Using the Nevanlinna theory of the value distribution of meromorphic functions, we investigate the existence problem of admissible algebroid solutions of generalized higher order algebraic differential equations.
For multivariate linear model Y=XΘ+ε, ~N(0, σ 2ΣV), this paper is concerned with the admissibility of linear estimators of estimable function SXΘ in the class of all estimators. All admissible linear estimators ...For multivariate linear model Y=XΘ+ε, ~N(0, σ 2ΣV), this paper is concerned with the admissibility of linear estimators of estimable function SXΘ in the class of all estimators. All admissible linear estimators of SXΘ are given under each of four definitions of admissibility.展开更多
In this paper, a better admissible class B+ is introduced and a new fixed point theorem for better admissible multimap is proved on abstract convex spaces. As a consequence, we deduce a new fixed point theorem on abs...In this paper, a better admissible class B+ is introduced and a new fixed point theorem for better admissible multimap is proved on abstract convex spaces. As a consequence, we deduce a new fixed point theorem on abstract convex Ф-spaces. Our main results generalize some recent work due to Lassonde, Kakutani, Browder, and Park展开更多
Let H. be the n-direct proded of Heisenbery group H, P the affine group of Hn. Then P ho a natural unitary representation U on L2(Hn). In this paper,the direct sum decomposition of irreducible invariant closed subspac...Let H. be the n-direct proded of Heisenbery group H, P the affine group of Hn. Then P ho a natural unitary representation U on L2(Hn). In this paper,the direct sum decomposition of irreducible invariant closed subspaces under unitary representation U for L2(Hn) is given. The restrictins of U on these subspaces are square-integrable. The charactedsation of admissible condition is obtained in ierms of the Fourier transform. By seleting appropriately an orthogonal wavelet basis and the wavelet transform,the authors obtain the orthogonal direct chin decomposinon of function space L2(P,dμl).展开更多
Let p(z) be a polynomial of degree at most n. In this paper we obtain some new results about the dependence of on [[P(Z)[ls for every α, β∈ C with |a|≤ 1, |β|〉 1, R 〉 r 〉 1, and s 〉 O. Our results not...Let p(z) be a polynomial of degree at most n. In this paper we obtain some new results about the dependence of on [[P(Z)[ls for every α, β∈ C with |a|≤ 1, |β|〉 1, R 〉 r 〉 1, and s 〉 O. Our results not only generalize some well known inequalities, but also are variety of interesting results deduced from them by a fairly uniform procedure.展开更多
In this paper, by using the topological degree method and some limiting arguments, the existence of admissible periodic bouncing solutions for a class of non-conservative semi-linear impact equations is proved.
Under maids loss, tall paper dicusses the admissibility of homgeneous or nonhomgeneous linear estimators of regresaion coefficient of multivarate linear model in some common classes of estimators, the necessary and su...Under maids loss, tall paper dicusses the admissibility of homgeneous or nonhomgeneous linear estimators of regresaion coefficient of multivarate linear model in some common classes of estimators, the necessary and sufficient conditions are obtained.The results indicate that the admissibility of linear estimetors in multiate linear model is different from the admiedbility of linear estimators in Gauss-Markoff model.展开更多
This paper investigates the problem of robust admissible analysis for uncertain singular delta operator systems(SDOSs).Firstly,we introduce the definition of generalized quadratic admissibility to ensure robust admiss...This paper investigates the problem of robust admissible analysis for uncertain singular delta operator systems(SDOSs).Firstly,we introduce the definition of generalized quadratic admissibility to ensure robust admissibility.Then,by means of LMI,a necessary and sufficient condition is given to prove a uncertain SDOS is generalized quadratic admissible.Finally,a numerical example is provided to demonstrate the effectiveness of the results in this paper.展开更多
Mechanical metamaterials are architectured cellular materials with unusual properties.Herein we report another type of metal mechanical metamaterials-their elastic admissible strain(EAS)is on the order of 0.1,compared...Mechanical metamaterials are architectured cellular materials with unusual properties.Herein we report another type of metal mechanical metamaterials-their elastic admissible strain(EAS)is on the order of 0.1,compared to about 0.01 for common metallic materials.Four conditions are required for a metal mechanical metamaterial to achieve this super EAS:(i)bending-dominated deformation;(ii)low density;(iii)an appropriate lattice topology,and(iv)an intrinsically high EAS for the lattice strut constituent material.The findings of this work extend perspectives on metal mechanical metamaterials.展开更多
The demand for titanium alloys simultaneously having high elastic admissible strain and large recovery strain for bio-implant applications is increasing.Ni-free Ti-based shape memory alloys are promising candidates fo...The demand for titanium alloys simultaneously having high elastic admissible strain and large recovery strain for bio-implant applications is increasing.Ni-free Ti-based shape memory alloys are promising candidates for obtaining the required multifunctional properties.In this study,a wide content range of(0-15)wt%of low-cost,toxicity-free,and high-biocompatible Sn element was added to the Ti-8Mo(wt%)alloy to study its effect on the superelastic recovery and mechanical properties of biomedical Ti-Mo-Sn alloys.By tailoring Sn content,desired multifunctional properties of high elastic admissible strain and room temperature superelasticity were achieved in the studied Ti-Mo-Sn alloys.It was found that the increase in Sn content stabilized theβphase and a singleβphase was obtained at room temperature in Ti-8Mo-(13,15)Sn alloys.The addition of Sn modified the lattice parameters of theα″martensite andβphase and affected the lattice deformation stain ofβ→α″.The lattice deformation strain along the[011]βdirection was found to be decreased by-0.26%/wt%Sn.The room temperature superelasticity with a recovery strain of 3.1%and an elastic admissible strain of 1%was obtained in the Ti-8Mo-13Sn alloy.As Sn content increased to 15 wt%,a high elastic admissible strain of 1.56%and a recovery strain of 2.0%were obtained.These Ti-Mo-Sn alloys with excellent multifunctional properties are promising candidates for bio-implant applications.展开更多
This paper is concerned with the attitude control of a three-axis-stabilized spacecraft which consists of a central rigid body and a flexible sun-tracking solar array driven by a solar array drive assembly. Based on t...This paper is concerned with the attitude control of a three-axis-stabilized spacecraft which consists of a central rigid body and a flexible sun-tracking solar array driven by a solar array drive assembly. Based on the linearization of the dynamics of the spacecraft and the modal identi- ties about the flexible and rigid coupling matrices, the spacecraft attitude dynamics is reduced to a formally singular system with periodically varying parameters, which is quite different from a space- craft with fixed appendages. In the framework of the singular control theory, the regularity and impulse-freeness of the singular system is analyzed and then admissible attitude controllers are designed by Lyapunov's method. To improve the robustness against system uncertainties, an H∞ optimal control is designed by optimizing the H∞ norm of the system transfer function matrix. Comparative numerical experiments are performed to verify the theoretical results.展开更多
Mode decision-maker is a critical component in the logic-based Integrated Estimation and Guidance(IEG) system. For the best possible estimation and guidance performance, the mode decision delay of the mode decision-ma...Mode decision-maker is a critical component in the logic-based Integrated Estimation and Guidance(IEG) system. For the best possible estimation and guidance performance, the mode decision delay of the mode decision-maker should be limited to a range as small as possible. This paper presents a numerical method for computing the maximal admissible mode decision delay that varies with time-to-go. Particular attention has been paid to highly maneuvering target interception in terminal guidance. The results of this research offer useful guidelines for the design of the mode decision-maker in IEG systems.展开更多
The problem of stabilizing switched linear systems under asynchronous switching is addressed.The admissible edge-dependent average dwell time method is applied to design a switching signal that comprises slow admissib...The problem of stabilizing switched linear systems under asynchronous switching is addressed.The admissible edge-dependent average dwell time method is applied to design a switching signal that comprises slow admissible edge-dependent average dwell time and fast admissible edge-dependent average dwell time.Under this switching signal,the restriction that the maximum delay of asynchronous switching is known in advance is removed.The constructed Lyapunov function is associated with both the system mode and controller mode.The stabilization criteria and the corresponding algorithm are presented to obtain the controller gains and to design the switching signal.Finally,two examples are given to demonstrate the effectiveness of the proposed results.展开更多
We present a brief survey on (Weakly) Admissible Meshes and corresponding Discrete Extremal Sets, namely Approximate Fekete Points and Discrete Leja Points.These provide new computational tools for polynomial least s...We present a brief survey on (Weakly) Admissible Meshes and corresponding Discrete Extremal Sets, namely Approximate Fekete Points and Discrete Leja Points.These provide new computational tools for polynomial least squares and interpolationon multidimensional compact sets, with different applications such as numerical cubature, digital filtering, spectral and high-order methods for PDEs.展开更多
BACKGROUND Fever is a common cause of medical consultation and hospital admission,particularly among children.Recently,the United Kingdom’s National Institute for Health and Care Excellence(NICE)updated its guideline...BACKGROUND Fever is a common cause of medical consultation and hospital admission,particularly among children.Recently,the United Kingdom’s National Institute for Health and Care Excellence(NICE)updated its guidelines for assessing fever in children under five years of age.The efficient assessment and management of children with fever are crucial for improving patient outcomes.AIM To evaluate fever assessment in hospitalized children and to assess its adherence with the NICE Fever in under 5s guideline.METHODS We conducted a retrospective cohort review of the electronic medical records of children under five years of age at the Department of Pediatrics,Salmaniya Medical Complex,Bahrain,between June and July 2023.Demographic data,vital signs during the first 48 h of admission,route of temperature measurement,and indications for admission were gathered.Fever was defined according to the NICE guideline.The children were divided into five groups according to their age(0-3 months,>3-6 months,>6-12 months,>12-36 months,and>36-60 months).Patients with and without fever were compared in terms of demography,indication for admission,route of temperature measurement,and other vital signs.Compliance with the NICE Fever in the under 5s guideline was assessed.Full compliance was defined as>95%,partial compliance as 70%-95%,and minimal compliance as≤69%.Pearson’sχ^(2),Student’s t test,the Mann-Whitney U test,and Spearman’s correlation coefficient(rs)were used for comparison.RESULTS Of the 136 patients reviewed,80(58.8%)were boys.The median age at admission was 14.2[interquartile range(IQR):1.7-44.4]months,with the most common age group being 36-60 months.Thirty-six(26.4%)patients had fever,and 100(73.6%)were afebrile.The commonest age group for febrile patients(>12-36 months)was older than the commonest age group for afebrile patients(0-3 months)(P=0.027).The median weight was 8.3(IQR:4.0-13.3)kg.Patients with fever had higher weight than those without fever[10.2(IQR:7.3-13.0)vs 7.1(IQR:3.8-13.3)kg,respectively](P=0.034).Gastrointestinal disease was the leading indication for hospital admission(n=47,34.6%).Patients with central nervous system diseases and fever of unknown etiology were more likely to be febrile(P=0.030 and P=0.011,respectively).The mean heart rate was higher in the febrile group than the afebrile group(140±24 vs 126±20 beats per minute,respectively)[P=0.001(confidence interval:5.8-21.9)]with a positive correlation between body temperature and heart rate,r=0.242,n=136,P=0.004.A higher proportion of febrile patients received paracetamol(n=35,81.3%)compared to the afebrile patients(n=8,18.6%)(P<0.001).The axillary route was the most commonly used for temperature measurements(n=40/42,95.2%),followed by the rectal route(n=2/42,4.8%).The department demonstrated full compliance with the NICE guideline for five criteria:the type of thermometer used,route and frequency of temperature measurement,frequency of heart rate measurement,and use of antipyretics as needed.Partial compliance was noted for two criteria,the threshold of fever at 38°C or more,and the respiratory rate assessment in febrile patients.Minimal compliance or no record was observed for the remaining three criteria;routine assessment of capillary refill,temperature reassessment 1-2 h after each antipyretic intake,and refraining from the use of tepid sponging.CONCLUSION This study showed that fever assessment in hospitalized children under five years of age was appropriate,but certain areas of adherence to the NICE guideline still need to be improved.展开更多
Let E■R be an interval. By studying an admissible family of branching mechanisms{ψt,t ∈E} introduced in Li [Ann. Probab., 42, 41-79(2014)], we construct a decreasing Levy-CRT-valued process {Tt, t ∈ E} by pruning ...Let E■R be an interval. By studying an admissible family of branching mechanisms{ψt,t ∈E} introduced in Li [Ann. Probab., 42, 41-79(2014)], we construct a decreasing Levy-CRT-valued process {Tt, t ∈ E} by pruning Lévy trees accordingly such that for each t ∈E, Tt is a ψt-Lévy tree. We also obtain an analogous process {Tt*,t ∈E} by pruning a critical Levy tree conditioned to be infinite. Under a regular condition on the admissible family of branching mechanisms, we show that the law of {Tt,t ∈E} at the ascension time A := inf{t ∈E;Tt is finite} can be represented by{Tt*,t∈E}.The results generalize those studied in Abraham and Delmas [Ann. Probab., 40, 1167-1211(2012)].展开更多
Suppose that we observe y|θ,τ∼N_(p)(Xθ,τ^(−1)I_(p)),where θ is an unknown vector with unknown precisionτ.Estimating the regression coefficient θ with known τ has been well studied.However,statistical properti...Suppose that we observe y|θ,τ∼N_(p)(Xθ,τ^(−1)I_(p)),where θ is an unknown vector with unknown precisionτ.Estimating the regression coefficient θ with known τ has been well studied.However,statistical properties such as admissibility in estimating θ with unknownτare not well studied.Han[(2009).Topics in shrinkage estimation and in causal inference(PhD thesis).Warton School,University of Pennsylvania]appears to be the first to consider the problem,developing sufficient conditions for the admissibility of estimating means of multivariate normal distributions with unknown variance.We generalise the sufficient conditions for admissibility and apply these results to the normal linear regression model.2-level and 3-level hierarchical models with unknown precisionτare investigated when a standard class of hierarchical priors leads to admissible estimators of θ under the normalised squared error loss.One reason to consider this problem is the importance of admissibility in the hierarchical prior selection,and we expect that our study could be helpful in providing some reference for choosing hierarchical priors.展开更多
In this paper, we study, mathematically speaking, the problem-the number of admissible preference orderings for the transitivity of simple majority vote(SMV) derived from Arrow’s Impossibility Theorem. In our researc...In this paper, we study, mathematically speaking, the problem-the number of admissible preference orderings for the transitivity of simple majority vote(SMV) derived from Arrow’s Impossibility Theorem. In our research, we find, by computer enumerating, that some results given by Craven are not correct. By defining a set of constraints, we give the recurrence formula of the local maximal number of admissible preference orderings and some other useful results.展开更多
文摘Using the Nevanlinna theory of the value distribution of meromorphic functions, we investigate the existence problem of admissible algebroid solutions of generalized higher order algebraic differential equations.
文摘For multivariate linear model Y=XΘ+ε, ~N(0, σ 2ΣV), this paper is concerned with the admissibility of linear estimators of estimable function SXΘ in the class of all estimators. All admissible linear estimators of SXΘ are given under each of four definitions of admissibility.
基金Supported by the National Science Foundation of China(Grant 10626025)Research Grant of Chongqing Key Laboratory of Operations Research and System Engineering
文摘In this paper, a better admissible class B+ is introduced and a new fixed point theorem for better admissible multimap is proved on abstract convex spaces. As a consequence, we deduce a new fixed point theorem on abstract convex Ф-spaces. Our main results generalize some recent work due to Lassonde, Kakutani, Browder, and Park
文摘Let H. be the n-direct proded of Heisenbery group H, P the affine group of Hn. Then P ho a natural unitary representation U on L2(Hn). In this paper,the direct sum decomposition of irreducible invariant closed subspaces under unitary representation U for L2(Hn) is given. The restrictins of U on these subspaces are square-integrable. The charactedsation of admissible condition is obtained in ierms of the Fourier transform. By seleting appropriately an orthogonal wavelet basis and the wavelet transform,the authors obtain the orthogonal direct chin decomposinon of function space L2(P,dμl).
文摘Let p(z) be a polynomial of degree at most n. In this paper we obtain some new results about the dependence of on [[P(Z)[ls for every α, β∈ C with |a|≤ 1, |β|〉 1, R 〉 r 〉 1, and s 〉 O. Our results not only generalize some well known inequalities, but also are variety of interesting results deduced from them by a fairly uniform procedure.
基金Supported by the NNSF of China(11571249)NSF of JiangSu Province(BK20171275)Supported by the grant of Innovative Training Program of College Students in Jiangsu province(201410324001Z)
文摘In this paper, by using the topological degree method and some limiting arguments, the existence of admissible periodic bouncing solutions for a class of non-conservative semi-linear impact equations is proved.
文摘Under maids loss, tall paper dicusses the admissibility of homgeneous or nonhomgeneous linear estimators of regresaion coefficient of multivarate linear model in some common classes of estimators, the necessary and sufficient conditions are obtained.The results indicate that the admissibility of linear estimetors in multiate linear model is different from the admiedbility of linear estimators in Gauss-Markoff model.
文摘This paper investigates the problem of robust admissible analysis for uncertain singular delta operator systems(SDOSs).Firstly,we introduce the definition of generalized quadratic admissibility to ensure robust admissibility.Then,by means of LMI,a necessary and sufficient condition is given to prove a uncertain SDOS is generalized quadratic admissible.Finally,a numerical example is provided to demonstrate the effectiveness of the results in this paper.
基金the China Scholarship Council(CSC)for a CSC scholarship(No.201706230108)Funding from the National Natural Science Foundation of China(No.51971145)and the Australian Research Council(Nos.DP200102666 and No.DE230101344)is acknowledged.
文摘Mechanical metamaterials are architectured cellular materials with unusual properties.Herein we report another type of metal mechanical metamaterials-their elastic admissible strain(EAS)is on the order of 0.1,compared to about 0.01 for common metallic materials.Four conditions are required for a metal mechanical metamaterial to achieve this super EAS:(i)bending-dominated deformation;(ii)low density;(iii)an appropriate lattice topology,and(iv)an intrinsically high EAS for the lattice strut constituent material.The findings of this work extend perspectives on metal mechanical metamaterials.
基金the Korean Ministry of Trade,Industry and Energy(Grant No.200116572).
文摘The demand for titanium alloys simultaneously having high elastic admissible strain and large recovery strain for bio-implant applications is increasing.Ni-free Ti-based shape memory alloys are promising candidates for obtaining the required multifunctional properties.In this study,a wide content range of(0-15)wt%of low-cost,toxicity-free,and high-biocompatible Sn element was added to the Ti-8Mo(wt%)alloy to study its effect on the superelastic recovery and mechanical properties of biomedical Ti-Mo-Sn alloys.By tailoring Sn content,desired multifunctional properties of high elastic admissible strain and room temperature superelasticity were achieved in the studied Ti-Mo-Sn alloys.It was found that the increase in Sn content stabilized theβphase and a singleβphase was obtained at room temperature in Ti-8Mo-(13,15)Sn alloys.The addition of Sn modified the lattice parameters of theα″martensite andβphase and affected the lattice deformation stain ofβ→α″.The lattice deformation strain along the[011]βdirection was found to be decreased by-0.26%/wt%Sn.The room temperature superelasticity with a recovery strain of 3.1%and an elastic admissible strain of 1%was obtained in the Ti-8Mo-13Sn alloy.As Sn content increased to 15 wt%,a high elastic admissible strain of 1.56%and a recovery strain of 2.0%were obtained.These Ti-Mo-Sn alloys with excellent multifunctional properties are promising candidates for bio-implant applications.
文摘This paper is concerned with the attitude control of a three-axis-stabilized spacecraft which consists of a central rigid body and a flexible sun-tracking solar array driven by a solar array drive assembly. Based on the linearization of the dynamics of the spacecraft and the modal identi- ties about the flexible and rigid coupling matrices, the spacecraft attitude dynamics is reduced to a formally singular system with periodically varying parameters, which is quite different from a space- craft with fixed appendages. In the framework of the singular control theory, the regularity and impulse-freeness of the singular system is analyzed and then admissible attitude controllers are designed by Lyapunov's method. To improve the robustness against system uncertainties, an H∞ optimal control is designed by optimizing the H∞ norm of the system transfer function matrix. Comparative numerical experiments are performed to verify the theoretical results.
文摘Mode decision-maker is a critical component in the logic-based Integrated Estimation and Guidance(IEG) system. For the best possible estimation and guidance performance, the mode decision delay of the mode decision-maker should be limited to a range as small as possible. This paper presents a numerical method for computing the maximal admissible mode decision delay that varies with time-to-go. Particular attention has been paid to highly maneuvering target interception in terminal guidance. The results of this research offer useful guidelines for the design of the mode decision-maker in IEG systems.
基金Project supported by the National Natural Science Foundation of China(Nos.61873331,61773236,and 61773235)the Natural Science Foundation of Shandong Province,China(No.ZR2020YQ48)。
文摘The problem of stabilizing switched linear systems under asynchronous switching is addressed.The admissible edge-dependent average dwell time method is applied to design a switching signal that comprises slow admissible edge-dependent average dwell time and fast admissible edge-dependent average dwell time.Under this switching signal,the restriction that the maximum delay of asynchronous switching is known in advance is removed.The constructed Lyapunov function is associated with both the system mode and controller mode.The stabilization criteria and the corresponding algorithm are presented to obtain the controller gains and to design the switching signal.Finally,two examples are given to demonstrate the effectiveness of the proposed results.
文摘We present a brief survey on (Weakly) Admissible Meshes and corresponding Discrete Extremal Sets, namely Approximate Fekete Points and Discrete Leja Points.These provide new computational tools for polynomial least squares and interpolationon multidimensional compact sets, with different applications such as numerical cubature, digital filtering, spectral and high-order methods for PDEs.
文摘BACKGROUND Fever is a common cause of medical consultation and hospital admission,particularly among children.Recently,the United Kingdom’s National Institute for Health and Care Excellence(NICE)updated its guidelines for assessing fever in children under five years of age.The efficient assessment and management of children with fever are crucial for improving patient outcomes.AIM To evaluate fever assessment in hospitalized children and to assess its adherence with the NICE Fever in under 5s guideline.METHODS We conducted a retrospective cohort review of the electronic medical records of children under five years of age at the Department of Pediatrics,Salmaniya Medical Complex,Bahrain,between June and July 2023.Demographic data,vital signs during the first 48 h of admission,route of temperature measurement,and indications for admission were gathered.Fever was defined according to the NICE guideline.The children were divided into five groups according to their age(0-3 months,>3-6 months,>6-12 months,>12-36 months,and>36-60 months).Patients with and without fever were compared in terms of demography,indication for admission,route of temperature measurement,and other vital signs.Compliance with the NICE Fever in the under 5s guideline was assessed.Full compliance was defined as>95%,partial compliance as 70%-95%,and minimal compliance as≤69%.Pearson’sχ^(2),Student’s t test,the Mann-Whitney U test,and Spearman’s correlation coefficient(rs)were used for comparison.RESULTS Of the 136 patients reviewed,80(58.8%)were boys.The median age at admission was 14.2[interquartile range(IQR):1.7-44.4]months,with the most common age group being 36-60 months.Thirty-six(26.4%)patients had fever,and 100(73.6%)were afebrile.The commonest age group for febrile patients(>12-36 months)was older than the commonest age group for afebrile patients(0-3 months)(P=0.027).The median weight was 8.3(IQR:4.0-13.3)kg.Patients with fever had higher weight than those without fever[10.2(IQR:7.3-13.0)vs 7.1(IQR:3.8-13.3)kg,respectively](P=0.034).Gastrointestinal disease was the leading indication for hospital admission(n=47,34.6%).Patients with central nervous system diseases and fever of unknown etiology were more likely to be febrile(P=0.030 and P=0.011,respectively).The mean heart rate was higher in the febrile group than the afebrile group(140±24 vs 126±20 beats per minute,respectively)[P=0.001(confidence interval:5.8-21.9)]with a positive correlation between body temperature and heart rate,r=0.242,n=136,P=0.004.A higher proportion of febrile patients received paracetamol(n=35,81.3%)compared to the afebrile patients(n=8,18.6%)(P<0.001).The axillary route was the most commonly used for temperature measurements(n=40/42,95.2%),followed by the rectal route(n=2/42,4.8%).The department demonstrated full compliance with the NICE guideline for five criteria:the type of thermometer used,route and frequency of temperature measurement,frequency of heart rate measurement,and use of antipyretics as needed.Partial compliance was noted for two criteria,the threshold of fever at 38°C or more,and the respiratory rate assessment in febrile patients.Minimal compliance or no record was observed for the remaining three criteria;routine assessment of capillary refill,temperature reassessment 1-2 h after each antipyretic intake,and refraining from the use of tepid sponging.CONCLUSION This study showed that fever assessment in hospitalized children under five years of age was appropriate,but certain areas of adherence to the NICE guideline still need to be improved.
基金supported by NSFC(Grant No.11801075)supported by NSFC(Grant Nos.11671041,11531001 and 11371061)the Fundamental Research Funds for the Central Universities in UIBE(Grant No.16QN04)
文摘Let E■R be an interval. By studying an admissible family of branching mechanisms{ψt,t ∈E} introduced in Li [Ann. Probab., 42, 41-79(2014)], we construct a decreasing Levy-CRT-valued process {Tt, t ∈ E} by pruning Lévy trees accordingly such that for each t ∈E, Tt is a ψt-Lévy tree. We also obtain an analogous process {Tt*,t ∈E} by pruning a critical Levy tree conditioned to be infinite. Under a regular condition on the admissible family of branching mechanisms, we show that the law of {Tt,t ∈E} at the ascension time A := inf{t ∈E;Tt is finite} can be represented by{Tt*,t∈E}.The results generalize those studied in Abraham and Delmas [Ann. Probab., 40, 1167-1211(2012)].
基金Supported by the National Natural Science Foundation of China (No. 10771173)the Natural Science Foundation of Henan Education Department (No. 2008B110012)+1 种基金the Science and Technology Program Project of Henan Province (No. 092300410187)the Youth Foundation of Luoyang Normal University
基金supported by the 111 Project of China(No.B14019)the National Natural Science Foundation of China[Grant No.11671146].
文摘Suppose that we observe y|θ,τ∼N_(p)(Xθ,τ^(−1)I_(p)),where θ is an unknown vector with unknown precisionτ.Estimating the regression coefficient θ with known τ has been well studied.However,statistical properties such as admissibility in estimating θ with unknownτare not well studied.Han[(2009).Topics in shrinkage estimation and in causal inference(PhD thesis).Warton School,University of Pennsylvania]appears to be the first to consider the problem,developing sufficient conditions for the admissibility of estimating means of multivariate normal distributions with unknown variance.We generalise the sufficient conditions for admissibility and apply these results to the normal linear regression model.2-level and 3-level hierarchical models with unknown precisionτare investigated when a standard class of hierarchical priors leads to admissible estimators of θ under the normalised squared error loss.One reason to consider this problem is the importance of admissibility in the hierarchical prior selection,and we expect that our study could be helpful in providing some reference for choosing hierarchical priors.
基金This project is supported by Doctoral Fundation of National Educational Committee.
文摘In this paper, we study, mathematically speaking, the problem-the number of admissible preference orderings for the transitivity of simple majority vote(SMV) derived from Arrow’s Impossibility Theorem. In our research, we find, by computer enumerating, that some results given by Craven are not correct. By defining a set of constraints, we give the recurrence formula of the local maximal number of admissible preference orderings and some other useful results.