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.

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 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 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.

A Module-theoretic Characterization of Algebraic Hypersurfaces

2018 ◽  
Vol 61 (1) ◽  
pp. 166-173
Author(s):  
Cleto B. Miranda-Neto
Keyword(s):  
Algebraic Variety ◽  
Characteristic Zero ◽  
Vector Fields ◽  
Exterior Power ◽  
Algebraic Hypersurfaces ◽  
Theoretic Characterization

AbstractIn this note we prove the following surprising characterization: if X ⊂ is an (embedded, non-empty, proper) algebraic variety deûned over a field k of characteristic zero, then X is a hypersurface if and only if the module of logarithmic vector fields of X is a reflexive -module. As a consequence of this result, we derive that if is a free -module, which is shown to be equivalent to the freeness of the t-th exterior power of for some (in fact, any) t ≤ n, then necessarily X is a Saito free divisor.

Central automorphisms of free nilpotent Lie algebras

2017 ◽  
Vol 16 (11) ◽  
pp. 1750205
Author(s):  
Özge Öztekin ◽  
Naime Ekici
Keyword(s):  
Lie Algebras ◽  
Finite Rank ◽  
Characteristic Zero ◽  
Sufficient Conditions ◽  
Nilpotency Class ◽  
Nilpotent Lie Algebra ◽  
Central Automorphism ◽  
Nilpotent Lie Algebras ◽  
Central Automorphisms

Let [Formula: see text] be the free nilpotent Lie algebra of finite rank [Formula: see text] [Formula: see text] and nilpotency class [Formula: see text] over a field of characteristic zero. We give a characterization of central automorphisms of [Formula: see text] and we find sufficient conditions for an automorphism of [Formula: see text] to be a central automorphism.

On representation of Poisson mixtures as Poisson sums and a characterization of the gamma distribution

1977 ◽  
Vol 82 (2) ◽  
pp. 297-300 ◽  
Author(s):  
A. V. Godambe
Keyword(s):  
Gamma Distribution ◽  
Exponential Type ◽  
Similar Condition ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Poisson Mixture ◽  
Mixing Distribution ◽  
Poisson Mixtures ◽  
Necessary And Sufficient

AbstractA necessary and sufficient condition for a Poisson mixture with an exponential type mixing distribution to be equivalently represented as a Poisson sum is obtained. The problem of deriving a similar condition under any mixing distribution on (0, ∞) is discussed. Finally, a characterization of the gamma distribution is obtained.

A characterization of the Poisson process

1974 ◽  
Vol 11 (1) ◽  
pp. 72-85 ◽  
Author(s):  
S. M. Samuels
Keyword(s):  
Poisson Process ◽  
Renewal Process ◽  
Poisson Processes ◽  
Renewal Processes ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Complete Proof ◽  
Necessary And Sufficient

Theorem: A necessary and sufficient condition for the superposition of two ordinary renewal processes to again be a renewal process is that they be Poisson processes.A complete proof of this theorem is given; also it is shown how the theorem follows from the corresponding one for the superposition of two stationary renewal processes.

scholarly journals One-relator groups and algebras related to polyhedral products

2021 ◽  
pp. 1-20
Author(s):  
Jelena Grbić ◽  
George Simmons ◽  
Marina Ilyasova ◽  
Taras Panov
Keyword(s):  
Homology Group ◽  
Homotopy Theory ◽  
Commutator Subgroup ◽  
Homology Groups ◽  
Homological Characterization ◽  
One Relator Groups ◽  
Combinatorial Condition ◽  
The Moment ◽  
Necessary And Sufficient

We link distinct concepts of geometric group theory and homotopy theory through underlying combinatorics. For a flag simplicial complex $K$ , we specify a necessary and sufficient combinatorial condition for the commutator subgroup $RC_K'$ of a right-angled Coxeter group, viewed as the fundamental group of the real moment-angle complex $\mathcal {R}_K$ , to be a one-relator group; and for the Pontryagin algebra $H_{*}(\Omega \mathcal {Z}_K)$ of the moment-angle complex to be a one-relator algebra. We also give a homological characterization of these properties. For $RC_K'$ , it is given by a condition on the homology group $H_2(\mathcal {R}_K)$ , whereas for $H_{*}(\Omega \mathcal {Z}_K)$ it is stated in terms of the bigrading of the homology groups of $\mathcal {Z}_K$ .

Separability criteria based on the Bloch representation of density matrices

2007 ◽  
Vol 7 (7) ◽  
pp. 624-638
Author(s):  
J. de Vicente
Keyword(s):  
Sufficient Conditions ◽  
Quantum Systems ◽  
Necessary Condition ◽  
Sufficient Condition ◽  
Pure Product ◽  
Separability Problem ◽  
Arbitrary Dimensions ◽  
Necessary And Sufficient ◽  
Bloch Representation

We study the separability of bipartite quantum systems in arbitrary dimensions using the Bloch representation of their density matrix. This approach enables us to find an alternative characterization of the separability problem, from which we derive a necessary condition and sufficient conditions for separability. For a certain class of states the necessary condition and a sufficient condition turn out to be equivalent, therefore yielding a necessary and sufficient condition. The proofs of the sufficient conditions are constructive, thus providing decompositions in pure product states for the states that satisfy them. We provide examples that show the ability of these conditions to detect entanglement. In particular, the necessary condition is proved to be strong enough to detect bound entangled states.

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