In this paper,by choosing some appropriate test functions,we prove the Weyl’s lemma for triharmonic functions based on the new type of mean value formulas.
With the increasing dimensionality of network traffic,extracting effective traffic features and improving the identification accuracy of different intrusion traffic have become critical in intrusion detection systems(...With the increasing dimensionality of network traffic,extracting effective traffic features and improving the identification accuracy of different intrusion traffic have become critical in intrusion detection systems(IDS).However,both unsupervised and semisupervised anomalous traffic detection methods suffer from the drawback of ignoring potential correlations between features,resulting in an analysis that is not an optimal set.Therefore,in order to extract more representative traffic features as well as to improve the accuracy of traffic identification,this paper proposes a feature dimensionality reduction method combining principal component analysis and Hotelling’s T^(2) and a multilayer convolutional bidirectional long short-term memory(MSC_BiLSTM)classifier model for network traffic intrusion detection.This method reduces the parameters and redundancy of the model by feature extraction and extracts the dependent features between the data by a bidirectional long short-term memory(BiLSTM)network,which fully considers the influence between the before and after features.The network traffic is first characteristically downscaled by principal component analysis(PCA),and then the downscaled principal components are used as input to Hotelling’s T^(2) to compare the differences between groups.For datasets with outliers,Hotelling’s T^(2) can help identify the groups where the outliers are located and quantitatively measure the extent of the outliers.Finally,a multilayer convolutional neural network and a BiLSTM network are used to extract the spatial and temporal features of network traffic data.The empirical consequences exhibit that the suggested approach in this manuscript attains superior outcomes in precision,recall and F1-score juxtaposed with the prevailing techniques.The results show that the intrusion detection accuracy,precision,and F1-score of the proposed MSC_BiLSTM model for the CIC-IDS 2017 dataset are 98.71%,95.97%,and 90.22%.展开更多
This article offers a simple but rigorous proof of Brouwer’s fixed point theorem using Sperner’s Lemma.The general method I have used so far in the proof is mainly to convert the n-dimensional shapes to the correspo...This article offers a simple but rigorous proof of Brouwer’s fixed point theorem using Sperner’s Lemma.The general method I have used so far in the proof is mainly to convert the n-dimensional shapes to the corresponding case under the Sperner’s Labeling and apply the Sperner’s Lemma to solve the question.展开更多
The proof by Andrew Wiles of Fermat’s Last Theorem in 1995 resolved the existence question for non-trivial solutions in integers x,y,zto the equation xn+yn=znfor n>2. There are none. Surprisingly, there are infini...The proof by Andrew Wiles of Fermat’s Last Theorem in 1995 resolved the existence question for non-trivial solutions in integers x,y,zto the equation xn+yn=znfor n>2. There are none. Surprisingly, there are infinitely many solutions if the problem is recast in terms of modular arithmetic. Over a hundred years ago Issai Schur was able to show that for any n there is always a sufficiently large prime p0such that for all primes p≥p0the congruence xn+yn≡zn(modp)has a non-trivial solution. Schur’s argument wasnon-constructive, and there is no systematic method available at present to construct specific examples for small primes. We offer a simple method for constructing all possible solutions to a large class of congruences of this type.展开更多
With the help of the classical Abel’s lemma on summation by parts and algorithm of q-hypergeometric summations, we deal with the summation, which can be written as multiplication of a q-hypergeometric term and q-harm...With the help of the classical Abel’s lemma on summation by parts and algorithm of q-hypergeometric summations, we deal with the summation, which can be written as multiplication of a q-hypergeometric term and q-harmonic numbers. This enables us to construct and prove identities on q-harmonic numbers. Several examples are also given.展开更多
This note presents a set of new versions of Barbalat＇s lemma combining with positive （negative） definite functions.Based on these results,a set of new formulations of Lyapunov-like lemma are established.A simple ex...This note presents a set of new versions of Barbalat＇s lemma combining with positive （negative） definite functions.Based on these results,a set of new formulations of Lyapunov-like lemma are established.A simple example shows the usefulness of our results.展开更多
On the basis of Hill＇s lemma for classical Cauchy continuum, a version of Hill＇s lemma for micro-macro homogenization modeling of heterogeneous Cosserat continuum is presented in the flame of average-field theory. T...On the basis of Hill＇s lemma for classical Cauchy continuum, a version of Hill＇s lemma for micro-macro homogenization modeling of heterogeneous Cosserat continuum is presented in the flame of average-field theory. The admissible boundary conditions required to prescribe on the representative volume element for the modeling are extracted and discussed to ensure the satisfaction of Hill-Mandel energy condition and the first-order average field theory.展开更多
A. Robinson＇s sequential lemma is extended to nets in general topological space, and obviously the case of nets in ^＊R is its corollary. As its application, the paper proves a property about topology of uniform conv...A. Robinson＇s sequential lemma is extended to nets in general topological space, and obviously the case of nets in ^＊R is its corollary. As its application, the paper proves a property about topology of uniform convergence.展开更多
This paper will define the scope of hotel industry,specifically use Michael Porter 's five forces to explain the natural environment and competitive situation in this field.The porter's theory would significan...This paper will define the scope of hotel industry,specifically use Michael Porter 's five forces to explain the natural environment and competitive situation in this field.The porter's theory would significantly help hotel managers to apply key marketing strategies and gain more competitive advantages.展开更多
Matrices and integral operators with off-diagonal decay appear in numerous areas of mathematics including numerical analysis and harmonic analysis, and they also play impor-tant roles in engineering science including ...Matrices and integral operators with off-diagonal decay appear in numerous areas of mathematics including numerical analysis and harmonic analysis, and they also play impor-tant roles in engineering science including signal processing and communication engineering. Wiener’s lemma states that the localization of matrices and integral operators are preserved un-der inversion. In this introductory note, we re-examine several approaches to Wiener’s lemma for matrices. We also review briefly some recent advances on localization preservation of operations including nonlinear inversion, matrix factorization and optimization.展开更多
We consider the five-point boundary value problem for a fifth-order differential equation, where the nonlinearity is superlinear at both the origin and +infinity. Our method of proof combines the Kneser’s theorem wit...We consider the five-point boundary value problem for a fifth-order differential equation, where the nonlinearity is superlinear at both the origin and +infinity. Our method of proof combines the Kneser’s theorem with the well-known from combinatorial topology Sperner’s lemma. We also notice that our geometric approach is strongly based on the associated vector field.展开更多
We introduced the fuzzy axioms of choice,fuzzy Zorn’s lemma and fuzzy well-ordering principle,which are the fuzzy versions of the axioms of choice,Zorn’s lemma and well-ordering principle,and discussed the relations...We introduced the fuzzy axioms of choice,fuzzy Zorn’s lemma and fuzzy well-ordering principle,which are the fuzzy versions of the axioms of choice,Zorn’s lemma and well-ordering principle,and discussed the relations among them.As an application of fuzzy Zorn’s lemma,we got the following results:(1)Every proper fuzzy ideal of a ring was contained in a maximal fuzzy ideal.(2)Every nonzero ring contained a fuzzy maximal ideal.(3)Introduced the notion of fuzzy nilpotent elements in a ring R,and proved that the intersection of all fuzzy prime ideals in a commutative ring R is the union of all fuzzy nilpotent elements in R.(4)Proposed the fuzzy version of Tychonoff Theorem and by use of fuzzy Zorn’s lemma,we proved the fuzzy Tychonoff Theorem.展开更多
In June 1995,the ’95 China Hotel Fair,held at the Beijing China World TradeCentre,displayed products from over200 exhibitors from 22 countries,includingChina.The global largest barbecue,All-China Cake Decoration Cont...In June 1995,the ’95 China Hotel Fair,held at the Beijing China World TradeCentre,displayed products from over200 exhibitors from 22 countries,includingChina.The global largest barbecue,All-China Cake Decoration Contest,Cream-Making Contest,China Baking Food andCandy Products Exhibition were also held.展开更多
Avala Hotel in Budva, Montenegro, has undergone three reconstructions. Each of them led to significant spatial changes. The first hotel established the foundation of urbanization process in Budva, the building was too...Avala Hotel in Budva, Montenegro, has undergone three reconstructions. Each of them led to significant spatial changes. The first hotel established the foundation of urbanization process in Budva, the building was too high compared to the old town walls in the surrounding and thus not well integrated. The second reconstruction was the only successful achievement. At this time, in the first detailed urban plan including hotel and its surrounding area, the conclusion was that it represents ＂high-quality, seaside-favorable ambience＂ that should not be harmed by further building expansion. The last, illegal reconstruction in 2006 resulted in over enlarged new building disrespectful of the surrounding and the previous design. Similarly, the 2008 new detailed urban plan was the creation of ＂investors＇ urban planning＂. Entirely driven by profit, it arranges building reconstructions with multiple enlargements. This study tends to point out contextual impacts of the three hotels on the surrounding area, with special focus on the last reconstruction and ＂investors＇ urban planning＂ phenomena. The applied research method is comparative, chronological analysis of the three hotels. The aim of this research paper is to inspire initiatives that will help overcoming declining and harmful synergy of architecture and new socio-economic phenomena. It is the only way leading to the significant architectural goal： creating refined, harmonized and high quality ambience.展开更多
基金Supported by National Natural Science Foundation of China(Grant Nos.11801006 and 12071489).
文摘In this paper,by choosing some appropriate test functions,we prove the Weyl’s lemma for triharmonic functions based on the new type of mean value formulas.
基金supported by Tianshan Talent Training Project-Xinjiang Science and Technology Innovation Team Program(2023TSYCTD).
文摘With the increasing dimensionality of network traffic,extracting effective traffic features and improving the identification accuracy of different intrusion traffic have become critical in intrusion detection systems(IDS).However,both unsupervised and semisupervised anomalous traffic detection methods suffer from the drawback of ignoring potential correlations between features,resulting in an analysis that is not an optimal set.Therefore,in order to extract more representative traffic features as well as to improve the accuracy of traffic identification,this paper proposes a feature dimensionality reduction method combining principal component analysis and Hotelling’s T^(2) and a multilayer convolutional bidirectional long short-term memory(MSC_BiLSTM)classifier model for network traffic intrusion detection.This method reduces the parameters and redundancy of the model by feature extraction and extracts the dependent features between the data by a bidirectional long short-term memory(BiLSTM)network,which fully considers the influence between the before and after features.The network traffic is first characteristically downscaled by principal component analysis(PCA),and then the downscaled principal components are used as input to Hotelling’s T^(2) to compare the differences between groups.For datasets with outliers,Hotelling’s T^(2) can help identify the groups where the outliers are located and quantitatively measure the extent of the outliers.Finally,a multilayer convolutional neural network and a BiLSTM network are used to extract the spatial and temporal features of network traffic data.The empirical consequences exhibit that the suggested approach in this manuscript attains superior outcomes in precision,recall and F1-score juxtaposed with the prevailing techniques.The results show that the intrusion detection accuracy,precision,and F1-score of the proposed MSC_BiLSTM model for the CIC-IDS 2017 dataset are 98.71%,95.97%,and 90.22%.
基金by Dr Kemp from National Mathematics and Science College.
文摘This article offers a simple but rigorous proof of Brouwer’s fixed point theorem using Sperner’s Lemma.The general method I have used so far in the proof is mainly to convert the n-dimensional shapes to the corresponding case under the Sperner’s Labeling and apply the Sperner’s Lemma to solve the question.
文摘The proof by Andrew Wiles of Fermat’s Last Theorem in 1995 resolved the existence question for non-trivial solutions in integers x,y,zto the equation xn+yn=znfor n>2. There are none. Surprisingly, there are infinitely many solutions if the problem is recast in terms of modular arithmetic. Over a hundred years ago Issai Schur was able to show that for any n there is always a sufficiently large prime p0such that for all primes p≥p0the congruence xn+yn≡zn(modp)has a non-trivial solution. Schur’s argument wasnon-constructive, and there is no systematic method available at present to construct specific examples for small primes. We offer a simple method for constructing all possible solutions to a large class of congruences of this type.
文摘With the help of the classical Abel’s lemma on summation by parts and algorithm of q-hypergeometric summations, we deal with the summation, which can be written as multiplication of a q-hypergeometric term and q-harmonic numbers. This enables us to construct and prove identities on q-harmonic numbers. Several examples are also given.
基金supported by National Natural Science Foundation of China(No.60710002,60974044)Program for Changjiang Scholars and Innovative Research Team in University
文摘This note presents a set of new versions of Barbalat＇s lemma combining with positive （negative） definite functions.Based on these results,a set of new formulations of Lyapunov-like lemma are established.A simple example shows the usefulness of our results.
基金supported by the National Natural Science Foundation of China (90715011, 10672033 and 10590354) the National Key Basic Research and Development Program (2002CB412709) the Australia Research Council through the ARC International Fellowship Offered at University of Newcastle (LX0666274)
文摘On the basis of Hill＇s lemma for classical Cauchy continuum, a version of Hill＇s lemma for micro-macro homogenization modeling of heterogeneous Cosserat continuum is presented in the flame of average-field theory. The admissible boundary conditions required to prescribe on the representative volume element for the modeling are extracted and discussed to ensure the satisfaction of Hill-Mandel energy condition and the first-order average field theory.
基金the Basic Research Foundation of Xi'an University Architecture Technology(JC0620)the Youth Science and Technology Foundation of Xi'an University of Architecture and Technology(QN0736)
文摘A. Robinson＇s sequential lemma is extended to nets in general topological space, and obviously the case of nets in ^＊R is its corollary. As its application, the paper proves a property about topology of uniform convergence.
文摘This paper will define the scope of hotel industry,specifically use Michael Porter 's five forces to explain the natural environment and competitive situation in this field.The porter's theory would significantly help hotel managers to apply key marketing strategies and gain more competitive advantages.
基金supported by Basic Science Research Program through the National Research Foundation of Korea(NRF)funded by the Ministry of Education,Science and Technology(2013R1A1A2005402)National Science Foundation(DMS-1109063)
文摘Matrices and integral operators with off-diagonal decay appear in numerous areas of mathematics including numerical analysis and harmonic analysis, and they also play impor-tant roles in engineering science including signal processing and communication engineering. Wiener’s lemma states that the localization of matrices and integral operators are preserved un-der inversion. In this introductory note, we re-examine several approaches to Wiener’s lemma for matrices. We also review briefly some recent advances on localization preservation of operations including nonlinear inversion, matrix factorization and optimization.
文摘We consider the five-point boundary value problem for a fifth-order differential equation, where the nonlinearity is superlinear at both the origin and +infinity. Our method of proof combines the Kneser’s theorem with the well-known from combinatorial topology Sperner’s lemma. We also notice that our geometric approach is strongly based on the associated vector field.
基金Supported by the National Natural Science Foundation of China(11971384)by the grant of Natural Science Basic Research Program of Shaanxi(Program No.2021JM-137)the Fundamental Research Funds for the Central Universities under grant QTZX2106,China 111 Project(B16037)and OPPO Research Fund.
文摘We introduced the fuzzy axioms of choice,fuzzy Zorn’s lemma and fuzzy well-ordering principle,which are the fuzzy versions of the axioms of choice,Zorn’s lemma and well-ordering principle,and discussed the relations among them.As an application of fuzzy Zorn’s lemma,we got the following results:(1)Every proper fuzzy ideal of a ring was contained in a maximal fuzzy ideal.(2)Every nonzero ring contained a fuzzy maximal ideal.(3)Introduced the notion of fuzzy nilpotent elements in a ring R,and proved that the intersection of all fuzzy prime ideals in a commutative ring R is the union of all fuzzy nilpotent elements in R.(4)Proposed the fuzzy version of Tychonoff Theorem and by use of fuzzy Zorn’s lemma,we proved the fuzzy Tychonoff Theorem.
文摘In June 1995,the ’95 China Hotel Fair,held at the Beijing China World TradeCentre,displayed products from over200 exhibitors from 22 countries,includingChina.The global largest barbecue,All-China Cake Decoration Contest,Cream-Making Contest,China Baking Food andCandy Products Exhibition were also held.
文摘Avala Hotel in Budva, Montenegro, has undergone three reconstructions. Each of them led to significant spatial changes. The first hotel established the foundation of urbanization process in Budva, the building was too high compared to the old town walls in the surrounding and thus not well integrated. The second reconstruction was the only successful achievement. At this time, in the first detailed urban plan including hotel and its surrounding area, the conclusion was that it represents ＂high-quality, seaside-favorable ambience＂ that should not be harmed by further building expansion. The last, illegal reconstruction in 2006 resulted in over enlarged new building disrespectful of the surrounding and the previous design. Similarly, the 2008 new detailed urban plan was the creation of ＂investors＇ urban planning＂. Entirely driven by profit, it arranges building reconstructions with multiple enlargements. This study tends to point out contextual impacts of the three hotels on the surrounding area, with special focus on the last reconstruction and ＂investors＇ urban planning＂ phenomena. The applied research method is comparative, chronological analysis of the three hotels. The aim of this research paper is to inspire initiatives that will help overcoming declining and harmful synergy of architecture and new socio-economic phenomena. It is the only way leading to the significant architectural goal： creating refined, harmonized and high quality ambience.
