Current Issue : January-March Volume : 2026 Issue Number : 1 Articles : 5 Articles
Assume that L is a simple Lie algebra of Cartan-type over an algebraically closed field with a characteristic p > 3. We demonstrate that all symmetric biderivations vanish by using weight space decompositions relative to a suitable torus and the standard Z-grading structures of L. We then conclude that every biderivation of L is inner, based on a general result concerning skew-symmetric biderivations. As the direct applications, we determine the linear commuting maps and commutative post-Lie algebra structures on L completely....
In this paper, we present Lie symmetry analysis of a generalized (1+1)-dimensional porous medium equation characterized by parameters m and d. Through group classification, we examine how these parameters influence the Lie symmetry structure of the equation. Our analysis establishes conditions under which the equation admits either a three-dimensional or a five-dimensional Lie algebra. Using the obtained symmetry algebras, we construct optimal systems of one-dimensional subalgebras. Subsequently, we derive invariant solutions corresponding to each subalgebra, providing explicit formulas in relevant parameter regimes. These solutions deepen our understanding of the nonlinear diffusion processes modeled by porous medium equations and offer valuable benchmarks for analytical and numerical studies....
This study presents a mathematical modelling approach to analyze the impact of family planning interventions on population growth dynamics. Using a compartmental model, the population is divided into six groups: Susceptible, Informed, Sexually Active Non-Users, Contraceptive Users, Non-Users and General Population. The model incorporates differential equations to describe transitions among these compartments, influenced by factors such as sexual behavior, contraceptive adoption, and public health education. Analytical techniques, including equilibrium analysis and the computation of the basic reproductive number were used to evaluate the model’s behavior and stability. Numerical simulations conducted in MATLAB revealed that increased contraceptive usage and awareness significantly reduce the number of high-risk individuals while stabilizing overall population growth. The reproductive number was shown to decrease as contraceptive uptake increased, confirming the effectiveness of intervention strategies. The findings highlight the importance of reproductive health education and contraceptive access in managing population growth, providing valuable insights for policymakers and public health planners. This study demonstrates the potential of mathematical modelling as a predictive and policy-support tool in reproductive health and demographic planning....
This work breaks a 180-year-old framework created by Hamilton both with regard to the use of imaginary quantities and the definition of a quaternion product. The general quaternionic algebraic structure we are considering was provided by the author in a previous work with a commutative product and will be provided here with a non-commutative product. We replace the imaginary units usually used in the theory of quaternions by linearly independent vectors and the usual Hamilton product rule by a Hamiltonian-adapted vector-valued vector product and prove both a new geometric property of this product and a vectorial adopted Euler type formula....
We investigate binary sequences generated by non-Markovian rules with memory length μ, similar to those adopted in elementary cellular automata. This generation procedure is equivalent to a shift register, and certain rules produce sequences with maximal periods, known as de Bruijn sequences. We introduce a novel methodology for generating de Bruijn sequences that combines (i) a set of derived properties that significantly reduce the space of feasible generating rules and (ii) a neural-network-based classifier that identifies which rules produce de Bruijn sequences. The experiments for some values of μ demonstrate the approach’s effectiveness and computational efficiency....
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