Extreme Version of Projectivity for Normed Modules Over Sequence Algebras

2013 ◽  
Vol 65 (3) ◽  
pp. 559-574 ◽  
Author(s):  
A. Ya. Helemskii
Keyword(s):  
The Other ◽  
Normed Algebra ◽  
Natural Conditions ◽  
Infinite Dimensional ◽  
Full Characterization ◽  
Other Hand ◽  
Finite Sequences ◽  
Sequence Algebra ◽  
Normed Module

AbstractWe define and study the so-called extreme version of the notion of a projective normed module. The relevant definition takes into account the exact value of the norm of the module in question, in contrast with the standard known definition that is formulated in terms of normtopology.After the discussion of the case where our normed algebra A is just C, we concentrate on the case of the next degree of complication, where A is a sequence algebra satisfying some natural conditions. The main results give a full characterization of extremely projective objects within the subcategory of the category of non-degenerate normed A-modules, consisting of the so-called homogeneous modules. We consider two cases, ‘non-complete’ and ‘complete’, and the respective answers turn out to be essentially different.In particular, all Banach non-degenerate homogeneous modules consisting of sequences are extremely projective within the category of Banach non-degenerate homogeneous modules. However, neither of them, provided it is infinite-dimensional, is extremely projective within the category of all normed non-degenerate homogeneous modules. On the other hand, submodules of these modules consisting of finite sequences are extremely projective within the latter category.

scholarly journals Concatenation of Finite Sequences

2019 ◽  
Vol 27 (1) ◽  
pp. 1-13
Author(s):  
Rafał Ziobro
Keyword(s):  
Finite Sequence ◽  
The Other ◽  
Other Hand ◽  
Finite Sequences ◽  
Initial Object

Summary The coexistence of “classical” finite sequences [1] and their zero-based equivalents finite 0-sequences [6] in Mizar has been regarded as a disadvantage. However the suggested replacement of the former type with the latter [5] has not yet been implemented, despite of several advantages of this form, such as the identity of length and domain operators [4]. On the other hand the number of theorems formalized using finite sequence notation is much larger then of those based on finite 0-sequences, so such translation would require quite an effort. The paper addresses this problem with another solution, using the Mizar system [3], [2]. Instead of removing one notation it is possible to introduce operators which would concatenate sequences of various types, and in this way allow utilization of the whole range of formalized theorems. While the operation could replace existing FS2XFS, XFS2FS commands (by using empty sequences as initial elements) its universal notation (independent on sequences that are concatenated to the initial object) allows to “forget” about the type of sequences that are concatenated on further positions, and thus simplify the proofs.

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 Generating Adjoint Groups

2019 ◽  
Vol 62 (3) ◽  
pp. 733-738 ◽  
Author(s):  
Be'eri Greenfeld
Keyword(s):  
Open Problem ◽  
Jacobson Radical ◽  
The Other ◽  
Adjoint Group ◽  
Finitely Generated ◽  
Infinite Dimensional ◽  
Other Hand ◽  
Nil Ring

AbstractWe prove two approximations of the open problem of whether the adjoint group of a non-nilpotent nil ring can be finitely generated. We show that the adjoint group of a non-nilpotent Jacobson radical cannot be boundedly generated and, on the other hand, construct a finitely generated, infinite-dimensional nil algebra whose adjoint group is generated by elements of bounded torsion.

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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