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Although it is customary to define polygons as certain families of edges, when considering polyhedra it is usual to view polygons as 2-dimensional pieces of the plane. If this rather illogical point of view is replaced by consistently understanding polygons as 1-dimensional complexes, the theory...
The paper gives a necessary and sufficient condition on the spectrum of a bounded linear operator on Banach space for the convergence of the series ∑
. Some properties of the sum are investigated.
In a geometric lattice every interval can be mapped isomorphically into an upper interval (containing 1) by a strong map. A natural question thus arises as to what extent certain assumptions on the “upper interval structure” determine the whole lattice. We consider conditions of the following...
We develop a formula for enumerating the partitions of a set up to the action of a group. We give some special cases of this formula and illustrate its use with an example. Some comments are made relating the formula to an earlier formula.
The Cauchy problem for a system of integro-differential equations of a standard type is considered. The authors justify a method for partial averaging of the considered problem for asymptotically large interval of variation of the independent variable.
The authors justify a version of the averaging method for solving boundary problems for systems of integro-differential equations of Fredholm type with fast and slow variables.
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