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arxiv.org/abs/2203.10891v1
We introduce a new theory of plane $\mathbb R$-tree, to define plane ICRT (inhomogeneous continuum random tree), and its looptree, fennec (a Gaussian free field on the looptree), and snake. We prove that a.s. the looptree is compact, and that a.s. th...
arxiv.org/abs/2506.14778v3
We establish that any affine manifold $(M,\nabla)$ endowed with a parallel volume form $ω,$ admits, in any conformal class of Riemannian metrics, a representative $H$ for which $\nabla$ is the Levi-Civita connection. This provides a constructive pro...
arxiv.org/abs/math/0511303v4
Geodesically complete affine manifolds are quotients of the Euclidean space through a properly discontinuous action of a subgroup of affine Euclidean transformations. An equivalent definition is that the tangent bundle of such a manifold admits a f...
arxiv.org/abs/1210.2525v2
Given a compact manifold $N^n \subset \mathbb{R}^ν$, $s \ge 1$ and $1 \le p < \infty$, we prove that the class of smooth maps on the cube with values into $N^n$ is strongly dense in the fractional Sobolev space $W^{s, p}(Q^m; N^n)$ when $N^n$ is $\l...
en.wikipedia.org/wiki/Diffuser_%28optics%29
transmit soft light. Diffused light can be easily obtained by reflecting light from a white surface, while more compact diffusers may use translucent material
www.bing.com/ck/a?!&&p=26f638a1e3a63ece6c2a7cf1f04b0fd12ee44f54b3563a14e38347130e5cc067JmltdHM9MTc3MjU4MjQwMA&ptn=3&ver=2&hsh=4&fclid=2db561b6-ecef-6cf5-28a9-76a4ed476ddc&u=a1aHR0cHM6Ly93d3cud29yZHJlZmVyZW5jZS5jb20vZGVmaW5pdGlvbi9yb2xsaW5n&ntb=1
to spread out, level, smooth, compact, or the like, as with a rolling pin, roller, the hands, etc.: to roll dough; to roll a tennis court. Metallurgy to form (metal) in a rolling mill.
arxiv.org/abs/2507.03591v1
We analyze the IIA supergravity solutions corresponding to a warped product of a 3D external Minkowski space and a 7D internal non-compact space, with the latter being the direct product of a deformed conifold and a circle. The specific construction...
arxiv.org/abs/0808.1058v1
We generalize a semi-norm for the Alexander polynomial of a connected, compact, oriented 3-manifold on its first cohomology group to a semi-norm for an arbitrary Laurent polynomial f on the dual vector space to the space of exponents of f. We deter...
arxiv.org/abs/2507.20734v3
We give an upper bound on the distance between a degeneracy slope for a very full essential lamination and a boundary slope of an essential surface embedded in a compact, orientable, irreducible, atoroidal 3-manifold with incompressible torus boundar...
www.bing.com/ck/a?!&&p=944e736ee2dc5befa014f6c7274fcbaaf1cc53adfa7391ee432d73dde2c253c6JmltdHM9MTc3MjU4MjQwMA&ptn=3&ver=2&hsh=4&fclid=2c478a8a-2947-6d44-326b-9d9828e76cf9&u=a1aHR0cHM6Ly93d3cud29yZHJlZmVyZW5jZS5jb20vZGVmaW5pdGlvbi9yb2xsaW5n&ntb=1
to spread out, level, smooth, compact, or the like, as with a rolling pin, roller, the hands, etc.: to roll dough; to roll a tennis court. Metallurgy to form (metal) in a rolling mill.
arxiv.org/abs/0901.1604v3
In this short note, we compute the Betti numbers of the moduli stack of flat SU(3)-bundles over a Klein bottle. We also handle the general compact group case over RP^2. In all cases the cohomology is found to be equivariantly formal, supporting a c...
arxiv.org/abs/1312.7450v2
We study the classifying space of a twisted loop group $L_σG$ where $G$ is a compact Lie group and $σ$ is an automorphism of $G$ of finite order modulo inner automorphisms. Equivalently, we study the $σ$-twisted adjoint action of $G$ on itself. We...
arxiv.org/abs/0902.4581v3
We use Morse theory of the Yang-Mills functional to compute the Betti numbers of the moduli stack of flat U(3)-bundles over a compact nonorientable surface. Our result establishes the antiperfection conjecture of Ho-Liu, and provides evidence for t...
arxiv.org/abs/astro-ph/9901276v1
The VLBI technique can image compact radio sources with resolutions of the order of the milliarcsecond and can determine astrometrically relative positions with submilliarcsecond precisions. We determined the angular separations among the radio sou...
arxiv.org/abs/1708.02665v1
Let $G$ be a finite group, $A$ a unital separable finite simple nuclear C*-algebra, and $α$ an action of $G$ on $A$. Assume that $A$ absorbs the Jiang-Su algebra $\mathcal{Z}$, the extremal boundary of the trace space of $A$ is compact and finite di...
www.bing.com/ck/a?!&&p=852dcd6da20041815d09e1b8595fa19bf2b78dc53fc7eb2410d26a0473f4f14bJmltdHM9MTc3MjU4MjQwMA&ptn=3&ver=2&hsh=4&fclid=2be23b62-1987-60b5-1d24-2c70184661f2&u=a1aHR0cHM6Ly9jb2FscGFpbC5jb20vY29hbC1mb3J1bS92aWV3dG9waWMucGhwP3Q9NTI0Njk&ntb=1
Feb 23, 2020 · Banking a fire is preparing a bituminous coal fire or even a wood fire at the evening time before going to bed. It is to arrange the fire to be compact shape and size and then ashes are layer …
