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Note on the Product Inequalities for Sequences of Multidimensional Integers
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作者 MA Li WANG Ru HAN Xin-fangi 《Chinese Quarterly Journal of Mathematics》 2020年第4期397-400,共4页
For multi-dimensional integer-valued sequence, a new proof of the upper-bound and lower-bound estimations on the product of all its components is given in this paper. Those estimations are very important to characteri... For multi-dimensional integer-valued sequence, a new proof of the upper-bound and lower-bound estimations on the product of all its components is given in this paper. Those estimations are very important to characterize the Kondratiev space of random test function, in which space it is convenient to study random distribution,random partial differential equation and other problems. 展开更多
关键词 Multidimensional integer value sequence Product inequality The upper-bound and lower-bound estimates
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A Comparative Analysis of the New -3(-n) - 1 Remer Conjecture and a Proof of the 3n + 1 Collatz Conjecture
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作者 Mike Remer 《Journal of Applied Mathematics and Physics》 2023年第8期2216-2220,共5页
This scientific paper is a comparative analysis of two mathematical conjectures. The newly proposed -3(-n) - 1 Remer conjecture and how it is related to and a proof of the more well known 3n + 1 Collatz conjecture. An... This scientific paper is a comparative analysis of two mathematical conjectures. The newly proposed -3(-n) - 1 Remer conjecture and how it is related to and a proof of the more well known 3n + 1 Collatz conjecture. An overview of both conjectures and their respective iterative processes will be presented. Showcasing their unique properties and behavior to each other. Through a detailed comparison, we highlight the similarities and differences between these two conjectures and discuss their significance in the field of mathematics. And how they prove each other to be true. 展开更多
关键词 -3(-n) - 1 Remer Conjecture 3n + 1 Collatz Conjecture Comparative Analysis PROOF Natural Numbers integer sequences Factorial Processes Par-tial Differential Equations Bounded Values Collatz Conjecture Collatz Algo-rithm Collatz Operator Collatz Compliance And Mathematical Conjectures
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Multi-period mine planning with multi-process routes 被引量:7
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作者 Mustafa Kumral 《International Journal of Mining Science and Technology》 SCIE EI 2013年第3期317-321,共5页
This paper attempts to optimize optimal capacities, block routing and mine sequencing problems in a mining system. The solution approach is based on a heuristics and the mixed integer programming (MIP). Unlike previou... This paper attempts to optimize optimal capacities, block routing and mine sequencing problems in a mining system. The solution approach is based on a heuristics and the mixed integer programming (MIP). Unlike previous sequential solution approaches, the problems are herein solved at the same time. Furthermore, the proposed approach guarantees practical solutions because it considers ore material distribution within orebody. The paper has two main contributions: (a) the proposed approach generates production rates in a manner that the capacities are satisfied; (b) the proposed approach does not use pre-defined marginal cut-off grades. Thus, idle capacity problem is eliminated and different scheduling combinations are allowed. To see the performance of the approach proposed, a case study is carried out using a gold data. The schedule generated shows that the approach can determine optimal production rates, block destination and sequencing effectively. 展开更多
关键词 Mine planning Multi-route Sequencing Production rates Heuristics Mixed integer programming
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