Petty's conjectured projection inequality is a famous open problem in the theory of convex bodies. In this paper, it is shown that an inequality relating to Lp-version of the Petty's conjectured projection inequalit...Petty's conjectured projection inequality is a famous open problem in the theory of convex bodies. In this paper, it is shown that an inequality relating to Lp-version of the Petty's conjectured projection inequality is developed by using the notions of the Lp-mixed volume and the Lp-dual mixed volume, the relation of the Lp-projection body and the geometric body Г-pK, the Bourgain-Milman inequality and the Lp-Bnsemann-Petty inequality. In addition, for each origin-symmetric convex body, by applying the Jensen inequality and the monotonicity of the geometric body Г-pK, the reverses of Lp-version of the Petty's conjectured projection inequality and the Lp-Petty projection inequality are given, respectively.展开更多
AIM To evaluate usefulness of single photon emission computed tomography(SPECT) with three-dimensional stereotactic surface projection(3D-SSP) in distinguishing between Alzheimer's disease(AD) and depression.METHO...AIM To evaluate usefulness of single photon emission computed tomography(SPECT) with three-dimensional stereotactic surface projection(3D-SSP) in distinguishing between Alzheimer's disease(AD) and depression.METHODS We studied 43 patients who presented with both depressive symptoms and memory disturbance. Each subject was evaluated using the following:(1) the Minimal Mental State Examination;(2) the Hamilton Rating Scale for Depression;(3) Clinical Global Impression-Severity scale(CGI-S); and(4) SPECT imaging with 3D-SSP.RESULTS The MMSE scores correlated significantly with the maximum Z-scores of AD-associated regions. CGI-S scores correlated significantly with the maximum Z-scores of depression-associated regions. Factor analysis identified three significant factors. Of these, Factor 1 could be interpreted as favouring a tendency for AD, Factor 2 as favouring a tendency for pseudo-dementia, and Factor 3 as favouring a depressive tendency.CONCLUSION We investigated whether these patients could be categorized as types: Type A(true AD), Type B(pseudodementia), Type C(occult AD), and Type D(true depression). The factor scores in factor analysis supported the validity of this classification. Our results suggest that SPECT with 3D-SSP is highly useful for distinguishing between depression and depressed mood in the early stage of AD.展开更多
As a national cultural property,General Zhang Fei’s Temple is the largest ancient architectural complex in the Three Gorges of the Yangtze River.It was built in the Han Dynasty and has a long history of nearly 2,000 ...As a national cultural property,General Zhang Fei’s Temple is the largest ancient architectural complex in the Three Gorges of the Yangtze River.It was built in the Han Dynasty and has a long history of nearly 2,000 years.In 1994,the Chinese government launched the Three Gorges Dam project at the Yangtze River and implemented the largest relocation project for the General Zhang Fei Temple to prevent it from being submerged.The temple was relocated 32 kilometers upstream along with the local people of Yunyang County,and the historic environment was rebuilt on the opposite side of the migrant city of New Yunyang County.The temple was restored successfully and the tradition of offering sacrifices to General Zhang Fei continued in the local community.The relocation project lasted for 8 years and became the largest cultural heritage conservation project of the People’s Republic of China at the end of the 20th century.This paper comprehensively summarizes and reviews the project goals,implementation process,and project highlights of this relocation,so as to provide an important case reference for heritage conservation projects in the future.展开更多
Xinqiao Gully is located in the area of the 2008 Wenchuan M_(s)8.0 earthquake in Sichuan province,China.Based on the investigation of the 2023"6-26"Xinqiao Gully debris flow event,this study assessed the eff...Xinqiao Gully is located in the area of the 2008 Wenchuan M_(s)8.0 earthquake in Sichuan province,China.Based on the investigation of the 2023"6-26"Xinqiao Gully debris flow event,this study assessed the effectiveness of the debris flow control project and evaluated the debris flow hazards.Through field investigation and numerical simulation methods,the indicators of flow intensity reduction rate and storage capacity fullness were proposed to quantify the effectiveness of the engineering measures in the debris flow event.The simulation results show that the debris flow control project reduced the flow intensity by41.05%to 64.61%.The storage capacity of the dam decreases gradually from upstream to the mouth of the gully,thus effectively intercepting and controlling the debris flow.By evaluating the debris flow of different recurrence intervals,further measures are recommended for managing debris flow events.展开更多
The following is up-to-date inform at ion about Tibet's Population.In 1995,there was a population about 2.43 million in the region,according to my estima-tion based on data from the 1990 census and annual sam-plin...The following is up-to-date inform at ion about Tibet's Population.In 1995,there was a population about 2.43 million in the region,according to my estima-tion based on data from the 1990 census and annual sam-pling surveys.The birth rate was 28 per thousand,the death rate ten per thousand and the natural increase rate 18 per thousand.展开更多
Learning a mapping between an input space and an output.space from training data canbe viewed as a problem of function approximation,which means that different criteria result in learningapproaches of different abilit...Learning a mapping between an input space and an output.space from training data canbe viewed as a problem of function approximation,which means that different criteria result in learningapproaches of different abilities.Among them,projection criterion proposed by one of the authors aimsdirectly at optimal generalization.The projection idea leads to three specific learning approaches,projection learning,partial projection learning,and averaged projection learning,and a framework of afamily of projection learning called S-L projection learning is established to discuss infinite kinds oflearning.S-L projection learning has a different form from the three methods,and it is not easy to analyzetheir relationship.This paper focuses on an equivalent form of S-L projection learning,which shows thatit is a transformed version of partial projection learning.展开更多
Although General Relativity is the classic example of a physical theory based on differential geometry, the momentum tensor is the only part of the field equation that is not derived from or interpreted with different...Although General Relativity is the classic example of a physical theory based on differential geometry, the momentum tensor is the only part of the field equation that is not derived from or interpreted with differential geometry. This work extends General Relativity and Einstein-Cartan theory by augmenting the Poincaré group with projective (special) conformal transformations, which are translations at conformal infinity. Momentum becomes a part of the differential geometry of spacetime. The Lie algebra of these transformations is represented by vectorfields on an associated Minkowski fiber space. Variation of projective conformal scalar curvature generates a 2-index tensor that serves as linear momentum in the field equations of General Relativity. The computation yields a constructive realization of Mach’s principle: local inertia is determined by local motion relative to mass at conformal infinity in each fiber. The vectorfields have a cellular structure that is similar to that of turbulent fluids.展开更多
Beginning with a 5D homogeneous universe [1], we have provided a plausible explanation of the self-rotation phenomenon of stellar objects previously with illustration of large number of star samples [2], via a 5D-4D p...Beginning with a 5D homogeneous universe [1], we have provided a plausible explanation of the self-rotation phenomenon of stellar objects previously with illustration of large number of star samples [2], via a 5D-4D projection. The origin of such rotation is the balance of the angular momenta of stars and that of positive and negative charged e-trino pairs, within a 3D ⊗1D?void of the stellar object, the existence of which is based on conservation/parity laws in physics if one starts with homogeneous 5D universe. While the in-phase e-trino pairs are proposed to be responsible for the generation of angular momentum, the anti-phase but oppositely charge pairs necessarily produce currents. In the 5D to 4D projection, one space variable in the 5D manifold was compacted to zero in most other 5D theories (including theories of Kaluza-Klein and Einstein [3] [4]). We have demonstrated, using the Fermat’s Last Theorem [5], that for validity of gauge invariance at the 4D-5D boundary, the 4th space variable in the 5D manifold is mapped into two current rings at both magnetic poles as required by Perelman entropy mapping;these loops are the origin of the dipolar magnetic field. One conclusion we draw is that there is no gravitational singularity, and hence no black holes in the universe, a result strongly supported by the recent discovery of many stars with masses well greater than 100 solar mass [6] [7] [8], without trace of phenomena observed (such as strong gamma and X ray emissions), which are supposed to be associated with black holes. We analyze the properties of such loop currents on the 4D-5D boundary, where Maxwell equations are valid. We derive explicit expressions for the dipolar fields over the whole temperature range. We then compare our prediction with measured surface magnetic fields of many stars. Since there is coupling in distribution between the in-phase and anti-phase pairs of e-trinos, the generated mag-netic field is directly related to the angular momentum, leading to the result that the magnetic field can be expressible in terms of only the mechanical variables (mass M, radius R, rotation period P)of a star, as if Maxwell equations are “hidden”. An explanation for the occurrence of this “un-expected result” is provided in Section (7.6). Therefore we provide satisfactory answers to a number of “mysteries” of magnetism in astrophysics such as the “Magnetic Bode’s Relation/Law” [9] and the experimental finding that B-P graph in the log-log plot is linear. Moreover, we have developed a new method for studying the relations among the data (M, R, P) during stellar evolution. Ten groups of stellar objects, effectively over 2000 samples are used in various parts of the analysis. We also explain the emergence of huge magnetic field in very old stars like White Dwarfs in terms of formation of 2D Semion state on stellar surface and release of magnetic flux as magnetic storms upon changing the 2D state back to 3D structure. Moreover, we provide an explanation, on the ground of the 5D theory, for the detection of extremely weak fields in Venus and Mars and the asymmetric distribution of magnetic field on the Martian surface. We predict the equatorial fields B of the newly discovered Trappist-1 star and the 6 nearest planets. The log B?−?log P graph for the 6 planets is linear and they satisfy the Magnetic Bode’s relation. Based on the above analysis, we have discovered several new laws of stellar magnetism, which are summarized in Section (7.6).展开更多
This paper collected and arranged competitive scientific research projects undertaken by Tropical Crops Genetic Resources Institute of Chinese Academy of Tropical Agricultural Sciences in 2003-2014. Through statistica...This paper collected and arranged competitive scientific research projects undertaken by Tropical Crops Genetic Resources Institute of Chinese Academy of Tropical Agricultural Sciences in 2003-2014. Through statistical analysis on quantity of projects,funded amount,age of person responsible,professional title of person responsible,academic degree of person responsible,research object,it discussed relevant characteristics and rules. Finally,it came up with pertinent measures and recommendations,in the hope of providing services for decision-making and scientific and technological management.展开更多
Water projects’ sediment deposition problems always cause widespread concerns. The gravity of them varies in accordance not only with reservoirs’ natural and socio-economic characteristics but also with their modes ...Water projects’ sediment deposition problems always cause widespread concerns. The gravity of them varies in accordance not only with reservoirs’ natural and socio-economic characteristics but also with their modes of operation. The unique characteristics, configuration and mode of operation of Three Gorges Project (TGP) reservoir are compared with those of several existing large reservoirs in this paper. As many reservoirs are troubling environment by gradually extending coarse sediment deposition at the uppermost end of fluctuating backwater region toward upstream, Gezhouba reservoir on Yangtze and Danjiangkou reservoir on Hanjiang have shown no trace of such upstream extension of sediment deposition in relevant prototype observation data for the past 20 and more years. TGP reservoir’s in-coming flow sediment conditions and configuration in plane are almost the same as those of Gezhouba reservoir, and TGP reservoir’s mode of operation(usually keeping a very low pool level for flood control in flood season and storing up in-coming flow only thenceafter) is similar to that of Danjiangkou reservoir. New findings of sediment research and prototype flow sediment investigations as well as new agenda of large hydro projects’ construction on Jinshajiang in nearest future assure the prospects of TGP sediment handling.展开更多
Recently, we developed the projective truncation approximation for the equation of motion of two-time Green's functions(Fan et al., Phys. Rev. B 97, 165140(2018)). In that approximation, the precision of results d...Recently, we developed the projective truncation approximation for the equation of motion of two-time Green's functions(Fan et al., Phys. Rev. B 97, 165140(2018)). In that approximation, the precision of results depends on the selection of operator basis. Here, for three successively larger operator bases, we calculate the local static averages and the impurity density of states of the single-band Anderson impurity model. The results converge systematically towards those of numerical renormalization group as the basis size is enlarged. We also propose a quantitative gauge of the truncation error within this method and demonstrate its usefulness using the Hubbard-I basis. We thus confirm that the projective truncation approximation is a method of controllable precision for quantum many-body systems.展开更多
We discuss the fact that there is a crucial contradiction within Von Neumann’s theory. We derive a proposition concerning a quantum expected value under an assumption of the existence of the orientation of reference ...We discuss the fact that there is a crucial contradiction within Von Neumann’s theory. We derive a proposition concerning a quantum expected value under an assumption of the existence of the orientation of reference frames in N spin-1/2 systems (1 ≤ N to a new constant . It may be said that a new type of the quantum theory early approaches Newton’s theory in the macroscopic scale than the old quantum theory does. We discuss how our solution is used in an implementation of Deutsch’s algorithm.展开更多
基金Project supported by the National Natural Science Foundation of China(No.10671117)the Key Science Research Foundation of Education Department of Hubei Province of China(No.2003A005).
文摘Petty's conjectured projection inequality is a famous open problem in the theory of convex bodies. In this paper, it is shown that an inequality relating to Lp-version of the Petty's conjectured projection inequality is developed by using the notions of the Lp-mixed volume and the Lp-dual mixed volume, the relation of the Lp-projection body and the geometric body Г-pK, the Bourgain-Milman inequality and the Lp-Bnsemann-Petty inequality. In addition, for each origin-symmetric convex body, by applying the Jensen inequality and the monotonicity of the geometric body Г-pK, the reverses of Lp-version of the Petty's conjectured projection inequality and the Lp-Petty projection inequality are given, respectively.
文摘AIM To evaluate usefulness of single photon emission computed tomography(SPECT) with three-dimensional stereotactic surface projection(3D-SSP) in distinguishing between Alzheimer's disease(AD) and depression.METHODS We studied 43 patients who presented with both depressive symptoms and memory disturbance. Each subject was evaluated using the following:(1) the Minimal Mental State Examination;(2) the Hamilton Rating Scale for Depression;(3) Clinical Global Impression-Severity scale(CGI-S); and(4) SPECT imaging with 3D-SSP.RESULTS The MMSE scores correlated significantly with the maximum Z-scores of AD-associated regions. CGI-S scores correlated significantly with the maximum Z-scores of depression-associated regions. Factor analysis identified three significant factors. Of these, Factor 1 could be interpreted as favouring a tendency for AD, Factor 2 as favouring a tendency for pseudo-dementia, and Factor 3 as favouring a depressive tendency.CONCLUSION We investigated whether these patients could be categorized as types: Type A(true AD), Type B(pseudodementia), Type C(occult AD), and Type D(true depression). The factor scores in factor analysis supported the validity of this classification. Our results suggest that SPECT with 3D-SSP is highly useful for distinguishing between depression and depressed mood in the early stage of AD.
文摘As a national cultural property,General Zhang Fei’s Temple is the largest ancient architectural complex in the Three Gorges of the Yangtze River.It was built in the Han Dynasty and has a long history of nearly 2,000 years.In 1994,the Chinese government launched the Three Gorges Dam project at the Yangtze River and implemented the largest relocation project for the General Zhang Fei Temple to prevent it from being submerged.The temple was relocated 32 kilometers upstream along with the local people of Yunyang County,and the historic environment was rebuilt on the opposite side of the migrant city of New Yunyang County.The temple was restored successfully and the tradition of offering sacrifices to General Zhang Fei continued in the local community.The relocation project lasted for 8 years and became the largest cultural heritage conservation project of the People’s Republic of China at the end of the 20th century.This paper comprehensively summarizes and reviews the project goals,implementation process,and project highlights of this relocation,so as to provide an important case reference for heritage conservation projects in the future.
基金supported by the project of the China Geological Survey(No.DD20221746)the National Natural Science Foundation of China(Grant Nos.41101086)。
文摘Xinqiao Gully is located in the area of the 2008 Wenchuan M_(s)8.0 earthquake in Sichuan province,China.Based on the investigation of the 2023"6-26"Xinqiao Gully debris flow event,this study assessed the effectiveness of the debris flow control project and evaluated the debris flow hazards.Through field investigation and numerical simulation methods,the indicators of flow intensity reduction rate and storage capacity fullness were proposed to quantify the effectiveness of the engineering measures in the debris flow event.The simulation results show that the debris flow control project reduced the flow intensity by41.05%to 64.61%.The storage capacity of the dam decreases gradually from upstream to the mouth of the gully,thus effectively intercepting and controlling the debris flow.By evaluating the debris flow of different recurrence intervals,further measures are recommended for managing debris flow events.
文摘The following is up-to-date inform at ion about Tibet's Population.In 1995,there was a population about 2.43 million in the region,according to my estima-tion based on data from the 1990 census and annual sam-pling surveys.The birth rate was 28 per thousand,the death rate ten per thousand and the natural increase rate 18 per thousand.
文摘Learning a mapping between an input space and an output.space from training data canbe viewed as a problem of function approximation,which means that different criteria result in learningapproaches of different abilities.Among them,projection criterion proposed by one of the authors aimsdirectly at optimal generalization.The projection idea leads to three specific learning approaches,projection learning,partial projection learning,and averaged projection learning,and a framework of afamily of projection learning called S-L projection learning is established to discuss infinite kinds oflearning.S-L projection learning has a different form from the three methods,and it is not easy to analyzetheir relationship.This paper focuses on an equivalent form of S-L projection learning,which shows thatit is a transformed version of partial projection learning.
文摘Although General Relativity is the classic example of a physical theory based on differential geometry, the momentum tensor is the only part of the field equation that is not derived from or interpreted with differential geometry. This work extends General Relativity and Einstein-Cartan theory by augmenting the Poincaré group with projective (special) conformal transformations, which are translations at conformal infinity. Momentum becomes a part of the differential geometry of spacetime. The Lie algebra of these transformations is represented by vectorfields on an associated Minkowski fiber space. Variation of projective conformal scalar curvature generates a 2-index tensor that serves as linear momentum in the field equations of General Relativity. The computation yields a constructive realization of Mach’s principle: local inertia is determined by local motion relative to mass at conformal infinity in each fiber. The vectorfields have a cellular structure that is similar to that of turbulent fluids.
文摘Beginning with a 5D homogeneous universe [1], we have provided a plausible explanation of the self-rotation phenomenon of stellar objects previously with illustration of large number of star samples [2], via a 5D-4D projection. The origin of such rotation is the balance of the angular momenta of stars and that of positive and negative charged e-trino pairs, within a 3D ⊗1D?void of the stellar object, the existence of which is based on conservation/parity laws in physics if one starts with homogeneous 5D universe. While the in-phase e-trino pairs are proposed to be responsible for the generation of angular momentum, the anti-phase but oppositely charge pairs necessarily produce currents. In the 5D to 4D projection, one space variable in the 5D manifold was compacted to zero in most other 5D theories (including theories of Kaluza-Klein and Einstein [3] [4]). We have demonstrated, using the Fermat’s Last Theorem [5], that for validity of gauge invariance at the 4D-5D boundary, the 4th space variable in the 5D manifold is mapped into two current rings at both magnetic poles as required by Perelman entropy mapping;these loops are the origin of the dipolar magnetic field. One conclusion we draw is that there is no gravitational singularity, and hence no black holes in the universe, a result strongly supported by the recent discovery of many stars with masses well greater than 100 solar mass [6] [7] [8], without trace of phenomena observed (such as strong gamma and X ray emissions), which are supposed to be associated with black holes. We analyze the properties of such loop currents on the 4D-5D boundary, where Maxwell equations are valid. We derive explicit expressions for the dipolar fields over the whole temperature range. We then compare our prediction with measured surface magnetic fields of many stars. Since there is coupling in distribution between the in-phase and anti-phase pairs of e-trinos, the generated mag-netic field is directly related to the angular momentum, leading to the result that the magnetic field can be expressible in terms of only the mechanical variables (mass M, radius R, rotation period P)of a star, as if Maxwell equations are “hidden”. An explanation for the occurrence of this “un-expected result” is provided in Section (7.6). Therefore we provide satisfactory answers to a number of “mysteries” of magnetism in astrophysics such as the “Magnetic Bode’s Relation/Law” [9] and the experimental finding that B-P graph in the log-log plot is linear. Moreover, we have developed a new method for studying the relations among the data (M, R, P) during stellar evolution. Ten groups of stellar objects, effectively over 2000 samples are used in various parts of the analysis. We also explain the emergence of huge magnetic field in very old stars like White Dwarfs in terms of formation of 2D Semion state on stellar surface and release of magnetic flux as magnetic storms upon changing the 2D state back to 3D structure. Moreover, we provide an explanation, on the ground of the 5D theory, for the detection of extremely weak fields in Venus and Mars and the asymmetric distribution of magnetic field on the Martian surface. We predict the equatorial fields B of the newly discovered Trappist-1 star and the 6 nearest planets. The log B?−?log P graph for the 6 planets is linear and they satisfy the Magnetic Bode’s relation. Based on the above analysis, we have discovered several new laws of stellar magnetism, which are summarized in Section (7.6).
基金Supported by Special Project for Reform of Non-profit Scientific Research Institution"Study on Whole Process Management of Agricultural Scientific and Technological Projects"
文摘This paper collected and arranged competitive scientific research projects undertaken by Tropical Crops Genetic Resources Institute of Chinese Academy of Tropical Agricultural Sciences in 2003-2014. Through statistical analysis on quantity of projects,funded amount,age of person responsible,professional title of person responsible,academic degree of person responsible,research object,it discussed relevant characteristics and rules. Finally,it came up with pertinent measures and recommendations,in the hope of providing services for decision-making and scientific and technological management.
文摘Water projects’ sediment deposition problems always cause widespread concerns. The gravity of them varies in accordance not only with reservoirs’ natural and socio-economic characteristics but also with their modes of operation. The unique characteristics, configuration and mode of operation of Three Gorges Project (TGP) reservoir are compared with those of several existing large reservoirs in this paper. As many reservoirs are troubling environment by gradually extending coarse sediment deposition at the uppermost end of fluctuating backwater region toward upstream, Gezhouba reservoir on Yangtze and Danjiangkou reservoir on Hanjiang have shown no trace of such upstream extension of sediment deposition in relevant prototype observation data for the past 20 and more years. TGP reservoir’s in-coming flow sediment conditions and configuration in plane are almost the same as those of Gezhouba reservoir, and TGP reservoir’s mode of operation(usually keeping a very low pool level for flood control in flood season and storing up in-coming flow only thenceafter) is similar to that of Danjiangkou reservoir. New findings of sediment research and prototype flow sediment investigations as well as new agenda of large hydro projects’ construction on Jinshajiang in nearest future assure the prospects of TGP sediment handling.
基金Project supported by the National Key Basic Research Program of China(Grant No.2012CB921704)the National Natural Science Foundation of China(Grant No.11374362)+1 种基金the Fundamental Research Funds for the Central Universitiesthe Research Funds of Renmin University of China(Grant No.15XNLQ03)
文摘Recently, we developed the projective truncation approximation for the equation of motion of two-time Green's functions(Fan et al., Phys. Rev. B 97, 165140(2018)). In that approximation, the precision of results depends on the selection of operator basis. Here, for three successively larger operator bases, we calculate the local static averages and the impurity density of states of the single-band Anderson impurity model. The results converge systematically towards those of numerical renormalization group as the basis size is enlarged. We also propose a quantitative gauge of the truncation error within this method and demonstrate its usefulness using the Hubbard-I basis. We thus confirm that the projective truncation approximation is a method of controllable precision for quantum many-body systems.
文摘We discuss the fact that there is a crucial contradiction within Von Neumann’s theory. We derive a proposition concerning a quantum expected value under an assumption of the existence of the orientation of reference frames in N spin-1/2 systems (1 ≤ N to a new constant . It may be said that a new type of the quantum theory early approaches Newton’s theory in the macroscopic scale than the old quantum theory does. We discuss how our solution is used in an implementation of Deutsch’s algorithm.