scholarly journals The Hilton-Spencer cycle theorems via Katona's shadow intersection theorem

2020 ◽  
Author(s):  
Peter Borg ◽  
Carl Feghali
Keyword(s):  
Intersection Theorem

scholarly journals Space variability of hydrological responses of Nature-Based Solutions and the resulting uncertainty

2020 ◽  
Author(s):  
Yangzi Qiu ◽  
Igor da Silva Rocha Paz ◽  
Feihu Chen ◽  
Pierre-Antoine Versini ◽  
Daniel Schertzer ◽  
...  
Keyword(s):  
Spatial Variability ◽  
Peak Flow ◽  
Hydrological Cycle ◽  
Green Roof ◽  
Spatial Arrangement ◽  
Intersection Theorem ◽  
Runoff Volume ◽  
Hydrological Responses ◽  
Total Runoff ◽  
The Impact

Abstract. During the last decades, the urban hydrological cycle has been strongly modified by the built environment, resulting in fast runoff and increasing the risk of waterlogging. Nature-Based Solutions (NBS), which apply green infrastructures, have been more and more widely considered as a sustainable approach for urban stormwater management. However, the assessment of NBS performance still requires further modelling development because of their hydrological responses sensitively depends on the representation of multiscale space variability of both the rainfall and the NBS distribution. Indeed, we initially argue this issue with the help of the multifractal intersection theorem. To illustrate the importance of this question, the spatial heterogeneous distributions of two series of NBS scenarios (porous pavement, rain garden, green roof, and combined) are quantified with the help of their fractal dimension. We point out consequences of their estimates. Then, a fully-distributed and physically-based hydrological model (Multi-Hydro) was applied to consider the studied catchment and these NBS scenarios with a spatial resolution of 10 m under two different types of rainfall: distributed and uniform, and for three rainfall events. These simulations show that the impact of spatial variability of rainfall on the uncertainty of peak flow of NBS scenarios ranges from about 8 % to 17 %, which is more pronounced than those of the total runoff volume. In addition, the spatial variability of the rainfall intensity at the largest rainfall peak responds almost linearly to the uncertainty of the peak flow of NBS scenarios. However, the hydrological responses of NBS scenarios are less affected by the spatial distribution of NBS. Finally, the intersection effects of the spatial variability of rainfall and the spatial arrangement of NBS seem more pronounced for the peak flow of green roof scenarios and the total runoff volume of combined scenarios.

scholarly journals Proof of an Intersection Theorem via Graph Homomorphisms

10.37236/1144 ◽  
2006 ◽  
Vol 13 (1) ◽  
Author(s):  
Irit Dinur ◽  
Ehud Friedgut
Keyword(s):  
Product Measure ◽  
Intersection Theorem ◽  
Intersecting Family ◽  
Graph Homomorphisms

Let $0 \leq p \leq 1/2 $ and let $\{0,1\}^n$ be endowed with the product measure $\mu_p$ defined by $\mu_p(x)=p^{|x|}(1-p)^{n-|x|}$, where $|x|=\sum x_i$. Let $I \subseteq \{0,1\}^n$ be an intersecting family, i.e. for every $x, y \in I$ there exists a coordinate $1 \leq i \leq n$ such that $x_i=y_i=1$. Then $\mu_p(I) \leq p.$ Our proof uses measure preserving homomorphisms between graphs.

scholarly journals On dual versions of Krull's intersection theorem

2007 ◽  
Vol 2 ◽  
pp. 2655-2659
Author(s):  
H. Ansari-Toroghy ◽  
F. Farshadifar
Keyword(s):  
Intersection Theorem

scholarly journals A Finite Set Intersection Theorem

1981 ◽  
Vol 2 (2) ◽  
pp. 127-129 ◽  
Author(s):  
P. Frankl ◽  
I.G. Rosenberg
Keyword(s):  
Intersection Theorem ◽  
Set Intersection ◽  
Finite Set

Complete Intersection Flat Dimension and the Intersection Theorem

2012 ◽  
Vol 19 (spec01) ◽  
pp. 1161-1166
Author(s):  
Parviz Sahandi ◽  
Tirdad Sharif ◽  
Siamak Yassemi
Keyword(s):  
Local Ring ◽  
Complete Intersection ◽  
Intersection Theorem ◽  
Finitely Generated ◽  
Finitely Generated Module ◽  
Gorenstein Dimension ◽  
Flat Dimension ◽  
Gorenstein Flat ◽  
Similar Extension

Any finitely generated module M over a local ring R is endowed with a complete intersection dimension CI-dim RM and a Gorenstein dimension G-dim RM. The Gorenstein dimension can be extended to all modules over the ring R. This paper presents a similar extension for the complete intersection dimension, and mentions the relation between this dimension and the Gorenstein flat dimension. In addition, we show that in the intersection theorem, the flat dimension can be replaced by the complete intersection flat dimension.

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