Non-Selfadjoint Perturbations of Selfadjoint Operators in Two Dimensions IIIa. One Branching Point

2008 ◽  
Vol 60 (3) ◽  
pp. 572-657 ◽  
Author(s):  
Michael Hitrik ◽  
Johannes Sjöstrand
Keyword(s):  
Saddle Point ◽  
Pseudodifferential Operators ◽  
Two Dimensions ◽  
Spectral Asymptotics ◽  
Selfadjoint Operators ◽  
Asymptotic Description ◽  
The Third ◽  
Branching Point ◽  
Dimension 2

AbstractThis is the third in a series of works devoted to spectral asymptotics for non-selfadjoint perturbations of selfadjoint h-pseudodifferential operators in dimension 2, having a periodic classical flow. Assuming that the strength ॉ of the perturbation is in the range h2 ≪ ॉ ≪ h1/2 (and may sometimes reach even smaller values), we get an asymptotic description of the eigenvalues in rectangles [−1/C, 1/C] + iॉ[F0 − 1/C, F0 + 1/C], C ≫ 1, when ॉF0 is a saddle point value of the flow average of the leading perturbation.

Coping with longitudinal data in research on developmental psychopathology

2006 ◽  
Vol 30 (1) ◽  
pp. 20-25 ◽  
Author(s):  
David A. Cole
Keyword(s):  
Data Collection ◽  
Longitudinal Data ◽  
Developmental Psychopathology ◽  
Careful Consideration ◽  
Two Dimensions ◽  
The Other ◽  
Outcome Variable ◽  
The Third ◽  
Data Analytic ◽  
Over Time

Many outcome variables in developmental psychopathology research are highly stable over time. In conventional longitudinal data analytic approaches such as multiple regression, controlling for prior levels of the outcome variable often yields little (if any) reliable variance in the dependent variable for putative predictors to explain. Three strategies for coping with this problem are described. One involves focusing on developmental periods of transition, in which the outcome of interest may be less stable. A second is to give careful consideration to the amount of time allowed to elapse between waves of data collection. The third is to consider trait-state-occasion models that partition the outcome variable into two dimensions: one entirely stable and trait-like, the other less stable and subject to occasion-specific fluctuations.

Theory of Electron Diffraction by Crystals

1967 ◽  
Vol 22 (4) ◽  
pp. 422-431 ◽  
Author(s):  
Kyozaburo Kambe
Keyword(s):  
Integral Equation ◽  
Electron Diffraction ◽  
General Theory ◽  
Green’S Function ◽  
Green's Function ◽  
Scattering Problem ◽  
Three Dimensional ◽  
Two Dimensions ◽  
The Third ◽  
Third Dimension

A general theory of electron diffraction by crystals is developed. The crystals are assumed to be infinitely extended in two dimensions and finite in the third dimension. For the scattering problem by this structure two-dimensionally expanded forms of GREEN’S function and integral equation are at first derived, and combined in single three-dimensional forms. EWALD’S method is applied to sum up the series for GREEN’S function.

scholarly journals THE EFFECT OF THE THIRD DIMENSION ON ROUGH SURFACES FORMED BY SEDIMENTING PARTICLES IN QUASI-TWO-DIMENSIONS

2002 ◽  
Vol 16 (08) ◽  
pp. 1217-1223 ◽  
Author(s):  
K. V. MCCLOUD ◽  
M. L. KURNAZ
Keyword(s):  
Two Dimensions ◽  
Scaling Analysis ◽  
Silica Spheres ◽  
Two Dimensional ◽  
One Dimensional ◽  
The Third ◽  
Roughness Exponent ◽  
Third Dimension ◽  
Dimensional Cell ◽  
Roughness Exponents

The roughness exponent of surfaces obtained by dispersing silica spheres into a quasi-two-dimensional cell is examined. The cell consists of two glass plates separated by a gap, which is comparable in size to the diameter of the beads. Previous work has shown that the quasi-one-dimensional surfaces formed have two roughness exponents in two length scales, which have a crossover length about 1 cm. We have studied the effect of changing the gap between the plates to a limit of about twice the diameter of the beads. If the conventional scaling analysis is performed, the roughness exponent is found to be robust against changes in the gap between the plates; however, the possibility that scaling does not hold should be taken seriously.

scholarly journals Lattice reduction in two dimensions: analyses under realistic probabilistic models

2007 ◽  
Vol DMTCS Proceedings vol. AH,... (Proceedings) ◽  
Author(s):  
Brigitte Vallée ◽  
Antonio Vera
Keyword(s):  
Dynamical Systems ◽  
Probabilistic Models ◽  
Two Dimensions ◽  
Lattice Reduction ◽  
Lll Algorithm ◽  
Transfer Operators ◽  
International Audience ◽  
Dimension 2

International audience The Gaussian algorithm for lattice reduction in dimension 2 is precisely analysed under a class of realistic probabilistic models, which are of interest when applying the Gauss algorithm "inside'' the LLL algorithm. The proofs deal with the underlying dynamical systems and transfer operators. All the main parameters are studied: execution parameters which describe the behaviour of the algorithm itself as well as output parameters, which describe the geometry of reduced bases.

scholarly journals Demonstration of Three-Dimensional Indoor Visible Light Positioning with Multiple Photodiodes and Reinforcement Learning

Sensors ◽  
2020 ◽  
Vol 20 (22) ◽  
pp. 6470
Author(s):  
Zhuo Zhang ◽  
Huayang Chen ◽  
Weikang Zeng ◽  
Xinlong Cao ◽  
Xuezhi Hong ◽  
...  
Keyword(s):  
Reinforcement Learning ◽  
Visible Light ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Location Based Services ◽  
Positioning Accuracy ◽  
The Third ◽  
Basic Model ◽  
3D Space ◽  
3D Positioning

To provide high-quality location-based services in the era of the Internet of Things, visible light positioning (VLP) is considered a promising technology for indoor positioning. In this paper, we study a multi-photodiodes (multi-PDs) three-dimensional (3D) indoor VLP system enhanced by reinforcement learning (RL), which can realize accurate positioning in the 3D space without any off-line training. The basic 3D positioning model is introduced, where without height information of the receiver, the initial height value is first estimated by exploring its relationship with the received signal strength (RSS), and then, the coordinates of the other two dimensions (i.e., X and Y in the horizontal plane) are calculated via trilateration based on the RSS. Two different RL processes, namely RL1 and RL2, are devised to form two methods that further improve horizontal and vertical positioning accuracy, respectively. A combination of RL1 and RL2 as the third proposed method enhances the overall 3D positioning accuracy. The positioning performance of the four presented 3D positioning methods, including the basic model without RL (i.e., Benchmark) and three RL based methods that run on top of the basic model, is evaluated experimentally. Experimental results verify that obviously higher 3D positioning accuracy is achieved by implementing any proposed RL based methods compared with the benchmark. The best performance is obtained when using the third RL based method that runs RL2 and RL1 sequentially. For the testbed that emulates a typical office environment with a height difference between the receiver and the transmitter ranging from 140 cm to 200 cm, an average 3D positioning error of 2.6 cm is reached by the best RL method, demonstrating at least 20% improvement compared to the basic model without performing RL.

People Planning by a Fixed Resource Method

1972 ◽  
Vol 34 (3) ◽  
pp. 799-806 ◽  
Author(s):  
John C. Baird ◽  
Virgil Graf ◽  
Richard Degerman
Keyword(s):  
Cluster Analysis ◽  
Outer Space ◽  
Three Dimensional ◽  
Two Dimensions ◽  
The Third ◽  
Complex Stimuli ◽  
The Mean ◽  
Highly Correlated ◽  
Third Dimension ◽  
The Ideal

Results are presented from a new method to determine a person's conception of complex stimuli. In three related experiments Ss expressed their views of ideal organisms by distributing a fixed resource among hypothetical properties of the ideal. The results from the experiments were highly correlated, lending weight to the reliability and generality of the approach. Cluster analysis and multidimensional scaling were used to group the properties in two dimensions, while the mean amount allocated to a property was represented in the third dimension. A three-dimensional plot was constructed for each of four ideals: the only organism on earth, a member of the only species on earth, an organism going into outer space, and an organism coming to earth from outer space.

Oligosiloxanediols as building blocks for supramolecular chemistry: hydrogen-bonded adducts with amines form supramolecular structures in zero, one and two dimensions

2000 ◽  
Vol 56 (2) ◽  
pp. 273-286 ◽  
Author(s):  
Brian O'Leary ◽  
Trevor R. Spalding ◽  
George Ferguson ◽  
Christopher Glidewell
Keyword(s):  
Hydrogen Bonds ◽  
Supramolecular Chemistry ◽  
Building Blocks ◽  
Two Dimensions ◽  
Supramolecular Structures ◽  
Structural Motif ◽  
Two Dimensional ◽  
The Third ◽  
A Chain ◽  
Hydrogen Bonded

The structure of 1,1,3,3,5,5-hexaphenyltrisiloxane-1,5-diol–pyrazine (4/1), (C36H32O4Si3)4·C4H4N2 (1), contains finite centrosymmetric aggregates; the diol units form dimers, by means of O—H...O hydrogen bonds, and pairs of such dimers are linked to the pyrazine by means of O—H...N hydrogen bonds. In 1,1,3,3,5,5-hexaphenyltrisiloxane-1,5-diol–pyridine (2/3), (C36H32O4Si3)2·(C5H5N)3 (2), the diol units are linked into centrosymmetric pairs by means of disordered O—H...O hydrogen bonds: two of the three pyridine molecules are linked to the diol dimer by means of ordered O—H...N hydrogen bonds, while the third pyridine unit, which is disordered across a centre of inversion, links the diol dimers into a C 3 3(9) chain by means of O—H...N and C—H...O hydrogen bonds. In 1,1,3,3-tetraphenyldisiloxane-1,3-diol–hexamethylenetetramine (1/1), (C24H22O3Si2)·C6H12N4 (3), the diol acts as a double donor and the hexamethylenetetramine acts as a double acceptor in ordered O—H...N hydrogen bonds and the structure consists of C 2 2(10) chains of alternating diol and amine units. In 1,1,3,3-tetraphenyldisiloxane-1,3-diol–2,2′-bipyridyl (1/1), C24H22O3Si2·C10H8N2 (4), there are two independent diol molecules, both lying across centres of inversion and therefore both containing linear Si—O—Si groups: each diol acts as a double donor of hydrogen bonds and the unique 2,2′-bipyridyl molecule acts as a double acceptor, thus forming C 2 2(11) chains of alternating diol and amine units. The structural motif in 1,1,3,3-tetraphenyldisiloxane-1,3-diol–pyrazine (2/1), (C24H22O3Si2)2·C4H4N2 (5), is a chain-of-rings: pairs of diol molecules are linked by O—H...O hydrogen bonds into centrosymmetric R 2 2(12) dimers and these dimers are linked into C 2 2(13) chains by means of O—H...N hydrogen bonds to the pyrazine units. 1,1,3,3-Tetraphenyldisiloxane-1,3-diol–pyridine (1/1), C24H22O3Si2·C5H5N (6), and 1,1,3,3-tetraphenyldisiloxane-1,3-diol–pyrimidine (1/1), C24H22O3Si2·C4H4N2 (7), are isomorphous: in each compound the amine unit is disordered across a centre of inversion. The diol molecules form C(6) chains, by means of disordered O—H...O hydrogen bonds, and these chains are linked into two-dimensional nets built from R 6 6(26) rings, by a combination of O—H...N and C—H...O hydrogen bonds.

scholarly journals An Ontology of Software: Series, Structure and Function

2020 ◽  
pp. 115-132
Author(s):  
Jorge Francisco Maldonado Serrano ◽  
Dairon Alfonso Rodríguez Ramírez ◽  
Paul B. Caceres ◽  
Johann Farith Petit Suárez
Keyword(s):  
Structure And Function ◽  
Two Dimensions ◽  
Philosophy Of Information ◽  
Structural Dimension ◽  
The Third ◽  
And Function

This article proposes a guideline to develop an ontology of software. The first section gives a brief introduction to the importance of such ontology as a possible conceptual grounding for the philosophy of software, philosophy of computing and philosophy of information. The second section presents the background of the scope of this article in terms of both a symbolic and materialistic approach to software. The third section deploys the basic guidelines with the expositions of the two dimensions of software: the serial dimension and the structural dimension. The first dimension consists of three series, while the second in the exposition of the structure of any program. The fourth and last section will deal with a better understanding of what we can call the digital universe.

scholarly journals Translation as an Ethical Relationship between Ethics and Politics. An Interpretive Reading of Emmanuel Levinas

Religions ◽  
2019 ◽  
Vol 10 (2) ◽  
pp. 135
Author(s):  
Mădălina Guzun
Keyword(s):  
Emmanuel Levinas ◽  
Two Dimensions ◽  
The Other ◽  
Main Question ◽  
The Third ◽  
Dual Relationship ◽  
The One ◽  
The Relationship ◽  
Interpretive Reading ◽  
Ethics And Politics

The otherness of the other, considered as foreignness, is deeply intertwined with the problem of translation and with the one of morality. How can the two of them be brought together based on the work of Emmanuel Levinas? The main question which leads my analysis is the following: does morality limit itself to the relationship with another person or does it concern society in its entirety? In the thought of Levinas, ethics is placed on the side of the dual relationship with the other, while the presence of the third institutes the realm of politics. At first glance, the two dimensions contradict each other, for the first one is characterized by infinity, overabundance, and love, while the second one comports a dimension of finitude, measure, symmetry, and justice. Yet these two domains always exist contemporaneously, each of them needing the limitation brought by its counterpart. How is their relationship to be thought? I will argue that the answer can be found within the domain of translation, understood as an essential asymmetry that is both harmonic and disruptive.

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