We derive the conditions for the existence of the unique solution of the two scale integral equation and the form of the solution, according to the method of the construction of the dyadic scale function. We give the ...We derive the conditions for the existence of the unique solution of the two scale integral equation and the form of the solution, according to the method of the construction of the dyadic scale function. We give the construction of the dyadic wavelet and its necessary and sufficient condition. As an application, we also develop a pyramid algorithm of the dyadic wavelet decomposition.展开更多
We propose an exact explicit closed-form Laguerre series expansion formula to compute the q-scale function of a spectrally negative Lévy process(SNLP),and other functions associated to the scale function for the ...We propose an exact explicit closed-form Laguerre series expansion formula to compute the q-scale function of a spectrally negative Lévy process(SNLP),and other functions associated to the scale function for the first time.The proposed closed-form formula for the scale function has many applications in applied probability and in particular in the Lévy insurance risk theory.We shall show that the new series expansion formulas can be used to express the expected discounted penalty functions,the moments of the present value of total dividend payments as well as the time value of Parisian ruin in the Lévy risk models.展开更多
The spherically layered media theory has wide applications for electromagnetic wave scattering analysis.Due to the involved Bessel functions,the conventional formulations of spherically layered media theory suffer fro...The spherically layered media theory has wide applications for electromagnetic wave scattering analysis.Due to the involved Bessel functions,the conventional formulations of spherically layered media theory suffer from numerical overflow or underflow when the Bessel function’s order is large,the argument is small or the argument has a large imaginary part.The first two issues have been solved recently by employing small-argument asymptotic formulas of Bessel functions,while the third issue remains unsolved.In this paper,the Bessel functions in the conventional formulation of the theory are replaced by scaled Bessel functions which have good numerical properties for high loss media,and stable formulas are derived.Numerical tests show that this approach can work properly with very high lossy media.Also,this approach can be seamlessly combined with the stable computation method for cases of small argument and large order of Bessel functions.展开更多
Poly-scale refinable function with dilation factor a is introduced. The existence of solution of poly-scale refinable equation is investigated. Specially, necessary and sufficient conditions for the orthonormality of ...Poly-scale refinable function with dilation factor a is introduced. The existence of solution of poly-scale refinable equation is investigated. Specially, necessary and sufficient conditions for the orthonormality of solution function Ф of poly-scale refinable equation with integer dilation factor a are established. Some properties of poly-scale refinable function are discussed. Several examples illustrating how to use the method to construct poly-scale refinable function are given.展开更多
Fifty-one patients with mild （n -- 14）, moderate （n = 10） and severe traumatic brain injury （n = 27） received early rehabilitation. Level of consciousness was evaluated using the Glasgow Coma Score Functional le...Fifty-one patients with mild （n -- 14）, moderate （n = 10） and severe traumatic brain injury （n = 27） received early rehabilitation. Level of consciousness was evaluated using the Glasgow Coma Score Functional level was determined using the Glasgow Outcome Score, whilst mobility was evaluated using the Mobility Scale for Acute Stroke. Activities of daily living were assessed using the Barthel Index. Following Bobath neurodevelopmental therapy, the level of consciousness was significantly improved in patients with moderate and severe traumatic brain injury, but was not greatly influenced in patients with mild traumatic brain injury. Mobility and functional level were significantly improved in patients with mild, moderate and severe traumatic brain injury. Gait recovery was more obvious in patients with mild traumatic brain injury than in patients with moderate and severe traumatic brain injury. Activities of daily living showed an improvement but this was insignificant except for patients with severe traumatic brain injury. Nevertheless, complete recovery was not acquired at discharge. Multiple regression analysis showed that gait and Glasgow Coma Scale scores can be considered predictors of functional outcomes following traumatic brain injury.展开更多
The spatial structures of China’s Major Function Zoning are important constraining indicators in all types of spatial planning and key parameters for accurately downscaling major functions.Taking the proportion of ur...The spatial structures of China’s Major Function Zoning are important constraining indicators in all types of spatial planning and key parameters for accurately downscaling major functions.Taking the proportion of urbanization zones,agricultural development zones and ecological security zones as the basic parameter,this paper explores the spatial structures of major function zoning at different scales using spatial statistics,spatial modeling and landscape metrics methods.The results show:First,major function zones have spatial gradient structures,which are prominently represented by latitudinal and longitudinal gradients,a coastal distance gradient,and an eastern-central-western gradient.Second,the pole-axis system structure and core-periphery structure exist at provincial scales.The general principle of the pole-axis structure is that as one moves along the distance axis,the proportion of urbanization zones decreases and the proportion of ecological security zones increases.This also means that the proportion of different function zones has a ring-shaped spatial differentiation principle with distance from the core.Third,there is a spatial mosaic structure at the city and county scale.This spatial mosaic structure has features of both spatial heterogeneity,such as agglomeration and dispersion,as well as of mutual,adjacent topological correlation and spatial proximity.The results of this study contribute to scientific knowledge on major function zones and the principles of spatial organization,and it acts as an important reference for China’s integrated geographical zoning.展开更多
Objectives: To examine the cross-sectional associations of the separate subscales of the Perceived Stress Scale (PSS) and tests measuring cognitive domains in older adults. Methods: 897 adults over the age of 70 free ...Objectives: To examine the cross-sectional associations of the separate subscales of the Perceived Stress Scale (PSS) and tests measuring cognitive domains in older adults. Methods: 897 adults over the age of 70 free of amnestic mild cognitive impairment and dementia and enrolled in the Einstein Aging Study made up the study sample. The PSS-14 was used to measure stress. Three cognitive domains (language, episodic memory, and frontal-executive) had previously been found using principle component analysis. Linear regression analyses were used to determine the relationship between the PSS subscales and cognitive domain function. Results: The study sample had a mean age of 79.1 years and 62.8% were female. Bivariate correlations show that the PSS-14 positively worded subscale of the PSS (PSS-PW) was significantly associated with all three cognitive domains (language: r = -0.15, p < 0.001;episodic memory: r = -0.16, p < 0.001;frontal-executive: r = -0.21, p <0.001) while the negatively worded subscale of the PSS (PSS-NW) was not significantly associated with any cognitive domain. In linear regression analyses adjusted for age, white race, gender, years of education, and depressive symptoms, the PSS-PW remained significantly associated with each of the cognitive domains. The PSS-NW was not associated with any cognitive domains in any model. The PSS-14 was significantly associated with language and episodic memory, but not the frontal-executive domain. Conclusion: Worse PSS-PW scores are associated with reduced cognitive function in the executive, memory, and language domains in nondemented older adults. The PSS-PW subscale correlated better with cognitive function than the overall PSS-14. Future research should evaluate the temporality of the association and if stress reduction therapies improve cognitive performance.展开更多
Water Vapor Chemistry" as a new science was discovered and established from trace analysis in Gu’s laboratory(Gu, 1991; Gu et al., 1991). Gu’s Function shows that the trace metal ion concentration in water vapo...Water Vapor Chemistry" as a new science was discovered and established from trace analysis in Gu’s laboratory(Gu, 1991; Gu et al., 1991). Gu’s Function shows that the trace metal ion concentration in water vapor has positive correlation to"specific electron affinity constant"last ionization potential Iz/ion valence Z and negative correlation to ion volume V and coordination number N(Gu, 1994). Gu’s Func-tion C=f[(Iz/Z)/VN]of the bond parameter in water vapor chemistry corresponds to the potential energy function Z’ e2/r in the Schrodinger Equation of quantum chemistry. In different ions with the same 2+ charge, the ion concentration of water-water vapor transfer may be much different. This shows that the 2+ charge of different ions has different attractive force (hydration force). This different attractive force of the charge can be scaled with the relative energy or charge size from Gu’s Function.展开更多
In this paper, we study the relationship between exponential dichotomy and quadratic Lyapunov function for the linear equation x△=A（t）x on time scales. Moreover, for the nonlinear perturbed equation x△= A（t）x ...In this paper, we study the relationship between exponential dichotomy and quadratic Lyapunov function for the linear equation x△=A（t）x on time scales. Moreover, for the nonlinear perturbed equation x△= A（t）x ＋ f（t, x） we give the instability of the zero solution when f is sufficiently small.展开更多
This paper investigates the existence of periodic solutions of a three-species food-chain diffusive system with Beddington-DeAngelis functional responses and time delays in a two-patch environment on time scales. By u...This paper investigates the existence of periodic solutions of a three-species food-chain diffusive system with Beddington-DeAngelis functional responses and time delays in a two-patch environment on time scales. By using a continuation theorem based on coincidence degree theory, we obtain sufficient criteria for the existence of periodic solutions for the system. Moreover, when the time scale T is chosen as R or Z, the existence of the periodic solutions of the corresponding continuous and discrete models follows. Therefore, the method is unified to provide the existence of the desired solutions for continuous differential equations and discrete difference equations.展开更多
This paper presents an economic lot-sizing problem with perishable inventory and general economies of scale cost functions. For the case with backlogging allowed, a mathematical model is formulated, and several proper...This paper presents an economic lot-sizing problem with perishable inventory and general economies of scale cost functions. For the case with backlogging allowed, a mathematical model is formulated, and several properties of the optimal solutions are explored. With the help of these optimality properties, a polynomial time approximation algorithm is developed by a new method. The new method adopts a shift technique to obtain a feasible solution of subproblem and takes the optimal solution of the subproblem as an approximation solution of our problem. The worst case performance for the approximation algorithm is proven to be （4√2 ＋ 5）/7. Finally, an instance illustrates that the bound is tight.展开更多
文摘We derive the conditions for the existence of the unique solution of the two scale integral equation and the form of the solution, according to the method of the construction of the dyadic scale function. We give the construction of the dyadic wavelet and its necessary and sufficient condition. As an application, we also develop a pyramid algorithm of the dyadic wavelet decomposition.
基金supported by the National Natural Science Foundation of China(No.12401612)the Natural Science Foundation of Chongqing(No.CSTB2025NSCQ-GPX1016)+3 种基金the Science and Technology Research Program of Chongqing Municipal Education Commission(No.KJQN202400508)the Chongqing Normal University Foundation(No.23XLB018)supported by National Science Foundation(NSF-CNS 2113906)the Chongqing Natural Science Foundation Joint Fund for Innovation and Development Project(No.CSTB2024NSCQ-LZX0085)。
文摘We propose an exact explicit closed-form Laguerre series expansion formula to compute the q-scale function of a spectrally negative Lévy process(SNLP),and other functions associated to the scale function for the first time.The proposed closed-form formula for the scale function has many applications in applied probability and in particular in the Lévy insurance risk theory.We shall show that the new series expansion formulas can be used to express the expected discounted penalty functions,the moments of the present value of total dividend payments as well as the time value of Parisian ruin in the Lévy risk models.
文摘The spherically layered media theory has wide applications for electromagnetic wave scattering analysis.Due to the involved Bessel functions,the conventional formulations of spherically layered media theory suffer from numerical overflow or underflow when the Bessel function’s order is large,the argument is small or the argument has a large imaginary part.The first two issues have been solved recently by employing small-argument asymptotic formulas of Bessel functions,while the third issue remains unsolved.In this paper,the Bessel functions in the conventional formulation of the theory are replaced by scaled Bessel functions which have good numerical properties for high loss media,and stable formulas are derived.Numerical tests show that this approach can work properly with very high lossy media.Also,this approach can be seamlessly combined with the stable computation method for cases of small argument and large order of Bessel functions.
基金Project supported by the Natural Science Foundation of Guangdong Province (Nos.032038, 05008289, 06105648) the Doctoral Foundation of Guangdong Province (No.04300917)
文摘Poly-scale refinable function with dilation factor a is introduced. The existence of solution of poly-scale refinable equation is investigated. Specially, necessary and sufficient conditions for the orthonormality of solution function Ф of poly-scale refinable equation with integer dilation factor a are established. Some properties of poly-scale refinable function are discussed. Several examples illustrating how to use the method to construct poly-scale refinable function are given.
文摘Fifty-one patients with mild （n -- 14）, moderate （n = 10） and severe traumatic brain injury （n = 27） received early rehabilitation. Level of consciousness was evaluated using the Glasgow Coma Score Functional level was determined using the Glasgow Outcome Score, whilst mobility was evaluated using the Mobility Scale for Acute Stroke. Activities of daily living were assessed using the Barthel Index. Following Bobath neurodevelopmental therapy, the level of consciousness was significantly improved in patients with moderate and severe traumatic brain injury, but was not greatly influenced in patients with mild traumatic brain injury. Mobility and functional level were significantly improved in patients with mild, moderate and severe traumatic brain injury. Gait recovery was more obvious in patients with mild traumatic brain injury than in patients with moderate and severe traumatic brain injury. Activities of daily living showed an improvement but this was insignificant except for patients with severe traumatic brain injury. Nevertheless, complete recovery was not acquired at discharge. Multiple regression analysis showed that gait and Glasgow Coma Scale scores can be considered predictors of functional outcomes following traumatic brain injury.
基金National Natural Science Foundation of China,No.41630644Innovative Think-tank Foundation for Young Scientists of China Association for Science and Technology,No.DXB-ZKQN-2017-048。
文摘The spatial structures of China’s Major Function Zoning are important constraining indicators in all types of spatial planning and key parameters for accurately downscaling major functions.Taking the proportion of urbanization zones,agricultural development zones and ecological security zones as the basic parameter,this paper explores the spatial structures of major function zoning at different scales using spatial statistics,spatial modeling and landscape metrics methods.The results show:First,major function zones have spatial gradient structures,which are prominently represented by latitudinal and longitudinal gradients,a coastal distance gradient,and an eastern-central-western gradient.Second,the pole-axis system structure and core-periphery structure exist at provincial scales.The general principle of the pole-axis structure is that as one moves along the distance axis,the proportion of urbanization zones decreases and the proportion of ecological security zones increases.This also means that the proportion of different function zones has a ring-shaped spatial differentiation principle with distance from the core.Third,there is a spatial mosaic structure at the city and county scale.This spatial mosaic structure has features of both spatial heterogeneity,such as agglomeration and dispersion,as well as of mutual,adjacent topological correlation and spatial proximity.The results of this study contribute to scientific knowledge on major function zones and the principles of spatial organization,and it acts as an important reference for China’s integrated geographical zoning.
文摘Objectives: To examine the cross-sectional associations of the separate subscales of the Perceived Stress Scale (PSS) and tests measuring cognitive domains in older adults. Methods: 897 adults over the age of 70 free of amnestic mild cognitive impairment and dementia and enrolled in the Einstein Aging Study made up the study sample. The PSS-14 was used to measure stress. Three cognitive domains (language, episodic memory, and frontal-executive) had previously been found using principle component analysis. Linear regression analyses were used to determine the relationship between the PSS subscales and cognitive domain function. Results: The study sample had a mean age of 79.1 years and 62.8% were female. Bivariate correlations show that the PSS-14 positively worded subscale of the PSS (PSS-PW) was significantly associated with all three cognitive domains (language: r = -0.15, p < 0.001;episodic memory: r = -0.16, p < 0.001;frontal-executive: r = -0.21, p <0.001) while the negatively worded subscale of the PSS (PSS-NW) was not significantly associated with any cognitive domain. In linear regression analyses adjusted for age, white race, gender, years of education, and depressive symptoms, the PSS-PW remained significantly associated with each of the cognitive domains. The PSS-NW was not associated with any cognitive domains in any model. The PSS-14 was significantly associated with language and episodic memory, but not the frontal-executive domain. Conclusion: Worse PSS-PW scores are associated with reduced cognitive function in the executive, memory, and language domains in nondemented older adults. The PSS-PW subscale correlated better with cognitive function than the overall PSS-14. Future research should evaluate the temporality of the association and if stress reduction therapies improve cognitive performance.
文摘Water Vapor Chemistry" as a new science was discovered and established from trace analysis in Gu’s laboratory(Gu, 1991; Gu et al., 1991). Gu’s Function shows that the trace metal ion concentration in water vapor has positive correlation to"specific electron affinity constant"last ionization potential Iz/ion valence Z and negative correlation to ion volume V and coordination number N(Gu, 1994). Gu’s Func-tion C=f[(Iz/Z)/VN]of the bond parameter in water vapor chemistry corresponds to the potential energy function Z’ e2/r in the Schrodinger Equation of quantum chemistry. In different ions with the same 2+ charge, the ion concentration of water-water vapor transfer may be much different. This shows that the 2+ charge of different ions has different attractive force (hydration force). This different attractive force of the charge can be scaled with the relative energy or charge size from Gu’s Function.
文摘In this paper, we study the relationship between exponential dichotomy and quadratic Lyapunov function for the linear equation x△=A（t）x on time scales. Moreover, for the nonlinear perturbed equation x△= A（t）x ＋ f（t, x） we give the instability of the zero solution when f is sufficiently small.
基金Supported by the Foundation for subjects development of Harbin University(No.HXK200716)
文摘This paper investigates the existence of periodic solutions of a three-species food-chain diffusive system with Beddington-DeAngelis functional responses and time delays in a two-patch environment on time scales. By using a continuation theorem based on coincidence degree theory, we obtain sufficient criteria for the existence of periodic solutions for the system. Moreover, when the time scale T is chosen as R or Z, the existence of the periodic solutions of the corresponding continuous and discrete models follows. Therefore, the method is unified to provide the existence of the desired solutions for continuous differential equations and discrete difference equations.
基金supported by National Natural Science Foundation of China (No. 10671108 and 70971076)Found for the Doctoral Program of Higher Education of Ministry of Education of China (No. 20070446001)+1 种基金Innovation Planning Project of Shandong Province (No. SDYY06034)Foundation of Qufu Normal University (No. XJZ200849)
文摘This paper presents an economic lot-sizing problem with perishable inventory and general economies of scale cost functions. For the case with backlogging allowed, a mathematical model is formulated, and several properties of the optimal solutions are explored. With the help of these optimality properties, a polynomial time approximation algorithm is developed by a new method. The new method adopts a shift technique to obtain a feasible solution of subproblem and takes the optimal solution of the subproblem as an approximation solution of our problem. The worst case performance for the approximation algorithm is proven to be （4√2 ＋ 5）/7. Finally, an instance illustrates that the bound is tight.
