The problem on the geometrc inequalities involving an n-dimensional simplex and its inscribed simplex is studied. An inequality is established, which reveals that the difference between the squared circumradius of the...The problem on the geometrc inequalities involving an n-dimensional simplex and its inscribed simplex is studied. An inequality is established, which reveals that the difference between the squared circumradius of the n-dimensional simplex and the squared distance between its circumcenter and barycenter times the squared circumradius of its inscribed simplex is not less than the 2(n-1)th power of n times its squared inradius, and is equal to when the simplex is regular and its inscribed siplex is a tangent point one. Deduction from this inequality reaches a generalization of n-dimensional Euler inequality indicating that the circumradius of the simplex is not less than the n-fold inradius. Another inequality is derived to present the relationship between the circumradius of the n-dimensional simplex and the circumradius and inradius of its pedal simplex.展开更多
Horizontal inscribed boards are the main form for working people to long for and pursue a better life,and are an important carrier of traditional culture. From the perspectives of sociology,architecture and ecological...Horizontal inscribed boards are the main form for working people to long for and pursue a better life,and are an important carrier of traditional culture. From the perspectives of sociology,architecture and ecological folklore,this article analyzes the intrinsic relationships between people’s values,neighborhoods,customs and horizontal inscribed boards,and interprets the decorative value,human value and modern value of horizontal inscribed boards through preliminarily studying the cultural connotation of horizontal inscribed boards in Jiuxia Village.展开更多
The volume of a cone is one third of the volume of a cylinder if they share same base and equal height. Let’s propose a hypothesis, if we expand the research area from cones to elliptical cones, could the maximum rat...The volume of a cone is one third of the volume of a cylinder if they share same base and equal height. Let’s propose a hypothesis, if we expand the research area from cones to elliptical cones, could the maximum ratio of volume beyond one third? This paper tries to pull away the veils of it. Firstly, we present four types of inscribed elliptical cones inside cylinders, and con-sequently all the other inscribed elliptical cones can be classified to these four types. Secondly, for each type of them, this paper discusses the corresponding volume ratio of the inscribed elliptical cone to the cylinder. It is concluded that the largest ratio of the volume of an inscribed cone to that of the cylinder is 1/3. Finally, two types whose ratio could reach 1/3 are given as examples.展开更多
As an important type of world heritage sites,cultural landscape has always been an important research subject.In order to explore the spatial distribution and evolution mode of cultural landscape all over the world,th...As an important type of world heritage sites,cultural landscape has always been an important research subject.In order to explore the spatial distribution and evolution mode of cultural landscape all over the world,the paper systematically elaborated the historical context of cultural landscape.The distribution characteristics were analyzed by statistical methods,and the connotation and evolution law represented by cultural landscape in different regions were expounded.The word frequency of regional heritage criteria was analyzed,and the local characteristics of each case were discussed.The research shows that the spatial distribution of global cultural landscape is unbalanced,mainly concentrated in Europe,and the spatial distribution characteristics are closely related to geographical environment,social history,economic development level and many other factors.In terms of inscribed criteria for world heritage sites,most cultural landscapes are mainly based on cultural criteria,but also involve natural criteria.The recognition and protection of cultural landscapes that simultaneously meet multiple criteria will become the focus in the future.展开更多
When we stare into our complex surroundings, we see objects of different shapes and sizes. However, the shape that is always present, regardless of the complexity of the object, is the circle. The circle is arguably t...When we stare into our complex surroundings, we see objects of different shapes and sizes. However, the shape that is always present, regardless of the complexity of the object, is the circle. The circle is arguably the most fascinating shape in the universe. A circle is defined as the set of all points equidistant from a given point, which, therefore, lies at the center of the circle. One of the various properties of circles is that it has infinite inscribed squares. This is because it is a continuous function, therefore if any point in the circle is transitioned by a specific factor, the other related points in the square would be shifted by the same factor. An ellipse is a similar shape with several inscribed squares. But does any closed curve have an inscribed square? This question was proposed by Otto Toeplitz in 1911 and to this day it is not answered. Another version of this problem is the inscribed rectangle problem which will be discussed in this paper.展开更多
We propose a high temperature-sensitive long period fiber grating（LPFG） sensor fabricated by using the femtosecond laser transversal-scanning method. The femtosecond pulses scan over the whole fiber core and some pa...We propose a high temperature-sensitive long period fiber grating（LPFG） sensor fabricated by using the femtosecond laser transversal-scanning method. The femtosecond pulses scan over the whole fiber core and some part of the cladding region; the modified regions are more extended. It is found that the LPFG-I fabricated by the transversal-scanning method shows higher temperature sensitivity and better temperature uniformity than that of LPFG-II written by the femtosecond laser point-by-point method. The LPFG-I with a temperature sensitivity of 75.96 pm/°C in the range of 25°C–400°C is measured. Moreover, in the range from 400°C to 800°C, a higher temperature sensitivity of 148.64 pm/°C and good linearity of 0.99 are achieved, while the temperature sensitivity of LPFG-II is only 95.55 pm/°C. LPFG-I exhibits better temperature characteristics, which, to the best of our knowledge, has the highest sensitivity in silica fiber temperature sensors.展开更多
We give a characterization of the boundaries of smooth strictly convex sets in the Euclidean plane R2?based on the existence and uniqueness of inscribed triangles.
Human rights are one of the widely acknowledged value systems in the international ,community. The core of human rights lies in the life and dignity of human beings. On the one hand, criminal procedure law is related ...Human rights are one of the widely acknowledged value systems in the international ,community. The core of human rights lies in the life and dignity of human beings. On the one hand, criminal procedure law is related to life and freedom, which is the concern of everybody. On the other hand, it involves direct dialogue between national power and citizens＇ fights.展开更多
Current guidelines for roundabout circulatory roadway width are based on a static method that does not consider circulatory speed. In addition, the roundabout entry width is based on practical experience. This paper p...Current guidelines for roundabout circulatory roadway width are based on a static method that does not consider circulatory speed. In addition, the roundabout entry width is based on practical experience. This paper presents a method for determining the circulatory and entry widths based on a two-dimensional vehicle dynamics model that involves a system of differential equations of curvilinear motion. The method considers the interactions between a vehicle and road geometric elements, including tire sideslip, vehicle weight, vehicle speed, and vehicle stability. Three design vehicles are considered： intermediate semitrailer （WB-12）, interstate semitrailer （WB-20）, and city transit bus （CITY-BUS）. Design guidelines for the required circulatory width are established for different circulatory speeds （0-60 krrgh） and different inscribed circle diameters （30-80 m）. To simplify the guidelines, for each design vehicle and for each inscribed circle diameter （ICD） the regression model of circulatory roadway width as a power function of circulatory speed was fitted. Guidelines for entry width were also established for typical conditions. The results show the efficiency of the proposed method which provides smaller values of circulatory roadway widths than those of current methods. The difference ranges from 0.4 to 0.6 m for CITY-BUS, 0.7-1.0 m for WB-12, and 1.3-2.0 m for WB-20. The proposed guidelines would be useful in case of spatial restrictions.展开更多
文摘The problem on the geometrc inequalities involving an n-dimensional simplex and its inscribed simplex is studied. An inequality is established, which reveals that the difference between the squared circumradius of the n-dimensional simplex and the squared distance between its circumcenter and barycenter times the squared circumradius of its inscribed simplex is not less than the 2(n-1)th power of n times its squared inradius, and is equal to when the simplex is regular and its inscribed siplex is a tangent point one. Deduction from this inequality reaches a generalization of n-dimensional Euler inequality indicating that the circumradius of the simplex is not less than the n-fold inradius. Another inequality is derived to present the relationship between the circumradius of the n-dimensional simplex and the circumradius and inradius of its pedal simplex.
基金Supported by National Natural Science Foundation of China(No.51768026)
文摘Horizontal inscribed boards are the main form for working people to long for and pursue a better life,and are an important carrier of traditional culture. From the perspectives of sociology,architecture and ecological folklore,this article analyzes the intrinsic relationships between people’s values,neighborhoods,customs and horizontal inscribed boards,and interprets the decorative value,human value and modern value of horizontal inscribed boards through preliminarily studying the cultural connotation of horizontal inscribed boards in Jiuxia Village.
文摘The volume of a cone is one third of the volume of a cylinder if they share same base and equal height. Let’s propose a hypothesis, if we expand the research area from cones to elliptical cones, could the maximum ratio of volume beyond one third? This paper tries to pull away the veils of it. Firstly, we present four types of inscribed elliptical cones inside cylinders, and con-sequently all the other inscribed elliptical cones can be classified to these four types. Secondly, for each type of them, this paper discusses the corresponding volume ratio of the inscribed elliptical cone to the cylinder. It is concluded that the largest ratio of the volume of an inscribed cone to that of the cylinder is 1/3. Finally, two types whose ratio could reach 1/3 are given as examples.
基金Sponsored by China Overseas Expertise Introduction Program for Discipline Innovation(D17016)Programme of State of Conservation of Wulingyuan World Natural Heritage Site(2022)。
文摘As an important type of world heritage sites,cultural landscape has always been an important research subject.In order to explore the spatial distribution and evolution mode of cultural landscape all over the world,the paper systematically elaborated the historical context of cultural landscape.The distribution characteristics were analyzed by statistical methods,and the connotation and evolution law represented by cultural landscape in different regions were expounded.The word frequency of regional heritage criteria was analyzed,and the local characteristics of each case were discussed.The research shows that the spatial distribution of global cultural landscape is unbalanced,mainly concentrated in Europe,and the spatial distribution characteristics are closely related to geographical environment,social history,economic development level and many other factors.In terms of inscribed criteria for world heritage sites,most cultural landscapes are mainly based on cultural criteria,but also involve natural criteria.The recognition and protection of cultural landscapes that simultaneously meet multiple criteria will become the focus in the future.
文摘When we stare into our complex surroundings, we see objects of different shapes and sizes. However, the shape that is always present, regardless of the complexity of the object, is the circle. The circle is arguably the most fascinating shape in the universe. A circle is defined as the set of all points equidistant from a given point, which, therefore, lies at the center of the circle. One of the various properties of circles is that it has infinite inscribed squares. This is because it is a continuous function, therefore if any point in the circle is transitioned by a specific factor, the other related points in the square would be shifted by the same factor. An ellipse is a similar shape with several inscribed squares. But does any closed curve have an inscribed square? This question was proposed by Otto Toeplitz in 1911 and to this day it is not answered. Another version of this problem is the inscribed rectangle problem which will be discussed in this paper.
基金supported by the National Natural Science Foundation of China(NSFC)(Nos.91323301,51505505,51475482,and 51475481)the Natural Science Foundation of Hunan Province(No.2016JJ3147)+2 种基金the China Postdoctoral Science Foundation(Nos.2015M572264 and 2016T90757)the Self-selected Topic Fund of State Key Laboratory of High Performance and Complex Manufacturing(No.ZZYJKT2015-08)the Fundamental Research Funds for the Central Universities of Central South University
文摘We propose a high temperature-sensitive long period fiber grating（LPFG） sensor fabricated by using the femtosecond laser transversal-scanning method. The femtosecond pulses scan over the whole fiber core and some part of the cladding region; the modified regions are more extended. It is found that the LPFG-I fabricated by the transversal-scanning method shows higher temperature sensitivity and better temperature uniformity than that of LPFG-II written by the femtosecond laser point-by-point method. The LPFG-I with a temperature sensitivity of 75.96 pm/°C in the range of 25°C–400°C is measured. Moreover, in the range from 400°C to 800°C, a higher temperature sensitivity of 148.64 pm/°C and good linearity of 0.99 are achieved, while the temperature sensitivity of LPFG-II is only 95.55 pm/°C. LPFG-I exhibits better temperature characteristics, which, to the best of our knowledge, has the highest sensitivity in silica fiber temperature sensors.
文摘We give a characterization of the boundaries of smooth strictly convex sets in the Euclidean plane R2?based on the existence and uniqueness of inscribed triangles.
文摘Human rights are one of the widely acknowledged value systems in the international ,community. The core of human rights lies in the life and dignity of human beings. On the one hand, criminal procedure law is related to life and freedom, which is the concern of everybody. On the other hand, it involves direct dialogue between national power and citizens＇ fights.
基金financial support of the Natural Sciences and Engineering Research Council of Canada (NSERC)
文摘Current guidelines for roundabout circulatory roadway width are based on a static method that does not consider circulatory speed. In addition, the roundabout entry width is based on practical experience. This paper presents a method for determining the circulatory and entry widths based on a two-dimensional vehicle dynamics model that involves a system of differential equations of curvilinear motion. The method considers the interactions between a vehicle and road geometric elements, including tire sideslip, vehicle weight, vehicle speed, and vehicle stability. Three design vehicles are considered： intermediate semitrailer （WB-12）, interstate semitrailer （WB-20）, and city transit bus （CITY-BUS）. Design guidelines for the required circulatory width are established for different circulatory speeds （0-60 krrgh） and different inscribed circle diameters （30-80 m）. To simplify the guidelines, for each design vehicle and for each inscribed circle diameter （ICD） the regression model of circulatory roadway width as a power function of circulatory speed was fitted. Guidelines for entry width were also established for typical conditions. The results show the efficiency of the proposed method which provides smaller values of circulatory roadway widths than those of current methods. The difference ranges from 0.4 to 0.6 m for CITY-BUS, 0.7-1.0 m for WB-12, and 1.3-2.0 m for WB-20. The proposed guidelines would be useful in case of spatial restrictions.
