Hodge filtration of hypergeometric integrals associated with an affine configuration of general position and a local Torelli theorem

1993 ◽  
pp. 167-178 ◽  
Author(s):  
A. Varchenko
Keyword(s):  
General Position ◽  
Hypergeometric Integrals ◽  
Hodge Filtration ◽  
Torelli Theorem

scholarly journals Variation of Mixed Hodge Structures Associated to an Equisingular One-dimensional Family of Calabi-Yau Threefolds

2020 ◽  
pp. 1-24
Author(s):  
Isidro Nieto-Baños ◽  
Pedro Luis del Angel-Rodriguez
Keyword(s):  
General Position ◽  
Singular Points ◽  
Good Position ◽  
Hodge Structures ◽  
One Dimensional ◽  
Double Points ◽  
Hodge Filtration ◽  
Starting Point ◽  
Mixed Hodge Structures

Abstract We study the variations of mixed Hodge structures (VMHS) associated with a pencil ${\mathcal{X}}$ of equisingular hypersurfaces of degree $d$ in $\mathbb{P}^{4}$ with only ordinary double points as singularities, as well as the variations of Hodge structures (VHS) associated with the desingularization of this family $\widetilde{{\mathcal{X}}}$ . The notion of a set of singular points being in homologically good position is introduced, and, by requiring that the subset of nodes in (algebraic) general position is also in homologically good position, we can extend Griffiths’ description of the $F^{2}$ -term of the Hodge filtration of the desingularization to this case, where we can also determine the possible limiting mixed Hodge structures (LMHS). The particular pencil ${\mathcal{X}}$ of quintic hypersurfaces with 100 singular double points with 86 of them in (algebraic) general position that served as the starting point for this paper is treated with particular attention.

Rationality revisited: Politicisation through planning rationality against the rationality of power

2021 ◽  
pp. 147309522110011
Author(s):  
Esin Özdemir
Keyword(s):  
Public Interest ◽  
General Position ◽  
Strong Relationship ◽  
Planning Theory ◽  
The Political ◽  
Rational Thinking ◽  
Liberal Democracies ◽  
Substantive Issue ◽  
Rational Consensus ◽  
Definition Of

In this article, I readdress the issue of rationality, which has been so far considered in western liberal democracies and in planning theory as procedural, and more recently as post-political in the post-foundational approach, aiming to show how it can gain a substantive and politicising character. I first discuss the problems and limits of the treatment of rational thinking as well as rational consensus-seeking as merely procedural and post-political. Secondly, utilising the notion of Realrationalität of Flyvbjerg, I discuss how rationality attains a politicising role due to its strong relationship with power. Using the concept of planning rationality aiming at public interest, I present the general position and actions of professional organisations in Turkey, focusing on the Chamber of City Planners, as an example illustrative of my argument. I finally argue that rationality becomes a substantive issue that politicizes planning, when it is put forward as an alternative to authoritarian market logic. In doing so, I adopt the Rancièrian definition of the political, defined as disclosure of a wrong and staging of equality. In conclusion, I first emphasize the importance of avoiding quick rejections of the concepts of rationality and consensus in the framework of planning activity and planning theory and secondly, call for a broader definition of the political; the political that is not confined to conflict but is open to rational thinking and rational consensus.

scholarly journals THE GENERAL POSITION NUMBER OF THE CARTESIAN PRODUCT OF TWO TREES

2020 ◽  
pp. 1-10
Author(s):  
JING TIAN ◽  
KEXIANG XU ◽  
SANDI KLAVŽAR
Keyword(s):  
Shortest Path ◽  
Connected Graph ◽  
General Position ◽  
Cartesian Product

Abstract The general position number of a connected graph is the cardinality of a largest set of vertices such that no three pairwise-distinct vertices from the set lie on a common shortest path. In this paper it is proved that the general position number is additive on the Cartesian product of two trees.

General position properties of ANR's

1982 ◽  
Vol 92 (3) ◽  
pp. 451-466 ◽  
Author(s):  
W. J. R. Mitchell
Keyword(s):  
Real Line ◽  
General Position ◽  
Cartesian Product ◽  
Vital Role ◽  
The Real ◽  
Homology Groups ◽  
Local Homology

This paper investigates the ‘general position’ properties which ANR's may possess. The most important of these is the disjoint discs property of Cannon (5), which plays a vital role in recent striking characterizations of manifolds (5, 9, 12, 18, 19, 22). Also considered are the property Δ of Borsuk(2) (which ensures an abundance of dimension-preserving maps), and the vanishing of local homology groups up to a given dimension (cf. (9)). Our main results give relations between these properties, and clarify their behaviour under the stabilization operation of taking cartesian product with the real line. In the last section these results are applied to give partial solutions to questions about homogeneous ANR's.

scholarly journals Na3Co2(As0.52P0.48)O4(As0.95P0.05)2O7

2013 ◽  
Vol 69 (12) ◽  
pp. i85-i86 ◽  
Author(s):  
Youssef Ben Smida ◽  
Abderrahmen Guesmi ◽  
Mohamed Faouzi Zid ◽  
Ahmed Driss
Keyword(s):  
Solid State ◽  
Solid State Reaction ◽  
Title Compound ◽  
General Position ◽  
Structural Model ◽  
Three Dimensional ◽  
The Other ◽  
Coordination Polyhedra ◽  
Bond Valence Sum ◽  
Full Occupancy

The title compound, trisodium dicobalt(II) (arsenate/phosphate) (diarsenate/diphosphate), was prepared by a solid-state reaction. It is isostructural with Na3Co2AsO4As2O7. The framework shows the presence of CoX22O12(X2 is statistically disordered with As0.95P0.05) units formed by sharing corners between Co1O6octahedra andX22O7groups. These units form layers perpendicular to [010]. Co2O6octahedra andX1O4(X1 = As0.54P0.46) tetrahedra form Co2X1O8chains parallel to [001]. Cohesion between layers and chains is ensured by theX22O7groups, giving rise to a three-dimensional framework with broad tunnels, running along thea- andc-axis directions, in which the Na+ions reside. The two Co2+cations, theX1 site and three of the seven O atoms lie on special positions, with site symmetries 2 andmfor the Co,mfor theX1, and 2 andm(× 2) for the O sites. One of two Na atoms is disordered over three special positions [occupancy ratios 0.877 (10):0.110 (13):0.066 (9)] and the other is in a general position with full occupancy. A comparison between structures such as K2CdP2O7, α-NaTiP2O7and K2MoO2P2O7is made. The proposed structural model is supported by charge-distribution (CHARDI) analysis and bond-valence-sum (BVS) calculations. The distortion of the coordination polyhedra is analyzed by means of the effective coordination number.

scholarly journals Stratifications of equivariant varieties

1977 ◽  
Vol 16 (2) ◽  
pp. 279-295 ◽  
Author(s):  
M.J. Field
Keyword(s):  
Lie Group ◽  
General Position ◽  
Higher Order ◽  
Order Conditions ◽  
Compact Lie Group ◽  
Algebraic Varieties ◽  
Equivariant Maps

Let G be a compact Lie group and V and W be linear G spaces. A study is made of the canonical stratification of some algebraic varieties that arise naturally in the theory of C∞ equivariant maps from V to W. The main corollary of our results is the equivalence of Bierstone's concept of “equivariant general position” with our own of “G transversal”. The paper concludes with a description of Bierstone's higher order conditions for equivariant maps in the framework of equisingularity sequences.

Handbook of Hypergeometric Integrals.

1978 ◽  
Vol 141 (4) ◽  
pp. 563
Author(s):  
B. W. Conolly ◽  
Harold Exton
Keyword(s):  
Hypergeometric Integrals
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