scholarly journals The complete one-loop dilation operator of $\mathcal{N} = 2$ SuperConformal QCD

2012 ◽  
Vol 2012 (7) ◽  
Author(s):  
Pedro Liendo ◽  
Elli Pomoni ◽  
Leonardo Rastelli
Keyword(s):  
Dilation Operator

scholarly journals SCATTERING THEORY FOR LATTICE OPERATORS IN DIMENSION d ≥ 3

2012 ◽  
Vol 24 (08) ◽  
pp. 1250020 ◽  
Author(s):  
JEAN BELLISSARD ◽  
HERMANN SCHULZ-BALDES
Keyword(s):  
Scattering Theory ◽  
Tight Binding ◽  
Gradient Flow ◽  
Index Theorem ◽  
Finite Range ◽  
Dilation Operator ◽  
Classical Energy ◽  
Energy Gradient ◽  
Embedded Eigenvalues ◽  
Levinson Theorem

This paper analyzes the scattering theory for periodic tight-binding Hamiltonians perturbed by a finite range impurity. The classical energy gradient flow is used to construct a conjugate (or dilation) operator to the unperturbed Hamiltonian. For dimension d ≥ 3, the wave operator is given by an explicit formula in terms of this dilation operator, the free resolvent and the perturbation. From this formula, the scattering and time delay operators can be read off. Using the index theorem approach, a Levinson theorem is proved which also holds in the presence of embedded eigenvalues and threshold singularities.

scholarly journals SEGMENTATION AND ANALYSIS METHOD FOR TWO-PHASE CERAMIC (HfB2-B4C) BASED ON THE DETECTION OF VIRTUAL BOUNDARIES

2019 ◽  
Vol 38 (1) ◽  
pp. 95 ◽  
Author(s):  
Yuexing Han ◽  
Chuanbin Lai ◽  
Bing Wang ◽  
Tianyi Hu ◽  
Dongli Hu ◽  
...  
Keyword(s):  
Spatial Clustering ◽  
Experimental Results ◽  
Analysis Method ◽  
Microstructural Characteristics ◽  
Two Phase ◽  
Classification Rate ◽  
Dilation Operator ◽  
Segmentation Accuracy ◽  
Occurrence Matrix

Microstructure of a material stores the genesis of the material and shows various properties of the material. To efficiently analyse the microstructure of a material, the segmentation of different phases or constituents is an important step. However, in general, due to the microstructure’s complexity, most of segmentation is manually done by human experts. It is challenging to automatically segment the material phases and the microstructure. In this work, we propose a method which combines the the dilation operator, GLCM (gray-level co-occurrence matrix), Hough transform and DBSCAN (density-based spatial clustering of applications with noise) for phases segmentation in the examples of certain material of eutectic HfB2-B4C ceramics. In the segmented regions, the further analysis for the microstructural elements is done with DBSCAN. The experimental results show that the proposed method achieves 95.75% segmentation accuracy for segmenting phases and 86.64% correct classification rate for the microstructure in the segmented phases. These experimental results show that our method is effective for the difficult task of the both segmentation and classification of the microstructural characteristics.

scholarly journals SHARPNESS OF SOME PROPERTIES OF WIENER AMALGAM AND MODULATION SPACES

2009 ◽  
Vol 80 (1) ◽  
pp. 105-116 ◽  
Author(s):  
ELENA CORDERO ◽  
FABIO NICOLA
Keyword(s):  
Modulation Spaces ◽  
Wiener Amalgam Spaces ◽  
Dilation Operator ◽  
Sharp Estimates ◽  
Amalgam Spaces ◽  
Scaling Arguments

AbstractWe prove sharp estimates for the dilation operator f(x)⟼f(λx), when acting on Wiener amalgam spaces W(Lp,Lq). Scaling arguments are also used to prove the sharpness of the known convolution and pointwise relations for modulation spaces Mp,q, as well as the optimality of an estimate for the Schrödinger propagator on modulation spaces.

Dilation operator in gauge theories

1984 ◽  
Vol 29 (6) ◽  
pp. 1175-1183 ◽  
Author(s):  
John Galayda
Keyword(s):  
Gauge Theories ◽  
Dilation Operator

scholarly journals On dilation operators and sampling numbers

2008 ◽  
Vol 6 (1) ◽  
pp. 17-46 ◽  
Author(s):  
Jan Vybíral
Keyword(s):  
Linear Operator ◽  
Open Problem ◽  
Besov Spaces ◽  
Bounded Linear Operator ◽  
Bounded Linear ◽  
Dilation Operator ◽  
Optimal Bounds ◽  
Limiting Case ◽  
General Method

We consider the dilation operatorsTk:f→f(2k.)in the frame of Besov spacesBpqs(ℝd)with 1≤p,q≤∞. Ifs> 0,Tkis a bounded linear operator fromBpqs(ℝd)into itself and there are optimal bounds for its norm, see [4, 2.3.1]. We study the situation in the cases= 0, an open problem mentioned also in [4]. It turns out, that new effects based on Littlewood-Paley theory appear. In the second part of the paper, we apply these results to the study of the so-called sampling numbers of the embeddingid:Bpq1s1(Ω)→Bpq20(Ω), whereΩ=(0,1)d. It was observed already in [13] that the estimates from above for the norm of the dilation operator have their immediate counterpart in the estimates from above for the sampling numbers. In this paper we show that even in the limiting cases2=0(left open so far), this general method supplies optimal results.

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