Operator-valued frames are natural generalization of frames that have been used in quantum comput... more Operator-valued frames are natural generalization of frames that have been used in quantum computing, packets encoding, etc. In this paper, we focus on developing the theory about operator-valued frames for finite Hilbert spaces. Some results concerning dilation, alternate dual, and existence of operator-valued frames are given. Then we characterize the optimal operatorvalued frames under the case which one packet of data is lost in transmission. At last we construct the operator-valued frames {V j } m j=1 with given frame operator S and satisfying V j V * j = α j I, where α ′ j s are positive numbers.
We investigate operator-valued frames with the structure of group-like unitary systems. We show t... more We investigate operator-valued frames with the structure of group-like unitary systems. We show that the commutant of a group-like unitary system can be characterized in terms of the analysis operators associated with all the operator-valued Bessel generators and give some sufficient and necessary conditions to describe when an operator-valued frame generator admits a Parseval dual. This extends work of J.Gabardo and D.Han but the proofs turn out to be more complicated. Then we characterize the Parseval operator-valued frame generators for certain unitary systems on a finite dimensional Hilbert space.
The Kato spectrum of an operator is deployed to give necessary and sufficient conditions for Brow... more The Kato spectrum of an operator is deployed to give necessary and sufficient conditions for Browder’s theorem to hold.
ISPRS International Journal of Geo-Information, 2021
The use of social media data provided powerful data support to reveal the spatiotemporal characte... more The use of social media data provided powerful data support to reveal the spatiotemporal characteristics and mechanisms of human activity, as it integrated rich spatiotemporal and textual semantic information. However, previous research has not fully utilized its semantic and spatiotemporal information, due to its technical and algorithmic limitations. The efficiency of the deep mining of textual semantic resources was also low. In this research, a multi-classification of text model, based on natural language processing technology and the Bidirectional Encoder Representations from Transformers (BERT) framework is constructed. The residents’ activities in Beijing were then classified using the Sina Weibo data in 2019. The results showed that the accuracy of the classifications was more than 90%. The types and distribution of residents’ activities were closely related to the characteristics of the activities and holiday arrangements. From the perspective of a short timescale, the acti...
The magnetic circuit of existing linear force motors does not consider the issue of energy utiliz... more The magnetic circuit of existing linear force motors does not consider the issue of energy utilization of permanent magnets, and the structure is complicated. To achieve high energy utilization and simplify the structure, this paper presents a novel magnetic circuit topology for the linear force motors of electro-hydraulic servo-proportional valves. In order to rapidly and accurately calculate the static characteristics of the force motor, an analytical model is established by using the equivalent magnetic circuit method. The model comprehensively considers the magnetic leakage effect, edge effect, and permeability nonlinearity. A prototype of the force motor is designed and manufactured, and a special experimental platform is built. The prototype force motor has a linear force-displacement characteristic and the output force increases with the increase of the excitation currents, which can reach about 41 N at 2 A. This indicates that it is suitable as an electro-mechanical converte...
Although a two-dimensional (2D) valve has excellent performance, the processing of its spiral gro... more Although a two-dimensional (2D) valve has excellent performance, the processing of its spiral groove has a high cost and is time-consuming. This paper proposes a novel torque motor based on an annulus air gap (TMAAG) to replace the negative feedback function of the spiral groove to reduce the machining difficulty. In order to study the torque change law of the TMAAG, the air gap permeance was analyzed, and then a qualitative analytical model was established. Orthogonal tests were carried out to initially select the crucial parameters, which were further optimized through a back propagation (BP) neural network and genetic algorithm. The prototype of TMAAG was machined, and a special experimental platform was built, and experiment results are similar to the simulation values, which verifies the accuracy of the air gap analysis and qualitative model. For torque-angle characteristics, the output torque increases with both current and rotation angle and reaches about 0.754 N·m with 2 A a...
Characteristic modeling is a control oriented modeling approach that takes into account both the ... more Characteristic modeling is a control oriented modeling approach that takes into account both the dynamic characteristics of the plant to be controlled and the performance specifications of the control system. In this article, we give an introductory overview of characteristic modeling. The basic concept, key features, and underlying mechanism are first reviewed. The characteristic modeling based control design and the stability of the closed-loop system are then illustrated. An example of successful applications of the characteristic modeling in control designs is recalled to demonstrate the effectiveness of the design method. Finally, motivations of the characteristic modeling are summarized and future work is proposed.
BGB-3111, a novel Bruton's tyrosine kinase (BTK) inhibitor, shows promising anti-cancer effects i... more BGB-3111, a novel Bruton's tyrosine kinase (BTK) inhibitor, shows promising anti-cancer effects in chronic lymphocytic leukemia/small lymphocytic lymphoma (CLL/SLL), mantle cell lymphoma (MCL), and Waldenstrom macroglobulinemia (WM). This study aimed to investigate the anti-cancer effects of BGB-3111 combined with bortezomib (BTZ) against the BTK-expressing MCL. We found that BTK, which was overexpressed in 59.4% of patients with MCL, was mainly characterized by high Ki67 and elevated MIPI scores. BGB-3111 strongly inhibited cell proliferation, induced cell cycle arrest in the G1/G0-phase, and promoted cell apoptosis in the MCL cells expressing BTK. BGB-3111 provides better safety than another BTK inhibitor, ibrutinib as ibrutinib inhibits the inducible T-cell kinase (ITK) as an off-target effect but BGB-3111 does not inhibit ITK. Low doses of BTZ enhanced the anti-cancer effect induced by the low dose of BGB-3111 by downregulating the expression levels of PARP and Bcl-2 and increasing the expression levels of cleaved PARP and cleaved caspase-9. In addition, low doses of BGB-3111, but not of BTZ, inhibited BTK phosphorylation. However, low-doses of BTZ strengthened the anti-cancer effect induced by the low-doses of BGB-3111 via synergistically suppressing the IκBα and P65 phosphorylation. Taken together, our findings validate that BGB-3111 is a novel and effective BTK inhibitor for MCL-expressing BTK. Hence, it can be harnessed as a potential therapeutic strategy through a combinatorial treatment comprising low-dose BGB-3111 and low-dose BTZ to gain strong anti-cancer effects and better safety for MCL patients.
This study aimed to investigate whether the inclusion of tumor size could improve the prognostic ... more This study aimed to investigate whether the inclusion of tumor size could improve the prognostic accuracy in patients with esophageal squamous cell cancer (ESCC). A total of 387 patients with ESCC who underwent curative resection were enrolled in this analysis. The patients were categorized into small-sized tumors (SSTs) and largesized tumors (LSTs) using an appropriate cutoff point for tumor size. Kaplan-Meier survival curve and log-rank test were used to evaluate the prognostic value of tumor size. A Cox regression model was adopted for multivariate analysis. Their accuracy was compared based on the presence or absence of tumor size. Using 3.5 cm as the optimal cutoff point, 228 and 159 patients presented with LSTs (≥ 3.5 cm) and SSTs (< 3.5 cm), respectively. The patients with LSTs had significantly worse prognoses than patients with SSTs (23.9% vs. 43.2%, P < 0.001). Multivariate analysis revealed that tumor size, histological type, invasion depth, and lymph node metastasis were independent predictors of overall survival. The addition of tumor size to the AJCC TNM staging improved the predictive accuracy of the 5-year survival rate by 3.9%. Further study showed that tumor size and T stage were independent predictors of the prognosis of node-negative patients, and the combination of tumor size and T stage improved the predictive accuracy by 3.7%. In conclusion, tumor size is indeed a simple and practical prognostic factor in patients with ESCC. It can be used to improve the prognostic accuracy of the current TNM staging, especially for patients with node-negative disease.
This paper studies the reachability problem of the switched linear discrete singular (SLDS) syste... more This paper studies the reachability problem of the switched linear discrete singular (SLDS) systems. Under the condition that all subsystems are regular, the reachability of the SLDS systems is characterized based on a peculiar repeatedly introduced switching sequence. The necessary and sufficient conditions are obtained for the reachability of the SLDS systems.
We introduce the operator-valued relative free entropy χ * B (X 1 , X 2 , • • • , Xn : B) of a fa... more We introduce the operator-valued relative free entropy χ * B (X 1 , X 2 , • • • , Xn : B) of a family of self-adjoint random variables X 1 , X 2 , • • • , Xn in a B-valued noncommutative probability space (A, E B , B). This notion extends D. Voiculescu's relative free entropy Φ * which defined in a tracial W*-noncommutative probability space to a more general context. The free entropy of a semicircular variable with conditional expectation covariance can be computed by using the modular frames and then we point out the relation between the free entropy of a semicircular variable and the index of a conditional expectation. At last, we obtain an estimate of the free entropy dimension δ * B,τ .
Weyl type theorems for p-hyponormal and M-hyponormal operators by Xiaohong Cao (Xi'an), Maozheng ... more Weyl type theorems for p-hyponormal and M-hyponormal operators by Xiaohong Cao (Xi'an), Maozheng Guo (Beijing) and Bin Meng (Beijing) Abstract. "Generalized Weyl's theorem holds" for an operator when the complement in the spectrum of the B-Weyl spectrum coincides with the isolated points of the spectrum which are eigenvalues; and "generalized a-Weyl's theorem holds" for an operator when the complement in the approximate point spectrum of the semi-B-essential approximate point spectrum coincides with the isolated points of the approximate point spectrum which are eigenvalues. If T or T * is p-hyponormal or M-hyponormal then for every f ∈ H(σ(T)), generalized Weyl's theorem holds for f (T), so Weyl's theorem holds for f (T), where H(σ(T)) denotes the set of all analytic functions on an open neighborhood of σ(T). Moreover, if T * is p-hyponormal or M-hyponormal then for every f ∈ H(σ(T)), generalized a-Weyl's theorem holds for f (T) and hence a-Weyl's theorem holds for f (T). a (T) = C \ σ a (T). An operator T ∈ B(H) is called Fredholm if it has closed finite-codimensional range and finite-dimensional null space. The index of a Fredholm operator T ∈ B(H) is given by ind(T) = n(T) − d(T). An operator T ∈ B(H) is called Weyl if it is Fredholm of index zero, and Browder if it is Fredholm of finite ascent and descent, or equivalently, if T is Fredholm and T − λI is invertible for all sufficiently small λ = 0 in C. For T ∈ B(H), we write α(T) for the ascent of T and β(T) for the descent of T .
The characteristic modeling problem of flight vehicles' attitude dynamics is considered in this p... more The characteristic modeling problem of flight vehicles' attitude dynamics is considered in this paper. In terms of the affine nonlinear system with triangle form of flight vehicles' attitude dynamics, a general method is presented to compress the dynamics into the characteristic model parameters, by introducing the time scale of nonlinear systems and a class of system states related compress functions. The parameter region and limit of the characteristic model are also given. From the given parameter region it is seen that the bound of the characteristic model parameters is dependent on the sampling period, the modeling error, the system order and the system change rate. The modeling error of the established characteristic model can be arbitrarily small according to the control precision, showing the difference between the characteristic model and other model reduction methods, that is, no system information is lost using this approach. On the basis of this modeling approach, the characteristic model of the flexible satellite attitude is established, as well as the bound and limit of the parameters, which sets a theoretical foundation for characteristic model based control design of flight vehicles. characteristic modeling, modeling error, time scale of nonlinear systems, spacecraft, attitude dynamics
Let σ ab (T) = {λ ∈ C : T − λI is not an upper semi-Fredholm operator with finite ascent} be the ... more Let σ ab (T) = {λ ∈ C : T − λI is not an upper semi-Fredholm operator with finite ascent} be the Browder essential approximate point spectrum of T ∈ B(H) and let σ d (T) = {λ ∈ C : T − λI is not surjective} be the surjective spectrum of T. In this paper it is shown that if M C = A C 0 B is a 2 × 2 upper triangular operator matrix acting on the Hilbert space H ⊕ K, then the passage from σ ab (A) ∪ σ ab (B) to σ ab (M C) is accomplished by removing certain open subsets of σ d (A) ∩ σ ab (B) from the former, that is, there is equality σ ab (A) ∪ σ ab (B) = σ ab (M C) ∪ G, where G is the union of certain of the holes in σ ab (M C) which happen to be subsets of σ d (A) ∩ σ ab (B). Weyl's theorem and Browder's theorem are liable to fail for 2 × 2 operator matrices. In this paper, it also explores how Weyl's theorem, Browder's theorem, a-Weyl's theorem and a-Browder's theorem survive for 2 × 2 upper triangular operator matrices on the Hilbert space.
Journal of Mathematical Analysis and Applications, 2005
We introduce the notion of operator-valued free Fisher information with respect to a positive map... more We introduce the notion of operator-valued free Fisher information with respect to a positive map of a random variable in an operator-valued noncommutative probability space and point out its close relations to the modular frames arising from conditional expectations. Then we can apply this notion on the study of frame theory, especially on the disjointness problem of modular frames arising from conditional expectations.
Journal of Mathematical Analysis and Applications, 2003
Two variants of the Weyl spectrum are discussed. We find, for example, that if one of them coinci... more Two variants of the Weyl spectrum are discussed. We find, for example, that if one of them coincides with the Browder spectrum then Weyl's theorem holds, and conversely for isoloid operators.
International Journal of Geographical Information Science, 2010
Mapping population distribution is an important field of geographical and related research becaus... more Mapping population distribution is an important field of geographical and related research because of the frequent need to combine spatial data representing socio-demographic information across various incompatible spatial units. However, the research may become very complex and difficult when a population in multiple places is estimated by various factors. Previous efforts in the field have contributed to the selection of appropriate independent variables and the creation of different population models. However, the level of accuracy obtainable with these studies is limited by the spatial heterogeneity of population distribution within the individual census districts, particularly in large rural areas. A high-accuracy modelling method for population estimation based on integration of Genetic Programming (GP) and Genetic Algorithms (GA) with Geographic Information Systems (GIS) is presented in this paper. GIS was applied to identify and quantify a set of natural and socioeconomic factors which contributed to population distribution, and then GP and GA were used to build and optimise the population model to automatically transform census population data to regular grids. The study indicated that the proposed method performed much better than the stepwise regression analysis and adapted gravity model methods in estimating the population of both urban and rural areas. More importantly, this proposed method could provide a single, unified approach to mapping population distribution in various areas because the paradigms of these algorithms are general.
The reachability problem of switched linear singular systems is investigated in this note. By usi... more The reachability problem of switched linear singular systems is investigated in this note. By using the geometric approach and the admissible control set introduced, a necessary condition and a sufficient condition on complete reachability are presented. The conditions are the same as those of the conventional (nonsingular) switched linear systems and normal (nonswitching) singular systems given in previous papers when the systems degenerate to normal singular systems and conventional switched systems, respectively.
Acta Mathematicae Applicatae Sinica, English Series, 2016
The DGMRES method for solving Drazin-inverse solution of singular linear systems is generally use... more The DGMRES method for solving Drazin-inverse solution of singular linear systems is generally used with restarting. But the restarting often slows down the convergence and DGMRES often stagnates. We show that adding some eigenvectors to the subspace can improve the convergence just like the method proposed by R.
Journal of Mathematical Analysis and Applications, 2005
When A ∈ B(H) and B ∈ B(K) are given, we denote by M C the operator acting on the infinite dimens... more When A ∈ B(H) and B ∈ B(K) are given, we denote by M C the operator acting on the infinite dimensional separable Hilbert space H ⊕ K of the form M C = A C 0 B. In this paper, it is shown that a 2 × 2 operator matrix M C is upper semi-Fredholm and ind(M C) 0 for some C ∈ B(K, H) if and only if A is upper semi-Fredholm and n(B) < ∞ and n(A) + n(B) d(A) + d(B) or n(B) = d(A) = ∞, if R(B) is closed, d(A) = ∞, if R(B) is not closed. We also give the necessary and sufficient conditions for which M C is Weyl or M C is lower semi-Fredholm with nonnegative index for some C ∈ B(K, H). In addition, we explore how Weyl's theorem, Browder's theorem, a-Weyl's theorem, and a-Browder's theorem survive for 2 × 2 upper triangular operator matrices on the Hilbert space.
Operator-valued frames are natural generalization of frames that have been used in quantum comput... more Operator-valued frames are natural generalization of frames that have been used in quantum computing, packets encoding, etc. In this paper, we focus on developing the theory about operator-valued frames for finite Hilbert spaces. Some results concerning dilation, alternate dual, and existence of operator-valued frames are given. Then we characterize the optimal operatorvalued frames under the case which one packet of data is lost in transmission. At last we construct the operator-valued frames {V j } m j=1 with given frame operator S and satisfying V j V * j = α j I, where α ′ j s are positive numbers.
We investigate operator-valued frames with the structure of group-like unitary systems. We show t... more We investigate operator-valued frames with the structure of group-like unitary systems. We show that the commutant of a group-like unitary system can be characterized in terms of the analysis operators associated with all the operator-valued Bessel generators and give some sufficient and necessary conditions to describe when an operator-valued frame generator admits a Parseval dual. This extends work of J.Gabardo and D.Han but the proofs turn out to be more complicated. Then we characterize the Parseval operator-valued frame generators for certain unitary systems on a finite dimensional Hilbert space.
The Kato spectrum of an operator is deployed to give necessary and sufficient conditions for Brow... more The Kato spectrum of an operator is deployed to give necessary and sufficient conditions for Browder’s theorem to hold.
ISPRS International Journal of Geo-Information, 2021
The use of social media data provided powerful data support to reveal the spatiotemporal characte... more The use of social media data provided powerful data support to reveal the spatiotemporal characteristics and mechanisms of human activity, as it integrated rich spatiotemporal and textual semantic information. However, previous research has not fully utilized its semantic and spatiotemporal information, due to its technical and algorithmic limitations. The efficiency of the deep mining of textual semantic resources was also low. In this research, a multi-classification of text model, based on natural language processing technology and the Bidirectional Encoder Representations from Transformers (BERT) framework is constructed. The residents’ activities in Beijing were then classified using the Sina Weibo data in 2019. The results showed that the accuracy of the classifications was more than 90%. The types and distribution of residents’ activities were closely related to the characteristics of the activities and holiday arrangements. From the perspective of a short timescale, the acti...
The magnetic circuit of existing linear force motors does not consider the issue of energy utiliz... more The magnetic circuit of existing linear force motors does not consider the issue of energy utilization of permanent magnets, and the structure is complicated. To achieve high energy utilization and simplify the structure, this paper presents a novel magnetic circuit topology for the linear force motors of electro-hydraulic servo-proportional valves. In order to rapidly and accurately calculate the static characteristics of the force motor, an analytical model is established by using the equivalent magnetic circuit method. The model comprehensively considers the magnetic leakage effect, edge effect, and permeability nonlinearity. A prototype of the force motor is designed and manufactured, and a special experimental platform is built. The prototype force motor has a linear force-displacement characteristic and the output force increases with the increase of the excitation currents, which can reach about 41 N at 2 A. This indicates that it is suitable as an electro-mechanical converte...
Although a two-dimensional (2D) valve has excellent performance, the processing of its spiral gro... more Although a two-dimensional (2D) valve has excellent performance, the processing of its spiral groove has a high cost and is time-consuming. This paper proposes a novel torque motor based on an annulus air gap (TMAAG) to replace the negative feedback function of the spiral groove to reduce the machining difficulty. In order to study the torque change law of the TMAAG, the air gap permeance was analyzed, and then a qualitative analytical model was established. Orthogonal tests were carried out to initially select the crucial parameters, which were further optimized through a back propagation (BP) neural network and genetic algorithm. The prototype of TMAAG was machined, and a special experimental platform was built, and experiment results are similar to the simulation values, which verifies the accuracy of the air gap analysis and qualitative model. For torque-angle characteristics, the output torque increases with both current and rotation angle and reaches about 0.754 N·m with 2 A a...
Characteristic modeling is a control oriented modeling approach that takes into account both the ... more Characteristic modeling is a control oriented modeling approach that takes into account both the dynamic characteristics of the plant to be controlled and the performance specifications of the control system. In this article, we give an introductory overview of characteristic modeling. The basic concept, key features, and underlying mechanism are first reviewed. The characteristic modeling based control design and the stability of the closed-loop system are then illustrated. An example of successful applications of the characteristic modeling in control designs is recalled to demonstrate the effectiveness of the design method. Finally, motivations of the characteristic modeling are summarized and future work is proposed.
BGB-3111, a novel Bruton's tyrosine kinase (BTK) inhibitor, shows promising anti-cancer effects i... more BGB-3111, a novel Bruton's tyrosine kinase (BTK) inhibitor, shows promising anti-cancer effects in chronic lymphocytic leukemia/small lymphocytic lymphoma (CLL/SLL), mantle cell lymphoma (MCL), and Waldenstrom macroglobulinemia (WM). This study aimed to investigate the anti-cancer effects of BGB-3111 combined with bortezomib (BTZ) against the BTK-expressing MCL. We found that BTK, which was overexpressed in 59.4% of patients with MCL, was mainly characterized by high Ki67 and elevated MIPI scores. BGB-3111 strongly inhibited cell proliferation, induced cell cycle arrest in the G1/G0-phase, and promoted cell apoptosis in the MCL cells expressing BTK. BGB-3111 provides better safety than another BTK inhibitor, ibrutinib as ibrutinib inhibits the inducible T-cell kinase (ITK) as an off-target effect but BGB-3111 does not inhibit ITK. Low doses of BTZ enhanced the anti-cancer effect induced by the low dose of BGB-3111 by downregulating the expression levels of PARP and Bcl-2 and increasing the expression levels of cleaved PARP and cleaved caspase-9. In addition, low doses of BGB-3111, but not of BTZ, inhibited BTK phosphorylation. However, low-doses of BTZ strengthened the anti-cancer effect induced by the low-doses of BGB-3111 via synergistically suppressing the IκBα and P65 phosphorylation. Taken together, our findings validate that BGB-3111 is a novel and effective BTK inhibitor for MCL-expressing BTK. Hence, it can be harnessed as a potential therapeutic strategy through a combinatorial treatment comprising low-dose BGB-3111 and low-dose BTZ to gain strong anti-cancer effects and better safety for MCL patients.
This study aimed to investigate whether the inclusion of tumor size could improve the prognostic ... more This study aimed to investigate whether the inclusion of tumor size could improve the prognostic accuracy in patients with esophageal squamous cell cancer (ESCC). A total of 387 patients with ESCC who underwent curative resection were enrolled in this analysis. The patients were categorized into small-sized tumors (SSTs) and largesized tumors (LSTs) using an appropriate cutoff point for tumor size. Kaplan-Meier survival curve and log-rank test were used to evaluate the prognostic value of tumor size. A Cox regression model was adopted for multivariate analysis. Their accuracy was compared based on the presence or absence of tumor size. Using 3.5 cm as the optimal cutoff point, 228 and 159 patients presented with LSTs (≥ 3.5 cm) and SSTs (< 3.5 cm), respectively. The patients with LSTs had significantly worse prognoses than patients with SSTs (23.9% vs. 43.2%, P < 0.001). Multivariate analysis revealed that tumor size, histological type, invasion depth, and lymph node metastasis were independent predictors of overall survival. The addition of tumor size to the AJCC TNM staging improved the predictive accuracy of the 5-year survival rate by 3.9%. Further study showed that tumor size and T stage were independent predictors of the prognosis of node-negative patients, and the combination of tumor size and T stage improved the predictive accuracy by 3.7%. In conclusion, tumor size is indeed a simple and practical prognostic factor in patients with ESCC. It can be used to improve the prognostic accuracy of the current TNM staging, especially for patients with node-negative disease.
This paper studies the reachability problem of the switched linear discrete singular (SLDS) syste... more This paper studies the reachability problem of the switched linear discrete singular (SLDS) systems. Under the condition that all subsystems are regular, the reachability of the SLDS systems is characterized based on a peculiar repeatedly introduced switching sequence. The necessary and sufficient conditions are obtained for the reachability of the SLDS systems.
We introduce the operator-valued relative free entropy χ * B (X 1 , X 2 , • • • , Xn : B) of a fa... more We introduce the operator-valued relative free entropy χ * B (X 1 , X 2 , • • • , Xn : B) of a family of self-adjoint random variables X 1 , X 2 , • • • , Xn in a B-valued noncommutative probability space (A, E B , B). This notion extends D. Voiculescu's relative free entropy Φ * which defined in a tracial W*-noncommutative probability space to a more general context. The free entropy of a semicircular variable with conditional expectation covariance can be computed by using the modular frames and then we point out the relation between the free entropy of a semicircular variable and the index of a conditional expectation. At last, we obtain an estimate of the free entropy dimension δ * B,τ .
Weyl type theorems for p-hyponormal and M-hyponormal operators by Xiaohong Cao (Xi'an), Maozheng ... more Weyl type theorems for p-hyponormal and M-hyponormal operators by Xiaohong Cao (Xi'an), Maozheng Guo (Beijing) and Bin Meng (Beijing) Abstract. "Generalized Weyl's theorem holds" for an operator when the complement in the spectrum of the B-Weyl spectrum coincides with the isolated points of the spectrum which are eigenvalues; and "generalized a-Weyl's theorem holds" for an operator when the complement in the approximate point spectrum of the semi-B-essential approximate point spectrum coincides with the isolated points of the approximate point spectrum which are eigenvalues. If T or T * is p-hyponormal or M-hyponormal then for every f ∈ H(σ(T)), generalized Weyl's theorem holds for f (T), so Weyl's theorem holds for f (T), where H(σ(T)) denotes the set of all analytic functions on an open neighborhood of σ(T). Moreover, if T * is p-hyponormal or M-hyponormal then for every f ∈ H(σ(T)), generalized a-Weyl's theorem holds for f (T) and hence a-Weyl's theorem holds for f (T). a (T) = C \ σ a (T). An operator T ∈ B(H) is called Fredholm if it has closed finite-codimensional range and finite-dimensional null space. The index of a Fredholm operator T ∈ B(H) is given by ind(T) = n(T) − d(T). An operator T ∈ B(H) is called Weyl if it is Fredholm of index zero, and Browder if it is Fredholm of finite ascent and descent, or equivalently, if T is Fredholm and T − λI is invertible for all sufficiently small λ = 0 in C. For T ∈ B(H), we write α(T) for the ascent of T and β(T) for the descent of T .
The characteristic modeling problem of flight vehicles' attitude dynamics is considered in this p... more The characteristic modeling problem of flight vehicles' attitude dynamics is considered in this paper. In terms of the affine nonlinear system with triangle form of flight vehicles' attitude dynamics, a general method is presented to compress the dynamics into the characteristic model parameters, by introducing the time scale of nonlinear systems and a class of system states related compress functions. The parameter region and limit of the characteristic model are also given. From the given parameter region it is seen that the bound of the characteristic model parameters is dependent on the sampling period, the modeling error, the system order and the system change rate. The modeling error of the established characteristic model can be arbitrarily small according to the control precision, showing the difference between the characteristic model and other model reduction methods, that is, no system information is lost using this approach. On the basis of this modeling approach, the characteristic model of the flexible satellite attitude is established, as well as the bound and limit of the parameters, which sets a theoretical foundation for characteristic model based control design of flight vehicles. characteristic modeling, modeling error, time scale of nonlinear systems, spacecraft, attitude dynamics
Let σ ab (T) = {λ ∈ C : T − λI is not an upper semi-Fredholm operator with finite ascent} be the ... more Let σ ab (T) = {λ ∈ C : T − λI is not an upper semi-Fredholm operator with finite ascent} be the Browder essential approximate point spectrum of T ∈ B(H) and let σ d (T) = {λ ∈ C : T − λI is not surjective} be the surjective spectrum of T. In this paper it is shown that if M C = A C 0 B is a 2 × 2 upper triangular operator matrix acting on the Hilbert space H ⊕ K, then the passage from σ ab (A) ∪ σ ab (B) to σ ab (M C) is accomplished by removing certain open subsets of σ d (A) ∩ σ ab (B) from the former, that is, there is equality σ ab (A) ∪ σ ab (B) = σ ab (M C) ∪ G, where G is the union of certain of the holes in σ ab (M C) which happen to be subsets of σ d (A) ∩ σ ab (B). Weyl's theorem and Browder's theorem are liable to fail for 2 × 2 operator matrices. In this paper, it also explores how Weyl's theorem, Browder's theorem, a-Weyl's theorem and a-Browder's theorem survive for 2 × 2 upper triangular operator matrices on the Hilbert space.
Journal of Mathematical Analysis and Applications, 2005
We introduce the notion of operator-valued free Fisher information with respect to a positive map... more We introduce the notion of operator-valued free Fisher information with respect to a positive map of a random variable in an operator-valued noncommutative probability space and point out its close relations to the modular frames arising from conditional expectations. Then we can apply this notion on the study of frame theory, especially on the disjointness problem of modular frames arising from conditional expectations.
Journal of Mathematical Analysis and Applications, 2003
Two variants of the Weyl spectrum are discussed. We find, for example, that if one of them coinci... more Two variants of the Weyl spectrum are discussed. We find, for example, that if one of them coincides with the Browder spectrum then Weyl's theorem holds, and conversely for isoloid operators.
International Journal of Geographical Information Science, 2010
Mapping population distribution is an important field of geographical and related research becaus... more Mapping population distribution is an important field of geographical and related research because of the frequent need to combine spatial data representing socio-demographic information across various incompatible spatial units. However, the research may become very complex and difficult when a population in multiple places is estimated by various factors. Previous efforts in the field have contributed to the selection of appropriate independent variables and the creation of different population models. However, the level of accuracy obtainable with these studies is limited by the spatial heterogeneity of population distribution within the individual census districts, particularly in large rural areas. A high-accuracy modelling method for population estimation based on integration of Genetic Programming (GP) and Genetic Algorithms (GA) with Geographic Information Systems (GIS) is presented in this paper. GIS was applied to identify and quantify a set of natural and socioeconomic factors which contributed to population distribution, and then GP and GA were used to build and optimise the population model to automatically transform census population data to regular grids. The study indicated that the proposed method performed much better than the stepwise regression analysis and adapted gravity model methods in estimating the population of both urban and rural areas. More importantly, this proposed method could provide a single, unified approach to mapping population distribution in various areas because the paradigms of these algorithms are general.
The reachability problem of switched linear singular systems is investigated in this note. By usi... more The reachability problem of switched linear singular systems is investigated in this note. By using the geometric approach and the admissible control set introduced, a necessary condition and a sufficient condition on complete reachability are presented. The conditions are the same as those of the conventional (nonsingular) switched linear systems and normal (nonswitching) singular systems given in previous papers when the systems degenerate to normal singular systems and conventional switched systems, respectively.
Acta Mathematicae Applicatae Sinica, English Series, 2016
The DGMRES method for solving Drazin-inverse solution of singular linear systems is generally use... more The DGMRES method for solving Drazin-inverse solution of singular linear systems is generally used with restarting. But the restarting often slows down the convergence and DGMRES often stagnates. We show that adding some eigenvectors to the subspace can improve the convergence just like the method proposed by R.
Journal of Mathematical Analysis and Applications, 2005
When A ∈ B(H) and B ∈ B(K) are given, we denote by M C the operator acting on the infinite dimens... more When A ∈ B(H) and B ∈ B(K) are given, we denote by M C the operator acting on the infinite dimensional separable Hilbert space H ⊕ K of the form M C = A C 0 B. In this paper, it is shown that a 2 × 2 operator matrix M C is upper semi-Fredholm and ind(M C) 0 for some C ∈ B(K, H) if and only if A is upper semi-Fredholm and n(B) < ∞ and n(A) + n(B) d(A) + d(B) or n(B) = d(A) = ∞, if R(B) is closed, d(A) = ∞, if R(B) is not closed. We also give the necessary and sufficient conditions for which M C is Weyl or M C is lower semi-Fredholm with nonnegative index for some C ∈ B(K, H). In addition, we explore how Weyl's theorem, Browder's theorem, a-Weyl's theorem, and a-Browder's theorem survive for 2 × 2 upper triangular operator matrices on the Hilbert space.
Uploads
Papers by Bin Meng