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For a discrete poset X , McCord proved that the natural map | X | → X , from the order complex to the poset with the Up topology, is a weak homotopy equivalence. Much later, Živaljević defined the notion of order complex for a topological poset. For a large class of topological posets we prove the analog of McCord's theorem, namely that the natural map from the order complex to the topological poset with the Up topology is a weak homotopy equivalence. A familiar topological example is the Grassmann poset G n (R) of proper non-zero linear subspaces of R n + 1 partially ordered by inclusion. But our motivation in topological combinatorics is to apply the theorem to posets associated with tropical phased matroids over the tropical phase hyperfield, and in particular to elucidate the tropical version of the MacPhersonian Conjecture. This is explained in Sect. 2. [ABSTRACT FROM AUTHOR]

During maize production and transportation, maize kernels frequently interact with mechanical components. To accurately simulate the interaction process between maize and mechanical components, it is essential to establish a reliable maize kernel model and input precise contact parameters. This study established polyhedral discrete element models of different maize kernels and calibrated the contact parameters between maize kernels and steel plates using the inclined plane method. The coefficients of restitution, static friction, and dynamic friction between maize and steel sheets were measured to be 0.5, 0.545, and 0.213, respectively. Subsequently, the contact parameters between maize kernels were determined through steepest climb tests and central composite design response surface tests. Then, the above parameters were optimized using Design-Expert software. The coefficients of restitution, static friction, and dynamic friction between maize kernels were measured to be 0.318, 0.182, and 0.232, respectively. Finally, the optimized parameters were validated using the angle of repose experiment, which found that the relative error between the experiment and the simulation was only 1.24%. The results indicated that the obtained contact parameters were accurate and reliable. [ABSTRACT FROM AUTHOR]

Two polyhedral silver‐thiolate clusters, [S@Ag16(Tab)10(MeCN)8](PF6)14 (Ag16) and [Ag12(Tab)6(DMF)12](PF6)12 (Ag12), were synthesized by using electroneutral Tab species as protective ligands (Tab=4‐(trimethylammonio)benzenethiolate, DMF=N,N‐dimethylformamide, MeCN=acetonitrile). Ag16 has a decahedral shape composed of eight pentagon {Ag5} units and two square {Ag4} units. The structure of Ag12 is a cuboctahedron, a classical Archimedean structure composed of six triangular faces and eight square faces. The former configuration is discovered in silver‐thiolate cluster for the first time, possibly benefited from the more flexible coordination between the Tab ligand and Ag+ facilitated by the electropositive −N(CH3)3+ substituent group. Third‐order nonlinear optical studies show that both clusters in DMF exhibit reverse saturate absorption response under the irradiation of 532 nm laser. [ABSTRACT FROM AUTHOR]

It is known that the flip distance between two triangulations of a convex polygon is related to the smallest number of tetrahedra in the triangulation of some polyhedron. The latter was used to compute the diameter of the flip graph of convex polygons with a large number of vertices. However, it is yet unknown whether the flip distance and this smallest number of tetrahedra are always the same or even close. In this work, we find examples to show that the ratio between these two numbers can be arbitrarily close to 32 $\frac{3}{2}$. We also propose two conjectures in the end, one about this ratio, and the other may have some implications on when two triangulations can achieve maximal distance. [ABSTRACT FROM AUTHOR]

Innovation in comminution is expected to continue unabated to address the inefficiencies that are inherent in comminution circuits. The rotary offset crusher (ROC) is a new comminution device with a promising performance potential in terms of throughput due to the enhanced speed of transportation induced by the centrifugal force of the discs. However, the processes driving the comminution of particles trapped in the conical space between the two discs of the crusher are not fully understood. To gain a better insight into the comminution process in this device, discrete element modeling (DEM) simulations were conducted to study the breakage of a single particle for the crusher operated under two different dynamic conditions, i.e., (1) a stationary top disc and (2) both discs rotating at the same speed. For both scenarios, the speed of the discs was varied between 550 and 2350 rpm. Experimental testwork was also conducted with the laboratory prototype to generate the data that were used to calibrate the breakage parameters of the Ab × t10 breakage model. Simulations were performed using polyhedral UG2 ore particles that were generated with the in-built particle generator in the DEM simulator. The simulated ROC, which is operated with both discs rotating, outperformed the ROC with a stationary top disc in terms of the specific input energy and throughput. The crusher with a stationary top disc is characterized by high shear forces (suggesting a higher wear rate), specific input energies greater than 1 kWh/t, and low throughputs (<50 kg/h). The ROC operated with a stationary disc is not recommended for hard rock applications due to expected excessive wear of crushing surfaces and higher energy consumption. The freewheeling discs are recommended, but there is scope to optimize the crusher performance in terms of the power draw, size reduction, and throughput by manipulating the difference between the speeds of the discs. There is also scope to optimize the crusher performance when it is simulated with many particles. Once the full performance potential of the ROC is established, it will then be important to benchmark it against the existing crushers in the minerals industry as well as other industries where crushers are used. [ABSTRACT FROM AUTHOR]

In our previous paper, it is proved that for any positive flow-spine P of a closed, oriented 3-manifold M, there exists a unique contact structure supported by P up to isotopy. In particular, this defines a map from the set of isotopy classes of positive flow-spines of M to the set of isotopy classes of contact structures on M. In this paper, we show that this map is surjective. As a corollary, we show that any flow-spine can be deformed to a positive flow-spine by applying first and second regular moves successively. [ABSTRACT FROM AUTHOR]

Polyhedrons, spheroids and bolas (PSBs) have been found in lithic series spanning two million years, but their purpose remains largely unknown. In this study, we propose a functional analysis of PSBs from nine assemblages from France and North Africa, ranging from 1.78 to 0.169 Ma. By combining use-wear, ergonomic and metric analyses with sequential experiments, we explore the meaning and diversity of these objects. Our experiments revealed two key findings: 1) the manufacture process creates intense traces on removal scars used as striking platforms, and 2) the existence of a paradox between the complexity of the manufacture process and their efficiency equal to that of cobbles. This can question the purpose of manufacturing a PSB instead of using a pebble, and may suggest an opportunistic recycling of PSB “preforms” (e.g. pebble tools, cores) in some cases. Our results also suggest that PSBs encompass a wide diversity of pieces with a cubical to rounded final shape. These objects may have been primarily used in heavy-duty tasks, some being possibly involved in different types of percussive activities (active or passive). Interestingly, our analyses suggest that there are similarities between PSBs respectively in South-western Europe and North Africa. By studying PSBs, we can gain insights not only into hominin behaviours, but also into regional traditions and the diffusion of techno-cultural practices during the Palaeolithic. [ABSTRACT FROM AUTHOR]

Three hundred years ago, Prince Rupert of Rhine showed that a unit cube has the property that one copy of it can be passed through a suitable hole in another copy. Under this situation, we say that a unit cube has the Rupert property. In the past years, there are many research studying about the Rupert property of many solids in R 3 . For higher dimensions, the n-dimensional cube and the regular n-simplex were studied to have the Rupert property. In this work, we focus on the Rupert property of some polyhedrons in n dimensions. In particular, we show that some particular n-dimensional simplices, generalized n-dimensional octahedrons and some related solids in R n have the Rupert property using arbitrarily small rotations and translations. [ABSTRACT FROM AUTHOR]

During maize production and transportation, maize kernels frequently interact with mechanical components. To accurately simulate the interaction process between maize and mechanical components, it is essential to establish a reliable maize kernel model and input precise contact parameters. This study established polyhedral discrete element models of different maize kernels and calibrated the contact parameters between maize kernels and steel plates using the inclined plane method. The coefficients of restitution, static friction, and dynamic friction between maize and steel sheets were measured to be 0.5, 0.545, and 0.213, respectively. Subsequently, the contact parameters between maize kernels were determined through steepest climb tests and central composite design response surface tests. Then, the above parameters were optimized using Design-Expert software. The coefficients of restitution, static friction, and dynamic friction between maize kernels were measured to be 0.318, 0.182, and 0.232, respectively. Finally, the optimized parameters were validated using the angle of repose experiment, which found that the relative error between the experiment and the simulation was only 1.24%. The results indicated that the obtained contact parameters were accurate and reliable.

We prove a comparison theorem for certain types of polyhedra in a 3-manifold with its scalar curvature bounded below by -6. The result confirms in some cases the Gromov dihedral rigidity conjecture in hyperbolic 3-space. [ABSTRACT FROM AUTHOR]

The article intends to present, in a primarily descriptive way, the fundamental features of the rich and varied itinerary - although bumpy and not always linear - of the reception of the conciliar decree on ecumenism Unitatis redintegratio, in the various articulations of catholicity. The post-conciliar time is divided into four stages: the first post-Council period and the expectation of an ecumenical spring; John Paul II and the season of popular ecumenism; ecumenism in the clash of civilizations storm; Pope Francis and the ecumenism of the polyhedron and of walking together. What is implied in this article is that, more than one hundred years after the start of the ecumenical movement, for today's Christians, who are immersed in the culture of post-modernity, dialogue between the churches should not be one option among many, to be pursued or not depending on the seasons, but the common form of being Christian today. [ABSTRACT FROM AUTHOR]

A closed quasigeodesic on a convex polyhedron is a closed curve that is locally straight outside of the vertices, where it forms an angle at most π on both sides. While the existence of a simple closed quasigeodesic on a convex polyhedron has been proved by Pogorelov in 1949, finding a polynomial-time algorithm to compute such a simple closed quasigeodesic has been repeatedly posed as an open problem. Our first contribution is to propose an extended definition of quasigeodesics in the intrinsic setting of (not necessarily convex) polyhedral spheres, and to prove the existence of a weakly simple closed quasigeodesic in such a setting. Our proof does not proceed via an approximation by smooth surfaces, but relies on an adaptation of the disk flow of Hass and Scott to the context of polyhedral surfaces. Our second result is to leverage this existence theorem to provide a finite algorithm to compute a weakly simple closed quasigeodesic on a polyhedral sphere. On a convex polyhedron, our algorithm computes a simple closed quasigeodesic, solving an open problem of Demaine, Hersterberg, and Ku. [ABSTRACT FROM AUTHOR]

We show that the multistage stochastic linear problem (MSLP) with an arbitrary cost distribution is equivalent to an MSLP on a finite scenario tree. We establish this exact quantization result by analyzing the polyhedral structure of MSLPs. In particular, we show that the expected cost-to-go functions are polyhedral and affine on the cells of a chamber complex, which is independent of the cost distribution. This leads to new complexity results, showing that MSLP becomes polynomial when certain parameters are fixed. [ABSTRACT FROM AUTHOR]

Innovation in comminution is expected to continue unabated to address the inefficiencies that are inherent in comminution circuits. The rotary offset crusher (ROC) is a new comminution device with a promising performance potential in terms of throughput due to the enhanced speed of transportation induced by the centrifugal force of the discs. However, the processes driving the comminution of particles trapped in the conical space between the two discs of the crusher are not fully understood. To gain a better insight into the comminution process in this device, discrete element modeling (DEM) simulations were conducted to study the breakage of a single particle for the crusher operated under two different dynamic conditions, i.e., (1) a stationary top disc and (2) both discs rotating at the same speed. For both scenarios, the speed of the discs was varied between 550 and 2350 rpm. Experimental testwork was also conducted with the laboratory prototype to generate the data that were used to calibrate the breakage parameters of the Ab × t10 breakage model. Simulations were performed using polyhedral UG2 ore particles that were generated with the in-built particle generator in the DEM simulator. The simulated ROC, which is operated with both discs rotating, outperformed the ROC with a stationary top disc in terms of the specific input energy and throughput. The crusher with a stationary top disc is characterized by high shear forces (suggesting a higher wear rate), specific input energies greater than 1 kWh/t, and low throughputs (

Growth factors play a critical role in wound healing, and finding a suitable biosustained-release system has always been a research hotspot. Bombyx mori cypovirus (BmCPV) is an insect virus, which produces polyhedra that encapsulate progeny virions. In this study, we found that the viral structural protein VP7 encoded by the BmCPV genomic dsRNAs S7 segment can interact with polyhedrin (Polh) encoded by the BmCPV genomic dsRNAs S10 segment. We also confirmed that the amino acid sequence at position 331-360 (VP7-tag) of VP7 is needed to interact with Polh. We found that VP7-tag can be used as an immobilization signal to direct the incorporation of foreign proteins into polyhedra. Furthermore, we constructed polyhedra (bFGF-polyhedra) containing basic fibroblast growth factor (bFGF) using a baculovirus expression system co-expressing Polh and bFGF-VP7 (fusion of VP7-tag to C-terminus of bFGF). We found that bFGF-VP7 embedded into polyhedra was difficult to degrade in the natural environment, and bFGF-VP7 was continuously released from the polyhedra, enhancing cell proliferation and migration. The animal model was used to assess the effect of bFGF-polyhedra spray on the healing of full-thickness wounds. bFGF-polyhedra promoted the expression of TGF-β1, α-SMA, and PCNA, inhibited the expression of proinflammatory factors NF-κB and COX-2, promoted the proliferation and differentiation of fibroblasts, enhanced collagen production and epidermal regeneration, and improved wound healing. These results indicated that bFGF-polyhedra has a promising potential for accelerating wound healing., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2024. Published by Elsevier B.V.)

Transformation from tetrahedral- to octahedral-network as OPF increases from 0.48 to 0.65. [Display omitted] • The correlation between structural characteristics and dynamics in relation to. • OPF. The competition between the increase of mobility due to structural. • transition and the decrease of mobility due to increase of packing fraction. • The structural phase transition happens at OPF of around 0.57–0.58. • The Diffusion coefficient can be calculated via concentration of GeOx polyhedrons and packing fraction (or free volume). Correlation between structure and dynamics of GeO 2 system under compression is investigated by molecular dynamics and Monte-Carlo methods. Results show that structural phase transition occurs at the range of oxygen packing factor from 0.55 to 0.60. Self-diffusion coefficient of Ge and O exhibits anomalous and depends on percentage of GeO x polyhedrons (x = 4,5,6) and packing factor/ free volume of model. The self-diffusion coefficient can be determined via percentage of GeO x units and free volume fraction. The data mining technique is applied to clarify the polyamorphism, structure and dynamics heterogeneities. The cause of anomalous diffusion has been elucidated. [ABSTRACT FROM AUTHOR]

Two polyhedral silver-thiolate clusters, [S@Ag 16 (Tab) 10 (MeCN) 8 ](PF 6 ) 14 (Ag 16 ) and [Ag 12 (Tab) 6 (DMF) 12 ](PF 6 ) 12 (Ag 12 ), were synthesized by using electroneutral Tab species as protective ligands (Tab=4-(trimethylammonio)benzenethiolate, DMF=N,N-dimethylformamide, MeCN=acetonitrile). Ag 16 has a decahedral shape composed of eight pentagon {Ag 5 } units and two square {Ag 4 } units. The structure of Ag 12 is a cuboctahedron, a classical Archimedean structure composed of six triangular faces and eight square faces. The former configuration is discovered in silver-thiolate cluster for the first time, possibly benefited from the more flexible coordination between the Tab ligand and Ag + facilitated by the electropositive -N(CH 3 ) 3 + substituent group. Third-order nonlinear optical studies show that both clusters in DMF exhibit reverse saturate absorption response under the irradiation of 532 nm laser., (© 2024 Wiley-VCH GmbH.)

Considering the spatial arrangement characteristics of bonded irregular particle systems, this paper first constructs irregular dilated polyhedron elements based on the Voronoi cutting algorithm and Minkowski Sum theory. Subsequently, by extending the traditional sphere-based BPM (Bonded Particle Model) to irregular particle elements, a novel dilated polyhedron bonding-breaking model considering different fracture modes is developed under arbitrary contact modes. A collision example between two bonded square particles and a rigid plate is adopted to verify the stability of the model. Later, the difference between the tensile-shear fracture mode and the mixed fracture mode with damage process for contact bond is compared by the discrete element simulations of the tension-fracture behavior between two bonded square particles and the uniaxial compression simulation of frozen ballast aggregate. Finally, the influence of section size on the lateral resistance of the ballast bed structure at low temperatures is discussed using the dilated polyhedron BPM. The results showed that the developed dilated polyhedron BPM considering different fracture modes can realize mechanical behaviours between bonded irregular particles. Compared with the tensile-shear fracture mode, the mixed fracture mode not only considers the combined effect of normal and tangential stress on the bond but also realizes the damage deformation and stiffness attenuation of the bond, which can achieve the "delayed" fracture effect. Meanwhile, the model also shows good reliability in analyzing large-scale engineering problems, such as the mechanical performance of low-temperature ballast beds. The research effectively develops the bonding and breaking model of irregular elements and provides a new perspective for the contact-bond-fracture behavior simulation of irregular granular materials. [Display omitted] • The bonded particle model for dilated polyhedron is developed and verified. • The differences between the two fracture modes are compared. • The lateral resistance performance of the low-temperature ballast bed is analyzed. [ABSTRACT FROM AUTHOR]

The electrochemical conversion of oxygen holds great promise in the development of sustainable energy for various applications, such as water electrolysis, regenerative fuel cells, and rechargeable metal-air batteries. Oxygen electrocatalysts are needed that are both highly efficient and affordable, since they can serve as alternatives to costly precious-metal-based catalysts. This aspect is particularly significant for their practical implementation on a large scale in the future. Herein, highly porous polyhedron-entrapped metal-organic framework (MOF)-assisted CoTe 2 /MnTe 2 heterostructure one-dimensional nanorods were initially synthesized using a simple hydrothermal strategy and then transformed into ZIF-67 followed by tellurization which was used as a bifunctional electrocatalyst for both the oxygen evolution reaction (OER) and oxygen reduction reaction (ORR). The designed MOF CoTe 2 /MnTe 2 nanorod electrocatalyst exhibited superior activity for both OER (η = 220 mV@ 10 mA cm -2 ) and ORR ( E 1/2 = 0.81 V vs RHE) and outstanding stability. The exceptional achievement could be primarily credited to the porous structure, interconnected designs, and deliberately created deficiencies that enhanced the electrocatalytic activity for the OER/ORR. This improvement was predominantly due to the enhanced electrochemical surface area and charge transfer inherent in the materials. Therefore, this simple and cost-effective method can be used to produce highly active bifunctional oxygen electrocatalysts.