Regularity of Iterative Hairpin Completions of Crossing (2, 2)-Words

2016 ◽  
Vol 27 (03) ◽  
pp. 375-389 ◽  
Author(s):  
Kayoko Shikishima-Tsuji
Keyword(s):  
Regular Language ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Formal Operation ◽  
One Step ◽  
The One ◽  
Necessary And Sufficient ◽  
Open Question ◽  
Context Free

Hairpin completion is a formal operation inspired from DNA biochemistry. It is known that the (one step) hairpin completion of a regular language is linear context-free, but not regular in general. Further, it is decidable whether the (one step) hairpin completion of a regular language is regular. However, it is an open question whether the iterated hairpin completion of a regular language is regular, even if it is a singleton. If the word is a non-crossing α-word, there are results, but for crossing words there are no results. In this paper, we give necessary and sufficient conditions that the iterated hairpin completion of a given crossing (2, 2)-α-word in [Formula: see text] is regular.

scholarly journals ON HYBRID SEQUENCES BUILT FROM NIEDERREITER–HALTON SEQUENCES AND KRONECKER SEQUENCES

2011 ◽  
Vol 84 (2) ◽  
pp. 238-254 ◽  
Author(s):  
ROSWITHA HOFER ◽  
PETER KRITZER
Keyword(s):  
Uniform Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
The Other ◽  
Future Research ◽  
Short Summary ◽  
The One ◽  
Halton Sequences ◽  
Necessary And Sufficient

AbstractWe discuss the distribution properties of hybrid sequences whose components stem from Niederreiter–Halton sequences on the one hand, and Kronecker sequences on the other. In this paper, we give necessary and sufficient conditions on the uniform distribution of such sequences, and derive a result regarding their discrepancy. We conclude with a short summary and a discussion of topics for future research.

Answerability

2018 ◽  
Author(s):  
Natalie Stoljar
Keyword(s):  
Moral Responsibility ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
The Other ◽  
Alternative Approach ◽  
The One ◽  
Necessary And Sufficient

This chapter defends externalist or “constitutively relational” conceptions of autonomy through an examination of an alternative approach developed by Andrea Westlund. Westlund develops her approach in response to what has been called the “agency dilemma.” On the one hand, constraining external circumstances seem to undermine autonomy; on the other, the claim that people are nonautonomous because of their circumstances seems to erase their agency and disrespect their evaluative commitments. This chapter distinguishes the necessary and sufficient conditions of several interrelated aspects of agency: autonomy, authentic agential perspective, and moral responsibility. I argue that whereas answerability may be sufficient for moral responsibility, it is not sufficient for autonomy. Objections to externalist conceptions of autonomy, including the agency dilemma, wrongly assume that denying autonomy implies erasing agency. Once it is recognized that autonomy does not always overlap with authentic agential perspective or moral responsibility, the objections lose their force.

scholarly journals Deciding eventual positivity of polynomials

1986 ◽  
Vol 6 (1) ◽  
pp. 57-79 ◽  
Author(s):  
David Handelman
Keyword(s):  
Positive Integer ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Positive Orthant ◽  
Newton Polyhedra ◽  
The One ◽  
Necessary And Sufficient

AbstractLet P and f be polynomials in several (real) variables, with P having no negative coefficients. We give necessary and sufficient conditions for there to exist a positive integer n with Pnf having no negative coefficients; roughly speaking, the conditions involve the behaviour of f as a function on the positive orthant, together with its behaviour on a boundary constructed from the supporting monomials of P. This completes a series of results due to Poincaré (1883), Meissner (1911), and Polyà (1927). The former discusses the one variable case, the latter two deal with the situation that the Newton polyhedra of both P and f be, respectively, standard hypercubes, standard simplices.

Paternalism and the Justification of Compulsory Education

1983 ◽  
Vol 27 (2) ◽  
pp. 137-150 ◽  
Author(s):  
Peter Hobson
Keyword(s):  
Sufficient Conditions ◽  
Compulsory Education ◽  
Necessary And Sufficient Conditions ◽  
The Other ◽  
Welfare Of The Child ◽  
The One ◽  
Necessary And Sufficient

This paper examines at a philosophical level the justification for making education compulsory, concentrating on those arguments based on the welfare of the child. These arguments rest on the principle of paternalism which, as a form of interference with a person's liberty, is distinguished from such interferences based on concern for the welfare of society on the one hand and with upholding a moral or religious principle on the other. After noting the dangers involved in the use of paternalism, possible ways of determining when it is justified are examined prior to presenting what this author holds to be the two necessary and sufficient conditions for justified paternalism. After some discussion and amplification of these conditions, they are applied to the case of compulsory education. It is found that they are satisfied in this case but only with regard to education up to a certain level. The paper ends by attempting to answer some possible objections to the argument presented.

scholarly journals CENTER PROBLEM FOR THIRD-ORDER ODEs

2013 ◽  
Vol 23 (05) ◽  
pp. 1350078 ◽  
Author(s):  
ADAM MAHDI
Keyword(s):  
Center Manifold ◽  
Sufficient Conditions ◽  
Positive Answer ◽  
Necessary And Sufficient Conditions ◽  
Center Problem ◽  
Local Center ◽  
Third Order ◽  
Quadratic Systems ◽  
Necessary And Sufficient ◽  
Open Question

We obtain necessary and sufficient conditions for the existence of a center on a local center manifold for three 4-parameter families of quadratic systems on ℝ3. We also give a positive answer to an open question posed in [Dias & Mello, 2010] related to similar systems.

Interpolation problems for ideals in nest algebras

1992 ◽  
Vol 111 (1) ◽  
pp. 151-160 ◽  
Author(s):  
M. Anoussis ◽  
E. G. Katsoulis ◽  
R. L. Moore ◽  
T. T. Trent
Keyword(s):  
Hilbert Space ◽  
Interpolation Problem ◽  
Bounded Operator ◽  
Sufficient Conditions ◽  
Compact Operators ◽  
Necessary And Sufficient Conditions ◽  
Nest Algebras ◽  
Interpolation Problems ◽  
The One ◽  
Necessary And Sufficient

AbstractGiven vectors x and y in a Hilbert space, an interpolating operator is a bounded operator T such that Tx = y. An interpolating operator for n vectors satisfies the equation Txt = yt, for i = 1, 2,, n. In this article, we continue the investigation of the one-vector interpolation problem for nest algebras that was begun by Lance. In particular, we require the interpolating operator to belong to certain ideals which have proved to be of importance in the study of nest algebras, namely, the compact operators, the radical, Larson's ideal, and certain other ideals. We obtain necessary and sufficient conditions for interpolation in each of these cases.

Two-weight weak and extra-weak type inequalities for the one-sided maximal operator

1993 ◽  
Vol 123 (6) ◽  
pp. 1109-1118
Author(s):  
Pedro Ortega Salvador ◽  
Luboš Pick
Keyword(s):  
Maximal Operator ◽  
Weak Type ◽  
Orlicz Spaces ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Weight Functions ◽  
The One ◽  
Image Position ◽  
Necessary And Sufficient

SynopsisLet be the one-sided maximal operator and let Ф be a convex non-decreasing function on (0, ∞), Ф(0) = 0. We present necessary and sufficient conditions on a couple of weight functions (σ, ϱ) such that the integral inqualities of weak typeand of extra-weak typehold. Our proofs do not refer to the theory of Orlicz spaces.

scholarly journals The game chromatic number of trees and forests

2015 ◽  
Vol Vol. 17 no.2 (Graph Theory) ◽  
Author(s):  
Charles Dunn ◽  
Victor Larsen ◽  
Kira Lindke ◽  
Troy Retter ◽  
Dustin Toci
Keyword(s):  
Computational Complexity ◽  
Chromatic Number ◽  
Polynomial Time ◽  
Maximum Degree ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Game Chromatic Number ◽  
International Audience ◽  
Necessary And Sufficient ◽  
Open Question

International audience While the game chromatic number of a forest is known to be at most 4, no simple criteria are known for determining the game chromatic number of a forest. We first state necessary and sufficient conditions for forests with game chromatic number 2 and then investigate the differences between forests with game chromatic number 3 and 4. In doing so, we present a minimal example of a forest with game chromatic number 4, criteria for determining in polynomial time the game chromatic number of a forest without vertices of degree 3, and an example of a forest with maximum degree 3 and game chromatic number 4. This gives partial progress on the open question of the computational complexity of the game chromatic number of a forest.

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