Objective:To study the effect of repetitive peripheral magnetic stimulation(rPMS)combined with conventional rehabilitation measures on shoulder dysfunction in early stroke.Methods:60 patients with shoulder dysfunction...Objective:To study the effect of repetitive peripheral magnetic stimulation(rPMS)combined with conventional rehabilitation measures on shoulder dysfunction in early stroke.Methods:60 patients with shoulder dysfunction in early stroke were selected,and all of them were admitted to our hospital from August 2021 to August 2023.The patients were randomly grouped into a control group(conventional rehabilitation measures intervention,30 cases)and an intervention group(rPMS and conventional rehabilitation measures intervention,30 cases)according to the lottery method.The pain scores,shoulder mobility,and motor function scores of the two groups were compared.Results:The pain score was lower in the intervention group,and the shoulder mobility and motor function scores were higher in the intervention group(P<0.05)as compared to that of the control group.Conclusion:The effect of combining rPMS and conventional rehabilitation measures in treating shoulder dysfunction in early stroke was remarkable and should be popularized.展开更多
Marriage is usually associated with happiness and harmony. But in Shakespear's Measure for Measure, it seems it is infused with power of law. Is it a clear-cut punishment or reward? Its qualities revolve around th...Marriage is usually associated with happiness and harmony. But in Shakespear's Measure for Measure, it seems it is infused with power of law. Is it a clear-cut punishment or reward? Its qualities revolve around the individual situations in which it occurs, which is interpreted and deployed by characters in the play in different ways.展开更多
Let X= (Ω, ■, ■_t, X_t,, θ_t, p~x) be a self-similar Markov process on (0,∞) with non-decreasing path. The exact Hausdorff and Packing measure functions of the image X([0,t] ) are obtained.
The terrestrial time-variable gravity measurements are characterized by a high signal-to-noise ratio and sensitivity to the sources of mass change in the Earth's crust.These gravity data have many applications,suc...The terrestrial time-variable gravity measurements are characterized by a high signal-to-noise ratio and sensitivity to the sources of mass change in the Earth's crust.These gravity data have many applications,such as surface deformation,groundwater storage changes,and mass migration before and after earthquakes.Based on repeated terrestrial gravity measurements at 198 gravity stations in the Sichuan-Yunnan region(SYR)from 2015 to 2017,we determine a time series of degree 120 gravity fields using the localized spherical harmonic(Slepian)basis functions.Our results show that adopting the first 6 Slepian basis functions is sufficient for effective localized Slepian modeling in the SYR.The differences between two gravity campaigns at the same time of year show an obvious correlation with tectonic features.The degree 120 timevariable gravity models presented in this paper will benefit the study of the regional mass migration inside the crust of the SYR and supplement the existing geophysical models for the China Seismic Experimental Site.展开更多
The research considers wavelike objects that are elements of even subalgebra of geometric algebra in three dimensions. The used formalism particularly eliminates long existing confusion about the reasons behind the ap...The research considers wavelike objects that are elements of even subalgebra of geometric algebra in three dimensions. The used formalism particularly eliminates long existing confusion about the reasons behind the appearance of the imaginary unit in quantum mechanics and introduces clear definition of wave functions. When a wave function acts through the Hopf fibration on a localized geometric algebra element, that is executing a measurement, the result can be named as “collapse” of the wave function.展开更多
The non-elementary integrals involving elementary exponential, hyperbolic and trigonometric functions, <img src="Edit_699140d3-f569-463e-b835-7ccdab822717.png" width="290" height="22" ...The non-elementary integrals involving elementary exponential, hyperbolic and trigonometric functions, <img src="Edit_699140d3-f569-463e-b835-7ccdab822717.png" width="290" height="22" alt="" /><img src="Edit_bdd10470-9b63-4b2d-9cec-636969547ca5.png" width="90" height="22" alt="" /><span style="white-space:normal;">and <img src="Edit_e9cd6876-e2b8-45cf-ba17-391f054679b4.png" width="90" height="21" alt="" /></span>where <span style="white-space:nowrap;"><em>α</em>,<span style="white-space:nowrap;"><em>η</em></span><em></em></span> and <span style="white-space:nowrap;"><em>β</em></span> are real or complex constants are evaluated in terms of the confluent hypergeometric function <sub>1</sub><em>F</em><sub>1</sub> and the hypergeometric function <sub>1</sub><em>F</em><sub>2</sub>. The hyperbolic and Euler identities are used to derive some identities involving exponential, hyperbolic, trigonometric functions and the hypergeometric functions <sub style="white-space:normal;">1</sub><em style="white-space:normal;">F</em><sub style="white-space:normal;">1</sub> and <sub style="white-space:normal;">1</sub><em style="white-space:normal;">F</em><sub style="white-space:normal;">2</sub>. Having evaluated, these non-elementary integrals, some new probability measures generalizing the gamma-type and Gaussian distributions are also obtained. The obtained generalized probability distributions may, for example, allow to perform better statistical tests than those already known (e.g. chi-square (<span style="white-space:nowrap;"><em>x</em><sup>2</sup></span>) statistical tests and other statistical tests constructed based on the central limit theorem (CLT)), while avoiding the use of computational approximations (or methods) which are in general expensive and associated with numerical errors.展开更多
Our brain is constantly active.Even at rest,the brain carries out essential functions such as maintenance of resting potentials,subthreshold synaptic activity,and spiking activity related to information processing.Thi...Our brain is constantly active.Even at rest,the brain carries out essential functions such as maintenance of resting potentials,subthreshold synaptic activity,and spiking activity related to information processing.This resting activity can be assessed with several in vivo tools,such as resting-state functional magnetic resonance imaging.This technique measures subtle changes in blood flow,volume,and oxygenation that occur over time.Although vascular in nature,resting-state functional magnetic resonance imaging is considered a reliable proxy of neural activity and several studies have shown that the brain is functionally divided into interacting neural networks called the“functional connectome”.展开更多
In this paper we study integer multiplicity rectifiable currents carried by the subgradient (subdifferential) graphs of semi-convex functions on an n-dimensional convex domain, and show a weak continuity theorem wit...In this paper we study integer multiplicity rectifiable currents carried by the subgradient (subdifferential) graphs of semi-convex functions on an n-dimensional convex domain, and show a weak continuity theorem with respect to pointwise convergence for such currents. As an application, the structure theorem of the Lagrangian currents for semi-convex functions is given and the k-Hessian measures are calculated by a different method in terms of currents.展开更多
In this paper we defineα-Carleson measure in the Bergman metric on bounded symmetric domains. Some necessary and sufficient conditions about it and Bloch functions on the domains are given.
Network is considered naturally as a wide range of different contexts, such as biological systems, social relationships as well as various technological scenarios. Investigation of the dynamic phenomena taking place i...Network is considered naturally as a wide range of different contexts, such as biological systems, social relationships as well as various technological scenarios. Investigation of the dynamic phenomena taking place in the network, determination of the structure of the network and community and description of the interactions between various elements of the network are the key issues in network analysis. One of the huge network structure challenges is the identification of the node(s) with an outstanding structural position within the network. The popular method for doing this is to calculate a measure of centrality. We examine node centrality measures such as degree, closeness, eigenvector, Katz and subgraph centrality for undirected networks. We show how the Katz centrality can be turned into degree and eigenvector centrality by considering limiting cases. Some existing centrality measures are linked to matrix functions. We extend this idea and examine the centrality measures based on general matrix functions and in particular, the logarithmic, cosine, sine, and hyperbolic functions. We also explore the concept of generalised Katz centrality. Various experiments are conducted for different networks generated by using random graph models. The results show that the logarithmic function in particular has potential as a centrality measure. Similar results were obtained for real-world networks.展开更多
If a vector valued function space with a Hausdorff locally convex topology has a property such that every closed strongly bounded subset is compact, then we name this property Helly's property. In this paper, we...If a vector valued function space with a Hausdorff locally convex topology has a property such that every closed strongly bounded subset is compact, then we name this property Helly's property. In this paper, we show a class of vector valued function spaces with Helly's property and consider convergence of vector measures and best approximations in function spaces in this class.展开更多
In 1958, Baker posed the question that if f and g are two permutable transcendental entire functions, must their Julia sets be the same? In order to study this problem of permutable transcendental entire functions, by...In 1958, Baker posed the question that if f and g are two permutable transcendental entire functions, must their Julia sets be the same? In order to study this problem of permutable transcendental entire functions, by the properties of permutable transcendental entire functions, we prove that if f and g are permutable transcendental entire functions, then mes (J(f)) = mes (J(g)). Moreover, we give some results about the zero measure of the Julia sets of the permutable transcendental entire functions family.展开更多
Let An∈M2(ℤ)be integral matrices such that the infinite convolution of Dirac measures with equal weightsμ{A_(n),n≥1}δA_(1)^(-1)D*δA_(1)^(-1)A_(2)^(-2)D*…is a probability measure with compact support,where D={(0,...Let An∈M2(ℤ)be integral matrices such that the infinite convolution of Dirac measures with equal weightsμ{A_(n),n≥1}δA_(1)^(-1)D*δA_(1)^(-1)A_(2)^(-2)D*…is a probability measure with compact support,where D={(0,0)^(t),(1,0)^(t),(0,1)^(t)}is the Sierpinski digit.We prove that there exists a setΛ⊂ℝ2 such that the family{e2πi〈λ,x〉:λ∈Λ} is an orthonormal basis of L^(2)(μ{A_(n),n≥1})if and only if 1/3(1,-1)A_(n)∈Z^(2)for n≥2 under some metric conditions on A_(n).展开更多
In this paper, the authors get the characterizations of the integral and Car-leson type measure both associated with the invariant gradient for little a-Bloch functions in the unit ball of Cn. As a consequence, some r...In this paper, the authors get the characterizations of the integral and Car-leson type measure both associated with the invariant gradient for little a-Bloch functions in the unit ball of Cn. As a consequence, some results of Ouyang C H, Yang W S and Zhao R H in [4] and a result of Yang W S in [10] are extended.展开更多
In this paper, The integral characterizations of alpha-Bloch (little alpha-Bloch) axe given in terms of higher radial derivative, and their characterizations of Caxleson type measure are obtained.
Traumatic brain injury(TBI) is a major contributor of long-term disability and a leading cause of death worldwide. A series of secondary injury cascades can contribute to cell death, tissue loss, and ultimately to the...Traumatic brain injury(TBI) is a major contributor of long-term disability and a leading cause of death worldwide. A series of secondary injury cascades can contribute to cell death, tissue loss, and ultimately to the development of functional impairments. However, there are currently no effective therapeutic interventions that improve brain outcomes following TBI. As a result, a number of experimental TBI models have been developed to recapitulate TBI injury mechanisms and to test the efficacy of potential therapeutics. The pig model has recently come to the forefront as the pig brain is closer in size, structure, and composition to the human brain compared to traditional rodent models, making it an ideal large animal model to study TBI pathophysiology and functional outcomes. This review will focus on the shared characteristics between humans and pigs that make them ideal for modeling TBI and will review the three most common pig TBI models–the diffuse axonal injury, the controlled cortical impact, and the fluid percussion models. It will also review current advances in functional outcome assessment measures and other non-invasive, translational TBI detection and measurement tools like biomarker analysis and magnetic resonance imaging. The use of pigs as TBI models and the continued development and improvement of translational assessment modalities have made significant contributions to unraveling the complex cascade of TBI sequela and provide an important means to study potential clinically relevant therapeutic interventions.展开更多
ABSTRACT The optimal Kalman gain was analyzed in a rigorous statistical framework. Emphasis was placed on a comprehensive understanding and interpretation of the current algorithm, especially when the measurement fun...ABSTRACT The optimal Kalman gain was analyzed in a rigorous statistical framework. Emphasis was placed on a comprehensive understanding and interpretation of the current algorithm, especially when the measurement function is nonlinear. It is argued that when the measurement function is nonlinear, the current ensemble Kalman Filter algorithm seems to contain implicit assumptions: the forecast of the measurement function is unbiased or the nonlinear measurement function is linearized. While the forecast of the model state is assumed to be unbiased, the two assumptions are actually equivalent. On the above basis, we present two modified Kalman gain algorithms. Compared to the current Kalman gain algorithm, the modified ones remove the above assumptions, thereby leading to smaller estimated errors. This outcome was confirmed experimentally, in which we used the simple Lorenz 3-component model as the test-bed. It was found that in such a simple nonlinear dynamical system, the modified Kalman gain can perform better than the current one. However, the application of the modified schemes to realistic models involving nonlinear measurement functions needs to be further investigated.展开更多
The Radial Basis Functions Neural Network (RBFNN) is used to establish the model of a response system through the input and output data of the system. The synchronization between a drive system and the response syst...The Radial Basis Functions Neural Network (RBFNN) is used to establish the model of a response system through the input and output data of the system. The synchronization between a drive system and the response system can be implemented by employing the RBFNN model and state feedback control. In this case, the exact mathematical model, which is the precondition for the conventional method, is unnecessary for implementing synchronization. The effect of the model error is investigated and a corresponding theorem is developed. The effect of the parameter perturbations and the measurement noise is investigated through simulations. The simulation results under different conditions show the effectiveness of the method.展开更多
文摘Objective:To study the effect of repetitive peripheral magnetic stimulation(rPMS)combined with conventional rehabilitation measures on shoulder dysfunction in early stroke.Methods:60 patients with shoulder dysfunction in early stroke were selected,and all of them were admitted to our hospital from August 2021 to August 2023.The patients were randomly grouped into a control group(conventional rehabilitation measures intervention,30 cases)and an intervention group(rPMS and conventional rehabilitation measures intervention,30 cases)according to the lottery method.The pain scores,shoulder mobility,and motor function scores of the two groups were compared.Results:The pain score was lower in the intervention group,and the shoulder mobility and motor function scores were higher in the intervention group(P<0.05)as compared to that of the control group.Conclusion:The effect of combining rPMS and conventional rehabilitation measures in treating shoulder dysfunction in early stroke was remarkable and should be popularized.
文摘Marriage is usually associated with happiness and harmony. But in Shakespear's Measure for Measure, it seems it is infused with power of law. Is it a clear-cut punishment or reward? Its qualities revolve around the individual situations in which it occurs, which is interpreted and deployed by characters in the play in different ways.
基金the National Natural Science Foundation of China
文摘Let X= (Ω, ■, ■_t, X_t,, θ_t, p~x) be a self-similar Markov process on (0,∞) with non-decreasing path. The exact Hausdorff and Packing measure functions of the image X([0,t] ) are obtained.
基金the National Natural Science Foundation of China(Nos.41974095,41774090,and U1939205)the Special Fund of the Institute of Geophysics,China Earthquake Administration(Nos.DQJB20X09,and DQJB21R30)The first author acknowledges support from the China Postdoctoral Science Foundation(No.2018M641424)。
文摘The terrestrial time-variable gravity measurements are characterized by a high signal-to-noise ratio and sensitivity to the sources of mass change in the Earth's crust.These gravity data have many applications,such as surface deformation,groundwater storage changes,and mass migration before and after earthquakes.Based on repeated terrestrial gravity measurements at 198 gravity stations in the Sichuan-Yunnan region(SYR)from 2015 to 2017,we determine a time series of degree 120 gravity fields using the localized spherical harmonic(Slepian)basis functions.Our results show that adopting the first 6 Slepian basis functions is sufficient for effective localized Slepian modeling in the SYR.The differences between two gravity campaigns at the same time of year show an obvious correlation with tectonic features.The degree 120 timevariable gravity models presented in this paper will benefit the study of the regional mass migration inside the crust of the SYR and supplement the existing geophysical models for the China Seismic Experimental Site.
文摘The research considers wavelike objects that are elements of even subalgebra of geometric algebra in three dimensions. The used formalism particularly eliminates long existing confusion about the reasons behind the appearance of the imaginary unit in quantum mechanics and introduces clear definition of wave functions. When a wave function acts through the Hopf fibration on a localized geometric algebra element, that is executing a measurement, the result can be named as “collapse” of the wave function.
文摘The non-elementary integrals involving elementary exponential, hyperbolic and trigonometric functions, <img src="Edit_699140d3-f569-463e-b835-7ccdab822717.png" width="290" height="22" alt="" /><img src="Edit_bdd10470-9b63-4b2d-9cec-636969547ca5.png" width="90" height="22" alt="" /><span style="white-space:normal;">and <img src="Edit_e9cd6876-e2b8-45cf-ba17-391f054679b4.png" width="90" height="21" alt="" /></span>where <span style="white-space:nowrap;"><em>α</em>,<span style="white-space:nowrap;"><em>η</em></span><em></em></span> and <span style="white-space:nowrap;"><em>β</em></span> are real or complex constants are evaluated in terms of the confluent hypergeometric function <sub>1</sub><em>F</em><sub>1</sub> and the hypergeometric function <sub>1</sub><em>F</em><sub>2</sub>. The hyperbolic and Euler identities are used to derive some identities involving exponential, hyperbolic, trigonometric functions and the hypergeometric functions <sub style="white-space:normal;">1</sub><em style="white-space:normal;">F</em><sub style="white-space:normal;">1</sub> and <sub style="white-space:normal;">1</sub><em style="white-space:normal;">F</em><sub style="white-space:normal;">2</sub>. Having evaluated, these non-elementary integrals, some new probability measures generalizing the gamma-type and Gaussian distributions are also obtained. The obtained generalized probability distributions may, for example, allow to perform better statistical tests than those already known (e.g. chi-square (<span style="white-space:nowrap;"><em>x</em><sup>2</sup></span>) statistical tests and other statistical tests constructed based on the central limit theorem (CLT)), while avoiding the use of computational approximations (or methods) which are in general expensive and associated with numerical errors.
文摘Our brain is constantly active.Even at rest,the brain carries out essential functions such as maintenance of resting potentials,subthreshold synaptic activity,and spiking activity related to information processing.This resting activity can be assessed with several in vivo tools,such as resting-state functional magnetic resonance imaging.This technique measures subtle changes in blood flow,volume,and oxygenation that occur over time.Although vascular in nature,resting-state functional magnetic resonance imaging is considered a reliable proxy of neural activity and several studies have shown that the brain is functionally divided into interacting neural networks called the“functional connectome”.
基金supported by NSF Grant of China(11131005,11301400)Hubei Key Laboratory of Applied Mathematics(Hubei University)
文摘In this paper we study integer multiplicity rectifiable currents carried by the subgradient (subdifferential) graphs of semi-convex functions on an n-dimensional convex domain, and show a weak continuity theorem with respect to pointwise convergence for such currents. As an application, the structure theorem of the Lagrangian currents for semi-convex functions is given and the k-Hessian measures are calculated by a different method in terms of currents.
文摘In this paper we defineα-Carleson measure in the Bergman metric on bounded symmetric domains. Some necessary and sufficient conditions about it and Bloch functions on the domains are given.
文摘Network is considered naturally as a wide range of different contexts, such as biological systems, social relationships as well as various technological scenarios. Investigation of the dynamic phenomena taking place in the network, determination of the structure of the network and community and description of the interactions between various elements of the network are the key issues in network analysis. One of the huge network structure challenges is the identification of the node(s) with an outstanding structural position within the network. The popular method for doing this is to calculate a measure of centrality. We examine node centrality measures such as degree, closeness, eigenvector, Katz and subgraph centrality for undirected networks. We show how the Katz centrality can be turned into degree and eigenvector centrality by considering limiting cases. Some existing centrality measures are linked to matrix functions. We extend this idea and examine the centrality measures based on general matrix functions and in particular, the logarithmic, cosine, sine, and hyperbolic functions. We also explore the concept of generalised Katz centrality. Various experiments are conducted for different networks generated by using random graph models. The results show that the logarithmic function in particular has potential as a centrality measure. Similar results were obtained for real-world networks.
文摘If a vector valued function space with a Hausdorff locally convex topology has a property such that every closed strongly bounded subset is compact, then we name this property Helly's property. In this paper, we show a class of vector valued function spaces with Helly's property and consider convergence of vector measures and best approximations in function spaces in this class.
文摘In 1958, Baker posed the question that if f and g are two permutable transcendental entire functions, must their Julia sets be the same? In order to study this problem of permutable transcendental entire functions, by the properties of permutable transcendental entire functions, we prove that if f and g are permutable transcendental entire functions, then mes (J(f)) = mes (J(g)). Moreover, we give some results about the zero measure of the Julia sets of the permutable transcendental entire functions family.
基金supported by the National Natural Science Foundation of China (Grant Nos. 12371087, 11971109,11971194, 11672074 and 12271185)supported by the program for Probability and Statistics:Theory and Application (Grant No. IRTL1704)+1 种基金the program for Innovative Research Team in Science and Technology in Fujian Province University (Grant No. IRTSTFJ)supported by Guangdong NSFC (Grant No. 2022A1515011124)
文摘Let An∈M2(ℤ)be integral matrices such that the infinite convolution of Dirac measures with equal weightsμ{A_(n),n≥1}δA_(1)^(-1)D*δA_(1)^(-1)A_(2)^(-2)D*…is a probability measure with compact support,where D={(0,0)^(t),(1,0)^(t),(0,1)^(t)}is the Sierpinski digit.We prove that there exists a setΛ⊂ℝ2 such that the family{e2πi〈λ,x〉:λ∈Λ} is an orthonormal basis of L^(2)(μ{A_(n),n≥1})if and only if 1/3(1,-1)A_(n)∈Z^(2)for n≥2 under some metric conditions on A_(n).
文摘In this paper, the authors get the characterizations of the integral and Car-leson type measure both associated with the invariant gradient for little a-Bloch functions in the unit ball of Cn. As a consequence, some results of Ouyang C H, Yang W S and Zhao R H in [4] and a result of Yang W S in [10] are extended.
基金The research is supported by NNSF of China(19771082)
文摘In this paper, The integral characterizations of alpha-Bloch (little alpha-Bloch) axe given in terms of higher radial derivative, and their characterizations of Caxleson type measure are obtained.
文摘Traumatic brain injury(TBI) is a major contributor of long-term disability and a leading cause of death worldwide. A series of secondary injury cascades can contribute to cell death, tissue loss, and ultimately to the development of functional impairments. However, there are currently no effective therapeutic interventions that improve brain outcomes following TBI. As a result, a number of experimental TBI models have been developed to recapitulate TBI injury mechanisms and to test the efficacy of potential therapeutics. The pig model has recently come to the forefront as the pig brain is closer in size, structure, and composition to the human brain compared to traditional rodent models, making it an ideal large animal model to study TBI pathophysiology and functional outcomes. This review will focus on the shared characteristics between humans and pigs that make them ideal for modeling TBI and will review the three most common pig TBI models–the diffuse axonal injury, the controlled cortical impact, and the fluid percussion models. It will also review current advances in functional outcome assessment measures and other non-invasive, translational TBI detection and measurement tools like biomarker analysis and magnetic resonance imaging. The use of pigs as TBI models and the continued development and improvement of translational assessment modalities have made significant contributions to unraveling the complex cascade of TBI sequela and provide an important means to study potential clinically relevant therapeutic interventions.
基金supported by research grants from the NSERC (Natural Sciences and Engineering Research Council of Canada) Discovery Programthe National Natural Science Foundation of China (Grant Nos.41276029 and 40730843)the National Basic Research Program (Grant No.2007CB816005)
文摘ABSTRACT The optimal Kalman gain was analyzed in a rigorous statistical framework. Emphasis was placed on a comprehensive understanding and interpretation of the current algorithm, especially when the measurement function is nonlinear. It is argued that when the measurement function is nonlinear, the current ensemble Kalman Filter algorithm seems to contain implicit assumptions: the forecast of the measurement function is unbiased or the nonlinear measurement function is linearized. While the forecast of the model state is assumed to be unbiased, the two assumptions are actually equivalent. On the above basis, we present two modified Kalman gain algorithms. Compared to the current Kalman gain algorithm, the modified ones remove the above assumptions, thereby leading to smaller estimated errors. This outcome was confirmed experimentally, in which we used the simple Lorenz 3-component model as the test-bed. It was found that in such a simple nonlinear dynamical system, the modified Kalman gain can perform better than the current one. However, the application of the modified schemes to realistic models involving nonlinear measurement functions needs to be further investigated.
基金This project was supported in part by the Science Foundation of Shanxi Province (2003F028)China Postdoctoral Science Foundation (20060390318).
文摘The Radial Basis Functions Neural Network (RBFNN) is used to establish the model of a response system through the input and output data of the system. The synchronization between a drive system and the response system can be implemented by employing the RBFNN model and state feedback control. In this case, the exact mathematical model, which is the precondition for the conventional method, is unnecessary for implementing synchronization. The effect of the model error is investigated and a corresponding theorem is developed. The effect of the parameter perturbations and the measurement noise is investigated through simulations. The simulation results under different conditions show the effectiveness of the method.