In this work we study the deflection and gravitational lensing of null and timelike signals in the Kiselev spacetime in the weak field limit, to investigate the effects of the equation of state parameter $\omega$ and the matter amount parameter $\alpha$. In doing this, we extend a perturbative method previously developed for asymptotically flat spacetimes whose metric functions have integer-power asymptotic expansions to the case that may or may not be asymptotically flat but with non-integer power expansions. It is found that in the asymptotically flat case ($-1/3<\omega<0$) the deflection angles are expressable as quasi-power series of the dimensionless quantities $M/b,~b/r_{s,d}$ and $\alpha/M^{1+3\omega}$ where $M,~b,~r_{s,d}$ are respectively the lens mass, impact parameter and source/detector radius. A similar series exist for the non-asymptotically flat case of ($-1<\omega<-1/3$), but with the closest radius $r_0$ replacing $b$. In the asymptotically flat (or non-flat) case, the increase of $\alpha$ or decrease of $\omega$ will increase (or increase) the deflection angle. Since the obtained deflection angles naturally take into account the finite distance effect of the source and the detector, we can establish an exact gravitational lensing equation, from which the apparent angles of the images and their magnifications are solved. It is found that generally for asymptotically flat case, increasing $\alpha$ or decreasing $\omega$ will increase the apparent angles of the images. While for non-asymptotically flat case, increasing $\alpha$ or $\omega$ will both lead to smaller apparent angles.

This is the first of a series of papers that will introduce a user-friendly, detailed, and modular Galactic Chemical Evolution Model, GalCEM, that tracks isotope masses as a function of time in a given galaxy. The list of tracked isotopes automatically adapts to the complete set provided by the input yields. The present iteration of GalCEM tracks 86 elements broken down into 451 isotopes. The prescription includes massive stars, low-to-intermediate-mass stars, and Type Ia supernovae as enrichment channels. We have developed a preprocessing tool that extracts multidimensional interpolation curves from the input yield tables. These interpolation curves improve the computation speeds of the full convolution integrals, which are computed for each isotope and for each enrichment channel. We map the integrand quantities onto consistent array grids in order to perform the numerical integration at each time step. The differential equation is solved with a fourth-order Runge–Kutta method. We constrain our analysis to the evolution of all light and intermediate elements from carbon to zinc, and lithium. Our results are consistent up to the extremely metal-poor regime with Galactic abundances. We provide tools to track the mass rate change of individual isotopes on a typical spiral galaxy with a final baryonic mass of 5 × 1010 M ⊙. Future iterations of the work will extend to the full periodic table by including the enrichment from neutron-capture channels as well as spatially dependent treatments of galaxy properties. GalCEM is publicly available at https://github.com/egjergo/GalCEM.