scholarly journals ONE DIMENSIONAL T.T.T STRUCTURES

2014 ◽  
Vol 79 (3) ◽  
pp. 748-775
Author(s):  
DANIEL LOWENGRUB
Keyword(s):  
Topological Group ◽  
Finite Number ◽  
Group Structure ◽  
Connected Components ◽  
Elementary Extension ◽  
Connected Component ◽  
Dimensional Simplex ◽  
One Dimensional ◽  
The Relationship ◽  
Uniformly Bounded

AbstractIn this paper we analyze the relationship between o-minimal structures and the notion of ω-saturated one-dimensional t.t.t structures. We prove that if removing any point from such a structure splits it into more than one definably connected component then it must be a one-dimensional simplex of a finite number of o-minimal structures. In addition, we show that even if removing points doesn’t split the structure, additional topological assumptions ensure that the structure is locally o-minimal. As a corollary we obtain the result that if an ω-saturated one-dimensional t.t.t structure admits a topological group structure then it is locally o-minimal. We also prove that the number of connected components in a definable family is uniformly bounded, which implies that an elementary extension of an ω-saturated one-dimensional t.t.t structure is t.t.t as well.

On nth roots and infinitely divisible elements in a connected Lie group

1981 ◽  
Vol 89 (2) ◽  
pp. 293-299 ◽  
Author(s):  
M. McCrudden
Keyword(s):  
Topological Group ◽  
Finite Number ◽  
Lie Groups ◽  
Lie Group ◽  
Connected Components ◽  
Compact Lie Group ◽  
Infinitely Divisible ◽  
Closed Set ◽  
Image Position ◽  
Connected Lie Group

For any group G, x ∈ G and n ∈ ℕ (the natural numbers), leti.e. the set of all nth roots of x in G. If G is a Hausdorff topological group, then Rn(x, G) is a closed set in G, but may otherwise be quite complicated. However, as we have observed in (4), if G is a compact Lie group, then Rn(x, G) always has a finite number of connected components, and this result has led us to wonder about the connectedness properties of Rn(x, G) for other Lie groups G. Here is the result.

‘Each Song Was Just Like a Little Sermon’

2018 ◽  
Author(s):  
Isaac Land
Keyword(s):  
Nineteenth Century ◽  
Golden Age ◽  
Military Training ◽  
One Dimensional ◽  
National Pride ◽  
Recent Scholarship ◽  
The Relationship

This chapter is central to the volume’s chronological contentions, as its argument accounts for the specialized, one-dimensional Dibdin of ‘Tom Bowling’ that has endured into recent scholarship. Focusing on Dibdin’s posthumous reception, it examines the moral and rhetorical difficulties of repackaging Dibdin’s works for a Victorian sensibility; it explores the specifics of mid-century concert culture previously highlighted by Derek Scott and William Weber as central to changes in nineteenth-century taste and programming; and it develops the theme of nostalgia into a revelatory consideration of the relationship between new naval technologies, national pride, and military training, and the songs, people, and language of a remembered Napoleonic ‘golden age’—to which Dibdin proves to have been as central, in the Victorian imagination, as Nelson.

Effect of mechanical restraint on the rate of corrosion in concrete

1998 ◽  
Vol 25 (1) ◽  
pp. 81-86 ◽  
Author(s):  
N Hearn ◽  
J Aiello
Keyword(s):  
Mix Design ◽  
Concrete Repair ◽  
Accelerated Corrosion ◽  
One Dimensional ◽  
Mechanical Restraint ◽  
Corrosion Rates ◽  
Accelerated Corrosion Tests ◽  
The Matrix ◽  
The Relationship

Experimental work on prismatic concrete specimens was conducted to determine the relationship between mechanical restraint and the rate of corrosion. The current together with the changes in strain of the confining frame were monitored during the accelerated corrosion tests. The effect of mix design and cracking on the corrosion rates was also investigated. The results show that one-dimensional mechanical restraint retards the corrosion process, as indicated by the reduction in the steel loss. Improved quality of the matrix, with and without cracking, reduces the rate of steel loss. In the inferior quality concrete, the effect of cracking on the corrosion rate is minimal.Key words: corrosion, concrete, repair.

Convexity of a discrete Carleman weighted objective functional in an inverse medium scattering problem

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Nguyen Trung Thành
Keyword(s):  
Finite Number ◽  
Scattering Problem ◽  
One Dimensional ◽  
Globally Convergent ◽  
Convergent Method ◽  
Inverse Medium ◽  
Inverse Medium Scattering ◽  
Objective Functional

AbstractWe investigate a globally convergent method for solving a one-dimensional inverse medium scattering problem using backscattering data at a finite number of frequencies. The proposed method is based on the minimization of a discrete Carleman weighted objective functional. The global convexity of this objective functional is proved.

scholarly journals A Novel Approach to the Analysis of the Soil Consolidation Problem by Using Non-Classical Rheological Schemes

2021 ◽  
Vol 11 (5) ◽  
pp. 1980
Author(s):  
Kazimierz Józefiak ◽  
Artur Zbiciak ◽  
Karol Brzeziński ◽  
Maciej Maślakowski
Keyword(s):  
Constitutive Models ◽  
Organic Soil ◽  
Organic Soils ◽  
Soil Consolidation ◽  
Flexible Tool ◽  
One Dimensional ◽  
Novel Approach ◽  
Soil Skeleton ◽  
The One ◽  
The Relationship

The paper presents classical and non-classical rheological schemes used to formulate constitutive models of the one-dimensional consolidation problem. The authors paid special attention to the secondary consolidation effects in organic soils as well as the soil over-consolidation phenomenon. The systems of partial differential equations were formulated for every model and solved numerically to obtain settlement curves. Selected numerical results were compared with standard oedometer laboratory test data carried out by the authors on organic soil samples. Additionally, plasticity phenomenon and non-classical rheological elements were included in order to take into account soil over-consolidation behaviour in the one-dimensional settlement model. A new way of formulating constitutive equations for the soil skeleton and predicting the relationship between the effective stress and strain or void ratio was presented. Rheological structures provide a flexible tool for creating complex constitutive relationships of soil.

scholarly journals Estimation for Two-Dimensional Nonsymmetric Coherently Distributed Source in L-Shaped Arrays

2018 ◽  
Vol 2018 ◽  
pp. 1-16
Author(s):  
Tao Wu ◽  
Zhenghong Deng ◽  
Qingyue Gu ◽  
Jiwei Xu
Keyword(s):  
Expectation Maximization ◽  
Two Dimensional ◽  
Signal Distribution ◽  
Distributed Source ◽  
One Dimensional ◽  
Least Squares Estimators ◽  
Iterative Calculation ◽  
Symmetric Source ◽  
Relationship Of ◽  
The Relationship

We explore the estimation of a two-dimensional (2D) nonsymmetric coherently distributed (CD) source using L-shaped arrays. Compared with a symmetric source, the modeling and estimation of a nonsymmetric source are more practical. A nonsymmetric CD source is established through modeling the deterministic angular signal distribution function as a summation of Gaussian probability density functions. Parameter estimation of the nonsymmetric distributed source is proposed under an expectation maximization (EM) framework. The proposed EM iterative calculation contains three steps in each cycle. Firstly, the nominal azimuth angles and nominal elevation angles of Gaussian components in the nonsymmetric source are obtained from the relationship of rotational invariance matrices. Then, angular spreads can be solved through one-dimensional (1D) searching based on nominal angles. Finally, the powers of Gaussian components are obtained by solving least-squares estimators. Simulations are conducted to verify the effectiveness of the nonsymmetric CD model and estimation technique.

The size of the connected components of excursion sets of χ2, t and F fields

1999 ◽  
Vol 31 (03) ◽  
pp. 579-595 ◽  
Author(s):  
J. Cao
Keyword(s):  
Positron Emission Tomography ◽  
Two Dimensions ◽  
Emission Tomography ◽  
Connected Components ◽  
Gaussian Fields ◽  
Connected Component ◽  
Test Statistic ◽  
Excursion Sets ◽  
Positron Emission ◽  
Excursion Set

The distribution of the size of one connected component and the largest connected component of the excursion set is derived for stationary χ2, t and F fields, in the limit of high or low thresholds. This extends previous results for stationary Gaussian fields (Nosko 1969, Adler 1981) and for χ2 fields in one and two dimensions (Aronowich and Adler 1986, 1988). An application of this is to detect regional changes in positron emission tomography (PET) images of blood flow in human brain, using the size of the largest connected component of the excursion set as a test statistic.

scholarly journals Land subsidence and hydrodynamic compaction of sedimentary basins

1998 ◽  
Vol 2 (2/3) ◽  
pp. 159-171 ◽  
Author(s):  
H. Kooi ◽  
J. J. de Vries
Keyword(s):  
Response Time ◽  
Land Subsidence ◽  
Sedimentary Basins ◽  
Sediment Loading ◽  
Dimensional Model ◽  
One Dimensional ◽  
Model Equations ◽  
Sediment Layers ◽  
The Relationship

Abstract. A one-dimensional model is used to investigate the relationship between land subsidence and compaction of basin sediments in response to sediment loading. Analysis of the model equations and numerical experiments demonstrate quasi-linear systems behaviour and show that rates of land subsidence due to compaction: (i) can attain a significant fraction (>40%) of the long-term sedimentation rate; (ii) are hydrodynamically delayed with respect to sediment loading. The delay is controlled by a compaction response time τc that can reach values of 10-5-107 yr for thick shale sequences. Both the behaviour of single sediment layers and multiple-layer systems are analysed. Subsequently the model is applied to the coastal area of the Netherlands to illustrate that lateral variability in compaction-derived land subsidence in sedimentary basins largely reflects the spatial variability in both sediment loading and compaction response time. Typical rates of compaction-derived subsidence predicted by the model are of the order of 0.1 mm/yr but may reach values in excess of 1 mm/yr under favourable conditions.

scholarly journals More on generalized topological groups

2013 ◽  
Vol 22 (1) ◽  
pp. 47-51
Author(s):  
MURAD HUSSAIN ◽  
◽  
MOIZ UD DIN KHAN ◽  
CENAP OZEL ◽  
◽  
...  
Keyword(s):  
Topological Group ◽  
Group Structure ◽  
Topological Groups

In the paper [Hussain, M., Khan, M. and Ozel, C., ¨ On Generalized Topological Groups] we defined the generalized topological group structure and we proved some basic results. In this work we introduce the notions of ultra Hausdorffness and ultra G-Hausdorffness and we give the relation between the ultra G-Hausdorffness and G-compactness.

scholarly journals On 2-Diffeomorphisms with One-Dimensional Basic Sets and a Finite Number of Moduli

2016 ◽  
Vol 16 (4) ◽  
pp. 727-749
Author(s):  
V. Z. Grines ◽  
Z. Grines ◽  
S. Van Strien
Keyword(s):  
Finite Number ◽  
One Dimensional ◽  
Basic Sets
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