scholarly journals Dimension Spectrum for Sofic Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Jung-Chao Ban ◽  
Chih-Hung Chang ◽  
Ting-Ju Chen ◽  
Mei-Shao Lin
Keyword(s):  
Nonnegative Matrix ◽  
Potential Functions ◽  
Entropy Spectrum ◽  
Positive Matrix ◽  
Dependent Case ◽  
Dimension Spectrum ◽  
Matrix Potential ◽  
Bernoulli Measure ◽  
Set Up ◽  
Affine Set

We study the dimension spectrum of sofic system with the potential functions being matrix valued. For finite-coordinate dependent positive matrix potential, we set up the entropy spectrum by constructing the quasi-Bernoulli measure and the cut-off method is applied to deal with the infinite-coordinate dependent case. We extend this method to nonnegative matrix and give a series of examples of the sofic-affine set on which we can compute the spectrum concretely.

scholarly journals Some Special Matrices of Real Elements and Their Properties

2006 ◽  
Vol 14 (4) ◽  
pp. 129-134
Author(s):  
Xiquan Liang ◽  
Fuguo Ge ◽  
Xiaopeng Yue
Keyword(s):  
Nonnegative Matrix ◽  
Positive Matrix

Some Special Matrices of Real Elements and Their Properties This article describes definitions of positive matrix, negative matrix, nonpositive matrix, nonnegative matrix, nonzero matrix, module matrix of real elements and their main properties, and we also give the basic inequalities in matrices of real elements.

Ruelle operator with weakly contractive iterated function systems

2012 ◽  
Vol 33 (4) ◽  
pp. 1265-1290 ◽  
Author(s):  
YUAN-LING YE
Keyword(s):  
Iterated Function Systems ◽  
Potential Functions ◽  
Lipschitz Continuous ◽  
Triple Systems ◽  
Ruelle Operator ◽  
Iterated Function ◽  
Continuous Potential ◽  
Set Up ◽  
Associated Family ◽  
Weakly Contractive

AbstractThe Ruelle operator has been studied extensively both in dynamical systems and iterated function systems (IFSs). Given a weakly contractive IFS $(X, \{w_j\}_{j=1}^m)$ and an associated family of positive continuous potential functions $\{p_j\}_{j=1}^m$, a triple system $(X, \{w_j\}_{j=1}^m, \{p_j\}_{j=1}^m)$is set up. In this paper we study Ruelle operators associated with the triple systems. The paper presents an easily verified condition. Under this condition, the Ruelle operator theorem holds provided that the potential functions are Dini continuous. Under the same condition, the Ruelle operator is quasi-compact, and the iterations sequence of the Ruelle operator converges with a specific geometric rate, if the potential functions are Lipschitz continuous.

scholarly journals Inequalities for the maximal eigenvalue of a nonnegative matrix

1997 ◽  
Vol 39 (3) ◽  
pp. 276-284 ◽  
Author(s):  
Lina Yeh
Keyword(s):  
Nonnegative Matrix ◽  
Maximal Eigenvalue ◽  
Positive Matrix

AbstractTwo-sided bounds are obtained for the maximal eigenvalue of a positive matrix by iterating computations of row sums. The result provides an algorithm for approximating the maximal eigenvalue of a nonnegative matrix.

-SPECTRUM OF SELF-SIMILAR MEASURES WITH OVERLAPS IN THE ABSENCE OF SECOND-ORDER IDENTITIES

2018 ◽  
Vol 106 (1) ◽  
pp. 56-103 ◽  
Author(s):  
SZE-MAN NGAI ◽  
YUANYUAN XIE
Keyword(s):  
Hausdorff Dimension ◽  
Finite Type ◽  
Iterated Function Systems ◽  
Second Order ◽  
Higher Dimension ◽  
Closed Formula ◽  
Dimension Spectrum ◽  
Iterated Function ◽  
Self Similar ◽  
Set Up

For the class of self-similar measures in $\mathbb{R}^{d}$ with overlaps that are essentially of finite type, we set up a framework for deriving a closed formula for the $L^{q}$-spectrum of the measure for $q\geq 0$. This framework allows us to include iterated function systems that have different contraction ratios and those in higher dimension. For self-similar measures with overlaps, closed formulas for the $L^{q}$-spectrum have only been obtained earlier for measures satisfying Strichartz’s second-order identities. We illustrate how to use our results to prove the differentiability of the $L^{q}$-spectrum, obtain the multifractal dimension spectrum, and compute the Hausdorff dimension of the measure.

Exact results for perturbation to total positivity and to total nonsingularity

2014 ◽  
Vol 27 ◽  
Author(s):  
Miriam Farber ◽  
Mitchell Faulk ◽  
Charles Johnson ◽  
Evan Marzion
Keyword(s):  
Nonnegative Matrix ◽  
Total Positivity ◽  
Projective Planes ◽  
Singular Matrix ◽  
Line Geometry ◽  
Positive Matrix ◽  
Totally Positive ◽  
Point Line ◽  
Totally Nonnegative Matrix ◽  
The Relationship

A study of the maximum number of equal entries in totally positive and totally nonsingular m-by-n, matrices for small values of m and n, is presented. Equal entries correspond to entries of the totally nonnegative matrix J that are not changed in producing a TP or TNS matrix. It is shown that the maximum number of equal entries in a 7-by-7 totally positive matrix is strictly smaller than that for a 7-by-7 totally non-singular matrix, but, this is the first pair (m; n) for which these maximum numbers differ. Using point-line geometry in the projective plane, a family of values for (m; n) for which these maximum numbers differ is presented. Generalization to the Hadamard core, as well as larger projective planes is also established. Finally, the relationship with C4 free graphs, along with a method for producing symmetric TP matrices with maximal symmetric arrangements of equal entries is discussed.

scholarly journals Comparison of PM10 Sources Profiles at 15 French Sites Using a Harmonized Constrained Positive Matrix Factorization Approach

Atmosphere ◽  
2019 ◽  
Vol 10 (6) ◽  
pp. 310 ◽  
Author(s):  
Samuël Weber ◽  
Dalia Salameh ◽  
Alexandre Albinet ◽  
Laurent Y. Alleman ◽  
Antoine Waked ◽  
...  
Keyword(s):  
Matrix Factorization ◽  
Road Transport ◽  
Positive Matrix Factorization ◽  
Primary Sources ◽  
Vehicle Exhaust ◽  
Positive Matrix ◽  
Residential Heating ◽  
Wood Burning ◽  
Set Up ◽  
Biogenic Aerosols

Receptor-oriented models, including positive matrix factorization (PMF) analyses, are now commonly used to elaborate and/or evaluate action plans to improve air quality. In this context, the SOURCES project has been set-up to gather and investigate in a harmonized way 15 datasets of chemical compounds from PM10 collected for PMF studies during a five-year period (2012–2016) in France. The present paper aims at giving an overview of the results obtained within this project, notably illustrating the behavior of key primary sources as well as focusing on their statistical robustness and representativeness. Overall, wood burning for residential heating as well as road transport were confirmed to be the two main primary sources strongly influencing PM10 loadings across the country. While wood burning profiles, as well as those dominated by secondary inorganic aerosols, present a rather good homogeneity among the sites investigated, some significant variabilities were observed for primary traffic factors, illustrating the need to better characterize the diversity of the various vehicle exhaust and non-exhaust emissions. Finally, natural sources, such as sea salts (widely observed in internal mixing with anthropogenic compounds), primary biogenic aerosols and/or terrigenous particles, were also found as non-negligible PM10 components at every investigated site.

scholarly journals Distance Matrix of a Class of Completely Positive Graphs: Determinant and Inverse

2020 ◽  
Vol 8 (1) ◽  
pp. 160-171
Author(s):  
Joyentanuj Das ◽  
Sachindranath Jayaraman ◽  
Sumit Mohanty
Keyword(s):  
Symmetric Matrix ◽  
Nonnegative Matrix ◽  
Distance Matrix ◽  
Laplacian Matrix ◽  
Positive Semidefinite ◽  
Positive Matrix ◽  
Completely Positive ◽  
Rank One ◽  
Principal Submatrices ◽  
Existing Result

AbstractA real symmetric matrix A is said to be completely positive if it can be written as BBt for some (not necessarily square) nonnegative matrix B. A simple graph G is called a completely positive graph if every matrix realization of G that is both nonnegative and positive semidefinite is a completely positive matrix. Our aim in this manuscript is to compute the determinant and inverse (when it exists) of the distance matrix of a class of completely positive graphs. We compute a matrix 𝒭 such that the inverse of the distance matrix of a class of completely positive graphs is expressed a linear combination of the Laplacian matrix, a rank one matrix of all ones and 𝒭. This expression is similar to the existing result for trees. We also bring out interesting spectral properties of some of the principal submatrices of 𝒭.

The Effects of Drying Techniques on Clay-Rich Soil Texture

1974 ◽  
Vol 32 ◽  
pp. 466-467
Author(s):  
T. G. Naymik
Keyword(s):  
Critical Point ◽  
Liquid Nitrogen ◽  
Liquid Nitrogen Temperature ◽  
Drying Methods ◽  
Air Drying ◽  
Freeze Dried ◽  
Critical Point Drying ◽  
Set Up ◽  
The Relationship ◽  
Quartz Grains

Three techniques were incorporated for drying clay-rich specimens: air-drying, freeze-drying and critical point drying. In air-drying, the specimens were set out for several days to dry or were placed in an oven (80°F) for several hours. The freeze-dried specimens were frozen by immersion in liquid nitrogen or in isopentane at near liquid nitrogen temperature and then were immediately placed in the freeze-dry vacuum chamber. The critical point specimens were molded in agar immediately after sampling. When the agar had set up the dehydration series, water-alcohol-amyl acetate-CO2 was carried out. The objectives were to compare the fabric plasmas (clays and precipitates), fabricskeletons (quartz grains) and the relationship between them for each drying technique. The three drying methods are not only applicable to the study of treated soils, but can be incorporated into all SEM clay soil studies.

Evaluation of Freezing Methods by Low Temperature X-Ray Diffraction

1977 ◽  
Vol 35 ◽  
pp. 330-333
Author(s):  
T. Gulik-Krzywicki ◽  
M.J. Costello
Keyword(s):  
Biological Materials ◽  
Molecular Organization ◽  
X Ray Diffraction ◽  
Glass Capillary ◽  
X Ray ◽  
Rate Dependent ◽  
Before And After ◽  
Freeze Etching ◽  
Diffraction Patterns ◽  
Set Up

Freeze-etching electron microscopy is currently one of the best methods for studying molecular organization of biological materials. Its application, however, is still limited by our imprecise knowledge about the perturbations of the original organization which may occur during quenching and fracturing of the samples and during the replication of fractured surfaces. Although it is well known that the preservation of the molecular organization of biological materials is critically dependent on the rate of freezing of the samples, little information is presently available concerning the nature and the extent of freezing-rate dependent perturbations of the original organizations. In order to obtain this information, we have developed a method based on the comparison of x-ray diffraction patterns of samples before and after freezing, prior to fracturing and replication.Our experimental set-up is shown in Fig. 1. The sample to be quenched is placed on its holder which is then mounted on a small metal holder (O) fixed on a glass capillary (p), whose position is controlled by a micromanipulator.

Eels Under Standing Wave Conditions

1982 ◽  
Vol 40 ◽  
pp. 492-495
Author(s):  
O.L. Krivanek ◽  
J. TaftØ
Keyword(s):  
Standing Wave ◽  
Wave Conditions ◽  
Set Up ◽  
A Site ◽  
Complex Crystal

It is well known that a standing electron wavefield can be set up in a crystal such that its intensity peaks at the atomic sites or between the sites or in the case of more complex crystal, at one or another type of a site. The effect is usually referred to as channelling but this term is not entirely appropriate; by analogy with the more established particle channelling, electrons would have to be described as channelling either through the channels or through the channel walls, depending on the diffraction conditions.

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