Most researches associated with target encircling control are focused on moving along a circular orbit under an ideal environment free from external disturbances.However,elliptical encirclement with a time-varying obs...Most researches associated with target encircling control are focused on moving along a circular orbit under an ideal environment free from external disturbances.However,elliptical encirclement with a time-varying observation radius,may permit a more flexible and high-efficacy enclosing solution,whilst the non-orthogonal property between axial and tangential speed components,non-ignorable environmental perturbations,and strict assignment requirements empower elliptical encircling control to be more challenging,and the relevant investigations are still open.Following this line,an appointed-time elliptical encircling control rule capable of reinforcing circumnavigation performances is developed to enable Unmanned Aerial Vehicles(UAVs)to move along a specified elliptical path within a predetermined reaching time.The remarkable merits of the designed strategy are that the relative distance controlling error can be guaranteed to evolve within specified regions with a designer-specified convergence behavior.Meanwhile,wind perturbations can be online counteracted based on an unknown system dynamics estimator(USDE)with only one regulating parameter and high computational efficiency.Lyapunov tool demonstrates that all involved error variables are ultimately limited,and simulations are implemented to confirm the usability of the suggested control algorithm.展开更多
High-order harmonic generation(HHG) of Ar atom in an elliptically polarized intense laser field is experimentally investigated in this work.Interestingly,the anomalous ellipticity dependence on the laser ellipticity(...High-order harmonic generation(HHG) of Ar atom in an elliptically polarized intense laser field is experimentally investigated in this work.Interestingly,the anomalous ellipticity dependence on the laser ellipticity(ε) in the lower-order harmonics is observed,specifically in the 13rd-order,which displays a maximal harmonic intensity at ε ≈ 0.1,rather than at ε = 0 as expected.This contradicts the general trend of harmonic yield,which typically decreases with the increase of laser ellipticity.In this study,we attribute this phenomenon to the disruption of the symmetry of the wave function by the Coulomb effect,leading to the generation of a harmonic with high ellipticity.This finding provides valuable insights into the behavior of elliptically polarized harmonics and opens up a potential way for exploring new applications in ultrafast spectroscopy and light–matter interactions.展开更多
The geometric characteristics of fractures within a rock mass can be inferred by the data sampling from boreholes or exposed surfaces.Recently,the universal elliptical disc(UED)model was developed to represent natural...The geometric characteristics of fractures within a rock mass can be inferred by the data sampling from boreholes or exposed surfaces.Recently,the universal elliptical disc(UED)model was developed to represent natural fractures,where the fracture is assumed to be an elliptical disc and the fracture orientation,rotation angle,length of the long axis and ratio of short-long axis lengths are considered as variables.This paper aims to estimate the fracture size-and azimuth-related parameters in the UED model based on the trace information from sampling windows.The stereological relationship between the trace length,size-and azimuth-related parameters of the UED model was established,and the formulae of the mean value and standard deviation of trace length were proposed.The proposed formulae were validated via the Monte Carlo simulations with less than 5%of error rate between the calculated and true values.With respect to the estimation of the size-and azimuth-related parameters using the trace length,an optimization method was developed based on the pre-assumed size and azimuth distribution forms.A hypothetical case study was designed to illustrate and verify the parameter estimation method,where three combinations of the sampling windows were used to estimate the parameters,and the results showed that the estimated values could agree well with the true values.Furthermore,a hypothetical three-dimensional(3D)elliptical fracture network was constructed,and the circular disc,non-UED and UED models were used to represent it.The simulated trace information from different models was compared,and the results clearly illustrated the superiority of the proposed UED model over the existing circular disc and non-UED models。展开更多
Circularly and elliptically polarized high-order harmonics have unique advantages when used in studying the chiral and magnetic features of matter.Here,we studied the polarization properties of high-order harmonics ge...Circularly and elliptically polarized high-order harmonics have unique advantages when used in studying the chiral and magnetic features of matter.Here,we studied the polarization properties of high-order harmonics generated from alignment nitrogen molecules driven by cross-linearly polarized two-color laser fields.Through adjusting various laser parameters and targets,such as the relative phase,the crossing angle,the intensity ratio of the driving fields,and the molecular alignment angle,we obtained highly elliptically polarized high-order harmonics with the same helicity in a wide spectral range.This provides a possible effective way to generate elliptically polarized attosecond pulses.Finally,we showed the probability of controlling the spectral range of elliptically polarized harmonics.展开更多
Elliptical airy vortex beams(EAVBs) can spontaneously form easily identifiable topological charge focal spots. They are used for topological charge detection of vortex beams because they have the abruptly autofocusing...Elliptical airy vortex beams(EAVBs) can spontaneously form easily identifiable topological charge focal spots. They are used for topological charge detection of vortex beams because they have the abruptly autofocusing properties of circular airy vortex beams and exhibit unique propagation characteristics. We study the use of the dynamic phase and Pancharatnam–Berry phase principles for generation and modulation of EAVBs by designing complex-amplitude metasurface and phase-only metasurface, at an operating wavelength of 1500 nm. It is found that the focusing pattern of EAVBs in the autofocusing plane splits into |m| + 1 tilted bright spots from the original ring, and the tilted direction is related to the sign of the topological charge number m. Due to the advantages of ultra-thin, ultra-light, and small size of the metasurface, our designed metasurface device has potential applications in improving the channel capacity based on orbital angular momentum communication, information coding, and particle capture compared to spatial light modulation systems that generate EAVBs.展开更多
Protecting the privacy of data in the multi-cloud is a crucial task.Data mining is a technique that protects the privacy of individual data while mining those data.The most significant task entails obtaining data from...Protecting the privacy of data in the multi-cloud is a crucial task.Data mining is a technique that protects the privacy of individual data while mining those data.The most significant task entails obtaining data from numerous remote databases.Mining algorithms can obtain sensitive information once the data is in the data warehouse.Many traditional algorithms/techniques promise to provide safe data transfer,storing,and retrieving over the cloud platform.These strategies are primarily concerned with protecting the privacy of user data.This study aims to present data mining with privacy protection(DMPP)using precise elliptic curve cryptography(PECC),which builds upon that algebraic elliptic curve infinitefields.This approach enables safe data exchange by utilizing a reliable data consolidation approach entirely reliant on rewritable data concealing techniques.Also,it outperforms data mining in terms of solid privacy procedures while maintaining the quality of the data.Average approximation error,computational cost,anonymizing time,and data loss are considered performance measures.The suggested approach is practical and applicable in real-world situations according to the experimentalfindings.展开更多
The constrained motion of a particle on an elliptical path is studied using Hamiltonian mechanics through Poisson bracket and Lagrangian mechanics through Euler Lagrange equation using non-natural Lagrangian. We calcu...The constrained motion of a particle on an elliptical path is studied using Hamiltonian mechanics through Poisson bracket and Lagrangian mechanics through Euler Lagrange equation using non-natural Lagrangian. We calculate the generalized momentum p<sub>θ</sub> and we find that this quantity is not conserved and the conjugate θ coordinate is not a cyclic coordinate.展开更多
Diffusion in narrow curved channels with dead-ends as in extracellular space in the biological tissues,e.g.,brain,tumors,muscles,etc.is a geometrically induced complex diffusion and is relevant to different kinds of b...Diffusion in narrow curved channels with dead-ends as in extracellular space in the biological tissues,e.g.,brain,tumors,muscles,etc.is a geometrically induced complex diffusion and is relevant to different kinds of biological,physical,and chemical systems.In this paper,we study the effects of geometry and confinement on the diffusion process in an elliptical comb-like structure and analyze its statistical properties.The ellipse domain whose boundary has the polar equationρ(θ)=b/√1−e^(2)cos^(2)θ with 0<e<1,θ∈[0,2π],and b as a constant,can be obtained through stretched radius r such that Υ=rρ(θ)with r∈[0,1].We suppose that,for fixed radius r=R,an elliptical motion takes place and is interspersed with a radial motion inward and outward of the ellipse.The probability distribution function(PDF)in the structure and the marginal PDF and mean square displacement(MSD)along the backbone are obtained numerically.The results show that a transient sub-diffusion behavior dominates the process for a time followed by a saturating state.The sub-diffusion regime and saturation threshold are affected by the length of the elliptical channel lateral branch and its curvature.展开更多
A future constellation of at least four geomagnetic satellites(designated Macao Scientific Satellite-1(MSS-1)and Macao Scientific Satellite-2(MSS-2))was recently proposed,to continue high-quality geomagnetic observati...A future constellation of at least four geomagnetic satellites(designated Macao Scientific Satellite-1(MSS-1)and Macao Scientific Satellite-2(MSS-2))was recently proposed,to continue high-quality geomagnetic observations in the post-Swarm period,focusing especially on collecting data that will provide a global,three-dimensional survey of the geomagnetic field.In this paper,we present a simulation of two years of orbits(2020.01.01-2022.01.01)of two satellites(tentatively denoted as MSS-2)that are constellated in elliptical(200×5,300 km)low-perigee orbits.By comparing error variances of Gauss coefficients,we investigate the sensitivity of lithospheric magnetic field modelling to data collected from various satellite orbits,including a near circular reference orbit of 300×350km,and elliptical orbit of 180×5,300 km,220×5,300 km,200×3,000 km and 200×1,500 km.We find that in two years the two MSS-2 satellites can collect 35,000 observations at altitude below 250 km,data that will be useful in advancing the quality of lithospheric magnetic field modelling;this number of observations reflects the fact that only 4.5%of the flight time of these satellites will be below250 km(just 6.4%of their flight time below 300 km).By combining observations from the MSS-2 satellites’elliptical orbits of 200×5,300km with observations from a circular reference orbit,the variance of the geomagnetic model can be reduced by a factor of 285 at spherical harmonic degree n=200 and by a factor of 1,300 at n=250.The planned lower perigee of their orbits allows the new satellites to collect data at unprecedentedly lower altitudes,thus dramatically improving the spatial resolution of satellite-derived lithospheric field models,(up to 80%at n=150).In addition,lowering the apogee increases the time interval during which the satellites fly at near-Earth altitudes,thus improving the model predictions at all spherical harmonic degrees(around 52%-62%at n=150).The upper limit of the expected improvement to the field model at the orbital apogee is not as good as at the perigee.However,data from the MSS-1 orbit can help fill the gap between data from the MSS-2 orbits and from the circular reference orbit for the low-degree part of the model.The feasibility of even lower-altitude flight requires further discussion with satellite engineers.展开更多
Laser-driven proton-induced x-ray emission(laser-PIXE) is a nuclear analysis method based on the compact laser ion accelerator. Due to the transient process of ion acceleration, the laser-PIXE signals are usually spur...Laser-driven proton-induced x-ray emission(laser-PIXE) is a nuclear analysis method based on the compact laser ion accelerator. Due to the transient process of ion acceleration, the laser-PIXE signals are usually spurted within nanoseconds and accompanied by strong electromagnetic pulses(EMP), so traditional multi-channel detectors are no longer applicable.In this work, we designed a reflective elliptical crystal spectrometer for the diagnosis of laser-PIXE. The device can detect the energy range of 1 keV–11 ke V with a high resolution. A calibration experiment was completed on the electrostatic accelerator of Peking University using samples of Al, Ti, Cu, and ceramic artifacts. The detection efficiency of the elliptical crystal spectrometer was obtained in the order of 10-9.展开更多
To benefit tissue removal and postoperative rehabilitation,increased efficiency and accuracy and reduced operating force are strongly required in the osteotomy.A novel elliptical vibration cutting(EVC)has been introdu...To benefit tissue removal and postoperative rehabilitation,increased efficiency and accuracy and reduced operating force are strongly required in the osteotomy.A novel elliptical vibration cutting(EVC)has been introduced for bone cutting compared with conventional cutting(CC)in this paper.With the assistance of high-speed microscope imaging and the dynamometer,the material removals of cortical bone and their cutting forces from two cutting regimes were recorded and analysed comprehensively,which clearly demonstrated the chip morphology improvement and the average cutting force reduction in the EVC process.It also revealed that the elliptical vibration of the cutting tool could promote fracture propagation along the shear direction.These new findings will be of important theoretical and practical values to apply the innovative EVC process to the surgical procedures of the osteotomy.展开更多
Nowadays,Wireless Sensor Network(WSN)is a modern technology with a wide range of applications and greatly attractive benefits,for example,self-governing,low expenditure on execution and data communication,long-term fu...Nowadays,Wireless Sensor Network(WSN)is a modern technology with a wide range of applications and greatly attractive benefits,for example,self-governing,low expenditure on execution and data communication,long-term function,and unsupervised access to the network.The Internet of Things(IoT)is an attractive,exciting paradigm.By applying communication technologies in sensors and supervising features,WSNs have initiated communication between the IoT devices.Though IoT offers access to the highest amount of information collected through WSNs,it leads to privacy management problems.Hence,this paper provides a Logistic Regression machine learning with the Elliptical Curve Cryptography technique(LRECC)to establish a secure IoT structure for preventing,detecting,and mitigating threats.This approach uses the Elliptical Curve Cryptography(ECC)algorithm to generate and distribute security keys.ECC algorithm is a light weight key;thus,it minimizes the routing overhead.Furthermore,the Logistic Regression machine learning technique selects the transmitter based on intelligent results.The main application of this approach is smart cities.This approach provides continuing reliable routing paths with small overheads.In addition,route nodes cooperate with IoT,and it handles the resources proficiently and minimizes the 29.95%delay.展开更多
We study equations in divergence form with piecewise Cαcoefficients.The domains contain corners and the discontinuity surfaces are attached to the edges of the corners.We obtain piecewise C^(1,α) estimates across th...We study equations in divergence form with piecewise Cαcoefficients.The domains contain corners and the discontinuity surfaces are attached to the edges of the corners.We obtain piecewise C^(1,α) estimates across the discontinuity surfaces and provide an example to illustrate the issue regarding the regularity at the corners.展开更多
This article concerns the integral related to the transverse comoving distance and, in turn, to the luminosity distance both in the standard non-flat and flat cosmology. The purpose is to determine a straightforward m...This article concerns the integral related to the transverse comoving distance and, in turn, to the luminosity distance both in the standard non-flat and flat cosmology. The purpose is to determine a straightforward mathematical formulation for the luminosity distance as function of the transverse comoving distance for all cosmology cases with a non-zero cosmological constant by adopting a different mindset. The applied method deals with incomplete elliptical integrals of the first kind associated with the polynomial roots admitted in the comoving distance integral according to the scientific literature. The outcome shows that the luminosity distance can be obtained by the combination of an analytical solution followed by a numerical integration in order to account for the redshift. This solution is solely compared to the current Gaussian quadrature method used as basic recognized algorithm in standard cosmology.展开更多
Let n≥2 and let L be a second-order elliptic operator of divergence form with coefficients consisting of both an elliptic symmetric part and a BMO anti-symmetric part in ℝ^(n).In this article,we consider the weighted...Let n≥2 and let L be a second-order elliptic operator of divergence form with coefficients consisting of both an elliptic symmetric part and a BMO anti-symmetric part in ℝ^(n).In this article,we consider the weighted Kato square root problem for L.More precisely,we prove that the square root L^(1/2)satisfies the weighted L^(p)estimates||L^(1/2)(f)||L_(ω)^p(R^(n))≤C||■f||L_(ω)^p(R^(n);R^(n))for any p∈(1,∞)andω∈Ap(ℝ^(n))(the class of Muckenhoupt weights),and that||■f||L_(ω)^p(R^(n);R^(n))≤C||L^(1/2)(f)||L_(ω)^p(R^(n))for any p∈(1,2+ε)andω∈Ap(ℝ^(n))∩RH_(2+ε/p),(R^(n))(the class of reverse Hölder weights),whereε∈(0,∞)is a constant depending only on n and the operator L,and where(2+ε/p)'denotes the Hölder conjugate exponent of 2+ε/p.Moreover,for any given q∈(2,∞),we give a sufficient condition to obtain that||■f||L_(ω)^p(R^(n);R^(n))≤C||L^(1/2)(f)||L_(ω)^p(R^(n))for any p∈(1,q)andω∈A_(p)(R^(n))∩pRH_(q/p),(R^(n)).As an application,we prove that when the coefficient matrix A that appears in L satisfies the small BMO condition,the Riesz transform∇L^(−1/2)is bounded on L_(ω)^(p)(ℝ^(n))for any given p∈(1,∞)andω∈Ap(ℝ^(n)).Furthermore,applications to the weighted L^(2)-regularity problem with the Dirichlet or the Neumann boundary condition are also given.展开更多
The elliptic curve cryptography algorithm represents a major advancement in the field of computer security. This innovative algorithm uses elliptic curves to encrypt and secure data, providing an exceptional level of ...The elliptic curve cryptography algorithm represents a major advancement in the field of computer security. This innovative algorithm uses elliptic curves to encrypt and secure data, providing an exceptional level of security while optimizing the efficiency of computer resources. This study focuses on how elliptic curves cryptography helps to protect sensitive data. Text is encrypted using the elliptic curve technique because it provides great security with a smaller key on devices with limited resources, such as mobile phones. The elliptic curves cryptography of this study is better than using a 256-bit RSA key. To achieve equivalent protection by using the elliptic curves cryptography, several Python libraries such as cryptography, pycryptodome, pyQt5, secp256k1, etc. were used. These technologies are used to develop a software based on elliptic curves. If built, the software helps to encrypt and decrypt data such as a text messages and it offers the authentication for the communication.展开更多
Remote sensing images carry crucial ground information,often involving the spatial distribution and spatiotemporal changes of surface elements.To safeguard this sensitive data,image encryption technology is essential....Remote sensing images carry crucial ground information,often involving the spatial distribution and spatiotemporal changes of surface elements.To safeguard this sensitive data,image encryption technology is essential.In this paper,a novel Fibonacci sine exponential map is designed,the hyperchaotic performance of which is particularly suitable for image encryption algorithms.An encryption algorithm tailored for handling the multi-band attributes of remote sensing images is proposed.The algorithm combines a three-dimensional synchronized scrambled diffusion operation with chaos to efficiently encrypt multiple images.Moreover,the keys are processed using an elliptic curve cryptosystem,eliminating the need for an additional channel to transmit the keys,thus enhancing security.Experimental results and algorithm analysis demonstrate that the algorithm offers strong security and high efficiency,making it suitable for remote sensing image encryption tasks.展开更多
This paper considers the regularity of solutions to mixed boundary value problems in small-angle regions for elliptic equations. By constructing a specific barrier function, we proved that under the assumption of suff...This paper considers the regularity of solutions to mixed boundary value problems in small-angle regions for elliptic equations. By constructing a specific barrier function, we proved that under the assumption of sufficient regularity of boundary conditions and coefficients, as long as the angle is sufficiently small, the regularity of the solution to the mixed boundary value problem of the second-order elliptic equation can reach any order.展开更多
In this article, we deal with weak solutions to non-degenerate sub-elliptic equations in the Heisenberg group, and study the regularities of solutions. We establish horizontal Calderón-Zygmund type estimate in Be...In this article, we deal with weak solutions to non-degenerate sub-elliptic equations in the Heisenberg group, and study the regularities of solutions. We establish horizontal Calderón-Zygmund type estimate in Besov spaces with more general assumptions on coefficients for both homogeneous equations and non-homogeneous equations. This study of regularity estimates expands the Calderón-Zygmund theory in the Heisenberg group.展开更多
An offset elliptical reflector antenna suitable for satellite application was designed and investigated when it was fed by a rectangular horn partially filled.with a dielectric..The.reflector antenna exhibits high gai...An offset elliptical reflector antenna suitable for satellite application was designed and investigated when it was fed by a rectangular horn partially filled.with a dielectric..The.reflector antenna exhibits high gain, low cross polarization. low sidelines and an elliptical beam. Al- though this study has been carried out in view of possible satellite applications, it is clear that this. antenna. is also suitable for use in radar antennas.展开更多
基金National Natural Science Foundation of China(Grant Nos.61803348,62173312,51922009)Shanxi Province Key Laboratory of Quantum Sensing and Precision Measurement(Grant No.201905D121001).
文摘Most researches associated with target encircling control are focused on moving along a circular orbit under an ideal environment free from external disturbances.However,elliptical encirclement with a time-varying observation radius,may permit a more flexible and high-efficacy enclosing solution,whilst the non-orthogonal property between axial and tangential speed components,non-ignorable environmental perturbations,and strict assignment requirements empower elliptical encircling control to be more challenging,and the relevant investigations are still open.Following this line,an appointed-time elliptical encircling control rule capable of reinforcing circumnavigation performances is developed to enable Unmanned Aerial Vehicles(UAVs)to move along a specified elliptical path within a predetermined reaching time.The remarkable merits of the designed strategy are that the relative distance controlling error can be guaranteed to evolve within specified regions with a designer-specified convergence behavior.Meanwhile,wind perturbations can be online counteracted based on an unknown system dynamics estimator(USDE)with only one regulating parameter and high computational efficiency.Lyapunov tool demonstrates that all involved error variables are ultimately limited,and simulations are implemented to confirm the usability of the suggested control algorithm.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.92250306,11974137,and 12304302)the National Key Program for Science and Technology Research and Development of China(Grant No.2019YFA0307700)+1 种基金the Natural Science Foundation of Jilin Province,China(Grant Nos.YDZJ202101ZYTS157 and YDZJ202201ZYTS314)the Scientific Research Foundation of the Education Department of Jilin Province,China(Grant No.JJKH20230283KJ)。
文摘High-order harmonic generation(HHG) of Ar atom in an elliptically polarized intense laser field is experimentally investigated in this work.Interestingly,the anomalous ellipticity dependence on the laser ellipticity(ε) in the lower-order harmonics is observed,specifically in the 13rd-order,which displays a maximal harmonic intensity at ε ≈ 0.1,rather than at ε = 0 as expected.This contradicts the general trend of harmonic yield,which typically decreases with the increase of laser ellipticity.In this study,we attribute this phenomenon to the disruption of the symmetry of the wave function by the Coulomb effect,leading to the generation of a harmonic with high ellipticity.This finding provides valuable insights into the behavior of elliptically polarized harmonics and opens up a potential way for exploring new applications in ultrafast spectroscopy and light–matter interactions.
基金funded by National Natural Science Foundation of China(Grant No.41972264)Zhejiang Provincial Natural Science Foundation of China(Grant No.LR22E080002)the Observation and Research Station of Geohazards in Zhejiang,Ministry of Natural Resources,China(Grant No.ZJDZGCZ-2021).
文摘The geometric characteristics of fractures within a rock mass can be inferred by the data sampling from boreholes or exposed surfaces.Recently,the universal elliptical disc(UED)model was developed to represent natural fractures,where the fracture is assumed to be an elliptical disc and the fracture orientation,rotation angle,length of the long axis and ratio of short-long axis lengths are considered as variables.This paper aims to estimate the fracture size-and azimuth-related parameters in the UED model based on the trace information from sampling windows.The stereological relationship between the trace length,size-and azimuth-related parameters of the UED model was established,and the formulae of the mean value and standard deviation of trace length were proposed.The proposed formulae were validated via the Monte Carlo simulations with less than 5%of error rate between the calculated and true values.With respect to the estimation of the size-and azimuth-related parameters using the trace length,an optimization method was developed based on the pre-assumed size and azimuth distribution forms.A hypothetical case study was designed to illustrate and verify the parameter estimation method,where three combinations of the sampling windows were used to estimate the parameters,and the results showed that the estimated values could agree well with the true values.Furthermore,a hypothetical three-dimensional(3D)elliptical fracture network was constructed,and the circular disc,non-UED and UED models were used to represent it.The simulated trace information from different models was compared,and the results clearly illustrated the superiority of the proposed UED model over the existing circular disc and non-UED models。
基金Project supported by the National Natural Science Foundation of China(Grant Nos.12104389,12074329,and 12004323)the Nanhu Scholars Program for Young Scholars of XYNU.
文摘Circularly and elliptically polarized high-order harmonics have unique advantages when used in studying the chiral and magnetic features of matter.Here,we studied the polarization properties of high-order harmonics generated from alignment nitrogen molecules driven by cross-linearly polarized two-color laser fields.Through adjusting various laser parameters and targets,such as the relative phase,the crossing angle,the intensity ratio of the driving fields,and the molecular alignment angle,we obtained highly elliptically polarized high-order harmonics with the same helicity in a wide spectral range.This provides a possible effective way to generate elliptically polarized attosecond pulses.Finally,we showed the probability of controlling the spectral range of elliptically polarized harmonics.
基金supported by the National Natural Science Foundation of China (Grant No. 61975185)the Natural Science Foundation of Zhejiang Province, China (Grant Nos. LY19F030004 and LY20F050002)。
文摘Elliptical airy vortex beams(EAVBs) can spontaneously form easily identifiable topological charge focal spots. They are used for topological charge detection of vortex beams because they have the abruptly autofocusing properties of circular airy vortex beams and exhibit unique propagation characteristics. We study the use of the dynamic phase and Pancharatnam–Berry phase principles for generation and modulation of EAVBs by designing complex-amplitude metasurface and phase-only metasurface, at an operating wavelength of 1500 nm. It is found that the focusing pattern of EAVBs in the autofocusing plane splits into |m| + 1 tilted bright spots from the original ring, and the tilted direction is related to the sign of the topological charge number m. Due to the advantages of ultra-thin, ultra-light, and small size of the metasurface, our designed metasurface device has potential applications in improving the channel capacity based on orbital angular momentum communication, information coding, and particle capture compared to spatial light modulation systems that generate EAVBs.
文摘Protecting the privacy of data in the multi-cloud is a crucial task.Data mining is a technique that protects the privacy of individual data while mining those data.The most significant task entails obtaining data from numerous remote databases.Mining algorithms can obtain sensitive information once the data is in the data warehouse.Many traditional algorithms/techniques promise to provide safe data transfer,storing,and retrieving over the cloud platform.These strategies are primarily concerned with protecting the privacy of user data.This study aims to present data mining with privacy protection(DMPP)using precise elliptic curve cryptography(PECC),which builds upon that algebraic elliptic curve infinitefields.This approach enables safe data exchange by utilizing a reliable data consolidation approach entirely reliant on rewritable data concealing techniques.Also,it outperforms data mining in terms of solid privacy procedures while maintaining the quality of the data.Average approximation error,computational cost,anonymizing time,and data loss are considered performance measures.The suggested approach is practical and applicable in real-world situations according to the experimentalfindings.
文摘The constrained motion of a particle on an elliptical path is studied using Hamiltonian mechanics through Poisson bracket and Lagrangian mechanics through Euler Lagrange equation using non-natural Lagrangian. We calculate the generalized momentum p<sub>θ</sub> and we find that this quantity is not conserved and the conjugate θ coordinate is not a cyclic coordinate.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.11772046 and 81870345)。
文摘Diffusion in narrow curved channels with dead-ends as in extracellular space in the biological tissues,e.g.,brain,tumors,muscles,etc.is a geometrically induced complex diffusion and is relevant to different kinds of biological,physical,and chemical systems.In this paper,we study the effects of geometry and confinement on the diffusion process in an elliptical comb-like structure and analyze its statistical properties.The ellipse domain whose boundary has the polar equationρ(θ)=b/√1−e^(2)cos^(2)θ with 0<e<1,θ∈[0,2π],and b as a constant,can be obtained through stretched radius r such that Υ=rρ(θ)with r∈[0,1].We suppose that,for fixed radius r=R,an elliptical motion takes place and is interspersed with a radial motion inward and outward of the ellipse.The probability distribution function(PDF)in the structure and the marginal PDF and mean square displacement(MSD)along the backbone are obtained numerically.The results show that a transient sub-diffusion behavior dominates the process for a time followed by a saturating state.The sub-diffusion regime and saturation threshold are affected by the length of the elliptical channel lateral branch and its curvature.
基金Y Jiang is supported by the Macao FoundationMacao Science and Technology Development Fund,grant No.0001/2019/A1by the Pre-research Project on Civil Aerospace Technologies No.D020303/D020308 funded by China National Space Administration。
文摘A future constellation of at least four geomagnetic satellites(designated Macao Scientific Satellite-1(MSS-1)and Macao Scientific Satellite-2(MSS-2))was recently proposed,to continue high-quality geomagnetic observations in the post-Swarm period,focusing especially on collecting data that will provide a global,three-dimensional survey of the geomagnetic field.In this paper,we present a simulation of two years of orbits(2020.01.01-2022.01.01)of two satellites(tentatively denoted as MSS-2)that are constellated in elliptical(200×5,300 km)low-perigee orbits.By comparing error variances of Gauss coefficients,we investigate the sensitivity of lithospheric magnetic field modelling to data collected from various satellite orbits,including a near circular reference orbit of 300×350km,and elliptical orbit of 180×5,300 km,220×5,300 km,200×3,000 km and 200×1,500 km.We find that in two years the two MSS-2 satellites can collect 35,000 observations at altitude below 250 km,data that will be useful in advancing the quality of lithospheric magnetic field modelling;this number of observations reflects the fact that only 4.5%of the flight time of these satellites will be below250 km(just 6.4%of their flight time below 300 km).By combining observations from the MSS-2 satellites’elliptical orbits of 200×5,300km with observations from a circular reference orbit,the variance of the geomagnetic model can be reduced by a factor of 285 at spherical harmonic degree n=200 and by a factor of 1,300 at n=250.The planned lower perigee of their orbits allows the new satellites to collect data at unprecedentedly lower altitudes,thus dramatically improving the spatial resolution of satellite-derived lithospheric field models,(up to 80%at n=150).In addition,lowering the apogee increases the time interval during which the satellites fly at near-Earth altitudes,thus improving the model predictions at all spherical harmonic degrees(around 52%-62%at n=150).The upper limit of the expected improvement to the field model at the orbital apogee is not as good as at the perigee.However,data from the MSS-1 orbit can help fill the gap between data from the MSS-2 orbits and from the circular reference orbit for the low-degree part of the model.The feasibility of even lower-altitude flight requires further discussion with satellite engineers.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 11975037 and 11921006)the National Grand Instrument Project of China (Grant Nos. 2019YFF01014400 and 2019YFF01014404)。
文摘Laser-driven proton-induced x-ray emission(laser-PIXE) is a nuclear analysis method based on the compact laser ion accelerator. Due to the transient process of ion acceleration, the laser-PIXE signals are usually spurted within nanoseconds and accompanied by strong electromagnetic pulses(EMP), so traditional multi-channel detectors are no longer applicable.In this work, we designed a reflective elliptical crystal spectrometer for the diagnosis of laser-PIXE. The device can detect the energy range of 1 keV–11 ke V with a high resolution. A calibration experiment was completed on the electrostatic accelerator of Peking University using samples of Al, Ti, Cu, and ceramic artifacts. The detection efficiency of the elliptical crystal spectrometer was obtained in the order of 10-9.
基金Supported by National Natural Science Foundation of China (Grant Nos.52005199 and 42241149)Shenzhen Fundamental Research Program (Grant Nos.JCYJ20200109150425085 and JCYJ20220818102601004)+2 种基金Shenzhen Science and Technology Program (Grant Nos.JSGG20201103100001004 and JSGG20220831105800001)Research Development Program of China (Grant No.2022YFB4602502)Knowledge Innovation Program of Wuhan-Basic Research (Grant No.2022010801010203)。
文摘To benefit tissue removal and postoperative rehabilitation,increased efficiency and accuracy and reduced operating force are strongly required in the osteotomy.A novel elliptical vibration cutting(EVC)has been introduced for bone cutting compared with conventional cutting(CC)in this paper.With the assistance of high-speed microscope imaging and the dynamometer,the material removals of cortical bone and their cutting forces from two cutting regimes were recorded and analysed comprehensively,which clearly demonstrated the chip morphology improvement and the average cutting force reduction in the EVC process.It also revealed that the elliptical vibration of the cutting tool could promote fracture propagation along the shear direction.These new findings will be of important theoretical and practical values to apply the innovative EVC process to the surgical procedures of the osteotomy.
文摘Nowadays,Wireless Sensor Network(WSN)is a modern technology with a wide range of applications and greatly attractive benefits,for example,self-governing,low expenditure on execution and data communication,long-term function,and unsupervised access to the network.The Internet of Things(IoT)is an attractive,exciting paradigm.By applying communication technologies in sensors and supervising features,WSNs have initiated communication between the IoT devices.Though IoT offers access to the highest amount of information collected through WSNs,it leads to privacy management problems.Hence,this paper provides a Logistic Regression machine learning with the Elliptical Curve Cryptography technique(LRECC)to establish a secure IoT structure for preventing,detecting,and mitigating threats.This approach uses the Elliptical Curve Cryptography(ECC)algorithm to generate and distribute security keys.ECC algorithm is a light weight key;thus,it minimizes the routing overhead.Furthermore,the Logistic Regression machine learning technique selects the transmitter based on intelligent results.The main application of this approach is smart cities.This approach provides continuing reliable routing paths with small overheads.In addition,route nodes cooperate with IoT,and it handles the resources proficiently and minimizes the 29.95%delay.
基金supported by National Natural Science Foundation of China(12061080,12161087 and 12261093)the Science and Technology Project of the Education Department of Jiangxi Province(GJJ211601)supported by National Natural Science Foundation of China(11871305).
文摘We study equations in divergence form with piecewise Cαcoefficients.The domains contain corners and the discontinuity surfaces are attached to the edges of the corners.We obtain piecewise C^(1,α) estimates across the discontinuity surfaces and provide an example to illustrate the issue regarding the regularity at the corners.
文摘This article concerns the integral related to the transverse comoving distance and, in turn, to the luminosity distance both in the standard non-flat and flat cosmology. The purpose is to determine a straightforward mathematical formulation for the luminosity distance as function of the transverse comoving distance for all cosmology cases with a non-zero cosmological constant by adopting a different mindset. The applied method deals with incomplete elliptical integrals of the first kind associated with the polynomial roots admitted in the comoving distance integral according to the scientific literature. The outcome shows that the luminosity distance can be obtained by the combination of an analytical solution followed by a numerical integration in order to account for the redshift. This solution is solely compared to the current Gaussian quadrature method used as basic recognized algorithm in standard cosmology.
基金supported by the Key Project of Gansu Provincial National Science Foundation(23JRRA1022)the National Natural Science Foundation of China(12071431)+1 种基金the Fundamental Research Funds for the Central Universities(lzujbky-2021-ey18)the Innovative Groups of Basic Research in Gansu Province(22JR5RA391).
文摘Let n≥2 and let L be a second-order elliptic operator of divergence form with coefficients consisting of both an elliptic symmetric part and a BMO anti-symmetric part in ℝ^(n).In this article,we consider the weighted Kato square root problem for L.More precisely,we prove that the square root L^(1/2)satisfies the weighted L^(p)estimates||L^(1/2)(f)||L_(ω)^p(R^(n))≤C||■f||L_(ω)^p(R^(n);R^(n))for any p∈(1,∞)andω∈Ap(ℝ^(n))(the class of Muckenhoupt weights),and that||■f||L_(ω)^p(R^(n);R^(n))≤C||L^(1/2)(f)||L_(ω)^p(R^(n))for any p∈(1,2+ε)andω∈Ap(ℝ^(n))∩RH_(2+ε/p),(R^(n))(the class of reverse Hölder weights),whereε∈(0,∞)is a constant depending only on n and the operator L,and where(2+ε/p)'denotes the Hölder conjugate exponent of 2+ε/p.Moreover,for any given q∈(2,∞),we give a sufficient condition to obtain that||■f||L_(ω)^p(R^(n);R^(n))≤C||L^(1/2)(f)||L_(ω)^p(R^(n))for any p∈(1,q)andω∈A_(p)(R^(n))∩pRH_(q/p),(R^(n)).As an application,we prove that when the coefficient matrix A that appears in L satisfies the small BMO condition,the Riesz transform∇L^(−1/2)is bounded on L_(ω)^(p)(ℝ^(n))for any given p∈(1,∞)andω∈Ap(ℝ^(n)).Furthermore,applications to the weighted L^(2)-regularity problem with the Dirichlet or the Neumann boundary condition are also given.
文摘The elliptic curve cryptography algorithm represents a major advancement in the field of computer security. This innovative algorithm uses elliptic curves to encrypt and secure data, providing an exceptional level of security while optimizing the efficiency of computer resources. This study focuses on how elliptic curves cryptography helps to protect sensitive data. Text is encrypted using the elliptic curve technique because it provides great security with a smaller key on devices with limited resources, such as mobile phones. The elliptic curves cryptography of this study is better than using a 256-bit RSA key. To achieve equivalent protection by using the elliptic curves cryptography, several Python libraries such as cryptography, pycryptodome, pyQt5, secp256k1, etc. were used. These technologies are used to develop a software based on elliptic curves. If built, the software helps to encrypt and decrypt data such as a text messages and it offers the authentication for the communication.
基金supported by the National Natural Science Foundation of China(Grant No.91948303)。
文摘Remote sensing images carry crucial ground information,often involving the spatial distribution and spatiotemporal changes of surface elements.To safeguard this sensitive data,image encryption technology is essential.In this paper,a novel Fibonacci sine exponential map is designed,the hyperchaotic performance of which is particularly suitable for image encryption algorithms.An encryption algorithm tailored for handling the multi-band attributes of remote sensing images is proposed.The algorithm combines a three-dimensional synchronized scrambled diffusion operation with chaos to efficiently encrypt multiple images.Moreover,the keys are processed using an elliptic curve cryptosystem,eliminating the need for an additional channel to transmit the keys,thus enhancing security.Experimental results and algorithm analysis demonstrate that the algorithm offers strong security and high efficiency,making it suitable for remote sensing image encryption tasks.
文摘This paper considers the regularity of solutions to mixed boundary value problems in small-angle regions for elliptic equations. By constructing a specific barrier function, we proved that under the assumption of sufficient regularity of boundary conditions and coefficients, as long as the angle is sufficiently small, the regularity of the solution to the mixed boundary value problem of the second-order elliptic equation can reach any order.
文摘In this article, we deal with weak solutions to non-degenerate sub-elliptic equations in the Heisenberg group, and study the regularities of solutions. We establish horizontal Calderón-Zygmund type estimate in Besov spaces with more general assumptions on coefficients for both homogeneous equations and non-homogeneous equations. This study of regularity estimates expands the Calderón-Zygmund theory in the Heisenberg group.
文摘An offset elliptical reflector antenna suitable for satellite application was designed and investigated when it was fed by a rectangular horn partially filled.with a dielectric..The.reflector antenna exhibits high gain, low cross polarization. low sidelines and an elliptical beam. Al- though this study has been carried out in view of possible satellite applications, it is clear that this. antenna. is also suitable for use in radar antennas.
