In this paper, we investigate the pseudo almost periodicity of the unique bounded solution for a nonlinear hyperbolic equation with piecewise constant argument. The equation under consideration is a mathematical model...In this paper, we investigate the pseudo almost periodicity of the unique bounded solution for a nonlinear hyperbolic equation with piecewise constant argument. The equation under consideration is a mathematical model for the dynamics of gas absorption,展开更多
To reduce computational costs, an improved form of the frequency domain boundary element method（BEM） is proposed for two-dimensional radiation and propagation acoustic problems in a subsonic uniform flow with arbitr...To reduce computational costs, an improved form of the frequency domain boundary element method（BEM） is proposed for two-dimensional radiation and propagation acoustic problems in a subsonic uniform flow with arbitrary orientation. The boundary integral equation（BIE） representation solves the two-dimensional convected Helmholtz equation（CHE） and its fundamental solution, which must satisfy a new Sommerfeld radiation condition（SRC） in the physical space. In order to facilitate conventional formulations, the variables of the advanced form are expressed only in terms of the acoustic pressure as well as its normal and tangential derivatives, and their multiplication operators are based on the convected Green＇s kernel and its modified derivative. The proposed approach significantly reduces the CPU times of classical computational codes for modeling acoustic domains with arbitrary mean flow. It is validated by a comparison with the analytical solutions for the sound radiation problems of monopole,dipole and quadrupole sources in the presence of a subsonic uniform flow with arbitrary orientation.展开更多
Based on the multivariate continuous time autoregressive （CAR） model, this paper presents a new time-domain modal identification method of linear time-invariant system driven by the uniformly modulated Gaussian rand...Based on the multivariate continuous time autoregressive （CAR） model, this paper presents a new time-domain modal identification method of linear time-invariant system driven by the uniformly modulated Gaussian random excitation. The method can identify the physical parameters of the system from the response data. First, the structural dynamic equation is transformed into a continuous time autoregressive model （CAR） of order 3. Second, based on the assumption that the uniformly modulated function is approximately equal to a constant matrix in a very short period of time and on the property of the strong solution of the stochastic differential equation, the uniformly modulated function is identified piecewise. Two special situations are discussed. Finally, by virtue of the Girsanov theorem, we introduce a likelihood function, which is just a con- ditional density function. Maximizing the likelihood function gives the exact maximum likelihood estimators of model parameters. Numerical results show that the method has high precision and the computation is efficient.展开更多
In the present paper, we study certain differential inequalities involving p-valent functions and obtain sufficient conditions for uniformly p-valent starlikeness and uniformly p-valent convexity. We also offer a corr...In the present paper, we study certain differential inequalities involving p-valent functions and obtain sufficient conditions for uniformly p-valent starlikeness and uniformly p-valent convexity. We also offer a correct version of some known criteria for uniformly p-valent starlike and uniformly p-valent convex functions.展开更多
This article studies on Cauchy’s function f （z） and its integral, （2πi）J[ f （z）] ≡ ■C f （t）dt/（t z） taken along a closed simple contour C, in regard to their comprehensive properties over the entire z =...This article studies on Cauchy’s function f （z） and its integral, （2πi）J[ f （z）] ≡ ■C f （t）dt/（t z） taken along a closed simple contour C, in regard to their comprehensive properties over the entire z = x ＋ iy plane consisted of the simply connected open domain D ＋ bounded by C and the open domain D outside C. （1） With f （z） assumed to be C n （n ∞-times continuously differentiable） z ∈ D ＋ and in a neighborhood of C, f （z） and its derivatives f （n） （z） are proved uniformly continuous in the closed domain D ＋ = [D ＋ ＋ C]. （2） Cauchy’s integral formulas and their derivatives z ∈ D ＋ （or z ∈ D ） are proved to converge uniformly in D ＋ （or in D = [D ＋C]）, respectively, thereby rendering the integral formulas valid over the entire z-plane. （3） The same claims （as for f （z） and J[ f （z）]） are shown extended to hold for the complement function F（z）, defined to be C n z ∈ D and about C. （4） The uniform convergence theorems for f （z） and F（z） shown for arbitrary contour C are adapted to find special domains in the upper or lower half z-planes and those inside and outside the unit circle ｜z｜ = 1 such that the four general- ized Hilbert-type integral transforms are proved. （5） Further, the singularity distribution of f （z） in D is elucidated by considering the direct problem exemplified with several typ- ical singularities prescribed in D . （6） A comparative study is made between generalized integral formulas and Plemelj’s formulas on their differing basic properties. （7） Physical sig- nificances of these formulas are illustrated with applicationsto nonlinear airfoil theory. （8） Finally, an unsolved inverse problem to determine all the singularities of Cauchy function f （z） in domain D , based on the continuous numerical value of f （z） z ∈ D ＋ = [D ＋ ＋ C], is presented for resolution as a conjecture.展开更多
Let f be a function, continuous and real valued on the segment △,△ (-∞,∞) and {Rn} be the sequence of the rational functions of best uniform approximation to fon △ of order (n,n). In the present work, the converg...Let f be a function, continuous and real valued on the segment △,△ (-∞,∞) and {Rn} be the sequence of the rational functions of best uniform approximation to fon △ of order (n,n). In the present work, the convergence of {Rn} in the complex plane is considered for the special caseswhen the poles (or the zeros, respectively) of {Rn} accumulate in the terms of weak convergence of measures to acompact set of zera capacity.As a consequence, sufficient conditions for the holomorphic and the meromorphic continuability of fare given.展开更多
In this paper,we give some new low differential uniformity of some power functions defined on finite fields with odd characteristic.As corollaries of the uniformity,we obtain two families of almost perfect nonlinear f...In this paper,we give some new low differential uniformity of some power functions defined on finite fields with odd characteristic.As corollaries of the uniformity,we obtain two families of almost perfect nonlinear functions in GF(3 n)and GF(5 n)separately.Our results can be used to prove the Dobbertin et al.'s conjecture.展开更多
In this work, a new approach to stability theory of functional differential equations is proposed. Instead of putting all components of the state variable x in one Liapunov-Razumikhin function, several functions of pa...In this work, a new approach to stability theory of functional differential equations is proposed. Instead of putting all components of the state variable x in one Liapunov-Razumikhin function, several functions of partial components of x, which can be much easier constructed. are used so that the conditions ensuring that stability are simpler and less restrictive. Also, an example is given to illustrate the advantages of the obtained results.展开更多
Crowd density estimation,in general,is a challenging task due to the large variation of head sizes in the crowds.Existing methods always use a multi-column convolutional neural network(MCNN)to adapt to this variation,...Crowd density estimation,in general,is a challenging task due to the large variation of head sizes in the crowds.Existing methods always use a multi-column convolutional neural network(MCNN)to adapt to this variation,which results in an average effect in areas with different densities and brings a lot of noise to the density map.To address this problem,we propose a new method called the segmentation-aware prior network(SAPNet),which generates a high-quality density map without noise based on a coarse head-segmentation map.SAPNet is composed of two networks,i.e.,a foreground-segmentation convolutional neural network(FS-CNN)as the front end and a crowd-regression convolutional neural network(CR-CNN)as the back end.With only the single dot annotation,we generate the ground truth of segmentation masks in heads.Then,based on the ground truth,FS-CNN outputs a coarse head-segmentation map,which helps eliminate the noise in regions without people in the density map.By inputting the head-segmentation map generated by the front end,CR-CNN performs accurate crowd counting estimation and generates a high-quality density map.We demonstrate SAPNet on four datasets(i.e.,ShanghaiTech,UCF-CC-50,WorldExpo’10,and UCSD),and show the state-of-the-art performances on ShanghaiTech part B and UCF-CC-50 datasets.展开更多
A new time-domain modal identification method of linear time-invariant system driven by the non-stationary Gaussian random excitation is introduced based on the continuous time AR model.The method can identify physica...A new time-domain modal identification method of linear time-invariant system driven by the non-stationary Gaussian random excitation is introduced based on the continuous time AR model.The method can identify physical parameters of the system from response data.In order to identify the parameters of the system,the structural dynamic equation is first transformed into the continuous time AR model,and subsequently written into the forms of observation equation and state equation which is just a stochastic differential equation.Secondly,under the assumption that the uniformly modulated function is approximately equal to a constant matrix in a very short time period,the uniformly modulated function is identified piecewise.Then,we present the exact maximum likelihood estimators of parameters by virtue of the Girsanov theorem.Finally,the modal parameters are identified by eigenanalysis.Numerical results show that the method we introduce here not only has high precision and robustness,but also has very high computing efficiency.Therefore,it is suitable for real-time modal identification.展开更多
Based on the continuous time AR model,this paper presents a new time-domain modal identification method of LTI system driven by the uniformly modulated lévy random excitation.The structural dynamic equation is fi...Based on the continuous time AR model,this paper presents a new time-domain modal identification method of LTI system driven by the uniformly modulated lévy random excitation.The structural dynamic equation is first transformed into the observation equation and the state equation(namely,stochastic differential equation).Based on the property of the strong solution of the stochastic differential equation,the uniformly modulated function is identified piecewise.Then by virtue of the Girsanov theorem,we present the exact maximum likelihood estimators of parameters.Finally,the modal parameters are identified by eigen analysis.Numerical results show that the method not only has high precision and robustness but also has very high computing efficiency.展开更多
Non-stationary characteristic in nature wind has a great effect on buffeting performance of long-span bridges.The influence of key parameters in non-stationary wind velocity models on nonlinear buffeting responses of ...Non-stationary characteristic in nature wind has a great effect on buffeting performance of long-span bridges.The influence of key parameters in non-stationary wind velocity models on nonlinear buffeting responses of a super long-span suspension bridge was investigated in this paper.Firstly,four non-stationary wind velocity models are established by combing the time-varying average wind velocity with an exponential function and the fluctuating wind velocity with four modulation functions,respectively.These non-stationary wind velocity models have obvious non-stationary characteristics and then are validated by the classical power spectrum densities.Finally,three displacement responses of the bridge deck under four different independent variables ofβin the exponential function and four modulation functions were compared,respectively.Results show that the turbulence intensities using two non-uniform modulation functions(NMF)are larger than those using uniform modulation functions(uMF).Moreover,the root mean square(RMS)values of three displacement responses increase with the decrease ofβ.Besides,the RMS values of three displacement under two NMFs are larger than those under two uMFs,and their RMS values under the second uMF are the smallest.展开更多
We give a classification of second-order polynomial solutions for the homogeneous k-Hessian equation σ_k[u] = 0. There are only two classes of polynomial solutions: One is convex polynomial; another one must not be(k...We give a classification of second-order polynomial solutions for the homogeneous k-Hessian equation σ_k[u] = 0. There are only two classes of polynomial solutions: One is convex polynomial; another one must not be(k + 1)-convex, and in the second case, the k-Hessian equations are uniformly elliptic with respect to that solution. Based on this classification, we obtain the existence of C∞local solution for nonhomogeneous term f without sign assumptions.展开更多
Let （Xt）t≥0 be a Lévy process taking values in R^d with absolutely continuous marginal distributions. Given a real measurable function f on R^d in Kato＇s class, we show that the empirical mean 1/t ∫ f（Xs）d...Let （Xt）t≥0 be a Lévy process taking values in R^d with absolutely continuous marginal distributions. Given a real measurable function f on R^d in Kato＇s class, we show that the empirical mean 1/t ∫ f（Xs）ds converges to a constant z in probability with an exponential rate if and only if f has a uniform mean z. This result improves a classical result of Kahane et al. and generalizes a similar result of L. Wu from the Brownian Motion to general Lévy processes.展开更多
For the infinite delay difference equations of the general form, two new uniform asymptotic stability criteria are established in terms of the discrete Liapunov functionals.
基金The NSF(001084)of Liaoning Provincethe Science Foundation of OUC and the NSF(10371010)of China
文摘In this paper, we investigate the pseudo almost periodicity of the unique bounded solution for a nonlinear hyperbolic equation with piecewise constant argument. The equation under consideration is a mathematical model for the dynamics of gas absorption,
基金supported by National Engineering School of Tunis (No.13039.1)
文摘To reduce computational costs, an improved form of the frequency domain boundary element method（BEM） is proposed for two-dimensional radiation and propagation acoustic problems in a subsonic uniform flow with arbitrary orientation. The boundary integral equation（BIE） representation solves the two-dimensional convected Helmholtz equation（CHE） and its fundamental solution, which must satisfy a new Sommerfeld radiation condition（SRC） in the physical space. In order to facilitate conventional formulations, the variables of the advanced form are expressed only in terms of the acoustic pressure as well as its normal and tangential derivatives, and their multiplication operators are based on the convected Green＇s kernel and its modified derivative. The proposed approach significantly reduces the CPU times of classical computational codes for modeling acoustic domains with arbitrary mean flow. It is validated by a comparison with the analytical solutions for the sound radiation problems of monopole,dipole and quadrupole sources in the presence of a subsonic uniform flow with arbitrary orientation.
基金supported by the National Natural Science Foundation of China (No. 50278017)
文摘Based on the multivariate continuous time autoregressive （CAR） model, this paper presents a new time-domain modal identification method of linear time-invariant system driven by the uniformly modulated Gaussian random excitation. The method can identify the physical parameters of the system from the response data. First, the structural dynamic equation is transformed into a continuous time autoregressive model （CAR） of order 3. Second, based on the assumption that the uniformly modulated function is approximately equal to a constant matrix in a very short period of time and on the property of the strong solution of the stochastic differential equation, the uniformly modulated function is identified piecewise. Two special situations are discussed. Finally, by virtue of the Girsanov theorem, we introduce a likelihood function, which is just a con- ditional density function. Maximizing the likelihood function gives the exact maximum likelihood estimators of model parameters. Numerical results show that the method has high precision and the computation is efficient.
文摘In the present paper, we study certain differential inequalities involving p-valent functions and obtain sufficient conditions for uniformly p-valent starlikeness and uniformly p-valent convexity. We also offer a correct version of some known criteria for uniformly p-valent starlike and uniformly p-valent convex functions.
文摘This article studies on Cauchy’s function f （z） and its integral, （2πi）J[ f （z）] ≡ ■C f （t）dt/（t z） taken along a closed simple contour C, in regard to their comprehensive properties over the entire z = x ＋ iy plane consisted of the simply connected open domain D ＋ bounded by C and the open domain D outside C. （1） With f （z） assumed to be C n （n ∞-times continuously differentiable） z ∈ D ＋ and in a neighborhood of C, f （z） and its derivatives f （n） （z） are proved uniformly continuous in the closed domain D ＋ = [D ＋ ＋ C]. （2） Cauchy’s integral formulas and their derivatives z ∈ D ＋ （or z ∈ D ） are proved to converge uniformly in D ＋ （or in D = [D ＋C]）, respectively, thereby rendering the integral formulas valid over the entire z-plane. （3） The same claims （as for f （z） and J[ f （z）]） are shown extended to hold for the complement function F（z）, defined to be C n z ∈ D and about C. （4） The uniform convergence theorems for f （z） and F（z） shown for arbitrary contour C are adapted to find special domains in the upper or lower half z-planes and those inside and outside the unit circle ｜z｜ = 1 such that the four general- ized Hilbert-type integral transforms are proved. （5） Further, the singularity distribution of f （z） in D is elucidated by considering the direct problem exemplified with several typ- ical singularities prescribed in D . （6） A comparative study is made between generalized integral formulas and Plemelj’s formulas on their differing basic properties. （7） Physical sig- nificances of these formulas are illustrated with applicationsto nonlinear airfoil theory. （8） Finally, an unsolved inverse problem to determine all the singularities of Cauchy function f （z） in domain D , based on the continuous numerical value of f （z） z ∈ D ＋ = [D ＋ ＋ C], is presented for resolution as a conjecture.
基金The work is supported by Project 69 with Ministry of ScienceEducation, Bulgaria.
文摘Let f be a function, continuous and real valued on the segment △,△ (-∞,∞) and {Rn} be the sequence of the rational functions of best uniform approximation to fon △ of order (n,n). In the present work, the convergence of {Rn} in the complex plane is considered for the special caseswhen the poles (or the zeros, respectively) of {Rn} accumulate in the terms of weak convergence of measures to acompact set of zera capacity.As a consequence, sufficient conditions for the holomorphic and the meromorphic continuability of fare given.
基金supported by National Natural Science Foundation of China(Grant Nos.10771078,60973135)
文摘In this paper,we give some new low differential uniformity of some power functions defined on finite fields with odd characteristic.As corollaries of the uniformity,we obtain two families of almost perfect nonlinear functions in GF(3 n)and GF(5 n)separately.Our results can be used to prove the Dobbertin et al.'s conjecture.
文摘In this work, a new approach to stability theory of functional differential equations is proposed. Instead of putting all components of the state variable x in one Liapunov-Razumikhin function, several functions of partial components of x, which can be much easier constructed. are used so that the conditions ensuring that stability are simpler and less restrictive. Also, an example is given to illustrate the advantages of the obtained results.
基金the National Natural Science Foundation of China(No.61775048)the Fundamental Research Funds for the Central UniversitiesChina(No.ZDXMPY20180103)。
文摘Crowd density estimation,in general,is a challenging task due to the large variation of head sizes in the crowds.Existing methods always use a multi-column convolutional neural network(MCNN)to adapt to this variation,which results in an average effect in areas with different densities and brings a lot of noise to the density map.To address this problem,we propose a new method called the segmentation-aware prior network(SAPNet),which generates a high-quality density map without noise based on a coarse head-segmentation map.SAPNet is composed of two networks,i.e.,a foreground-segmentation convolutional neural network(FS-CNN)as the front end and a crowd-regression convolutional neural network(CR-CNN)as the back end.With only the single dot annotation,we generate the ground truth of segmentation masks in heads.Then,based on the ground truth,FS-CNN outputs a coarse head-segmentation map,which helps eliminate the noise in regions without people in the density map.By inputting the head-segmentation map generated by the front end,CR-CNN performs accurate crowd counting estimation and generates a high-quality density map.We demonstrate SAPNet on four datasets(i.e.,ShanghaiTech,UCF-CC-50,WorldExpo’10,and UCSD),and show the state-of-the-art performances on ShanghaiTech part B and UCF-CC-50 datasets.
基金Supported by the Major Project of National Natural Science Foundation of China(Grant No.50278017)
文摘A new time-domain modal identification method of linear time-invariant system driven by the non-stationary Gaussian random excitation is introduced based on the continuous time AR model.The method can identify physical parameters of the system from response data.In order to identify the parameters of the system,the structural dynamic equation is first transformed into the continuous time AR model,and subsequently written into the forms of observation equation and state equation which is just a stochastic differential equation.Secondly,under the assumption that the uniformly modulated function is approximately equal to a constant matrix in a very short time period,the uniformly modulated function is identified piecewise.Then,we present the exact maximum likelihood estimators of parameters by virtue of the Girsanov theorem.Finally,the modal parameters are identified by eigenanalysis.Numerical results show that the method we introduce here not only has high precision and robustness,but also has very high computing efficiency.Therefore,it is suitable for real-time modal identification.
文摘Based on the continuous time AR model,this paper presents a new time-domain modal identification method of LTI system driven by the uniformly modulated lévy random excitation.The structural dynamic equation is first transformed into the observation equation and the state equation(namely,stochastic differential equation).Based on the property of the strong solution of the stochastic differential equation,the uniformly modulated function is identified piecewise.Then by virtue of the Girsanov theorem,we present the exact maximum likelihood estimators of parameters.Finally,the modal parameters are identified by eigen analysis.Numerical results show that the method not only has high precision and robustness but also has very high computing efficiency.
基金the National Natural Science Foundation of China(Nos.52278311,52178503,U2005216,and 51908374)the Guangdong Basic and Applied Basic Research Foundation(No.2023A1515030148)+2 种基金the Shenzhen Science and Technology Innovation Program(Nos.JCYJ20220531101609020,KQTD20200820113004005,and GJHZ20220913143006012)the Foundation of State Key Laboratory for Disaster Reduction in Civil Engineering,Tongji University(No.SLDRCE19-B-10)the National Key Laboratory of Green and Long-Life Road Engineering in Extreme Environment.
文摘Non-stationary characteristic in nature wind has a great effect on buffeting performance of long-span bridges.The influence of key parameters in non-stationary wind velocity models on nonlinear buffeting responses of a super long-span suspension bridge was investigated in this paper.Firstly,four non-stationary wind velocity models are established by combing the time-varying average wind velocity with an exponential function and the fluctuating wind velocity with four modulation functions,respectively.These non-stationary wind velocity models have obvious non-stationary characteristics and then are validated by the classical power spectrum densities.Finally,three displacement responses of the bridge deck under four different independent variables ofβin the exponential function and four modulation functions were compared,respectively.Results show that the turbulence intensities using two non-uniform modulation functions(NMF)are larger than those using uniform modulation functions(uMF).Moreover,the root mean square(RMS)values of three displacement responses increase with the decrease ofβ.Besides,the RMS values of three displacement under two NMFs are larger than those under two uMFs,and their RMS values under the second uMF are the smallest.
基金supported by National Natural Science Foundation of China (Grant Nos. 11171339 and 11171261)National Center for Mathematics and Interdisciplinary Sciences
文摘We give a classification of second-order polynomial solutions for the homogeneous k-Hessian equation σ_k[u] = 0. There are only two classes of polynomial solutions: One is convex polynomial; another one must not be(k + 1)-convex, and in the second case, the k-Hessian equations are uniformly elliptic with respect to that solution. Based on this classification, we obtain the existence of C∞local solution for nonhomogeneous term f without sign assumptions.
文摘Let （Xt）t≥0 be a Lévy process taking values in R^d with absolutely continuous marginal distributions. Given a real measurable function f on R^d in Kato＇s class, we show that the empirical mean 1/t ∫ f（Xs）ds converges to a constant z in probability with an exponential rate if and only if f has a uniform mean z. This result improves a classical result of Kahane et al. and generalizes a similar result of L. Wu from the Brownian Motion to general Lévy processes.
基金Project supported by the National Natural Science Foundation of China (No. 19831030).
文摘For the infinite delay difference equations of the general form, two new uniform asymptotic stability criteria are established in terms of the discrete Liapunov functionals.
