Search results for "Expansive"

Isomorphically expansive mappings in $l_2$

1997

Experimental study of a naturally weathered stiff clay

2016

Studying the shear strength of a naturally weathered clay is important to understand rain-induced slope failures in weathered soils. However, experimental studies on naturally weathered soils are limited. The paper focuses on the laboratory experimental investigation carried out to analyse the shear strength of a naturally weathered stiff clay that can be found in unsaturated conditions in situ. This has an important practical relevance in the evaluation of the stability conditions of natural slopes at clay outcrops. Different experimental techniques of suction measurement were used to obtain the soil-water retention curve of the clay over a wide range of suctions. Scanning electronic micr…

Fixed point theory for a class of generalized nonexpansive mappings

2011

AbstractIn this paper we introduce two new classes of generalized nonexpansive mapping and we study both the existence of fixed points and their asymptotic behavior.

On approximating curves associated with nonexpansive mappings

2011

Let X be a Banach space with metric d. Let T, N : X → X be a strict d-contraction and a d-nonexpansive map, respectively. In this paper we investigate the properties of the approximating curve associated with T and N. Moreover, following [3], we consider the approximating curve associated with a holomorphic map f : B → α B and a ρ-nonexpansive map M : B → B, where B is the open unit ball of a complex Hilbert space H, ρ is the hyperbolic metric defined on B and 0 ≤ α < 1. We give conditions on f and M for this curve to be injective, and we show that this curve is continuous.

Fabric evolution and the related swelling behaviour of a sand/bentonite mixture upon hydro-chemo-mechanical loadings

2015

This experimental study investigates the swelling behaviour of an 80/20 sand/bentonite mixture and the associated fabric evolution under different hydro-chemo-mechanical loadings. Free and confined swelling tests are performed on specimens compacted to different dry densities and wetted with different pore fluids. Controlled suction confined swelling tests are performed to determine the suction–swelling pressure relationship for two different densities. An extensive microstructural characterisation is performed to relate the observed swelling behaviour to the evolution of the different pore networks during wetting. Based on the microstructural analysis, an expression is proposed to determi…

Topological properties of cellular automata on trees

2012

We prove that there do not exist positively expansive cellular automata defined on the full k-ary tree shift (for k>=2). Moreover, we investigate some topological properties of these automata and their relationships, namely permutivity, surjectivity, preinjectivity, right-closingness and openness.

Symmetry reduction of a model in spherical symmetry for benign tumor

2004

A PDEs system, describing the expansive growth of a benign tumor and the phe- nomenon of encapsulation, is studied via a group analysis approach. A weak equiv- alence classi¯cation is obtained and the original PDEs system is reduced to an ODEs system. Numerical simulations are performed both for ODEs and PDEs, which turn out to be in perfect agreement between each other, showing a realistic enough description of the biological process.

AN APPLICATION OF A FIXED POINT THEOREM FOR NONEXPANSIVE OPERATORS

2014

Abstract. In this note, we present an application of a recent xed point theorem by Ricceri to a two-point boundary value problem. KeyWords and Phrases: Fixed point, nonexpansive operator, two-point boundary value problem. 2010 Mathematics Subject Classi cation: 34K10, 47H09, 47H10.

MR3104897 Reviewed Mawhin, J. Variations on some finite-dimensional fixed-point theorems. Translation of Ukraïn. Mat. Zh. 65 (2013), no. 2, 266–272. …

2014

Inglese:The author presents an interesting discussion on three fundamental results in the literature and related theory: the Poincaré-Miranda theorem [C. Miranda, Boll. Un. Mat. Ital. (2) 3 (1940), 5–7; MR0004775 (3,60b)], the Pireddu-Zanolin fixed point theorem [M. Pireddu and F. Zanolin, Topol. Methods Nonlinear Anal. 30 (2007), no. 2, 279–319; MR2387829 (2009a:37032)] and the Zgliczyński fixed point theorem [P. Zgliczyński, Nonlinear Anal. 46 (2001), no. 7, Ser. A: Theory Methods, 1039–1062; MR1866738 (2002h:37032)]. The author provides generalizations of the last two fixed point theorems by using the original technique that he developed in a previous paper and the Poincaré-Miranda theor…

On the structure of the set of equivalent norms on ℓ1 with the fixed point property

2012

Abstract Let A be the set of all equivalent norms on l 1 which satisfy the FPP. We prove that A contains rays. In fact, every renorming in l 1 which verifies condition (⁎) in Theorem 2.1 is the starting point of a (closed or open) ray composed by equivalent norms on l 1 with the FPP. The standard norm ‖ ⋅ ‖ 1 or P.K. Linʼs norm defined in Lin (2008) [12] are examples of such norms. Moreover, we study some topological properties of the set A with respect to some equivalent metrics defined on the set of all norms on l 1 equivalent to ‖ ⋅ ‖ 1 .