scholarly journals Hypersurfaces with parallel difference tensor

1998 ◽  
Vol 24 (1) ◽  
pp. 43-60 ◽  
Author(s):  
Franki DILLEN ◽  
Luc VRANCKEN
Keyword(s):  
Difference Tensor ◽  
Parallel Difference

scholarly journals Characterization of affine ruled surfaces

1997 ◽  
Vol 39 (1) ◽  
pp. 17-20 ◽  
Author(s):  
Włodzimierz Jelonek
Keyword(s):  
Shape Operator ◽  
Ruled Surfaces ◽  
Affine Sphere ◽  
Affine Surface ◽  
Codazzi Tensor ◽  
Difference Tensor ◽  
The Difference ◽  
In The Beginning ◽  
Affine Metric

The aim of this paper is to give certain conditions characterizing ruled affine surfaces in terms of the Blaschke structure (∇, h, S) induced on a surface (M, f) in ℝ3. The investigation of affine ruled surfaces was started by W. Blaschke in the beginning of our century (see [1]). The description of affine ruled surfaces can be also found in the book [11], [3] and [7]. Ruled extremal surfaces are described in [9]. We show in the present paper that a shape operator S is a Codazzi tensor with respect to the Levi-Civita connection ∇ of affine metric h if and only if (M, f) is an affine sphere or a ruled surface. Affine surfaces with ∇S = 0 are described in [2] (see also [4]). We also show that a surface which is not an affine sphere is ruled iff im(S - HI) =ker(S - HI) and ket(S - HI) ⊂ ker dH. Finally we prove that an affine surface with indefinite affine metric is a ruled affine sphere if and only if the difference tensor K is a Codazzi tensor with respect to ∇.

scholarly journals Transfer of cadmium from ants to ant-lions

1995 ◽  
Vol 6 (2-3) ◽  
pp. 133-138 ◽  
Author(s):  
Pekka Nuorteva
Keyword(s):  
Larval Development ◽  
Food Chain ◽  
Important Food ◽  
Free Living ◽  
Food Items ◽  
Parallel Difference ◽  
Ant Lion ◽  
Formica Aquilonia ◽  
Sparse Population ◽  
Harmful Effects

Ants have been found to bear exceptionally high loads of Cd and other metals, but are in general quite resistant to the toxic effects of Cd. Possible harmful effects caused to their predators by high Cd content have not been studied. Detection of a sparse population of ant-lions on a beach at Padva in Bromarv, offered the possibility to make some preliminary observations of such harmfull effects. AAS-analyses showed that free-living ant-lion larvae bear a Cd load of 4.5 ppm/dwt in young larvae, 8.5 ppm in old ones. This corresponded approximately to the level occurring in their most important food items in Padva (4.5 ppm mean for workers of Formica rufibarbis Fabricius and 6.1 ppm for foragers of F. fusca Linnaeus). The level of Cd in the single ant-lion imago caught (0.5 ppm) was clearly lower than in larvae. Among the Cdantagonistic metals, Cu showed levels in ant-lions two- or three-fold those found in ants, whereas no parallel difference existed for Zn levels. During larval development the level of the essential Cu diminished to half whereas the level of Zn increased two-fold. The fate of surplus cadmium in the food chain was followed experimentally by feeding a forest-living colony of Formica aquilonia Yarrow with 0.5 kg honey containing 600 mg CdCl2 This elevated the Cd content of surface workers up to a level1 O-f old that considered normal, 90-100 ppm (n = 4), and of the inside workers up to 5-fold, 36-61 ppm (n = 6). When surface workers were fed to ant-lion larvae ad libidum, larval Cd content rose in one week to the level of the food (87 ppm). When the feeding of ant-lion larvae was continued by feeding them inside workers for additional 4 weeks, these larvae showed a Cd level (49 ppm), similar to that of their food; then when the feeding had continued for 8 weeks, the level, however, rose to 120 ppm. All ant-lion larvae, including those with the highest Cd content, were fully active and showed no symptoms of disease. Artificial Cd-feeding had no clear effect on the Cu-levels in ants or ant-lions, but Zn responded by an increase from the natural level of 501-603 ppm to 560-1 200 ppm.

scholarly journals Creating ‘international communities’ in southern Spain: Self-segregation and ‘institutional whiteness’ in Swedish lifestyle migration

2018 ◽  
Vol 22 (5-6) ◽  
pp. 799-816 ◽  
Author(s):  
Catrin Lundström
Keyword(s):  
European Identity ◽  
Anglo Saxon ◽  
Spanish Society ◽  
Cultural Boundaries ◽  
The Social ◽  
Part Time ◽  
Parallel Difference ◽  
Western European ◽  
Cultural Similarity ◽  
North Western

This article examines intra-European relations in narratives of Swedish lifestyle migrants living permanently or part-time on the Spanish Sun Coast. It pays particular attention to the complexities of Swedish migrants’ cultural identities and patterns of self-segregation in the Spanish society by investigating the following questions: How do boundaries of social networks that Swedish lifestyle migrants participate in, or interrelate, with a sense of ‘likeness’? In what ways are the formation of these ‘international’ networks mediated through ideas of cultural similarity and parallel difference, and how do such notions both override and uphold boundaries tied to social, cultural and racial divisions? It is argued that the formation of so-called ‘international communities’ on the Spanish Sun Coast tend to cluster mainly north-western European lifestyle migrants, which calls for an analysis of ‘orientations’ towards a certain ‘likeness’, and the function of these spaces and communities as spaces of ‘institutional whiteness’ that work as a ‘meeting point’ where some bodies tend to feel comfortable as they already belong here. The social and cultural boundaries that surround these communities destabilises the idea of a common, culturally homogeneous European identity and display intra-European racial divisions mediated through discourses of cultural differences. What appears is a south–north divide built upon a deep Swedish postcolonial identification with Anglo Saxon and north-western European countries and cultures, and a parallel dis-identification with (the former colonial powers in) southern Europe.

scholarly journals A new parallel difference algorithm based on improved alternating segment Crank–Nicolson scheme for time fractional reaction–diffusion equation

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Xiaozhong Yang ◽  
Xu Dang
Keyword(s):  
Parallel Computing ◽  
Diffusion Equation ◽  
Difference Scheme ◽  
Reaction Diffusion ◽  
Difference Schemes ◽  
Reaction Diffusion Equation ◽  
Stability And Convergence ◽  
Parallel Difference ◽  
Fractional Reaction ◽  
Crank Nicolson

Abstract The fractional reaction–diffusion equation has profound physical and engineering background, and its rapid solution research is of important scientific significance and engineering application value. In this paper, we propose a parallel computing method of mixed difference scheme for time fractional reaction–diffusion equation and construct a class of improved alternating segment Crank–Nicolson (IASC–N) difference schemes. The class of parallel difference schemes constructed in this paper, based on the classical Crank–Nicolson (C–N) scheme and classical explicit and implicit schemes, combines with alternating segment techniques. We illustrate the unique existence, unconditional stability, and convergence of the parallel difference scheme solution theoretically. Numerical experiments verify the theoretical analysis, which shows that the IASC–N scheme has second order spatial accuracy and $2-\alpha $ 2 − α order temporal accuracy, and the computational efficiency is greatly improved compared with the implicit scheme and C–N scheme. The IASC–N scheme has ideal computation accuracy and obvious parallel computing properties, showing that the IASC–N parallel difference method is effective for solving time fractional reaction–diffusion equation.

scholarly journals A New Class of Difference Methods with Intrinsic Parallelism for Burgers–Fisher Equation

2020 ◽  
Vol 2020 ◽  
pp. 1-17
Author(s):  
Yueyue Pan ◽  
Lifei Wu ◽  
Xiaozhong Yang
Keyword(s):  
Stability And Convergence ◽  
Fisher Equation ◽  
Spatial Accuracy ◽  
New Class ◽  
Intrinsic Parallelism ◽  
Parallel Difference ◽  
Difference Methods ◽  
Explicit And Implicit Schemes ◽  
The Difference ◽  
Time Accuracy

This paper proposes a new class of difference methods with intrinsic parallelism for solving the Burgers–Fisher equation. A new class of parallel difference schemes of pure alternating segment explicit-implicit (PASE-I) and pure alternating segment implicit-explicit (PASI-E) are constructed by taking simple classical explicit and implicit schemes, combined with the alternating segment technique. The existence, uniqueness, linear absolute stability, and convergence for the solutions of PASE-I and PASI-E schemes are well illustrated. Both theoretical analysis and numerical experiments show that PASE-I and PASI-E schemes are linearly absolute stable, with 2-order time accuracy and 2-order spatial accuracy. Compared with the implicit scheme and the Crank–Nicolson (C-N) scheme, the computational efficiency of the PASE-I (PASI-E) scheme is greatly improved. The PASE-I and PASI-E schemes have obvious parallel computing properties, which show that the difference methods with intrinsic parallelism in this paper are feasible to solve the Burgers–Fisher equation.

scholarly journals A classification of isotropic affine hyperspheres

2016 ◽  
Vol 27 (09) ◽  
pp. 1650074 ◽  
Author(s):  
Marilena Moruz ◽  
Luc Vrancken
Keyword(s):  
Acta Math ◽  
Complete Classification ◽  
Positive Definite ◽  
Affine Hypersurface ◽  
Affine Hypersphere ◽  
Difference Tensor ◽  
Affine Spheres

We study affine hypersurfaces [Formula: see text], which have isotropic difference tensor. Note that, any surface always has isotropic difference tensor. In case that the metric is positive definite, such hypersurfaces have been previously studied in [O. Birembaux and M. Djoric, Isotropic affine spheres, Acta Math. Sinica 28(10) 1955–1972.] and [O. Birembaux and L. Vrancken, Isotropic affine hypersurfaces of dimension 5, J. Math. Anal. Appl. 417(2) (2014) 918–962.] We first show that the dimension of an isotropic affine hypersurface is either [Formula: see text], [Formula: see text], [Formula: see text] or [Formula: see text]. Next, we assume that [Formula: see text] is an affine hypersphere and we obtain for each of the possible dimensions a complete classification.

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