This paper discusses the problem that making the air flowing into the room maximized by rotating the windows. Two models are built for rotary windows with 2 and 3 sashes respectively. Based on these models and the assumption of wind blowing from different directions with equal chance, the optimal way of opening windows is calculated by using Pascal programs on computer. Finally, the optimal design for window ventilation is found via comparing maximum value of wind quantity in two situations.

We study period integrals of CY hypersurfaces in a partial flag variety. We construct a holonomic system of differential equations which govern the period integrals. By means of representation theory, a set of generators of the system can be described explicitly. The results are also generalized to CY complete intersections. The construction of these new systems of differential equations have lead us to the notion of a tautological system.

We derive an asymptotic formula which counts the number of abelian extensions of prime degrees over rational function fields. Specifically, let l be a rational prime and K a rational function field F_q(t) with l\nmid q. Let Discf (F/K) denote the finite discriminant of F over K. Denote the number of abelian l-extensions F/K with deg (Discf (F/K)) = (l − 1)αn by a_l(n), where α = α(q, l) is the order of q in the multiplicative group (Z/lZ)^\times. We give a explicit asymptotic formula for a_l(n). In the case of cubic extensions with q ≡ 2 (mod 3), our formula gives an exact analogue of Cohn’s classical formula.

No abstract uploaded!

Laser scanning is an effective tool for acquiring geometric attributes of trees and vegetation, which lays a solid foundation for 3-dimensional tree modelling. Existing studies on tree modelling from laser scanning data are vast. However, some works cannot guarantee sufficient modelling accuracy, while some other works are mainly rule-based and therefore highly depend on user inputs. In this paper, we propose a novel method to accurately and automatically reconstruct detailed 3D tree models from laser scans. We first extract an initial tree skeleton from the input point cloud by establishing a minimum spanning tree using the Dijkstra shortest-path algorithm. Then, the initial tree skeleton is pruned by iteratively removing redundant components. After that, an optimization-based approach is performed to fit a sequence of cylinders to approximate the geometry of the tree branches. Experiments on various types of trees from different data sources demonstrate the effectiveness and robustness of our method. The overall fitting error (i.e., the distance between the input points and the output model) is less than 10 cm. The reconstructed tree models can be further applied in the precise estimation of tree attributes, urban landscape visualization, etc. The source code of this work is freely available at https://github.com/tudelft3d/adtree