a f(x) dx (which one would use for instance to compute the work required to move a particle from a to b). For simplicity we shall restrict attention here to functions f : R → R which are continuous on the entire real line (and similarly, when we come to differential forms, we shall only discuss forms which are continuous on the entire domain). We shall also informally use terminology such as “i...

Perovskite-type oxides of LaFe(1+x)O(3+δ) (x = 0.0, 0.2, 0.5 and 0.7) were synthesized by citrate sol–gel methodto ensure the formation of nanosized perovskites. The physicochemical properties of these LaFe(1+x)O(3+δ)materials were characterized by thermal gravimetric/differential analyses, Fourier transform infraredspectroscopy, X-ray powder diffraction, scanning electron and...

An R-module M is called strongly noncosingular if it has no nonzero Rad-small (cosingular) homomorphic image in the sense of Harada. It is proven that (1) an R-module M is strongly noncosingular if and only if M is coatomic and noncosingular; (2) a right perfect ring R is Artinian hereditary serial if and only if the class of injective modules coincides with the class of (strongly) noncosingula...

In the present paper, we establish first relation between perturbation of upper Fredholm and strictly singular, then lower semi-Fredholm cosingular linear relations. Most importantly in Theorem 3.4, show that P(F?(X,Y)) coincides with SC(X,Y).We bring to light, relationship essential spectra a multivalued operator its selection

We study the spectral radius of connected non-regular graphs. Let λ1(n,Δ) be the maximum spectral radius among all connected non-regular graphs with n vertices and maximum degree Δ. We prove that Δ− λ1(n,Δ)=Θ(Δ/n). This improves two recent results by Stevanović and Zhang, respectively. © 2007 Elsevier Inc. All rights reserved.

We show the existence of Banach spaces X, Y such that the set of strictly singular operators ᏿(X,Y) (resp., the set of strictly cosingular operators Ꮿ᏿(X,Y)) would be strictly included in F + (X,Y) (resp., F − (X,Y)) for the nonempty class of closed densely defined upper semi-Fredholm operators Φ + (X,Y) (resp., for the nonempty class of closed densely defined lower semi-Fredholm operators Φ − ...