as multiple satellites cover the target location at different time stamp which is not possible by a single large satellite. (3) Increase in Data Throughput: Each satellite in the network transmits data, when it is at perigee. The data throughput of the network increases, as data is transmitted by multiple satellites. Therefore, the throughput is increased by n-fold. (4) Continuous Connectivity: The data captured by one satellite in the network is made available to other using multi-hop communication. Thus the proposed topology also increases the continuous connectivity between satellites and also with the ground station. (5) Increases lifetime and Network Reliability: The SBWSN accomplishes its mission task even when one/more satellites encounters functional failure. The satellites in the network can reconfigure themselves and continue the mission task. Thus SBWSN also reduces the risk of mission failure and ensures mission reliability. Due to reconfiguration the lifetime of the network is also increased. The proposed topology is used for small satellites (specially nano and pico satellites) network, which permit the single board satellite weighing less than 10 kg (Pico satellite less than 1 kg and nano satellites less than 10 kg). The advantage of these small satellites network over single large satellite is low cost and reduced development time, as it uses commercially of the shelf (COTS) components. In this paper, we propose network architecture formed by the spherically embedded clusters formed by polyhedron. The vertices of polyhedron have both pentagonal (Fp) and hexagonal (Fh) faces with K regular graphs such that K ≥ 3, with genus equal to 1. The vertices of these polyhedron form the sink nodes and the other nodes are sensing nodes. Here satellites and nodes are interchangeably used. Sensing nodes are used for data gathering (pico/nano), while sink nodes are higher capability nodes which perform computational extensive operations in the network (nano or macro satellites). The sensing and sink nodes transmit data to the ground station when they are at perigee. The main objective of the proposed work is, technology demonstration of low cost, distributed small satellites network for earth observations replacing single huge satellite.

SpherePHD: Applying CNNs on 360 ° Images With Non-Euclidean Spherical PolyHeDron Representation.

Omni-directional images are becoming more prevalent for understanding the scene of all directions around a camera, as they provide a much wider field-of-view (FoV) compared to conventional images. In this work, we present a novel approach to represent omni-directional images and suggest how to apply CNNs on the proposed image representation. The proposed image representation method utilizes a spherical polyhedron to reduce distortion introduced inevitably when sampling pixels on a non-Euclidean spherical surface around the camera center. To apply convolution operation on our representation of images, we stack the neighboring pixels on top of each pixel and multiply with trainable parameters. This approach enables us to apply the same CNN architectures used in conventional euclidean 2D images on our proposed method in a straightforward manner. Compared to the previous work, we additionally compare different designs of kernels that can be applied to our proposed method. We also show that our method outperforms in monocular depth estimation task compared to other state-of-the-art representation methods of omni-directional images. In addition, we propose a novel method to fit bounding ellipses of arbitrary orientation using object detection networks and apply it to an omni-directional real-world human detection dataset.

A novel method of determining the optimal polyhedral orientation for discrete global grid systems applicable to regional-scale areas of interest

ABSTRACT The polyhedral discrete global grid system (DGGS) is a multi-resolution discrete earth reference model supporting the fusion and processing of multi-source geospatial information. The orientation of the polyhedron relative to the earth is one of its key design choices, used when constructing the grid system, as the efficiency of indexing will decrease if local areas of interest extend over multiple faces of the spherical polyhedron. To date, most research has focused on global-scale applications while almost no rigorous mathematical models have been established for determining orientation parameters. In this paper, we propose a method for determining the optimal polyhedral orientation of DGGSs for areas of interest on a regional scale. The proposed method avoids splitting local or regional target areas across multiple polyhedral faces. At the same time, it effectively handles geospatial data at a global scale because of the inherent characteristics of DGGSs. Results show that the orientation determined by this method successfully guarantees that target areas are located at the center of a single polyhedral face. The orientation process determined by this novel method reduces distortions and is more adaptable to different geographical areas, scales, and base polyhedrons than those employed by existing procedures.

Effect of Manufacturing Process of Master Alloy Powders on Homogeneity of Sintered Ti-5Al-1Fe by Blended Elemental Powder Metallurgy

To narrow down the candidates of the alloying element powders for Ti-5Al-1Fe products manufactured with BE/PM, two master alloy powders, atomized spherical 5Al-1Fe and crushed-andground polyhedron 5Al-1Fe-4Ti ternary powders, were investigated with emphasizing on homogeneity of alloying elements, Al and Fe, in sintered Ti-5Al-1Fe. Intense Al segregation is recognized in the sintered specimen manufactured using 5Al-1Fe atomized powders, while strong segregation is not observed in the specimen manufactured using 5Al-1Fe-4Ti crushed-and-ground powders. Density of sintered specimen manufactured using 5Al-1Fe atomized powders is lower than that manufactured using 5Al-1Fe-4Ti crushed-and-ground powders. Al segregation and lower sintered density are probably caused by lower density of the powder substance, high flowability of spherical powders and phase constitutions some of which have low melting points. Those factors have to be taken into account to manufacture sintered titanium alloys with high homogeneity by BE/PM.

The task 3 of forming a network on the sphere from the circles of the same radius

one of the methods of formation of geometric networks of arches of the same radius using regular spherical polyhedra is Investigated. The conditions of the task of placing the specified network on the sphere are set. The criterion for evaluating the effectiveness of solving the problem is the minimum number of standard sizes of segments of the dome arches, the possibility of using technologies of enlarging assembly. The solution of one variant of the problem of placing a geometric network on a spherical cube and, accordingly, on a sphere is given. Placement on the sphere of arches of one radius, different from placement in the form of meridians, has an effective solution in the form of a network with minimal dimensions of arch segments and nodes of paired arches formed on the basis of circles of identical radii formed on the basis of regular spherical polyhedra. The problem is solved by constructing an independent framework of arches of the same radius on the basis of paired circles of the same radius in the spherical cube system.

Spherical Tiling with GeoGebra

The theory of spherical tilings is an interesting and fruitful field, attracting, among other researchers, mathematicians. It is a transverse topic crossing several mathematical areas such as geometry, algebra, topology and number theory, but it is also an object of interest for other scientific fields such as chemistry, physics, art and architecture. Here, we make use of GeoGebra to establish some results, describing a class of monohedral spherical tilings and inferring some conjectures. This will highlight how the use of this software has been crucial for the construction of new knowledge in mathematics with applications in different areas of engineering.

Enhanced microbial metabolism in one stage partial nitritation-anammox system treating low strength wastewater by novel composite carrier

One stage partial nitritation-anammox (PN-A) process has attracted more and more attention due to the low investment cost but the instability in treating low strength wastewater. In this study, for producing a novel composite carrier that could provide high ammonia microenvironment in low strength wastewater, the zeolites and floating materials were combined in the spherical shell and distributed evenly by the spherical polyhedron. And a moving bed biofilm reactor (MBBR) with the composite carriers and ordinary carriers without zeolites as control group was operated for nearly 120 days. The PN-A process were realized in 53 days, and the total nitrogen removal efficiency reached around 85% at influent ammonium concentration of 50 mg/L finally. Analysis of 16S rRNA gene sequencing revealed that the composite carriers showed significant promotion on the proliferation of ammonium oxidizing bacteria (AOB) and enrichment of anaerobic ammonium oxidizing bacteria (AnAOB), accounting for 19.14% and 41.65% on the surface, respectively. Moreover, the existence of relative higher abundance of ammonia on the composite carrier surface was validated by the metabolite biomarker of glutamate and especially spermidine. The metabolomics analysis and 16S rRNA function prediction showed that the protein synthesis pathway was obviously upregulated on the composite carriers surface compared with that on the ordinary carriers surface. The higher abundance of glutamate and putrescine indicated that the composite carrier could stimulate the metabolism and growth of bacteria. The present study provided a functional carrier to realize the transformation of activated sludge system into PN-A system treating low strength wastewater, which is significant to the application of the process in mainstream.

Classification of spherical tilings by congruent quadrangles over pseudo-double wheels (II)—the isohedral case

We classify all edge-to-edge spherical isohedral 4-gonal tilings such that the skeletons are pseudo-double wheels. For this, we characterize these spherical tilings by a quadratic equation for the cosine of an edge-length. By the classification, we see: there are indeed two non-congruent, edge-to-edge spherical isohedral 4-gonal tilings such that the skeletons are the same pseudo-double wheel and the cyclic list of the four inner angles of the tiles are the same. This contrasts with that every edge-to-edge spherical tiling by congruent 3-gons is determined by the skeleton and the inner angles of the skeleton. We show that for a particular spherical isohedral tiling over the pseudodouble wheel of twelve faces, the quadratic equation has a double solution and the copies of the tile also organize a spherical non-isohedral tiling over the same skeleton.

Cationic gold clusters with eight valence electrons: possible spherical aromatic systems with Sigma holes.

The energetically preferred structures of the gold clusters Au9+, Au113+, and Au124+ with eight skeletal electrons have been studied by density functional theory for comparison with the 8-electron Au102+ cluster shown previously to have a highly favored Td tetracapped octahedral structure. The low-energy structures for the Au9+ and Au113+ clusters are found to be similar relatively spherical polyhedra. Such systems can be considered to exhibit spherical aromaticity in accord with their filled 1S21P6 shells, their diatropic NICS(0) values ranging from -21.4 to -44.3 ppm, and their shielding cone surfaces. However, the preferred spherical polyhedra for Au9+ and Au113+ are not the same as the closo deltahedra found in the BnHn2- borane dianions. Instead they have smaller internal cavities formed by capping faces of smaller deltahedra or by formation of internal Au-Au bonds. The lowest energy Au124+ structures are not similar nearly spherical polyhedral structures. Instead they are derived from planar gold subclusters by adding more gold atoms to form tetrahedral Au4 bubbles. The planar origin of the low-energy Au124+ structures relates to the energetic preference for neutral Au<14 clusters for planar structures or nearly planar structures containing small polyhedral bubbles. The presence of σ-holes has been identified on the surfaces of the complete series of the Aun(n-8)+ (n = 9 to 12) clusters. The strength of their electrostatic interactions is predicted to increase upon increasing cluster size.

Network from the circles of the same radius for sustainable energy-efficient roof structures

In this research paper, we investigated one of the methods of formation of geometric networks of arches of the same radius using regular spherical polyhedra. The variants of cutting sustainable energy-efficient coatings of buildings in the form of spherical domes are proposed. The task conditions of placing the specified network on the sphere are set. The criterion for evaluating the effectiveness of solving the problem is the minimum number of standard sizes of segments of the dome arches, the possibility of using pre-assembly technologies. The solution of one variant of the problem as placing the network on a spherical icosahedron and, accordingly, on a sphere is given. The placement of arches of one radius on the sphere, different from the location in the form of meridians, has an effective solution in the form of a network with minimal dimensions of arch segments and with nodes of paired arches comprised on the basis of circles of the same radii formed on the ground of regular spherical polyhedra. The problem is solved by constructing and combining in a system of regular spherical polyhedral with independent frameworks of arches of the same radius on the basis of paired circles of equal radius.

A new class of monohedral pentagonal spherical tilings with GeoGebra

By a monohedral spherical tiling we mean a decomposition of the sphere by geodesic congruent polygons. Here, making use of GeoGebra, a well known free interactive mathematics software, we show how to generate new classes of monohedral non-convex triangular and new non-convex pentagonal spherical tilings, changing the side gluing rules of the regular spherical tetrahedral tiling, by means of a local action of particular subgroups of spherical isometries. In both cases each face has \pi as area measure. In relation to the new class of pentagonal tilings, we describe some of their properties and show the existence, in a special case, of an associated dihedral triangular spherical tiling, that is, a tiling composed by two sets of congruent triangles. These classes of spherical tilings have emerged as a result of an interative construction process, only possible by the use of newly produced GeoGebra tools and the dynamic interaction capabilities of this software.