scholarly journals Systolic geometry and simplicial complexity for groups

2019 ◽  
Vol 2019 (757) ◽  
pp. 247-277
Author(s):  
Ivan Babenko ◽  
Florent Balacheff ◽  
Guillaume Bulteau
Keyword(s):  
Isomorphism Classes ◽  
Combinatorial Invariant ◽  
Satisfactory Answer

AbstractTwenty years ago Gromov asked about how large is the set of isomorphism classes of groups whose systolic area is bounded from above. This article introduces a new combinatorial invariant for finitely presentable groups called simplicial complexity that allows to obtain a quite satisfactory answer to his question. Using this new complexity, we also derive new results on systolic area for groups that specify its topological behaviour.

scholarly journals Share Contract Revisited: A New Transaction Cost Approach

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Jian Ding ◽  
Yixiao Zhou
Keyword(s):  
Hong Kong ◽  
Transaction Cost ◽  
Empirical Studies ◽  
Theoretical Explanation ◽  
Empirical Testing ◽  
Cost Approach ◽  
Satisfactory Answer ◽  
The Impact

Abstract The purpose of this paper is to explore how sharecropping contracts are chosen over fixed-rent contracts. There are two concerning issues. First, theoretical explanation has been criticized for not providing a satisfactory answer to the question as to why share contracts are chosen. Second, among the existing empirical studies, there are great controversies about the impact of variance of output. Inspired by the latest insights from (Cheung, S. N. S. 2014. Economic Explanation. Hong Kong: Arcadia Press.), this paper not only provides an explanation for the choice of share contract that is suitable for empirical testing, but also solves the puzzle over variance of output.

scholarly journals Low-temperature nucleation anomaly in silicate glasses shown to be artifact in a 5BaO·8SiO2 glass

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Xinsheng Xia ◽  
D. C. Van Hoesen ◽  
Matthew E. McKenzie ◽  
Randall E. Youngman ◽  
K. F. Kelton
Keyword(s):  
Nucleation Rate ◽  
Experimental Approach ◽  
Cluster Formation ◽  
Heating Time ◽  
Silicate Glasses ◽  
Nucleation Theory ◽  
Classical Nucleation Theory ◽  
Real Phenomenon ◽  
Satisfactory Answer ◽  
Over 40 Years

AbstractFor over 40 years, measurements of the nucleation rates in a large number of silicate glasses have indicated a breakdown in the Classical Nucleation Theory at temperatures below that of the peak nucleation rate. The data show that instead of steadily decreasing with decreasing temperature, the work of critical cluster formation enters a plateau and even starts to increase. Many explanations have been offered to explain this anomaly, but none have provided a satisfactory answer. We present an experimental approach to demonstrate explicitly for the example of a 5BaO ∙ 8SiO2 glass that the anomaly is not a real phenomenon, but instead an artifact arising from an insufficient heating time at low temperatures. Heating times much longer than previously used at a temperature 50 K below the peak nucleation rate temperature give results that are consistent with the predictions of the Classical Nucleation Theory. These results raise the question of whether the claimed anomaly is also an artifact in other glasses.

scholarly journals Invariant connections and invariant holomorphic bundles on homogeneous manifolds

2014 ◽  
Vol 12 (1) ◽  
pp. 1-13
Author(s):  
Indranil Biswas ◽  
Andrei Teleman
Keyword(s):  
Lie Group ◽  
Complex Structure ◽  
Differentiable Manifold ◽  
Equivalence Classes ◽  
Transitive Action ◽  
Isomorphism Classes ◽  
Finite Dimensional ◽  
Group A ◽  
Holomorphic Bundles ◽  
Invariant Gauge

AbstractLet X be a differentiable manifold endowed with a transitive action α: A×X→X of a Lie group A. Let K be a Lie group. Under suitable technical assumptions, we give explicit classification theorems, in terms of explicit finite dimensional quotients, of three classes of objects:equivalence classes of α-invariant K-connections on X α-invariant gauge classes of K-connections on X, andα-invariant isomorphism classes of pairs (Q,P) consisting of a holomorphic Kℂ-bundle Q → X and a K-reduction P of Q (when X has an α-invariant complex structure).

Evaluating the sufficiency of proposed security measures in favour of building objects

2021 ◽  
Vol 12 (1) ◽  
pp. 66-66
Author(s):  
Josef Reitšpís ◽  
Jozefína Drotárová
Keyword(s):  
Limited Area ◽  
Security Measures ◽  
Exact Methods ◽  
Technical Standards ◽  
Security Environment ◽  
Intentional Actions ◽  
Protection Systems ◽  
Level Of Knowledge ◽  
Satisfactory Answer

Security is understood as one of the basic life needs of people. However, it is necessary to realize that security is a natural quality of the environment where people live and is designated as a security environment. The need for sacurity is part of implementing sacurity measures that are created in compliance with a certain level of knowledge and needs. The content of this process can be characterized as a set of answers to primary questions (What is to be protected? – protected interest, Why to protect?, What to protect from? – threats) and secondary questions (Who will provide the protection?, How will the protection be provided?, When will the protection be provided?, By means of what will the protection be provided?, What price will the protection be provided for? etc.). From this viewpoint it is necessary to pay attention primarily to the problems concerning property protection from intentional actions focusing on protecting a particular building onject. In case of building objects it is primarily about the protection of tangible and intangible properties that are part of a particular limited area (mostly a building object) that is in possession or administration of a particular state or a private subject. The issues are dealt with by legal regulations, technical standards and various technical books. These usually concentrate on a particular area, kind of a building object and/or environment. However, none of them focuses on the property protection in a complex way and does not provide a satisfactory answer to the question "How to create protection systems in view of their sufficiency, complexity and balance in the technical and economic spheres?" That is why it is a social interest to search for new standardized procedures based on exact methods by means of which it will be possible, in empiric or intuitive ways, to exactly evaluate the effectivness of the existing or proposed property protection systems, including the formal desposition of results in project solutions Keywords: Project, Project documentation, Attack, Intervention and Detection time, Resistance of a building object, Modeling, Simulating

scholarly journals CATEGORIFICATION OF QUANTUM GENERALIZED KAC–MOODY ALGEBRAS AND CRYSTAL BASES

2012 ◽  
Vol 23 (11) ◽  
pp. 1250116 ◽  
Author(s):  
SEOK-JIN KANG ◽  
SE-JIN OH ◽  
EUIYONG PARK
Keyword(s):  
Crystal Structures ◽  
Grothendieck Group ◽  
Integral Form ◽  
Cartan Matrix ◽  
Algebra Homomorphism ◽  
Finitely Generated ◽  
Moody Algebra ◽  
Graded Modules ◽  
Isomorphism Classes ◽  
Highest Weight

We construct and investigate the structure of the Khovanov-Lauda–Rouquier algebras R and their cyclotomic quotients Rλ which give a categorification of quantum generalized Kac–Moody algebras. Let U𝔸(𝔤) be the integral form of the quantum generalized Kac–Moody algebra associated with a Borcherds–Cartan matrix A = (aij)i, j ∈ I and let K0(R) be the Grothendieck group of finitely generated projective graded R-modules. We prove that there exists an injective algebra homomorphism [Formula: see text] and that Φ is an isomorphism if aii ≠ 0 for all i ∈ I. Let B(∞) and B(λ) be the crystals of [Formula: see text] and V(λ), respectively, where V(λ) is the irreducible highest weight Uq(𝔤)-module. We denote by 𝔅(∞) and 𝔅(λ) the isomorphism classes of irreducible graded modules over R and Rλ, respectively. If aii ≠ 0 for all i ∈ I, we define the Uq(𝔤)-crystal structures on 𝔅(∞) and 𝔅(λ), and show that there exist crystal isomorphisms 𝔅(∞) ≃ B(∞) and 𝔅(λ) ≃ B(λ). One of the key ingredients of our approach is the perfect basis theory for generalized Kac–Moody algebras.

scholarly journals XXVIII. A further account of the case of William Carey, whose muscles began to be ossified: In a letter to the Right Honourable the Lord Cadogan, F. R. S. from the Rev. William Henry, D. D. F. R. S

1761 ◽  
Vol 52 ◽  
pp. 143-145
Keyword(s):  
Considerable Distance ◽  
Satisfactory Answer ◽  
The Right

My Lord, I Should have long before this time acknowledged your Lordship's Letter, of the 19th of February, and your inquiries concerning William Carey, the ossified young man; but as your letter came to me in the country, where I was at a considerable distance from all opportunities of making a full and satisfactory inquiry, I judged, that it would be more acceptable to your Lordship, that I should defer giving you trouble, until I could give you a satisfactory answer.

scholarly journals Locally soluble groups with min-n.

1974 ◽  
Vol 17 (3) ◽  
pp. 305-318 ◽  
Author(s):  
H. Heineken ◽  
J. S. Wilson
Keyword(s):  
Soluble Group ◽  
Free Groups ◽  
Torsion Group ◽  
Minimal Condition ◽  
Normal Subgroups ◽  
Soluble Groups ◽  
Isomorphism Classes ◽  
Torsion Groups ◽  
Torsion Free ◽  
General Method

It was shown by Baer in [1] that every soluble group satisfying Min-n, the minimal condition for normal subgroups, is a torsion group. Examples of non-soluble locally soluble groups satisfying Min-n have been known for some time (see McLain [2]), and these examples too are periodic. This raises the question whether all locally soluble groups with Min-n are torsion groups. We prove here that this is not the case, by establishing the existence of non-trivial locally soluble torsion-free groups satisfying Min-n. Rather than exhibiting one such group G, we give a general method for constructing examples; the reader will then be able to see that a variety of additional conditions may be imposed on G. It will follow, for instance, that G may be a Hopf group whose normal subgroups are linearly ordered by inclusion and are all complemented in G; further, that the countable groups G with these properties fall into exactly isomorphism classes. Again, there are exactly isomorphism classes of countable groups G which have hypercentral nonnilpotent Hirsch-Plotkin radical, and which at the same time are isomorphic to all their non-trivial homomorphic images.

Random Dieudonné modules, random -divisible groups, and random curves over finite fields

2013 ◽  
Vol 12 (3) ◽  
pp. 651-676 ◽  
Author(s):  
Bryden Cais ◽  
Jordan S. Ellenberg ◽  
David Zureick-Brown
Keyword(s):  
Probability Distribution ◽  
Finite Field ◽  
Random Matrix ◽  
Hyperelliptic Curve ◽  
Hyperelliptic Curves ◽  
Plane Curves ◽  
Random Curves ◽  
Isomorphism Classes ◽  
Curves Over Finite Fields ◽  
Divisible Groups

AbstractWe describe a probability distribution on isomorphism classes of principally quasi-polarized $p$-divisible groups over a finite field $k$ of characteristic $p$ which can reasonably be thought of as a ‘uniform distribution’, and we compute the distribution of various statistics ($p$-corank, $a$-number, etc.) of $p$-divisible groups drawn from this distribution. It is then natural to ask to what extent the $p$-divisible groups attached to a randomly chosen hyperelliptic curve (respectively, curve; respectively, abelian variety) over $k$ are uniformly distributed in this sense. This heuristic is analogous to conjectures of Cohen–Lenstra type for $\text{char~} k\not = p$, in which case the random $p$-divisible group is defined by a random matrix recording the action of Frobenius. Extensive numerical investigation reveals some cases of agreement with the heuristic and some interesting discrepancies. For example, plane curves over ${\mathbf{F} }_{3} $ appear substantially less likely to be ordinary than hyperelliptic curves over ${\mathbf{F} }_{3} $.

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