Properties of gravitationally bound dark compact ultra dense objects

We consider compact astrophysical objects formed from dark matter fermions of mass 250 GeV to 100 TeV or from massless fermions hidden by vacuum structure of similar energy scale. These objects have maximum stable masses of sub-planetary scale and radii of micron to centimeter scale. We describe the surface gravity and tidal forces near these compact ultra dense objects, as pertinent to signatures of their collisions with visible matter objects.     

Spectral analytic comparisons for data augmentation

The sandwich algorithm (SA) is an alternative to the data augmentation (DA) algorithm that uses an extra simulation step at each iteration. In this paper, we show that the sandwich algorithm always converges at least as fast as the DA algorithm, in the Markov operator norm sense. We also establish conditions under which the spectrum of SA dominates that of DA. An example illustrates the results.     

Quasi‐convexly dense and suitable sets in the arc component of a compact group

Let G be an abelian topological group. The symbol $\widehat{G}Let G be an abelian topological group. The symbol $\widehat{G}$ denotes the group of all continuous characters $\chi :G\rightarrow {\mathbb T}$ endowed with the compact open topology. A subset E of G is said to be qc‐dense in G provided that χ(E)?φ([? 1/4, 1/4]) holds only for the trivial character $\chi \in \widehat{G}$, where $\varphi : {\mathbb R}\rightarrow {\mathbb T}={\mathbb R}/{\mathbb Z}$ is the canonical homomorphism. A super‐sequence is a non‐empty compact Hausdorff space S with at most one non‐isolated point (to which S converges). We prove that an infinite compact abelian group G is connected if and only if its arc component G_a contains a super‐sequence converging to 0 that is qc‐dense in G. This gives as a corollary a recent theorem of Außenhofer: For a connected locally compact abelian group G, the restriction homomorphism $r:\widehat{G}\rightarrow \widehat{G}_a$ defined by $r(\chi )=\chi \upharpoonright _{G_a}$ for $\chi \in \widehat{G}$, is a topological isomorphism. We show that an infinite compact group G is connected if and only if its arc component G_a contains a super‐sequence converging to the identity that is qc‐dense in G and generates a dense subgroup of G. We also offer a short alternative proof of the result of Hofmann and Morris on the existence of suitable sets of minimal size in the arc component of a compact connected group.     

Some properties for the attractors

For the continuous flows defined on a topological space, we have discussed some properties for the invariant sets and their domains of influence. We have proved the following open problem posed by C. Conley: an attractor in a locally connected compact Hausdorff invariant set has finitely many components. In the meantime, two necessary and sufficient conditions for a set to be an attractor have been given.     

THE （u＋К）-ORBIT OF ESSENTIALLY NORMAL OPERATORS AND COMPACT PERTURBATIONS OF STRONGLY IRREDUCIBLE OPERATORS

Let Н be a complex,separable,infinite dimensional Hilbert space,T∈L(Н),(U+κ)(T) denotes the (U+κ)-orbit of T,i.e.,(U+κ)(T)={R^-1 TR:R is invertible and of the form unitary plus compact}.Let Ω be an analytic and simply connected Cauchy domain in C and n∈N,A（Ω,n）denotes the class of operators,each of which satisfies (i) T is essentially normal;(ii)σ(T)=Ω^-,ρF（T）∩σ（T）=Ω;（iii）ind(λ-T)=-n,nul(λ-T)=0,(λ∈Ω）。it is proved that given T1,T2∈A(Ω,n）and c>0,there exists a compact operator K with ||K||<ε such that T1+K∈(u+κ)(T2),this result generalizes a result of P.S.Guinand and L.Marcoux[6,15],Furthermore,the authors give a character of the norm closure of (u+κ)(T),and prove that for each T∈А(Ω,n）,there exists a compact (SI) perturbation of T whose norm can be arbitrarily small.     

套代数中根理想的w*闭包

利用零化子的技巧,完全刻划了套代数中根Ｒ、ｒ的ω＊闭包,得到Ｒ＾Ｗ＊ｒ＝Ｈ＝（Ｒｒ∩Ｋ（Ｋ）＊＊,其中Ｒ＾Ｗ＊ｒ为Ｒｒ的Ｗ＊闭包,Ｋ＝｛Ｔ∈Ｒ（Ｋ）：Ｐ（Ｎ－）ＴＰ（Ｎ）＝０,Ａ↓Ｎ∈Ｎ｝;并且作为零化子和Ｒ＾Ｗ＊刻划的应用,给出了Ｒｒ中类Ｅｒｄｏｓ稠密性定理的一个新的证明和距离公式。     

一类函数方程的Cm解的存在性和惟一性

本文讨论了较为广泛的一类函数方程G（x,f(x),f^2(H2(x,f(x)),…,f^n(Hn(x,f(x),…,f^n-1(x))))=0, 对任x∈J.其中n≥,J为实数轴R 的连通闭子集,G∈C^m(J^n 1,R),Hk∈C^m(J^k,R),k=2,…,n.对任一个整数m≥0,本文在较弱的条件下讨论下该方程的C^m解的存在性和惟一性。     

关于双曲空间形式的一个注记

本文主要证明一个具有光滑边界的紧黎曼流形,如果有非平凡解,则就等度量同构与双曲空间形式 会的紧区域,这里Ｄ～２■是■的Ｈｅｓｓｉａｎ与ｇ是Ｍ上的黎曼度量． 还证明关于上述方程的边值问题,只有混合边值问题,而且当ｃ＜－１时有解．     

LaH分子的X1∑+态的势能函数

应用原子分析反应静力学原理导出ＬａＨ分子的电子状态和可能的离解极限,考虑相对论紧致有效势ＰＣＥＰ（Ｒｅｌａｔｉｖｉｓｔｉｃ Ｃｏｍｐａｃｔ Ｅｆｆｅｃｔｉｖｅ Ｐｏｔｅｎｔｉａｌ）近似下,用ＱＣＩＳＤ方法计算了ＬａＨ分子基态Ｘ＾１Σ＾＋的平衡几何Ｒｅ和离解能Ｄｅ为２．１２５Ａ和２．６２３ｅＶ,并在计算出来的一系列背地里点势能基础上,用正规方程组拟合Ｍｕｒｒｅｌｌ－Ｓｏｒｂｉｅ（Ｍ－Ｓ）势能函数,得