A modified Newton-Jarratt’s composition

Abstract  A reduced composition technique has been used on Newton and Jarratt’s methods in order to obtain an optimal relation between
convergence order, functional evaluations and number of operations. Following this aim, a family of methods is obtained whose
efficiency indices are proved to be better for systems of nonlinear equations.

• Content Type Journal Article
• Category Original Paper
• DOI 10.1007/s11075-009-9359-z
• Authors
  
  
  • Alicia Cordero, Universidad Politécnica de Valencia Instituto de Matemática Multidisciplinar Camino de Vera, s/n 46022 Valencia Spain
  • José L. Hueso, Universidad Politécnica de Valencia Instituto de Matemática Multidisciplinar Camino de Vera, s/n 46022 Valencia Spain
  • Eulalia Martínez, Universidad Politécnica de Valencia Instituto de Matemática Pura y Aplicada Camino de Vera, s/n 46022 Valencia Spain
  • Juan R. Torregrosa, Universidad Politécnica de Valencia Instituto de Matemática Multidisciplinar Camino de Vera, s/n 46022 Valencia Spain
  
  

• Journal Numerical Algorithms
• Online ISSN 1572-9265
• Print ISSN 1017-1398

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Original source : http://www.springerlink.com/content/16614pg2787650...

Greedy Drawings of Triangulations

Abstract  
Greedy Routing is a class of routing algorithms in which the packets are forwarded in a manner that reduces the distance to the destination
at every step. In an attempt to provide theoretical guarantees for a class of greedy routing algorithms, Papadimitriou and
Ratajczak (Theor. Comput. Sci. 344(1):3–14, 2005) came up with the following conjecture:

Any 3-connected planar graph can be drawn in the plane such that for every pair of vertices s and t a distance decreasing path can be found. A path s=v
₁,v
₂,…,v

_k
=t in a drawing is said to be distance decreasing if ‖v

_i
−t‖<‖v

_i−1−t‖,2≤i≤k where ‖…‖ denotes the Euclidean distance.

We settle this conjecture in the affirmative for the case of triangulations.

A partitioning of the edges of a triangulation G into 3 trees, called the realizer of G, was first developed by Schnyder who also gave a drawing algorithm based on this. We generalize Schnyder’s algorithm to obtain
a whole class of drawings of any given triangulation G. We show, using the Knaster–Kuratowski–Mazurkiewicz Theorem, that some drawing of G belonging to this class is greedy.

• Content Type Journal Article
• DOI 10.1007/s00454-009-9235-6
• Authors
  
  
  • Raghavan Dhandapani, New York University Courant Institute of Mathematical Sciences New York NY 10012 USA
  
  

• Journal Discrete and Computational Geometry
• Online ISSN 1432-0444
• Print ISSN 0179-5376

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Original source : http://www.springerlink.com/content/y71u68566g5623...

Nonspherical Noble Metal Nanoparticles: Colloid-Chemical Synthesis and Morphology Control

Metal nanoparticles have been the subject of widespread research over the past two decades. In recent years, noble metals have been the focus of numerous studies involving synthesis, characterization, and applications. Synthesis of an impressive range of noble metal nanoparticles with varied morphologies has been reported. Researchers have made a great progress in learning how to engineer materials on a nanometer length scale that has led to the understanding of the fundamental size- and shape-dependent properties of matter and to devising of new applications. In this article, we review the recent progress in the colloid-chemical synthesis of nonspherical nanoparticles of a few important noble metals (mainly Ag, Au, Pd, and Pt), highlighting the factors that influence the particle morphology and discussing the mechanisms behind the nonspherical shape evolution. The article attempts to present a thorough discussion of the basic principles as well as state-of-the-art morphology control in noble metal nanoparticles.

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Original source : http://dx.doi.org/10.1002%2Fadma.200901271...