inventory control is one of the most important issues in supply chain management. in this paper, a three-echelon production, distribution, inventory system composed of one producer, a set of wholesalers and retailers is considered. costumers' demands can be approximated by a normal distribution and the inventory policy is a kind of continuous review (r, q). in this paper, a model based on ...

A general analytical scheme for computing the n-fold convolution of exponentialsum distribution functions has been developed in this paper. The n-fold convolution is first expressed by multiple sums of recursive integrals. These recursive integrals are then reconstructed with a series of delta functions to avoid separations of integrations. Part of the recursive integrals has been solved analyt...

We reintroduce an interpretation of the kth-fold self convolution of the Catalan numbers by showing that they count the number of words in symbols X and Y , where the total number of Y ’s is k more than the total number of X’s, and at no time are there more Y ’s than k plus the number of X’s. Using this, we exhibit some of the wide variety of combinatorial interpretations of the kth-fold self c...

The effectiveness of convolutional neural networks stems in large part from their ability to exploit the translation invariance that is inherent in many learning problems. Recently, it was shown that CNNs can exploit other sources of invariance, such as rotation invariance, by using group convolutions instead of planar convolutions. However, for reasons of performance and ease of implementation...

this article presents a unified approach to the abstract notions of partial convolution and involution in $l^p$-function spaces over semi-direct product of locally compact groups. let $h$ and $k$ be locally compact groups and $tau:hto aut(k)$ be a continuous homomorphism.  let $g_tau=hltimes_tau k$ be the semi-direct product of $h$ and $k$ with respect to $tau$. we define left and right $tau$-c...