The purpose of this paper is to present a general universal formula for <span style="font-family:Verdana;"><span style="font-family:Verdana;">k<span style="font-family:Verdana;&...The purpose of this paper is to present a general universal formula for <span style="font-family:Verdana;"><span style="font-family:Verdana;">k<span style="font-family:Verdana;"><span style="font-family:Verdana;">-variate survival functions for arbitrary <span style="font-family:Verdana;"><span style="font-family:Verdana;">k<span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> = 2, 3, <span style="font-family:;" "=""><span style="font-family:Verdana;">...<span style="font-family:Verdana;">, given all the univariate marginal survival functions. This universal form of <span style="font-family:Verdana;"><span style="font-family:Verdana;">k<span style="font-family:Verdana;"><span style="font-family:Verdana;">-variate probability distributions was obtained by means of “dependence functions” named “joiners” in the text. These joiners determine all the involved stochastic dependencies between the underlying random variables. However, in order that the presented formula (the form) represents a legitimate survival function, some necessary and sufficient conditions for the joiners had to be found. Basically, finding those conditions is the main task of this paper. This task was successfully performed for the case <span style="font-family:Verdana;"><span style="font-family:Verdana;">k<span style="font-family:Verdana;"><span style="font-family:Verdana;"> = 2 and the main results for the case <span style="font-family:Verdana;"><span style="font-family:Verdana;">k<span style="font-family:Verdana;"><span style="font-family:Verdana;"> = 3 were formulated as Theorem 1 and Theorem 2 in Section 4. Nevertheless, the hypothetical conditions valid for the general <span style="font-family:Verdana;"><span style="font-family:Verdana;">k<span style="font-family:Verdana;"><span style="font-family:Verdana;"> ≥ 4 case were also formulated in Section 3 as the (very convincing) Hypothesis. As for the sufficient conditions for both the <span style="font-family:Verdana;"><span style="font-family:Verdana;">k<span style="font-family:Verdana;"><span style="font-family:;" "=""><span style="font-family:Verdana;"> = 3 and <span style="font-family:Verdana;"><span style="font-family:Verdana;">k<span style="font-family:Verdana;"><span style="font-family:Verdana;"> ≥ 4 cases, the full generality was not achieved since two restrictions were imposed. Firstly, we limited ourselves to the, defined in the text, “continuous cases” (when the corresponding joint density exists and is continuous), and secondly we consider positive stochastic dependencies only. Nevertheless, the class of the <span style="font-family:Verdana;"><span style="font-family:Verdana;">k<span style="font-family:Verdana;"><span style="font-family:Verdana;">-variate distributions which can be constructed is very wide. The presented method of construction by means of joiners can be considered competitive to the <span style="font-family:Verdana;"><span style="font-family:Verdana;">copula<span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> methodology. As it is suggested in the paper the possibility of building a common theory of both copulae and joiners is quite possible, and the joiners may play the role of tools within the theory of copulae, and vice versa copulae may, for example, be used for finding proper joiners. Another independent feature of the joiners methodology is the possibility of constructing many new stochastic processes including stationary and Markovian.展开更多
Taking the greenway construction in Harbin City for example, this paper proposed the design method of integrating greenway and tourism resources, and used greenway to connect tourism resources.Moreover, the applicatio...Taking the greenway construction in Harbin City for example, this paper proposed the design method of integrating greenway and tourism resources, and used greenway to connect tourism resources.Moreover, the application of fusion design in greenway construction was explored from 3 perspectives,namely the fusion theory of tourism resource and greenway, fusion pattern, and fusion application,providing a new referential concept for the primary greenway construction in Harbin.展开更多
文摘The purpose of this paper is to present a general universal formula for <span style="font-family:Verdana;"><span style="font-family:Verdana;">k<span style="font-family:Verdana;"><span style="font-family:Verdana;">-variate survival functions for arbitrary <span style="font-family:Verdana;"><span style="font-family:Verdana;">k<span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> = 2, 3, <span style="font-family:;" "=""><span style="font-family:Verdana;">...<span style="font-family:Verdana;">, given all the univariate marginal survival functions. This universal form of <span style="font-family:Verdana;"><span style="font-family:Verdana;">k<span style="font-family:Verdana;"><span style="font-family:Verdana;">-variate probability distributions was obtained by means of “dependence functions” named “joiners” in the text. These joiners determine all the involved stochastic dependencies between the underlying random variables. However, in order that the presented formula (the form) represents a legitimate survival function, some necessary and sufficient conditions for the joiners had to be found. Basically, finding those conditions is the main task of this paper. This task was successfully performed for the case <span style="font-family:Verdana;"><span style="font-family:Verdana;">k<span style="font-family:Verdana;"><span style="font-family:Verdana;"> = 2 and the main results for the case <span style="font-family:Verdana;"><span style="font-family:Verdana;">k<span style="font-family:Verdana;"><span style="font-family:Verdana;"> = 3 were formulated as Theorem 1 and Theorem 2 in Section 4. Nevertheless, the hypothetical conditions valid for the general <span style="font-family:Verdana;"><span style="font-family:Verdana;">k<span style="font-family:Verdana;"><span style="font-family:Verdana;"> ≥ 4 case were also formulated in Section 3 as the (very convincing) Hypothesis. As for the sufficient conditions for both the <span style="font-family:Verdana;"><span style="font-family:Verdana;">k<span style="font-family:Verdana;"><span style="font-family:;" "=""><span style="font-family:Verdana;"> = 3 and <span style="font-family:Verdana;"><span style="font-family:Verdana;">k<span style="font-family:Verdana;"><span style="font-family:Verdana;"> ≥ 4 cases, the full generality was not achieved since two restrictions were imposed. Firstly, we limited ourselves to the, defined in the text, “continuous cases” (when the corresponding joint density exists and is continuous), and secondly we consider positive stochastic dependencies only. Nevertheless, the class of the <span style="font-family:Verdana;"><span style="font-family:Verdana;">k<span style="font-family:Verdana;"><span style="font-family:Verdana;">-variate distributions which can be constructed is very wide. The presented method of construction by means of joiners can be considered competitive to the <span style="font-family:Verdana;"><span style="font-family:Verdana;">copula<span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> methodology. As it is suggested in the paper the possibility of building a common theory of both copulae and joiners is quite possible, and the joiners may play the role of tools within the theory of copulae, and vice versa copulae may, for example, be used for finding proper joiners. Another independent feature of the joiners methodology is the possibility of constructing many new stochastic processes including stationary and Markovian.
文摘Taking the greenway construction in Harbin City for example, this paper proposed the design method of integrating greenway and tourism resources, and used greenway to connect tourism resources.Moreover, the application of fusion design in greenway construction was explored from 3 perspectives,namely the fusion theory of tourism resource and greenway, fusion pattern, and fusion application,providing a new referential concept for the primary greenway construction in Harbin.
