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The amendibility of a spin-0 and spin-1 particle with a combined potential in the presence of the Duffin-Kemmer-Petiau wave equation is highly recommendable. Thus, the approximate bound state of the Duffin-Kemmer-Petiauequation and Schrӧdinger equation were obtained with a combination of Hulthẻn and Yukawa potentials in theframework of asymptotic iteration method and parametric Nikiforov-Uvarov method respectively […]

Let (MN,g,e−fdv) be a complete smooth metric measure space with ∞-Bakry–Émery Riccitensor bounded from below. We derive elliptic gradient estimates for positive solutions of a weighted nonlinear parabolic equation (Δf−∂∂t)u(x, t)+q(x, t)uα(x, t)=0, where (x,t)∈MN×(−∞,∞) and α is an arbitrary constant. As Applications we prove a Liouville-type theorem for positive ancient solutions and Harnack-type inequalities […]

Let p,φbe the weighted p-Laplacian defined on a smooth metric measure space.We study the evolution and monotonicity formulas for the first eigenvalue,λ1=λ(p,φ), of p,φunder the Ricci-harmonic flow. We derive some monotonicquantities involving the first eigenvalue, and as a consequence, this shows that λ1ismonotonically nondecreasing and almost everywhere differentiable along the flowexistence https://eprints.lmu.edu.ng/id/eprint/2312