Let A be a finite multiset of integers. A second multiset of integers T is said to be an A-tiling of level d if every integer can be expressed in exactly d ways as the sum of an element of A and of an element of T . The set T is indecomposable if it cannot be written as the disjoint union of two proper subsets that are also A-tilings. In this paper we show how to construct indecomposable tiling...

the performance of a decision making unit (dmu) can be evaluated in either across-sectional or a time-series manner, and data envelopment analysis (dea) is a useful method for both types of evaluation. the malmquist productivity index (mpi) evaluates the change in efficiency of a dmu between two time periods. it is defined as the product of the catch-up and frontier-shift terms. in this paper, ...

drought as a natural but temporary imbalance of water availability is the interaction between natural environment and human life resulting in diminished water resources availability and reduced carrying capacity of the ecosystems. drought indices are essential elements for an efficient drought monitoring system. these indices make the transforming information of climatic anomalies easier and al...

rainfall is recognized as one of the main triggering factors of landslides. researchers have long attempted to determine the amount of precipitation required to trigger slope failures. one of the landslide zones in iran is chaharmahal & bakhtiari province where many landslides cause high casualties in recent decades. it is significant that most of these landslides occur after a rainy period...