Summery: We show that a family of smooth stable curves defined on the interior of a log regular scheme is extended to a log smooth scheme over the whole log regular scheme, if it is so at each generic point of the boundary, under a very mild assumption. We also include a proof of the fact that a log smooth scheme over a discrete valuation ring has potentially a semi-stable model. As a consequen...

In this paper, we propose a 3D geometry compression technique for densely sampled surface meshes. Based on a 3D multiresolution analysis (performed by a 3D Discrete Wavelet Transform for semi-regular meshes), this scheme includes a model-based bit allocation process across the wavelet subbands and an efficient surface adapted weighted criterion for 3D wavelet coefficient coordinates. This permi...

Given a set A $\mathbb {A}$ consisting of positive integers 1 < 2 ⋯ k $a_1<a_2<\cdots <a_k$ and k-term partition P : n + = $P: n_1+n_2 \cdots n_k=n$ , find the extremal denominators regular semi-regular continued fraction [ 0 ; x … ] $[0;x_1,x_2,\ldots ,x_n]$ with partial quotients i ∈ $x_i\in \mathbb where each $a_i$ occurs precisely $n_i$ times in sequence $x_1,x_2,\ldots ,x_n$ . In 1983, G. ...

We obtain a formula for the modulus of metric regularity of a mapping defined by a semi-infinite system of equalities and inequalities. Based on this formula, we prove a theorem of Eckart-Young type for such set-valued infinite-dimensional mappings: given a metrically regular mapping F of this kind, the infimum of the norm of a linear function g such that F + g is not metrically regular is equa...

We report the angular diameters of two Mira variables (U Ari and Z Sco), three semi-regular and irregular variables (SW Vir, η Gem and µ Gem) and a supergiant semi-regular variable (TV Gem) by lunar occultation observations in the near-infrared broad K-band (2.2 µm). Lunar occultations of η Gem and µ Gem were also observed for the first time simultaneously in both K and L ′ bands yielding angul...

The paper formulates projective dependency grammars in terms of constraints on a string based encoding of dependency trees and develops an approach to obtain a regular approximation for these grammars. In the approach, dependency analyses are encoded with balanced bracketing that encodes dependency relations among the words of the analyzed sentence. The brackets, thus, indicate dependencies rat...

Locales provide a module system for the Isabelle proof assistant. Recently, locales have been ported to the new Isar format for structured proofs. At the same time, they have been extended by locale expressions, a language for composing locale specifications, and by structures, which provide syntax for algebraic structures. The present paper presents both and is suitable as a tutorial to locale...