The minimal widths of three bounded subsets of the unit sphere associated to a unit vector in a normed linear space are studied,and three related geometric constants are introduced.New characterizations of inner produ...The minimal widths of three bounded subsets of the unit sphere associated to a unit vector in a normed linear space are studied,and three related geometric constants are introduced.New characterizations of inner product spaces are also presented.From the perspective of minimal width,strongε-symmetry of Birkhoff orthogonality is introduced,and its relation toε-symmetry of Birkhoff orthogonality is shown.Unlike most of the existing parameters of the underlying space,these new constants are full dimensional in nature.展开更多
In this paper,some refinements of norm equalities and inequalities of combination of two orthogonal projections are established.We use certain norm inequalities for positive contraction operator to establish norm ineq...In this paper,some refinements of norm equalities and inequalities of combination of two orthogonal projections are established.We use certain norm inequalities for positive contraction operator to establish norm inequalities for combination of orthogonal projections on a Hilbert space.Furthermore,we give necessary and sufficient conditions under which the norm of the above combination of o`rthogonal projections attains its optimal value.展开更多
Based on numerical solutions of the time-dependent Schr ¨odinger equation, we theoretically investigate the photoelectron spectrum of hydrogen atoms ionized by a pair of ultrashort, intense, and orthogonally pola...Based on numerical solutions of the time-dependent Schr ¨odinger equation, we theoretically investigate the photoelectron spectrum of hydrogen atoms ionized by a pair of ultrashort, intense, and orthogonally polarized laser pulses with a relative time delay in a pump–probe configuration. The pump pulse resonantly excites electrons from the 1s and 2p levels,inducing Rabi oscillations. The resulting dynamically enhanced Autler–Townes(AT) splitting is observed in the photoelectron energy spectrum upon interaction with the second probe pulse. In contrast to the previous parallel-polarization scheme, the proposed orthogonal-polarization configuration enables the resolution of dynamically enhanced AT splitting over a considerably wider range of probe photon energies.展开更多
Electron dynamics during non-sequential double ionization(NSDI) is one of the most attractive areas of research in the field of laser–atom or laser–molecule interaction. Based on the classic two-dimensional model, w...Electron dynamics during non-sequential double ionization(NSDI) is one of the most attractive areas of research in the field of laser–atom or laser–molecule interaction. Based on the classic two-dimensional model, we study the process of NSDI of argon atoms driven by a few-cycle orthogonal two-color laser field composed of 800 nm and 400 nm laser pulses. By changing the relative phase of the two laser pulses, a localized enhancement of NSDI yield is observed at 0.5πand 1.5π, which could be attributed to a rapid and substantial increase in the number of electrons returning to the parent ion within extremely short time intervals at these specific phases. Through the analysis of the electron–electron momentum correlations within different time windows of NSDI events and the angular distributions of emitted electrons in different channels, we observe a more pronounced electron–electron correlation phenomenon in the recollision-induced ionization(RII) channel. This is attributed to the shorter delay time in the RII channel.展开更多
Orthogonal matrices have become a vital means for coding and signal processing owing to their unique distributional properties.Although orthogonal matrices based on amplitude or phase combinations have been extensivel...Orthogonal matrices have become a vital means for coding and signal processing owing to their unique distributional properties.Although orthogonal matrices based on amplitude or phase combinations have been extensively explored,the orthogonal matrix of polarization combinations(OMPC)is a novel,relatively unexplored concept.Herein,we propose a method for constructing OMPCs of any dimension encompassing 4n(where n is 1,2,4,8,…)mutually orthogonal 2ncomponent polarization combinations.In the field of holography,the integration of polarization multiplexing techniques with polarization-sensitive materials is expected to emerge as a groundbreaking approach for multichannel hologram multiplexing,offering considerable enhancements in data storage capacity and security.A multidimensional OMPC enables the realization of multichannel multiplexing and dynamical modulation of information in polarization holographic recording.Despite consolidating all information into a single position within the material,we effectively avoided extraneous crosstalk during the reconstruction process.Our results show that achieving four distinct holographic images individually and simultaneously depends on the polarization combination represented by the incident wave.This discovery opens up a new avenue for achieving highly holographic information storage and dynamically displayed information,harnessing the potential of OMPC to expand the heretofore limited dimensionality of orthogonal polarization.展开更多
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)la...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.展开更多
Influence of multiple structural parameters on the performance of a gun launch system driven by highpressure reactive gases is important for structural design and performance adjustment.A coupled lumped parameter mode...Influence of multiple structural parameters on the performance of a gun launch system driven by highpressure reactive gases is important for structural design and performance adjustment.A coupled lumped parameter model was utilized to predict the propellant combustion,and a dynamic finite element method was applied to approximate the mechanical interactions between the projectile and the barrel.The combustion and the mechanical interactions were coupled through a user subroutine interface in ABAQUS.The correctness and the capability of the finite element approximations in capturing small structural changes were validated by comparing predicted resistance with experiments.Based on the coupled model,the influence of structural parameters of a medium-caliber gun on the system performance was investigated.In order to reduce the research costs,orthogonal tests were designed to investigate the comprehensive effects of the parameters.According to statistical analysis,the important order of the structural parameters on the launching process was obtained.The results indicate that the influence of the width of the rotating band stands out among the studied parameters in the gun.The work provides a method to investigate the influence of multiple parameters on system performance and gives guidance for controlling the system performance.展开更多
We study the parameter estimation of a nonlinear chaotic system,which can be essentially formulated as a multidimensional optimization problem.In this paper,an orthogonal learning cuckoo search algorithm is used to es...We study the parameter estimation of a nonlinear chaotic system,which can be essentially formulated as a multidimensional optimization problem.In this paper,an orthogonal learning cuckoo search algorithm is used to estimate the parameters of chaotic systems.This algorithm can combine the stochastic exploration of the cuckoo search and the exploitation capability of the orthogonal learning strategy.Experiments are conducted on the Lorenz system and the Chen system.The proposed algorithm is used to estimate the parameters for these two systems.Simulation results and comparisons demonstrate that the proposed algorithm is better or at least comparable to the particle swarm optimization and the genetic algorithm when considering the quality of the solutions obtained.展开更多
An orthogonal design was used to optimize SSR-PCR amplification system using Panax ginseng genomic DNA as template. Four levels of five factors （DNA template, Taq DNA polymerase, Mg^2＋, primer, and dNTP） and anneal...An orthogonal design was used to optimize SSR-PCR amplification system using Panax ginseng genomic DNA as template. Four levels of five factors （DNA template, Taq DNA polymerase, Mg^2＋, primer, and dNTP） and annealing temperature have been tested separately in this system. The results demonstrated the reaction efficiency was affected by these factors. Based on the results, a stable, productive and reproducible PCR system and cycling program for amplifying a ginseng SSR locus were obtained： 20 μL system containing 1.0 U Taq DNA polymerase, 2.0 mmol·L^-1 Mg^2＋, 0.2 mmol·L^-1 dNTPs, 0.3 μmol·L^-1 SSR primer, 60 ng· μla^-1 DNA template, performed with a program of 94℃ for 5 min, 94℃ for 30 s, annealing at 56.3℃ for 30 s, 72℃ for 1 min, 37 cycles, finishing at 72℃ for 7 min, and storing at 4℃.展开更多
The polarization switching（PS） and polarization bistability（PB） characteristics of a 1550-nm vertical-cavity surfaceemitting laser（VCSEL） subjected to orthogonal optical injection are systematically investigated...The polarization switching（PS） and polarization bistability（PB） characteristics of a 1550-nm vertical-cavity surfaceemitting laser（VCSEL） subjected to orthogonal optical injection are systematically investigated.The simulated results show that the PS and polarization-resolved nonlinear dynamical states of the VCSEL are critically dependent on the changing paths of the injected power.The polarization dynamics for different scanning directions of the injected power is presented to explain the polarization evolution during the formation of PS.In the case of forward scanning injected power,with the increase of frequency detuning level between the VCSEL and the injected light,the injected power required for PS gradually increases for negative frequency detuning but exhibits fluctuations for positive frequency detuning.In the case of reversely scanning injected power,the injected power required for PS displays fluctuant changes within the whole frequency detuning range.Specifically,PS may disappear under certain negative frequency detuning and large bias current.Furthermore,the hysteresis width as a function of the frequency detuning is calculated,and the regions for the appearance and disappearance of PB have been determined in the parameter space of the bias current and frequency detuning.展开更多
Let G be a graph and f an integer-valued function defined on V(G). It is proved that every (0,mf - m+1)-graph G has a (0,f)-factorization orthogonal to any given subgraph with m edges.
Let G be a bipartite graph with vertex set V(G) and edge set E(G), and let g and f be two positive integer-valued functions defined on V(G) such that g(x) ≤ f(x) for every vertex x of V(G). Then a (g, f)-factor of G ...Let G be a bipartite graph with vertex set V(G) and edge set E(G), and let g and f be two positive integer-valued functions defined on V(G) such that g(x) ≤ f(x) for every vertex x of V(G). Then a (g, f)-factor of G is a spanning subgraph H of G such that g(x) ≤ dH(x) 5 f(x) for each x ∈ V(H). A (g, f)-factorization of G is a partition of E(G) into edge-disjoint (g, f)-factors. Let F = {F1, F2,…… ， Fm } and H be a factorization and a subgraph of G, respectively. If F, 1 ≤ i ≤ m， has exactly one edge in common with H, then it is said that ■ is orthogonal to H. It is proved that every bipartite (mg + m - 1, mf - m + 1 )-graph G has a (g, f)-factorization orthogonal to k vertex disjoint m-subgraphs of G if 2-k ≤ g(x) for all x ∈ V(G). Furthermore, it is showed that the results in this paper are best possible.展开更多
Time-resolved particle image velocimetry（TRPIV） experiments are performed to investigate the coherent structure＇s performance of riblets in a turbulent boundary layer（TBL） at a friction Reynolds number of 185. To...Time-resolved particle image velocimetry（TRPIV） experiments are performed to investigate the coherent structure＇s performance of riblets in a turbulent boundary layer（TBL） at a friction Reynolds number of 185. To visualize the energetic large-scale coherent structures（CSs） over a smooth surface and riblets, the proper orthogonal decomposition（POD） and finite-time Lyapunov exponent（FTLE） are used to identify the CSs in the TBL. Spatial-temporal correlation is implemented to obtain the characters and transport properties of typical CSs in the FTLE fields. The results demonstrate that the generic flow structures, such as hairpin-like vortices, are also observed in the boundary layer flow over the riblets, consistent with its smooth counterpart. Low-order POD modes are more sensitive to the riblets in comparison with the high-order ones,and the wall-normal movement of the most energy-containing structures are suppressed over riblets. The spatial correlation analysis of the FTLE fields indicates that the evolution process of the hairpin vortex over riblets are inhibited. An apparent decrease of the convection velocity over riblets is noted, which is believed to reduce the ejection/sweep motions associated with high shear stress from the viscous sublayer. These reductions exhibit inhibition of momentum transfer among the structures near the wall in the TBL flows.展开更多
An efficient two-step quantum key distribution （QKD） protocol with orthogonal product states in the （×）（n ≥3） Hilbert space is presented. In this protocol, the particles in the orthogonal product states fo...An efficient two-step quantum key distribution （QKD） protocol with orthogonal product states in the （×）（n ≥3） Hilbert space is presented. In this protocol, the particles in the orthogonal product states form two particle sequences. The sender, Alice, first sends one sequence to the receiver, Bob. After Bob receives the first particle sequence, Alice and Bob check eavesdropping by measuring a fraction of particles randomly chosen. After ensuring the security of the quantum channel, Alice sends the other particle sequence to Bob. By making an orthogonal measurement on the two particle sequences, Bob can obtain the information of the orthogonal product states sent by Alice. This protocol has many distinct features such as great capacity, high efficiency in that it uses all orthogonal product states in distributing the key except those chosen for checking eavesdroppers.展开更多
The geometry of an inductively coupled plasma （ICP） etcher is usually considered to be an important factor for determining both plasma and process uniformity over a large wafer. During the past few decades, these pa...The geometry of an inductively coupled plasma （ICP） etcher is usually considered to be an important factor for determining both plasma and process uniformity over a large wafer. During the past few decades, these parameters were determined by the ＂trial and error＂ method, resulting in wastes of time and funds. In this paper, a new approach of regression orthogonal design with plasma simulation experiments is proposed to investigate the sensitivity of the structural parameters on the uniformity of plasma characteristics. The tool for simulating plasma is CFD-ACE＋, which is commercial multi-physical modeling software that has been proven to be accurate for plasma simulation. The simulated experimental results are analyzed to get a regression equation on three structural parameters. Through this equation, engineers can compute the uniformity of the electron number density rapidly without modeling by CFD-ACE＋. An optimization performed at the end produces good results.展开更多
In this survey we give a brief introduction to orthogonal polynomials, including a short review of classical asymptotic methods. Then we turn to a discussion of the Riemann-Hilbert formulation of orthogonal polynomial...In this survey we give a brief introduction to orthogonal polynomials, including a short review of classical asymptotic methods. Then we turn to a discussion of the Riemann-Hilbert formulation of orthogonal polynomials, and the Delft ＆ Zhou method of steepest descent. We illustrate this new approach, and a modified version, with the Hermite polynomials. Other recent progress of this method is also mentioned, including applications to discrete orthogonal polynomials, orthogonal polynomials on curves, multiple orthogonal polynomials, and certain orthogonal polynomials with singular behavior.展开更多
Aim To Research the temperature distribution in orthogonal metal machining and to build a finite element analysis model about the temperature distribution. Methods With the finite element method of thermal conductio...Aim To Research the temperature distribution in orthogonal metal machining and to build a finite element analysis model about the temperature distribution. Methods With the finite element method of thermal conduction, the temperature distributions in various machining conditions were computed according to the experimental data such as cutting force, shear angle, etc. Results The computational results agree with some classic experimental results, and thermal effect due to process parameters was observed. Conclusion The finite element analysis model is reasonable, and it's a feasible scheme for studying the temperature distribution in orthogonal metal machining system.展开更多
An efficient quantum key distribution （QKD） protocol with orthogonal product states in the 3 3 Hilbert space is presented. The sender, Alice, disorders the orthogonal product state sequence and sends it to Bob. Aft...An efficient quantum key distribution （QKD） protocol with orthogonal product states in the 3 3 Hilbert space is presented. The sender, Alice, disorders the orthogonal product state sequence and sends it to Bob. After Alice has published the matching information of the particle sequence, Bob recovers the correct correspondences and makes an orthogonal measurement on the orthogonal product states to obtain the information sent by Alice. Finally, security analysis is also made.展开更多
基金supported by the National Natural Science Foundation of China(12071444,12201581)the Fundamental Research Program of Shanxi Province of China(202103021223191).
文摘The minimal widths of three bounded subsets of the unit sphere associated to a unit vector in a normed linear space are studied,and three related geometric constants are introduced.New characterizations of inner product spaces are also presented.From the perspective of minimal width,strongε-symmetry of Birkhoff orthogonality is introduced,and its relation toε-symmetry of Birkhoff orthogonality is shown.Unlike most of the existing parameters of the underlying space,these new constants are full dimensional in nature.
文摘In this paper,some refinements of norm equalities and inequalities of combination of two orthogonal projections are established.We use certain norm inequalities for positive contraction operator to establish norm inequalities for combination of orthogonal projections on a Hilbert space.Furthermore,we give necessary and sufficient conditions under which the norm of the above combination of o`rthogonal projections attains its optimal value.
基金supported by the National Natural Science Foundation of China(Grant Nos.12074265,12234002,and 92250303)the Guangdong Basic and Applied Basic Research Foundation(Grant No.2022A1515010329)。
文摘Based on numerical solutions of the time-dependent Schr ¨odinger equation, we theoretically investigate the photoelectron spectrum of hydrogen atoms ionized by a pair of ultrashort, intense, and orthogonally polarized laser pulses with a relative time delay in a pump–probe configuration. The pump pulse resonantly excites electrons from the 1s and 2p levels,inducing Rabi oscillations. The resulting dynamically enhanced Autler–Townes(AT) splitting is observed in the photoelectron energy spectrum upon interaction with the second probe pulse. In contrast to the previous parallel-polarization scheme, the proposed orthogonal-polarization configuration enables the resolution of dynamically enhanced AT splitting over a considerably wider range of probe photon energies.
基金partly supported by the National Natural Science Foundation of China (Grant Nos. 12034008,12250003, and 11727810)the Program of Introducing Talents of Discipline to Universities 111 Project (B12024)。
文摘Electron dynamics during non-sequential double ionization(NSDI) is one of the most attractive areas of research in the field of laser–atom or laser–molecule interaction. Based on the classic two-dimensional model, we study the process of NSDI of argon atoms driven by a few-cycle orthogonal two-color laser field composed of 800 nm and 400 nm laser pulses. By changing the relative phase of the two laser pulses, a localized enhancement of NSDI yield is observed at 0.5πand 1.5π, which could be attributed to a rapid and substantial increase in the number of electrons returning to the parent ion within extremely short time intervals at these specific phases. Through the analysis of the electron–electron momentum correlations within different time windows of NSDI events and the angular distributions of emitted electrons in different channels, we observe a more pronounced electron–electron correlation phenomenon in the recollision-induced ionization(RII) channel. This is attributed to the shorter delay time in the RII channel.
基金financial supports from National Key Research and Development Program of China(2018YFA0701800)Fujian Province Major Science and Technology Program(2020HZ01012)+1 种基金National Natural Science Foundation of China(NSFC)(U22A2080)China Scholarship Council(202109107007).
文摘Orthogonal matrices have become a vital means for coding and signal processing owing to their unique distributional properties.Although orthogonal matrices based on amplitude or phase combinations have been extensively explored,the orthogonal matrix of polarization combinations(OMPC)is a novel,relatively unexplored concept.Herein,we propose a method for constructing OMPCs of any dimension encompassing 4n(where n is 1,2,4,8,…)mutually orthogonal 2ncomponent polarization combinations.In the field of holography,the integration of polarization multiplexing techniques with polarization-sensitive materials is expected to emerge as a groundbreaking approach for multichannel hologram multiplexing,offering considerable enhancements in data storage capacity and security.A multidimensional OMPC enables the realization of multichannel multiplexing and dynamical modulation of information in polarization holographic recording.Despite consolidating all information into a single position within the material,we effectively avoided extraneous crosstalk during the reconstruction process.Our results show that achieving four distinct holographic images individually and simultaneously depends on the polarization combination represented by the incident wave.This discovery opens up a new avenue for achieving highly holographic information storage and dynamically displayed information,harnessing the potential of OMPC to expand the heretofore limited dimensionality of orthogonal polarization.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.12204132 and 12304376)Excellent Youth Science Foundation of Shandong Province (Overseas) (Grant No.2022HWYQ-073)+1 种基金the Fundamental Research Funds for the Central Universities (Grant No.HIT.OCEF.2022042)Natural Science Foundation of Shandong Province (Grant No.ZR2023QA075)。
文摘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.
基金the financial support from the Postgraduate Research&Practice Innovation Program of Jiangsu Province(Grant No.KYLX_0399)
文摘Influence of multiple structural parameters on the performance of a gun launch system driven by highpressure reactive gases is important for structural design and performance adjustment.A coupled lumped parameter model was utilized to predict the propellant combustion,and a dynamic finite element method was applied to approximate the mechanical interactions between the projectile and the barrel.The combustion and the mechanical interactions were coupled through a user subroutine interface in ABAQUS.The correctness and the capability of the finite element approximations in capturing small structural changes were validated by comparing predicted resistance with experiments.Based on the coupled model,the influence of structural parameters of a medium-caliber gun on the system performance was investigated.In order to reduce the research costs,orthogonal tests were designed to investigate the comprehensive effects of the parameters.According to statistical analysis,the important order of the structural parameters on the launching process was obtained.The results indicate that the influence of the width of the rotating band stands out among the studied parameters in the gun.The work provides a method to investigate the influence of multiple parameters on system performance and gives guidance for controlling the system performance.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 60473042,60573067 and 60803102)
文摘We study the parameter estimation of a nonlinear chaotic system,which can be essentially formulated as a multidimensional optimization problem.In this paper,an orthogonal learning cuckoo search algorithm is used to estimate the parameters of chaotic systems.This algorithm can combine the stochastic exploration of the cuckoo search and the exploitation capability of the orthogonal learning strategy.Experiments are conducted on the Lorenz system and the Chen system.The proposed algorithm is used to estimate the parameters for these two systems.Simulation results and comparisons demonstrate that the proposed algorithm is better or at least comparable to the particle swarm optimization and the genetic algorithm when considering the quality of the solutions obtained.
基金This research was supported by Department of Wildlife Conservation, State Forestry Administration, P. R. China.
文摘An orthogonal design was used to optimize SSR-PCR amplification system using Panax ginseng genomic DNA as template. Four levels of five factors （DNA template, Taq DNA polymerase, Mg^2＋, primer, and dNTP） and annealing temperature have been tested separately in this system. The results demonstrated the reaction efficiency was affected by these factors. Based on the results, a stable, productive and reproducible PCR system and cycling program for amplifying a ginseng SSR locus were obtained： 20 μL system containing 1.0 U Taq DNA polymerase, 2.0 mmol·L^-1 Mg^2＋, 0.2 mmol·L^-1 dNTPs, 0.3 μmol·L^-1 SSR primer, 60 ng· μla^-1 DNA template, performed with a program of 94℃ for 5 min, 94℃ for 30 s, annealing at 56.3℃ for 30 s, 72℃ for 1 min, 37 cycles, finishing at 72℃ for 7 min, and storing at 4℃.
基金supported by the National Natural Science Foundation of China(Grant Nos.61178011,61275116,and 61475127)the Natural Science Foundation of Chongqing City,China(Grant No.2012jjB40011)
文摘The polarization switching（PS） and polarization bistability（PB） characteristics of a 1550-nm vertical-cavity surfaceemitting laser（VCSEL） subjected to orthogonal optical injection are systematically investigated.The simulated results show that the PS and polarization-resolved nonlinear dynamical states of the VCSEL are critically dependent on the changing paths of the injected power.The polarization dynamics for different scanning directions of the injected power is presented to explain the polarization evolution during the formation of PS.In the case of forward scanning injected power,with the increase of frequency detuning level between the VCSEL and the injected light,the injected power required for PS gradually increases for negative frequency detuning but exhibits fluctuations for positive frequency detuning.In the case of reversely scanning injected power,the injected power required for PS displays fluctuant changes within the whole frequency detuning range.Specifically,PS may disappear under certain negative frequency detuning and large bias current.Furthermore,the hysteresis width as a function of the frequency detuning is calculated,and the regions for the appearance and disappearance of PB have been determined in the parameter space of the bias current and frequency detuning.
文摘Let G be a graph and f an integer-valued function defined on V(G). It is proved that every (0,mf - m+1)-graph G has a (0,f)-factorization orthogonal to any given subgraph with m edges.
基金This work was supported by NNSF. RFDP and NNSF of shandong province(Z2000A02 ).
文摘Let G be a bipartite graph with vertex set V(G) and edge set E(G), and let g and f be two positive integer-valued functions defined on V(G) such that g(x) ≤ f(x) for every vertex x of V(G). Then a (g, f)-factor of G is a spanning subgraph H of G such that g(x) ≤ dH(x) 5 f(x) for each x ∈ V(H). A (g, f)-factorization of G is a partition of E(G) into edge-disjoint (g, f)-factors. Let F = {F1, F2,…… ， Fm } and H be a factorization and a subgraph of G, respectively. If F, 1 ≤ i ≤ m， has exactly one edge in common with H, then it is said that ■ is orthogonal to H. It is proved that every bipartite (mg + m - 1, mf - m + 1 )-graph G has a (g, f)-factorization orthogonal to k vertex disjoint m-subgraphs of G if 2-k ≤ g(x) for all x ∈ V(G). Furthermore, it is showed that the results in this paper are best possible.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11332006,11732010,11572221,and 11502066)the Natural Science Foundation of Tianjin City(Grant No.18JCQNJC5100)
文摘Time-resolved particle image velocimetry（TRPIV） experiments are performed to investigate the coherent structure＇s performance of riblets in a turbulent boundary layer（TBL） at a friction Reynolds number of 185. To visualize the energetic large-scale coherent structures（CSs） over a smooth surface and riblets, the proper orthogonal decomposition（POD） and finite-time Lyapunov exponent（FTLE） are used to identify the CSs in the TBL. Spatial-temporal correlation is implemented to obtain the characters and transport properties of typical CSs in the FTLE fields. The results demonstrate that the generic flow structures, such as hairpin-like vortices, are also observed in the boundary layer flow over the riblets, consistent with its smooth counterpart. Low-order POD modes are more sensitive to the riblets in comparison with the high-order ones,and the wall-normal movement of the most energy-containing structures are suppressed over riblets. The spatial correlation analysis of the FTLE fields indicates that the evolution process of the hairpin vortex over riblets are inhibited. An apparent decrease of the convection velocity over riblets is noted, which is believed to reduce the ejection/sweep motions associated with high shear stress from the viscous sublayer. These reductions exhibit inhibition of momentum transfer among the structures near the wall in the TBL flows.
基金Project supported by the National Natural Science Foundation of China （Grant No 60373059）, the Doctoral Programs Foundation of the Ministry of Education of China （Grant No 20040013007）, and the Major Research plan of the National Natural Science Foundation of China （Grant No 90604023）.
文摘An efficient two-step quantum key distribution （QKD） protocol with orthogonal product states in the （×）（n ≥3） Hilbert space is presented. In this protocol, the particles in the orthogonal product states form two particle sequences. The sender, Alice, first sends one sequence to the receiver, Bob. After Bob receives the first particle sequence, Alice and Bob check eavesdropping by measuring a fraction of particles randomly chosen. After ensuring the security of the quantum channel, Alice sends the other particle sequence to Bob. By making an orthogonal measurement on the two particle sequences, Bob can obtain the information of the orthogonal product states sent by Alice. This protocol has many distinct features such as great capacity, high efficiency in that it uses all orthogonal product states in distributing the key except those chosen for checking eavesdroppers.
基金supported by Important National Science & Technology Specific Projects of China (No.2) (Nos.2009ZX02001,2011ZX02403)
文摘The geometry of an inductively coupled plasma （ICP） etcher is usually considered to be an important factor for determining both plasma and process uniformity over a large wafer. During the past few decades, these parameters were determined by the ＂trial and error＂ method, resulting in wastes of time and funds. In this paper, a new approach of regression orthogonal design with plasma simulation experiments is proposed to investigate the sensitivity of the structural parameters on the uniformity of plasma characteristics. The tool for simulating plasma is CFD-ACE＋, which is commercial multi-physical modeling software that has been proven to be accurate for plasma simulation. The simulated experimental results are analyzed to get a regression equation on three structural parameters. Through this equation, engineers can compute the uniformity of the electron number density rapidly without modeling by CFD-ACE＋. An optimization performed at the end produces good results.
基金supported in part by the National Natural Science Foundation of China (10471154 and 10871212)
文摘In this survey we give a brief introduction to orthogonal polynomials, including a short review of classical asymptotic methods. Then we turn to a discussion of the Riemann-Hilbert formulation of orthogonal polynomials, and the Delft ＆ Zhou method of steepest descent. We illustrate this new approach, and a modified version, with the Hermite polynomials. Other recent progress of this method is also mentioned, including applications to discrete orthogonal polynomials, orthogonal polynomials on curves, multiple orthogonal polynomials, and certain orthogonal polynomials with singular behavior.
文摘Aim To Research the temperature distribution in orthogonal metal machining and to build a finite element analysis model about the temperature distribution. Methods With the finite element method of thermal conduction, the temperature distributions in various machining conditions were computed according to the experimental data such as cutting force, shear angle, etc. Results The computational results agree with some classic experimental results, and thermal effect due to process parameters was observed. Conclusion The finite element analysis model is reasonable, and it's a feasible scheme for studying the temperature distribution in orthogonal metal machining system.
基金Project supported by the National High Technology Development Program of China （Grant Nos 2006AA01Z419 and 2006AA01Z440）, the Major Program of the National Natural Science Foundation of China （Grant No 90604023）, the National Research Foundation for the Doctoral Program of Higher Education of China （Grant No 20040013007）, National Laboratory for Modern Communications Science Foundation of China （Grant No 9140C110101.0.601）.
文摘An efficient quantum key distribution （QKD） protocol with orthogonal product states in the 3 3 Hilbert space is presented. The sender, Alice, disorders the orthogonal product state sequence and sends it to Bob. After Alice has published the matching information of the particle sequence, Bob recovers the correct correspondences and makes an orthogonal measurement on the orthogonal product states to obtain the information sent by Alice. Finally, security analysis is also made.
