It is quite easy to stochastically distort an original count variable to obtain a new count variable with relatively more variability than in the original variable. Many popular overdispersion models (variance greater than mean) can indeed be obtained by mixtures, compounding or randomlystopped sums. There is no analogous stochastic mechanism for the construction of underdispersed count variables (variance less than mean), starting from an original count distribution of interest. This work proposes a generic method to stochastically distort an original count variable to obtain a new count variable with relatively less variability than in the original variable. The proposed mechanism, termed condensation, attracts probability masses from the quantiles in the tails of the original distribution and redirect them toward quantiles around the expected value. If the original distribution can be simulated, then the simulation of variates from a condensed distribution is straightforward. Moreover, condensed distributions have a simple mean-parametrization, a characteristic useful in a count regression context. An application to the negative binomial distribution resulted in a distribution allowing under, equi and overdispersion. In addition to graphical insights, fields of applications of special cases of condensed Poisson and condensed negative binomial distributions were pointed out as an indication of the potential of condensation for a flexible analysis of count data

As the largest energy consumer and carbon emitter, China has made substantial efforts to improve energy efficiency for decrease energy consumption, while the energy rebound effect determines its effectiveness. The embodied energy consumption of construction projects accounted for nearly one-sixth of the total economy's energy consumption in China. This paper is based on the logical relationship among capital input, technological progress, economic growth, and energy consumption, adapting an alternative estimation model to estimate the energy rebound effect for the construction industry in China for the first time. Empirical results in our paper reveal that the energy rebound effect for the construction industry in China is about 59.5% for the period of 1990–2014. The results indicate that the energy rebound effect does exist in China’s construction industry and it presented a fluctuating declining trend. This implies that half of the energy savings by technological progress is achieved. In addition, China’s government should implement proper energy pricing reforms and energy taxes to promote the sustainable development of China’s construction industry.

Multi-receiver encryption enables a sender to encrypt a message and transmit the ciphertext to a set of authorized users, while no one out this group of authorized users can decrypt the message. Multi-receiver encryption is of great importance in many sectors such as broadcast communication, cloud computing, wireless communications, networking applications, e-voting, lottery, and medical applications. This paper proposes an efficient multi-receiver public key encryption scheme based on Lucas sequences. The results of the computational analysis show that, projected scheme is better against renown attacks and prevailing anonymous multireceiver algorithms

In this paper, we study the asymptotic properties of slowly varying functions of one real variable in the sense of Karamata. We establish analogs of fundamental theorems on uniform convergence and integral representation for slowly varying functions with remainder depending on the types of remainder. We also prove several important theorems on the asymptotic representation of integrals of Karamata functions. Under certain conditions, we observe a “narrowing” of classes of slowly varying functions concerning the types of remainder. At the end of the paper, we discuss the possibilities of application of slowly varying functions in the theory of stochastic branching systems. In particular, under the condition of the finiteness of the moment of the type Exlnx for the particle transformation intensity, it is established that the property of slow variation with remainder is implicitly present in the asymptotic structure of a non-critical Markov branching random system.