The Correlation between the Zeroth-Order General Randic Indices and the π-Electronic Energies of Hexagonal Systems

A formula was proved for computing the zeroth-order general Randic index of a hexagonal system to explore the correlation between the zeroth-order general Randic index and the π-electronic energy of a hexagonal system.As a consequence,the extremal hexagonal systems with minimum or maximum zeroth-order general Randic index were completely characterized.Moreover,by using the least-square fit method and regression analysis,a new and close relation was found between the zeroth-order general Randic index and the π-electronic energy of a hexagonal system.So the zeroth-order general Randic index is a good measure of the π-electronic energies for benzenoid hydrocarbons.

A Generalized Array Factor for Time-Modulated Hexagonal Based Antenna Array Geometry With Novel Trapezoidal Switching

The concept of the time-modulated array has been emerging as an alternative to the complex phase shifters,which lowers the cost of the array feeding network due to the utilization of radio frequency(RF)switches.The various forms of hexagonal antenna array geometries can be used for applications like surveillance tracking in phased array radar and wireless communication systems.This work proposes the generalized array factor(AF)for the hexagonal antenna array geometry based on time modulation.The time modulation in generalized hexagonal geometry can maintain the fixed static amplitude excitation,giving more flexibility over time.Furthermore,a novel trapezoidal switching function is also proposed and applied to the generalized array factor to enable future researchers to use this array factor in the field of advancement to observe how switching schemes like trapezoidal and rectangular affect the array pattern's side lobe level(SLL).The generalized equation can be utilized for the analysis and synthesis of radiation characteristics of the time-modulated hexagonal array(TMHA),time-modulated concentric hexagonal array(TMCHA),time-modulated hexagonal cylindrical array(TMHCA),and time-modulated hexagonal concentric cylindrical array(TMHCCA).The numerical result illustrates the generation of AF of time-modulated hexagonal structures and also shows that the trapezoidal switching sequence outperforms the rectangular switch using the cat swarm optimization(CSO)approach.

Anti-forcing spectrum of any cata-condensed hexagonal system is continuous

The anti-forcing number of a perfect matching M of a graph G is the minimal number of edges not in M whose removal makes M a unique perfect matching of the resulting graph. The anti-forcing spectrum of G is the set of anti-forcing numbers over all perfect matchings of G. In this paper, we prove that the anti-forcing spectrum of any cata-condensed hexagonal system is continuous, that is, it is a finite set of consecutive integers.

A THEOREM CONCERNING PERFECT MATCHINGS IN HEXAGONAL SYSTEMS

In the present paper a theorem is established which offers some necessary and sufficient eonditionsfor a hexagonal system to have perfect matchings.

THE ENUMERATION OF SEVERAL CLASSES OF HEXAGONAL SYSTEMS

In [1], we introduced the concept of z-transformation graphs of perfect matchings of hexagonal systems and showed that the z-transformation graph of perfect matchings of a hexagonal system has at most two vertices of degree one. In this paper, we enumerate the hexagonal systems whose z-transformation graphs have a vertex of degree one. In particular, such hexagonal systems with various symmetries are also enumerated.

Polarization of plane wave propagating inside elastic hexagonal system solids

Based on the reported physical parameters for hexagonal system solids,we have calculated the effects of anisotropy on polarization of plane P-wave propagation.Herein we report the results of calculations and the newly observed physical phenomena.It is found that,for a given propagation,if the polarization is parallel to the wave vector,so also to the Poynting vector.In such a case,the phase velocity is identical to the energy velocity;the quasi P-wave degenerates to a pure P-wave along the propagation.It is also noted that if the polarization is parallel to the Poynting vector but not to the wave vector,the propagating wave cannot be a pure P-wave.Furthermore,the polarization in a quasi P-wave may deviate from the wave vector for more than 45°,but the deviation from the Poynting vector is always less than 45°.The energy velocity of a quasi SV-wave can be larger than that of the quasi P-wave in some propagation directions,even though the phase velocity of a quasi SV-wave may never be larger than either the phase velocity or energy velocity of the quasi P-wave.Finally,in case of parameters ε=0 and δ*≠0,the polarization of a quasi P-wave has an observed symmetry at a 45°phase angle.The anisotropy of a hexagonal system solid determines if a pure P-wave can be created and what the propagation direction is for a plane wave propagating inside such a hexagonal system solid.

Porous heterostructure of graphene/hexagonal boron nitride as an efficient electrocatalyst for hydrogen peroxide generation

Compared with the traditional heteroatom doping,employing heterostructure is a new modulating approach for carbon-based electrocatalysts.Herein,a facile ball milling-assisted route is proposed to synthesize porous carbon materials composed of abundant graphene/hexagonal boron nitride(G/h-BN)heterostructures.Metal Ni powder and nanoscale h-BN sheets are used as a catalytic substrate/hard template and“nucleation seed”for the formation of the heterostructure,respectively.As-prepared G/h-BN heterostructures exhibit enhanced electrocatalytic activity toward H_(2)O_(2) generation with 86%-95%selectivity at the range of 0.45-0.75 V versus reversible hydrogen electrode(RHE)and a positive onset potential of 0.79 versus RHE(defined at a ring current density of 0.3 mA cm^(-2))in the alkaline solution.In a flow cell,G/h-BN heterostructured electrocatalyst has a H_(2)O_(2) production rate of up to 762 mmol g_(catalyst)^(-1) h^(-1) and Faradaic efficiency of over 75%during 12 h testing,superior to the reported carbon-based electrocatalysts.The density functional theory simulation suggests that the B atoms at the interface of the G/h-BN heterostructure are the key active sites.This research provides a new route to activate carbon catalysts toward highly active and selective O_(2)-to-H_(2)O_(2) conversion.

Thermal-induced interfacial behavior of a thin one-dimensional hexagonal quasicrystal film

In this paper,we investigate the interfacial behavior of a thin one-dimensional(1D)hexagonal quasicrystal(QC)film bonded on an elastic substrate subjected to a mismatch strain due to thermal variation.The contact interface is assumed to be nonslipping,with both perfectly bonded and debonded boundary conditions.The Fourier transform technique is adopted to establish the integral equations in terms of interfacial shear stress,which are solved as a linear algebraic system by approximating the unknown phonon interfacial shear stress via the series expansion of the Chebyshev polynomials.The expressions are explicitly obtained for the phonon interfacial shear stress,internal normal stress,and stress intensity factors(SIFs).Finally,based on numerical calculations,we briefly discuss the effects of the material mismatch,the geometry of the QC film,and the debonded length and location on stresses and SIFs.

High-Throughput Growth of Hexagonal Boron Nitride Film Using Porous-Structure Isolation Layer

Chemical vapor deposition is considered as the most hopeful method for the synthesis of large-area high-quality hexagonal boron nitride on the substrate of catalytic metal. However, the size the hexagonal boron nitride films are limited to the size of growth chamber, which indicates a lower production efficiency. In this paper, the utilization efficiency of growth chamber is highly improved by alternately stacking multiple pieces of Cu foils and carbon fiber surface felt with porous structure. Uniform and continuous hexagonal boron nitride films are prepared on Cu foils through chemical vapor deposition utilizing ammonia borane as the precursor. This work develops a simple and practicable method for high-throughput preparation of hexagonal boron nitride films, which could contribute to the industrial application of hexagonal boron nitride. .

Elastic Field of a Straight Dislocation in One Dimensional Hexagonal Quasicrystals *L

Aim To study dislocation elasticity theory in quasicrystals. Methods A dislocation was separated into pure edge part and pure screw part and their superposition was used to find the elastic field. Results and Conclusion The elastic solution of a straight dislocation parallel to the quasiperiodic axis in 1D hexagonal quasicrystals was obtained and the generalized Peach Koehler force on a dislocation in quasicrystals was given.

Synthesis and photoluminescence properties of single-crystal ZnO hexagonal pyramids by PEG400-assisted thermal decomposition route

Large-scale synthesis of ZnO hexagonal pyramids was achieved by a simple thermal decomposition route of precursor at 240 oC in the presence of PEG400. The precursor was obtained by room-temperature solid-state grinding reaction between Zn（CH3COO）2-2H2O and Na2CO3. Crystal structure and morphology of the products were analyzed and characterized by X-ray diffraction （XRD）, scanning electron microscopy （SEM）, transmission electron microscopy （TEM） and high-resolution transmission electron microscopy （HRTEM）. The results of further experiments show that PEG400 has an important role in the formation of ZnO hexagonal pyramids. Difference between the single and double hexagonal pyramid structure may come from the special thermal decomposition reaction. The photoluminescence （PL） spectra of ZnO hexagonal pyramids exhibit strong near-band-edge emission at about 386 nm and weak green emission at about 550 nm. The Raman-active vibration at about 435 cm-1 suggests that the ZnO hexagonal pyramids have high crystallinity.

Polarization pinning at antiphase boundaries in multiferroic YbFeO_(3)

The switching characteristics of ferroelectrics and multiferroics are influenced by the interaction of topological defects with domain walls.We report on the pinning of polarization due to antiphase boundaries in thin films of the multiferroic hexagonal YbFeO_(3).We have directly resolved the atomic structure of a sharp antiphase boundary(APB)in YbFeO_(3) thin films using a combination of aberration-corrected scanning transmission electron microscopy(STEM)and total energy calculations based on density-functional theory(DFT).We find the presence of a layer of FeO_(6) octahedra at the APB that bridges the adjacent domains.STEM imaging shows a reversal in the direction of polarization on moving across the APB,which DFT calculations confirm is structural in nature as the polarization reversal reduces the distortion of the FeO_(6) octahedral layer at the APB.Such APBs in hexagonal perovskites are expected to serve as domain-wall pinning sites and hinder ferroelectric switching of the domains.

Boron Nitride-Integrated Lithium Batteries:Exploring Innovations in Longevity and Performance

The current global warming,coupled with the growing demand for energy in our daily lives,necessitates the development of more efficient and reliable energy storage devices.Lithium batteries(LBs)are at the forefront of emerging power sources addressing these challenges.Recent studies have shown that integrating hexagonal boron nitride(h-BN)nanomaterials into LBs enhances the safety,longevity,and electrochemical performance of all LB components,including electrodes,electrolytes,and separators,thereby suggesting their potential value in advancing eco-friendly energy solutions.This review provides an overview of the most recent applications of h-BN nanomaterials in LBs.It begins with an informative introduction to h-BN nanomaterials and their relevant properties in the context of LB applications.Subsequently,it addresses the challenges posed by h-BN and discusses existing strategies to overcome these limitations,offering valuable insights into the potential of BN nanomaterials.The review then proceeds to outline the functions of h-BN in LB components,emphasizing the molecular-level mechanisms responsible for performance improvements.Finally,the review concludes by presenting the current challenges and prospects of integrating h-BN nanomaterials into battery research.

Effects of BN on the Mechanical and Thermal Properties of PP/BN Composites

In order to explore the thermal conductivity of polypropylene(PP)/hexagonal boron nitride(BN) composites,PP composites filled with different proportions of BN were prepared through extrution compounding,injection moulding and compression moulding.The composites were filled with BN particles of 5 and 20 μm respectively,and their mass fractions in composites were considered.Percentage of BN was varied from 0 to 25wt% in steps of 5wt%.The effects of BN filler on mechanical properties of the composites were evaluated.The thermal behaviors were studied using DSC and TGA,and the thermal conductivity was also investigated by Laser Flash Device and the Model of 3D Heat Conduction respectively.The experimental results show that impact strength of PP/BN can be enhanced with the addition of BN,but that composites exhibit lower breaking elongation & tensile strength when compared to unfilled ones.It is found that mass fraction of BN influenced the final thermal stability and degree of crystallization of PP matrix,the degree of crystallization of PP with 15wt% of 20 μm BN can be improved by 25% than neat PP.Meanwhile,crystallization temperatures of PP composites are elevated by about 10 ℃.The thermal conductivity results demonstrate that the maximum value of the thermal conductivity is achieved from PP/BN with 20wt% of 20 μm BN,higher than that of pure PP by 95.65%,close to the simulation one.

Recension of boron nitride phase diagram based on high-pressure and high-temperature experiments

Cubic boron nitride and hexagonal boron nitride are the two predominant crystalline structures of boron nitride.They can interconvert under varying pressure and temperature conditions.However,this transformation requires overcoming significant potential barriers in dynamics,which poses great difficulty in determining the c-BN/h-BN phase boundary.This study used high-pressure in situ differential thermal measurements to ascertain the temperature of h-BN/c-BN conversion within the commonly used pressure range(3-6 GPa)for the industrial synthesis of c-BN to constrain the P-T phase boundary of h-BN/c-BN in the pressure-temperature range as much as possible.Based on the analysis of the experimental data,it is determined that the relationship between pressure and temperature conforms to the following equation:P=a+1/bT.Here,P denotes the pressure(GPa)and T is the temperature(K).The coefficients are a=-3.8±0.8 GPa and b=229.8±17.1 GPa/K.These findings call into question existing high-pressure and high-temperature phase diagrams of boron nitride,which seem to overstate the phase boundary temperature between c-BN and h-BN.The BN phase diagram obtained from this study can provide critical temperature and pressure condition guidance for the industrial synthesis of c-BN,thus optimizing synthesis efficiency and product performance.

Super Performance InGaP/GaAs Heterojunction Bipolar Transistor with Hexagonal Emitter

Super performance InGaP/GaAs heterojunction bipolar transistors (HBTs) with hexagonal emitter are described.The fabricated HBT shows excellent DC characteristics with low V CE offset voltage (<0 15V) and low knee voltage (<0 5V).Over 14V of the collector base breakdown voltage BV CBO and over 9V of the collector emitter breakdown voltage BV CEO are obtained.For a self aligned InGaP/GaAs HBT with 2μm×10μm emitter area,the f T is extrapolated to 92GHz and f max is extrapolated to 105GHz.These great values are obtained due to the hexagonal emitter and laterally etched undercut (LEU) of collector,indicating the great potential of InGaP/GaAs HBTs for high speed digital circuit and microwave power applications.

Graphite Carbone Structure

Carbon graphite is a crystalline form of carbon consisting of layers of hexagonal carbon atoms arranged in a two-dimensional “graphene” structure. Graphene layers are stacked on top of each other, forming a three-dimensional structure with a high degree of anisotropy. The carbon atoms within each layer are linked together by strong covalent bonds, creating a strong, stable lattice structure. However, the layers themselves are held together by weak van der Waals forces, enabling them to slide easily over each other. The properties of carbon graphite are highly dependent on the orientation and alignment of the graphene layers. When the layers are aligned parallel to each other, the material exhibits high strength and stiffness along the alignment direction, but is weaker and more flexible in other directions. Carbon graphite is used in a variety of applications where high strength, rigidity and electrical conductivity are required. Some common applications include electrical contacts, electric motor brushes, and as a structural material in aerospace and defense applications. The aim of our work is to describe the structure of graphite, its physical and chemical properties and its applications.

Fuzzy Inventory Model under Selling Price Dependent Demand and Variable Deterioration with Fully Backlogged Shortages

The objective is to develop a model considering demand dependent on selling price and deterioration occurs after a certain period of time, which follows two-parameter Weibull distribution. Shortages are allowed and fully backlogged. Fuzzy optimal solution is obtained by considering hexagonal fuzzy numbers and for defuzzification Graded Mean Integration Representation Method. A numerical example is provided for the illustration of crisp and fuzzy, both models. To observe the effect of changes in parameters, sensitivity analysis is carried out.

Exact analytic solutions for an elliptic hole with asymmetric collinear cracks in a one-dimensional hexagonal quasi-crystal

Using the complex variable function method and the technique of conformal mapping, the anti-plane shear problem of an elliptic hole with asymmetric colfinear cracks in a one-dimensional hexagonal quasi-crystal is solved, and the exact analytic solutions of the stress intensity factors （SIFs） for mode Ⅲ problem are obtained. Under the limiting conditions, the present results reduce to the Griffith crack and many new results obtained as well, such as the circular hole with asymmetric collinear cracks, the elliptic hole with a straight crack, the mode T crack, the cross crack and so on. As far as the phonon field is concerned, these results, which play an important role in many practical and theoretical applications, are shown to be in good agreement with the classical results.

Simulation on damage effectiveness of hexagonal prism aimable warhead with multi-point synchronous initiations

In order to study the impacts of warhead geometry and initiation pattern on the lethality of aimable warhead, multi-point synchronous initiated hexagonal prism and cylindrical warheads were compared through numerical simulation, combined with theoretical formulas of fragment decelera- tion and target plugging. Enhancements of fragment velocity, kinetic energy and density toward the target and target destructions were analyzed. The results show that hexagonal prism warhead can produce dense fragment beams and enhance average velocity and kinetic energy with asymmetric eight-point initiation by 24. 13% and 54. 52% respectively, which are higher than those of the isomet- ric or same weight cylindrical warhead. The effective fragments are still relatively concentrated in an area of 8 m × 2 m for the hexagonal prism warhead when the distance between warhead and target is 40 m.