When each continuous operator is regular, II

How to Use MRP in Continuous Production Industries When Order Type is Lot for Lot

The Materials Requirements Planning (MRP) method that is applied in production planning and management has some weaknesses. One of its weaknesses is that the time in MRP method is discrete, and is considered as time period. Hence we are not able to order our requirements at irregular time moments or periods. In this paper, a new form of MRP is introduced that is named Continuous Materials Requi...

When is time continuous ? q

Continuous-time stochastic processes are approximations to physically realizable phenomena. We quantify one aspect of the approximation errors by characterizing the asymptotic distribution of the replication errors that arise from delta-hedging derivative securities in discrete time, and introducing the notion of temporal granularity which measures the extent to which discrete-time implementati...

Data mining when each data point is a network

We discuss the problem of extending data mining approaches to cases in which data points arise in the form of individual graphs. Being able to find the intrinsic low-dimensionality in ensembles of graphs can be useful in a variety of modeling contexts, especially when coarse-graining the detailed graph information is of interest. One of the main challenges in mining graph data is the definition...

When every $P$-flat ideal is flat

In this paper‎, ‎we study the class of rings in which every $P$-flat‎ ‎ideal is flat and which will be called $PFF$-rings‎. ‎In particular‎, ‎Von Neumann regular rings‎, ‎hereditary rings‎, ‎semi-hereditary ring‎, ‎PID and arithmetical rings are examples of $PFF$-rings‎. ‎In the context domain‎, ‎this notion coincide with‎ ‎Pr"{u}fer domain‎. ‎We provide necessary and sufficient conditions for‎...

Each Non - Zero Convolution Operator on the Entire Functions Admits a Continuous Linear Right Inverse