The Analytic Network Process (ANP) is a multicriteria theory of measurement used to derive relative priority scales of absolute numbers from individual judgments (or from actual measurements normalized to a relative f...The Analytic Network Process (ANP) is a multicriteria theory of measurement used to derive relative priority scales of absolute numbers from individual judgments (or from actual measurements normalized to a relative form) that also belong to a fundamental scale of absolute numbers. These judgments represent the relative influence, of one of two elements over the other in a pairwise comparison process on a third element in the system, with respect to an underlying control criterion. Through its supermatrix, whose entries are themselves matrices of column priorities, the ANP synthesizes the outcome of dependence and feedback within and between clusters of elements. The Analytic Hierarchy Process (AHP) with its independence assumptions on upper levels from lower levels and the independence of the elements in a level is a special case of the ANP. The ANP is an essential tool for articulating our understanding of a decision problem. One had to overcome the limitation of linear hierarchic structures and their mathematical consequences. This part on the ANP summarizes and illustrates the basic concepts of the ANP and shows how informed intuitive judgments can lead to real life answers that are matched by actual measurements in the real world (for example, relative dollar values) as illustrated in market share examples that rely on judgments and not on numerical data.展开更多
This is a survey on normal distributions and the related central limit theorem under sublinear expectation.We also present Brownian motion under sublinear expectations and the related stochastic calculus of It's t...This is a survey on normal distributions and the related central limit theorem under sublinear expectation.We also present Brownian motion under sublinear expectations and the related stochastic calculus of It's type.The results provide new and robust tools for the problem of probability model uncertainty arising in financial risk,statistics and other industrial problems.展开更多
Metasurfaces are artificially structured thin films with unusual properties on demand. Different from metamaterials, the metasurfaces change the electromagnetic waves mainly by exploiting the boundary conditions, rath...Metasurfaces are artificially structured thin films with unusual properties on demand. Different from metamaterials, the metasurfaces change the electromagnetic waves mainly by exploiting the boundary conditions, rather than the constitutive parameters in three dimensional(3D) spaces. Despite the intrinsic similarities in the operational principles, there is not a universal theory available for the understanding and design of metasurface-based devices. In this article, we propose the concept of metasurface waves(M-waves) and provide a general theory to describe the principles of them. Most importantly, it is shown that the M-waves share some fundamental properties such as extremely short wavelength, abrupt phase change and strong chromatic dispersion, which make them different from traditional bulk waves. It is shown that these properties can enable many important applications such as subwavelength imaging and lithography, planar optical devices, broadband anti-reflection, absorption and polarization conversion. Our results demonstrated unambiguously that traditional laws of diffraction, refraction, reflection and absorption should be revised by using the novel properties of M-waves. The theory provided here may pave the way for the design of new electromagnetic devices and further improvement of metasurfaces. The exotic properties of metasurfaces may also form the foundations for two new sub-disciplines called "subwavelength surface electromagnetics" and "subwavelength electromagnetics".展开更多
Kolmogorov's exponential inequalities are basic tools for studying the strong limit theorems such as the classical laws of the iterated logarithm for both independent and dependent random variables. This paper est...Kolmogorov's exponential inequalities are basic tools for studying the strong limit theorems such as the classical laws of the iterated logarithm for both independent and dependent random variables. This paper establishes the Kolmogorov type exponential inequalities of the partial sums of independent random variables as well as negatively dependent random variables under the sub-linear expectations. As applications of the exponential inequalities, the laws of the iterated logarithm in the sense of non-additive capacities are proved for independent or negatively dependent identically distributed random variables with finite second order moments.For deriving a lower bound of an exponential inequality, a central limit theorem is also proved under the sublinear expectation for random variables with only finite variances.展开更多
Distribution of vegetation is closely coupled with climate; the climate controls distribution of vegetation and the vegetation type reflects regional climates. To reveal vegetation_climate relationships is the foundat...Distribution of vegetation is closely coupled with climate; the climate controls distribution of vegetation and the vegetation type reflects regional climates. To reveal vegetation_climate relationships is the foundation for understanding the vegetation distribution and theoretically serving vegetation regionalization. Vegetation regionalization is a theoretical integration of vegetation studies and provides a base for physiogeographical regionalization as well as agriculture and forestry regionalization. Based on a brief historical overview on studies of vegetation_climate relationships and vegetation regionalization conducted in China, we review the principles, bases and major schemes of previous vegetation regionalization and discuss on several contentious boundaries of vegetation zones in the present paper. We proposed that, under the circumstances that the primary vegetation has been destroyed in most parts of China, the division of vegetation zones/regions should be based on the distribution of primary and its secondary vegetation types and climatic indices that delimit distribution of the vegetation types. This not only reveals the closed relationship between vegetation and climate, but also is feasible practically. Although there still are divergence of views on the name and their boundaries of the several vegetation zones, it is commonly accepted that there are eight major vegetation regions in China, i.e. cold temperate needleleaf forest region, temperate needleleaf and broadleaf mixed forest region, warm temperate deciduous broadleaf forest region, subtropical evergreen broadleaf forest region, tropical monsoon forest and rain forest region, temperate steppe region, temperate desert region, and Qinghai_Xizang (Tibetan) Plateau high_cold vegetation region. Analyzing characteristics of vegetation and climate of major vegetation boundaries, we suggested that: 1) Qinling Mountain_Huaihe River line is an important arid/humid climatic, but not a thermal climatic boundary, and thus can not also be regarde展开更多
The concept of truth degrees of formulas in Lukasiewicz n-valued propositional logic Ln is proposed. A limit theorem is obtained, which says that the truth function τ-n induced by truth degrees converges to the integ...The concept of truth degrees of formulas in Lukasiewicz n-valued propositional logic Ln is proposed. A limit theorem is obtained, which says that the truth function τ-n induced by truth degrees converges to the integrated truth function τ when n converges to infinite. Hence this limit theorem builds a bridge between the discrete valued Lukasiewicz logic and the continuous valued Lukasiewicz logic. Moreover, the results obtained in the present paper is a natural generalization of the corresponding results obtained in two-valued propositional logic.展开更多
文摘The Analytic Network Process (ANP) is a multicriteria theory of measurement used to derive relative priority scales of absolute numbers from individual judgments (or from actual measurements normalized to a relative form) that also belong to a fundamental scale of absolute numbers. These judgments represent the relative influence, of one of two elements over the other in a pairwise comparison process on a third element in the system, with respect to an underlying control criterion. Through its supermatrix, whose entries are themselves matrices of column priorities, the ANP synthesizes the outcome of dependence and feedback within and between clusters of elements. The Analytic Hierarchy Process (AHP) with its independence assumptions on upper levels from lower levels and the independence of the elements in a level is a special case of the ANP. The ANP is an essential tool for articulating our understanding of a decision problem. One had to overcome the limitation of linear hierarchic structures and their mathematical consequences. This part on the ANP summarizes and illustrates the basic concepts of the ANP and shows how informed intuitive judgments can lead to real life answers that are matched by actual measurements in the real world (for example, relative dollar values) as illustrated in market share examples that rely on judgments and not on numerical data.
基金supported by National Basic Research Program of China (Grant No.2007CB814900)(Financial Risk)
文摘This is a survey on normal distributions and the related central limit theorem under sublinear expectation.We also present Brownian motion under sublinear expectations and the related stochastic calculus of It's type.The results provide new and robust tools for the problem of probability model uncertainty arising in financial risk,statistics and other industrial problems.
基金supported by the National Program on Key Basic Research Project(Grant No.2013CBA01700)the National Natural Science Foundation of China(Grant No.61138002)
文摘Metasurfaces are artificially structured thin films with unusual properties on demand. Different from metamaterials, the metasurfaces change the electromagnetic waves mainly by exploiting the boundary conditions, rather than the constitutive parameters in three dimensional(3D) spaces. Despite the intrinsic similarities in the operational principles, there is not a universal theory available for the understanding and design of metasurface-based devices. In this article, we propose the concept of metasurface waves(M-waves) and provide a general theory to describe the principles of them. Most importantly, it is shown that the M-waves share some fundamental properties such as extremely short wavelength, abrupt phase change and strong chromatic dispersion, which make them different from traditional bulk waves. It is shown that these properties can enable many important applications such as subwavelength imaging and lithography, planar optical devices, broadband anti-reflection, absorption and polarization conversion. Our results demonstrated unambiguously that traditional laws of diffraction, refraction, reflection and absorption should be revised by using the novel properties of M-waves. The theory provided here may pave the way for the design of new electromagnetic devices and further improvement of metasurfaces. The exotic properties of metasurfaces may also form the foundations for two new sub-disciplines called "subwavelength surface electromagnetics" and "subwavelength electromagnetics".
基金supported by National Natural Science Foundation of China (Grant No. 11225104)the National Basic Research Program of China (Grant No. 2015CB352302)the Fundamental Research Funds for the Central Universities
文摘Kolmogorov's exponential inequalities are basic tools for studying the strong limit theorems such as the classical laws of the iterated logarithm for both independent and dependent random variables. This paper establishes the Kolmogorov type exponential inequalities of the partial sums of independent random variables as well as negatively dependent random variables under the sub-linear expectations. As applications of the exponential inequalities, the laws of the iterated logarithm in the sense of non-additive capacities are proved for independent or negatively dependent identically distributed random variables with finite second order moments.For deriving a lower bound of an exponential inequality, a central limit theorem is also proved under the sublinear expectation for random variables with only finite variances.
文摘Distribution of vegetation is closely coupled with climate; the climate controls distribution of vegetation and the vegetation type reflects regional climates. To reveal vegetation_climate relationships is the foundation for understanding the vegetation distribution and theoretically serving vegetation regionalization. Vegetation regionalization is a theoretical integration of vegetation studies and provides a base for physiogeographical regionalization as well as agriculture and forestry regionalization. Based on a brief historical overview on studies of vegetation_climate relationships and vegetation regionalization conducted in China, we review the principles, bases and major schemes of previous vegetation regionalization and discuss on several contentious boundaries of vegetation zones in the present paper. We proposed that, under the circumstances that the primary vegetation has been destroyed in most parts of China, the division of vegetation zones/regions should be based on the distribution of primary and its secondary vegetation types and climatic indices that delimit distribution of the vegetation types. This not only reveals the closed relationship between vegetation and climate, but also is feasible practically. Although there still are divergence of views on the name and their boundaries of the several vegetation zones, it is commonly accepted that there are eight major vegetation regions in China, i.e. cold temperate needleleaf forest region, temperate needleleaf and broadleaf mixed forest region, warm temperate deciduous broadleaf forest region, subtropical evergreen broadleaf forest region, tropical monsoon forest and rain forest region, temperate steppe region, temperate desert region, and Qinghai_Xizang (Tibetan) Plateau high_cold vegetation region. Analyzing characteristics of vegetation and climate of major vegetation boundaries, we suggested that: 1) Qinling Mountain_Huaihe River line is an important arid/humid climatic, but not a thermal climatic boundary, and thus can not also be regarde
基金This work was supported by the National Natural Science Foundation of China(Grant No．10331010)
文摘The concept of truth degrees of formulas in Lukasiewicz n-valued propositional logic Ln is proposed. A limit theorem is obtained, which says that the truth function τ-n induced by truth degrees converges to the integrated truth function τ when n converges to infinite. Hence this limit theorem builds a bridge between the discrete valued Lukasiewicz logic and the continuous valued Lukasiewicz logic. Moreover, the results obtained in the present paper is a natural generalization of the corresponding results obtained in two-valued propositional logic.
