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In topology, the notions of the fundamental group and the universal cover are closely intertwined. By importing usual notions from topology into the algebraic and arithmetic setting, we construct a ...
Wh ile D-O p tim al exp er im ental d es ign s ar e u s ed w ith gr eat f r equ en cy in s u r f ace r es p on s e an alys is th ey als o offer a m ech an is m to s cr een f actor s an d f actor inte...
This paper investigates the impact and potential use of the cut-cell vertical discretisation for forecasts coveringve days and climate simulations.
Earthquake is an abrupt displacement of the earth's crust caused by the discharge of strain collected along faults or by volcanic eruptions. Earthquake as a recurring natural cataclysm has always be...
In this work we give a complete description of the set covering polyhedron of circulant matrices $C^k_{sk}$ with $s = 2,3$ and $k\geq 3 $ by linear inequalities. In particular, we prove that every non...
It is known that any surface knot can be transformed to an unknotted surface knot or a surface knot which has a diagram with no triple points by a finite number of 1-handle additions. The minimum numb...
We discuss various uniform structures and topologies on the universal covering space $\widetilde X$ and on the fundamental group $\pi_1(X,x_0)$. We introduce a canonical uniform structure $CU(X)$ on a...
We consider the optimal covering of fractal sets in a two-dimensional space using ellipses which become increasingly anisotropic as their size is reduced. If the semi-minor axis is \epsilon and the se...
The self-similarity of complex networks is typically investigated through computational algorithms the primary task of which is to cover the structure with a minimal number of boxes. Here we introduce...
In this paper we study the covering numbers of the space of convex and uniformly bounded functions in multi-dimension. We find optimal upper and lower bounds for the $\epsilon$-covering number of $\C(...
We fill a lacuna in the literature by giving a version in dimension 1 of the Relative Hurewicz Theorem, and relate this to abelianisations of groupoids, covering spaces,covering morphisms of groupoids...
The main results of this note are:• It is consistent that every subparacompact space X of size !1 is a D-space.
It is well known that in an exact covering system in Z, the biggest modulus must be repeated. Very recently, S. Kim proved an analogous result for certain quadratic fields. In this paper, we prove tha...
Inspired by the "generalized t-designs" defined by Cameron [P. J. Cameron, A generalisation of t-designs, Discrete Math. 309 (2009), 4835--4842], we define a new class of combinatorial designs which ...
We prove that if an ultrafilter L is not coherent to a Q-point, then each analytic non-sigma-bounded topological group G admits an increasing chain of its proper subgroups such that: ...

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