‎The aim of this paper is to establish the equivalence between the concepts‎ ‎of an $S$-metric space and a cone $S$-metric space using some topological‎ ‎approaches‎. ‎We introduce a new notion of a $TVS$-cone $S$-metric space using‎ ‎some facts about topological vector spaces‎. ‎We see that the known results on‎ ‎cone $S$-metric spaces (or $N$-cone metric spaces) can be directly obtained‎ from...

Ultimate limits of an open pit, which define its size and shape at the end of the mine’s life, is the pit with the highest profit value. A number of algorithms such as floating or moving cone method, floating cone method II and the corrected forms of this method, the Korobov algorithm and the corrected form of this method, dynamic programming and the Lerchs and Grossmann algorithm based on grap...

In this paper we give a geometric characterization of the cones of toric varieties that are complete intersections. In particular, we prove that the class of complete intersection cones is the smallest class of cones which is closed under direct sum and contains all simplex cones. Further, we show that the number of the extreme rays of such a cone, which is less than or equal to 2n − 2, is exac...

where / ^ 0, F is a proper subset of {1, 2, . . . , n) and the symbol 1_ is used for "exclusive or": i JL j £ V means i G V, j £ V or i (? V,j(z V. The metrics (2) are extreme rays of the metric cone and are called Hamming rays. The convex hull of these rays is called the Hamming cone Hn and we call d Hamming, if d Ç Hn. Such metrics are also called L-embeddable (e.g., [2]) or addressable (e.g....

With the advent and wide spread use of computers a number of algorithms have been developed to determine the optimum ultimate pit limits in open pit mining. The main objective of these algorithms is to find groups of blocks that should be removed to yield the maximum overall mining profit under specified economic conditions and technological constraints. The most common methods are: Lerchs and ...

In this paper we introduce the cone bounded linear mapping and demonstrate a proof to show that the cone norm is continuous. Among other things, we prove the open mapping theorem and the closed graph theorem in TVS-cone normed spaces. We also show that under some restrictions on the cone, two cone norms are equivalent if and only if the topologies induced by them are the same. In the sequel, we...

ultimate limits of an open pit, which define its size and shape at the end of the mine’s life, is the pit with the highest profit value. a number of algorithms such as floating or moving cone method, floating cone method ii and the corrected forms of this method, the korobov algorithm and the corrected form of this method, dynamic programming and the lerchs and grossmann algorithm based on grap...