On the number of connected components of the space of trigonometric polynomials of degreen with2n different critical values

1997 ◽  
Vol 62 (4) ◽  
pp. 529-534 ◽  
Author(s):  
B. Shapiro
Keyword(s):  
Critical Values ◽  
Trigonometric Polynomials ◽  
Connected Components

scholarly journals Homological Percolation: The Formation of Giant k-Cycles

2020 ◽  
Author(s):  
Omer Bobrowski ◽  
Primoz Skraba
Keyword(s):  
Thermodynamic Limit ◽  
Exponential Decay ◽  
Algebraic Topology ◽  
Percolation Model ◽  
Critical Values ◽  
Giant Component ◽  
Connected Components ◽  
Continuum Percolation ◽  
Dimensional Torus ◽  
Higher Dimensional

Abstract In this paper we introduce and study a higher dimensional analogue of the giant component in continuum percolation. Using the language of algebraic topology, we define the notion of giant $k$-dimensional cycles (with $0$-cycles being connected components). Considering a continuum percolation model in the flat $d$-dimensional torus, we show that all the giant $k$-cycles ($1\le k \le d-1$) appear in the regime known as the thermodynamic limit. We also prove that the thresholds for the emergence of the giant $k$-cycles are increasing in $k$ and are tightly related to the critical values in continuum percolation. Finally, we provide bounds for the exponential decay of the probabilities of giant cycles appearing.

Critical Values

2008 ◽  
Vol 3 (3) ◽  
pp. 201-202
Author(s):  
Keith Krehbiel
Keyword(s):  
Critical Values

Approximation of Unbounded Functions by Trigonometric Polynomials

2017 ◽  
Vol 13 (4) ◽  
pp. 106-116
Author(s):  
Alaa A. Auad ◽  
◽  
Mousa M. Khrajan
Keyword(s):  
Trigonometric Polynomials

Approximate Solution Of A Singular Integral Equation With A Multiplicative Cauchy Kernel In The Half-Plane

2008 ◽  
Vol 8 (2) ◽  
pp. 143-154 ◽  
Author(s):  
P. KARCZMAREK
Keyword(s):  
Integral Equation ◽  
Approximate Solution ◽  
Singular Integral Equation ◽  
Half Plane ◽  
Singular Integral ◽  
Trigonometric Polynomials ◽  
Cauchy Kernel

AbstractIn this paper, Jacobi and trigonometric polynomials are used to con-struct the approximate solution of a singular integral equation with multiplicative Cauchy kernel in the half-plane.

The algorithm of the color signal recognition at landing an unmanned aerial vehicle on an aircraft carrier in autonomous mode

2020 ◽  
pp. 78
Keyword(s):  
Unmanned Aerial Vehicle ◽  
Treatment Method ◽  
Recognition Algorithm ◽  
Connected Components ◽  
Preliminary Treatment ◽  
Signal Recognition ◽  
Aircraft Carrier ◽  
Halftone Image ◽  
Glide Path ◽  
Aerial Vehicle

The movement along the glide path of an unmanned aerial vehicle during landing on an aircraft carrier is investigated. The implementation of this task is realized in the conditions of radio silence of the aircraft carrier. The algorithm for treatment information from an optical landing system installed on an aircraft carrier is developed. The algorithm of the color signal recognition assumes the usage of the image frame preliminary treatment method via a downsample function, that performs the decimation process, the HSV model, the Otsu’s method for calculating the binarization threshold for a halftone image, and the method of separating the connected Two-Pass components. Keywords unmanned aerial vehicle; aircraft carrier; approach; glide path; optical landing system; color signal recognition algorithm; decimation; connected components; halftone image binarization

scholarly journals Detecting Heterogeneity of Substitution Along DNA and Protein Sequences

Genetics ◽  
1996 ◽  
Vol 143 (1) ◽  
pp. 589-602 ◽  
Author(s):  
Peter J E Goss ◽  
R C Lewontin
Keyword(s):  
Null Hypothesis ◽  
Nonuniform Distribution ◽  
Critical Values ◽  
Third Order ◽  
Variance Test ◽  
Data Set ◽  
Significance Level ◽  
Uniformly Most Powerful Test ◽  
Interval Lengths ◽  
Uniformly Most Powerful

Abstract Regions of differing constraint, mutation rate or recombination along a sequence of DNA or amino acids lead to a nonuniform distribution of polymorphism within species or fixed differences between species. The power of five tests to reject the null hypothesis of a uniform distribution is studied for four classes of alternate hypothesis. The tests explored are the variance of interval lengths; a modified variance test, which includes covariance between neighboring intervals; the length of the longest interval; the length of the shortest third-order interval; and a composite test. Although there is no uniformly most powerful test over the range of alternate hypotheses tested, the variance and modified variance tests usually have the highest power. Therefore, we recommend that one of these two tests be used to test departure from uniformity in all circumstances. Tables of critical values for the variance and modified variance tests are given. The critical values depend both on the number of events and the number of positions in the sequence. A computer program is available on request that calculates both the critical values for a specified number of events and number of positions as well as the significance level of a given data set.

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