Generalized reduction theorems for model-theoretic analogs of the class of coanalytic sets

1993 ◽  
Vol 58 (1) ◽  
pp. 81-98
Author(s):  
Shaughan Lavine
Keyword(s):  
Pairwise Disjoint ◽  
Admissible Set ◽  
Effective Version ◽  
Reduction Property ◽  
Uniformization Property ◽  
Weakly Stable

AbstractLet be an admissible set. A sentence of the form is a sentence if φ ∈ (φ is ∨ Φ where Φ is an -r.e. set of sentences from ). A sentence of the form is an , sentence if φ is a sentence. A class of structures is, for example, a ∀1 class if it is the class of models of a ∀1() sentence. Thus ∀1() is a class of classes of structures, and so forth.Let i, be the structure 〈i, <〉, for i > 0. Let Γ be a class of classes of structures. We say that a sequence J1, …, Ji,…, i < ω, of classes of structures is a Γ sequence if Ji ∈ Γ, i < ω, and there is I ∈ Γ such that ∈ Ji, if and only if [],i, where [,] is the disjoint sum. A class Γ of classes of structures has the easy uniformization property if for every Γ sequence J1,…, Ji,…, i < ω, there is a Γ sequence J′t, …, J′i, …, i < ω, such that J′i ⊆ Ji, i < ω, ⋃J′i = ⋃Ji, and the J′i are pairwise disjoint. The easy uniformization property is an effective version of Kuratowski's generalized reduction property that is closely related to Moschovakis's (topological) easy uniformization property.We show over countable structures that ∀1() and ∃2() have the easy uniformization property if is a countable admissible set with an infinite member, that and have the easy uniformization property if α is countable, admissible, and not weakly stable, and that and have the easy uniformization properly. The results proved are more general. The result for answers a question of Vaught(1980).

Low-Reynolds-number flow around an oscillating circular cylinder at low Keulegan–Carpenter numbers

1998 ◽  
Vol 360 ◽  
pp. 249-271 ◽  
Author(s):  
H. DÜTSCH ◽  
F. DURST ◽  
S. BECKER ◽  
H. LIENHART
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Time Step ◽  
Time Resolved ◽  
Reynolds Number Flow ◽  
Line Force ◽  
Number Flow ◽  
Weakly Stable ◽  
Fluid Behaviour ◽  
Good Agreement

Time-averaged LDA measurements and time-resolved numerical flow predictions were performed to investigate the laminar flow induced by the harmonic in-line oscillation of a circular cylinder in water at rest. The key parameters, Reynolds number Re and Keulegan–Carpenter number KC, were varied to study three parameter combinations in detail. Good agreement was observed for Re=100 and KC=5 between measurements and predictions comparing phase-averaged velocity vectors. For Re=200 and KC=10 weakly stable and non-periodic flow patterns occurred, which made repeatable time-averaged measurements impossible. Nevertheless, the experimentally visualized vortex dynamics was reproduced by the two-dimensional computations. For the third combination, Re=210 and KC=6, which refers to a totally different flow regime, the computations again resulted in the correct fluid behaviour. Applying the widely used model of Morison et al. (1950) to the computed in-line force history, the drag and the added-mass coefficients were calculated and compared for different grid levels and time steps. Using these to reproduce the force functions revealed deviations from those originally computed as already noted in previous studies. They were found to be much higher than the deviations for the coarsest computational grid or the largest time step. The comparison of several in-line force coefficients with results obtained experimentally by Kühtz (1996) for β=35 confirmed that force predictions could also be reliably obtained by the computations.

scholarly journals Climatological Features of the Weakly and Very Stably Stratified Nocturnal Boundary Layers. Part II: Regime Occupation and Transition Statistics and the Influence of External Drivers

2019 ◽  
Vol 76 (11) ◽  
pp. 3485-3504 ◽  
Author(s):  
Carsten Abraham ◽  
Adam H. Monahan
Keyword(s):  
Complex Terrain ◽  
Cloud Cover ◽  
Companion Paper ◽  
Statistical Features ◽  
Clear Sky ◽  
Cloud Coverage ◽  
Weakly Stable ◽  
Sky Conditions ◽  
Regime Transitions

Abstract In a companion paper hidden Markov model (HMM) analyses have been conducted to classify the nocturnal stably stratified boundary layer (SBL) into weakly stable (wSBL) and very stable (vSBL) conditions at different tower sites on the basis of long-term Reynolds-averaged mean data. The resulting HMM regime sequences allow analysis of long-term (climatological) SBL regime statistics. In particular, statistical features of very persistent wSBL and vSBL nights, in which a single regime lasts for the entire night, are contrasted with those of nights with SBL regime transitions. The occurrence of very persistent nights is seasonally dependent and more likely in homogeneous surroundings than in regions with complex terrain. When transitions occur, their timing is not seasonally dependent, but transitions are enhanced close to sunset (for land-based sites). The regime event durations depict remarkably similar distributions across all stations with peaks in transition likelihood approximately 1–2 h after a preceding transition. At Cabauw in the Netherlands, very persistent wSBL and vSBL nights are usually accompanied by overcast conditions with strong geostrophic winds Ugeo or clear-sky conditions with weak Ugeo, respectively. In contrast, SBL regime transitions can neither be linked to magnitudes in Ugeo and cloud coverage nor to specific tendencies in Ugeo. However, regime transitions can be initiated by changes in low-level cloud cover.

scholarly journals On the computation of planetary boundary-layer height using the bulk Richardson number method

2014 ◽  
Vol 7 (6) ◽  
pp. 2599-2611 ◽  
Author(s):  
Y. Zhang ◽  
Z. Gao ◽  
D. Li ◽  
Y. Li ◽  
N. Zhang ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Planetary Boundary Layer ◽  
Richardson Number ◽  
Potential Temperature ◽  
Bulk Richardson Number ◽  
Stable Boundary Layers ◽  
Stable Boundary ◽  
Field Campaigns ◽  
Weakly Stable

Abstract. Experimental data from four field campaigns are used to explore the variability of the bulk Richardson number of the entire planetary boundary layer (PBL), Ribc, which is a key parameter for calculating the PBL height (PBLH) in numerical weather and climate models with the bulk Richardson number method. First, the PBLHs of three different thermally stratified boundary layers (i.e., strongly stable boundary layers, weakly stable boundary layers, and unstable boundary layers) from the four field campaigns are determined using the turbulence method, the potential temperature gradient method, the low-level jet method, and the modified parcel method. Then for each type of boundary layer, an optimal Ribc is obtained through linear fitting and statistical error minimization methods so that the bulk Richardson method with this optimal Ribc yields similar estimates of PBLHs as the methods mentioned above. We find that the optimal Ribc increases as the PBL becomes more unstable: 0.24 for strongly stable boundary layers, 0.31 for weakly stable boundary layers, and 0.39 for unstable boundary layers. Compared with previous schemes that use a single value of Ribc in calculating the PBLH for all types of boundary layers, the new values of Ribc proposed by this study yield more accurate estimates of PBLHs.

Weakly Stable Relations and Inductive Limits ofC*-algebras

2003 ◽  
Vol 46 (4) ◽  
pp. 588-596
Author(s):  
Martha Salerno Monteiro
Keyword(s):  
Exact Representation ◽  
Approximate Representation ◽  
Inductive Limits ◽  
Weakly Stable ◽  
Formal Relations

AbstractWe show that ifAis a class ofC*-algebras for which the set of formal relationsRis weakly stable, thenRis weakly stable for the classBthat containsAand all the inductive limits that can be constructed with theC*-algebras inA.A set of formal relationsRis said to beweakly stablefor a classofC*-algebras if, in anyC*-algebra A ∈, close to an approximate representation of the setRinAthere is an exact representation ofRinA.

scholarly journals Weakly stable operators

1979 ◽  
Vol 70 (1) ◽  
pp. 170-179 ◽  
Author(s):  
Robert E O'Brien
Keyword(s):  
Weakly Stable

On stability of queueing networks with job deadlines

2003 ◽  
Vol 40 (2) ◽  
pp. 293-304 ◽  
Author(s):  
Amy R. Ward ◽  
Nicholas Bambos
Keyword(s):  
Sojourn Time ◽  
Queueing Networks ◽  
Single Server ◽  
Single Server Queue ◽  
Interesting Phenomenon ◽  
Single Node ◽  
Service Disciplines ◽  
Server Queue ◽  
Weakly Stable ◽  
Networks Of Queues

In this paper, we consider a single-server queue with stationary input, where each job joining the queue has an associated deadline. The deadline is a time constraint on job sojourn time and may be finite or infinite. If the job does not complete service before its deadline expires, it abandons the queue and the partial service it may have received up to that point is wasted. When the queue operates under a first-come-first served discipline, we establish conditions under which the actual workload process—that is, the work the server eventually processes—is unstable, weakly stable, and strongly stable. An interesting phenomenon observed is that in a nontrivial portion of the parameter space, the queue is weakly stable, but not strongly stable. We also indicate how our results apply to other nonidling service disciplines. We finally extend the results for a single node to acyclic (feed-forward) networks of queues with either per-queue or network-wide deadlines.

scholarly journals Nighttime wind and scalar variability within and above an Amazonian canopy

2018 ◽  
Vol 18 (5) ◽  
pp. 3083-3099 ◽  
Author(s):  
Pablo E. S. Oliveira ◽  
Otávio C. Acevedo ◽  
Matthias Sörgel ◽  
Anywhere Tsokankunku ◽  
Stefan Wolff ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Low Frequency ◽  
Amazon Forest ◽  
Stable Regime ◽  
Stable Conditions ◽  
Weakly Stable ◽  
The Stability ◽  
The Relationship ◽  
Temporal Windows ◽  
Scalar Variability

Abstract. Nocturnal turbulent kinetic energy (TKE) and fluxes of energy, CO2 and O3 between the Amazon forest and the atmosphere are evaluated for a 20-day campaign at the Amazon Tall Tower Observatory (ATTO) site. The distinction of these quantities between fully turbulent (weakly stable) and intermittent (very stable) nights is discussed. Spectral analysis indicates that low-frequency, nonturbulent fluctuations are responsible for a large portion of the variability observed on intermittent nights. In these conditions, the low-frequency exchange may dominate over the turbulent transfer. In particular, we show that within the canopy most of the exchange of CO2 and H2O happens on temporal scales longer than 100 s. At 80 m, on the other hand, the turbulent fluxes are almost absent in such very stable conditions, suggesting a boundary layer shallower than 80 m. The relationship between TKE and mean winds shows that the stable boundary layer switches from the very stable to the weakly stable regime during intermittent bursts of turbulence. In general, fluxes estimated with long temporal windows that account for low-frequency effects are more dependent on the stability over a deeper layer above the forest than they are on the stability between the top of the canopy and its interior, suggesting that low-frequency processes are controlled over a deeper layer above the forest.

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