It is proved that the class of operator equations F(y) = f solvable by a DSM (dynamical systems method) Newton-type method, u̇ = −[F (u) + a(t)I]−1[Fu(t) + a(t)u − f ], u(0) = u0, (∗) is large. Here F : X → X is a continuously Fréchet differentiable operator in a Banach space X , a(t) : [0, ∞) → C is a function, limt→∞ |a(t)| = 0, and there exists a y ∈ X such that F(y) = f . Under weak assumpti...

For any time bound f , let H(f) denote the hierarchy conjecture which means that the restriction of the numbers of work tapes of deterministic Turing machines to b ∈ N generates an infinite hierarchy of proper subclasses DTIMEb(f) ⊂ DTIME(f). We show that H(f) implies separations of deterministic from nondeterministic time classes. H(f) follows from the gap property, G(f), which says that there...

Article history: Received 15 September 2010 Available online 22 November 2011 Communicated by F. Roli

The F-index of a graph G is the sum of the cubes of the degrees of the vertices of G. In this paper, explicit expressions for the F-index of different transformation graphs of type Gxyz with x, y, z ∈ {−,+} are obtained. F-index for semitotal point graph and semitotal line graph are also obtained here. MSC (2010): Primary: 05C35; Secondary: 05C07, 05C40

Due to the decreasing trend of rangelands, many native species are vulnerable and even at risk of extinction. Therefore, seed preservation and propagation of native species of rangelands and recognition of the characteristics of grazing, drought tolerance and their production potential are very beneficial. In this study, the five species of Festuca ovina, Festuca rubra, Br...

Given a graph G and a function f : V (G)→ {0,1,2, . . .}, a subset D of V (G) is called an f -dominating set of G if every vertex x outside D is adjacent to at least f (x) vertices in D. In this article we study a few graphical invariants relating to this concept. 2010 Mathematics Subject Classification: 05C69

On the basis of the construction of index system, by the factor analysis and the model of coupled coordination degree, the coupled coordination degrees in 2005 and 2010 between development of urban land intensive use system and social economic system are studied in 17 ground level cities of Shandong province. The first results showed that f(x) and f(y) in 2010 were higher than in 2005, which in...

NRC’s Portage system participated in the English-French (E-F) and French-English (F-E) translation tasks of the ACL WMT 2010 evaluation. The most notable improvement over earlier versions of Portage is an efficient implementation of lattice MERT. While Portage has typically performed well in Chinese to English MT evaluations, most recently in the NIST09 evaluation, our participation in WMT 2010...

The Retinex algorithm originally presented by Land and McCann uses random paths to explore the image. Throughout the decades, many versions of the Retinex algorithm have been proposed, mainly differing in the way they explore the image, with e.g. random paths, random samples, convolution masks, and variational formulations. In this paper, we propose a step back towards the origin, replacing ran...