A recent effort used two rational maps on the Riemann sphere to produce polyhedral structures with properties exemplified by a soccer ball. A key feature of these maps is their respect for the rotational symmetries of the icosahedron. The present art...
Enhancing the limited utilization and overall yield of Pt-based catalysts is essential for advancing proton exchange membrane fuel cell technology. Herein, we report a facile one-pot method that utilizes TEG as both a solvent and a reductant to effic...
A differential game of m,
The transport process is an important part of the research of fluid dynamics, especially when it comes to tracer advection in the atmosphere or ocean dynamics. In this paper, a series of high-order semi-Lagrangian methods for the transport process on...
Thermal stability of core-shell structured nanoparticles is of vital importance to their practical applications at elevated temperature. Understanding the evolution of chemical distribution and the crystal structure of core-shell nanostructures with...
An accurate and cost-effective micro sun sensor based on the extraction of the sun vector using a phenomenon called the “black sun” is presented. Unlike conventional image-based sun sensors where there is difficulty in accurately detectin...
Deep neural networks often suffer from the degradation of fine-grained features during feature transmission. To mitigate this issue, we propose an innovative CNN architecture, Football Net, which is designed to enhance feature propagation. By introdu...
Phage display technology involves the surface genetic engineering of phages to expose desirable proteins or peptides whose gene sequences are packaged within phage genomes, thereby rendering direct linkage between genotype with phenotype feasible. Th...
This work reports on the preparation and gas transport performance of mixed matrix membranes (MMMs) based on the polymer of intrinsic microporosity (PIM-1) and potassium dodecahydrododecaborate (K2B12H12) as inorganic particles (IPs). The effect of I...
Based on the analysis of the problems in the generation algorithm of discrete grid systems domestically and abroad, a new universal algorithm for the unit duplication of a polyhedral discrete grid is proposed, and its core is “simple unit repli...
In this article, we have an explicit description of the binary isosahedral group as a 600-cell. We introduce a method to construct binary polyhedral groups as a subset of quaternions
On a descriptive level, this paper presents a number of logical fragments which require the Boolean algebra
We first briefly summarize several well-known properties of regular tessellations of the three two-dimensional maximally symmetric manifolds,
We employ molecular dynamics simulations to investigate the self-assembly of amphiphilic Janus particles in a slit-pore consisting of two plane-parallel, soft walls. The Janus particles are modeled as soft spheres with an embedded unit vector pointin...
This paper considers the optimal sensor configuration for inertial navigation systems which have redundant inertial sensors such as gyroscopes and accelerometers. We suggest a method to determine the optimal sensor configuration which considers both...
We present a novel analytical method as an efficient approach to design a geodesic-faceted array (GFA) for achieving a beam performance equivalent to that of a typical spherical array (SA). GFA is a triangle-based quasi-spherical configuration, which...
Vertices and symmetries of regular and irregular chiral polyhedra are represented by quaternions with the use of Coxeter graphs. A new technique is introduced to construct the chiral Archimedean solids, the snub cube and snub dodecahedron together wi...
Although pressured metallic glass (MG) has been reported in the literature; there are few studies focusing on pressure effects on the structure; dynamics and its plastic deformation. In this paper; we report on and characterize; via molecular dynamic...
Living organisms are constructed from proteins that assemble into biomolecular complexes, each with a unique shape and function. Our knowledge about the structure–activity relationship of these complexes is still limited, mainly because of thei...
It is estimated that over 60% of known tailed phages are siphophages, which are characterized by a long, flexible, and non-contractile tail. Nevertheless, entire high-resolution structures of siphophages remain scarce. Using cryo-EM, we resolved the...
Chalcogen atoms are a class of substituents capable of generating inner and outer derivatives of boron clusters. It is well known that chalcogenated boron clusters can form strong σ-hole interactions when a chalcogen atom is a part of an icosah...
It is known that the volume of a convex polyhedron can be increased by suitable isometric deformation of its surface resulting in a non-convex shape. Deformation patterns and the associated enclosed volumes of the Platonic polyhedra were theoreticall...
The ground state structures of copper clusters with different sizes along with their aggregation have been systematic investigated using Amsterdam Density Functional (ADF) and Atomistix ToolKit (ATK) programs. On the basis of geometry optimization, s...
Molecular dynamics simulations are performed to investigate the changes of packing structures, and thermodynamic quantities including internal energy, entropy, and free energy are used to determine temperature regime and transition time of atomic pac...
In this work, composite materials were obtained by spark plasma sintering of an Al12Mg17-B-Si powder mixture. The structure, phase composition, and mechanical properties of the obtained composites were studied. It was found that various compounds bas...
The Caspar–Klug (CK) classification of viruses is discussed by parallel examination of geometry of icosahedral geodesic domes, fullerenes, and viruses. The underlying symmetry of all structures is explained and thoroughly visually represented....
In this paper, we explore the catalytic CO2 reduction process on 13-atom bimetallic nanoclusters with icosahedron geometry. As copper and nickel atoms may be positioned in different locations and either separated into groups or uniformly distributed,...
In Chuanming Zong’s program to attack Hadwiger’s covering conjecture, which is a longstanding open problem from Convex and Discrete Geometry, it is essential to estimate covering functionals of convex bodies effectively. Recently, He et a...
A bilaterally symmetrical convex dodecahedron consisting of twelve quadrilateral faces is derived from the icosahedron via a process akin to Fuller’s Jitterbug Transformation. The unusual zygomorphic dodecahedron so obtained is shown to harbor a bila...
GP4, a new Ralstonia solanacearum phage, is a short-tailed phage. Few structures of Ralstonia solanacearum phages have been resolved to near-atomic resolution until now. Here, we present a 3.7 Å resolution structure of the GP4 head by cryo-elec...
With the continuous development of general aviation, the contradiction between the air demand of general aviation low-altitude airspace and civil aviation routes is sharp. The difficulty of airspace planning is complex and changeable, and the existin...
The geometries and energetics of the n-vertex polyhedral dicobaltadithiaboranes and dicobaltadiselenaboranes Cp2Co2E2Bn−4Hn−4 (E = S, Se; n = 8 to 12) have been investigated via the density functional theory. Most of the lowest-energy str...
A topological interlocking assembly (TIA) is an assembly of blocks together with a non-empty subset of blocks called the frame such that every non-empty set of blocks is kinematically constrained and can therefore not be removed from the assembly wit...
The aim of this study was to fabricate mini-tablets of polyhedrons containing theophylline using a fused deposition modeling (FDM) 3D printer, and to evaluate the correlation between release kinetics models and their geometric shapes. The filaments c...
We develop the combinatorics of edge symmetry and edge colorings under the action of the edge group for icosahedral giant fullerenes from C80 to C240. We use computational symmetry techniques that employ Sheehan’s modification of Pόlya’s...
The Goldberg construction of symmetric cages involves pasting a patch cut out of a regular tiling onto the faces of a Platonic host polyhedron, resulting in a cage with the same symmetry as the host. For example, cutting equilateral triangular patche...
Analytical paradigms have limited conventional form-finding methods of tensegrities; therefore, an innovative approach is urgently needed. This paper proposes a new form-finding method based on state-of-the-art deep learning techniques. One of the st...
A robot trajectory teaching system with a vision-based positioning pen, which we called Solpen, is developed to generate pose paths of six degrees of freedom (6-DoF) for vision-guided robotics applications such as welding, cutting, painting, or polis...
Discrete global grid systems (DGGSs) are an emerging multiresolution 3D model used to integrate and analyze big earth data. The characteristic of multiresolution is usually realized by hierarchically subdividing cells on the sphere using certain refi...
The packing and assembly of Platonic solids have fascinated mathematicians for ages. Recently, this fundamental geometrical problem has also attracted the attention of physicists, chemists, and engineers. This growing interest is due to the rapid adv...
This study introduces an innovative integration of Laban Movement Analysis (LMA) with biomechanical principles to examine the golf swing dynamics from an ecological perspective. Traditionally, LMA focuses on the qualitative aspects of movement, often...
Two knots; just two rudimentary knots, the unknot and the trefoil. That’s all we need to build a model of the elementary particles of physics, one with fermions and bosons, hadrons and leptons, interactions weak and strong and the attributes of spin,...
The study of the electrochemical catalyst conversion of renewable electricity and carbon oxides into chemical fuels attracts a great deal of attention by different researchers. The main role of this process is in mitigating the worldwide energy crisi...
Metal nanoparticles (NPs) are ubiquitous in many fields, from nanotechnology to heterogeneous catalysis, with properties differing from those of single-crystal surfaces and bulks. A key aspect is the size-dependent evolution of NP properties toward t...
Japanese encephalitis virus (JEV) is an enveloped icosahedral capsid virus with a prime neutralizing epitope present in E protein domain III (EDIII). E dimers are rearranged into a five-fold symmetry of icosahedrons. Cholera toxin B (CTB) and heat-la...
The icosahedron and the dodecahedron have the same graph structures as their algebraic conjugates, the great dodecahedron and the great stellated dodecahedron. All four polyhedra are equilateral and have planar faces—thus “EP”&mdash...
The amount of information collected about the Earth has become extremely large. With this information comes the demand for integration, processing, visualization and distribution of this data so that it can be leveraged to solve real-world problems....
The whimsical Las Vegas/Monte Carlo cubic dice are generalized to construct the combinatorial problem of enumerating all n-dimensional hypercube dice and dice of other shapes that exhibit cubic, icosahedral, and higher symmetries. By utilizing powerf...
Over the past few decades, plenty of visualization software for the structural analysis of disordered/complex systems has been developed, but the uniqueness and correctness of structural quantification for such systems are still challenging. This pap...
Among C60’s diverse functionalities, its potential application in CO2 sequestration has gained increasing interest. However, the processes involved are sensitive to the molecule’s electronic structure, aspects of which remain debated and...
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