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
The implementation of China's rural revitalization strategy will surely release a huge financial demand in rural areas.How to use the petty credit loan in rural financial institutions to develop rural economy is a...The implementation of China's rural revitalization strategy will surely release a huge financial demand in rural areas.How to use the petty credit loan in rural financial institutions to develop rural economy is an effective way to implement the rural revitalization strategy.This paper first analyzes the significance of petty credit loan in rural financial institutions for rural revitalization strategy,then introduces the remarkable contribution of petty credit loan in China's rural financial institutions to actively solving the problems of farmers about difficult financing and expensive financing and elaborates on the main problems of petty credit loan business in rural financial institutions that still exist in the process of supporting rural revitalization,and finally gives several suggestions on solving the problems about the financing of farmers and the development of petty credit loan business in rural financial institutions.展开更多
Petty maintenance projects cost lowly relative to other projects, project time limit is short. The characteristics such as form much shape also have particularity for its audit. This paper the existent actual conditio...Petty maintenance projects cost lowly relative to other projects, project time limit is short. The characteristics such as form much shape also have particularity for its audit. This paper the existent actual condition in scattered project settlement combination own working experience, put forward some methods for petty maintenance project audit.展开更多
Recently, Lutwak, Yang and Zhang posed the notion of Lp-projection body and established the Lp-analog of the Petty projection inequality. In this paper, the notion of Lp-mixed projection body is introduced--the Lp-pro...Recently, Lutwak, Yang and Zhang posed the notion of Lp-projection body and established the Lp-analog of the Petty projection inequality. In this paper, the notion of Lp-mixed projection body is introduced--the Lp-projection body being a special case. The Petty projection inequality, as well as Lutwak＇s quermassintegrals （Lp-mixed quermassintegrals） extension of the Petty projection inequality, is established for Lp-mixed projection body.展开更多
In this paper,the definition of the general L p-mixed projection bodies is introduced,and the general L p-projection bodies given by Ludwig is a special case for the general L p-mixed projection bodies.Then the Petty ...In this paper,the definition of the general L p-mixed projection bodies is introduced,and the general L p-projection bodies given by Ludwig is a special case for the general L p-mixed projection bodies.Then the Petty projection inequality for the general L p-mixed projection bodies is shown.Moreover,the monotonicity for the general L p-mixed projection bodies is obtained.展开更多
It is proved that if K is an origin-symmetric convex body in R^2 and Π^*K is the polar projection body of K,then the volumes of K and Π^*K satisfy the inequality V(K)V(Π^*K)≥2 with equality if K is a parallelogram.
Haruki Murakami is a serious belles-lettres writer with a title of petty bourgeois. With calm perspective, his writing points to the profound problems of human society, and also criticizes and analyses the history of ...Haruki Murakami is a serious belles-lettres writer with a title of petty bourgeois. With calm perspective, his writing points to the profound problems of human society, and also criticizes and analyses the history of World War II which is a closely guarded secret to most Japanese. The important topics of his literature are generally about the exposure of human nature under special time background, various deep problems accompanying with modern civilization, and the wounds brought to human by wars.展开更多
Reisner proved a reverse of the Blaschke-Santal5 inequality for zonoid bodies, Bourgain and Milman showed another reverse of the Blaschke-Santal5 inequality for centered convex bodies. In this paper, two reverses of t...Reisner proved a reverse of the Blaschke-Santal5 inequality for zonoid bodies, Bourgain and Milman showed another reverse of the Blaschke-Santal5 inequality for centered convex bodies. In this paper, two reverses of the Blaschke-Santal5 inequality for convex bodies are given by the Petty projection inequality and above two reverses. Further, using above methods, we also obtain two analogues of the Petty＇s conjecture for projection bodies, respectively.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The implementation of China's rural revitalization strategy will surely release a huge financial demand in rural areas.How to use the petty credit loan in rural financial institutions to develop rural economy is an effective way to implement the rural revitalization strategy.This paper first analyzes the significance of petty credit loan in rural financial institutions for rural revitalization strategy,then introduces the remarkable contribution of petty credit loan in China's rural financial institutions to actively solving the problems of farmers about difficult financing and expensive financing and elaborates on the main problems of petty credit loan business in rural financial institutions that still exist in the process of supporting rural revitalization,and finally gives several suggestions on solving the problems about the financing of farmers and the development of petty credit loan business in rural financial institutions.
文摘Petty maintenance projects cost lowly relative to other projects, project time limit is short. The characteristics such as form much shape also have particularity for its audit. This paper the existent actual condition in scattered project settlement combination own working experience, put forward some methods for petty maintenance project audit.
基金Research supported in part by the Natural Science Foundation of China(Grant No.10671117)Academic Mainstay Foundation of Hubei Province of China(Grant No.2003A005)
文摘Recently, Lutwak, Yang and Zhang posed the notion of Lp-projection body and established the Lp-analog of the Petty projection inequality. In this paper, the notion of Lp-mixed projection body is introduced--the Lp-projection body being a special case. The Petty projection inequality, as well as Lutwak＇s quermassintegrals （Lp-mixed quermassintegrals） extension of the Petty projection inequality, is established for Lp-mixed projection body.
文摘In this paper,the definition of the general L p-mixed projection bodies is introduced,and the general L p-projection bodies given by Ludwig is a special case for the general L p-mixed projection bodies.Then the Petty projection inequality for the general L p-mixed projection bodies is shown.Moreover,the monotonicity for the general L p-mixed projection bodies is obtained.
基金Supported by the Funds of the Basic and Advanced Research Project of CQCSTC(cstc2015jcyjA00009)Scientific and Technological Research Program of Chongqing Municipal Education Commission(KJ1500628)
文摘It is proved that if K is an origin-symmetric convex body in R^2 and Π^*K is the polar projection body of K,then the volumes of K and Π^*K satisfy the inequality V(K)V(Π^*K)≥2 with equality if K is a parallelogram.
文摘Haruki Murakami is a serious belles-lettres writer with a title of petty bourgeois. With calm perspective, his writing points to the profound problems of human society, and also criticizes and analyses the history of World War II which is a closely guarded secret to most Japanese. The important topics of his literature are generally about the exposure of human nature under special time background, various deep problems accompanying with modern civilization, and the wounds brought to human by wars.
基金Foundation item： Supported by the National Natural Science Foundation of China（10671117） Supported by the Innovation Foundation of Graduate Student of China Three Gorges University（2012CX077）
文摘Reisner proved a reverse of the Blaschke-Santal5 inequality for zonoid bodies, Bourgain and Milman showed another reverse of the Blaschke-Santal5 inequality for centered convex bodies. In this paper, two reverses of the Blaschke-Santal5 inequality for convex bodies are given by the Petty projection inequality and above two reverses. Further, using above methods, we also obtain two analogues of the Petty＇s conjecture for projection bodies, respectively.
