High-efficiency sodium storage of Co_(0.85)Se/WSe_(2) encapsulated in N-doped carbon polyhedron via vacancy and heterojunction engineering

With the advantage of fast charge transfer,heterojunction engineering is identified as a viable method to reinforce the anodes'sodium storage performance.Also,vacancies can effectively strengthen the Na+adsorption ability and provide extra active sites for Na+adsorption.However,their synchronous engineering is rarely reported.Herein,a hybrid of Co_(0.85)Se/WSe_(2) heterostructure with Se vacancies and N-doped carbon polyhedron(CoWSe/NCP)has been fabricated for the first time via a hydrothermal and subsequent selenization strategy.Spherical aberration-corrected transmission electron microscopy confirms the phase interface of the Co_(0.85)Se/WSe_(2) heterostructure and the existence of Se vacancies.Density functional theory simulations reveal the accelerated charge transfer and enhanced Na+adsorption ability,which are contributed by the Co_(0.85)Se/WSe_(2) heterostructure and Se vacancies,respectively.As expected,the CoWSe/NCP anode in sodium-ion battery achieves outstanding rate capability(339.6 mAh g^(−1) at 20 A g^(−1)),outperforming almost all Co/W-based selenides.

Unique NiFe–NiCoO2 hollow polyhedron as bifunctional electrocatalysts for water splitting

It is of significance to design of stable and cost-effective electrocatalyst for water splitting with high efficiency in an alkaline medium.The major obstacles for practical application of water splitting devices are lack of high-efficiency and low-cost electrocatalysts with low overpotential for both HER and OER.In this paper,we report a NiFe alloy decorated NiCoO2 hollow polyhedron(denoted as Ni Fe–Ni Co O2)by using[NiFe(CN)6]- intercalated NiCo–LDH as precursor.As evidenced by the electrochemical active surface area,the resultant Ni Fe–Ni Co O2 composite shows unique hollow nanostructure,which can not only provide abundant mass transport channels,but also increase the contact area of the NiFe–Ni Co O2 material with the electrolyte.The overpotential(η)demand is 286 mV for OER and 102 mV for HER at the current density of 10 mA/cm2 in an alkaline medium of 1 M KOH for the NiFe/NiCoO2 composite.This work provides a new pathway for preparation of the highly efficient bifunctional electrocatalysts for water splitting.

Facile synthesis of the Mn_(3)O_(4)polyhedron grown on N-doped honeycomb carbon as high-performance negative material for lithium-ion batteries

Because of their large volume variation and inferior electrical conductivity,Mn_(3)O_(4)-based oxide anode materials have short cyclic lives and poor rate capability,which obstructs their development.In this study,we successfully prepared a Mn_(3)O_(4)/N-doped honeycomb carbon composite using a smart and facile synthetic method.The Mn_(3)O_(4)nanopolyhedra are grown on N-doped honeycomb carbon,which evidently mitigates the volume change in the charging and discharging processes but also improves the electrochemical reaction kinetics.More importantly,the Mn-O-C bond in the Mn_(3)O_(4)/N-doped honeycomb carbon composite benefits electrochemical reversibility.These features of the Mn_(3)O_(4)/N-doped honeycomb carbon(NHC)composite are responsible for its superior electrochemical performance.When used for Li-ion batteries,the Mn_(3)O_(4)/N-doped honeycomb carbon anode exhibits a high reversible capacity of 598 mAh·g^(−1)after 350 cycles at 1 A·g^(−1).Even at 2 A·g^(−1),the Mn_(3)O_(4)/NHC anode still delivers a high capacity of 472 mAh·g^(−1).This work provides a new prospect for synthesizing and developing manganese-based oxide materials for energy storage.

Ratio of In-Sphere Volume to Polyhedron Volume of the Great Pyramid Compared to Selected Convex Polyhedral Solids

The architecture of the Great Pyramid at Giza is based on fascinating golden mean geometry. Recently the ratio of the in-sphere volume to the pyramid volume was calculated. One yields as result RV = π ⋅ φ5, where is the golden mean. It is important that the number φ5 is a fundamental constant of nature describing phase transition from microscopic to cosmic scale. In this contribution the relatively small volume ratio of the Great Pyramid was compared to that of selected convex polyhedral solids such as the Platonic solids respectively the face-rich truncated icosahedron (bucky ball) as one of Archimedes’ solids leading to effective filling of the polyhedron by its in-sphere and therefore the highest volume ratio of the selected examples. The smallest ratio was found for the Great Pyramid. A regression analysis delivers the highly reliable volume ratio relation , where nF represents the number of polyhedron faces and b approximates the silver mean. For less-symmetrical solids with a unique axis (tetragonal pyramids) the in-sphere can be replaced by a biaxial ellipsoid of maximum volume to adjust the RV relation more reliably.

Optimal fuzzy PID controller with adjustable factors based on flexible polyhedron search algorithm

A new kind of optimal fuzzy PID controller is proposed, which contains two parts. One is an on line fuzzy inference system, and the other is a conventional PID controller. In the fuzzy inference system, three adjustable factors x p, x i , and x d are introduced. Their functions are to further modify and optimize the result of the fuzzy inference so as to make the controller have the optimal control effect on a given object. The optimal values of these adjustable factors are determined based on the ITAE criterion and the Nelder and Mead′s flexible polyhedron search algorithm. This optimal fuzzy PID controller has been used to control the executive motor of the intelligent artificial leg designed by the authors. The result of computer simulation indicates that this controller is very effective and can be widely used to control different kinds of objects and processes.

Improved non-uniform subdivision scheme with modified Eigen-polyhedron

In this study,a systematic refinement method was developed for non-uniform Catmull-Clark subdivision surfaces to improve the quality of the surface at extraordinary points(EPs).The developed method modifies the eigenpolyhedron by designing the angles between two adjacent edges that contain an EP.Refinement rules are then formulated with the help of the modified eigenpolyhedron.Numerical experiments show that the method significantly improves the performance of the subdivision surface for non-uniform parameterization.

Fast,Exact and Robust Set Operations on Polyhedrons Using Localized Constructive Solid Geometry Trees

Regularized Boolean operations have been widely used in 3D modeling systems. However, evaluating Boolean operations may be quite numerically unstable and time consuming, especially for iterated set operations. A novel and unified technique is proposed in this paper for computing single and iterated set operations efficiently, robustly and exactly. An adaptive octree is combined with a nested constructive solid geometry （CSG） tree by this technique. The intersection handling is restricted to the cells in the octree where intersection actually occurs. Within those cells, a CSG tree template is instanced by the surfaces and the tree is converted to planebased binary space partitioning （BSP） for set evaluation; Moreover, the surface classification is restricted to the ceils in the octree where the surfaces only come from a model and are within the bounding-boxes of other polyhedrons. These two ways bring about the efficiency and scalability of the operations, in terms of runtime and memory. As all surfaces in such a cell have the same classification relation, they are classified as a whole. Robustness and exactness are achieved by integrating plane-based geometry representation with adaptive geometry predicate technique in intersection handling, and by applying divide-and-conquer arithmetic on surface classification. Experimental results demonstrate that the proposed approach can guarantee the robustness of Boolean computations and runs faster than other existing approaches.

Ferromagnetic Calculation of Terbium Dysprosium and Holmium with Polyhedron Electron Shell

Based on the regular polyhedron model of multi-electronic atom combined with the Bohr hypothesis, the following supposition is put forward: the electron momentum multiplied by the inscribed sphere radius of edges of each regular polyhedron is equal to the Planck constant. The relationship between saturation magnetization rates and Planck constants is determined, and the ferromagnetism of atoms is obtained from regular dodecahedron and regular hexahedron. Then, terbium, dysprosium, and holmium saturation magnetization rate are obtained from electronic regular polyhedron configuration. Derivation of matter wave formula is from thermodynamics, avoiding over speed of light.

The Atomic Regular Polyhedron Electronic Shell

The periodic table of elements is arranged based on a series of regular polyhedron. The stability of inert gas atoms can be explained by the distribution of electrons, as well as their motion and magnetic force structure. A magnetic force regular octahedron is proposed. It is a unique configuration that best satisfies the convergence of electrons moving in the same direction within regular polyhedra. In the case of an electrostatic force crust, the formal electron spin accounts for the crusts intrinsic magnetic moment exceeding the speed of light. If one is to consider that the electron has a magnetic outer layer and an electrostatic inner layer, then the question can be solved and abovementioned inference can provide the basis for magnetic force and momentum for the regular octahedron model. The electron periphery has twenty-petal adsorptive substances;the existence of adsorptive substance causes the magnetic force greater than the electrostatic force. Each electronic shell in the regular polyhedron is in accordance with the electron configuration of periodic table of elements;the kinetic track of each electron is a surface of regular polyhedron. The magnetic properties of iron, cobalt, and nickel can be explained by the regular dodecahedron electronic shell of an atom. The electron orbit converged from reverse direction can explain diamond. The adsorptive substances found in atomic nuclei and electrons are defined as magnetic particles called magnetons. The thermodynamic magneton theory can be better explained when it is analyzed using principles of thermodynamics, superconductivity, viscosity, and even in the creation of glass. The structure of the light is a helical line.

Solvothermal Synthesis of Polyhedron Cobalt Nanomaterials

Co nanostructure tetradecahedron shape like were prepared via a simple solvothermal route. The shape and size of Co nanopolyhedron were tuned by changing the volume composition of the solvents and the synthesis temperature. Phase purity was confirmed by X-ray diffraction （XRD） and crystal size was determined by scanning electron microscopy （SEM）. The magnetic hysteresis loops of the polyhedron wareneasured using a SQUID magnetometer at 5 and 300 K. The results show ferromagnetic characteristics with coercivities of 22 and 15 Oe, respectively.

Two Algorithms for Fast Polyhedron Ray-Tracing

This note presents two fast polyhedron ray-tracing algorithms that can be applied not only in ray-convex polyhedron intersection, but also in ray-concave polyhedron intersection (Algorithm 2 permits polygons to contain internal loops of not).In the basis of surface trian gulation, Algorithm 1 can accelerate the surface normal vector interpolation by the intersection point's parameters. And besides, Algorithm 2 does not need any pre_procession such as surface triangulation. Moreover, it requires a few memories with more difficult operations such as division, extraction of roots and transcendental functions avoided entirely. Their simplicity and efficiency permit easy software or hardware implementation.

Ternary alloy and metal oxides embedded in yolk–shell polyhedrons as bifunctional oxygen electrocatalyst

To improve the efficiency of oxygen electrolysis,exploiting bifunctional electrocatalysts with excellent activity and stability is extremely important due to the four-electron transfer dynamics of oxygen evolution reaction(OER)and oxygen reduction reaction(ORR).Herein,a series of yolk-shell hollow polyhedrons(YHPs)embedded with NiCoFe ternary alloy and metal oxides,which are named YHP-x(x=1,2,3,4),were reported.By controlled etching multi-layered zeolitic imidazolate frameworks and following pyrolytic integration,YHPs are endowed with mass transfer tunnels,accessible inner active sites,and good electrical conductivity.Due to the synergetic effect of the alloy,metal oxides and the yolk-shell structure,YHP-1 exhibits excellent ORR performance with a half-wave potential of 0.79 V and YHP-2 displays superior OER performance with a low overpotential of 257 mV at 10 mA cm−2.The strategy described in this work can be extended to a number of hollow/yolk-shell electrocatalysts for water splitting and metal–air batteries.

Synthesis and facet-dependent photocatalytic activity of strontium titanate polyhedron nanocrystals

Cubic-perovskite （SrTiO3） has a great potential to be utilized in a wide range of applications. However, currently very little is known about the shape and facet effects of SrTiO3 on their physicochemical properties. This is largely owing to the difficulties in controlling the morphology of facets during synthesis. Herein, we describe a facile route for the facet- and size-controlled fabrication of single- crystalline SrTiO3 triangular prisms with highly exposed {101} side faces and {111} end faces. Theoretical and experimental studies of their photocatalytic performance have shown that triangular prisms exhibit superior photocatalytic activities than nanocubes with exposed （001） faces for the degradation of organic contaminants, which may be primarily attributed to the much higher surface energy of {101} facets （2.97 J/m^2） and {111} facets （2.80 J/m^2） than of that of {001} facets （0.98 J/m^2）.

Porous carbon polyhedrons coupled with bimetallic CoNi alloys for frequency selective wave absorption at ultralow filler loading

Combining suitable microstructure and dielectric-magnetic synergy effect is conducive to achieve lightweight,broadband,and high-efficiency microwave absorbing materials within low filler loading.Herein,porous carbon polyhedrons coupled with bimetallic CoNi alloys were synthesized by using metalorganic frameworks(MOFs)as a template and subsequent pyrolysis treatment.Electromagnetic analysis indicated that the existence of metal Ni element could influence the wave attenuation capacity effectively,resulting in frequency selective wave absorption performance.Additionally,the pyrolysis temperature was also closely related to wave absorption intensity.The Co_(2)Ni_(1)/C/PVDF composites calcined at 800℃ possessed outstanding wave absorption performance at an ultra-low filler loading of 5 wt%.The minimum reflection loss value achieved-52 dB(10.8 GHz)under the matched thickness of 3 mm.Moreover,the broadest effective absorption bandwidth(RL<-10 dB)reached 6.2 dB(11.8-18 GHz)for Co/C-800/PVDF composites when the thickness turned into 2 mm.The remarkable wave attenuation ability was mainly ascribed to magnetic and dielectric loss,impedance matching as well as porous structure effect.

Functional substitution of coordination polyhedron in crystal structure of silicates

On the bases of the study of comparative crystal chemistry of silicates it has been concluded that the octahedra and square pyramids of Ti-0 and Zr-0 play functional role of tetrahedra of Si-0 in the construction of crystal structures. Therefore, those silicates may be named titano-and zircono-silicates. Because of the functional similarity of coordination polyhedra, the structures of cristobalite and feldspar have been compared with those of perovskite and garnet, respectively. As a new concept, the functional replacement of tetrahedra by octahedra and/or pyramids is defined by the authors of this paper for favorable comparison of relative crystal structures.

Uniform design over a convex polyhedron

A new method, called the simplex method, is proposed to generate the uniform design over a convex polyhedron in n-dimensional Euclidean

An orientation method and analysis of optical radiation sources based on polyhedron and parallel incident light

The spatial orientation of optical radiation sources has long been the hot topic in the aerospace and the military applications.Current researches mainly focus on the high precision orientation on the partial field of view.Thus,combination of several partial fields of view is required to achieve orientation when the field of view exceeds 180°,which results in the increase of size,weight,power consumption and the cost.By defining radiation energy and direction of the optical radiation source as a vector and applying the cosine law of radiation and vector theorem,it is shown that the vector can be obtained from unit normal vectors on the three un-coplanar surfaces and from the energy projected by the optical radiation source.Based on this,an orientation method with 360° full field of view by a polyhedron is suggested,the mathematical formula for anti-multipath interference is supposed and the error upper limit is derived.The feasibility and effectiveness of this method are validated by measurements and simulation.An accuracy better than 2.866° and 0.574° is achieved when the ratio of measurement error of energy on arbitrary surface and the true value are 5% and 1%,respectively,given the matrix composed of unit normal vectors on three measurement surfaces is orthogonal.

Enhance gas-separation efficiency of mixed matrix membranes by lamellarly arranged metal-organic polyhedron

Eliminating the nonselective permeation path inside the mixed-matrix membranes(MMMs)is critical for fabrication of gas separation membranes.We demonstrate that by utilizing the phase separation of block copolymers,we are able to introduce metal-organic polyhedrons(MOPs)with precise pore sizes into a polymer matrix and form an ordered layered structure.We also prove that,by arranging MOP cages into a continuous nanosheet-like layer structure,we are able to generate repeated MOP-effective pathways and deplete the MOP-free permeation pathways,thus enhancing the gas-separation efficiency of MMMs.

The Singular Integral of an Analytic Polyhedron

Combining R.Harvey and J.Porking′s methods and traditional methods, we define the current Cauchy principal values in this paper by using homotopy formula and integral transformations. We study the boundary value of Weil type polyhedron integrals and obtain Plemelj formulas, which are different from the methods usually in the studies of boundary value problems.

Carbon polyhedrons formed by squares and hexagons obeying isolated square rule

To gain insight into the structures and stability of F4F6 polyhedrons formed by squares and hexagons,a density functional theory study was performed on all isomers of F4F6 polyhedrons with sizes from 8 to 60.The calculated results demonstrate that the six squares tend to isolate from each other,i.e.these F4F6 polyhedrons obey the isolated square rule.Those isomers with fewer B44 bonds(square-square adjacencies) are more stable than those with more B44 bonds,i.e.they obey square adjacency penalty rule.Both of the two rules in F4F6 polyhedrons are in the same status as the isolated pentagon rule and pentagon adjacency penalty rule in F5F6 fullerenes and can be used to screen the lowest energy isomers of F4F6 polyhedrons as IPR and PAPR do in classic fullerenes.Structural analysis demonstrates that the pyramidalization of carbon atoms at the square-square adjacencies determines the stability of corresponding structures.