Mathematical Methods I

ABS-Type Methods for Solving $m$ Linear Equations in $frac{m}{k}$ Steps for $k=1,2,cdots,m$

‎The ABS methods‎, ‎introduced by Abaffy‎, ‎Broyden and Spedicato‎, ‎are‎‎direct iteration methods for solving a linear system where the‎‎$i$-th iteration satisfies the first $i$ equations‎, ‎therefore a‎ ‎system of $m$ equations is solved in at most $m$ steps‎. ‎In this‎‎paper‎, ‎we introduce a class of ABS-type methods for solving a full row‎‎rank linear equations‎, ‎w...

Development of a Mathematical Model for Prediction of Pollutants Emission in D. I. Diesel Engines

Major pollutants emission from Direct-Injection (D.I) diesel engines are predicted by means of a mathematical model. In order to construct such a model, an integral Multi-Zone Combustion Model (MZCM) is formulated, which basically consists of jet mixing and combustion submodels. In MZCM, variation of injection pressure is considered. Also time period of ignition delay is predicted by considerin...

Some Properties of I-Closed Modules

An Example of Data Dependence Result for The Class of Almost Contraction Mappings

In the present paper, we show that $S^*$ iteration method can be used to approximate fixed point of almost contraction mappings. Furthermore, we prove that this iteration method is equivalent to CR iteration method  and it produces a slow convergence rate compared to the CR iteration method for the class of almost contraction mappings. We also present table and graphic to support this result. F...

Half-Century Journey from Synthetic Organic Chemistry to Mathematical Stereochemistry through Chemoinformatics

My half-century journey started from synthetic organic chemistry. During the first stage of my journey, my interest in stereochemistry was initiated through the investigation on the participation of steric effects in reactive intermediates, cylophanes, strained heterocycles, and organic compounds for photography. In chemoinformatics as the next stage of the journey, I proposed the concept of im...

‎Finite iterative methods for solving systems of linear matrix equations over reflexive and anti-reflexive matrices

A matrix $Pintextmd{C}^{ntimes n}$ is called a generalized reflection matrix if $P^{H}=P$ and $P^{2}=I$‎. ‎An $ntimes n$‎ ‎complex matrix $A$ is said to be a reflexive (anti-reflexive) matrix with respect to the generalized reflection matrix $P$ if $A=PAP$ ($A=-PAP$)‎. ‎In this paper‎, ‎we introduce two iterative methods for solving the pair of matrix equations $AXB=C$ and $DXE=F$ over reflexiv...