and Applied Analysis 3 Proof. Let α1, α2, . . . , αr be the base ofW and αr 1, . . . , αn ofU. If the constraints ofA onW are lIW and U is a k-complement space of A for W , then Aαi lαi, i 1, . . . , r and there exists a1j , . . . , arj making Aαj − kαj a1jα1 · · · arjαr , that is, Aαj a1jα1 · · · arjαr kαj , j r 1, . . . , n. So A α1, . . . , αr , αr 1, . . . , αn α1, . . . , αr , αr 1, . . . ...

Herbal products derived from Hemidesmus indicus (L.) R. Br. ex Schult, Leucas aspera (Wild.), Plumbago zeylanica L., and Tridax procumbens (L.) R. Br. ex Schult. are widely used in traditional medicine. Though the extracts of these plants were found to be antimicrobial in nature and have the potential to be used in clinics, the mechanism of action of is not reported. The ethanolic extracts of H...

Assume that G = (V, E) is an undirected graph with vertex set V and edge set E. The ball Br(v) denotes the vertices within graphical distance r from v. A subset C ⊆ V is called an (r,≤ l)-locating-dominating code of type B if the sets Ir(F ) = ⋃ v∈F (Br(v)∩C) are distinct for all subsets F ⊆ V \C with at most l vertices. A subset C ⊆ V is an (r,≤ l)-locatingdominating code of type A if sets Ir(...

The proton-nucleon cross section ratio R = Br(Υ → l+l−) · dσ(Υ)/dy|y=0 /σ(J/ψ) has been measured with the HERA-B spectrometer in fixed-target proton-nucleus collisions at 920 GeV proton beam energy corresponding to a proton-nucleon cms energy of √ s = 41.6 GeV. The combined results for the decay channels Υ → e+e− and Υ → μ+μ− yield a ratio R = (9.0±2.1) ·10−6 . The corresponding Υ production cr...

We analyse the dependence of the rates of the LFV charged lepton decays µ → e + γ, τ → e+γ, τ → µ+γ (l i → l j +γ) and their ratios, predicted in the class of SUSY theories with seesaw mechanism of ν-mass generation and soft SUSY breaking with universal boundary conditions at the GUT scale, on the Majorana CP-violation phases in the PMNS neutrino mixing matrix and the " leptogenesis " CP-violat...