Takens’ time delay embedding theorem is shown to hold for finitedimensional subsets of infinite-dimensional spaces, thereby generalising previous results which were only valid for subsets of finite-dimensional spaces: Let X be a subset of a Hilbert space with upper box-counting dimension d and ‘thickness exponent’ τ , which is invariant under a Lipschitz map Φ. Suppose that E , the set of all f...

Periodic flaccid paralysis of skeletal muscle occurring in a thyrotoxic patient, an unusual and dramatic event, is seen predominantly in Oriental men. It is important to remember the clinical association between periodic paralysis and thyrotoxicosis.

In this paper, an estimation of the Gaussian noise variance based on observed (measured) maximums of subsets of samples is given. Circumstances of the measurement environment being limited, only maximums of subsets of samples are available and the non-constant variance of the Gaussian noise can be estimated. In the case of power line noise, the variance of the zero mean Gaussian noise is a peri...

Systemic properties of living cells are the result of molecular dynamics governed by so-called genetic regulatory networks (GRN). These networks capture all possible features of cells and are responsible for the immense levels of adaptation characteristic to living systems. At any point in time only small subsets of these networks are active. Any active subset of the GRN leads to the expression...

Let $S_n$ be the symmetric group on the set $[n]={1, 2, ldots, n}$. For $gin S_n$ let $fix(g)$ denote the number of fixed points of $g$. A subset $S$ of $S_n$ is called $t$-emph{transitive} if for any two $t$-tuples $(x_1,x_2,ldots,x_t)$ and $(y_1,y_2,ldots ,y_t)$ of distinct elements of $[n]$, there exists $gin S$ such that $x_{i}^g=y_{i}$ for any $1leq ileq t$ and additionally $S$ is called e...

Abstract Let G be a $\sigma $ -finite abelian group, i.e., $G=\bigcup _{n\geq 1} G_n$ where $(G_n)_{n\geq 1}$ is nondecreasing sequence of finite subgroups. For any $A\subset G$ , let $\underline {\mathrm {d}}( A ):=\liminf _{n\to \infty }\frac {|A\cap G_n|}{|G_n|}$ its lower asymptotic density. We show that for subsets and B whenever A+B )<\underline )+\underline )$ the sumset $A+B$ must pe...