Exponential Sequence in the Operational Calculus Model for the nTH-Order Forward Difference

In the paper, there has been determined an exponential element in the discrete model of the non-classical Bittner operational calculus for the nth-order forward difference.

Unbiased Direct DGM(1,1) Model of Non-Homogeneous Exponential Sequence and its Application in Electric Load Forecasting

The traditional GM (1,1) has been used widely in the load forecasting, however, there are many defects in the GM (1,1). In order to overcome these defects and expand the application scope of the grey model in load forecasting, a new load forecasting method based on DDGM(1,1) is presented. First, the recursive solution of DDGM(1,1) is given. Then, based on the solution, the unbiased property for non-homogeneous exponential incremental sequence of this model is proved. It is applied to some load forecasting and is compared with the traditional GM (1,1) model.The results show that the presented forecasting method is superior obviously to traditional methods, and it can be used for the approximate non-homogeneous exponential incremental load forecasting generally.

The Large Sieve Inequality for the Exponential Sequence λ[O(n15/14+o(1))] Modulo Primes

Let ƛ be a fixed integer exceeding 1 and sn any strictly increasing sequence of positive integers satisfying sn ≤ n15/14+o(1). In this paper we give a version of the large sieve inequality for the sequence ƛsn. In particular, we obtain nontrivial estimates of the associated trigonometric sums “on average” and establish equidistribution properties of the numbers ƛsn, n ≤ p(log p)2+ϵ, modulo p for most primes p.

Extending the correlation structure of exponential autoregressive–moving-average processes

Some recent constructions for the generation of dependent sequences of identically distributed negative exponential random variables with specific correlation structures are generalized. This is achieved by attributing a correlation structure to the binary sequence which controls the generation of the exponentials. The procedure causes the autocorrelation function of the exponential sequence to copy that of the binary sequence and thus be extended to include negative values and other values beyond the usual range.