The matrix optics formalism is applied to show that a simple Gaussian equation enough relate object and image distances in an optical system consisting of arbitrary number thick lenses cascade immersed air. First, the case single lens was studied. Applying sequentially matrixes corresponding refraction displacement ray, imposing certain conditions on behavior bunch rays being refracted by lens,...

Root ofPlumbago indica Linn is used in ayurveda and siddha medicine for the treatment of colic inflammations bronchitis, helminthiasis, hemorrhoids, elephantiasis, hepatosplenomegaly, amenorrhea, odontalgia, piles, and diabetes. The present study aims to investigate the anatomical characters of thin and thick root and to confirm the physicochemical characters of the root. Anatomical st...

The purpose of this paper is to further the study of countably thick modules via weak injectivity. Among others, for some classes M of modules in σ[M ] we study when direct sums of modules from M satisfies a property P in σ[M ]. In particular, we get characterization of locally countably thick modules, a generalization of locally q.f.d. modules.