Advanced Mathematical Models and Applications

Maintaining adequate capitalization is paramount for banks to ensure financial stability and regulatory compliance. This paper employs the Differential Transform Method (DTM) to solve a proposed dynamic model of bank capital adequacy, focusing on the relationship between a bank’s capital and its risk-weighted assets (RWAs). Three settings of RWAs growth, namely constant, linearly increasing, and exponentially increasing, are explored, with their respective parameter setups embedded. The effectiveness of the DTM is validated through comparisons of the obtained solutions with their corresponding exact solutions, demonstrating its ability to accurately simulate capital adequacy dynamics under varying RWAs growth patterns. The equilibrium analysis reveals that the steady-state level of capital adequacy is directly proportional to the bank’s assets, emphasizing the importance of asset growth for financial stability. Stability analysis indicates that a positive decay rate is crucial for resilience against perturbations. These findings underscore the application of mathematical modeling using DTM in aiding banks’ capital management strategies amidst evolving financial landscapes, ensuring they maintain adequate capital levels and respond effectively to economic shocks.

S.O. Edeki

Advanced mathematical models & applications.

MATHEMATICAL MODELING AND ANALYSIS OF BANK CAPITAL ADEQUACY DYNAMICS

银行资本充足率动态的数学建模与分析

This research displays nonlinear RLC circuit equation applying the fractional Adomian Decomposition Method (ADM) to investigate an approximate analytical solution. Where the fractional derivative described here as in the Caputo definition. The result behavior obtained by ADM is displayed graphically and numerically where it indicates a great consist compared with those obtained by other methods

Reem G. Thunibat

DEMONSTRATING NON-LINEAR RLC CIRCUIT EQUATION BY INVOLVING FRACTIONAL ADOMIAN DECOMPOSITION METHOD BY CAPUTO DEFINITION

通过Caputo定义的分形Adomian分解法演示非线性RLC电路方程

The paper presents analytical expressions for solving the problem of continuation of the electromagnetic field in the frequency domain for a horizontally layered medium. The numerical solution algorithm uses layerwise recalculation of the required quantities, for which analytical expressions are presented in a form that allows calculations and layerwise recalculation without the accumulation of rounding errors. The solution to the continuation problem is obtained as a solution to the cost functional minimization problem. The strong convexity of the functional is proven, which implies the existence of a unique solution to the problem posed. Before solving the continuation problem, it is proposed to apply the Butterworth filter to smooth the radargrams and the Hilbert transform technique to clarify the coordinates of the discontinuity points of the medium.

A.T. Kussainova

OPTIMIZATION APPROACH FOR SOLVING THE CONTINUATION PROBLEM IN FREQUENCY DOMAIN

频域中连续性问题的优化求解方法

The purpose of this work is to research the numerical results of the comparison of the synchronization speed of ring neural networks with unidirectional and bidirectional coupling. Each neuron is linearly coupled with the others and represented by a system of reaction-diffusion equations of the FitzHugh-Nagumo type. The result shows that the necessary coupling strength for the synchronization in two cases increases when the number of neurons increases. In other words, the greater the number of neurons in the ring networks is, the more difficult the synchronization occurs. Moreover, synchronizing the ring networks with bidirectional coupling is easier than the one with unidirectional coupling over the same given number of neurons.

Phan Van Long Em

COMPARISON OF SYNCHRONIZATION SPEED OF RING NETWORKS OF REACTION-DIFFUSION EQUATIONS OF FITZHUGH-NAGUMO TYPE WITH UNIDIRECTIONAL AND BIDIRECTIONAL COUPLING

反应-扩散方程Fitzhugh-Nagumo型环形网络在单向和双向耦合下的同步速度比较

This article provides a comprehensive analysis and proof of the Generalized Least Deviation Method (GLDM) in the context of time series forecasting, with a particular focus on optimal model order selection and the conditions that lead to zero coefficients. Central to this study is the GLDM Estimator, which determines the coefficients {aj} n(m) j=1 by minimizing the objective function F(a), defined as the sum of the arctangents of the absolute deviations from observed time series data {yt} T t=1 ⊂ R. The research not only proves GLDM’s ability to capture complex data interactions but also demonstrates its adaptability to varying model orders, showing that the selection of the optimal model order is influenced by the underlying characteristics of the data rather than just the data size. For example, temperature data with pronounced seasonal patterns and autocorrelations demands a fifth-order model, whereas wind speed and COVID-19 death cases in Russia are effectively modeled by a second-order structure. The study further examines the implications of higher-order models, advocating for a customized approach to model selection that enhances both predictive accuracy and interpretability in time series forecasting.

Publication Information	Publisher: Jomard Publishing，Publishing cycle: ，Journal Type: journal，Open Access Journals: No
Basic data	Year of publication: 2021，Proportion of original research papers: ，Self Citation Rate:， Gold OA Rate:

Advanced Mathematical Models and Applications

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MATHEMATICAL MODELING AND ANALYSIS OF BANK CAPITAL ADEQUACY DYNAMICS

DEMONSTRATING NON-LINEAR RLC CIRCUIT EQUATION BY INVOLVING FRACTIONAL ADOMIAN DECOMPOSITION METHOD BY CAPUTO DEFINITION

OPTIMIZATION APPROACH FOR SOLVING THE CONTINUATION PROBLEM IN FREQUENCY DOMAIN

COMPARISON OF SYNCHRONIZATION SPEED OF RING NETWORKS OF REACTION-DIFFUSION EQUATIONS OF FITZHUGH-NAGUMO TYPE WITH UNIDIRECTIONAL AND BIDIRECTIONAL COUPLING

PROVING OPTIMAL MODEL SELECTION AND ZERO COEFFICIENT CASES IN TIME SERIES FORECASTING WITH THE GENERALIZED LEAST DEVIATION ALGORITHM

MATHEMATICAL MODELING AND ANALYSIS OF BANK CAPITAL ADEQUACY DYNAMICS

DEMONSTRATING NON-LINEAR RLC CIRCUIT EQUATION BY INVOLVING FRACTIONAL ADOMIAN DECOMPOSITION METHOD BY CAPUTO DEFINITION

OPTIMIZATION APPROACH FOR SOLVING THE CONTINUATION PROBLEM IN FREQUENCY DOMAIN

COMPARISON OF SYNCHRONIZATION SPEED OF RING NETWORKS OF REACTION-DIFFUSION EQUATIONS OF FITZHUGH-NAGUMO TYPE WITH UNIDIRECTIONAL AND BIDIRECTIONAL COUPLING

PROVING OPTIMAL MODEL SELECTION AND ZERO COEFFICIENT CASES IN TIME SERIES FORECASTING WITH THE GENERALIZED LEAST DEVIATION ALGORITHM

ISSN	2519-4445
h-index	8