The interpretation of representations and generalization powers has been a long-standing challenge in the fields of machine learning(ML)and artificial intelligence.This study contributes to understanding the emergence...The interpretation of representations and generalization powers has been a long-standing challenge in the fields of machine learning(ML)and artificial intelligence.This study contributes to understanding the emergence of universal scaling laws in quantum-probabilistic ML.We consider the generative tensor network(GTN)in the form of a matrix-product state as an example and show that with an untrained GTN(such as a random TN state),the negative logarithmic likelihood(NLL)L generally increases linearly with the number of features M,that is,L≃kM+const.This is a consequence of the so-called“catastrophe of orthogonality,”which states that quantum many-body states tend to become exponentially orthogonal to each other as M increases.This study reveals that,while gaining information through training,the linear-scaling law is suppressed by a negative quadratic correction,leading to L≃βM−αM^(2)+const.The scaling coefficients exhibit logarithmic relationships with the number of training samples and quantum channelsχ.The emergence of a quadratic correction term in the NLL for the testing(training)set can be regarded as evidence of the generalization(representation)power of the GTN.Over-parameterization can be identified by the deviation in the values ofαbetween the training and testing sets while increasingχ.We further investigate how orthogonality in the quantum-feature map relates to the satisfaction of quantum-probabilistic interpretation and the representation and generalization powers of the GTN.Unveiling universal scaling laws in quantum-probabilistic ML would be a valuable step toward establishing a white-box ML scheme interpreted within the quantum-probabilistic framework.展开更多
In the present paper,we prove the existence,non-existence and multiplicity of positive normalized solutions(λ_(c),u_(c))∈R×H^(1)(R^(N))to the general Kirchhoff problem-M■,satisfying the normalization constrain...In the present paper,we prove the existence,non-existence and multiplicity of positive normalized solutions(λ_(c),u_(c))∈R×H^(1)(R^(N))to the general Kirchhoff problem-M■,satisfying the normalization constraint f_(R)^N u^2dx=c,where M∈C([0,∞))is a given function satisfying some suitable assumptions.Our argument is not by the classical variational method,but by a global branch approach developed by Jeanjean et al.[J Math Pures Appl,2024,183:44–75]and a direct correspondence,so we can handle in a unified way the nonlinearities g(s),which are either mass subcritical,mass critical or mass supercritical.展开更多
Discrete feedback control was designed to stabilize an unstable hybrid neutral stochastic differential delay system(HNSDDS) under a highly nonlinear constraint in the H_∞ and exponential forms.Nevertheless,the existi...Discrete feedback control was designed to stabilize an unstable hybrid neutral stochastic differential delay system(HNSDDS) under a highly nonlinear constraint in the H_∞ and exponential forms.Nevertheless,the existing work just adapted to autonomous cases,and the obtained results were mainly on exponential stabilization.In comparison with autonomous cases,non-autonomous systems are of great interest and represent an important challenge.Accordingly,discrete feedback control has here been adjusted with a time factor to stabilize an unstable non-autonomous HNSDDS,in which new Lyapunov-Krasovskii functionals and some novel technologies are adopted.It should be noted,in particular,that the stabilization can be achieved not only in the routine H_∞ and exponential forms,but also the polynomial form and even a general form.展开更多
Traditionally, simplification has been used in scientific modeling practices. However, recent advancements in deep learning techniques have provided a means to represent complex models. As a result, deep neural networ...Traditionally, simplification has been used in scientific modeling practices. However, recent advancements in deep learning techniques have provided a means to represent complex models. As a result, deep neural networks should be able to approximate the complex models, with a high degree of generalization. To achieve generalization, it is necessary to have a diverse range of examples in the training of the neural network, for example in data-driven FWI, training data should cover the expected subsurface models. To meet this requirement, we porposed a method to create geologically meaningful velocity models with complex structures and severe topography. However, it is important to note that generalization comes with its own set of challenges.Because of significant variation in topography of the generated velocity models, we need to include this information as an additional input data in training of the network. Therefore, we have transformed the seismic data to a fixed datum to incorporate geometric information. Additionally, we have enhanced the network's performance by introducing a term in the network loss function. Multiple metrics have been employed to evaluate the performance of the network. The results indicate that by providing the necessary information to the network and employing computational techniques to refine the model's accuracy, deep neural networks are capable of accurately estimating velocity models in complex environments characterized by extreme topography.展开更多
The general layout of 6th generation semi-submersible drilling platforms is the main factor impacting the efficiency of their drilling operations. This paper provides a compound/integrated algorithm based on process f...The general layout of 6th generation semi-submersible drilling platforms is the main factor impacting the efficiency of their drilling operations. This paper provides a compound/integrated algorithm based on process flow that is aimed at improving efficiency, while giving attention to stability and safety at the same time. The paper describes the process flow of dual drilling centers and a hierarchical division of rigs based on the different modes of transportation of various drilling support systems. The general layout-centripetal overall arrangement spatially was determined based on drilling efficiency. We derived our modules according to drilling functionality; the modules became our basic layout units. We applied different layout algorithm to mark out the upper and lower decks. That is, the upper deck was designed based on the lowest transportation cost while the lower deck＇s calculations were based on the best-fit scope. Storage configurations in columns and pontoons were also considered for the layout design. Finally the center of gravity was taken into consideration and the general layout was adjusted accordingly, to result in an optimal center of gravity. The methodology of the general layout can provide a reference for implementation of domestic designs of semi-submersible rigs.展开更多
Objective Neuraxial block is the most common anesthesia method for cesarean section(CS).However,for some urgent and high-risk cesarean delivery,general anesthesia(GA)also plays a very important role.We aimed to find o...Objective Neuraxial block is the most common anesthesia method for cesarean section(CS).However,for some urgent and high-risk cesarean delivery,general anesthesia(GA)also plays a very important role.We aimed to find out the reasons of choosing GA for CS in our center and the factors that may be related to the maternal and fetal outcomes.Methods We retrospectively selected parturients who had CS procedures under GA in Peking Union Medical College Hospital from January 1,2014 to December 31,2016.Clinical data(baseline maternal status,preoperative status,perioperative information,maternal and fetal outcomes)of parturients and neonates were collected and analyzed.We summarized the common reasons for applying general anesthesia,and compared the back-to-ICU ratio and hospital stay time between parturients with different maternal American Society of Anesthesiologists(ASA)grade,gestational weeks and intraoperative blood loss,as well as the fetal one-minute Apgar score between different maternal ASA grade and gestational weeks.Results There were 98 cases of CS under GA enrolled in the study.Among the maternal and fetal factors,pregnancy with internal or surgical diseases is the most common reason(59 cases,60.2%)for choosing GA,followed by the placenta and fetal membrane abnormalities(38 cases,38.8%)and the pregnancy-specific disorders(36 cases,36.7%).ASA gradeⅢ-Ⅳof parturients(χ2=44.3,P<0.05),gestation period<37 weeks(χ2=23.4,P<0.05),and blood loss>800 ml(χ2=5.5,P<0.05)were related to the higher postoperative intensive care unit(ICU)rate in parturients.ASA gradeⅢ-Ⅳof parturients(t=-2.99,P<0.05),gestation period<37 weeks(t=2.47,P<0.05)were related to the longer hospital stay.ASA gradeⅢ-Ⅳof parturients(t=2.21,P=0.01)and gestation period<37 weeks(t=-3.21,P=0.002)were related to the lower one-minute Apgar score of neonates.Conclusion Pregnancy with internal or surgical diseases is the most common reason for choosing GA for CS.High ASA grade and short gestation period were the related factors of high postoperative ICU ratio for parturients and low one-minute Apgar score for neonates.展开更多
Necessary and sufficient conditions for equalities between a 2 y′(I-P Xx)y and minimum norm quadratic unbiased estimator of variance under the general linear model, where a 2 is a known positive number, are...Necessary and sufficient conditions for equalities between a 2 y′(I-P Xx)y and minimum norm quadratic unbiased estimator of variance under the general linear model, where a 2 is a known positive number, are derived. Further, when the Gauss? Markov estimators and the ordinary least squares estimator are identical, a relative simply equivalent condition is obtained. At last, this condition is applied to an interesting example.展开更多
Generally unitary solution to the system of martix equations over the quaternion field [X mA ns =B ns ,X nn C nt =D nt ] is considered. A necessary and sufficient condition for the existence o...Generally unitary solution to the system of martix equations over the quaternion field [X mA ns =B ns ,X nn C nt =D nt ] is considered. A necessary and sufficient condition for the existence of and the expression for the generally unitary solution of the system are derived.展开更多
This paper studies the generalization capability of feedforward neural networks (FNN).The mechanism of FNNs for classification is investigated from the geometric and probabilistic viewpoints. It is pointed out that th...This paper studies the generalization capability of feedforward neural networks (FNN).The mechanism of FNNs for classification is investigated from the geometric and probabilistic viewpoints. It is pointed out that the outputs of the output layer in the FNNs for classification correspond to the estimates of posteriori probability of the input pattern samples with desired outputs 1 or 0. The theorem for the generalized kernel function in the radial basis function networks (RBFN) is given. For an 2-layer perceptron network (2-LPN). an idea of using extended samples to improve generalization capability is proposed. Finally. the experimental results of radar target classification are given to verify the generaliztion capability of the RBFNs.展开更多
The address term"老师"is used widely in modem society.This paper mainly studies the general use of the address term"老师".It raised the hypothesis firstly.Then some questionnaires were handed out t...The address term"老师"is used widely in modem society.This paper mainly studies the general use of the address term"老师".It raised the hypothesis firstly.Then some questionnaires were handed out to collect the data for the analysis.According to the statistics,this phenomenon is analyzed and interpreted.It is due to both psychological and social factors.展开更多
The implementation of general education is the only way to train higher vocational complex talents.Through analysis ofthe feasibility of developing general education in public English courses of higher vocational coll...The implementation of general education is the only way to train higher vocational complex talents.Through analysis ofthe feasibility of developing general education in public English courses of higher vocational colleges,it is hoped that the reform ofpublic English will be promoted effectively.展开更多
Dictionary has many functions, in which the function of definition is of very importance because the main purpose of dictionary is providing the entry's meaning information for the readers so that the readers can ...Dictionary has many functions, in which the function of definition is of very importance because the main purpose of dictionary is providing the entry's meaning information for the readers so that the readers can understand and use the entry-word and the realization of the purpose completely depends on lexicographical definition. However, the function of definition is limited, which need the exemplification to assist it. Therefore, the exemplification becomes very important, too. Good exemplification can assist definition, provide grammatical information, and supplement the information usage and so on. Many researches studied the exemplification of dictionary, its principles and so on. Dictionary changed much with the development of technology and many kinds of electronic dictionaries appeared. Few studies are involved with the new-type dictionary. Based on the general principles of the exemplification in a learner's printed dictionary, it is necessary to construct the general principles about the exemplification in the electronic learner's dictionary.展开更多
Name system has developed simultaneously with the change of world language.Generalities of Chinese names and English names are discussed from 8 aspects.Meanwhile,the structural changes of names in Chinese and English ...Name system has developed simultaneously with the change of world language.Generalities of Chinese names and English names are discussed from 8 aspects.Meanwhile,the structural changes of names in Chinese and English are also contrasted in order to make some further exploration.Readers may more deeply understand the specific regularity of the individual languages after knowing several generalities.展开更多
The initial boundary value problem for a viscoelastic equation ｜ u t ｜ ρ u tt △u-△u tt ＋ t 0 g（ts）△u（s）ds ＋ ｜ u t ｜ m u t = ｜ u ｜ p u in a bounded domain is considered, where ρ, m, p 〉 0 and g is a n...The initial boundary value problem for a viscoelastic equation ｜ u t ｜ ρ u tt △u-△u tt ＋ t 0 g（ts）△u（s）ds ＋ ｜ u t ｜ m u t = ｜ u ｜ p u in a bounded domain is considered, where ρ, m, p 〉 0 and g is a nonnegative and decaying function. The general uniform decay of solution energy is discussed under some conditions on the relaxation function g and the initial data by adopting the method of [14, 15, 19]. This work generalizes and improves earlier results in the literature.展开更多
A variable coefficient viscoelastic equation with a time-varying delay in the boundary feedback and acoustic boundary conditions and nonlinear source term is considered.Under suitable assumptions, general decay result...A variable coefficient viscoelastic equation with a time-varying delay in the boundary feedback and acoustic boundary conditions and nonlinear source term is considered.Under suitable assumptions, general decay results of the energy are established via suitable Lyapunov functionals and some properties of the convex functions. Our result is obtained without imposing any restrictive growth assumption on the damping term and the elements of the matrix A and the kernel function g.展开更多
Wireless communication involving unmanned aerial vehicles(UAVs)is expected to play an important role in future wireless networks.However,different from conventional terrestrial communication systems,UAVs typically hav...Wireless communication involving unmanned aerial vehicles(UAVs)is expected to play an important role in future wireless networks.However,different from conventional terrestrial communication systems,UAVs typically have rather limited onboard energy on one hand,and require additional flying energy consumption on the other hand.This renders energy-efficient UAV communication with smart energy expenditure of paramount importance.In this paper,via extensive flight experiments,we aim to firstly validate the recently derived theoretical energy model for rotary-wing UAVs,and then develop a general model for those complicated flight scenarios where rigorous theoretical model derivation is quite challenging,if not impossible.Specifically,we first investigate how UAV power consumption varies with its flying speed for the simplest straight-and-level flight.With about 12,000 valid power-speed data points collected,we first apply the model-based curve fitting to obtain the modelling parameters based on the theoretical closed-form energy model in the existing literature.In addition,in order to exclude the potential bias caused by the theoretical energy model,the obtained measurement data is also trained using a model-free deep neural network.It is found that the obtained curve from both methods can match quite well with the theoretical energy model.Next,we further extend the study to arbitrary 2-dimensional(2-D)flight,where,to our best knowledge,no rigorous theoretical derivation is available for the closed-form energy model as a function of its flying speed,direction,and acceleration.To fill the gap,we first propose a heuristic energy model for these more complicated cases,and then provide experimental validation based on the measurement results for circular level flight.展开更多
We consider a quasilinear heat system in the presence of an integral term and establish a general and optimal decay result from which improves and generalizes several stability results in the literature.
A viscoelastic equation with Balakrishnan-Taylor damping and nonlinear boundary/interior sources is considered in a bounded domain. Under appropriate assumptions ira- posed on the source and the damping, we establish ...A viscoelastic equation with Balakrishnan-Taylor damping and nonlinear boundary/interior sources is considered in a bounded domain. Under appropriate assumptions ira- posed on the source and the damping, we establish uniform decay rate of the solution energy in terms of the behavior of the nonlinear feedback and the relaxation function, without setting any restrictive growth assumptions on the damping at the origin and weakening the usual assumptions on the relaxation function.展开更多
基金supported in part by the Beijing Natural Science Foundation (Grant No. 1232025)the Ministry of Education Key Laboratory of Quantum Physics and Photonic Quantum Information (Grant No. ZYGX2024K020)Academy for Multidisciplinary Studies, Capital Normal University.
文摘The interpretation of representations and generalization powers has been a long-standing challenge in the fields of machine learning(ML)and artificial intelligence.This study contributes to understanding the emergence of universal scaling laws in quantum-probabilistic ML.We consider the generative tensor network(GTN)in the form of a matrix-product state as an example and show that with an untrained GTN(such as a random TN state),the negative logarithmic likelihood(NLL)L generally increases linearly with the number of features M,that is,L≃kM+const.This is a consequence of the so-called“catastrophe of orthogonality,”which states that quantum many-body states tend to become exponentially orthogonal to each other as M increases.This study reveals that,while gaining information through training,the linear-scaling law is suppressed by a negative quadratic correction,leading to L≃βM−αM^(2)+const.The scaling coefficients exhibit logarithmic relationships with the number of training samples and quantum channelsχ.The emergence of a quadratic correction term in the NLL for the testing(training)set can be regarded as evidence of the generalization(representation)power of the GTN.Over-parameterization can be identified by the deviation in the values ofαbetween the training and testing sets while increasingχ.We further investigate how orthogonality in the quantum-feature map relates to the satisfaction of quantum-probabilistic interpretation and the representation and generalization powers of the GTN.Unveiling universal scaling laws in quantum-probabilistic ML would be a valuable step toward establishing a white-box ML scheme interpreted within the quantum-probabilistic framework.
基金supported by the NSFC(12271184)the Guangzhou Basic and Applied Basic Research Foundation(2024A04J10001).
文摘In the present paper,we prove the existence,non-existence and multiplicity of positive normalized solutions(λ_(c),u_(c))∈R×H^(1)(R^(N))to the general Kirchhoff problem-M■,satisfying the normalization constraint f_(R)^N u^2dx=c,where M∈C([0,∞))is a given function satisfying some suitable assumptions.Our argument is not by the classical variational method,but by a global branch approach developed by Jeanjean et al.[J Math Pures Appl,2024,183:44–75]and a direct correspondence,so we can handle in a unified way the nonlinearities g(s),which are either mass subcritical,mass critical or mass supercritical.
基金supported by the National Natural Science Foundation of China(61833005)the Humanities and Social Science Fund of Ministry of Education of China(23YJAZH031)+1 种基金the Natural Science Foundation of Hebei Province of China(A2023209002,A2019209005)the Tangshan Science and Technology Bureau Program of Hebei Province of China(19130222g)。
文摘Discrete feedback control was designed to stabilize an unstable hybrid neutral stochastic differential delay system(HNSDDS) under a highly nonlinear constraint in the H_∞ and exponential forms.Nevertheless,the existing work just adapted to autonomous cases,and the obtained results were mainly on exponential stabilization.In comparison with autonomous cases,non-autonomous systems are of great interest and represent an important challenge.Accordingly,discrete feedback control has here been adjusted with a time factor to stabilize an unstable non-autonomous HNSDDS,in which new Lyapunov-Krasovskii functionals and some novel technologies are adopted.It should be noted,in particular,that the stabilization can be achieved not only in the routine H_∞ and exponential forms,but also the polynomial form and even a general form.
文摘Traditionally, simplification has been used in scientific modeling practices. However, recent advancements in deep learning techniques have provided a means to represent complex models. As a result, deep neural networks should be able to approximate the complex models, with a high degree of generalization. To achieve generalization, it is necessary to have a diverse range of examples in the training of the neural network, for example in data-driven FWI, training data should cover the expected subsurface models. To meet this requirement, we porposed a method to create geologically meaningful velocity models with complex structures and severe topography. However, it is important to note that generalization comes with its own set of challenges.Because of significant variation in topography of the generated velocity models, we need to include this information as an additional input data in training of the network. Therefore, we have transformed the seismic data to a fixed datum to incorporate geometric information. Additionally, we have enhanced the network's performance by introducing a term in the network loss function. Multiple metrics have been employed to evaluate the performance of the network. The results indicate that by providing the necessary information to the network and employing computational techniques to refine the model's accuracy, deep neural networks are capable of accurately estimating velocity models in complex environments characterized by extreme topography.
基金Supported by the National High Technology Research and Development Program of China (863 Program) under Grant No.2006AA09A104
文摘The general layout of 6th generation semi-submersible drilling platforms is the main factor impacting the efficiency of their drilling operations. This paper provides a compound/integrated algorithm based on process flow that is aimed at improving efficiency, while giving attention to stability and safety at the same time. The paper describes the process flow of dual drilling centers and a hierarchical division of rigs based on the different modes of transportation of various drilling support systems. The general layout-centripetal overall arrangement spatially was determined based on drilling efficiency. We derived our modules according to drilling functionality; the modules became our basic layout units. We applied different layout algorithm to mark out the upper and lower decks. That is, the upper deck was designed based on the lowest transportation cost while the lower deck＇s calculations were based on the best-fit scope. Storage configurations in columns and pontoons were also considered for the layout design. Finally the center of gravity was taken into consideration and the general layout was adjusted accordingly, to result in an optimal center of gravity. The methodology of the general layout can provide a reference for implementation of domestic designs of semi-submersible rigs.
基金Fund supported by the CAMS Innovation Fund for Medical Sciences(CIFMS:2016-12M-3-024)~~
文摘Objective Neuraxial block is the most common anesthesia method for cesarean section(CS).However,for some urgent and high-risk cesarean delivery,general anesthesia(GA)also plays a very important role.We aimed to find out the reasons of choosing GA for CS in our center and the factors that may be related to the maternal and fetal outcomes.Methods We retrospectively selected parturients who had CS procedures under GA in Peking Union Medical College Hospital from January 1,2014 to December 31,2016.Clinical data(baseline maternal status,preoperative status,perioperative information,maternal and fetal outcomes)of parturients and neonates were collected and analyzed.We summarized the common reasons for applying general anesthesia,and compared the back-to-ICU ratio and hospital stay time between parturients with different maternal American Society of Anesthesiologists(ASA)grade,gestational weeks and intraoperative blood loss,as well as the fetal one-minute Apgar score between different maternal ASA grade and gestational weeks.Results There were 98 cases of CS under GA enrolled in the study.Among the maternal and fetal factors,pregnancy with internal or surgical diseases is the most common reason(59 cases,60.2%)for choosing GA,followed by the placenta and fetal membrane abnormalities(38 cases,38.8%)and the pregnancy-specific disorders(36 cases,36.7%).ASA gradeⅢ-Ⅳof parturients(χ2=44.3,P<0.05),gestation period<37 weeks(χ2=23.4,P<0.05),and blood loss>800 ml(χ2=5.5,P<0.05)were related to the higher postoperative intensive care unit(ICU)rate in parturients.ASA gradeⅢ-Ⅳof parturients(t=-2.99,P<0.05),gestation period<37 weeks(t=2.47,P<0.05)were related to the longer hospital stay.ASA gradeⅢ-Ⅳof parturients(t=2.21,P=0.01)and gestation period<37 weeks(t=-3.21,P=0.002)were related to the lower one-minute Apgar score of neonates.Conclusion Pregnancy with internal or surgical diseases is the most common reason for choosing GA for CS.High ASA grade and short gestation period were the related factors of high postoperative ICU ratio for parturients and low one-minute Apgar score for neonates.
文摘Necessary and sufficient conditions for equalities between a 2 y′(I-P Xx)y and minimum norm quadratic unbiased estimator of variance under the general linear model, where a 2 is a known positive number, are derived. Further, when the Gauss? Markov estimators and the ordinary least squares estimator are identical, a relative simply equivalent condition is obtained. At last, this condition is applied to an interesting example.
文摘Generally unitary solution to the system of martix equations over the quaternion field [X mA ns =B ns ,X nn C nt =D nt ] is considered. A necessary and sufficient condition for the existence of and the expression for the generally unitary solution of the system are derived.
文摘This paper studies the generalization capability of feedforward neural networks (FNN).The mechanism of FNNs for classification is investigated from the geometric and probabilistic viewpoints. It is pointed out that the outputs of the output layer in the FNNs for classification correspond to the estimates of posteriori probability of the input pattern samples with desired outputs 1 or 0. The theorem for the generalized kernel function in the radial basis function networks (RBFN) is given. For an 2-layer perceptron network (2-LPN). an idea of using extended samples to improve generalization capability is proposed. Finally. the experimental results of radar target classification are given to verify the generaliztion capability of the RBFNs.
文摘The address term"老师"is used widely in modem society.This paper mainly studies the general use of the address term"老师".It raised the hypothesis firstly.Then some questionnaires were handed out to collect the data for the analysis.According to the statistics,this phenomenon is analyzed and interpreted.It is due to both psychological and social factors.
文摘The implementation of general education is the only way to train higher vocational complex talents.Through analysis ofthe feasibility of developing general education in public English courses of higher vocational colleges,it is hoped that the reform ofpublic English will be promoted effectively.
文摘Dictionary has many functions, in which the function of definition is of very importance because the main purpose of dictionary is providing the entry's meaning information for the readers so that the readers can understand and use the entry-word and the realization of the purpose completely depends on lexicographical definition. However, the function of definition is limited, which need the exemplification to assist it. Therefore, the exemplification becomes very important, too. Good exemplification can assist definition, provide grammatical information, and supplement the information usage and so on. Many researches studied the exemplification of dictionary, its principles and so on. Dictionary changed much with the development of technology and many kinds of electronic dictionaries appeared. Few studies are involved with the new-type dictionary. Based on the general principles of the exemplification in a learner's printed dictionary, it is necessary to construct the general principles about the exemplification in the electronic learner's dictionary.
文摘Name system has developed simultaneously with the change of world language.Generalities of Chinese names and English names are discussed from 8 aspects.Meanwhile,the structural changes of names in Chinese and English are also contrasted in order to make some further exploration.Readers may more deeply understand the specific regularity of the individual languages after knowing several generalities.
文摘The initial boundary value problem for a viscoelastic equation ｜ u t ｜ ρ u tt △u-△u tt ＋ t 0 g（ts）△u（s）ds ＋ ｜ u t ｜ m u t = ｜ u ｜ p u in a bounded domain is considered, where ρ, m, p 〉 0 and g is a nonnegative and decaying function. The general uniform decay of solution energy is discussed under some conditions on the relaxation function g and the initial data by adopting the method of [14, 15, 19]. This work generalizes and improves earlier results in the literature.
文摘A variable coefficient viscoelastic equation with a time-varying delay in the boundary feedback and acoustic boundary conditions and nonlinear source term is considered.Under suitable assumptions, general decay results of the energy are established via suitable Lyapunov functionals and some properties of the convex functions. Our result is obtained without imposing any restrictive growth assumption on the damping term and the elements of the matrix A and the kernel function g.
基金This work was supported in part by the Program for Innovative Talents and Entrepreneur in Jiangsu Province under Grant 1104000402in part by the Research Fund by Nanjing Government under Grant 1104000396+4 种基金in part by the National Science Foundation of China under Grants 62001109&61921004in part by the China Postdoctoral Science Foundation under Grants BX20200083&2020M681456in part by the Fundamental Research Funds for the Central Universities of China under Grants 3204002004A2&2242020R20011in part by the open research fund of the National and Local Joint Engineering Laboratory of RF Integration and Micro-Assembly Technology under Grant No.KFJJ20180205in part by the NUPTSF Grants No.NY218113&No.NY219077.
文摘Wireless communication involving unmanned aerial vehicles(UAVs)is expected to play an important role in future wireless networks.However,different from conventional terrestrial communication systems,UAVs typically have rather limited onboard energy on one hand,and require additional flying energy consumption on the other hand.This renders energy-efficient UAV communication with smart energy expenditure of paramount importance.In this paper,via extensive flight experiments,we aim to firstly validate the recently derived theoretical energy model for rotary-wing UAVs,and then develop a general model for those complicated flight scenarios where rigorous theoretical model derivation is quite challenging,if not impossible.Specifically,we first investigate how UAV power consumption varies with its flying speed for the simplest straight-and-level flight.With about 12,000 valid power-speed data points collected,we first apply the model-based curve fitting to obtain the modelling parameters based on the theoretical closed-form energy model in the existing literature.In addition,in order to exclude the potential bias caused by the theoretical energy model,the obtained measurement data is also trained using a model-free deep neural network.It is found that the obtained curve from both methods can match quite well with the theoretical energy model.Next,we further extend the study to arbitrary 2-dimensional(2-D)flight,where,to our best knowledge,no rigorous theoretical derivation is available for the closed-form energy model as a function of its flying speed,direction,and acceleration.To fill the gap,we first propose a heuristic energy model for these more complicated cases,and then provide experimental validation based on the measurement results for circular level flight.
基金partially funded by KFUP Munder Project#IN161006
文摘We consider a quasilinear heat system in the presence of an integral term and establish a general and optimal decay result from which improves and generalizes several stability results in the literature.
文摘A viscoelastic equation with Balakrishnan-Taylor damping and nonlinear boundary/interior sources is considered in a bounded domain. Under appropriate assumptions ira- posed on the source and the damping, we establish uniform decay rate of the solution energy in terms of the behavior of the nonlinear feedback and the relaxation function, without setting any restrictive growth assumptions on the damping at the origin and weakening the usual assumptions on the relaxation function.
