Minimal Translation Hypersurfaces in Euclidean Space

The graph of a function f defined in some open set of the Euclidean space of dimension (p + q) is said to be a translation graph if f may be expressed as the sum of two independent functions ? and ψ defined in open sets of the Euclidean spaces of dimension p and q, respectively. We obtain a useful expression for the mean curvature of the graph of f in terms of the Laplacian, the gradient of ? and ψ as well as of the mean curvatures of their graphs. We study translation graphs having zero mean curvature, that is, minimal translation graphs, by imposing natural conditions on ? and ψ, like harmonicity, minimality and eikonality (constant norm of the gradient), giving several examples as well as characterization results.     

Number 85

Reviews are listed in order of appearance in the sources indicated. In multidisciplinary review journals, only those reviews which fall within the scope of this Journal are included. Sources are listed alphabetically in three categories: regularly issued review journals and series volumes, contributed volumes, and other monographs. Titles are numbered serially, and these numbers are used for reference in the index. Major English-language sources of critical reviews are covered. Encyclopedic treatises, annual surveys such as Specialist Periodical Reports, and compilations of symposia proceedings are omitted. This installment of Recent Reviews covers principally the early part of the 2007 literature. Previous installment: J. Org. Chem. 2007, 72 (7), 2699-706.     

Shubnikov-de Haas effect in tricrystals of the system of alloys Bi1−x Sbx (x=0.1; 0.13) with n-type conductivity

The Shubnikov-de Haas effect has been investigated in tricrystals of the alloy system Bi_1−x Sb_x (x=0.1; 0.13) with n-type conductivity in stationary (up to 14 T) and pulsed (up to 40 T) magnetic fields. Reconstruction of the internal boundary of the tricrystals was observed, along with a number of new component oscillations of ρ(B) indicating a rotation of the constant-energy surfaces of the L electrons on the intercrystallite boundary at an angle of ∼74° in the binary-trigonal plane. Fiz. Tverd. Tela (St. Petersburg) 41, 991–993 (June 1999)     

On some Closed Magnetic Curves on a 3-torus

We consider two magnetic fields on the 3-torus obtained from two different contact forms on the Euclidean 3-space and we study when their corresponding normal magnetic curves are closed. We obtain periodicity conditions analogues to those for the closed geodesics on the torus.     

JOC Recent Reviews, Number 81

Reviews are listed in order of appearance in the sources indicated. In multidisciplinary review journals, only those reviews which fall within the scope of this Journal are included. Sources are listed alphabetically in three categories: regularly issued review journals and series volumes, contributed volumes, and other monographs. Titles are numbered serially, and these numbers are used for reference in the index. Major English-language sources of critical reviews are covered. Encyclopedic treatises, annual surveys such as Specialist Periodical Reports, and compilations of symposia proceedings are omitted. This installment of Recent Reviews covers principally the early part of the 2006 literature. Previous installment: J. Org. Chem. 2006, 71(7), 2926-34.     

On the complexity and analysis of auxetic systems

A challenge in creating a model for an auxetic system based on a formalism that is fully computable, is the aim of this paper. Two major levels of complexity are discussed in a way of understanding the structure and processes that define an auxetic system. The auxeticity and structural complexity are interpreted in the light of Cosserat elasticity which admits degrees of freedom not present in classical elasticity, i.e. the rotation of points in the material, and a couple per unit area or the couple stress. The Young'modulus computing for a laminated periodic system made up of alternating aluminum and an auxetic material is an example of computing complexity. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)