In this paper, a lower bound of maximal dimensions of commutable matrix spaces (CMS) is given. It is found that the linear dependence of a group of one to one commutable matrices is related to whether some equations i...In this paper, a lower bound of maximal dimensions of commutable matrix spaces (CMS) is given. It is found that the linear dependence of a group of one to one commutable matrices is related to whether some equations in system can be eliminated. The corresponding relation is given. By introducing conceptions of eliminating set and eliminating index, we give an estimation of upper bound of maximal dimensions of CMS. For special cases n=5,6, the further estimation of maximal dimensions of CMS is presented.展开更多
Theory has it that increasing the step length improves the accuracy of a method. In order to affirm this we increased the step length of the concept in [1] by one to get k = 5. The technique of collocation and interpo...Theory has it that increasing the step length improves the accuracy of a method. In order to affirm this we increased the step length of the concept in [1] by one to get k = 5. The technique of collocation and interpolation of the power series approximate solution at some selected grid points is considered so as to generate continuous linear multistep methods with constant step sizes. Two, three and four interpolation points are considered to generate the continuous predictor-corrector methods which are implemented in block method respectively. The proposed methods when tested on some numerical examples performed more efficiently than those of [1]. Interestingly the concept of self starting [2] and that of constant order are reaffirmed in our new methods.展开更多
This paper focuses on derivation of a uniform order 8 implicit block method for the direct solution of general second order differential equations through continuous coefficients of Linear Multi-step Method (LMM). The...This paper focuses on derivation of a uniform order 8 implicit block method for the direct solution of general second order differential equations through continuous coefficients of Linear Multi-step Method (LMM). The continuous formulation and its first derivatives were evaluated at some selected grid and off grid points to obtain our proposed method. The superiority of the method over the existing methods is established numerically.展开更多
The existing recognition algorithms of space-time block code(STBC)for multi-antenna(MA)orthogonal frequencydivision multiplexing(OFDM)systems use feature extraction and hypothesis testing to identify the signal types ...The existing recognition algorithms of space-time block code(STBC)for multi-antenna(MA)orthogonal frequencydivision multiplexing(OFDM)systems use feature extraction and hypothesis testing to identify the signal types in a complex communication environment.However,owing to the restrictions on the prior information and channel conditions,these existing algorithms cannot perform well under strong interference and noncooperative communication conditions.To overcome these defects,this study introduces deep learning into the STBCOFDM signal recognition field and proposes a recognition method based on the fourth-order lag moment spectrum(FOLMS)and attention-guided multi-scale dilated convolution network(AMDCNet).The fourth-order lag moment vectors of the received signals are calculated,and vectors are stitched to form two-dimensional FOLMS,which is used as the input of the deep learning-based model.Then,the multi-scale dilated convolution is used to extract the details of images at different scales,and a convolutional block attention module(CBAM)is introduced to construct the attention-guided multi-scale dilated convolution module(AMDCM)to make the network be more focused on the target area and obtian the multi-scale guided features.Finally,the concatenate fusion,residual block and fully-connected layers are applied to acquire the STBC-OFDM signal types.Simulation experiments show that the average recognition probability of the proposed method at−12 dB is higher than 98%.Compared with the existing algorithms,the recognition performance of the proposed method is significantly improved and has good adaptability to environments with strong disturbances.In addition,the proposed deep learning-based model can directly identify the pre-processed FOLMS samples without a priori information on channel and noise,which is more suitable for non-cooperative communication systems than the existing algorithms.展开更多
Many initial value problems are difficult to be solved using ordinary,explicit step-by-step methods because most of these problems are considered stiff.Certain implicit methods,however,are capable of solving stiff ord...Many initial value problems are difficult to be solved using ordinary,explicit step-by-step methods because most of these problems are considered stiff.Certain implicit methods,however,are capable of solving stiff ordinary differential equations(ODEs)usually found in most applied problems.This study aims to develop a new numerical method,namely the high order variable step variable order block backward differentiation formula(VSVOHOBBDF)for the main purpose of approximating the solutions of third order ODEs.The computational work of the VSVO-HOBBDF method was carried out using the strategy of varying the step size and order in a single code.The order of the proposed method was then discussed in detail.The advancement of this strategy is intended to enhance the efficiency of the proposed method to approximate solutions effectively.In order to confirm the efficiency of the VSVO-HOBBDF method over the two ODE solvers in MATLAB,particularly ode15s and ode23s,a numerical experiment was conducted on a set of stiff problems.The numerical results prove that for this particular set of problem,the use of the proposed method is more efficient than the comparable methods.VSVO-HOBBDF method is thus recommended as a reliable alternative solver for the third order ODEs.展开更多
Nowadays the E-bank systems witnessed huge growth due to the huge developments in the internet and technologies.The transmitted information represents crucial information that is exposed to various kinds of attacks.Th...Nowadays the E-bank systems witnessed huge growth due to the huge developments in the internet and technologies.The transmitted information represents crucial information that is exposed to various kinds of attacks.This paper presents a new block cipher technique to provide security to the transmitted information between the customers and the ebank systems.The proposed algorithm consists of 10 rounds,each round involves 5 operations.The operations involve Add round key,Sub bytes,Zigzag method,convert to vector,and Magic Square of order 11.The purpose of this algorithm is to make use of the complexity of the Magic Square algorithm,the speed of addition operation,the confusion provided by the zigzag,using these operations with Galois field 28 GF(28),and repeating these operations for several rounds to build fast high secure encryption algorithm.This algorithm is designed to provide fast with high complexity and security which is suitable to encrypt the data that is transmitted over the internet.Speed,complexity,and The National Institute of Standards and Technology Framework NIST suite tests were done.The complexity of the proposed algorithm is=((256)32)r+1∗((256)89)r+1+(256)121.The proposed technique gives higher speed and security in the encryption and decryption phases,according to the results of the experiments.The degree of randomness has grown by 31.8 percent.Due to a decrease in the time of encrypting and decrypting,as well as the usage of the central processing unit(CPU),efficiency is improved.The encryption process throughput is enhanced by 13%,while the decryption process throughput is increased by 11.6 percent with the recommended approach.展开更多
基金Supported by the Youth Mainstay Teacher Foundation of HunanProvince Educational Committee
文摘In this paper, a lower bound of maximal dimensions of commutable matrix spaces (CMS) is given. It is found that the linear dependence of a group of one to one commutable matrices is related to whether some equations in system can be eliminated. The corresponding relation is given. By introducing conceptions of eliminating set and eliminating index, we give an estimation of upper bound of maximal dimensions of CMS. For special cases n=5,6, the further estimation of maximal dimensions of CMS is presented.
文摘Theory has it that increasing the step length improves the accuracy of a method. In order to affirm this we increased the step length of the concept in [1] by one to get k = 5. The technique of collocation and interpolation of the power series approximate solution at some selected grid points is considered so as to generate continuous linear multistep methods with constant step sizes. Two, three and four interpolation points are considered to generate the continuous predictor-corrector methods which are implemented in block method respectively. The proposed methods when tested on some numerical examples performed more efficiently than those of [1]. Interestingly the concept of self starting [2] and that of constant order are reaffirmed in our new methods.
文摘This paper focuses on derivation of a uniform order 8 implicit block method for the direct solution of general second order differential equations through continuous coefficients of Linear Multi-step Method (LMM). The continuous formulation and its first derivatives were evaluated at some selected grid and off grid points to obtain our proposed method. The superiority of the method over the existing methods is established numerically.
基金supported by the National Natural Science Foundation of China(91538201)the Taishan Scholar Foundation of China(ts201511020).
文摘The existing recognition algorithms of space-time block code(STBC)for multi-antenna(MA)orthogonal frequencydivision multiplexing(OFDM)systems use feature extraction and hypothesis testing to identify the signal types in a complex communication environment.However,owing to the restrictions on the prior information and channel conditions,these existing algorithms cannot perform well under strong interference and noncooperative communication conditions.To overcome these defects,this study introduces deep learning into the STBCOFDM signal recognition field and proposes a recognition method based on the fourth-order lag moment spectrum(FOLMS)and attention-guided multi-scale dilated convolution network(AMDCNet).The fourth-order lag moment vectors of the received signals are calculated,and vectors are stitched to form two-dimensional FOLMS,which is used as the input of the deep learning-based model.Then,the multi-scale dilated convolution is used to extract the details of images at different scales,and a convolutional block attention module(CBAM)is introduced to construct the attention-guided multi-scale dilated convolution module(AMDCM)to make the network be more focused on the target area and obtian the multi-scale guided features.Finally,the concatenate fusion,residual block and fully-connected layers are applied to acquire the STBC-OFDM signal types.Simulation experiments show that the average recognition probability of the proposed method at−12 dB is higher than 98%.Compared with the existing algorithms,the recognition performance of the proposed method is significantly improved and has good adaptability to environments with strong disturbances.In addition,the proposed deep learning-based model can directly identify the pre-processed FOLMS samples without a priori information on channel and noise,which is more suitable for non-cooperative communication systems than the existing algorithms.
基金funded by Fundamental Research Grant Scheme Universiti Sains Malaysia,Grant No.203/PJJAUH/6711688 received by S.A.M.Yatim.Url at http://www.research.usm.my/default.asp?tag=3&f=1&k=1.
文摘Many initial value problems are difficult to be solved using ordinary,explicit step-by-step methods because most of these problems are considered stiff.Certain implicit methods,however,are capable of solving stiff ordinary differential equations(ODEs)usually found in most applied problems.This study aims to develop a new numerical method,namely the high order variable step variable order block backward differentiation formula(VSVOHOBBDF)for the main purpose of approximating the solutions of third order ODEs.The computational work of the VSVO-HOBBDF method was carried out using the strategy of varying the step size and order in a single code.The order of the proposed method was then discussed in detail.The advancement of this strategy is intended to enhance the efficiency of the proposed method to approximate solutions effectively.In order to confirm the efficiency of the VSVO-HOBBDF method over the two ODE solvers in MATLAB,particularly ode15s and ode23s,a numerical experiment was conducted on a set of stiff problems.The numerical results prove that for this particular set of problem,the use of the proposed method is more efficient than the comparable methods.VSVO-HOBBDF method is thus recommended as a reliable alternative solver for the third order ODEs.
文摘Nowadays the E-bank systems witnessed huge growth due to the huge developments in the internet and technologies.The transmitted information represents crucial information that is exposed to various kinds of attacks.This paper presents a new block cipher technique to provide security to the transmitted information between the customers and the ebank systems.The proposed algorithm consists of 10 rounds,each round involves 5 operations.The operations involve Add round key,Sub bytes,Zigzag method,convert to vector,and Magic Square of order 11.The purpose of this algorithm is to make use of the complexity of the Magic Square algorithm,the speed of addition operation,the confusion provided by the zigzag,using these operations with Galois field 28 GF(28),and repeating these operations for several rounds to build fast high secure encryption algorithm.This algorithm is designed to provide fast with high complexity and security which is suitable to encrypt the data that is transmitted over the internet.Speed,complexity,and The National Institute of Standards and Technology Framework NIST suite tests were done.The complexity of the proposed algorithm is=((256)32)r+1∗((256)89)r+1+(256)121.The proposed technique gives higher speed and security in the encryption and decryption phases,according to the results of the experiments.The degree of randomness has grown by 31.8 percent.Due to a decrease in the time of encrypting and decrypting,as well as the usage of the central processing unit(CPU),efficiency is improved.The encryption process throughput is enhanced by 13%,while the decryption process throughput is increased by 11.6 percent with the recommended approach.
