z is y less than x : z 比x 少y , z=x-y , 单独说 y less than x 就是比 x 少y , 也就是 x-y ; 如果不说少多少,就变成了比较两数大小的不等式 z is less than x : z 比x 小,也就是 z 小于x, z<x . 总结起来 x-y 一共有五种说法: 1. y subtracted from x (subtract y ...
The process does not terminate with octonions: applying the Cayley–Dickson construction, greater 2n-dimensional algebras can be constructed, for any positive integer n. For n>3, however, as anticipated, they all include non-trivial zero divisors, i.e. they have problems in a general ...
Using methods from classical absolute stability theory, combined with recent results on input-to-state stability (ISS) of Lur’e systems, we derive necessary and sufficient conditions for a class of Lur’e systems to have the converging-input converging-state (CICS) property. In particular, we ...
, as it is not defined in a non-integer number of dimensions. therefore, in the present work we consider the proposal of ref. [ 93 ], and take \(\gamma _5\) anticommuting with all the other \(\gamma ^\mu \) matrices in arbitrary d dimensions. this prescription offers the ...
The function ρ:N→N is defined by ρ(x)=min{ρ(P,x):P∈B(x)} (for x∈N). We also consider inf{s(P):P∈B(N)}. This is an element of N̄, either an integer or infinity, that we denote by Λ and call the ET-lub (short for ET least upper bound). Whether Λ is ...
thus the reason to remove them from the applicable samples rather than from the data in general. In addition, we used correlations and autocorrelations to identify samples in which an entire chromosome or chromosome arm appeared to be subclonally duplicated or deleted (sub-integer change in copy...
1.Select Start > Programs > Oracle Business Intelligence > BI Administration to open the Administration Tool.2.Select File > New Repository.3. Enter a name for the repository. In this tutorial the repository name is BISAMPLE.4. Leave the default location as is. It points to the default ...
The order of an element a\in G is the smallest possible positive integer m s.t. a^m=e. If such m does not exist, we write |a|=\infty. Thm 9: if a,b\in G, m,n\in \mathbb Z^+ then (1) a^{m+n}=a^{m}a^{n}; (2) (a^m)^n=a^{mn}; and (3) When G is ...
1]. For example, if ν1a is an even (odd) integer then the corner charge Q1a measured with respect Wyckoff position 1a is equal to 0 (1/2) \({\rm{mod}}\,1\), i.e.,\({Q}_{1a}={\nu }_{1a}/2\,{\rm{mod}}\,1\). Note that only the fractional part of the corner ...
Sexual reproduction is almost ubiquitous among extant eukaryotes. As most asexual lineages are short-lived, abandoning sex is commonly regarded as an evolutionary dead end. Still, putative anciently asexual lineages challenge this view. One of the most s