Some Problems on Random Intervals and Annihilating
نویسنده
چکیده
BY P . ERDŐS AND P . NEY Hungarian Academy of Sciences and University of Wisconsin Particles perform independent random walks on the integers, and are annihilated if they cross paths or land at the same point. The problem is to determine whether the origin is hit infinitely often . The answer is shown to depend on the initial distribution of particles in accordance with a "log log law ." Several equivalent models are mentioned .
منابع مشابه
Finitely Generated Annihilating-Ideal Graph of Commutative Rings
Let $R$ be a commutative ring and $mathbb{A}(R)$ be the set of all ideals with non-zero annihilators. Assume that $mathbb{A}^*(R)=mathbb{A}(R)diagdown {0}$ and $mathbb{F}(R)$ denote the set of all finitely generated ideals of $R$. In this paper, we introduce and investigate the {it finitely generated subgraph} of the annihilating-ideal graph of $R$, denoted by $mathbb{AG}_F(R)$. It is the (undi...
متن کاملThe sum-annihilating essential ideal graph of a commutative ring
Let $R$ be a commutative ring with identity. An ideal $I$ of a ring $R$is called an annihilating ideal if there exists $rin Rsetminus {0}$ such that $Ir=(0)$ and an ideal $I$ of$R$ is called an essential ideal if $I$ has non-zero intersectionwith every other non-zero ideal of $R$. Thesum-annihilating essential ideal graph of $R$, denoted by $mathcal{AE}_R$, isa graph whose vertex set is the set...
متن کاملSolving Inverse Sturm-Liouville Problems with Transmission Conditions on Two Disjoint Intervals
In the present paper, some spectral properties of boundary value problems of Sturm-Liouville type on two disjoint bounded intervals with transmission boundary conditions are investigated. Uniqueness theorems for the solution of the inverse problem are proved, then we study the reconstructing of the coefficients of the Sturm-Liouville problem by the spectrtal mappings method.
متن کاملOn the girth of the annihilating-ideal graph of a commutative ring
The annihilating-ideal graph of a commutative ring $R$ is denoted by $AG(R)$, whose vertices are all nonzero ideals of $R$ with nonzero annihilators and two distinct vertices $I$ and $J$ are adjacent if and only if $IJ=0$. In this article, we completely characterize rings $R$ when $gr(AG(R))neq 3$.
متن کاملOptimal Non-Parametric Prediction Intervals for Order Statistics with Random Sample Size
In many experiments, such as biology and quality control problems, sample size cannot always be considered as a constant value. Therefore, the problem of predicting future data when the sample size is an integer-valued random variable can be an important issue. This paper describes the prediction problem of future order statistics based on upper and lower records. Two different cases for the ...
متن کامل