The energy E(G) of a graph G is equal to the sum of the absolute values of the eigenvalues of G. Several classes of graphs are known that satisfy the condition E(G) > n , where n is the number of vertices. We now show that the same property holds for (i) biregular graphs of degree a b , with q quadrangles, if q<= abn/4 and 5<=a < b = 0 (iii) triregular graphs of degree 1, a, b that are quadran...

in this paper, we represent an inexact inverse subspace iteration method for com- puting a few eigenpairs of the generalized eigenvalue problem ax = bx[q. ye and p. zhang, inexact inverse subspace iteration for generalized eigenvalue problems, linear algebra and its application, 434 (2011) 1697-1715 ]. in particular, the linear convergence property of the inverse subspace iteration is preserved.

Let Vn(q) be the n-dimensional vector space over the finite field with q elements and K a selected k-dimensional subspace of Vn(q). Let C[n, k, t] denote the set of all subspaces S’s such that dim(S ∩K) ≥ t. We show that C[n, k, t] has the normalized matching property, which yields that C[n, k, t] has the strong Sperner property and the LYM property.

We exhibit an example of a line bundle M on a smooth complex projective variety Y s.t. M satisfies Property Np for some p, the p-module of a minimal resolution of the ideal of the embedding of Y by M is nonzero and M does not satisfy Property Np. Let M be a very ample line bundle on a smooth complex projective variety Y and let φM : Y → P(H (Y,M)) be the map associated to M . We recall the defi...

and Applied Analysis 3 For 0 < q ≤ 1 we have t0D q t x t 1 Γ ( 1 − q d dt (∫ t t0 x s t − s q ds ) , ( 0 < q ≤ 1, c t0D q t x t 1 Γ ( 1 − q ∫ t t0 x′ s t − s q ds, ( 0 < q ≤ 1. 2.2 Some properties of Riemann-Liouville and Caputo derivatives are recalled below 1–3 . Property 1. When 0 < q ≤ 1, we have c t0D q t x t t0D q t x t − x t0 Γ ( 1 − q t − t0 −q. 2.3 In particular, if x t0 0, we have c t...