Generalized arcwise-connected functions and characterizations of local-global minimum properties

We introduce a new class of generalized arcwise connected functions and discuss their basic properties. Our generalization is illustrated by an example and an application is given for a mathematical programming problem involving this new class of functions.

Download Full-text

Properties of the beta coefficient of the global minimum variance portfolio

Mathematical Modeling and Computing ◽

10.23939/mmc2021.01.011 ◽

2020 ◽

Vol 8 (1) ◽

pp. 11-21

Author(s):

S. M. Yaroshko ◽

◽

M. V. Zabolotskyy ◽

T. M. Zabolotskyy ◽

◽

...

Keyword(s):

Confidence Interval ◽

Asymptotic Distribution ◽

Global Minimum ◽

Asset Returns ◽

Minimum Variance ◽

Benchmark Portfolio ◽

Beta Coefficient ◽

Minimum Variance Portfolio ◽

Global Minimum Variance Portfolio ◽

Daily Returns

The paper is devoted to the investigation of statistical properties of the sample estimator of the beta coefficient in the case when the weights of benchmark portfolio are constant and for the target portfolio, the global minimum variance portfolio is taken. We provide the asymptotic distribution of the sample estimator of the beta coefficient assuming that the asset returns are multivariate normally distributed. Based on the asymptotic distribution we construct the confidence interval for the beta coefficient. We use the daily returns on the assets included in the DAX index for the period from 01.01.2018 to 30.09.2019 to compare empirical and asymptotic means, variances and densities of the standardized estimator for the beta coefficient. We obtain that the bias of the sample estimator converges to zero very slowly for a large number of assets in the portfolio. We present the adjusted estimator of the beta coefficient for which convergence of the empirical variances to the asymptotic ones is not significantly slower than for a sample estimator but the bias of the adjusted estimator is significantly smaller.

Download Full-text

Researching nitrogen solubility in nitrogen-containing austenitic steels at melting and recrystallization by CALPHAD method

Voprosy Materialovedeniya ◽

10.22349/1994-6716-2018-96-4-53-66 ◽

2019 ◽

pp. 53-66 ◽

Cited By ~ 1

Author(s):

L. A. Smirnov ◽

I. I. Gorbachev ◽

V. V. Popov ◽

A. Yu. Pasynkov ◽

A. S. Oryshchenko ◽

...

Keyword(s):

Global Minimum ◽

Nitrogen Solubility ◽

Thermodynamic Description ◽

Solidus Temperature ◽

Liquidus Line ◽

Calphad Method ◽

Austenitic Steels ◽

Nitrogen Transfer ◽

Fixed Nitrogen ◽

System Phase

The CALPHAD method has been employed to compose thermodynamic description of the Fe–Cr–Mn–Ni–Si–C–N system. Using an algorithm based on finding a global minimum of Gibbs energy, the calculations of system phase composition were performed in the temperature range from 1750°C to hardening and in the range of compositions corresponding to 04Kh20N6G11M2AFB steel. Calculations showed that at temperatures above liquidus line, Cr and Mn increase nitrogen solubility in the melt, while Ni and Si reduce it. With an increase in the content of Cr, Mn, Ni, and Si in steel in the studied composition range, both liquidus and solidus temperature decrease. The degree of influence on these temperatures of Cr, Mn, Ni and Si within the steel grade is different and ranges from ~3 to ~14°C. Calculations taking into account the possibility of nitrogen transfer between steel and the atmosphere of air showed that the amount of fixed nitrogen in the alloy under study varies, depending on the composition of the steel and temperature, from ~0.3 to ~0.6 wt%. As the temperature decreases from liquidus to solidus, the amount of fixed nitrogen increases, with the exception of those steel compositions when ferrite and not austenite is released from the liquid phase.

Download Full-text