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Mathematics, Volume 6, Issue 8

August 2018 - 14 articles

Cover Story: To simultaneously address uncertainties in the rock mechanical properties and high computational requirements associated with the conventional model predictive control approach to calculating the control moves at each sampling time, we proposed an approximate dynamic programming-based approach for the closed-loop control of hydraulic fracturing to achieve the target proppant concentration at the end of pumping, which is directly related to the production rate of oil reservoirs. View this paper.
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Articles (14)

  • Article
  • Open Access
5 Citations
3,552 Views
10 Pages

30 July 2018

This paper considers resource allocation among producers (agents) in the case where the Principal knows nothing about their cost functions while the agents have Markovian awareness about his/her strategies. We use a dynamic setup of the stochastic in...

  • Article
  • Open Access
10 Citations
4,128 Views
14 Pages

Hypersurfaces with Generalized 1-Type Gauss Maps

  • Dae Won Yoon,
  • Dong-Soo Kim,
  • Young Ho Kim and
  • Jae Won Lee

26 July 2018

In this paper, we study submanifolds in a Euclidean space with a generalized 1-type Gauss map. The Gauss map, G, of a submanifold in the n-dimensional Euclidean space, En, is said to be of generalized 1-type if, for the Laplace operator, Δ, on...

  • Article
  • Open Access
33 Citations
8,348 Views
14 Pages

The Analytical Solution for the Black-Scholes Equation with Two Assets in the Liouville-Caputo Fractional Derivative Sense

  • Panumart Sawangtong,
  • Kamonchat Trachoo,
  • Wannika Sawangtong and
  • Benchawan Wiwattanapataphee

25 July 2018

It is well known that the Black-Scholes model is used to establish the behavior of the option pricing in the financial market. In this paper, we propose the modified version of Black-Scholes model with two assets based on the Liouville-Caputo fractio...

  • Article
  • Open Access
3 Citations
4,646 Views
13 Pages

24 July 2018

This paper deals with an infective process of type SIS, taking place in a closed population of moderate size that is inspected periodically. Our aim is to study the number of inspections that find the epidemic process still in progress. As the underl...

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Mathematics - ISSN 2227-7390