scholarly journals A characterization of normed M-spaces

1983 ◽  
Vol 24 (1) ◽  
pp. 89-92 ◽  
Author(s):  
Garfield C. Schmidt
Keyword(s):  
Linear Space ◽  
Linear Structure ◽  
Topological Spaces ◽  
Intrinsic Properties ◽  
Small Step ◽  
Linear Lattice ◽  
Linear Spaces ◽  
And Topology ◽  
Necessary And Sufficient

Linear spaces on which both an order and a topology are defined and related in various ways have been studied for some time now. Given an order on a linear space it is sometimes possible to define a useful topology using the order and linear structure. In this note we focus on a special type of space called a linear lattice and determine those lattice properties which are both necessary and sufficient for the existence of a classical norm, called an M-norm, for the lattice. This result is a small step in a program to determine which intrinsic order properties of an ordered linear space are necessary and sufficient for the existence of various given types of topologies for the space. This study parallels, in a certain sense, the study of purely topological spaces to determine intrinsic properties of a topology which make it metrizable and the study of the relation between order and topology on spaces which have no algebraic structure, or. algebraic structures other than a linear one.

scholarly journals Weakly externally hyperconvex subsets and hyperconvex gluings

2016 ◽  
Vol 09 (03) ◽  
pp. 379-407
Author(s):  
Benjamin Miesch ◽  
Maël Pavón
Keyword(s):  
Metric Spaces ◽  
Maximum Norm ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Linear Spaces ◽  
Full Characterization ◽  
Finite Dimensional ◽  
Hyperconvex Space ◽  
Necessary And Sufficient

We give a necessary and sufficient condition under which gluings of hyperconvex metric spaces along weakly externally hyperconvex subsets are hyperconvex. This leads to a full characterization of hyperconvex gluings of two isometric copies of the same hyperconvex space. Furthermore, we investigate the case of gluings of finite dimensional hyperconvex linear spaces along linear subspaces. For this purpose, we characterize the weakly externally hyperconvex subsets of [Formula: see text] endowed with the maximum norm.

scholarly journals Which abelian tensor categories are geometric?

2018 ◽  
Vol 2018 (734) ◽  
pp. 145-186 ◽  
Author(s):  
Daniel Schäppi
Keyword(s):  
Characteristic Zero ◽  
Intrinsic Properties ◽  
Tensor Categories ◽  
Projective Varieties ◽  
Coherent Sheaves ◽  
Geometric Objects ◽  
Necessary And Sufficient ◽  
Tannaka Duality ◽  
Tannakian Categories

AbstractFor a large class of geometric objects, the passage to categories of quasi-coherent sheaves provides an embedding in the 2-category of abelian tensor categories. The notion of weakly Tannakian categories introduced by the author gives a characterization of tensor categories in the image of this embedding.However, this notion requires additional structure to be present, namely a fiber functor. For the case of classical Tannakian categories in characteristic zero, Deligne has found intrinsic properties—expressible entirely within the language of tensor categories—which are necessary and sufficient for the existence of a fiber functor. In this paper we generalize Deligne’s result to weakly Tannakian categories in characteristic zero. The class of geometric objects whose tensor categories of quasi-coherent sheaves can be recognized in this manner includes both the gerbes arising in classical Tannaka duality and more classical geometric objects such as projective varieties over a field of characteristic zero.Our proof uses a different perspective on fiber functors, which we formalize through the notion of geometric tensor categories. A second application of this perspective allows us to describe categories of quasi-coherent sheaves on fiber products.

“Topologically Indexed Function Spaces and Adjoint Functors”

1982 ◽  
Vol 25 (2) ◽  
pp. 169-178
Author(s):  
S. B. Niefield
Keyword(s):  
Topological Space ◽  
Sufficient Conditions ◽  
Function Spaces ◽  
Topological Spaces ◽  
Product Topology ◽  
Adjoint Functors ◽  
Point Space ◽  
Continuous Maps ◽  
Necessary And Sufficient

AbstractLet Top denote the category of topological spaces and continuous maps. In this paper we discuss families of function spaces indexed by the elements of a topological space T, and their relationship to the characterization of right adjoints Top/S → Top/T, where S is also a topological space. After reducing the problem to the case where S is a one-point space, we describe a class of right adjoints Top → Top/T, and then show that every right adjoint Top → Top/T is isomorphic to one of this form. We conclude by giving necessary and sufficient conditions for a left adjoint Top/T → Top to be isomorphic to one of the form − XTY, where Y is a space over T, and xT denotes the fiber product with the product topology.

Fuzzifying bornological linear spaces

2021 ◽  
pp. 1-12
Author(s):  
Zhen-Yu Jin ◽  
Cong-Hua Yan
Keyword(s):  
Linear Structure ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Normed Spaces ◽  
Linear Spaces ◽  
Probabilistic Normed Spaces ◽  
Necessary And Sufficient ◽  
Topological Linear

In this paper, a notion of fuzzifying bornological linear spaces is introduced and the necessary and sufficient condition for fuzzifying bornologies to be compatible with linear structure is discussed. The characterizations of convergence and separation in fuzzifying bornological linear spaces are showed. In particular, some examples with respect to linear fuzzifying bornologies induced by probabilistic normed spaces and fuzzifying topological linear spaces are also provided.

Linear fuzzifying uniformities

2021 ◽  
pp. 1-12
Author(s):  
Zhen-Yu Jin ◽  
Cong-Hua Yan
Keyword(s):  
Linear Space ◽  
Linear Structure ◽  
Translation Invariant ◽  
Linear Spaces ◽  
Hausdorff Separation

The main purpose of this paper is to study Hutton type fuzzifying uniformities on linear spaces. Firstly, we show that if a base of a fuzzifying uniformity defined over a linear space is translation-invariant, balanced and absorbed, then it generates a linear fuzzifying topology. From this linear fuzzifying topology, we can construct a new linear fuzzifying uniformity (i.e., a fuzzifying uniformity compatible with the linear structure) which is equivalent to the original fuzzifying uniformity. Secondly, the Hausdorff separation and complete boundedness in linear fuzzifying uniformities are investigated. In addition, as an example, the linear fuzzifying uniformity induced by a fuzzy norm is also discussed.

scholarly journals Characterization of convergence in fuzzy topological spaces

1985 ◽  
Vol 8 (3) ◽  
pp. 497-511 ◽  
Author(s):  
E. Lowen ◽  
R. Lowen
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Topological Spaces ◽  
Fuzzy Topology ◽  
Fuzzy Topological Spaces ◽  
Necessary And Sufficient

In a fuzzy topology on a setX, the limit of a prefilter (i.e. a filter in the lattice[0,1]X) is calculated from the fuzzy closure. In this way convergence is derived from a fuzzy topology. In our paper we start with any rule “lim” which to any prefilter𝔇onXassigns, a functionlim𝔇∈[0,1]X. We give necessary and sufficient conditions for the function𝔇→lim𝔇in order that it can be derived from a fuzzy topology.

scholarly journals Mating Type in Chlamydomonas Is Specified by mid, the Minus-Dominance Gene

Genetics ◽  
1997 ◽  
Vol 146 (3) ◽  
pp. 859-869 ◽  
Author(s):  
Patrick J Ferris ◽  
Ursula W Goodenough
Keyword(s):  
Transcription Factor ◽  
Mating Type ◽  
Codon Bias ◽  
Leucine Zipper ◽  
Laboratory Strain ◽  
Leucine Zipper Motif ◽  
Type Locus ◽  
Diploid Cells ◽  
Necessary And Sufficient

Diploid cells of Chlamydomonas reinhardtii that are heterozygous at the mating-type locus (mt  +/mt  –) differentiate as minus gametes, a phenomenon known as minus dominance. We report the cloning and characterization of a gene that is necessary and sufficient to exert this minus dominance over the plus differentiation program. The gene, called mid, is located in the rearranged (R) domain of the mt  – locus, and has duplicated and transposed to an autosome in a laboratory strain. The imp11 mt  – mutant, which differentiates as a fusion-incompetent plus gamete, carries a point mutation in mid. Like the fus1 gene in the mt  + locus, mid displays low codon bias compared with other nuclear genes. The mid sequence carries a putative leucine zipper motif, suggesting that it functions as a transcription factor to switch on the minus program and switch off the plus program of gametic differentiation. This is the first sex-determination gene to be characterized in a green organism.

scholarly journals Homological epimorphisms, homotopy epimorphisms and acyclic maps

2020 ◽  
Vol 32 (6) ◽  
pp. 1395-1406
Author(s):  
Joseph Chuang ◽  
Andrey Lazarev
Keyword(s):  
Wide Class ◽  
Topological Spaces ◽  
Loop Spaces ◽  
Graded Algebras ◽  
Differential Graded Algebras ◽  
Algebraic Description ◽  
Acyclic Map ◽  
Induced Maps

AbstractWe show that the notions of homotopy epimorphism and homological epimorphism in the category of differential graded algebras are equivalent. As an application we obtain a characterization of acyclic maps of topological spaces in terms of induced maps of their chain algebras of based loop spaces. In the case of a universal acyclic map we obtain, for a wide class of spaces, an explicit algebraic description for these induced maps in terms of derived localization.

scholarly journals On cryptographic properties of (n + 1)-bit S-boxes constructed by known n-bit S-boxes

2020 ◽  
Vol 15 (1) ◽  
pp. 258-265
Author(s):  
Yu Zhou ◽  
Daoguang Mu ◽  
Xinfeng Dong
Keyword(s):  
Sufficient Conditions ◽  
Sum Of Squares ◽  
Basic Component ◽  
Necessary And Sufficient Conditions ◽  
Autocorrelation Functions ◽  
Walsh Spectrum ◽  
Cryptographic Algorithms ◽  
Necessary And Sufficient ◽  
Relationship Of

AbstractS-box is the basic component of symmetric cryptographic algorithms, and its cryptographic properties play a key role in security of the algorithms. In this paper we give the distributions of Walsh spectrum and the distributions of autocorrelation functions for (n + 1)-bit S-boxes in [12]. We obtain the nonlinearity of (n + 1)-bit S-boxes, and one necessary and sufficient conditions of (n + 1)-bit S-boxes satisfying m-order resilient. Meanwhile, we also give one characterization of (n + 1)-bit S-boxes satisfying t-order propagation criterion. Finally, we give one relationship of the sum-of-squares indicators between an n-bit S-box S0 and the (n + 1)-bit S-box S (which is constructed by S0).

In Situ Characterization of the Mechanical Behavior of Gecko's Spatulae by Atomic Force Microscopy

2013 ◽  
Vol 22 ◽  
pp. 85-93
Author(s):  
Shuang Yi Liu ◽  
Min Min Tang ◽  
Ai Kah Soh ◽  
Liang Hong
Keyword(s):  
Mechanical Behavior ◽  
Hierarchical Level ◽  
Intrinsic Properties ◽  
In Situ Characterization ◽  
Force Microscopy ◽  
Atomic Force ◽  
Theoretical Predictions ◽  
Multi Mode

In-situ characterization of the mechanical behavior of geckos spatula has been carried out in detail using multi-mode AFM system. Combining successful application of a novel AFM mode, i.e. Harmonix microscopy, the more detail elastic properties of spatula is brought to light. The results obtained show the variation of the mechanical properties on the hierarchical level of a seta, even for the different locations, pad and stalk of the spatula. A model, which has been validated using the existing experimental data and phenomena as well as theoretical predictions for geckos adhesion, crawling and self-cleaning of spatulae, is proposed in this paper. Through contrast of adhesive and craw ability of the gecko on the surfaces with different surface roughness, and measurement of the surface adhesive behaviors of Teflon, the most effective adhesion of the gecko is more dependent on the intrinsic properties of the surface which is adhered.

Sign in / Sign up

Export Citation Format

Share Document