The Class of Atomic Exponential Basis Functions EFup_(n)(x,ω)-Development and Application

The purpose of this paper is to present the class of atomic basis functions(ABFs)which are of exponential type and are denoted by EFupn(x,ω).While ABFs of the algebraic type are already represented in the numerical modeling of various problems inmathematical physics and computationalmechanics,ABFs of the exponential type have not yet been sufficiently researched.These functions,unlike the ABFs of the algebraic type Fupn(x),contain the tension parameterω,which gives them additional approximation properties.Exponential monomials up to the nth degree can be described exactly by the linear combination of the functions EFupn(x,ω).The function EFupn for n=0 is called the“mother”ABF of the exponential type,i.e.,EFup0(x,ω)≡Eup(x,ω).In other words,the functions EFupn(x,ω)are elements of the linear vector space EUPn and retain all the properties of their“mother”function Eup(x,ω).Thus,this paper,in terms of its content and purpose,can be understood as a sequel of the article by Brajcic Kurbasa et al.,which shows the basic properties and application of the basis function Eup(x,ω).This paper presents,in an analogous way,the development and application of the exponential basis functions EFupn(x,ω).Here,for the first time,expressions for calculating the values of the functions EFupn(x,ω)and their derivatives are given in a form suitable for application in numerical analyses,which is shown in the verification examples of the approximations of known functions.

Tailoring local structures of atomically dispersed copper sites for highly selective CO_(2) electroreduction

Atomically‐dispersed copper sites coordinated with nitrogen‐doped carbon(Cu–N–C)can provide novel possibilities to enable highly selective and active electrochemical CO_(2) reduction reactions.However,the construction of optimal local electronic structures for nitrogen‐coordinated Cu sites(Cu–N_(4))on carbon remains challenging.Here,we synthesized the Cu–N–C catalysts with atomically‐dispersed edge‐hosted Cu–N_(4) sites(Cu–N_(4)C_(8))located in a micropore between two graphitic sheets via a facile method to control the concentration of metal precursor.Edge‐hosted Cu–N_(4)C_(8) catalysts outperformed the previously reported M–N–C catalysts for CO_(2)‐to‐CO conversion,achieving a maximum CO Faradaic efficiency(FECO)of 96%,a CO current density of–8.97 mA cm^(–2) at–0.8 V versus reversible hydrogen electrode(RHE),and over FECO of 90%from–0.6 to–1.0 V versus RHE.Computational studies revealed that the micropore of the graphitic layer in edge‐hosted Cu–N_(4)C_(8) sites causes the d‐orbital energy level of the Cu atom to shift upward,which in return decreases the occupancy of antibonding states in the*COOH binding.This research suggests new insights into tailoring the locally coordinated structure of the electrocatalyst at the atomic scale to achieve highly selective electrocatalytic reactions.

Single-atom catalysts based on polarization switching of ferroelectric In_(2)Se_(3)for N2 reduction

The polarization switching plays a crucial role in controlling the final products in the catalytic pro-cess.The effect of polarization orientation on nitrogen reduction was investigated by anchoring transition metal atoms to form active centers on ferroelectric material In_(2)Se_(3).During the polariza-tion switching process,the difference in surface electrostatic potential leads to a redistribution of electronic states.This affects the interaction strength between the adsorbed small molecules and the catalyst substrate,thereby altering the reaction barrier.In addition,the surface states must be considered to prevent the adsorption of other small molecules(such as*O,*OH,and*H).Further-more,the V@↓-In_(2)Se_(3)possesses excellent catalytic properties,high electrochemical and thermody-namic stability,which facilitates the catalytic process.Machine learning also helps us further ex-plore the underlying mechanisms.The systematic investigation provides novel insights into the design and application of two-dimensional switchable ferroelectric catalysts for various chemical processes.

The influences of large earthquake signals on the recovery of surface waves from ambient noise cross-correlation functions

Ambient noise tomography(ANT)has been widely used to image crust and upmost mantle structures.ANT assumes that sources of ambient noise are diffuse and evenly distributed in space and the energy of different modes is equipartitioned.At present,the sources of the primary and the secondary microseisms are well studied,but there are only a few on the studies of long-period ambient noise sources.In this study,we study the effects of large earthquake signals on the recovery of surface waves from seismic ambient noise data recorded by seismic stations from the US permanent networks and Global Seismographic Network(GSN).Our results show that large earthquake signals play an important role on the recovery of long-period surface waves from ambient noise cross-correlation functions.Our results are consistent with previous studies that suggest the contribution of earthquake signals to the recovery of surface waves from cross-correlations of ambient noise is dominant at periods larger than 20–40 s.

Catalytic activity of V_(2)CO_(2) MXene supported transition metal single atoms for oxygen reduction and hydrogen oxidation reactions:A density functional theory calculation study

Two-dimensional(2D)MXene and single-atom(SA)catalysts are two frontier research fields in catalysis.2D materials with unique geometric and electronic structures can modulate the catalytic performance of supported SAs,which,in turn,affect the intrinsic activity of 2D materials.Density functional theory calculations were used to systematically explore the potential of O-terminated V2C MXene(V_(2)CO_(2))-supported transition metal(TM)SAs,including a series of 3d,4d,and 5d metals,as oxygen reduction reaction(ORR)and hydrogen oxidation reaction(HOR)catalysts.The combination of TM SAs and V_(2)CO_(2)changes their electronic structure and enriches the active sites,and consequently regulates the intermediate adsorption energy and catalytic activity for ORR and HOR.Among the investigated TM-V_(2)CO_(2)models,Sc-,Mn-,Rh-,and PtMCCh showed high ORR activity,while Sc-,Ti-,V-,Cr-,and Mn-V_(2)CO_(2)exhibited high HOR activity.Specifically,Mn-and Sc-V_(2)CO_(2)are expected to serve as highly efficient and cost-effective bifunctional catalysts for fuel cells because of their high catalytic activity and stability.This work provides theoretical guidance for the rational design of efficient ORR and HOR bifunctional catalysts.

Theory and Properties of Atomic Spacetime

Following A. Einsteins aspirations for an atomic theory, a novel theory of spacetime quantization/atomization based on finite Atomic AString Functions evolving since the 1970s is offered. Atomization Theorems allow representing polynomials, analytic functions, and solutions of General Relativity via the superposition of solitonic atoms which can be associated with flexible spacetime quanta, metriants, or elementary distortions. With multiple interpretations discussed, discrete-continuous spacetime is conceptualized as a lattice network of flexible solitonic atoms adjusting locations to reproduce different metrics. The theory may offer some variants of unified field theory under research based on Atomic AString Function where, like in string theory, fields become interconnected having a common mathematical ancestor.

Reconstruction of sub cross-correlation cancellation technique for unambiguous acquisition of BOC(kn, n) signals

In order to solve the problem of ambiguous acquisition of BOC signals caused by its property of multiple peaks,an unambiguous acquisition algorithm named reconstruction of sub cross-correlation cancellation technique(RSCCT)for BOC(kn,n)signals is proposed.In this paper,the principle of signal decomposition is combined with the traditional acquisition algorithm structure,and then based on the method of reconstructing the correlation function.The method firstly gets the sub-pseudorandom noise(PRN)code by decomposing the local PRN code,then uses BOC(kn,n)and the sub-PRN code cross-correlation to get the sub cross-correlation function.Finally,the correlation peak with a single peak is obtained by reconstructing the sub cross-correlation function so that the ambiguities of BOC acquisition are removed.The simulation shows that RSCCT can completely eliminate the side peaks of BOC(kn,n)group signals while maintaining the narrow correlation of BOC,and its computational complexity is equivalent to sub carrier phase cancellation(SCPC)and autocorrelation side-peak cancellation technique(ASPeCT),and it reduces the computational complexity relative to BPSK-like.For BOC(n,n),the acquisition sensitivity of RSCCT is 3.25 dB,0.81 dB and 0.25 dB higher than binary phase shift keying(BPSK)-like,SCPC and ASPeCT at the acquisition probability of 90%,respectively.The peak to average power ratio is 1.91,3.0 and 3.7 times higher than ASPeCT,SCPC and BPSK-like at SNR=–20 dB,respectively.For BOC(2n,n),the acquisition sensitivity of RSCCT is 5.5 dB,1.25 dB and 2.69 dB higher than BPSK-like,SCPC and ASPeCT at the acquisition probability of 90%,respectively.The peak to average power ratio is 1.02,1.68 and 2.12 times higher than ASPeCT,SCPC and BPSK-like at SNR=–20 dB,respectively.

Temporal-spatial cross-correlation analysis of non-stationary near-surface wind speed time series

Temporal-spatial cross-correlation analysis of non-stationary wind speed time series plays a crucial role in wind field reconstruction as well as in wind pattern recognition.Firstly,the near-surface wind speed time series recorded at different locations are studied using the detrended fluctuation analysis(DFA),and the corresponding scaling exponents are larger than 1.This indicates that all these wind speed time series have non-stationary characteristics.Secondly,concerning this special feature( i.e.,non-stationarity)of wind signals,a cross-correlation analysis method,namely detrended cross-correlation analysis(DCCA) coefficient,is employed to evaluate the temporal-spatial cross-correlations between non-stationary time series of different anemometer pairs.Finally,experiments on ten wind speed data synchronously collected by the ten anemometers with equidistant arrangement illustrate that the method of DCCA cross-correlation coefficient can accurately analyze full-scale temporal-spatial cross-correlation between non-stationary time series and also can easily identify the seasonal component,while three traditional cross-correlation techniques(i.e.,Pearson coefficient,cross-correlation function,and DCCA method) cannot give us these information directly.

Detrended cross-correlation analysis of electroencephalogram

In the paper we use detrended cross-correlation analysis （DCCA） to study the electroencephalograms of healthy young subjects and healthy old subjects. It is found that the cross-correlation between different leads of a healthy young subject is larger than that of a healthy old subject. It was shown that the cross-correlation relationship decreases with the aging process and the phenomenon can help to diagnose whether the subject＇s brain function is healthy or not.

Density Functional Study of the C Atom Adsorption on the α-Fe_2O_3 (001) Surface

The adsorption of C atoms on the α-Fe2O3（001） surface was studied based on density function theory（DFT） ,in which the exchange-correlation potential was chosen as the PBE（Perdew,Burke and Ernzerhof） generalized gradient approximation（GGA） with a plane wave basis set. Upon the optimization on different adsorption sites with coverage of 1/20 and 1/5 ML,it was found that the adsorption of C atoms on the α-Fe2O3（001） surface was chemical adsorption. The coverage can affect the adsorption behavior greatly. Under low coverage,the most stable adsorption geometry lied on the bridged site with the adsorption energy of about 3.22 eV; however,under high coverage,it located at the top site with the energy change of 8.79 eV. Strong chemical reaction has occurred between the C and O atoms at this site. The density of states and population analysis showed that the s,p orbitals of C and p orbital of O give the most contribution to the adsorption bonding. During the adsorption process,O atom shares the electrons with C,and C can only affect the outermost and subsurface layers of α-Fe2O3; the third layer can not be affected obviously.

Oxygen Atom Transfer Reaction of Manganese-oxo Corrole toward Dimethyl Sulfide: a Density Functional Study

The effects of axial ligand on the oxygen atom transfer(OAT)reaction from 5,10,15-tris(pentafluorophenyl)corrole((tpfc)MnVO)to dimethyl sulfide(DMS)have been investigated by density functional theory(DFT)calculations.Imidazole(Im),4-methylimidazole(4-MI)and pyridine(Py)were selected as the axial ligands.The results revealed that the axial ligand can form coordinate bond with(tpfc)MnVO in the transition state(TS)of the OAT reaction.The axial coordination favored charge transferring from(tpfc)MnVO to DMS,and weakened the Mn≡O bond in both singlet and triplet states.Furthermore,axial coordination can reduce the energy barrier of neutral(tpfc)MnVO from 23.62 kJ·mol^-1 to less than 3 kJ·mol^-1 in the triplet state,which is significantly lower than in the singlet state.This makes(tpfc)MnVO tend to direct the OAT reaction via triplet state pathway.On the other hand,the energy barriers of[(tpfc)MnVIO]+species from disproportionation pathway increased from 1.26 to 33.95 kJ·mol^-1 in a doublet state.This suggests axial ligands were conducive for direct(tpfc)MnVO OAT reaction pathway.

Charge transfer and orbital reconstruction of non‐noble transition metal single‐atoms anchored on Ti_(2)CT_(x)‐MXenes for highly selective CO_(2) electrochemical reduction

Inspired by MXene nanosheets and their regulation of surface functional groups,a series of Ti_(2)C‐based single‐atom electrocatalysts(TM@Ti_(2)CT_(x),TM=V,Cr,Mn,Fe,Co,and Ni)with two dif‐ferent functional groups(T=–O and–S)was designed.The CO_(2)RR catalytic performance was stud‐ied using well‐defined ab initio calculations.Our results show that the CO_(2) molecule can be more readily activated on TM@Ti_(2)CO_(2) than the TM@Ti_(2)CS_(2) surface.Bader charge analysis reveals that the Ti_(2)CO_(2) substrate is involved in the adsorption reaction,and enough electrons are injected into the 2π*u orbital of CO_(2),leading to a V‐shaped CO_(2) molecular configuration and partial negative charge distribution.The V‐shaped CO_(2) further reduces the difficulty of the first hydrogenation reac‐tion step.The calculatedΔG of the first hydrogenation reaction on TM@Ti_(2)CO_(2) was significantly lower than that of the TM@Ti_(2)CS_(2) counterpart.However,the subsequent CO_(2) reduction pathways show that the UL of the potential determining step on TM@Ti_(2)CS_(2) is smaller than that of TM@Ti_(2)CO_(2).Combining the advantages of both TM@Ti_(2)CS_(2) and TM@Ti_(2)CO_(2),we designed a mixed functional group surface with–O and–S to anchor TM atoms.The results show that Cr atoms an‐chored on the surface of mixed functional groups exhibit high catalytic activity for the selective production of CH4.This study opens an exciting new avenue for the rational design of highly selec‐tive MXene‐based single‐atom CO_(2)RR electrocatalysts.

Transition‐metal‐atom‐pairs deposited on g‐CN monolayer for nitrogen reduction reaction:Density functional theory calculations

The development of highly active DFT catalysts for an electrocatalytic N_(2)reduction reaction(NRR)under mild conditions is a difficult challenge.In this study,a series of atom‐pair catalysts(APCs)for an NRR were fabricated using transition‐metal(TM)atoms(TM=Sc−Zn)doped into g‐CN monolayers.The electrochemical mechanism of APCs for an NRR has been reported by well‐defined density functional theory calculations.The calculated limiting potentials were−0.47 and−0.78 V for the Fe_(2)@CN and Co_(2)@CN catalysts,respectively.Owing to its high suppression of hydrogen evolution reactions,Co_(2)@CN is a superior electrocatalytic material for a N_(2)fixation.Stable Fe_(2)@CN may be a strongly attractive material for an NRR with a relatively low overpotential after an improvement in the selectivity.The two‐way charge transfer affirmed the donation‐acceptance procedure between N_(2)and Fe_(2)@CN or Co_(2)@CN,which play a crucial role in the activation of inert N≡N bonds.This study provides an in‐depth investigation into atom‐pair catalysts and will open up new avenues for highly efficient g‐CN‐based nanostructures for an NRR.

Single Pt Atoms Supported on Oxidized Graphene as a Promising Catalyst for Hydrolysis of Ammonia Borane

Based on density functional theory calculations,the full hydrolysis of per NH3BH3 molecule to produce three hydrogen molecules on single Pt atoms supported on oxidized graphene(Pt1/Gr-O)is investigated.It is suggested that the first hydrogen molecule is produced by the combination of two hydrogen atoms from two successive B-H bonds breaking.Then one H2O molecule attacks the left*BHNH3 group(*represents adsorbed state)to form*BH(H2O)NH3 and the elongated O-H bond is easily broken to produce*BH(OH)NH3.The second H2O molecule attacks*BH(OH)NH3 to form*BH(OH)(H2O)NH3 and the breaking of O-H bond pointing to the plane of Pt1/Gr-O results in the desorption of BH(OH)2NH3.The second hydrogen molecule is produced from two hydrogen atoms coming from two H2O molecules and Pt1/Gr-O is recovered after the releasing of hydrogen molecule.The third hydrogen molecule is generated by the further hydrolysis of BH(OH)2NH3 in water solution.The rate-limiting step of the whole process is the combination of one H2O molecule and*BHNH3 with an energy barrier of 16.1 kcal/mol.Thus,Pt1/Gr-O is suggested to be a promising catalyst for hydrolysis of NH3BH3 at room temperature.

Atomic Spacetime Model Based on Atomic AString Functions

A novel model of spacetime and fields atomization based on Atomic Series over finite Atomic AString Functions is offered. Formulated Atomization Theorems allow representing polynomials, analytic functions, and solutions of field equations including General Relativity via superposition of solitonic atoms which can be associated with flexible spacetime quantum, metriants, or elementary distortions. Spacetime is conceptualized as a lattice of flexible Atomic Solitons adjusting locations to reproduce different metrics and other physical fields. It may offer the variants of unified field theory based on Atomic Solitons where, like in string theory, fields become interconnected having a common mathematical ancestor.

Single‐atomic Co‐B_(2)N_(2)sites anchored on carbon nanotube arrays promote lithium polysulfide conversion in lithium-sulfur batteries

Due to low cost,high capacity,and high energy density,lithium–sulfur(Li–S)batteries have attracted much attention;however,their cycling performance was largely limited by the poor redox kinetics and low sulfur utilization.Herein,predicted by density functional theory calculations,single‐atomic Co‐B2N2 site‐imbedded boron and nitrogen co‐doped carbon nanotubes(SA‐Co/BNC)were designed to accomplish high sulfur loading,fast kinetic,and long service period Li–S batteries.Experiments proved that Co‐B2N2 atomic sites can effectively catalyze lithium polysulfide conversion.Therefore,the electrodes delivered a specific capacity of 1106 mAh g−1 at 0.2 C after 100 cycles and exhibited an outstanding cycle performance over 1000 cycles at 1 C with a decay rate of 0.032%per cycle.Our study offers a new strategy to couple the combined effect of nanocarriers and single‐atomic catalysts in novel coordination environments for high‐performance Li–S batteries.

Entanglement of two atoms interacting with a dissipative coherent cavity field without rotating wave approximation

Considering two identical two-level atoms interacting with a single-model dissipative coherent cavity field without rotating wave approximation, we explore the entanglement dynamics of the two atoms prepared in different states using concurrence. Interestingly, our results show that the entanglement between the two atoms that initially disentangled will come up to a large constant rapidly, and then keeps steady in the following time or always has its maximum when prepared in some special Bell states. The model considered in this study is a good candidate for quantum information processing especially for quantum computation as steady high-degree atomic entanglement resource obtained in dissipative cavit.

Atomic pair distribution function method development at the Shanghai Synchrotron Radiation Facility

The atomic pair distribution function（PDF） reveals the interatomic distance in a material directly in real-space. It is a very powerful method to characterize the local structure of materials. With the help of the third generation synchrotron facility and spallation neutron source worldwide, the PDF method has developed quickly both experimentally and theoretically in recent years. Recently this method was successfully implemented at the Shanghai Synchrotron Radiation Facility（SSRF）. The data quality is very high and this ensures the applicability of the method to study the subtle structural changes in complex materials. In this article, we introduce in detail this new method and show some experimental data we collected.

The role of copper in enhancing the performance of heteronuclear diatomic catalysts for the electrochemical CO_(2)conversion to C_(1) chemicals

Diatomic catalysts(DACs)with two adjacent metal atoms supported on graphene can offer diverse functionalities,overcoming the inherent limitations of single atom catalysts(SACs).In this study,density functional theory calculations were conducted to investigate the reactivity of the carbon dioxide(CO_(2))reduction reaction(CO_(2)RR)on metal sites of both DACs and SACs,as well as their synergistic effects on activity and selectivity.Calculation of the Gibbs free energies of CO_(2)RR and associated values of the limiting potentials to generate C_(1) products showed that Cu acts as a promoter rather than an active catalytic centre in the catalytic CO_(2)conversion on heteronuclear DACs(CuN_(4)-MN_(4)),improving the catalytic activity on the other metal compared to the related SAC MN_(4).Cu enhances the initial reduction of CO_(2)by promoting orbital hybridization between the key intermediate*COOH 2p-orbitals and the metals 3d-orbitals around the Fermi level.This degree of hybridization in the DACs CuN_(4)-MN_(4) decreases from Fe to Co,Ni,and Zn.Our work demonstrates how Cu regulates the CO_(2)RR performance of heteronuclear DACs,offering an effective approach to designing practical,stable,and high-performing diatomic catalysts for CO_(2)electroreduction.

Wave function for the squeezed atomic coherent state in entangled state representation and some of its applications

Based on the Einstein, Podolsky, and Rosen （EPR） entangled state representation, this paper introduces the wave function for the squeezed atomic coherent state （SACS）, which turns out to be just proportional to a single-variable ordinary Hermite polynomial of order 2j. As important applications of the wave function, the Wigner function of the SACS and its marginal distribution are obtained and the eigenproblems of some Hamiltonians for the generalized angular momentum system are solved.