Consider the Teichmuller mapping f associated with in the unit disc D and the class of all quasiconformal mappings in D with the boundary values of f. For a special holomorphic function, the present paper gives the ne...Consider the Teichmuller mapping f associated with in the unit disc D and the class of all quasiconformal mappings in D with the boundary values of f. For a special holomorphic function, the present paper gives the necessary and sufficient condition on, such that f is uniquely extremal among the class. Further, for a general holomorphic function, the anthors suggest the models of the best possible growth conditions on, such that f is extremal or uniquely extremal among the class respectively.展开更多
Let (?)(z) be holomorphic in the unit disk △ and meromorphic on △. Suppose / is a Teichmuller mapping with complex dilatation In 1968, Sethares conjectured that f is extremal if and only if either (i)(?) has a doubl...Let (?)(z) be holomorphic in the unit disk △ and meromorphic on △. Suppose / is a Teichmuller mapping with complex dilatation In 1968, Sethares conjectured that f is extremal if and only if either (i)(?) has a double pole or (ii)(?) has no pole of order exceeding two on (?)△. The 'if' part of the conjecture had been solved by himself. We will give the affirmative answer to the 'only if' part of the conjecture. In addition, a more general criterion for extremality of quasiconformal mappings is constructed in this paper, which generalizes the 'if' part of Sethares' conjecture and improves the result by Reich and Shapiro in 1990.展开更多
In this paper shift ergodicity and related topics are studied for certain stationary processes. We first present a simple proof of the conclusion that every stationary Markov process is a generalized convex combinatio...In this paper shift ergodicity and related topics are studied for certain stationary processes. We first present a simple proof of the conclusion that every stationary Markov process is a generalized convex combination of stationary ergodic Markov processes. A direct consequence is that a stationary distribution of a Markov process is extremal if and only if the corresponding stationary Markov process is time ergodic and every stationary distribution is a generalized convex combination of such extremal ones. We then consider space ergodicity for spin flip particle systems. We prove space shift ergodicity and mixing for certain extremal invariant measures for a class of spin systems, in which most of the typical models, such as the Voter Models and the Contact Models, are included. As a consequence of these results we see that for such systems, under each of those extremal invariant measures, the space and time means of an observable coincide, an important phenomenon in statistical physics. Our results provide partial answers to certain interesting problems in spin systems.展开更多
Given a compact Riemann surface S with finitely many punctures, in this paper we obtain a new extremality property of a Jenkins-Strebel differentialψon S. As a consequence, we obtain the solutions of several kinds of...Given a compact Riemann surface S with finitely many punctures, in this paper we obtain a new extremality property of a Jenkins-Strebel differentialψon S. As a consequence, we obtain the solutions of several kinds of moduli problems on 5.展开更多
It is proved that if f is a Teichmuller self-mapping of the unit disk with a holomorphic quadratic deferential and satisfies the growth condition m(ψ，r)= o((1 -r)-), r→1, for any s>1, then f is extremal, and the...It is proved that if f is a Teichmuller self-mapping of the unit disk with a holomorphic quadratic deferential and satisfies the growth condition m(ψ，r)= o((1 -r)-), r→1, for any s>1, then f is extremal, and there exists a sequence {tn}, 0<tn<1, /lim, tn =1, such that {(tnz)} is a Hamilton sequence. It is the precision of a theorem of Reich-Strebel in 1974, and gives a fairly satisfactory answer to a question of Reich in 1988.展开更多
An increase in the extremality of natural processes is a consequence of warming, aridization, and desertification. The authors consider the processes of warming, aridization, and desertification to be the parts of a s...An increase in the extremality of natural processes is a consequence of warming, aridization, and desertification. The authors consider the processes of warming, aridization, and desertification to be the parts of a single system and major destabilizing factors of ecological balance. Destabilization is expressed in the growth of natural processes extremality. Ecosystems of Transbaikalia were once characterized by a different natural contrast and amplitude. Warming, aridization and desertification have led to an increase of environmental regimes tensions. This is demonstrated quantitatively by the root-mean-square difference of atmospheric and soil parameters. Quantitative indicators of aridization are estimated using Walter-Gossen climate charts. Permafrost zone response information to the long-term warming is provided as well.展开更多
A universal relation between the leading correction to the entropy and extremality was proposed in the work of Goon and Penco.In this paper,we extend this work to massive gravity and investigate thermodynamic extremal...A universal relation between the leading correction to the entropy and extremality was proposed in the work of Goon and Penco.In this paper,we extend this work to massive gravity and investigate thermodynamic extremality relations in a topologically higher-dimensional black hole.A rescaled cosmological constant is added to the action of the massive gravity as a perturbative correction.This correction modifies the extremality bound of the black hole and leads to shifts in the mass,entropy,etc.Regarding the cosmological constant as a variable related to pressure,we obtain the thermodynamic extremality relations between the mass and entropy,pressure,charge,and parameters ci by accurate calculations.Finally,these relations are verified by a triple product identity,which shows that the universal relation exists in black holes.展开更多
Changes of extreme events due to greenhouse effects (2 × CO<SUB>2</SUB>) over East Asia, with a focus on the China region as simulated by a regional climate model (RegCM2), are investigated. The model...Changes of extreme events due to greenhouse effects (2 × CO<SUB>2</SUB>) over East Asia, with a focus on the China region as simulated by a regional climate model (RegCM2), are investigated. The model is nested to a global coupled ocean-atmosphere model (CSIRO R21L9 AOGCM). Analysis of the control run of the regional model indicates that it can reproduce well the extreme events in China. Statistically significant changes of the events are analyzed. Results show that both daily maximum and daily minimum temperature increase in 2 × CO<SUB>2</SUB> conditions, while the diurnal temperature range decreases. The number of hot spell days increases while the number of cold spell days decreases. The number of rainy days and heavy rain days increases over some sub-regions of China. The 2 × CO<SUB>2</SUB> conditions also cause some changes in the tropical storms affecting China.展开更多
Based on hourly precipitation data in eastern China in the warm season during 1961-2000,spatial distributions of frequency for 20 mm h 1 and 50 mm h 1 precipitation were analyzed,and the criteria of short-duration rai...Based on hourly precipitation data in eastern China in the warm season during 1961-2000,spatial distributions of frequency for 20 mm h 1 and 50 mm h 1 precipitation were analyzed,and the criteria of short-duration rainfall events and severe rainfall events are discussed.Furthermore,the percentile method was used to define local hourly extreme precipitation;based on this,diurnal variations and trends in extreme precipitation were further studied.The results of this study show that,over Yunnan,South China,North China,and Northeast China,the most frequent extreme precipitation events occur most frequently in late afternoon and/or early evening.In the Guizhou Plateau and the Sichuan Basin,the maximum frequency of extreme precipitation events occurs in the late night and/or early morning.And in the western Sichuan Plateau,the maximum frequency occurs in the middle of the night.The frequency of extreme precipitation （based on hourly rainfall measurements） has increased in most parts of eastern China,especially in Northeast China and the middle and lower reaches of the Yangtze River,but precipitation has decreased significantly in North China in the past 50 years.In addition,stations in the Guizhou Plateau and the middle and lower reaches of the Yangtze River exhibit significant increasing trends in hourly precipitation extremes during the nighttime more than during the daytime.展开更多
文摘Consider the Teichmuller mapping f associated with in the unit disc D and the class of all quasiconformal mappings in D with the boundary values of f. For a special holomorphic function, the present paper gives the necessary and sufficient condition on, such that f is uniquely extremal among the class. Further, for a general holomorphic function, the anthors suggest the models of the best possible growth conditions on, such that f is extremal or uniquely extremal among the class respectively.
文摘Let (?)(z) be holomorphic in the unit disk △ and meromorphic on △. Suppose / is a Teichmuller mapping with complex dilatation In 1968, Sethares conjectured that f is extremal if and only if either (i)(?) has a double pole or (ii)(?) has no pole of order exceeding two on (?)△. The 'if' part of the conjecture had been solved by himself. We will give the affirmative answer to the 'only if' part of the conjecture. In addition, a more general criterion for extremality of quasiconformal mappings is constructed in this paper, which generalizes the 'if' part of Sethares' conjecture and improves the result by Reich and Shapiro in 1990.
基金the National Natural Science Foundation of China (Grant No. 10071008).
文摘In this paper shift ergodicity and related topics are studied for certain stationary processes. We first present a simple proof of the conclusion that every stationary Markov process is a generalized convex combination of stationary ergodic Markov processes. A direct consequence is that a stationary distribution of a Markov process is extremal if and only if the corresponding stationary Markov process is time ergodic and every stationary distribution is a generalized convex combination of such extremal ones. We then consider space ergodicity for spin flip particle systems. We prove space shift ergodicity and mixing for certain extremal invariant measures for a class of spin systems, in which most of the typical models, such as the Voter Models and the Contact Models, are included. As a consequence of these results we see that for such systems, under each of those extremal invariant measures, the space and time means of an observable coincide, an important phenomenon in statistical physics. Our results provide partial answers to certain interesting problems in spin systems.
基金This work was partially supported by the National Natural Science Foundation of China (Grant No. 10501046).
文摘Given a compact Riemann surface S with finitely many punctures, in this paper we obtain a new extremality property of a Jenkins-Strebel differentialψon S. As a consequence, we obtain the solutions of several kinds of moduli problems on 5.
基金the National Natural Science Foundation of China!(No.19531060), the DoctoralProgram Fundation of the Ministry of Education o
文摘It is proved that if f is a Teichmuller self-mapping of the unit disk with a holomorphic quadratic deferential and satisfies the growth condition m(ψ，r)= o((1 -r)-), r→1, for any s>1, then f is extremal, and there exists a sequence {tn}, 0<tn<1, /lim, tn =1, such that {(tnz)} is a Hamilton sequence. It is the precision of a theorem of Reich-Strebel in 1974, and gives a fairly satisfactory answer to a question of Reich in 1988.
基金partially supported by the Russian Geographical Society(grant No.13-05-41378)
文摘An increase in the extremality of natural processes is a consequence of warming, aridization, and desertification. The authors consider the processes of warming, aridization, and desertification to be the parts of a single system and major destabilizing factors of ecological balance. Destabilization is expressed in the growth of natural processes extremality. Ecosystems of Transbaikalia were once characterized by a different natural contrast and amplitude. Warming, aridization and desertification have led to an increase of environmental regimes tensions. This is demonstrated quantitatively by the root-mean-square difference of atmospheric and soil parameters. Quantitative indicators of aridization are estimated using Walter-Gossen climate charts. Permafrost zone response information to the long-term warming is provided as well.
基金Supported by NSF C(11875196,11375121,11205125,11005016)Xihua University Talent Project(Z201021)。
文摘A universal relation between the leading correction to the entropy and extremality was proposed in the work of Goon and Penco.In this paper,we extend this work to massive gravity and investigate thermodynamic extremality relations in a topologically higher-dimensional black hole.A rescaled cosmological constant is added to the action of the massive gravity as a perturbative correction.This correction modifies the extremality bound of the black hole and leads to shifts in the mass,entropy,etc.Regarding the cosmological constant as a variable related to pressure,we obtain the thermodynamic extremality relations between the mass and entropy,pressure,charge,and parameters ci by accurate calculations.Finally,these relations are verified by a triple product identity,which shows that the universal relation exists in black holes.
基金Thanks are due to CSIRO in Australia and the Institute of Botany,Chinese Academy of Sciences,National Climate Center of China , for providing the data sets of the GCM and the vegetation coverThis research was supported by the National Natural Science Foundation of China under Grant No, 40125014National Key Programme for Developing Basic Sciences (G1998040900-part 1).
文摘Changes of extreme events due to greenhouse effects (2 × CO<SUB>2</SUB>) over East Asia, with a focus on the China region as simulated by a regional climate model (RegCM2), are investigated. The model is nested to a global coupled ocean-atmosphere model (CSIRO R21L9 AOGCM). Analysis of the control run of the regional model indicates that it can reproduce well the extreme events in China. Statistically significant changes of the events are analyzed. Results show that both daily maximum and daily minimum temperature increase in 2 × CO<SUB>2</SUB> conditions, while the diurnal temperature range decreases. The number of hot spell days increases while the number of cold spell days decreases. The number of rainy days and heavy rain days increases over some sub-regions of China. The 2 × CO<SUB>2</SUB> conditions also cause some changes in the tropical storms affecting China.
基金supported by the R & D Special Fund for Public Welfare Industry (meteorology)(GYHY201106018)National Key Program for Developing Basic Sciences (Grant No. 2006CB400503)
文摘Based on hourly precipitation data in eastern China in the warm season during 1961-2000,spatial distributions of frequency for 20 mm h 1 and 50 mm h 1 precipitation were analyzed,and the criteria of short-duration rainfall events and severe rainfall events are discussed.Furthermore,the percentile method was used to define local hourly extreme precipitation;based on this,diurnal variations and trends in extreme precipitation were further studied.The results of this study show that,over Yunnan,South China,North China,and Northeast China,the most frequent extreme precipitation events occur most frequently in late afternoon and/or early evening.In the Guizhou Plateau and the Sichuan Basin,the maximum frequency of extreme precipitation events occurs in the late night and/or early morning.And in the western Sichuan Plateau,the maximum frequency occurs in the middle of the night.The frequency of extreme precipitation （based on hourly rainfall measurements） has increased in most parts of eastern China,especially in Northeast China and the middle and lower reaches of the Yangtze River,but precipitation has decreased significantly in North China in the past 50 years.In addition,stations in the Guizhou Plateau and the middle and lower reaches of the Yangtze River exhibit significant increasing trends in hourly precipitation extremes during the nighttime more than during the daytime.
