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ASSESSMENT OF SOIL HEAVY METAL DISTRIBUTION IN NALAIKH DISTRICT, ULAANBAATAR, MONGOLIA
(GMIT, 2022) Shinetsetseg Lkhagvasuren; Supervisor 1: Dr. Martin Knippertz; Supervisor 2: Prof. Dr. Gantuya Ganbat
This research aims to assess the distribution and contamination levels of heavy metals (As, Cd, Cr, Cu, Ni, Pb, and Zn) in the soil of Nalaikh District, Ulaanbaatar, Mongolia. Soil samples were collected from various locations, including mining sites, residential areas, and along roadsides, and analyzed using X-Ray Fluorescence (XRF) spectrometry. The findings indicate that the concentrations of certain heavy metals exceed the natural background levels. The environmental quality was evaluated using the Geo-accumulation Index ($I_{geo}$) and the Contamination Factor (CF). The results suggest that mining activities, coal extraction, and urbanization are the primary contributors to soil contamination in the region. This study provides essential data for environmental monitoring and the development of soil remediation strategies in Nalaikh District
ON GAP FUNCTIONS FOR QUASI-EQUILIBRIUM PROBLEMS VIA DUALITY
(Springer Nature, 2024-03-06) Lkhamsuren Altangerel
We extend gap functions to quasi-equilibrium problems by using the duality results. In particular, we obtain new results for quasi-equilibrium problems known earlier for equilibrium problems and mixed quasi-variational inequalities. Bibliography: 12 titles.
Gap functions for quasi-variational inequalities via duality
(Springer Nature, 2018-01-10) Altangerel, L.
This paper deals with an application of duality theory in optimization to the construction of gap functions for quasi-variational inequalities. The same approach was investigated for variational inequalities and equilibrium problems in (Pac. J.
Optim. 2(3): 667-678, 2006; Asia-Pac. J. Oper. Res. 24(3): 353-371, 2007), and the study shows that we can obtain some previous results for variational inequalities as special cases. Moreover, some applications dealing with the generalized Nash equilibrium problems and mixed variational inequalities are presented.
Dividends and Compound Poisson-processes: A new Stochastic Stock Price Model
(World Scientific, 2022-05-30) Battulga Gankhuu, Jacob Kleinow, Altangerel Lkhamsuren, Andreas Horsch
This study introduces a stochastic multi-period dividend discount model (DDM) that includes (i) a compound nonhomogenous Poisson process for dividend growth and (ii) the probability of firm default. We obtain maximum likelihood (ML) estimators and confidence interval formulas of our model parameters. We apply the model to a set of firms from the S&P 500 index using historical dividend and price data over a 42-year period. Interestingly, stock price estimations calculated with the model are close to the observable prices. Overall, we prove that the model can be a useful tool for stock pricing.
An Exact Penalty Approach and Conjugate Duality for Generalized Nash Equilibrium Problems with Coupling and Shared Constraints
(Иркутского государственного университета, 2020-09-11) Altangerel, L. & Battur, G.
Generalized Nash Equilibrium Problems (GNEP) have been attracted by many researchers in the field of game theory, operational research, engineering, economics as well as telecommunication in recent two decades. One of the most important classes of GNEP is a convex GNEP with jointly convex or shared constraints which has been studied extensively. It is considered to be one of the most challenging classes of problems in the field. Moreover, there is a gap in the studies on the GNEP with coupling and shared constraints. The aim of this paper is to investigate the relationship between an exact penalty approach and conjugate duality in convex optimization for the GNEP with coupling and shared constraints. In association with necessary optimality conditions, we obtained the parameterized variational inequality problems. This problem has provided an opportunity to solve many other GNEs. Some numerical results are also presented.