If an operator is not invertible, we are interested if there is a subspace such that the reduction of the operator to that subspace is invertible. In this paper we give a spectral approach to generalized inverses cons...If an operator is not invertible, we are interested if there is a subspace such that the reduction of the operator to that subspace is invertible. In this paper we give a spectral approach to generalized inverses considering the subspace determined by the range of the spectral projection associated with an operator and a spectral set containing the point 0. We compare the cases, 0 is a simple pole of the resolvent function, 0 is a pole of order n of the resolvent function, 0 is an isolated point of the spectrum, and 0 is contained in a circularly isolated spectral set.展开更多
In this paper, we derive five basic identities for Sheffer polynomials by using generalized Pascal functional and Wronskian matrices. Then we apply twelve basic identities for Sheffer polynomials, seven from previous ...In this paper, we derive five basic identities for Sheffer polynomials by using generalized Pascal functional and Wronskian matrices. Then we apply twelve basic identities for Sheffer polynomials, seven from previous results, to degenerate Bernoulli polynomials and Korobov polynomials of the first kind and get some new identities. In addition, letting λ→ 0 in such identities gives us those for Bernoulli polynomials and Bernoulli polynomials of the second kind.展开更多
We shall give natural generalized solutions of Hadamard and tensor products equations for matrices by the concept of the Tikhonov regularization combined with the theory of reproducing kernels.
Intrusion detection is critical to guaranteeing the safety of the data in the network.Even though,since Internet commerce has grown at a breakneck pace,network traffic kinds are rising daily,and network behavior chara...Intrusion detection is critical to guaranteeing the safety of the data in the network.Even though,since Internet commerce has grown at a breakneck pace,network traffic kinds are rising daily,and network behavior characteristics are becoming increasingly complicated,posing significant hurdles to intrusion detection.The challenges in terms of false positives,false negatives,low detection accuracy,high running time,adversarial attacks,uncertain attacks,etc.lead to insecure Intrusion Detection System(IDS).To offset the existing challenge,the work has developed a secure Data Mining Intrusion detection system(DataMIDS)framework using Functional Perturbation(FP)feature selection and Bengio Nesterov Momentum-based Tuned Generative Adversarial Network(BNM-tGAN)attack detection technique.The data mining-based framework provides shallow learning of features and emphasizes feature engineering as well as selection.Initially,the IDS data are analyzed for missing values based on the Marginal Likelihood Fisher Information Matrix technique(MLFIMT)that identifies the relationship among the missing values and attack classes.Based on the analysis,the missing values are classified as Missing Completely at Random(MCAR),Missing at random(MAR),Missing Not at Random(MNAR),and handled according to the types.Thereafter,categorical features are handled followed by feature scaling using Absolute Median Division based Robust Scalar(AMDRS)and the Handling of the imbalanced dataset.The selection of relevant features is initiated using FP that uses‘3’Feature Selection(FS)techniques i.e.,Inverse Chi Square based Flamingo Search(ICS-FSO)wrapper method,Hyperparameter Tuned Threshold based Decision Tree(HpTT-DT)embedded method,and Xavier Normal Distribution based Relief(XavND-Relief)filter method.Finally,the selected features are trained and tested for detecting attacks using BNM-tGAN.The Experimental analysis demonstrates that the introduced DataMIDS framework produces an accurate diagnosis about the attack with low computation time.The work avoids false alarm rate of attacks and remains to be relatively robust against malicious attacks as compared to existing methods.展开更多
V Strela提出的两尺度相似变换(TST)在研究多小波的构造与性质中发挥着十分重要的作用.在文中,我们提出了广义共轭两尺度相似变换(GCTST)的概念.利用广义逆矩阵的分解及单边逆的相关理论,详细地研究了GCTST变换对矩阵符号特征值影响,这...V Strela提出的两尺度相似变换(TST)在研究多小波的构造与性质中发挥着十分重要的作用.在文中,我们提出了广义共轭两尺度相似变换(GCTST)的概念.利用广义逆矩阵的分解及单边逆的相关理论,详细地研究了GCTST变换对矩阵符号特征值影响,这种技巧在其他相关文献中很少使用.证明了GCTST可以保持多尺度函数的逼近阶,平衡非平衡的多尺度函数及保持对称性等.通过最后的算例,说明GCTST是可行的有效的,而且可以减少或增加多尺度函数的重数.展开更多
文摘If an operator is not invertible, we are interested if there is a subspace such that the reduction of the operator to that subspace is invertible. In this paper we give a spectral approach to generalized inverses considering the subspace determined by the range of the spectral projection associated with an operator and a spectral set containing the point 0. We compare the cases, 0 is a simple pole of the resolvent function, 0 is a pole of order n of the resolvent function, 0 is an isolated point of the spectrum, and 0 is contained in a circularly isolated spectral set.
基金supported by the Research Grant of Kwangwoon University in 2018
文摘In this paper, we derive five basic identities for Sheffer polynomials by using generalized Pascal functional and Wronskian matrices. Then we apply twelve basic identities for Sheffer polynomials, seven from previous results, to degenerate Bernoulli polynomials and Korobov polynomials of the first kind and get some new identities. In addition, letting λ→ 0 in such identities gives us those for Bernoulli polynomials and Bernoulli polynomials of the second kind.
文摘We shall give natural generalized solutions of Hadamard and tensor products equations for matrices by the concept of the Tikhonov regularization combined with the theory of reproducing kernels.
文摘Intrusion detection is critical to guaranteeing the safety of the data in the network.Even though,since Internet commerce has grown at a breakneck pace,network traffic kinds are rising daily,and network behavior characteristics are becoming increasingly complicated,posing significant hurdles to intrusion detection.The challenges in terms of false positives,false negatives,low detection accuracy,high running time,adversarial attacks,uncertain attacks,etc.lead to insecure Intrusion Detection System(IDS).To offset the existing challenge,the work has developed a secure Data Mining Intrusion detection system(DataMIDS)framework using Functional Perturbation(FP)feature selection and Bengio Nesterov Momentum-based Tuned Generative Adversarial Network(BNM-tGAN)attack detection technique.The data mining-based framework provides shallow learning of features and emphasizes feature engineering as well as selection.Initially,the IDS data are analyzed for missing values based on the Marginal Likelihood Fisher Information Matrix technique(MLFIMT)that identifies the relationship among the missing values and attack classes.Based on the analysis,the missing values are classified as Missing Completely at Random(MCAR),Missing at random(MAR),Missing Not at Random(MNAR),and handled according to the types.Thereafter,categorical features are handled followed by feature scaling using Absolute Median Division based Robust Scalar(AMDRS)and the Handling of the imbalanced dataset.The selection of relevant features is initiated using FP that uses‘3’Feature Selection(FS)techniques i.e.,Inverse Chi Square based Flamingo Search(ICS-FSO)wrapper method,Hyperparameter Tuned Threshold based Decision Tree(HpTT-DT)embedded method,and Xavier Normal Distribution based Relief(XavND-Relief)filter method.Finally,the selected features are trained and tested for detecting attacks using BNM-tGAN.The Experimental analysis demonstrates that the introduced DataMIDS framework produces an accurate diagnosis about the attack with low computation time.The work avoids false alarm rate of attacks and remains to be relatively robust against malicious attacks as compared to existing methods.
