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.

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.

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. .

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.

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.

Hexagonal boron nitride adsorbent: Synthesis, performance tailoring and applications

Hexagonal boron nitride(h-BN),with unique structural and properties,has shown enormous potentitoward variety of possible applications.By virtue of partially-ionic character of BN chemical bonds anusually large specific surface area,h-BN-related nanostructures exhibit appealing adsorption propertiewhich can be widely applied for separation and purification towards energy and environment treatmenIn this review,recent progress in designing h-BN micro,nano-structure,controlled synthesis,performancoptimizing as well as energy and environment-related adsorption applications are summarized.Strategieto tailor the h-BN can be classified as morphology control,element doping,defect control and surfacmodification,focusing on how to optimize the adsorption performance.In order to insight the intrinsimechanism of tuning strategies for property optimization,the significant adsorption applications of h-Btowards hydrogen storage,CO2 capture,pollutants removal from water and adsorption desulfurization arpresented.

The interaction between a screw dislocation and a wedge-shaped crack in one-dimensional hexagonal piezoelectric quasicrystals

Based on the fundamental equations of piezoelasticity of quasicrystal material,we investigated the interaction between a screw dislocation and a wedge-shaped crack in the piezoelectricity of one-dimensional hexagonal quasicrystals.Explicit analytical solutions are obtained for stress and electric displacement intensity factors of the crack,as well as the force on dislocation.The derivation is based on the conformal mapping method and the perturbation technique.The influences of the wedge angle and dislocation location on the image force are also discussed.The results obtained in this paper can be fully reduced to some special cases already available or deriving new ones.

Crushing analysis and multi-objective optimization of bitubular hexagonal columns with ribs

In order to improve the crashworthiness of thin-walled columns, the energy absorption characteristics of three columns under quasi-static axial crushing loads were analyzed through LS-DYNA. Numerical results show that the energy absorption capability of the bitubular hexagonal columns with middle to middle(MTM) ribs is the best, followed by the bitubular hexagonal columns with corner to corner(CTC) ribs and the bitubular hexagonal columns without(NOT) ribs, respectively. Then, the MTM rib was optimized by using multi-objective particle swarm optimization algorithm. Through the analysis of the Pareto front for specific energy absorption(SEA, A_(se)) and peak crushing force(PCF, F_(pc)), it is found that there is a vertex on the Pareto front. The vertex has the design parameters of t_1=1.2 mm, t_2=1.2 mm, A_(se)=11.3729 k J/kg, F_(pc)=235.8491 kN. When the PCF is in a certain size, on the left of the vertex, the point with t_2=1.2 mm has the biggest SEA, meanwhile on the right of the vertex, the point with t_1=1.2 mm has the biggest SEA. Finally, the global sensitivity analysis was conducted to investigate the effect of two design parameters. The result is obtained that both SEA and PCF for MTM are more sensitive to t_1 rather than t_2 in the design domain.

Characterization of a Y-type hexagonal ferrite-based frequency tunable microwave absorber

A Y-type hexaferrite rod with the composition of Ba2COl.8Cuo.2Fe12022 was presented as an absorbing material with high absorb- anee. Its high absorbance and wide absorption band result from ferromagnetic resonance （FMR） that is self-biased by strong shape and mag- netocrystaUine anisotropy fields. Around the FMR frequency the specimen of the ferrite rods exhibits very high absorbance and the FMR frequency can be tuned by the rod dimension. In addition to the high absorbance and the wide tunable absorption band, the microwave ab- sorber has another advantage of light weight due to the use of the ferrite rods instead of ferrite slabs.

A study of transition from n-to p-type based on hexagonal WO3 nanorods sensor

Hexagonal WO3 nanorods are fabricated by a facile hydrothermal process at 180 ℃ using sodium tungstate and sodium chloride as starting materials. The morphology, structure, and composition of the prepared nanorods are studied by scanning electron microscopy, X-ray diffraction spectroscopy, and energy dispersive spectroscopy. It is found that the agglomeration of the nanorods is strongly dependent on the PH value of the reaction solution. Uniform and isolated WO3 nanorods with diameters ranging from 100 nm-150 nm and lengths up to several micrometers are obtained at PH = 2.5 and the nanorods are identified as being hexagonal in phase structure. The sensing characteristics of the WO3 nanorod sensor are obtained by measuring the dynamic response to NO2 with concentrations in the range 0.5 ppm-5 ppm and at working temperatures in the range 25 ℃-250 ℃. The obtained WO3 nanorods sensors are found to exhibit opposite sensing behaviors, depending on the working temperature. When being exposed to oxidizing NO2 gas, the WO3 nanorod sensor behaves as an n-type semiconductor as expected when the working temperature is higher than 50 ℃, whereas, it behaves as a p-type semiconductor below 50 ℃. The origin of the n- to p-type transition is correlated with the formation of an inversion layer at the surface of the WO3 nanorod at room temperature. This finding is useful for making new room temperature NO2 sensors based on hexagonal WO3 nanorods.

Interaction between a screw dislocation and an elliptical hole with two asymmetrical cracks in a one-dimensional hexagonal quasicrystal with piezoelectric effect

The interaction between a screw dislocation and an elliptical hole with two asymmetrical cracks in a one-dimensional(1 D) hexagonal quasicrystal with piezoelectric effect is considered. A general formula of the generalized stress field, the field intensity factor, and the image force is derived, and the special cases are discussed. Several numerical examples are given to show the effects of the material properties and the dislocation position on the field intensity factors and the image forces.

TIME-HARMONIC DYNAMIC GREEN'S FUNCTIONS FOR ONE-DIMENSIONAL HEXAGONAL QUASICRYSTALS

Quasicrystals have additional phason degrees of freedom not found in conventional crystals. In this paper, we present an exact solution for time-harmonic dynamic Green＇s function of one-dimensional hexagonal quasicrystals with the Laue classes 6/mh and 6/mhmm. Through the introduction of two new functions φ and ψ, the original problem is reduced to the determination of Green＇s functions for two independent Helmholtz equations. The explicit expressions of displacement and stress fields are presented and their asymptotic behaviors are discussed. The static Green＇s function can be obtained by letting the circular frequency approach zero.

N-hydroxyphthalimide anchored on hexagonal boron nitride as a metal-free heterogeneous catalyst for deep oxidative desulfurization

A metal-free N-hydroxyphthalimide/hexagonal boron nitride(NHPI/h-BN)catalytic system was developed for deep oxidative desulfurization(ODS)of fuel oils.Detailed experiments find that the heterogenization process of loading NHPI on h-BN not only benefits to the dispersion and utilization of NHPI,but also can significantly promote the catalytic performance.By employing NHPI/h-BN as the catalyst,azodiisobutyronitrile(AIBN)as the metal-free initiator,a 95%conversion of dibenzothiophene(DBT)can be acquired under the reaction conditions of 120°C and atmospheric pressure with molecular oxygen(O_(2))as oxidant.Moreover,the heterogenization is convenient for the regeneration of the catalyst with>94%DBT conversion after being recycled seven times.Characterizations illustrate that the promoted catalytic activity along with the regenerability originate from the interactions between NHPI and h-BN.The catalytic mechanism study shows that molecular oxygen is readily activated by the NHPI/h-BN to form a superoxide radical(O_(2)^(·-)),which oxidize DBT to DBTO2 for desulfurization.