In this article,a high-order scheme,which is formulated by combining the quadratic finite element method in space with a second-order time discrete scheme,is developed for looking for the numerical solution of a two-d...In this article,a high-order scheme,which is formulated by combining the quadratic finite element method in space with a second-order time discrete scheme,is developed for looking for the numerical solution of a two-dimensional nonlinear time fractional thermal diffusion model.The time Caputo fractional derivative is approximated by using the L2-1formula,the first-order derivative and nonlinear term are discretized by some second-order approximation formulas,and the quadratic finite element is used to approximate the spatial direction.The error accuracy O(h3+t2)is obtained,which is verified by the numerical results.展开更多
We propose a new fractional two-dimensional triangle function combination discrete chaotic map(2D-TFCDM)with the discrete fractional difference.Moreover,the chaos behaviors of the proposed map are observed and the bif...We propose a new fractional two-dimensional triangle function combination discrete chaotic map(2D-TFCDM)with the discrete fractional difference.Moreover,the chaos behaviors of the proposed map are observed and the bifurcation diagrams,the largest Lyapunov exponent plot,and the phase portraits are derived,respectively.Finally,with the secret keys generated by Menezes-Vanstone elliptic curve cryptosystem,we apply the discrete fractional map into color image encryption.After that,the image encryption algorithm is analyzed in four aspects and the result indicates that the proposed algorithm is more superior than the other algorithms.展开更多
In this article,some high-order local discontinuous Galerkin(LDG)schemes based on some second-order θ approximation formulas in time are presented to solve a two-dimen-sional nonlinear fractional diffusion equation.T...In this article,some high-order local discontinuous Galerkin(LDG)schemes based on some second-order θ approximation formulas in time are presented to solve a two-dimen-sional nonlinear fractional diffusion equation.The unconditional stability of the LDG scheme is proved,and an a priori error estimate with O(h^(k+1)+At^(2))is derived,where k≥0 denotes the index of the basis function.Extensive numerical results with Q^(k)(k=0,1,2,3)elements are provided to confirm our theoretical results,which also show that the second-order convergence rate in time is not impacted by the changed parameter θ.展开更多
For two-dimensional(2D)time fractional diffusion equations,we construct a numerical method based on a local discontinuous Galerkin(LDG)method in space and a finite differ-ence scheme in time.We investigate the numeric...For two-dimensional(2D)time fractional diffusion equations,we construct a numerical method based on a local discontinuous Galerkin(LDG)method in space and a finite differ-ence scheme in time.We investigate the numerical stability and convergence of the method for both rectangular and triangular meshes and show that the method is unconditionally stable.Numerical results indicate the effectiveness and accuracy of the method and con-firm the analysis.展开更多
A two-dimensional generalized Langevin equation is proposed to describe the protein conformational change, compatible to the electron transfer process governed by atomic packing density model. We assume a fractional G...A two-dimensional generalized Langevin equation is proposed to describe the protein conformational change, compatible to the electron transfer process governed by atomic packing density model. We assume a fractional Gaussian noise and a white noise through bond and through space coordinates respectively, and introduce the coupling effect coming from both fluctuations and equilibrium variances. The general expressions for autocorrelation functions of distance fluctuation and fluorescence lifetime variation are derived, based on which the exact conformational change dynamics can be evaluated with the aid of numerical Laplace inversion technique. We explicitly elaborate the short time and long time approximations. The relationship between the two-diraensional description and the one-dimensional theory is also discussed.展开更多
Let Ф（u ×v, k, Aa, Ac） be the largest possible number of codewords among all two- dimensional （u ×v, k, λa, λc） optical orthogonal codes. A 2-D （u× v, k, λa, λ）-OOC with Ф（u× v, k, λ...Let Ф（u ×v, k, Aa, Ac） be the largest possible number of codewords among all two- dimensional （u ×v, k, λa, λc） optical orthogonal codes. A 2-D （u× v, k, λa, λ）-OOC with Ф（u× v, k, λa, λc） codewords is said to be maximum. In this paper, the number of codewords of a maximum 2-D （u × v, 4, 1, 3）-OOC has been determined.展开更多
This work investigates synchronization of two fractional unified hyperchaotic systems via impulsive control.The stable theory about impulsive fractional equation is studied based on the stable theory about fractional ...This work investigates synchronization of two fractional unified hyperchaotic systems via impulsive control.The stable theory about impulsive fractional equation is studied based on the stable theory about fractional linear system.Then according to the theorem proposed the sufficient condition on feedback strength and impulsive interval are established to guarantee the synchronization.Numerical simulations show the effectiveness of the theorem.展开更多
This paper combines improved Hamming codes and parity codes to assure the reliability of memory in presence of multiple bit upsets with low cost overhead.The redundancy bits of improved Hamming codes will be appended ...This paper combines improved Hamming codes and parity codes to assure the reliability of memory in presence of multiple bit upsets with low cost overhead.The redundancy bits of improved Hamming codes will be appended at the end of data bits,which eliminates the overhead of interspersing the redundancy bits at the encoder and decoder.The reliability of memory is further enhanced by the layout architecture of redundancy bits and data bits.The proposed scheme has been implemented in Verilog and synthesized using the Synopsys tools.The results reveal that the proposed method has about 19% less area penalties and 13% less power consumption comparing with the current two-dimensional error codes,and its latency of encoder and decoder is 63% less than that of Hamming codes.展开更多
In order to solve the recognition of polyphase code radar signal, this paper gives two methods based on Frank code, i.e. the high-order spectrum recognition method and the fractional Fourier transform (FRFT) method, b...In order to solve the recognition of polyphase code radar signal, this paper gives two methods based on Frank code, i.e. the high-order spectrum recognition method and the fractional Fourier transform (FRFT) method, by analyzing the micro characteristics of polyphase code signals in time and frequency domain respectively. And a recognition algorithm based on Wigner-Hough transform (WHT) is developed in this paper. We verify the validity of each method by computer simulation and give relative merits and demerits. A set of results demonstrate that the algorithm based on Wigner-Hough transform has better recognition performance in low signal-to-noise (SNR) than others.展开更多
Based on the equivalent integro-differential form of the considered problem, a numerical approach to solving the two-dimensional nonlinear time fractional wave equations(NTFWEs) is considered in this paper. To this e...Based on the equivalent integro-differential form of the considered problem, a numerical approach to solving the two-dimensional nonlinear time fractional wave equations(NTFWEs) is considered in this paper. To this end, an alternating direction implicit(ADI) numerical scheme is derived. The scheme is established by combining the secondorder convolution quadrature formula and Crank–Nicolson technique in time and afourth-order difference approach in space. The convergence and unconditional stability of the proposed compact ADI scheme are strictly discussed after a concise solvabilityanalysis. A numerical example is shown to demonstrate the theoretical analysis.展开更多
The desert plant Rhazya stricta has anticancer and antimicrobial properties, and is widely used in indigenous medicines of Saudi Arabia. However, the therapeutic benefits rely on an accurate identification of this spe...The desert plant Rhazya stricta has anticancer and antimicrobial properties, and is widely used in indigenous medicines of Saudi Arabia. However, the therapeutic benefits rely on an accurate identification of this species. The authenticity of R. stricta and other medicinal plants and herbs procured from local markets can be questionable due to a lack of clear phenotypic traits. DNA barcoding is an emerging technology for rapid and accurate species identification. In this study, six candidate chloroplastid barcodes were investigated for the authentication of R. stricta. We compared the DNA sequences from fifty locally collected and five market samples of R. stricta with database sequences of R. stricta and seven closely related species. We found that the coding regions matK, rbcL, rpoB, and rpoC1 were highly similar among the taxa. By contrast, the intergenic spacers psbK-psbI and atpF-atpH were variable loci distinct for the medicinal plant R. stricta. psbK-psbI clearly discriminated R. stricta samples as an efficient single locus marker, whereas a two-locus marker combination comprising psbK-psbI + atpF-atpH was also promising according to results from the Basic Local Alignment Search Tool and a maximum likelihood gene tree generated using PHyML. Two-dimensional DNA barcodes (i.e., QR codes) for the psbK-psbI and psbK-psbI + atpF-atpH regions were created for the validation of fresh or dried R. stricta samples.展开更多
This paper briefly introduces the characteristics and structure of symbol QR two-dimensional code, a detailed analysis of the image processing method to identify QR code of the whole process, and the bilinear mapping ...This paper briefly introduces the characteristics and structure of symbol QR two-dimensional code, a detailed analysis of the image processing method to identify QR code of the whole process, and the bilinear mapping method is applied to image correction, the final steps of decoding are given. The actual test results show that, the design algorithm has theoretical and practical, this recognition system can correctly read QR code, and has high recognition rate and recognition speed, has practical value and application prospect.展开更多
In this work, we have studied the vacancy formation energy of TiN alloy of structure B2 of size 10 × 10 × 10 for nitrogen percentages of 45%, 50% and 55% under the influence of temperature at 1320 K, 1420 K ...In this work, we have studied the vacancy formation energy of TiN alloy of structure B2 of size 10 × 10 × 10 for nitrogen percentages of 45%, 50% and 55% under the influence of temperature at 1320 K, 1420 K and 1520 K using the Modified Embedded Atom Method MEAM under the calculation code LAMMPS version 2020. This study has enabled us to understand the behavior of the TiN alloy under different nitrogen percentages in terms of total energy, vacancy formation energy, crystalline parameter, occupancy rate and order parameter. For total energy, we have shown that as temperature increases, total energy decreases, making it easier to obtain TiN at higher temperatures;reaching the value of -7344.9169 eV for the 55% nitrogen structure for the temperature of 1420 K. For the energy of formation, we have shown that the compounds obtained at 1320 K and 1520 K have a more considerable energy of formation than that obtained at 1420 K. The study of fractions and the order parameter showed us that the structure of TiN with 55% nitrogen is less likely, as the composition obtained is at most 53.35%.展开更多
基金the National Natural Science Fund(11661058,11761053)Natural Science Fund of Inner Mongolia Autonomous Region(2016MS0102,2017MS0107)+1 种基金Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region(NJYT-17-A07)National Undergraduate Innovative Training Project of Inner Mongolia University(201710126026).
文摘In this article,a high-order scheme,which is formulated by combining the quadratic finite element method in space with a second-order time discrete scheme,is developed for looking for the numerical solution of a two-dimensional nonlinear time fractional thermal diffusion model.The time Caputo fractional derivative is approximated by using the L2-1formula,the first-order derivative and nonlinear term are discretized by some second-order approximation formulas,and the quadratic finite element is used to approximate the spatial direction.The error accuracy O(h3+t2)is obtained,which is verified by the numerical results.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61072147 and 11271008)
文摘We propose a new fractional two-dimensional triangle function combination discrete chaotic map(2D-TFCDM)with the discrete fractional difference.Moreover,the chaos behaviors of the proposed map are observed and the bifurcation diagrams,the largest Lyapunov exponent plot,and the phase portraits are derived,respectively.Finally,with the secret keys generated by Menezes-Vanstone elliptic curve cryptosystem,we apply the discrete fractional map into color image encryption.After that,the image encryption algorithm is analyzed in four aspects and the result indicates that the proposed algorithm is more superior than the other algorithms.
基金This work is supported by the National Natural Science Foundation of China(11661058,11761053)the Natural Science Foundation of Inner Mongolia(2017MS0107)the Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region(NJYT-17-A07).
文摘In this article,some high-order local discontinuous Galerkin(LDG)schemes based on some second-order θ approximation formulas in time are presented to solve a two-dimen-sional nonlinear fractional diffusion equation.The unconditional stability of the LDG scheme is proved,and an a priori error estimate with O(h^(k+1)+At^(2))is derived,where k≥0 denotes the index of the basis function.Extensive numerical results with Q^(k)(k=0,1,2,3)elements are provided to confirm our theoretical results,which also show that the second-order convergence rate in time is not impacted by the changed parameter θ.
文摘For two-dimensional(2D)time fractional diffusion equations,we construct a numerical method based on a local discontinuous Galerkin(LDG)method in space and a finite differ-ence scheme in time.We investigate the numerical stability and convergence of the method for both rectangular and triangular meshes and show that the method is unconditionally stable.Numerical results indicate the effectiveness and accuracy of the method and con-firm the analysis.
基金This work was supported by the National Natural Science Foundation of China （No.20973119 and No.21033008）.
文摘A two-dimensional generalized Langevin equation is proposed to describe the protein conformational change, compatible to the electron transfer process governed by atomic packing density model. We assume a fractional Gaussian noise and a white noise through bond and through space coordinates respectively, and introduce the coupling effect coming from both fluctuations and equilibrium variances. The general expressions for autocorrelation functions of distance fluctuation and fluorescence lifetime variation are derived, based on which the exact conformational change dynamics can be evaluated with the aid of numerical Laplace inversion technique. We explicitly elaborate the short time and long time approximations. The relationship between the two-diraensional description and the one-dimensional theory is also discussed.
基金Supported by the National Natural Science Foundation of China(61071221,10831002)
文摘Let Ф（u ×v, k, Aa, Ac） be the largest possible number of codewords among all two- dimensional （u ×v, k, λa, λc） optical orthogonal codes. A 2-D （u× v, k, λa, λ）-OOC with Ф（u× v, k, λa, λc） codewords is said to be maximum. In this paper, the number of codewords of a maximum 2-D （u × v, 4, 1, 3）-OOC has been determined.
基金Key Creative Project of Shanghai Education Community,China(No.13ZZ050)Key Basic Research Project of Shanghai,China(No.12JC1400400)
文摘This work investigates synchronization of two fractional unified hyperchaotic systems via impulsive control.The stable theory about impulsive fractional equation is studied based on the stable theory about fractional linear system.Then according to the theorem proposed the sufficient condition on feedback strength and impulsive interval are established to guarantee the synchronization.Numerical simulations show the effectiveness of the theorem.
基金Sponsored by the Opening Project of National Key Laboratory of Science and Technology on Reliability PhysicsApplication Technology of Electrical Component(Grant No.ZHD200903)
文摘This paper combines improved Hamming codes and parity codes to assure the reliability of memory in presence of multiple bit upsets with low cost overhead.The redundancy bits of improved Hamming codes will be appended at the end of data bits,which eliminates the overhead of interspersing the redundancy bits at the encoder and decoder.The reliability of memory is further enhanced by the layout architecture of redundancy bits and data bits.The proposed scheme has been implemented in Verilog and synthesized using the Synopsys tools.The results reveal that the proposed method has about 19% less area penalties and 13% less power consumption comparing with the current two-dimensional error codes,and its latency of encoder and decoder is 63% less than that of Hamming codes.
文摘In order to solve the recognition of polyphase code radar signal, this paper gives two methods based on Frank code, i.e. the high-order spectrum recognition method and the fractional Fourier transform (FRFT) method, by analyzing the micro characteristics of polyphase code signals in time and frequency domain respectively. And a recognition algorithm based on Wigner-Hough transform (WHT) is developed in this paper. We verify the validity of each method by computer simulation and give relative merits and demerits. A set of results demonstrate that the algorithm based on Wigner-Hough transform has better recognition performance in low signal-to-noise (SNR) than others.
基金This survey is supported by the National Natural Science Foundation of China(Grant No.11371029)the Quality Engineering Project of Colleges and Universities in Anhui Province(Grant No.2018kfk136).
文摘Based on the equivalent integro-differential form of the considered problem, a numerical approach to solving the two-dimensional nonlinear time fractional wave equations(NTFWEs) is considered in this paper. To this end, an alternating direction implicit(ADI) numerical scheme is derived. The scheme is established by combining the secondorder convolution quadrature formula and Crank–Nicolson technique in time and afourth-order difference approach in space. The convergence and unconditional stability of the proposed compact ADI scheme are strictly discussed after a concise solvabilityanalysis. A numerical example is shown to demonstrate the theoretical analysis.
文摘The desert plant Rhazya stricta has anticancer and antimicrobial properties, and is widely used in indigenous medicines of Saudi Arabia. However, the therapeutic benefits rely on an accurate identification of this species. The authenticity of R. stricta and other medicinal plants and herbs procured from local markets can be questionable due to a lack of clear phenotypic traits. DNA barcoding is an emerging technology for rapid and accurate species identification. In this study, six candidate chloroplastid barcodes were investigated for the authentication of R. stricta. We compared the DNA sequences from fifty locally collected and five market samples of R. stricta with database sequences of R. stricta and seven closely related species. We found that the coding regions matK, rbcL, rpoB, and rpoC1 were highly similar among the taxa. By contrast, the intergenic spacers psbK-psbI and atpF-atpH were variable loci distinct for the medicinal plant R. stricta. psbK-psbI clearly discriminated R. stricta samples as an efficient single locus marker, whereas a two-locus marker combination comprising psbK-psbI + atpF-atpH was also promising according to results from the Basic Local Alignment Search Tool and a maximum likelihood gene tree generated using PHyML. Two-dimensional DNA barcodes (i.e., QR codes) for the psbK-psbI and psbK-psbI + atpF-atpH regions were created for the validation of fresh or dried R. stricta samples.
文摘This paper briefly introduces the characteristics and structure of symbol QR two-dimensional code, a detailed analysis of the image processing method to identify QR code of the whole process, and the bilinear mapping method is applied to image correction, the final steps of decoding are given. The actual test results show that, the design algorithm has theoretical and practical, this recognition system can correctly read QR code, and has high recognition rate and recognition speed, has practical value and application prospect.
文摘In this work, we have studied the vacancy formation energy of TiN alloy of structure B2 of size 10 × 10 × 10 for nitrogen percentages of 45%, 50% and 55% under the influence of temperature at 1320 K, 1420 K and 1520 K using the Modified Embedded Atom Method MEAM under the calculation code LAMMPS version 2020. This study has enabled us to understand the behavior of the TiN alloy under different nitrogen percentages in terms of total energy, vacancy formation energy, crystalline parameter, occupancy rate and order parameter. For total energy, we have shown that as temperature increases, total energy decreases, making it easier to obtain TiN at higher temperatures;reaching the value of -7344.9169 eV for the 55% nitrogen structure for the temperature of 1420 K. For the energy of formation, we have shown that the compounds obtained at 1320 K and 1520 K have a more considerable energy of formation than that obtained at 1420 K. The study of fractions and the order parameter showed us that the structure of TiN with 55% nitrogen is less likely, as the composition obtained is at most 53.35%.
