Research on the Industrial Energy Eco-Efficiency Evolution Characteristics of the Yangtze River Economic Belt in the Temporal and Spatial Dimension, China

Based on the panel data of the 11 provinces along the Yangtze River Economic Belt from 1997 to 2015, the super slack-based model (Super-SBM) model is adopted to calculate the provincial-level eco-efficiency of industrial energy. While bringing in time series analysis and spatial differentiation feature analysis, the traditional and spatial Markov probability transition matrix is established. This study delves into the spatial-temporal dynamic evolution traits of the eco-efficiency of industrial energy along the Yangtze River Economic Belt. According to the results: the eco-efficiency of industrial energy of the Yangtze River Economic Belt manifests “single crest” evolution and distribution traits from left to right and top to bottom, indicating that the eco-efficiency of industrial energy of the Yangtze River Economic Belt is steadily improving gradually. However, the overall level is still low and there is still ample room for the improvement of the eco-efficiency of industrial energy. Furthermore, the eco-efficiency of industrial energy along the Yangtze River Economic Belt is elevating. The geographical spatial pattern plays a pivotal role in the spatial and temporal evolution of eco-efficiency of industrial energy, and the spatial agglomeration traits are noticeable.

Studying the Global Bifurcation Involving Wada Boundary Metamorphosis by a Method of Generalized Cell Mapping with Sampling-Adaptive Interpolation

In this paper, a new method of Generalized Cell Mapping with Sampling-Adaptive Interpolation (GCMSAI) is presented in order to enhance the efficiency of the computation of one-step probability transition matrix of the Generalized Cell Mapping method (GCM). Integrations with one mapping step are replaced by sampling-adaptive interpolations of third order. An explicit formula of interpolation error is derived for a sampling-adaptive control to switch on integrations for the accuracy of computations with GCMSAI. By applying the proposed method to a two-dimensional forced damped pendulum system, global bifurcations are investigated with observations of boundary metamorphoses including full to partial and partial to partial as well as the birth of fully Wada boundary. Moreover GCMSAI requires a computational time of one thirtieth up to one fiftieth compared to that of the previous GCM.

MODEL STOKASTIK RANTAI MARKOV EMPAT STATUS PADA PENENTUAN NILAI HIDUP PELANGGAN

Customer Lifetime Value, familiar as CLV is valuability a customer in marketing system. High CLV has a meaning that the customer will bring in a big return for a firm. CLV is determined by some factors, as retention rate, acquisition rate, some costs, product price, and interest rates. Markov Chain is one of model that used to determine CLV. In Markov Chain, a customer is assumed some state. Transition inter states are assumed Markovian. Here, we make CLV model using Markov Chain with four states. There are four type of model that have four states. Each type have different transition chart and of course have different probability transition matrix. Here, we describe every type of CLV model using Markov Chain.

Random Walks in the Presence of Absorbing Barriers in Parrondo's Games

For a multi-agent spatial Parrondo's model that it is composed of games A and B, we use the discrete time Markov chains to derive the probability transition matrix. Then, we respectively deduce the stationary distribution for games A and B played individually and the randomized combination of game A + B. We notice that under a specific set of parameters, two absorbing states instead of a fixed stationary distribution exist in game B. However, the randomized game A + B can jump out of the absorbing states of game B and has a fixed stationary distribution because of the "agitating" role of game A. Moreover, starting at different initial states, we deduce the probabilities of absorption at the two absorbing barriers.

A Band and Bound Technique for Simple Random Algorithms

A simple random algorithm (SRA) is an algorithm whose behavior is governed by a first-order Markov chain. The expected time complexity of an SRA, given its initial state, is essentially the time to absorption of the underlying chain. The standard approach in computing the expected runtime is numerical. Under certain conditions on the probability transition matrix of an SRA, bounds on its expected runtime can be obtained using simple probabilistic arguments. In particular, one can obtain upper and lower (average time) logarithmic bounds for certain algorithms based on SRAs.