On Triangle Interpolation Approximation of the Double Function

本文以两组不同的节点构造了一个组合型的二元三角插值多项式算子Lmn(f;x,y)，并且研究了二元连续周期函数对这个算子的收敛性及收敛阶的估计等问题。

Compression Properties and Energy Absorption of A Novel Double Curved Beam Negative Stiffness Honeycomb Structures

This paper presents the design of a novel honeycomb structure with a double curved beam.The purpose of this design is to achieve vibration isolation for the main engine of an offshore platform and reduce impact loads.An analytical formula for the force-displacement relationship of the honeycomb single-cell structure is presented based on the modal superposition method.This formula provides a theoretical basis for predicting the compression performance of honeycomb structures.The effects of structural geometric parameters,series and parallel connection methods on the mechanical and energy absorption properties are investigated through mathematical modeling and experimental methods.Furthermore,the study focuses on the vibration isolation and impact resistance performance of honeycomb panels.The results show that the designed honeycomb structure has good mechanical and energy absorption performance,and its energy absorption effect is related to the geometric parameters and series and parallel connection methods of the structure.The isolation efficiency of the honeycomb with 4 rows and 3 columns reaches 38%.The initial isolation frequency of the isolator is 11.7 Hz.

Steering the energy sharing of electrons in nonsequential double ionization with orthogonally polarized two-color field

Using the semiclassical ensemble model,the dependence of relative amplitude for the recollision dynamics in nonsequential double ionization(NSDI)of neon atom driven by the orthogonally polarized two-color field(OTC)laser field is theoretically studied.And the dynamics in two typical collision pathways,recollision-impact-ionization(RII)and recollisionexcitation with subsequent ionization(RESI),is systematically explored.Our results reveal that the V-shaped structure in the correlated momentum distribution is mainly caused by the RII mechanism when the relative amplitude of the OTC laser field is zero,and the first ionized electrons will quickly skim through the nucleus and share few energy with the second electron.As the relative amplitude increases,the V-shaped structure gradually disappears and electrons are concentrated on the diagonal in the electron correlation spectrum,indicating that the energy sharing after electrons collision is symmetric for OTC laser fields with large relative amplitudes.Our studies show that changing the relative amplitude of the OTC laser field can efficiently control the electron–electron collisions and energy exchange efficiency in the NSDI process.

Pure Electric and Pure Magnetic Resonances in Near-Infrared Metal Double-Triangle Metamaterial Arrays

We experimentally and numerically investigate the optical properties of metamaterial arrays composed of double partially-overlapped metallic nanotriangles fabricated by an angle-resolved nanosphere lithography.We demonstrate that each double-triangle can be viewed as an artificial magnetic element analogous to the conventional metal split-ring-resonator.It is shown that under normal-incidence conditions,individual double-triangle can exhibit a strong local magnetic resonance,but the collective response of the metamaterial arrays is purely electric because magnetic resonances of the two double-triangles in a unit cell having opposite openings are out of phase.For oblique incidences the metamaterial arrays are shown to support a pure magnetic response at the same frequency band.Therefore,switchable electric and magnetic resonances are achieved in double-triangle arrays.Moreover,both the electric and magnetic resonances axe shown to allow for a tunability over a large spectral range down to near-infrared.

Formation Mechanism and Binding Energy for Equilateral Triangle Structure of He3^+ Cluster

The formation mechanism for the equilateral triangle structure of the He-3(+) cluster is proposed. The curve of the total energy versus the internuclear distance R for this structure has been calculated by the method of a modified arrangement channel quantum mechanics. The result shows that the curve has a minimal -7.81373 a. u at R = 1.55 a(0). The binding energy of He-3(+) with respect to He+He++He was calculated to be 0.1064 a.u. (about 2.89 eV). This means that the He-3(+) cluster may be formed in the equilateral triangle structure stably by the interaction of He+ with two helium atoms.

The binding energy of a hydrogenic impurity in self-assembled double quantum dots

The binding energy of a hydrogenic impurity in self-assembled double quantum dots is calculated via the finitedifference method. The variation in binding energy with donor position, structure parameters and external magnetic field is studied in detail. The results found are： （i） the binding energy has a complex behaviour due to coupling between the two dots; （ii） the binding energy is much larger when the donor is placed in the centre of one dot than in other positions; and （iii） the external magnetic field has different effects on the binding energy for different quantum-dot sizes or lateral confinements.

A double toroidal analyzer for scanning probe electron energy spectrometer

An ultra-high vacuum （UHV） compatible electron spectrometer employing a double toroidal analyzer has been de- veloped. It is designed to be combined with a custom-made scanning tunneling microscope （STM） to study the spatially localized electron energy spectrum on a surface. A tip-sample system composed of a piezo-driven field-emission tungsten tip and a sample of highly ordered pyrolytic graphite （HOPG） is employed to test the performance of the spectrometer. Two-dimensional images of the energy-resolved and angle-dispersed electrons backscattered from the surface of HOPG are obtained, the performance is optimized and the spectrometer is calibrated. A complete electron energy loss spectrum covering the elastic peak to the secondary electron peaks for the HOPG surface, acquired at a tip voltage of -140 V and a sample current of 0.5 pA, is presented, demonstrating the viability of the spectrometer.

Layered double hydroxides as electrode materials for flexible energy storage devices

To prevent and mitigate environmental degradation,high-performance and cost-effective electrochemical flexible energy storage systems need to be urgently developed.This demand has led to an increase in research on electrode materials for high-capacity flexible supercapacitors and secondary batteries,which have greatly aided the development of contemporary digital communications and electric vehicles.The use of layered double hydroxides(LDHs)as electrode materials has shown productive results over the last decade,owing to their easy production,versatile composition,low cost,and excellent physicochemical features.This review highlights the distinctive 2D sheet-like structures and electrochemical characteristics of LDH materials,as well as current developments in their fabrication strategies for expanding the application scope of LDHs as electrode materials for flexible supercapacitors and alkali metal(Li,Na,K)ion batteries.

Formation Mechanism and Binding Energy for Equilateral Triangle Structure of Li3 Cluster

The formation mechanism for the equilateral triangle structure of Lia cluster is proposed. The curve of the total energy versus the interatomic distance for this structure has been calculated by using the method of Gou＇s Modified Arrangement Channel Quantum Mechanics. The result shows that the curve has a minimal energy of-22.338 60 a.u at R = 5.82 ao. The total energy of Lia when R approaches co has the value of-22.284 09 a.u. This is also the total energy of three lithium atoms dissociated from Lia. The difference value of 0.0545 08 a.u. for the above two energy values is the dissociation energy of Li3 cluster, which is also its binding energy. Therefore the binding energy per lithium atom for Lia is 0.018 169 a.u. = 0.494 eV, which is greater than the binding energy of 0.453 eV per atom for Li2 calculated in a previous work. This means that the Li3 cluster may be formed in the equilateral triangle structure of side length R = 5.82ao stably with a stronger binding from the symmetrical interaction among the three lithium atoms.

Federated double DQN based multi-energy microgrid energy management strategy considering carbon emissions

Multi-energy microgrids(MEMG)play an important role in promoting carbon neutrality and achieving sustainable development.This study investigates an effective energy management strategy(EMS)for MEMG.First,an energy management system model that allows for intra-microgrid energy conversion is developed,and the corresponding Markov decision process(MDP)problem is formulated.Subsequently,an improved double deep Q network(iDDQN)algorithm is proposed to enhance the exploration ability by modifying the calculation of the Q value,and a prioritized experience replay(PER)is introduced into the iDDQN to improve the training speed and effectiveness.Finally,taking advantage of the federated learning(FL)and iDDQN algorithms,a federated iDDQN is proposed to design an MEMG energy management strategy to enable each microgrid to share its experiences in the form of local neural network(NN)parameters with the federation layer,thus ensuring the privacy and security of data.The simulation results validate the superior performance of the proposed energy management strategy in minimizing the economic costs of the MEMG while reducing CO_2 emissions and protecting data privacy.

Evaluation of the Double Snap-Through Mechanism on the Wave Energy Converter’s Performance

Lower efficiencies induce higher energy costs and pose a barrier to wave energy devices'commercial applications.Therefore,the efficiency enhancement of wave energy converters has received much attention in recent decades.The reported research presents the double snap-through mechanism applied to a hemispheric point absorber type wave energy converter(WEC)to improve the energy absorption perfomance.The double snap-through mechanism comprises four oblique springs mounted in an X-configuration.This provides the WEC with different dynamic stability behaviors depending on the particular geometric and physical parameters employed.The efficiency of these different WEC behaviors(linear,bistable,and tristable)was initially evaluated under the action of regular waves.The results for bistable or tristable responses indicated significant improvements in the WEC's energy capture efficiency.Furthermore,the WEC frequency bandwidth was shown to be significantly enlarged when the tristable mode was in operation.However,the corresponding tristable trajectory showed intra-well behavior in the middle potential well,which induced a more severe low-energy absorption when a small wave amplitude acted on the WEC compared to when the bistable WEC was employed.Nevertheless,positive effects were observed when appropriate initial conditions were imposed.The results also showed that for bistable or tristable responses,a suitable spring stiffness may cause the buoy to oscillate in high energy modes.

Chemical composition,energy and amino acid digestibility in double-low rapeseed meal fed to growing pigs

Background： The nutritional value of rapeseed meal may be variable due to the variation of its chemical composition. And a precise understandin9 of the nutritional value of an ingredient is beneficial for the accurate diet formulation and reduction of feed costs. This study was conducted to determine the chemical composition, dicjestible energy （DE） and metabolizable enercjy （ME） content, and apparent ileal digestibility （AID） and standardized ileal dicjestibility （SID） of amino acids （AA） for growincj pigs. Thirteen solvent-extracted double-low rapeseed meal （DLIRSM） samples were obtained from the main double-low rapeseed producing areas in China. Methods： The DE and ME contents of the 13 DLRSM samples were measured in cjrowin9 pigs （six pigs per DLRSM sample, average initial body weicjht （BW） =48.3 kg）. The AID and SID of AA of 10 DLRSM samples were determined in 12 crossbred barrows （average initial BW = 35.3 kcj） by using two 6 x 6 Latin square designs. Each Latin square comprised one N-flee diet and 5 DLRSM test diets. Results： The chemical composition of DLRSM varied among samples, and the coefficient of variation was greater than ]0 % for ether extract （EE）, neutral detergent fiber （NDF）, acid detergent fiber （ADF）, calcium （Ca）, and total 91ucosinolates. The AA content of DLRSM varied among samples especially for lysine （Lys） and methionine （Met）. On a dry matter （DM） basis, the apparent total tract digestibility （ATFD） of gross energy （GE）, the DE and ME and the ME：DE ratio of DLRSM averaged 62.39 %, 2862 kcal/k9 and 2723 kcal/kcj, and 94.95 %, respectively. The mean value of S1D of Lys was 70.52 % which varied from 66.54-76.54 %. The SID of crude protein （CP）, Met, and threonine （Thr） averaged 72.81%, 82.41%, and 69.76 %, respectively. Conclusions： There was great variability in chemical composition especially in the concentration of EE, NDF and ADF, but no significant differences in energy content of the DLIRSM samples were observed. In addition, the AID and SID of all AA were relatively similar amoncj DLRSM samples except for that of Lys.

Oscillation and Conversion Performance of Double-Float Wave Energy Converter

In this study, we investigated the hydrodynamic and energy conversion performance of a double-float wave energy converter(WEC) based on the linear theory of water waves. The generator power take-off(PTO) system is modeled as a combination of a linear viscous damping and a linear spring. Using the frequency domain method, the optimal damping coefficient of the generator PTO system is derived to achieve the optimal conversion efficiency(capture width ratio).Based on the potential flow theory and the higher-order boundary element method(HOBEM), we constructed a threedimensional model of double-float WEC to study its hydrodynamic performance and response in the time domain. Only the heave motion of the two-body system is considered and a virtual function is introduced to decouple the motions of the floats. The energy conversion character of the double-float WEC is also evaluated. The investigation is carried out over a wide range of incident wave frequency. By analyzing the effects of the incident wave frequency, we derive the PTO's damping coefficient for the double-float WEC's capture width ratio and the relationships between the capture width ratio and the natural frequencies of the lower and upper floats. In addition, it is capable to modify the natural frequencies of the two floats by changing the stiffness coefficients of the PTO and mooring systems. We found that the natural frequencies of the device can directly influence the peak frequency of the capture width, which may provide an important reference for the design of WECs.

BINDING ENERGY OF THE SHALLOW DONOR IN （CdTe）_m／（ZnTe）_n STRAINED DOUBLE QUANTUM WELL

In this paper the binding energy of the shallow.donor in CdTe/ZnTe strained double quantum well was calculated.The effect of the finite well potential and strain,resulting from the lattice mismatch,on the binding energy of the impurity is included in a variational framework.The binding energy is obtained as a function of the well width,barrier width,and impurity position in the barrier by using a variational method.The result of the present calculation shows that the variational law of the binding energy is similar to that of unstrained materials.

The Calculation of Ground State Energies of Double-Electron Systems in an Uniform Magnetic Field below 10~9 G

Energies for the ground states of double electron systems in a uniform magnetic field B≤ 10 9 G are calculated by using the modified Slater basis and configuration interaction method, and the result for energy in zero magnetic field is comparable with those obtained by different methods.

Formation Mechanism and Binding Energy for Equilateral Triangle Structure of He3+ Cluster

The formation mechanism for the equilateral triangle structure of the He3+ cluster is proposed. The curveof the total energy versus the internuclear distance R for this structure has been calculated by the method of a modifiedarrangement channel quantum mechanics. The result shows that the curve has a minimal -7.81373 a.u at 1 = 1.55 a0.The binding energy of He3+ with respect to He+He+ +He was calculated to be 0.1064 a.u. (about 2.89 eV). This meansthat the He3+ cluster may be formed in the equilateral triangle structure stably by the interaction of He+ with two heliumatoms.

Internal energy and specific antiferromagnetic heat in a ferromagnetic- double layers

The internal energy and specific heat of a Heisenberg ferro- antiferromagnetic double-layer system are studied by using spin-wave theory and the retarded Green function method at low temperatures. Numerical results show that the antiferromagnetic intralayer coupling J2 has an important influence on internal energy and specific heat for a four-sublattice system with antiferromagnetic （or ferrimagnetic） interlayer couplings.

Reconstructing Equation of State for Dark Energy in Double Complex Symmetric Gravitational Theory

We propose to study the accelerating expansion of the universe in the double complex symmetric gravitational theory （DCSGT）. The universe we live in is taken as the real part of the whole spacetime MC^4（J）, which is double complex. By introducing the spatially flat FRW metric, not only the double Friedmann equations but also the two constraint conditions py = 0 and J^2 = 1 are obtained. Farthermore, using parametric DL（z） ansatz, we reconstruct the ω/（z） and V（Ф） for dark energy from real observational data. We find that in the two cases of J = i, pJ = 0, and J = ε, pJ≠0, the corresponding equations of state ω＇（z） remain close to -1 at present （z = 0） and change from below -1 to above -1. The results illustrate that the whole spacetime, i.e. the double complex spacetime MC^4（J）, may be either ordinary complex （J = i, pJ = 0） or hyperbolic complex （J = ε, pJ≠ 0）. And the fate of the universe would be Big Rip in the future.

Computing Dark Energy and Ordinary Energy of the Cosmos as a Double Eigenvalue Problem

We compute the dark energy and ordinary energy density of the cosmos as a double Eigenvalue problem. In addition, we validate the result using two different theories. The first theory is based on Witten’s 11 dimensional spacetime and the second is based on ‘tHooft’s fractal renormalization spacetime. In all cases, the robust result is E(O) = mc2/22 for ordinary energy and E(D) = mc2(21/22) for dark energy. Adding E(O) to E(D) we obtain Einstein’s famous equation which confirms special relativity, although it adds a quantum twist to its interpretation. This new interpretation is vital because it brings relativity theory in line with modern cosmological measurements and observations. In particular, we replace calculus by Weyl scaling in all computation which is essentially transfinite discrete.

A Double Threshold Energy Detection-Based Neural Network for Cognitive Radio Networks

In cognitive radio networks(CoR),the performance of cooperative spectrum sensing is improved by reducing the overall error rate or maximizing the detection probability.Several optimization methods are usually used to optimize the number of user-chosen for cooperation and the threshold selection.However,these methods do not take into account the effect of sample size and its effect on improving CoR performance.In general,a large sample size results in more reliable detection,but takes longer sensing time and increases complexity.Thus,the locally sensed sample size is an optimization problem.Therefore,optimizing the local sample size for each cognitive user helps to improve CoR performance.In this study,two new methods are proposed to find the optimum sample size to achieve objective-based improved(single/double)threshold energy detection,these methods are the optimum sample size N^(*)and neural networks(NN)optimization.Through the evaluation,it was found that the proposed methods outperform the traditional sample size selection in terms of the total error rate,detection probability,and throughput.