Miyanishi's characterization of singularities appearing on 𝔸1-fibrations does not hold in higher dimensions

2013 ◽  
Author(s):  
Takashi Kishimoto
Keyword(s):  
Higher Dimensions

scholarly journals Controllability of Continuous Bimodal Linear Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
Josep Ferrer ◽  
Juan R. Pacha ◽  
Marta Peña
Keyword(s):  
Linear Systems ◽  
Higher Dimensions ◽  
Linear Dynamics ◽  
Explicit Characterization ◽  
Separating Hyperplane

We consider bimodal linear systems consisting of two linear dynamics acting on each side of a given hyperplane, assuming continuity along the separating hyperplane. We prove that the study of controllability can be reduced to the unobservable case, and for these ones we obtain a simple explicit characterization of controllability for dimensions 2 and 3, as well as some partial criteria for higher dimensions.

PROJECTED ENTANGLED STATES: PROPERTIES AND APPLICATIONS

2006 ◽  
Vol 20 (30n31) ◽  
pp. 5142-5153 ◽  
Author(s):  
F. VERSTRAETE ◽  
M. WOLF ◽  
D. PÉREZ-GARCÍA ◽  
J. I. CIRAC
Keyword(s):  
Numerical Algorithms ◽  
Higher Dimensions ◽  
Two Dimensions ◽  
One Dimension ◽  
Entangled States ◽  
Matrix Product ◽  
Many Body ◽  
Many Body Systems ◽  
Dimension One

We present a new characterization of quantum states, what we call Projected Entangled-Pair States (PEPS). This characterization is based on constructing pairs of maximally entangled states in a Hilbert space of dimension D2, and then projecting those states in subspaces of dimension d. In one dimension, one recovers the familiar matrix product states, whereas in higher dimensions this procedure gives rise to other interesting states. We have used this new parametrization to construct numerical algorithms to simulate the ground state properties and dynamics of certain quantum-many body systems in two dimensions.

scholarly journals The Funk–Radon transform for hyperplane sections through a common point

2020 ◽  
Vol 10 (3) ◽  
Author(s):  
Michael Quellmalz
Keyword(s):  
Radon Transform ◽  
Higher Dimensions ◽  
Common Point ◽  
Mean Values ◽  
Generalized Radon Transform ◽  
Spherical Radon Transform ◽  
Range Characterization ◽  
Hyperplane Sections

Abstract The Funk–Radon transform, also known as the spherical Radon transform, assigns to a function on the sphere its mean values along all great circles. Since its invention by Paul Funk in 1911, the Funk–Radon transform has been generalized to other families of circles as well as to higher dimensions. We are particularly interested in the following generalization: we consider the intersections of the sphere with hyperplanes containing a common point inside the sphere. If this point is the origin, this is the same as the aforementioned Funk–Radon transform. We give an injectivity result and a range characterization of this generalized Radon transform by finding a relation with the classical Funk–Radon transform.

scholarly journals A characterization of 3D steady Euler flows using commuting zero-flux homologies

2020 ◽  
pp. 1-16
Author(s):  
DANIEL PERALTA-SALAS ◽  
ANA RECHTMAN ◽  
FRANCISCO TORRES DE LIZAUR
Keyword(s):  
Euler Equations ◽  
Vector Fields ◽  
Higher Dimensions ◽  
Riemannian Metric ◽  
Euler Flows ◽  
Homological Characterization ◽  
Steady Solutions ◽  
Volume Preserving

We characterize, using commuting zero-flux homologies, those volume-preserving vector fields on a 3-manifold that are steady solutions of the Euler equations for some Riemannian metric. This result extends Sullivan’s homological characterization of geodesible flows in the volume-preserving case. As an application, we show that steady Euler flows cannot be constructed using plugs (as in Wilson’s or Kuperberg’s constructions). Analogous results in higher dimensions are also proved.

Multidimensional Signal Analysis

2009 ◽  
Author(s):  
Robert J Marks II
Keyword(s):  
Fourier Transform ◽  
Fourier Series ◽  
Higher Dimensions ◽  
Two Dimensions ◽  
One Dimension ◽  
One Dimensional ◽  
Multidimensional Signals ◽  
Multidimensional Signal ◽  
The Fourier Transform

N dimensional signals are characterized as values in an N dimensional space. Each point in the space is assigned a value, possibly complex. Each dimension in the space can be discrete, continuous, or on a time scale. A black and white movie can be modelled as a three dimensional signal.Acolor picture can be modelled as three signals in two dimensions, one each, for example, for red, green and blue. This chapter explores Fourier characterization of different types of multidimensional signals and corresponding applications. Some signal characterizations are straightforward extensions of their one dimensional counterparts. Others, even in two dimensions, have properties not found in one dimensional signals. We are fortunate to be able to visualize structures in two, three, and sometimes four dimensions. It assists in the intuitive generalization of properties to higher dimensions. Fourier characterization of multidimensional signals allows straightforward modelling of reconstruction of images from their tomographic projections. Doing so is the foundation of certain medical and industrial imaging, including CAT (for computed axial tomography) scans. Multidimensional Fourier series are based on models found in nature in periodically replicated crystal Bravais lattices [987, 1188]. As is one dimension, the Fourier series components can be found from sampling the Fourier transform of a single period of the periodic signal. The multidimensional cosine transform, a relative of the Fourier transform, is used in image compression such as JPG images. Multidimensional signals can be filtered. The McClellan transform is a powerful method for the design of multidimensional filters, including generalization of the large catalog of zero phase one dimensional FIR filters into higher dimensions. As in one dimension, the multidimensional sampling theorem is the Fourier dual of the Fourier series. Unlike one dimension, sampling can be performed at the Nyquist density with a resulting dependency among sample values. This property can be used to reduce the sampling density of certain images below that of Nyquist, or to restore lost samples from those remaining. Multidimensional signal and image analysis is also the topic of Chapter 9 on time frequency representations, and Chapter 11 where POCS is applied signals in higher dimensions.

scholarly journals A quantitative Balian–Low theorem for higher dimensions

2020 ◽  
Vol 27 (3) ◽  
pp. 469-477
Author(s):  
Faruk Temur
Keyword(s):  
Dimension Reduction ◽  
Riesz Basis ◽  
Higher Dimensions ◽  
Riesz Bases ◽  
Zak Transform ◽  
Transform Methods

AbstractWe extend the quantitative Balian–Low theorem of Nitzan and Olsen to higher dimensions. We use Zak transform methods and dimension reduction. The characterization of the Gabor–Riesz bases by the Zak transform allows us to reduce the problem to the quasiperiodicity and the boundedness from below of the Zak transforms of the Gabor–Riesz basis generators, two properties for which dimension reduction is possible.

The M-Band Symmetric Orthogonal Scaling Function in Higher Dimensions

2013 ◽  
Vol 482 ◽  
pp. 322-325
Author(s):  
Fang Jun Zhang
Keyword(s):  
Image Processing ◽  
Signal Processing ◽  
Scaling Function ◽  
Higher Dimensions ◽  
One Dimension ◽  
Wavelet Theory

Wavelet theory has a key role in signal processing and image processing. In this paper, the characterization of the M-band symmetric orthogonal scaling function is obtained in higher dimensions. Then, a symmetric cardinal orthogonal scaling function is classified. The existing some results in one dimension are generalized to the case of higher dimensions.

The Characterization of a Kind of Vector-Valued Multivariate Wavelet Packets with Composite Dilation Matrix

2010 ◽  
Vol 439-440 ◽  
pp. 932-937
Author(s):  
Yin Hong Xia ◽  
Hua Li
Keyword(s):  
Operator Theory ◽  
Matrix Theory ◽  
Higher Dimensions ◽  
Wavelet Packets ◽  
Riesz Bases ◽  
Analysis Method ◽  
Time Frequency ◽  
Dilation Matrix ◽  
Vector Valued

In this article, the notion of a kind of multivariate vector-valued wavelet packets with composite dilation matrix is introduced. A new method for designing a kind of biorthogonal vector- valued wavelet packets in higher dimensions is developed and their biorthogonality property is inv- -estigated by virtue of matrix theory, time-frequency analysis method, and operator theory. Two biorthogonality formulas concerning these wavelet packets are presented. Moreover, it is shown how to gain new Riesz bases of space by constructing a series of subspace of wavelet packets.

scholarly journals Miyanishi's characterization of the affine 3-space does not hold in higher dimensions

2000 ◽  
Vol 50 (6) ◽  
pp. 1649-1669 ◽  
Author(s):  
Shulim Kaliman ◽  
Mikhail Zaidenberg
Keyword(s):  
Higher Dimensions

Morphological Characterization of Mycobacteriophage R1

1974 ◽  
Vol 32 ◽  
pp. 254-255
Author(s):  
B. L. Soloff ◽  
T. A. Rado
Keyword(s):  
Carbon Source ◽  
Stationary Phase ◽  
Growth Phase ◽  
Minimal Medium ◽  
Morphological Characterization ◽  
Logarithmic Growth Phase ◽  
Complete Lysis ◽  
Lysogenic Culture ◽  
Logarithmic Growth

Mycobacteriophage R1 was originally isolated from a lysogenic culture of M. butyricum. The virus was propagated on a leucine-requiring derivative of M. smegmatis, 607 leu−, isolated by nitrosoguanidine mutagenesis of typestrain ATCC 607. Growth was accomplished in a minimal medium containing glycerol and glucose as carbon source and enriched by the addition of 80 μg/ ml L-leucine. Bacteria in early logarithmic growth phase were infected with virus at a multiplicity of 5, and incubated with aeration for 8 hours. The partially lysed suspension was diluted 1:10 in growth medium and incubated for a further 8 hours. This permitted stationary phase cells to re-enter logarithmic growth and resulted in complete lysis of the culture.

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