Search results for "Natural class"
showing 5 items of 5 documents
Analysis of Optimal High Resolution and Fixed Rate Scalar Quantization
2009
In 2001, Hui and Neuhoff proposed a uniform quantizer with overload for the quantization of scalar signals and derived the asymptotically optimal size of the quantization bins in the high-bitrate limit. The purpose of the present paper is to prove a quantitatively more precise version of this result which, at the same time, is valid for a more general, quite natural class of probability distributions that requires only little regularity and includes, for instance, positive Lipschitz-continuous functions of unit integral.
Images and Preimages of Null Sets
2013
In this chapter we study conditions that guarantee that our mapping maps sets of measure zero to sets of measure zero. We start with the problem in general Sobolev spaces, after which we establish a better result for mappings of finite distortion. Then we introduce a natural class of counterexamples to statements of this type and finally we give a weak condition under which the preimage of a set of measure zero has measure zero for mappings of finite distortion.
The conjugacy problem in subgroups of right-angled Artin groups
2009
We prove that the conjugacy problem in right-angled Artin groups (RAAGs), as well as in a large and natural class of subgroups of RAAGs, can be solved in linear-time. This class of subgroups contains, for instance, all graph braid groups (i.e. fundamental groups of configuration spaces of points in graphs), many hyperbolic groups, and it coincides with the class of fundamental groups of ``special cube complexes'' studied independently by Haglund and Wise.
Specification on the interval
1997
We study the consequences of discontinuities on the specification property for interval maps. After giving a necessary and sufficient condition for a piecewise monotonic, piecewise continuous map to have this property, we show that for a large and natural class of families of such maps (including the β \beta -transformations), the set of parameters for which the specification property holds, though dense, has zero Lebesgue measure. Thus, regarding the specification property, the general case is at the opposite of the continuous case solved by A.M. Blokh (Russian Math. Surveys 38 (1983), 133–134) (for which we give a proof).
Relative cohomology spaces for some osp($n|2$)-modules
2018
International audience; In this work, we describe the H-invariant, so(n)-relative cohomology of a natural class of osp(n|2)-modules M, for n ≠ 2. The Lie superalgebra osp(n|2) can be realized as a superalgebra of vector fields on the superline R1|n. This yields canonical actions on spaces of densities and differential operators on the superline. The above result gives the zero, first, and second cohomology spaces for these modules of densities and differential operators.