scholarly journals Complexity of random smooth functions on compact manifolds

2014 ◽  
Vol 63 (4) ◽  
pp. 1037-1065 ◽  
Author(s):  
Liviu Nicolaescu
Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 981
Author(s):  
Eran Liberman ◽  
Mina Teicher

Symmetry between mathematical constructions is a very desired phenomena in mathematics in general, and in algebraic geometry in particular. For line arrangements, symmetry between topological characterizations and the combinatorics of the arrangement has often been studied, and the first counterexample where symmetry breaks is in dimension 13. In the first part of this paper, we shall prove that two arrangements of smooth compact manifolds of any dimension that are connected through smooth functions are homeomorphic. In the second part, we prove this in the affine case in dimension 4.


Author(s):  
Enembe O. Okokon ◽  
Tarja Yli-Tuomi ◽  
Taina Siponen ◽  
Pekka Tiittanen ◽  
Anu W. Turunen ◽  
...  

Urban dwellers are simultaneously exposed to several environmental health risk factors. This study aimed to examine the relationship between long-term exposure to fine particulate matter (PM2.5, diameter < 2.5 µm) of residential-wood-burning and road-traffic origin, road-traffic noise, green space around participants’ homes, and hypertension. In 2015 and 2016, we conducted a survey of residents of the Helsinki Capital Region to determine their perceptions of environmental quality and safety, lifestyles, and health statuses. Recent antihypertensive medication was used as an indicator of current hypertensive illness. Individual-level exposure was estimated by linking residential coordinates with modelled outdoor levels of wood-smoke- and traffic-related PM2.5, road-traffic noise, and coverage of natural spaces. Relationships between exposure and hypertension were modelled using multi-exposure and single-exposure binary logistic regression while taking smooth functions into account. Twenty-eight percent of the participants were current users of antihypertensive medication. The odds ratios (95% confidence interval) for antihypertensive use were 1.12 (0.78–1.57); 0.97 (0.76–1.26); 0.98 (0.93–1.04) and 0.99 (0.94–1.04) for wood-smoke PM2.5, road-traffic PM2.5, road-traffic noise, and coverage of green space, respectively. We found no evidence of an effect of the investigated urban exposures on prevalent hypertension in the Helsinki Capital Region.


2020 ◽  
pp. 101537
Author(s):  
Deimer J.J. Aleans ◽  
Sergio A. Tozoni
Keyword(s):  

1997 ◽  
Vol 20 (2) ◽  
pp. 397-402 ◽  
Author(s):  
E. M. E. Zayed

The spectral functionΘ(t)=∑i=1∞exp(−tλj), where{λj}j=1∞are the eigenvalues of the negative Laplace-Beltrami operator−Δ, is studied for a compact Riemannian manifoldΩof dimension “k” with a smooth boundary∂Ω, where a finite number of piecewise impedance boundary conditions(∂∂ni+γi)u=0on the parts∂Ωi(i=1,…,m)of the boundary∂Ωcan be considered, such that∂Ω=∪i=1m∂Ωi, andγi(i=1,…,m)are assumed to be smooth functions which are not strictly positive.


Sign in / Sign up

Export Citation Format

Share Document