scholarly journals Singularities at a dense set of temperature singularities in the Husimi tree

1998 ◽  
Vol 57 (2) ◽  
pp. 2452-2454 ◽  
Author(s):  
A. E. Alahverdian ◽  
N. S. Ananikian ◽  
S. K. Dallakian
Keyword(s):  
Husimi Tree ◽  
Dense Set

Generic rotation sets

2020 ◽  
pp. 1-13
Author(s):  
SEBASTIÁN PAVEZ-MOLINA
Keyword(s):  
Dynamical System ◽  
Convex Body ◽  
Probability Measures ◽  
Topological Dynamical System ◽  
Continuous Vector ◽  
Rotation Set ◽  
Vector Valued Function ◽  
Vector Valued ◽  
Uniquely Ergodic ◽  
Dense Set

Abstract Let $(X,T)$ be a topological dynamical system. Given a continuous vector-valued function $F \in C(X, \mathbb {R}^{d})$ called a potential, we define its rotation set $R(F)$ as the set of integrals of F with respect to all T-invariant probability measures, which is a convex body of $\mathbb {R}^{d}$ . In this paper we study the geometry of rotation sets. We prove that if T is a non-uniquely ergodic topological dynamical system with a dense set of periodic measures, then the map $R(\cdot )$ is open with respect to the uniform topologies. As a consequence, we obtain that the rotation set of a generic potential is strictly convex and has $C^{1}$ boundary. Furthermore, we prove that the map $R(\cdot )$ is surjective, extending a result of Kucherenko and Wolf.

scholarly journals Structure theorems in tame expansions of o-minimal structures by a dense set

2020 ◽  
Vol 239 (1) ◽  
pp. 435-500 ◽  
Author(s):  
Pantelis E. Eleftheriou ◽  
Ayhan Günaydin ◽  
Philipp Hieronymi
Keyword(s):  
Structure Theorems ◽  
Dense Set

Large deletions of the PROS1 gene in a large fraction of mutation-negative patients with protein S deficiency

2005 ◽  
Vol 94 (11) ◽  
pp. 951-957 ◽  
Author(s):  
Andreas Hillarp ◽  
Torbjörn Säll ◽  
Bengt Zöller ◽  
Björn Dahlbäck ◽  
Christer Halldén ◽  
...  
Keyword(s):  
Haplotype Analysis ◽  
Large Fraction ◽  
Protein S ◽  
Protein S Deficiency ◽  
Autosomal Dominant Disorder ◽  
Detection Techniques ◽  
Large Deletions ◽  
S Deficiency ◽  
Normal Individuals ◽  
Dense Set

SummaryProtein S deficiency is an autosomal dominant disorder that results from mutations in the PROS1 gene. Conventional mutation detection techniques fail to detect a pathogenic PROS1 mutation in approximately 50% of cases. The present study investigates whether large deletions of PROS1 are found in families where mutations in the PROS1 gene have not been found despite sequencing. For this purpose, a dense set of SNP and microsatellite markers were used in segregation analysis to identify deletions. Large deletions were identified by this technique in three out of eight investigated families (38%). The deletions encompassed at least 35 kb, 437 kb and 449 kb respectively. The deletions were confirmed by quantitative PCR. Haplotype analysis showed that the three large deletions and the five other disease haplotypes were all different. All of the eight disease haplotypes co-segregated with protein S deficiency, but each of the five non-deletion haplotypes were present also in normal individuals. In conclusion: Large deletions of PROS1 are relatively common in protein S deficiency patients and screening for large deletions in PROS1 mutation-negative individuals are therefore warranted.

scholarly journals Dense set of negative Schwarzian maps whose critical points have minimal limit sets

1998 ◽  
Vol 4 (1) ◽  
pp. 141-158
Author(s):  
Alexander Blokh ◽  
◽  
Michał Misiurewicz ◽  
Keyword(s):  
Critical Points ◽  
Limit Sets ◽  
Dense Set

scholarly journals Nearly ordinary Galois deformations over arbitrary number fields

2008 ◽  
Vol 8 (1) ◽  
pp. 99-177 ◽  
Author(s):  
Frank Calegari ◽  
Barry Mazur
Keyword(s):  
Arbitrary Number ◽  
Quadratic Field ◽  
Galois Representations ◽  
Galois Representation ◽  
Number Fields ◽  
Base Change ◽  
Deformation Spaces ◽  
Totally Real ◽  
Set Of Points ◽  
Dense Set

AbstractLet K be an arbitrary number field, and let ρ : Gal($\math{\bar{K}}$/K) → GL2(E) be a nearly ordinary irreducible geometric Galois representation. In this paper, we study the nearly ordinary deformations of ρ. When K is totally real and ρ is modular, results of Hida imply that the nearly ordinary deformation space associated to ρ contains a Zariski dense set of points corresponding to ‘automorphic’ Galois representations. We conjecture that if K is not totally real, then this is never the case, except in three exceptional cases, corresponding to: (1) ‘base change’, (2) ‘CM’ forms, and (3) ‘even’ representations. The latter case conjecturally can only occur if the image of ρ is finite. Our results come in two flavours. First, we prove a general result for Artin representations, conditional on a strengthening of the Leopoldt Conjecture. Second, when K is an imaginary quadratic field, we prove an unconditional result that implies the existence of ‘many’ positive-dimensional components (of certain deformation spaces) that do not contain infinitely many classical points. Also included are some speculative remarks about ‘p-adic functoriality’, as well as some remarks on how our methods should apply to n-dimensional representations of Gal($\math{\bar{\QQ}}$/ℚ) when n > 2.

scholarly journals Partitions with independent iterates in random dynamical systems

2009 ◽  
Vol 30 (2) ◽  
pp. 361-377 ◽  
Author(s):  
BORIS BEGUN ◽  
ANDRÉS DEL JUNCO
Keyword(s):  
Dynamical Systems ◽  
Random Dynamical Systems ◽  
Weakly Mixing ◽  
Dense Set ◽  
Measure Preserving Actions

AbstractKrengel characterized weakly mixing actions (X,T) as those measure-preserving actions having a dense set of partitions of X with infinitely many jointly independent images under iterates of T. Using the tools developed in later papers—one by del Junco, Reinhold and Weiss, another by del Junco and Begun—we prove analogues of these results for weakly mixing random dynamical systems (in other words, relatively weakly mixing systems).

Unimolecular Dissociation from a Dense Set of States

1996 ◽  
Vol 100 (19) ◽  
pp. 7962-7971 ◽  
Author(s):  
F. Remacle ◽  
R. D. Levine
Keyword(s):  
Unimolecular Dissociation ◽  
Dense Set

A Second Construction of Autodual Objects

2012 ◽  
Author(s):  
Nicholas M. Katz
Keyword(s):  
Split Form ◽  
Dense Set

This chapter works on the split form 𝔾ₘ/k, Spec(k[x; 1/x]). It begins with a geometrically irreducible lisse sheaf Ƒ on an open dense set U ⊂ 𝔾ₘ which is ι‎-pure of weight zero and which is self-dual: Ƒ ≅ F with hook and macron.

Title XX Environment

2019 ◽  
Author(s):  
Sacha Garben
Keyword(s):  
Environmental Protection ◽  
Criminal Law ◽  
Policy Making ◽  
Environmental Law ◽  
Case Law ◽  
Legal Basis ◽  
Common Concern ◽  
Law And Policy ◽  
Dense Set ◽  
The Eu

The environment does not respect man-made borders, and is of common concern and interest of all mankind. As such, it is an area that merits and requires cross-border law and policy making par excellence. This should be reflected in the strong role played by the EU, which has a firm Treaty mandate and duty to protect the environment, features a rich body of case law, and boasts a dense set of secondary legislation. The very good reasons for this notwithstanding, it remains a remarkable development considering the absence of any reference to the environment in the original Treaties. Although a programme for action in this area was soon adopted in 1973, only in the 1986 SEA was an environmental legal basis introduced. Much of the initial environmental acquis was therefore developed by the Commission, the Council, and later the EP on the basis of other Treaty provisions, such as (now) Articles 114, 115, and 352 TFEU. EU environmental protection also owes a debt to the ECJ, which included it in the legitimate objectives on the basis of which MS could derogate from the free movement provisions. The Court has interpreted the provisions of EU environmental law generally in a protective manner, and endorsed the use of criminal law for the effective enforcement of EU environmental legislation.

Analytic Functions with an Irregular Linearly Measurable Set of Singular Points

1952 ◽  
Vol 4 ◽  
pp. 424-435 ◽  
Author(s):  
I. E. Glover
Keyword(s):  
Imaginary Part ◽  
Analytic Functions ◽  
Singular Points ◽  
Definite Integrals ◽  
Singular Sets ◽  
Dense Point ◽  
Point Set ◽  
Dense Point Set ◽  
Nowhere Dense Set ◽  
Dense Set

V. V. Golubev, in his study [6], has constructed, by using definite integrals, various examples of analytic functions having a perfect nowhere-dense set of singular points. These functions were shown to be single-valued with a bounded imaginary part. In attempting to extend his work to the problem of constructing analytic functions having perfect, nowhere-dense singular sets under quite general conditions, he posed the following question: Given an arbitrary, perfect, nowhere-dense point-set E of positive measure in the complex plane, is it possible to construct, by passing a Jordan curve through E and by using definite integrals, an example of a single-valued analytic function, which has E as its singular set, with its imaginary part bounded.

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