scholarly journals More about uniform upper bounds on ideals of turing degrees

1983 ◽  
Vol 48 (2) ◽  
pp. 441-457
Author(s):  
Harold T. Hodes
Keyword(s):  
Upper Bound ◽  
Upper Bounds ◽  
Turing Degrees ◽  
Trial And Error ◽  
Minimal Member

AbstractLet I be a countable jump ideal in = 〈The Turing degrees, ≤〉. The central theorem of this paper is:a is a uniform upper bound on I iff a computes the join of an I-exact pair whose double jump a(1) computes.We may replace “the join of an I-exact pair” in the above theorem by “a weak uniform upper bound on I”.We also answer two minimality questions: the class of uniform upper bounds on I never has a minimal member; if ⋃I = Lα[A] ⋂ ωω for α admissible or a limit of admissibles, the same holds for nice uniform upper bounds.The central technique used in proving these theorems consists in this: by trial and error construct a generic sequence approximating the desired object; simultaneously settle definitely on finite pieces of that object; make sure that the guessing settles down to the object determined by the limit of these finite pieces.

Upper bounds on locally countable admissible initial segments of a Turing degree hierarchy

1981 ◽  
Vol 46 (4) ◽  
pp. 753-760 ◽  
Author(s):  
Harold T. Hodes
Keyword(s):  
Upper Bound ◽  
Upper Bounds ◽  
Turing Degree ◽  
Turing Degrees ◽  
Locally Countable

AbstractWhere AR is the set of arithmetic Turing degrees, 0(ω) is the least member of {a(2) ∣ a is an upper bound on AR}. This situation is quite different if we examine HYP, the set of hyperarithmetic degrees. We shall prove (Corollary 1) that there is an a, an upper bound on HYP, whose hyperjump is the degree of Kleene's . This paper generalizes this example, using an iteration of the jump operation into the transfinite which is based on results of Jensen and is detailed in [3] and [4]. In § 1 we review the basic definitions from [3] which are needed to state the general results.

scholarly journals Uniform upper bounds on ideals of turing degrees

1978 ◽  
Vol 43 (3) ◽  
pp. 601-612 ◽  
Author(s):  
Harold T. Hodes
Keyword(s):  
Upper Bound ◽  
Upper Bounds ◽  
Turing Degrees ◽  
Hierarchy Theory ◽  
Countable Ordinal ◽  
Limit Ordinal ◽  
Theoretic Motivation ◽  
Increasing Function

Given I, a reasonable countable set of Turing degrees, can we find some sort of canonical strict upper bound on I? If I = {a ∣ a ≤ b}, the upper bound on I which springs to mind is b′. But what if I is closed under jump? This question arises naturally out of the question which motivates a large part of hierarchy theory: Is there a canonical increasing function from a countable ordinal, preferably a large one, into D, the set of Turing degrees? If d is to be such a function, it is natural to require that d(α + 1) = d(α)′; but how should d(λ) depend on d ↾ λ, where λ is a limit ordinal?For any I ⊆ D, let MI, = ⋃I. Towards making the above questions precise, we introduce ideals of Turing degrees.Definition 1. I ⊆ D is an ideal iff I is closed under jump and join, and I is downward-closed, i.e., if a ≤ b & b ϵ I then a ϵ I.The following definition reflects the hierarchy-theoretic motivation for this paper.Definition 2. For I ⊆ D and A ⊆ ω, I is an A-hierarchy ideal iff for some countable ordinal α, MI = Lα[A]∩ ωω.All hierarchy ideals are ideals, but not conversely.Early in the game Spector knocked out the best sort of canonicity for upper bounds on ideals, proving that no set of degrees closed under jump has a least upper bound.

Upper bounds on the energy dissipation in turbulent precession

1996 ◽  
Vol 321 ◽  
pp. 335-370 ◽  
Author(s):  
R. R. Kerswell
Keyword(s):  
Experimental Data ◽  
Energy Dissipation ◽  
Viscous Dissipation ◽  
Upper Bound ◽  
Dissipation Rate ◽  
Oblate Spheroid ◽  
Upper Bounds ◽  
Precession Rate ◽  
Long Cylinder

Rigorous upper bounds on the viscous dissipation rate are identified for two commonly studied precessing fluid-filled configurations: an oblate spheroid and a long cylinder. The latter represents an interesting new application of the upper-bounding techniques developed by Howard and Busse. A novel ‘background’ method recently introduced by Doering & Constantin is also used to deduce in both instances an upper bound which is independent of the fluid's viscosity and the forcing precession rate. Experimental data provide some evidence that the observed viscous dissipation rate mirrors this behaviour at sufficiently high precessional forcing. Implications are then discussed for the Earth's precessional response.

scholarly journals The Essential Dimension of Stacks of Parabolic Vector Bundles over Curves

2012 ◽  
Vol 10 (3) ◽  
pp. 455-488 ◽  
Author(s):  
Indranil Biswas ◽  
Ajneet Dhillon ◽  
Nicole Lemire
Keyword(s):  
Lower Bounds ◽  
Upper Bound ◽  
Vector Bundles ◽  
Upper Bounds ◽  
Essential Dimension ◽  
Parabolic Structure ◽  
Moduli Stack

AbstractWe find upper bounds on the essential dimension of the moduli stack of parabolic vector bundles over a curve. When there is no parabolic structure, we improve the known upper bound on the essential dimension of the usual moduli stack. Our calculations also give lower bounds on the essential dimension of the semistable locus inside the moduli stack of vector bundles of rank r and degree d without parabolic structure.

ances and covariances obtained from REML are normally distributed with expectation vector and variance-covariance matrix equal to the fol-low  ing, r  espectiv    ely,   When σˆ > 0.04, let νˆ = δˆ + σˆ + σˆ − 2ωˆ + σˆ − (1 + c (7.6) be an estimate for the (7.3) reference-scaled metric in accordance with FDA Guidance (2001) and using a REML UN model. Then (Patter-son, 2003; Patterson and Jones, 2002b), this estimate is asymptotically normally distributed and unbiased with E[νˆ ] = δ +σ − (1 + c and Var[νˆ ] = 4σ + l + 4l + (1 + c ) (l )+ 2l −2(1+c − 2(1+c +4(1+c −2(1+c . Similarly, for the constant-scaled metric, when σˆ ≤ 0.04, νˆ = δˆ + σˆ + σˆ − 2ωˆ + σˆ − σˆ − 0.04(c ) (7.7) E[νˆ ] = δ +σ − 0.04(c ) Var[νˆ ] = 4σ + l + 4l + 2l − 2l − 4l + 4l − 2l . The required asymptotic upper bound √ of the 90% confidence interval can √ then be calculated as νˆ + 1.645× V̂ ar[νˆ ] or νˆ + 1.645× V̂ ar[νˆ ], where the variances are obtained by ‘plugging in’ the estimated values of the variances and covariances obtained from SAS proc mixed into the formulae for Var[νˆ ] or Var[νˆ ]. The necessary SAS code to do this is given in Appendix B. The output reveals that σˆ = 0.0714 and the upper bound is−0.060 for log(AUC). For log(Cmax), σˆ = 0.1060 and the upper bound is −0.055. As both of these upper bounds are below zero, IBE can be claimed.

2003 ◽  
pp. 367-367
Keyword(s):  
Confidence Interval ◽  
Covariance Matrix ◽  
Upper Bound ◽  
Upper Bounds ◽  
Fda Guidance ◽  
Asymptotic Upper Bound ◽  
Variance Covariance Matrix ◽  
Normally Distributed

Models of arithmetic and upper bounds for arithmetic sets

1994 ◽  
Vol 59 (3) ◽  
pp. 977-983 ◽  
Author(s):  
Alistair H. Lachlan ◽  
Robert I. Soare
Keyword(s):  
Upper Bound ◽  
Upper Bounds ◽  
Models Of Arithmetic

AbstractWe settle a question in the literature about degrees of models of true arithmetic and upper bounds for the arithmetic sets. We prove that there is a model of true arithmetic whose degree is not a uniform upper bound for the arithmetic sets. The proof involves two forcing constructions.

Eventually infinite time Turing machine degrees: infinite time decidable reals

2000 ◽  
Vol 65 (3) ◽  
pp. 1193-1203 ◽  
Author(s):  
P.D. Welch
Keyword(s):  
Turing Machine ◽  
Initial Segment ◽  
Upper Bounds ◽  
Turing Degrees ◽  
Turing Machines ◽  
Jump Operator ◽  
Infinite Time

AbstractWe characterise explicitly the decidable predicates on integers of Infinite Time Turing machines, in terms of admissibility theory and the constructible hierarchy. We do this by pinning down ζ, the least ordinal not the length of any eventual output of an Infinite Time Turing machine (halting or otherwise); using this the Infinite Time Turing Degrees are considered, and it is shown how the jump operator coincides with the production of mastercodes for the constructible hierarchy; further that the natural ordinals associated with the jump operator satisfy a Spector criterion, and correspond to the Lζ-stables. It also implies that the machines devised are “Σ2 Complete” amongst all such other possible machines. It is shown that least upper bounds of an “eventual jump” hierarchy exist on an initial segment.

ON THE QUASI-STATIONARY DISTRIBUTION OF SIS MODELS

2016 ◽  
Vol 30 (4) ◽  
pp. 622-639 ◽  
Author(s):  
Gaofeng Da ◽  
Maochao Xu ◽  
Shouhuai Xu
Keyword(s):  
Stationary Distribution ◽  
Upper Bound ◽  
Hazard Rate ◽  
State Of The Art ◽  
Upper Bounds ◽  
Hazard Rate Order ◽  
Reversed Hazard Rate ◽  
Novel Method ◽  
Better Than ◽  
Quasi Stationary Distribution

In this paper, we propose a novel method for constructing upper bounds of the quasi-stationary distribution of SIS processes. Using this method, we obtain an upper bound that is better than the state-of-the-art upper bound. Moreover, we prove that the fixed point map Φ [7] actually preserves the equilibrium reversed hazard rate order under a certain condition. This allows us to further improve the upper bound. Some numerical results are presented to illustrate the results.

scholarly journals Upper bounds for geodesic periods over hyperbolic manifolds

2018 ◽  
Vol 29 (01) ◽  
pp. 1850009
Author(s):  
Feng Su
Keyword(s):  
Upper Bound ◽  
Upper Bounds ◽  
Hyperbolic Manifolds ◽  
Maass Forms ◽  
Maass Form ◽  
Ambient Manifold

We prove an upper bound for geodesic periods of Maass forms over hyperbolic manifolds. By definition, such periods are integrals of Maass forms restricted to a special geodesic cycle of the ambient manifold, against a Maass form on the cycle. Under certain restrictions, the bound will be uniform.

Injective Hulls of Semilattices

1970 ◽  
Vol 13 (1) ◽  
pp. 115-118 ◽  
Author(s):  
G. Bruns ◽  
H. Lakser
Keyword(s):  
Upper Bound ◽  
Partially Ordered Set ◽  
Binary Operation ◽  
Ordered Set ◽  
Upper Bounds ◽  
Partial Ordering ◽  
Partially Ordered ◽  
Image Position ◽  
Injective Hulls

A (meet-) semilattice is an algebra with one binary operation ∧, which is associative, commutative and idempotent. Throughout this paper we are working in the category of semilattices. All categorical or general algebraic notions are to be understood in this category. In every semilattice S the relationdefines a partial ordering of S. The symbol "∨" denotes least upper bounds under this partial ordering. If it is not clear from the context in which partially ordered set a least upper bound is taken, we add this set as an index to the symbol; for example, ∨AX denotes the least upper bound of X in the partially ordered set A.

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