in this paper we introduce the concept of weakly prime ternary subsemimodules of a ternary semimodule over a ternary semiring and obtain some characterizations of weakly prime ternary subsemimodules. we prove that if $n$ is a weakly prime subtractive ternary subsemimodule of a ternary $r$-semimodule $m$, then either $n$ is a prime ternary subsemimodule or $(n : m)(n : m)n = 0$. if $n$ is a $q$-...

In this paper we introduce the concept of weakly prime ternary subsemimodules of a ternary semimodule over a ternary semiring and obtain some characterizations of weakly prime ternary subsemimodules. We prove that if $N$ is a weakly prime subtractive ternary subsemimodule of a ternary $R$-semimodule $M$, then either $N$ is a prime ternary subsemimodule or $(N : M)(N : M)N = 0$. If $N$ is a $Q$-...

The partitioning behavior of W in a multicomponent Ni-based superalloy and in a ternary Ni–Al–W alloy is investigated using atom-probe tomography APT and first-principles calculations. APT observations indicate that whereas W partitions preferentially to the L12 -precipitates in the ternary alloy, its partitioning behavior is reversed in favor of the fcc -matrix in the multicomponent alloy. Fir...

We consider subsemimodules and convex subsets of semimodules over semirings with an idempotent addition. We introduce a nonlinear projection on subsemimodules: the projection of a point is the maximal approximation from below of the point in the subsemimodule. We use this projection to separate a point from a convex set. We also show that the projection minimizes the analogue of Hilbert’s proje...

We introduce several modifications of the partitioning schemes used in Hoare’s quicksort and quickselect algorithms, including ternary schemes which identify keys less or greater than the pivot. We give estimates for the numbers of swaps made by each scheme. Our computational experiments indicate that ternary schemes allow quickselect to identify all keys equal to the selected key at little add...

Uhlmann, J.K., Adaptive partitioning strategies for ternary tree structures, Pattern Recognition Letters 12 (1991) 537-541. Test results of three adaptive partition strategies for constructing multidimensional ternary trees are presented. Such trees can be used to efficiently identify correlated measurements with error bounds that can be represented as finite volumes.

Towards More Power Efficient IP Lookup Engines. (December 2005) Seraj Ahmad, Bachelor of Technology, Indian Institute of Technology, Guwahati, India Chair of Advisory Committee: Dr. Rabi N. Mahapatra The IP lookup in internet routers requires implementation of the longest prefix match algorithm. The software or hardware implementations of routing trie based approaches require several memory acc...

Let be a commutative semiring. A semimodule over semiring is fully prime if each proper subsemimodule of prime. This research aims to investigate the relationship between direct sum subsemimodules and , semimodule.