Asian Journal of Mathematical Sciences(AJMS)

SPECTRAL THEORY AND FUNCTIONAL CALCULI IN THE REFLEXIVE BANACH SPACES

Mykola Ivanovich Yaremenko — Sun, 15 Sep 2024 00:00:00 +0000

This article establishes the correspondence between the functional calculi for the operator defined on the
Banach spaces and the spectral decomposition. We show that there is a functional calculus on Borel
algebra for each well-bounded operator ABLX 
, which uniquely corresponds with a multiplication
operator on some  , ,  p L   
.

COEFFICIENT ESTIMATES FOR CERTAIN SUBCLASSES OF ANALYTIC AND BI-UNIVALENT FUNCTION ASSOCIA

Krisn Pratap Meena — Sun, 15 Sep 2024 00:00:00 +0000

Characterizing and estimating coefficients for subclasses of analytic and bi-univalent functions using
fractional derivative operators. In this paper, we propose two novel subclasses within the realm of
analytic and bi-univalent functions defined in the open unit disk U. By introducing these subclasses, we
derive estimates for the initial two Taylor-Maclaurin coefficients, specifically | | 2 a and
| | 3 a
, pertaining to
functions falling within these newly defined categories. This research paper sheds light on the behavior of
functions in these subclasses and contributes to the broader understanding of their analytic and geometric
properties.

PAGERANK-INSPIRED APPROACH FOR MODELING LONG-TERM BEHAVIOR IN STOCHASTIC GENE REGULATORY NETWORKS

Ebaifiyegha Ebimapogba Anthony — Sun, 15 Sep 2024 00:00:00 +0000

Gene regulatory network (GRN) play a crucial role in understanding the complex interac-tions between
genes and their regulatory elements. However, accurately modeling the long-term behavior of GRNs
under stochasticity remains a challenging task. In this study, we propose a methodology that leverages the
concept of PageRank, originally developed for ranking web pages, to analyze the long-term behavior of
GRNs. This approach involves constructing a directed graph representation of the GRN, where genes are
represented as nodes and regulatory interactions as directed edges. We then adapt the PageRank
algorithm to the GRN context, considering the stochastic nature of gene expression and incorporating the
inherent randomness in regulatory interactions. By iteratively computing the PageRank scores, we obtain
a ranking of the transition states based on their long-term influence within the network. To evaluate the
effectiveness of our approach, we apply it to synthetic GRN models. Our findings cap-tured essential
aspects of the long-term behavior in stochastic GRNs. We observe that genes with higher PageRank
scores tend to have a greater influence on the overall network dynamics and exhibit more stable and
persistent expression patterns

AN IMPROVED MULTI-DERIVATIVE HYBRID LINEAR MULTISTEP METHODS FOR DIRECT SOLUTION OF THIRDORDER ORDINARY DIFFERENTIAL EQUATIONS

T.V. Abejide — Sun, 15 Sep 2024 00:00:00 +0000

This article considered an improved multi-derivative Hybrid linear multistep methods (IMDHLMM) for
direct solution of third-order ordinary differential equations. Power series was used as the basis function
in the derivation of the method. An approximate solution from the basis function was interpolated at
some selected off-grid points while the third derivative of the approximate solution was collocated at all
grid and off-grid points to generate a system of linear equations for the determination of the unknown
parameters. The basic properties of the method such as order, consistency, zero stability, region of
absolute stability and convergence was tested. The method was implemented in block mode to solve third
order ordinary differential equations inlcuding Genesio equation to demonstrate the usability and
efficiency of the methods. The absolute error obtained in the numerical experiments showed a better
performance of the present method over some of the existing methods in the literature.