A characterization of sets of n points which determine n hyperplanes

1968 ◽  
Vol 64 (3) ◽  
pp. 585-588 ◽  
Author(s):  
J. G. Basterfield ◽  
L. M. Kelly
Keyword(s):  
Projective Space ◽  
The Other ◽  
Finite Projective Space ◽  
Other Hand ◽  
Finite Set ◽  
Set Of Points

Suppose N is a set of points of a d-dimensional incidence space S and {Ha}, a ∈ I, a set of hyperplanes of S such that Hi ∈ {Ha} if and only if Hi ∩ N spans Hi. N is then said to determine {Ha}. We are interested here in the case in which N is a finite set of n points in S and I = {1, 2,…, n}; that is to say when a set of n points determines precisely n hyperplanes. Such a situation occurs in E3, for example, when N spans E3 and is a subset of two (skew) lines, or in E2 if N spans the space and n − 1 of the points are on a line. On the other hand, the n points of a finite projective space determine precisely n hyperplanes so that the structure of a set of n points determining n hyperplanes is not at once transparent.

scholarly journals Deformation of finite morphisms and smoothing of ropes

2008 ◽  
Vol 144 (3) ◽  
pp. 673-688 ◽  
Author(s):  
Francisco Javier Gallego ◽  
Miguel González ◽  
Bangere P. Purnaprajna
Keyword(s):  
General Theory ◽  
Projective Space ◽  
General Result ◽  
The Other ◽  
Independent Interest ◽  
Higher Dimension ◽  
Smooth Curves ◽  
Other Hand ◽  
Finite Covers ◽  
The One

AbstractIn this paper we prove that most ropes of arbitrary multiplicity supported on smooth curves can be smoothed. By a rope being smoothable we mean that the rope is the flat limit of a family of smooth, irreducible curves. To construct a smoothing, we connect, on the one hand, deformations of a finite morphism to projective space and, on the other hand, morphisms from a rope to projective space. We also prove a general result of independent interest, namely that finite covers onto smooth irreducible curves embedded in projective space can be deformed to a family of 1:1 maps. We apply our general theory to prove the smoothing of ropes of multiplicity 3 on P1. Even though this paper focuses on ropes of dimension 1, our method yields a general approach to deal with the smoothing of ropes of higher dimension.

A Characterization of the Topological Dimension

1982 ◽  
Vol 25 (4) ◽  
pp. 487-490
Author(s):  
Gerd Rodé
Keyword(s):  
Hausdorff Space ◽  
The Other ◽  
Natural Numbers ◽  
Topological Dimension ◽  
Other Hand ◽  
The One

AbstractThis paper gives a new characterization of the dimension of a normal Hausdorff space, which joins together the Eilenberg-Otto characterization and the characterization by finite coverings. The link is furnished by the notion of a system of faces of a certain type (N1,..., NK), where N1,..., NK, K are natural numbers. It is shown that a space X contains a system of faces of type (N1,..., NK) if and only if dim(X) ≥ N1 + … + NK. The two limit cases of the theorem, namely Nk = 1 for 1 ≤ k ≤ K on the one hand, and K = 1 on the other hand, give the two known results mentioned above.

scholarly journals Maqui berry vs Sloe berry – Liquor-based Beverage for New Development

2015 ◽  
Vol 10 (1) ◽  
pp. 1934578X1501000
Author(s):  
Amadeo Gironés-Vilaplana ◽  
Diego A. Moreno ◽  
Cristina García-Viguera
Keyword(s):  
The Other ◽  
Northern Spain ◽  
Organoleptic Properties ◽  
Beneficial Effects ◽  
Other Hand ◽  
New Development ◽  
Aristotelia Chilensis ◽  
Maqui Berry ◽  
Over Time

“Pacharán” is an aniseed liquor-based beverage made with sloe berry ( Prunus spinosa L.) that has been produced in northern Spain. On the other hand, maqui berry ( Aristotelia chilensis) is a common edible berry from Chile, and currently under study because of its multiple beneficial effects on health. The aim of this work was to design a new aniseed liquor-based beverage with maqui berry, as an industrial alternative to a traditional alcoholic product with bioactive berries. The characterization of its composition, compared with the traditional “Pacharán”, and its evolution during maceration (6 and 12 months) showed that the new maqui liquor had significantly-higher anthocyanin retention over time. More studies on the organoleptic properties and bioactivity are underway.

scholarly journals Ontology, Ontologies and the “I” of FAIR

2020 ◽  
Vol 2 (1-2) ◽  
pp. 181-191 ◽  
Author(s):  
Giancarlo Guizzardi
Keyword(s):  
Value Of Information ◽  
Direct Consequence ◽  
Semantic Interoperability ◽  
The Other ◽  
Added Value ◽  
Computational Tools ◽  
Other Hand ◽  
Guiding Principles

According to the FAIR guiding principles, one of the central attributes for maximizing the added value of information artifacts is interoperability. In this paper, I discuss the importance, and propose a characterization of the notion of Semantic Interoperability. Moreover, I show that a direct consequence of this view is that Semantic Interoperability cannot be achieved without the support of, on one hand, (i) ontologies, as meaning contracts capturing the conceptualizations represented in information artifacts and, on the other hand, of (ii) Ontology, as a discipline proposing formal meth- ods and theories for clarifying these conceptualizations and articulating their representations. In particular, I discuss the fundamental role of formal ontological theories (in the latter sense) to properly ground the construction of representation languages, as well as methodological and computational tools for supporting the engineering of ontologies (in the former sense) in the context of FAIR.

scholarly journals ON THE DEFINITIONS OF SOBOLEV AND BV SPACES INTO SINGULAR SPACES AND THE TRACE PROBLEM

2007 ◽  
Vol 09 (04) ◽  
pp. 473-513 ◽  
Author(s):  
DAVID CHIRON
Keyword(s):  
Sobolev Spaces ◽  
Metric Spaces ◽  
The Other ◽  
Dirichlet Energy ◽  
Singular Spaces ◽  
Other Hand ◽  
The One

The purpose of this paper is to relate two notions of Sobolev and BV spaces into metric spaces, due to Korevaar and Schoen on the one hand, and Jost on the other hand. We prove that these two notions coincide and define the same p-energies. We review also other definitions, due to Ambrosio (for BV maps into metric spaces), Reshetnyak and finally to the notion of Newtonian–Sobolev spaces. These last approaches define the same Sobolev (or BV) spaces, but with a different energy, which does not extend the standard Dirichlet energy. We also prove a characterization of Sobolev spaces in the spirit of Bourgain, Brezis and Mironescu in terms of "limit" of the space Ws,p as s → 1, 0 < s < 1, and finally following the approach proposed by Nguyen. We also establish the [Formula: see text] regularity of traces of maps in Ws,p (0 < s ≤ 1 < sp).

Entitlement Theories of Justice: From Nozick to Roemer and Beyond

1985 ◽  
Vol 1 (1) ◽  
pp. 69-81 ◽  
Author(s):  
Robert J. van der Veen ◽  
Philippe Van Parijs
Keyword(s):  
The Other ◽  
Robert Nozick ◽  
Other Hand ◽  
Entitlement Theory ◽  
Theories Of Justice ◽  
Principle Of Justice ◽  
Principles Of Justice ◽  
The One ◽  
Alternative Theories

In Anarchy, State, and Utopia, Robert Nozick contrasts entitlement theories of justice and “traditional” theories such as Rawls', utilitarianism or egalitarianism, and advocates the former against the latter. What exactly is an entitlement theory (or conception or principle) of justice? Nozick's book offers two distinct characterizations. On the one hand, he explicitly describes “the general outlines of the entitlement theory” as maintaining “that the holdings of a person are just if he is entitled to them by the principles of justice in acquisition and transfer, or by the principle of rectification of injustice (as specified by the first two principles of just acquisition and transfer)” (Nozick, 1974, p. 153). On the other hand, his famous “Wilt Chamberlain” argument against alternative theories is first said to apply to (all) “non-entitlement conceptions” (p. 160), and later to any “end-state principle or distributional patterned principle of justice” (p. 163) — which amounts to an implicit characterization of an entitlement conception (theory, principle) as a conception of justice which is neither end-state nor patterned.

ON THE POWER OF DETERMINISTIC AND SEQUENTIAL COMMUNICATING P SYSTEMS

2007 ◽  
Vol 18 (02) ◽  
pp. 415-431 ◽  
Author(s):  
LUDĚK CIENCIALA ◽  
LUCIE CIENCIALOVÁ ◽  
PIERLUIGI FRISCO ◽  
PETR SOSÍK
Keyword(s):  
The Other ◽  
P Systems ◽  
Computational Power ◽  
Other Hand ◽  
Mode 2 ◽  
Parallel Mode ◽  
Sequential Mode

We characterize the computational power of several restricted variants of communicating P systems. We show that 2-deterministic communicating P systems with 2 membranes, working in either minimally or maximally parallel mode, are computationally universal. Considering the sequential mode, 2 membranes are shown to characterize the power of partially blind multicounter machines. Next, a characterization of the power of 1-deterministic communicating P systems is given. Finally, we show that the nondeterministic variant in maximally parallel mode is universal already with 1 membrane. These results demonstrate differences in computational power between nondeterminism, 2-determinism and 1-determinism, on one hand, and between sequential, minimally and maximally parallel modes, on the other hand.

Characterization of texture and microstructure of electrodeposited Ni layers

2008 ◽  
Vol 1112 ◽  
Author(s):  
Homuro Noda ◽  
Akinobu Shibata ◽  
Masato Sone ◽  
Chiemi Ishiyama ◽  
Yakichi Higo
Keyword(s):  
Growth Direction ◽  
Fiber Texture ◽  
The Other ◽  
Cu Substrate ◽  
Other Hand ◽  
Columnar Grains

AbstractThe texture and microstructure of electrodeposited Ni layers formed in an additive-free Watt's bath were investigated. The microstructure of the electrodeposited Ni layer consists of fine columnar grains extending along the growth direction. The major texture components of electrodeposited Ni layers on Ni-P substrate were (112) and (110) fibers. On the other hand, electrodeposited Ni layers on Cu substrate had a strong (110) fiber texture. In the vicinity of the interface between the electrodeposited Ni layer and the Cu substrate, obvious epitaxial regions were not observed. Many twins parallel to the growth direction were observed in the electrodeposited Ni layer. It is suggested that grains with a twin relationship grew preferentially during the electrodeposition reaction.

scholarly journals De NovoSequencing and Characterization of the Transcriptome of Dwarf Polish Wheat (Triticum polonicumL.)

2016 ◽  
Vol 2016 ◽  
pp. 1-6 ◽  
Author(s):  
Yi Wang ◽  
Chao Wang ◽  
Xiaolu Wang ◽  
Fan Peng ◽  
Ruijiao Wang ◽  
...  
Keyword(s):  
Genome Sequencing ◽  
Wheat Genome ◽  
The Other ◽  
Crucial Step ◽  
Functional Types ◽  
Other Hand ◽  
Genome Sequencing Consortium ◽  
Stems And Leaves ◽  
Wheat Transcriptome

Construction as well as characterization of a polish wheat transcriptome is a crucial step to study useful traits of polish wheat. In this study, a transcriptome, including 76,014 unigenes, was assembled from dwarf polish wheat (DPW) roots, stems, and leaves using the software of Trinity. Among these unigenes, 61,748 (81.23%) unigenes were functionally annotated in public databases and classified into differentially functional types. Aligning this transcriptome against draft wheat genome released by the International Wheat Genome Sequencing Consortium (IWGSC), 57,331 (75.42%) unigenes, including 26,122 AB-specific and 2,622 D-specific unigenes, were mapped on A, B, and/or D genomes. Compared with the transcriptome ofT. turgidum, 56,343 unigenes were matched with 103,327 unigenes ofT. turgidum. Compared with the genomes of rice and barley, 14,404 and 7,007 unigenes were matched with 14,608 genes of barley and 7,708 genes of rice, respectively. On the other hand, 2,148, 1,611, and 2,707 unigenes were expressed specifically in roots, stems, and leaves, respectively. Finally, 5,531 SSR sequences were observed from 4,531 unigenes, and 518 primer pairs were designed.

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