scholarly journals Distribution of the eigenvalues of a random system of homogeneous polynomials

2016 ◽  
Vol 497 ◽  
pp. 88-107 ◽  
Author(s):  
Paul Breiding ◽  
Peter Bürgisser
Keyword(s):  
Homogeneous Polynomials ◽  
Random System

HUBUNGAN KEPADATAN BIVALVIA DENGAN PARAMETER LINGKUNGAN DI PESISIR TANJUNG PURA KABUPATEN BANGKA TENGAH

2020 ◽  
Vol 13 (2) ◽  
pp. 112-121
Author(s):  
Sudiyar . ◽  
Okto Supratman ◽  
Indra Ambalika Syari
Keyword(s):  
Negative Impact ◽  
Principal Component ◽  
Environmental Parameters ◽  
Data Retrieval ◽  
Distribution Patterns ◽  
Random System ◽  
System Method ◽  
Relationship Of ◽  
The Relationship ◽  
Anadara Granosa

The destructive fishing feared will give a negative impact on the survival of this organism. This study aims to analyze the density of bivalves, distribution patterns, and to analyze the relationship of bivalves with environmental parameters in Tanjung Pura village. This research was conducted in March 2019. The systematic random system method was used for collecting data of bivalves. The collecting Data retrieval divided into five research stasions. The results obtained 6 types of bivalves from 3 families and the total is 115 individuals. The highest bivalve density is 4.56 ind / m², and the lowest bivalves are located at station 2,1.56 ind / m²,  The pattern of bivalve distribution in the Coastal of Tanjung Pura Village is grouping. The results of principal component analysis (PCA) showed that Anadara granosa species was positively correlated with TSS r = 0.890, Dosinia contusa, Anomalocardia squamosa, Mererix meretrix, Placamen isabellina, and Tellinella spengleri were positively correlated with currents r = 0.933.

Voronoi Analysis of a Soccer Game

2004 ◽  
Vol 9 (3) ◽  
pp. 233-240 ◽  
Author(s):  
S. Kim
Keyword(s):  
Collective Behavior ◽  
Quantitative Assessment ◽  
The Other ◽  
Analysis Method ◽  
Random System ◽  
Soccer Game ◽  
Voronoi Polygons ◽  
The Mean

This paper describes a Voronoi analysis method to analyze a soccer game. It is important for us to know the quantitative assessment of contribution done by a player or a team in the game as an individual or collective behavior. The mean numbers of vertices are reported to be 5–6, which is a little less than those of a perfect random system. Voronoi polygons areas can be used in evaluating the dominance of a team over the other. By introducing an excess Voronoi area, we can draw some fruitful results to appraise a player or a team rather quantitatively.

An Inequality for Homogeneous Polynomials on ℝn

2005 ◽  
Vol 112 (3) ◽  
pp. 264-266
Author(s):  
Luo Xuebo ◽  
Zhu-Jun Zheng
Keyword(s):  
Homogeneous Polynomials

Random exponential attractor for second-order nonautonomous stochastic lattice systems with multiplicative white noise

2019 ◽  
Vol 19 (06) ◽  
pp. 1950044
Author(s):  
Haijuan Su ◽  
Shengfan Zhou ◽  
Luyao Wu
Keyword(s):  
White Noise ◽  
Weighted Space ◽  
Sufficient Conditions ◽  
Second Order ◽  
Lattice System ◽  
Exponential Attractor ◽  
Lattice Systems ◽  
Random System ◽  
Multiplicative White Noise ◽  
Infinite Sequences

We studied the existence of a random exponential attractor in the weighted space of infinite sequences for second-order nonautonomous stochastic lattice system with linear multiplicative white noise. Firstly, we present some sufficient conditions for the existence of a random exponential attractor for a continuous cocycle defined on a weighted space of infinite sequences. Secondly, we transferred the second-order stochastic lattice system with multiplicative white noise into a random lattice system without noise through the Ornstein–Uhlenbeck process, whose solutions generate a continuous cocycle on a weighted space of infinite sequences. Thirdly, we estimated the bound and tail of solutions for the random system. Fourthly, we verified the Lipschitz continuity of the continuous cocycle and decomposed the difference between two solutions into a sum of two parts, and carefully estimated the bound of the norm of each part and the expectations of some random variables. Finally, we obtained the existence of a random exponential attractor for the considered system.

scholarly journals THE POLYNOMIAL NUMERICAL INDEX OF A BANACH SPACE

2006 ◽  
Vol 49 (1) ◽  
pp. 39-52 ◽  
Author(s):  
Yun Sung Choi ◽  
Domingo Garcia ◽  
Sung Guen Kim ◽  
Manuel Maestre
Keyword(s):  
Banach Space ◽  
Positive Integer ◽  
Banach Spaces ◽  
Compact Space ◽  
Linear Operators ◽  
Homogeneous Polynomials ◽  
Numerical Radius ◽  
Disc Algebra ◽  
Multilinear Maps ◽  
Numerical Index

AbstractIn this paper, we introduce the polynomial numerical index of order $k$ of a Banach space, generalizing to $k$-homogeneous polynomials the ‘classical’ numerical index defined by Lumer in the 1970s for linear operators. We also prove some results. Let $k$ be a positive integer. We then have the following:(i) $n^{(k)}(C(K))=1$ for every scattered compact space $K$.(ii) The inequality $n^{(k)}(E)\geq k^{k/(1-k)}$ for every complex Banach space $E$ and the constant $k^{k/(1-k)}$ is sharp.(iii) The inequalities$$ n^{(k)}(E)\leq n^{(k-1)}(E)\leq\frac{k^{(k+(1/(k-1)))}}{(k-1)^{k-1}}n^{(k)}(E) $$for every Banach space $E$.(iv) The relation between the polynomial numerical index of $c_0$, $l_1$, $l_{\infty}$ sums of Banach spaces and the infimum of the polynomial numerical indices of them.(v) The relation between the polynomial numerical index of the space $C(K,E)$ and the polynomial numerical index of $E$.(vi) The inequality $n^{(k)}(E^{**})\leq n^{(k)}(E)$ for every Banach space $E$.Finally, some results about the numerical radius of multilinear maps and homogeneous polynomials on $C(K)$ and the disc algebra are given.

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