Platinum-based(Pt)catalysts are notoriously susceptible to deactivation in industrial chemical processes due to carbon monoxide(CO)poisoning.Overcoming this poisoning deactivation of Pt-based catalysts while enhancing...Platinum-based(Pt)catalysts are notoriously susceptible to deactivation in industrial chemical processes due to carbon monoxide(CO)poisoning.Overcoming this poisoning deactivation of Pt-based catalysts while enhancing their catalytic activity,selectivity,and durability remains a major challenge.Herein,we propose a strategy to enhance the CO tolerance of Pt clusters(Pt_n)by introducing neighboring functionalized vip single atoms(such as Fe,Co,Ni,Cu,Sb,and Bi).Among them,antimony(Sb)single atoms(SAs)exhibit significant performance enhancement,achieving 99%CO selectivity and 33.6%CO_(2)conversion at 450℃,Experimental results and density functional theory(DFT)calculations indicate the optimization arises from the electronic interaction between neighboring functionalized Sb SAs and Pt clusters,leading to optimal 5d electron redistribution in Pt clusters compared to other functionalized vip single atoms.The redistribution of 5d electrons weaken both theσdonation andπbackdonation interactions,resulting in a weakened bond strength with CO and enhancing catalyst activity and selectivity.In situ environmental transmission electron microscopy(ETEM)further demonstrates the exception thermal stability of the catalyst,even under H_(2)at 700℃.Notably,the functionalized Sb SAs also improve CO tolerance in various heterogenous catalysts,including Co/CeO_(2),Ni/CeO_(2),Pt/Al_(2)O_(3),and Pt/CeO_(2)-C.This finding provides an effective approach to overcome the primary challenge of CO poisoning in Pt-based catalysts,making their broader applications in various industrial catalysts.展开更多
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 t...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.展开更多
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 solutio...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.展开更多
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...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.展开更多
In present article a number of results are described in a systematic way concerning both signal and image processing problems with respect to atomic functions theory and Prouhet-Tbue-Morse sequence.
This paper presents exponential Atomic Basis Functions(ABF),which are called Eup(x;w).These functions are infinitely differentiable finite functions that unlike algebraic up(x)basis functions,have an unspecified param...This paper presents exponential Atomic Basis Functions(ABF),which are called Eup(x;w).These functions are infinitely differentiable finite functions that unlike algebraic up(x)basis functions,have an unspecified parameter-frequency w.Numerical experiments show that this class of atomic functions has good approximation properties,especially in the case of large gradients(Gibbs phenomenon).In this work,for the first time,the properties of exponential ABF are thoroughly investigated and the expression for calculating the value of the basis function at an arbitrary point of the domain is given in a form suitable for implementation in numerical analysis.Application of these basis functions is shown in the function approximation example.The procedure for determining the best frequencies,which gives the smallest approximation error in terms of the least squares method,is presented.展开更多
The possibility of using finite atomic functions of Kravchenko-Rvachev for description of the laws of distribution of the refractive index of the troposphere,the intensity of the scattering from the sea,seasonal behav...The possibility of using finite atomic functions of Kravchenko-Rvachev for description of the laws of distribution of the refractive index of the troposphere,the intensity of the scattering from the sea,seasonal behavior unit radar cross section(RCS)of land areas with vegetation covering,as well as the spectrum of electromagnetic spikes of lithospheric origin is considered.展开更多
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 m...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.展开更多
Based on theorems, the Atomic AString Functions theory, evolving since the 1970s, is introduced into Quantum Mechanics to represent a wave function via the shifts and stretches of smooth finite Atomic Function pulses/...Based on theorems, the Atomic AString Functions theory, evolving since the 1970s, is introduced into Quantum Mechanics to represent a wave function via the shifts and stretches of smooth finite Atomic Function pulses/solitonic atoms. It leads to a novel ‘atomic interpretation’ where wave functions become the superpositions of localized Atomic Wave Functions, which can also describe collapsed wave functions, represent Gaussians, uphold Heisenberg’s uncertainly principle, and a more generic concept of Atomic Harmonic Oscillator. Atomic Functions can solve the boundary wave function discontinuity problem for particle-in-a-box and other solutions by introducing atomic wave packets. It highlights some limitations of the Schrödinger equation, yielding harmonic representations that may not be flexible enough to satisfy complex boundary conditions. The theory follows more generic research on Atomic Spacetime, quantum gravity, and field theories to derive common mathematical blocks of unified fields similar to loop quantum gravity and strings theories.展开更多
Raoultian activity coefficients γ0c of C in infinitely dilute Fe-C binary melts at temperatures of 1833, 1873, 1923, and 1973 K have been determined from the converted mass action concentrations Nc of C in Fe-C binar...Raoultian activity coefficients γ0c of C in infinitely dilute Fe-C binary melts at temperatures of 1833, 1873, 1923, and 1973 K have been determined from the converted mass action concentrations Nc of C in Fe-C binary melts by the developed AMCT-Ni model based on the atom-molecule coexistence theory （AMCT）. The obtained expression of γ0c by the developed AMCT-Ni model has been evaluated to be accurate based on the reported ones from the literature. Meanwhile, three activity coefficients γc,f%,c, andfH,c of C coupled with activity aR,C or a%,c or aH,c have been obtained by the developed AMCT-Ni model and assessed through comparing with the predicted ones by other models from the literature. The first-order activity interaction coefficients ec, ec, and hcc related to γc f%,c, and fH,c are also determined and assessed in comparison with the reported ones from the literature. Furthermore, the integral molar mixing thermodynamic functions such as AmixHm,Fe-C, △mix-Sm,Fe-C, and △mixGm,Fe-C of Fe-C binary melts over a temperature range from 1833 to 1973 K have been determined and evaluated to be valid based on the determined ones from the literature.展开更多
Three novel branched polyamines N,N,N’,N’-tetrakis-[3((pyridine-2-methyl)-amine) propyl]-1,4- butanediamine (1), N,N,N’,N’-tetrakis-[N-((2-methylpyridine)ethyl)propanamide]ethylenediamine (2) and N,N,N’,N’-tetra...Three novel branched polyamines N,N,N’,N’-tetrakis-[3((pyridine-2-methyl)-amine) propyl]-1,4- butanediamine (1), N,N,N’,N’-tetrakis-[N-((2-methylpyridine)ethyl)propanamide]ethylenediamine (2) and N,N,N’,N’-tetrakis-[3((2-hidroxibenziliden)-amine)propyl]-1,4-butanediamine (3), were synthesized starting from 2-pyridinecarboxaldeyde with DAB-Am-4 for 1, PAMAM G0 for 2 and from salicylaldehyde with DAB-Am-4 for 3. The pathway reactions have been proposed by 1H-NMR, IR and Atomic Absorption Spectroscopy. The optimal reaction time was set by IR spectroscopy following aldehyde? peak modification. 1 and 2 were obtained as both hydrochlorides and as free amines and 3 only as free imine. These polyamines were characterized by UV-Vis, IR, 1H-NMR and 13C-NMR and Mass Spectrometry.展开更多
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 ...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.展开更多
The following article has been retracted due to the investigation of complaints received against it. The Editorial Board found that substantial portions of the text came from other published papers. The scientific com...The following article has been retracted due to the investigation of complaints received against it. The Editorial Board found that substantial portions of the text came from other published papers. The scientific community takes a very strong view on this matter, and the Health treats all unethical behavior such as plagiarism seriously. This paper published in Vol.3 No. 4, 334-339, 2012, has been removed from this site.展开更多
The reactions of anionic zirconium oxide clusters ZrxOy- with C2H6 and C4H10 are investi-gated by a time of flight mass spectrometer coupled with a laser vaporization cluster source.Hydrogen containing products Zr2O5H...The reactions of anionic zirconium oxide clusters ZrxOy- with C2H6 and C4H10 are investi-gated by a time of flight mass spectrometer coupled with a laser vaporization cluster source.Hydrogen containing products Zr2O5H- and Zr3O7H- are observed after the reaction. Den-sity functional theory calculations indicate that the hydrogen abstraction is favorable in the reaction of Zr2O5- with C2H6, which supports that the observed Zr2O5H- and Zr3O7H- are due to hydrogen atom abstraction from the alkane molecules. This work shows a newpossible pathway in the reaction of zirconium oxide cluster anions with alkane molecules.展开更多
The modified atomic transformations are constructed and proved. On their basis the new complex analytic wavelets are obtained. The proof of the Fourier transforms existence in L~ and L2 on the basis of the theory of a...The modified atomic transformations are constructed and proved. On their basis the new complex analytic wavelets are obtained. The proof of the Fourier transforms existence in L~ and L2 on the basis of the theory of atomic functions （AF） are presented. The numerical experiments of digital time series processing and physical analysis of the results confirm the efficiency of the proposed transforms.展开更多
On the basis of modified atomic transformations the new WA-systems of Kravchenko functions are constructed.As an example the digital processing of time series of the various physical nature processing is considered.Th...On the basis of modified atomic transformations the new WA-systems of Kravchenko functions are constructed.As an example the digital processing of time series of the various physical nature processing is considered.The numerical experiments and physical analysis of the results confirm the efficiency of the proposed WA-systems of Kravchenko functions.展开更多
基金financially supported by the Shanghai RisingStar Program(No.23QA1403700)the National Natural Science Foundation of China(NSFC,Grant No.U2230102)+1 种基金the sponsored by National Key Research and Development Program of China(No.2021YFB3502200)the Shanghai Technical Service Center of Science and Engineering Computing,Shanghai University.
文摘Platinum-based(Pt)catalysts are notoriously susceptible to deactivation in industrial chemical processes due to carbon monoxide(CO)poisoning.Overcoming this poisoning deactivation of Pt-based catalysts while enhancing their catalytic activity,selectivity,and durability remains a major challenge.Herein,we propose a strategy to enhance the CO tolerance of Pt clusters(Pt_n)by introducing neighboring functionalized vip single atoms(such as Fe,Co,Ni,Cu,Sb,and Bi).Among them,antimony(Sb)single atoms(SAs)exhibit significant performance enhancement,achieving 99%CO selectivity and 33.6%CO_(2)conversion at 450℃,Experimental results and density functional theory(DFT)calculations indicate the optimization arises from the electronic interaction between neighboring functionalized Sb SAs and Pt clusters,leading to optimal 5d electron redistribution in Pt clusters compared to other functionalized vip single atoms.The redistribution of 5d electrons weaken both theσdonation andπbackdonation interactions,resulting in a weakened bond strength with CO and enhancing catalyst activity and selectivity.In situ environmental transmission electron microscopy(ETEM)further demonstrates the exception thermal stability of the catalyst,even under H_(2)at 700℃.Notably,the functionalized Sb SAs also improve CO tolerance in various heterogenous catalysts,including Co/CeO_(2),Ni/CeO_(2),Pt/Al_(2)O_(3),and Pt/CeO_(2)-C.This finding provides an effective approach to overcome the primary challenge of CO poisoning in Pt-based catalysts,making their broader applications in various industrial catalysts.
基金Project supported by the National Natural Science Foundation of China(Grant No.U1232112)the National Key Basic Research Program of China(Grant No.2012CB825700)
文摘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.
文摘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.
基金Project supported by the Foundation for Key Program of Ministry of Education (Nos.108033 and 107119)State Key Development Program for Basic Research of China (No.2009CB219801)+4 种基金the National High Technology Research and Development Program of China (No.2008AA05Z302)NNSFC (No.50976032)NSF of Beijing (No.3101001)the Specialized Basic Research Fund for Center Higher Education (No.09ZG03)Doctor Fund of North China Electric Power University (No.200822015)
文摘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.
基金Russian Foundation for Basic Research(No.130212065)
文摘In present article a number of results are described in a systematic way concerning both signal and image processing problems with respect to atomic functions theory and Prouhet-Tbue-Morse sequence.
文摘This paper presents exponential Atomic Basis Functions(ABF),which are called Eup(x;w).These functions are infinitely differentiable finite functions that unlike algebraic up(x)basis functions,have an unspecified parameter-frequency w.Numerical experiments show that this class of atomic functions has good approximation properties,especially in the case of large gradients(Gibbs phenomenon).In this work,for the first time,the properties of exponential ABF are thoroughly investigated and the expression for calculating the value of the basis function at an arbitrary point of the domain is given in a form suitable for implementation in numerical analysis.Application of these basis functions is shown in the function approximation example.The procedure for determining the best frequencies,which gives the smallest approximation error in terms of the least squares method,is presented.
文摘The possibility of using finite atomic functions of Kravchenko-Rvachev for description of the laws of distribution of the refractive index of the troposphere,the intensity of the scattering from the sea,seasonal behavior unit radar cross section(RCS)of land areas with vegetation covering,as well as the spectrum of electromagnetic spikes of lithospheric origin is considered.
基金supported through Project KK.01.1.1.02.0027a project co-financed by the Croatian Government and the European Union through the European Regional Development Fund-the Competitiveness and Cohesion Operational Programme.
文摘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.
文摘Based on theorems, the Atomic AString Functions theory, evolving since the 1970s, is introduced into Quantum Mechanics to represent a wave function via the shifts and stretches of smooth finite Atomic Function pulses/solitonic atoms. It leads to a novel ‘atomic interpretation’ where wave functions become the superpositions of localized Atomic Wave Functions, which can also describe collapsed wave functions, represent Gaussians, uphold Heisenberg’s uncertainly principle, and a more generic concept of Atomic Harmonic Oscillator. Atomic Functions can solve the boundary wave function discontinuity problem for particle-in-a-box and other solutions by introducing atomic wave packets. It highlights some limitations of the Schrödinger equation, yielding harmonic representations that may not be flexible enough to satisfy complex boundary conditions. The theory follows more generic research on Atomic Spacetime, quantum gravity, and field theories to derive common mathematical blocks of unified fields similar to loop quantum gravity and strings theories.
文摘Raoultian activity coefficients γ0c of C in infinitely dilute Fe-C binary melts at temperatures of 1833, 1873, 1923, and 1973 K have been determined from the converted mass action concentrations Nc of C in Fe-C binary melts by the developed AMCT-Ni model based on the atom-molecule coexistence theory （AMCT）. The obtained expression of γ0c by the developed AMCT-Ni model has been evaluated to be accurate based on the reported ones from the literature. Meanwhile, three activity coefficients γc,f%,c, andfH,c of C coupled with activity aR,C or a%,c or aH,c have been obtained by the developed AMCT-Ni model and assessed through comparing with the predicted ones by other models from the literature. The first-order activity interaction coefficients ec, ec, and hcc related to γc f%,c, and fH,c are also determined and assessed in comparison with the reported ones from the literature. Furthermore, the integral molar mixing thermodynamic functions such as AmixHm,Fe-C, △mix-Sm,Fe-C, and △mixGm,Fe-C of Fe-C binary melts over a temperature range from 1833 to 1973 K have been determined and evaluated to be valid based on the determined ones from the literature.
文摘Three novel branched polyamines N,N,N’,N’-tetrakis-[3((pyridine-2-methyl)-amine) propyl]-1,4- butanediamine (1), N,N,N’,N’-tetrakis-[N-((2-methylpyridine)ethyl)propanamide]ethylenediamine (2) and N,N,N’,N’-tetrakis-[3((2-hidroxibenziliden)-amine)propyl]-1,4-butanediamine (3), were synthesized starting from 2-pyridinecarboxaldeyde with DAB-Am-4 for 1, PAMAM G0 for 2 and from salicylaldehyde with DAB-Am-4 for 3. The pathway reactions have been proposed by 1H-NMR, IR and Atomic Absorption Spectroscopy. The optimal reaction time was set by IR spectroscopy following aldehyde? peak modification. 1 and 2 were obtained as both hydrochlorides and as free amines and 3 only as free imine. These polyamines were characterized by UV-Vis, IR, 1H-NMR and 13C-NMR and Mass Spectrometry.
基金Project supported by the Natural Science Foundation of Shandong Province, China (Grant No. Y2008A23)
文摘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.
文摘The following article has been retracted due to the investigation of complaints received against it. The Editorial Board found that substantial portions of the text came from other published papers. The scientific community takes a very strong view on this matter, and the Health treats all unethical behavior such as plagiarism seriously. This paper published in Vol.3 No. 4, 334-339, 2012, has been removed from this site.
基金This work was supported by the Chinese Academy of Sciences （Hundred Talents Fund）, the National Natural Science Foundation of China （No.20703048 and No.20803083）, and the Center of Molecular Science Foundation of Institute of Chemistry, Chinese Academy of Sciences （No.CMS-LX200902）.
文摘The reactions of anionic zirconium oxide clusters ZrxOy- with C2H6 and C4H10 are investi-gated by a time of flight mass spectrometer coupled with a laser vaporization cluster source.Hydrogen containing products Zr2O5H- and Zr3O7H- are observed after the reaction. Den-sity functional theory calculations indicate that the hydrogen abstraction is favorable in the reaction of Zr2O5- with C2H6, which supports that the observed Zr2O5H- and Zr3O7H- are due to hydrogen atom abstraction from the alkane molecules. This work shows a newpossible pathway in the reaction of zirconium oxide cluster anions with alkane molecules.
文摘The modified atomic transformations are constructed and proved. On their basis the new complex analytic wavelets are obtained. The proof of the Fourier transforms existence in L~ and L2 on the basis of the theory of atomic functions （AF） are presented. The numerical experiments of digital time series processing and physical analysis of the results confirm the efficiency of the proposed transforms.
基金Russian Foundation for Basic Research(RFBR)(No.12-02-90425)
文摘On the basis of modified atomic transformations the new WA-systems of Kravchenko functions are constructed.As an example the digital processing of time series of the various physical nature processing is considered.The numerical experiments and physical analysis of the results confirm the efficiency of the proposed WA-systems of Kravchenko functions.
