scholarly journals The Alternation Hierarchy for the Theory of mu-lattices

2000 ◽  
Vol 7 (29) ◽  
Author(s):  
Luigi Santocanale
Keyword(s):  
Fixed Point ◽  
Fixed Number ◽  
Hierarchy Problem ◽  
Explicit Characterization

The alternation hierarchy problem asks whether every mu-term,<br />that is a term built up using also a least fixed point constructor<br />as well as a greatest fixed point constructor, is equivalent to a<br />mu-term where the number of nested fixed point of a different type<br />is bounded by a fixed number.<br />In this paper we give a proof that the alternation hierarchy<br />for the theory of mu-lattices is strict, meaning that such number<br />does not exist if mu-terms are built up from the basic lattice <br />operations and are interpreted as expected. The proof relies on the<br />explicit characterization of free mu-lattices by means of games and<br />strategies.

scholarly journals Fixed Points of the Evacuation of Maximal Chains on Fuss Shapes

10.37236/6898 ◽  
2018 ◽  
Vol 25 (1) ◽  
Author(s):  
Sen-Peng Eu ◽  
Tung-Shan Fu ◽  
Hsiang-Chun Hsu ◽  
Yu-Pei Huang
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Hasse Diagram ◽  
Linear Extensions ◽  
Rectangular Shape ◽  
Explicit Characterization ◽  
Finite Poset ◽  
Maximal Chains

For a partition $\lambda$ of an integer, we associate $\lambda$ with a slender poset $P$ the Hasse diagram of which resembles the Ferrers diagram of $\lambda$. Let $X$ be the set of maximal chains of $P$. We consider Stanley's involution $\epsilon:X\rightarrow X$, which is extended from Schützenberger's evacuation on linear extensions of a finite poset. We present an explicit characterization of the fixed points of the map $\epsilon:X\rightarrow X$ when $\lambda$ is a stretched staircase or a rectangular shape. Unexpectedly, the fixed points have a nice structure, i.e., a fixed point can be decomposed in half into two chains such that the first half and the second half are the evacuation of each other. As a consequence, we prove anew Stembridge's $q=-1$ phenomenon for the maximal chains of $P$ under the involution $\epsilon$ for the restricted shapes.

Microbrook, Mesobrook, Macrobrook

2019 ◽  
Vol 2 (4) ◽  
pp. 245-253 ◽  
Author(s):  
Sebastian Jilke ◽  
Asmus Leth Olsen ◽  
William Resh ◽  
Saba Siddiki
Keyword(s):  
Problem Solving ◽  
Public Administration ◽  
Theory And Practice ◽  
Levels Of Analysis ◽  
Explicit Characterization ◽  
Methodological Perspective ◽  
Level Of Analysis ◽  
Effective Problem

Abstract This article assesses the field of public administration from a conceptual and methodological perspective. We urge public administration scholars to resolve the ambiguities that mire our scholarship due to the inadequate treatment of levels of analysis in our research. Overall, we encourage methodological accountability through a more explicit characterization of one’s research by the level of analysis to which it relates. We argue that this particular form of accountability is critical for effective problem solving for advancing theory and practice.

scholarly journals Controllability of Continuous Bimodal Linear Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
Josep Ferrer ◽  
Juan R. Pacha ◽  
Marta Peña
Keyword(s):  
Linear Systems ◽  
Higher Dimensions ◽  
Linear Dynamics ◽  
Explicit Characterization ◽  
Separating Hyperplane

We consider bimodal linear systems consisting of two linear dynamics acting on each side of a given hyperplane, assuming continuity along the separating hyperplane. We prove that the study of controllability can be reduced to the unobservable case, and for these ones we obtain a simple explicit characterization of controllability for dimensions 2 and 3, as well as some partial criteria for higher dimensions.

scholarly journals Point configurations, phylogenetic trees, and dissimilarity vectors

2021 ◽  
Vol 118 (12) ◽  
pp. e2021244118
Author(s):  
Alessio Caminata ◽  
Noah Giansiracusa ◽  
Han-Bom Moon ◽  
Luca Schaffler
Keyword(s):  
Phylogenetic Trees ◽  
Geometric Interpretation ◽  
Explicit Characterization ◽  
Point Configurations ◽  
Definition Of ◽  
Tropical Basis ◽  
The Way

In 2004, Pachter and Speyer introduced the higher dissimilarity maps for phylogenetic trees and asked two important questions about their relation to the tropical Grassmannian. Multiple authors, using independent methods, answered affirmatively the first of these questions, showing that dissimilarity vectors lie on the tropical Grassmannian, but the second question, whether the set of dissimilarity vectors forms a tropical subvariety, remained opened. We resolve this question by showing that the tropical balancing condition fails. However, by replacing the definition of the dissimilarity map with a weighted variant, we show that weighted dissimilarity vectors form a tropical subvariety of the tropical Grassmannian in exactly the way that Pachter and Speyer envisioned. Moreover, we provide a geometric interpretation in terms of configurations of points on rational normal curves and construct a finite tropical basis that yields an explicit characterization of weighted dissimilarity vectors.

A Characterization of the Compound-Exponential Type Distributions

2011 ◽  
Vol 54 (3) ◽  
pp. 464-471
Author(s):  
Tea-Yuan Hwang ◽  
Chin-Yuan Hu
Keyword(s):  
Fixed Point ◽  
Exponential Type ◽  
Existence And Uniqueness ◽  
Fixed Point Equation ◽  
Point Equation

AbstractIn this paper, a fixed point equation of the compound-exponential type distributions is derived, and under some regular conditions, both the existence and uniqueness of this fixed point equation are investigated. A question posed by Pitman and Yor can be partially answered by using our approach.

A Characterization of the Hughes Planes

1965 ◽  
Vol 17 ◽  
pp. 916-922 ◽  
Author(s):  
T. G. Ostrom
Keyword(s):  
Fixed Point ◽  
Projective Plane ◽  
Related Notion ◽  
Fixed Line

Baer (1) introduced the term "(p,L)-collineation" to denote a central collineation with centre p and axis L. We shall find it convenient to use a modification of the related notion of "(p, L)-transitivity."Definition. Let π0 be a subplane of the projective plane π. Let L be a fixed line of π0, and let p be a fixed point of π0. Let r and s be any two points of π0 that are collinear with p, distinct from p, and not on L. If, for each such choice of r and s, there is a (p, L)-collineation of π that (1) carries π0 into itself and (2) carries r into s, we shall say that π is (p, L, π0)-transitive.

Knowledge Management Ontology

2011 ◽  
pp. 397-402 ◽  
Author(s):  
Clyde W. Holsapple ◽  
K. D. Joshi
Keyword(s):  
Knowledge Management ◽  
Explicit Characterization

Many definitions of ontology are posited in the literature (see Guarino, 2004). Here, we adopt Gruber’s (1995) view which defines ontologies as simplified and explicit specification of a phenomenon. In this article, we posit an ontology that explicates the components of knowledge management (KM) phenomena. This explicit characterization of knowledge management can help in systematically understanding or modeling KM phenomenon.

Supercuspidal representations and preservation principle of theta correspondence

2019 ◽  
Vol 2019 (750) ◽  
pp. 1-52
Author(s):  
Shu-Yen Pan
Keyword(s):  
Unitary Group ◽  
Orthogonal Group ◽  
Classical Groups ◽  
Theta Correspondence ◽  
Dual Pairs ◽  
Supercuspidal Representations ◽  
Explicit Characterization ◽  
A Chain

Abstract The preservation principle of the local theta correspondence predicts the existence of a chain of irreducible supercuspidal representations of p-adic classical groups. In this paper, we give an explicit characterization of the chain starting from an irreducible supercuspidal representations of a unitary group of one variable or an orthogonal group of two variables. In particular, we define the Lusztig-like correspondence of generic cuspidal data for p-adic groups and establish its relation with local theta correspondence of supercuspidal representations for p-adic dual pairs.

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