Perfect anomalous reflections have been demonstrated in optical phase gradient metasurfaces(PGMs),but they suffer from single-frequency(narrow-band)response due to the intrinsic limitation of natural geometric periodi...Perfect anomalous reflections have been demonstrated in optical phase gradient metasurfaces(PGMs),but they suffer from single-frequency(narrow-band)response due to the intrinsic limitation of natural geometric periodicity.Here,we provide both numerical and analytical evidence that a depth gradient metasurface can achieve discrete ultra-broadband perfect anomalous reflection in the microwave range in the absence of geometric periodicity.Remarkably,by adjusting the operating frequency of the incident wave,the same effect can be steadily obtained via a physically equivalent phase periodicity in the PGM.Based on this mechanism,a perfect retroreflector with a broadband response ranging from 1 GHz to 40 GHz is realized.Our work has promising applications in communication,source tracking,and military satellites.展开更多
In this study,the wave motion in elastodynamics for unbounded media is modeled using an unsplit-field perfectly matched layer(PML)formulation that is solved by employing an isogeometric analysis(IGA).In the adopted co...In this study,the wave motion in elastodynamics for unbounded media is modeled using an unsplit-field perfectly matched layer(PML)formulation that is solved by employing an isogeometric analysis(IGA).In the adopted combination,the non-uniform rational B-spline(NURBS)functions are employed as basis functions.Moreover,the unbounded and artificial domains,defined in the PML method,are contained in a single patch domain.Based on the proposed scheme,the approximation of the geometry problem is set in a new scheme in which the PML’s absorbing and attenuation properties and the description of traveling waves can be represented.This includes a higher continuity and smoother approximation of the computed domain.As high-order NURBS basis functions are non-interpolatory,a penalty method is present to apply a time-dependent displacement load.The performance of the NURBS-based PML is analyzed through numerical examples for 1D and 2D domains,considering homogeneous and heterogeneous media.Further,we verify the long-time numerical stability of the present method.The developed method can be used to simulate hypothetical stratified domains commonly encountered in soil-structure interaction analyses.展开更多
Broadband and perfect terahertz absorber based on multilayer metamaterial using cross-ring patterned structures is proposed and investigated.The structure of the absorber is double absorption layers consisting of a ch...Broadband and perfect terahertz absorber based on multilayer metamaterial using cross-ring patterned structures is proposed and investigated.The structure of the absorber is double absorption layers consisting of a chromium cross ring and eight isosceles right triangles.The unique structure of the double absorbing layers excites the electric dipole multimode resonance,giving rise to high absorption performance.Meanwhile,the influence of construal parameters on absorber behavior is also discussed.The numerical results show that the absorption achieves over 90%ranging from 2.45 THz to 6.25 THz and 99%absorption in the range of 3.7—5.3 THz.The realization of broadband and perfect absorber is described using the impedance matching principle.It is obviously found that the absorber is insensitive to the high angle of incidence for both transverse electric(TE)and transverse magnetic(TM)polarizations.Compared with the former reports,this absorber has remarkable improved absorption efficiency and smaller period.The terahertz absorber may be found applications in the fields of energy capture and thermal detection.展开更多
Acoustic wave isolation and noise reduction are significant challenges in the fields of physics and various applications.Traditional noise-control devices are often hampered by substantial size limitations,and their o...Acoustic wave isolation and noise reduction are significant challenges in the fields of physics and various applications.Traditional noise-control devices are often hampered by substantial size limitations,and their operational efficacy is generally restricted to planar waveforms.In this study,we demonstrate perfect confinement of acoustic vortex waves using an acoustic metacage consisting of phase-gradient metasurfaces.By leveraging the parity-reversed diffraction rule of phase-gradient metasurfaces,the designed metacage exhibited remarkable capabilities for the perfect confinement of acoustic vortex waves,showing robust performance even in the presence of source offsets.These findings present a promising strategy for developing precise and adaptable acoustic confinement technologies.展开更多
1 Tuan Pham was feeling pretty good about himself as he approached the 12-mile mark of the Long Beach Half Marathon in Southern California.The run was the 47-year-old's seventh such event,and he couldn't wait ...1 Tuan Pham was feeling pretty good about himself as he approached the 12-mile mark of the Long Beach Half Marathon in Southern California.The run was the 47-year-old's seventh such event,and he couldn't wait to celebrate at the finish line with his teenage son,who had raced ahead.Pham took another step or two,and that was the last thing he could remember.展开更多
We theoretically and experimentally investigate thermal dynamics involved soliton microcomb generation in silicon oxynitride microresonators. Importantly, auxiliary laser heat balance scheme with flexible thermal mani...We theoretically and experimentally investigate thermal dynamics involved soliton microcomb generation in silicon oxynitride microresonators. Importantly, auxiliary laser heat balance scheme with flexible thermal manipulation is introduced to circumvent thermal instability and the intra-cavity temperature can be tuned from 60 ℃ to 41.5 ℃ via the commercial thermoelectric controller. As a result, various perfect soliton states with ultra-smooth spectral envelopes are observed on a well-designed and fabricated microresonator with homogeneous sidewall and thickness where spatial modes interaction and distortion are eliminated. The pre-reported spectral abrupt jumps due to mode hybridization are completely avoided and solitons tail oscillation vanishes simultaneously. This reported ideal coherent comb source without residual temporal and spectral noise will facilitate practical applications such as spectroscopy, ranging and astrocomb calibration.展开更多
In this paper, the attack detection problem is investigated for a class of closed-loop systems subjected to unknownbutbounded noises in the presence of stealthy attacks. The measurement outputs from the sensors are qu...In this paper, the attack detection problem is investigated for a class of closed-loop systems subjected to unknownbutbounded noises in the presence of stealthy attacks. The measurement outputs from the sensors are quantized before transmission.A specific type of perfect stealthy attack, which meets certain rather stringent conditions, is taken into account. Such attacks could be injected by adversaries into both the sensor-toestimator and controller-to-actuator channels, with the aim of disrupting the normal data flow. For the purpose of defending against these perfect stealthy attacks, a novel scheme based on watermarks is developed. This scheme includes the injection of watermarks(applied to data prior to quantization) and the recovery of data(implemented before the data reaches the estimator).The watermark-based scheme is designed to be both timevarying and hidden from adversaries through incorporating a time-varying and bounded watermark signal. Subsequently, a watermark-based attack detection strategy is proposed which thoroughly considers the characteristics of perfect stealthy attacks,thereby ensuring that an alarm is activated upon the occurrence of such attacks. An example is provided to demonstrate the efficacy of the proposed mechanism for detecting attacks.展开更多
Lithography is a Key enabling technique in modern micro/nano scale technology.Achieving the optimal trade-off between resolution,throughput,and cost remains a central focus in the ongoing development.However,current l...Lithography is a Key enabling technique in modern micro/nano scale technology.Achieving the optimal trade-off between resolution,throughput,and cost remains a central focus in the ongoing development.However,current lithographic techniques such as direct-write,projection,and extreme ultraviolet lithography achieve higher resolution at the expense of increased complexity in optical systems or the use of shorter-wavelength light sources,thus raising the overall cost of production.Here,we present a cost-effective and wafer-level perfect conformal contact lithography at the diffraction limit.By leveraging a transferable photoresist,the technique ensures optimal contact between the mask and photoresist with zero-gap,facilitating the transfer of patterns at the diffraction limit while maintaining high fidelity and uniformity across large wafers.This technique applies to a wide range of complex surfaces,including non-conductive glass surfaces,flexible substrates,and curved surfaces.The proposed technique expands the potential of contact photolithography for novel device architectures and practic al manufacturing processes.展开更多
Consider a graph G=(V,E).A perfect double Roman dominating function(PDRDF for short)is a function h:V→{0,1,2,3}that satisfies the condition∑_(y∈NG[x],h(y)≥1)h(y)=|{y∈NG(x):h(y)≥1}|+2 for any x∈V with h(x)≤1.Th...Consider a graph G=(V,E).A perfect double Roman dominating function(PDRDF for short)is a function h:V→{0,1,2,3}that satisfies the condition∑_(y∈NG[x],h(y)≥1)h(y)=|{y∈NG(x):h(y)≥1}|+2 for any x∈V with h(x)≤1.The weightω(h)of this function is∑_(y∈V)h(y).The perfect double Roman domination number(PDRD-number)of G,denoted byγ_(dR)^(p)(G),is defined as the minimum weight among all PDRDFs of G.This article presents a comprehensive analysis of the PDRD-number of connected cographs,demonstrating that it falls within the set{2,3,4,5,6}.Furthermore,it establishes that for any integer i≥7,there is a connected cograph G such that its PDRD-number is equal to i.展开更多
The nonsplitting perfectly matched layer （NPML） absorbing boundary condition （ABC） was first provided by Wang and Tang （2003） for the finite-difference simulation of elastic wave propagation in solids. In this p...The nonsplitting perfectly matched layer （NPML） absorbing boundary condition （ABC） was first provided by Wang and Tang （2003） for the finite-difference simulation of elastic wave propagation in solids. In this paper, the method is developed to extend the NPML to simulating elastic wave propagation in poroelastic media. Biot＇s equations are discretized and approximated to a staggered-grid by applying a fourth-order accurate central difference in space and a second-order accurate central difference in time. A cylindrical twolayer seismic model and a borehole model are chosen to validate the effectiveness of the NPML. The results show that the numerical solutions agree well with the solutions of the discrete wavenumber （DW） method.展开更多
Reverse-time migration in finite space requires effective boundary processing technology to eliminate the artificial truncation boundary effect in the migration result.On the basis of the elastic velocity-stress equat...Reverse-time migration in finite space requires effective boundary processing technology to eliminate the artificial truncation boundary effect in the migration result.On the basis of the elastic velocity-stress equations in vertical transversely isotropic media and the idea of the conventional split perfectly matched layer（PML）,the PML wave equations in reverse-time migration are derived in this paper and then the high order staggered grid discrete schemes are subsequently given.Aiming at the＂reflections＂from the boundary to the computational domain,as well as the effect of seismic event＇s abrupt changes at the two ends of the seismic array,the PML arrangement in reverse-time migration is given.The synthetic and real elastic,prestack,multi-component,reverse-time depth migration results demonstrate that this method has much better absorbing effects than other methods and the joint migration produces good imaging results.展开更多
The perfectly matched layer （PML） is a highly efficient absorbing boundary condition used for the numerical modeling of seismic wave equation. The article focuses on the application of this technique to finite-eleme...The perfectly matched layer （PML） is a highly efficient absorbing boundary condition used for the numerical modeling of seismic wave equation. The article focuses on the application of this technique to finite-element time-domain numerical modeling of elastic wave equation. However, the finite-element time-domain scheme is based on the second- order wave equation in displacement formulation. Thus, the first-order PML in velocity-stress formulation cannot be directly applied to this scheme. In this article, we derive the finite- element matrix equations of second-order PML in displacement formulation, and accomplish the implementation of PML in finite-element time-domain modeling of elastic wave equation. The PML has an approximate zero reflection coefficients for bulk and surface waves in the finite-element modeling of P-SV and SH wave propagation in the 2D homogeneous elastic media. The numerical experiments using a two-layer model with irregular topography validate the efficiency of PML in the modeling of seismic wave propagation in geological models with complex structures and heterogeneous media.展开更多
The perfect sequences are so ideal that all out-of-phase autocorrelation coefficients are zero, and if the sequences are used as the coding modulating signal for the phase-modulated radar, there will be no interferenc...The perfect sequences are so ideal that all out-of-phase autocorrelation coefficients are zero, and if the sequences are used as the coding modulating signal for the phase-modulated radar, there will be no interference of side lobes theoretically. However, it has been proved that there are no binary perfect sequences of period 4 〈 n ≤ 12100. Hence, the almost perfect sequences with all out-of-phase autocorrelation coefficients as zero except one are of great practice in engineering. Currently, the cyclic difference set is one of most effective tools to analyze the binary sequences with perfect periodic autocorrelation function. In this article, two characteristic formulas corresponding to the autocorrelation and symmetric structure of almost perfect sequences are calculated respectively. All almost perfect sequences with period n, which is a multiple of 4, can be figured out by the two formulas. Several almost perfect sequences with different periods have been hunted by the program based on the two formulas and then applied to the simulation program and practical application for ionospheric sounding.展开更多
This article presents very original and relatively brief or very brief proofs about of two famous problems: 1) Are there any odd perfect numbers? and 2) “Fermat’s last theorem: A new proof of theorem and its general...This article presents very original and relatively brief or very brief proofs about of two famous problems: 1) Are there any odd perfect numbers? and 2) “Fermat’s last theorem: A new proof of theorem and its generalization”. They are achieved with elementary mathematics. This is why these proofs can be easily understood by any mathematician or anyone who knows basic mathematics. Note that, in both problems, proof by contradiction was used as a method of proof. The first of the two problems to date has not been resolved. Its proof is completely original and was not based on the work of other researchers. On the contrary, it was based on a simple observation that all natural divisors of a positive integer appear in pairs. The aim of the first work is to solve one of the unsolved, for many years, problems of the mathematics which belong to the field of number theory. I believe that if the present proof is recognized by the mathematical community, it may signal a different way of solving unsolved problems. For the second problem, it is very important the fact that it is generalized to an arbitrarily large number of variables. This generalization is essentially a new theorem in the field of the number theory. To the classical problem, two solutions are given, which are presented in the chronological order in which they were achieved. Note that the second solution is very short and does not exceed one and a half pages. This leads me to believe that Fermat, as a great mathematician was not lying and that he had probably solved the problem, as he stated in his historic its letter, with a correspondingly brief solution. To win the bet on the question of whether Fermat was telling truth or lying, go immediately to the end of this article before the General Conclusions.展开更多
As an efficient artificial truncating boundary condition, conformal perfectly matched layer (CPML) is a kind of multilayer anisotropic absorbing media. To reduce computing effort of CPML, this article proposes a layer...As an efficient artificial truncating boundary condition, conformal perfectly matched layer (CPML) is a kind of multilayer anisotropic absorbing media. To reduce computing effort of CPML, this article proposes a layer-oriented element integration algorithm. In this algorithm, the relative dielectric constant and permeability are considered as constants for each the very thin monolayer of CPML, and the element integration of multilayer along the normal direction is substituted by the element integration of m...展开更多
Let n be a positive integer satisfying n >1; ω(n) denotes the number of distinct prime factors of n ; σ(n) denotes the sum of the positive divisors of n . If σ(n)=2n then n is said to be a perfect number and if ...Let n be a positive integer satisfying n >1; ω(n) denotes the number of distinct prime factors of n ; σ(n) denotes the sum of the positive divisors of n . If σ(n)=2n then n is said to be a perfect number and if σ(n)=kn(k≥3) then n is said to be a multiply perfect number. In this paper according to Euler theorem and Fermat theorem, we discuss the result of σ(n)=ω(n)n and prove that only n=2 3·3·5, 2 5·3·7, 2 5·3 3·5·7 satisfies σ(n)= ω(n) n(ω(n)≥3). ...展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.12274313,62275184,and 62411540033)Collaborative Innovation Center of Suzhou Nano Science and Technology,Suzhou Basic Research Project(Grant No.SJC2023003)+1 种基金the Gusu Leading Talent Plan for Scientific and Technological Innovation and Entrepreneurship(Grant No.ZXL2024400)the Priority Academic Program Development of Jiangsu Higher Education Institutions.
文摘Perfect anomalous reflections have been demonstrated in optical phase gradient metasurfaces(PGMs),but they suffer from single-frequency(narrow-band)response due to the intrinsic limitation of natural geometric periodicity.Here,we provide both numerical and analytical evidence that a depth gradient metasurface can achieve discrete ultra-broadband perfect anomalous reflection in the microwave range in the absence of geometric periodicity.Remarkably,by adjusting the operating frequency of the incident wave,the same effect can be steadily obtained via a physically equivalent phase periodicity in the PGM.Based on this mechanism,a perfect retroreflector with a broadband response ranging from 1 GHz to 40 GHz is realized.Our work has promising applications in communication,source tracking,and military satellites.
文摘In this study,the wave motion in elastodynamics for unbounded media is modeled using an unsplit-field perfectly matched layer(PML)formulation that is solved by employing an isogeometric analysis(IGA).In the adopted combination,the non-uniform rational B-spline(NURBS)functions are employed as basis functions.Moreover,the unbounded and artificial domains,defined in the PML method,are contained in a single patch domain.Based on the proposed scheme,the approximation of the geometry problem is set in a new scheme in which the PML’s absorbing and attenuation properties and the description of traveling waves can be represented.This includes a higher continuity and smoother approximation of the computed domain.As high-order NURBS basis functions are non-interpolatory,a penalty method is present to apply a time-dependent displacement load.The performance of the NURBS-based PML is analyzed through numerical examples for 1D and 2D domains,considering homogeneous and heterogeneous media.Further,we verify the long-time numerical stability of the present method.The developed method can be used to simulate hypothetical stratified domains commonly encountered in soil-structure interaction analyses.
基金supported by the National Natural Science Foundation of China(No.61505160)the Innovation Capability Support Program of Shaanxi(No.2018KJXX-042)+1 种基金the Natural Science Basic Research Program of Shaanxi(No.2019JM-084)the State Key Laboratory of Transient Optics and Photonics(No.SKLST202108)。
文摘Broadband and perfect terahertz absorber based on multilayer metamaterial using cross-ring patterned structures is proposed and investigated.The structure of the absorber is double absorption layers consisting of a chromium cross ring and eight isosceles right triangles.The unique structure of the double absorbing layers excites the electric dipole multimode resonance,giving rise to high absorption performance.Meanwhile,the influence of construal parameters on absorber behavior is also discussed.The numerical results show that the absorption achieves over 90%ranging from 2.45 THz to 6.25 THz and 99%absorption in the range of 3.7—5.3 THz.The realization of broadband and perfect absorber is described using the impedance matching principle.It is obviously found that the absorber is insensitive to the high angle of incidence for both transverse electric(TE)and transverse magnetic(TM)polarizations.Compared with the former reports,this absorber has remarkable improved absorption efficiency and smaller period.The terahertz absorber may be found applications in the fields of energy capture and thermal detection.
基金supported by the Undergraduate Training Program for Innovation and Entrepreneurship,Soochow University(Grant No.202410285001Z)the National Natural Science Foundation of China(Grant Nos.12274313 and 12374293)。
文摘Acoustic wave isolation and noise reduction are significant challenges in the fields of physics and various applications.Traditional noise-control devices are often hampered by substantial size limitations,and their operational efficacy is generally restricted to planar waveforms.In this study,we demonstrate perfect confinement of acoustic vortex waves using an acoustic metacage consisting of phase-gradient metasurfaces.By leveraging the parity-reversed diffraction rule of phase-gradient metasurfaces,the designed metacage exhibited remarkable capabilities for the perfect confinement of acoustic vortex waves,showing robust performance even in the presence of source offsets.These findings present a promising strategy for developing precise and adaptable acoustic confinement technologies.
文摘1 Tuan Pham was feeling pretty good about himself as he approached the 12-mile mark of the Long Beach Half Marathon in Southern California.The run was the 47-year-old's seventh such event,and he couldn't wait to celebrate at the finish line with his teenage son,who had raced ahead.Pham took another step or two,and that was the last thing he could remember.
基金supported by the National Natural Science Foundation of China(NSFC)(No.12204381,62205370)the fund of Natural Science Fundamental Research Program of Shaanxi Province(2023-JC-QN-0645)+1 种基金Startup Funding from Shanghai Institute of Optics and Fine Mechanics,Chinese Academy of Science(24JR521001)Shanghai Magnolia Talent Plan Pujiang Project(24PJD125).
文摘We theoretically and experimentally investigate thermal dynamics involved soliton microcomb generation in silicon oxynitride microresonators. Importantly, auxiliary laser heat balance scheme with flexible thermal manipulation is introduced to circumvent thermal instability and the intra-cavity temperature can be tuned from 60 ℃ to 41.5 ℃ via the commercial thermoelectric controller. As a result, various perfect soliton states with ultra-smooth spectral envelopes are observed on a well-designed and fabricated microresonator with homogeneous sidewall and thickness where spatial modes interaction and distortion are eliminated. The pre-reported spectral abrupt jumps due to mode hybridization are completely avoided and solitons tail oscillation vanishes simultaneously. This reported ideal coherent comb source without residual temporal and spectral noise will facilitate practical applications such as spectroscopy, ranging and astrocomb calibration.
基金supported in part by the National Natural Science Foundation of China(61933007,62273087,62273088,U21A2019)the Shanghai Pujiang Program of China(22PJ1400400)+2 种基金the Hainan Province Science and Technology Special Fund of China(ZDYF2022SHFZ105)the Royal Society of U.K.the Alexander von Humboldt Foundation of Germany
文摘In this paper, the attack detection problem is investigated for a class of closed-loop systems subjected to unknownbutbounded noises in the presence of stealthy attacks. The measurement outputs from the sensors are quantized before transmission.A specific type of perfect stealthy attack, which meets certain rather stringent conditions, is taken into account. Such attacks could be injected by adversaries into both the sensor-toestimator and controller-to-actuator channels, with the aim of disrupting the normal data flow. For the purpose of defending against these perfect stealthy attacks, a novel scheme based on watermarks is developed. This scheme includes the injection of watermarks(applied to data prior to quantization) and the recovery of data(implemented before the data reaches the estimator).The watermark-based scheme is designed to be both timevarying and hidden from adversaries through incorporating a time-varying and bounded watermark signal. Subsequently, a watermark-based attack detection strategy is proposed which thoroughly considers the characteristics of perfect stealthy attacks,thereby ensuring that an alarm is activated upon the occurrence of such attacks. An example is provided to demonstrate the efficacy of the proposed mechanism for detecting attacks.
基金supported by the National Key Research and Development Program of China (2022YFB4602600)National Natural Science Foundation of China (Grant Nos. 52425508 & 52221001)the Hunan Provincial Natural Science Foundation of China (2025JJ60286)。
文摘Lithography is a Key enabling technique in modern micro/nano scale technology.Achieving the optimal trade-off between resolution,throughput,and cost remains a central focus in the ongoing development.However,current lithographic techniques such as direct-write,projection,and extreme ultraviolet lithography achieve higher resolution at the expense of increased complexity in optical systems or the use of shorter-wavelength light sources,thus raising the overall cost of production.Here,we present a cost-effective and wafer-level perfect conformal contact lithography at the diffraction limit.By leveraging a transferable photoresist,the technique ensures optimal contact between the mask and photoresist with zero-gap,facilitating the transfer of patterns at the diffraction limit while maintaining high fidelity and uniformity across large wafers.This technique applies to a wide range of complex surfaces,including non-conductive glass surfaces,flexible substrates,and curved surfaces.The proposed technique expands the potential of contact photolithography for novel device architectures and practic al manufacturing processes.
基金Supported by the National Natural Science Foundation Youth Fund of China(Grant No.11701059)The Chongqing Natural Science Foundation Innovation and Development Joint Fund(Municipal Education Commission)(Grant No.CSTB2022NSCQ-LZX0003)The Open Research Fund of Key Laboratory of Nonlinear Analysis&Applications(Central China Normal University),Ministry of Education,P.R.China。
文摘Consider a graph G=(V,E).A perfect double Roman dominating function(PDRDF for short)is a function h:V→{0,1,2,3}that satisfies the condition∑_(y∈NG[x],h(y)≥1)h(y)=|{y∈NG(x):h(y)≥1}|+2 for any x∈V with h(x)≤1.The weightω(h)of this function is∑_(y∈V)h(y).The perfect double Roman domination number(PDRD-number)of G,denoted byγ_(dR)^(p)(G),is defined as the minimum weight among all PDRDFs of G.This article presents a comprehensive analysis of the PDRD-number of connected cographs,demonstrating that it falls within the set{2,3,4,5,6}.Furthermore,it establishes that for any integer i≥7,there is a connected cograph G such that its PDRD-number is equal to i.
基金This research was supported by Natural Science Foundation of China (No. 403740043).
文摘The nonsplitting perfectly matched layer （NPML） absorbing boundary condition （ABC） was first provided by Wang and Tang （2003） for the finite-difference simulation of elastic wave propagation in solids. In this paper, the method is developed to extend the NPML to simulating elastic wave propagation in poroelastic media. Biot＇s equations are discretized and approximated to a staggered-grid by applying a fourth-order accurate central difference in space and a second-order accurate central difference in time. A cylindrical twolayer seismic model and a borehole model are chosen to validate the effectiveness of the NPML. The results show that the numerical solutions agree well with the solutions of the discrete wavenumber （DW） method.
基金supported by the 863 Program(Grant No.2006AA06Z202)Open Fund of the Key Laboratory of Geophysical Exploration of CNPC(Grant No.GPKL0802)+1 种基金CNPC Young Innovation Fund(Grant No.05E7028)the Program for New Century Excellent Talents in University(Grant No.NCET-07-0845)
文摘Reverse-time migration in finite space requires effective boundary processing technology to eliminate the artificial truncation boundary effect in the migration result.On the basis of the elastic velocity-stress equations in vertical transversely isotropic media and the idea of the conventional split perfectly matched layer（PML）,the PML wave equations in reverse-time migration are derived in this paper and then the high order staggered grid discrete schemes are subsequently given.Aiming at the＂reflections＂from the boundary to the computational domain,as well as the effect of seismic event＇s abrupt changes at the two ends of the seismic array,the PML arrangement in reverse-time migration is given.The synthetic and real elastic,prestack,multi-component,reverse-time depth migration results demonstrate that this method has much better absorbing effects than other methods and the joint migration produces good imaging results.
基金sponsored by the National Natural Science Foundation of China Research(Grant No.41274138)the Science Foundation of China University of Petroleum(Beijing)(No.KYJJ2012-05-02)
文摘The perfectly matched layer （PML） is a highly efficient absorbing boundary condition used for the numerical modeling of seismic wave equation. The article focuses on the application of this technique to finite-element time-domain numerical modeling of elastic wave equation. However, the finite-element time-domain scheme is based on the second- order wave equation in displacement formulation. Thus, the first-order PML in velocity-stress formulation cannot be directly applied to this scheme. In this article, we derive the finite- element matrix equations of second-order PML in displacement formulation, and accomplish the implementation of PML in finite-element time-domain modeling of elastic wave equation. The PML has an approximate zero reflection coefficients for bulk and surface waves in the finite-element modeling of P-SV and SH wave propagation in the 2D homogeneous elastic media. The numerical experiments using a two-layer model with irregular topography validate the efficiency of PML in the modeling of seismic wave propagation in geological models with complex structures and heterogeneous media.
基金This poject was supported by the National Natural Science Foundation of China (40474066).
文摘The perfect sequences are so ideal that all out-of-phase autocorrelation coefficients are zero, and if the sequences are used as the coding modulating signal for the phase-modulated radar, there will be no interference of side lobes theoretically. However, it has been proved that there are no binary perfect sequences of period 4 〈 n ≤ 12100. Hence, the almost perfect sequences with all out-of-phase autocorrelation coefficients as zero except one are of great practice in engineering. Currently, the cyclic difference set is one of most effective tools to analyze the binary sequences with perfect periodic autocorrelation function. In this article, two characteristic formulas corresponding to the autocorrelation and symmetric structure of almost perfect sequences are calculated respectively. All almost perfect sequences with period n, which is a multiple of 4, can be figured out by the two formulas. Several almost perfect sequences with different periods have been hunted by the program based on the two formulas and then applied to the simulation program and practical application for ionospheric sounding.
文摘This article presents very original and relatively brief or very brief proofs about of two famous problems: 1) Are there any odd perfect numbers? and 2) “Fermat’s last theorem: A new proof of theorem and its generalization”. They are achieved with elementary mathematics. This is why these proofs can be easily understood by any mathematician or anyone who knows basic mathematics. Note that, in both problems, proof by contradiction was used as a method of proof. The first of the two problems to date has not been resolved. Its proof is completely original and was not based on the work of other researchers. On the contrary, it was based on a simple observation that all natural divisors of a positive integer appear in pairs. The aim of the first work is to solve one of the unsolved, for many years, problems of the mathematics which belong to the field of number theory. I believe that if the present proof is recognized by the mathematical community, it may signal a different way of solving unsolved problems. For the second problem, it is very important the fact that it is generalized to an arbitrarily large number of variables. This generalization is essentially a new theorem in the field of the number theory. To the classical problem, two solutions are given, which are presented in the chronological order in which they were achieved. Note that the second solution is very short and does not exceed one and a half pages. This leads me to believe that Fermat, as a great mathematician was not lying and that he had probably solved the problem, as he stated in his historic its letter, with a correspondingly brief solution. To win the bet on the question of whether Fermat was telling truth or lying, go immediately to the end of this article before the General Conclusions.
基金National Natural Science Foundation of China (10477018) Science and Technology Innovation Foundation of North-western Polytechnical University (W016143)
文摘As an efficient artificial truncating boundary condition, conformal perfectly matched layer (CPML) is a kind of multilayer anisotropic absorbing media. To reduce computing effort of CPML, this article proposes a layer-oriented element integration algorithm. In this algorithm, the relative dielectric constant and permeability are considered as constants for each the very thin monolayer of CPML, and the element integration of multilayer along the normal direction is substituted by the element integration of m...
文摘Let n be a positive integer satisfying n >1; ω(n) denotes the number of distinct prime factors of n ; σ(n) denotes the sum of the positive divisors of n . If σ(n)=2n then n is said to be a perfect number and if σ(n)=kn(k≥3) then n is said to be a multiply perfect number. In this paper according to Euler theorem and Fermat theorem, we discuss the result of σ(n)=ω(n)n and prove that only n=2 3·3·5, 2 5·3·7, 2 5·3 3·5·7 satisfies σ(n)= ω(n) n(ω(n)≥3). ...
