We prove that for every two convex polytopes P, Q ∈ R with vol(P ) = vol(Q), there exists a continuous piecewise-linear (PL) volume-preserving map f : P → Q. The result extends to general PL-manifolds. The proof is inexplicit and uses the corresponding fact in the smooth category, proved by Moser in [Mo]. We conclude with various examples and combinatorial applications.

The aim of this paper is to show that, in various situations, the only continuous linear map that transforms a convolution product into a pointwise product is a Fourier transform. We focus on the cyclic groups Z/nZ, the integers Z, the Torus T and the real line. We also ask a related question for the twisted convolution. In memory of A. Hulanicki.

We propose a feature space maximum a posteriori (MAP) linear regression framework to adapt parameters for context dependent deep neural network hidden Markov models (CD-DNNHMMs). Due to the huge amount of parameters used in DNN acoustic models in large vocabulary continuous speech recognition, the problem of over-fitting can be severe in DNN adaptation, thus often impair the robustness of the a...

‎Let $R$ be a ring‎ ‎with the Jacobson radical $J(R)$ and let $picolon Rto R/J(R)$ be‎ the canonical map‎. ‎Then $pi$ induces an order preserving group homomorphism‎ ‎$K_0picolon K_0(R)to K_0(R/J(R))$ and an‎ ‎affine continuous map $S(K_0pi)$ between the state space $St(R/J(R))$ and the‎ ‎state space $St(R).$‎ ‎In this paper‎, ‎we consider the natural affine map $S(K_0pi).$ We give a condition ...

the dynamical behavior of a map on the unit interval has been the subject of much contemporary research. in this paper, we will consider the relation between the continuity of the map cof and cof for some positive integer k, where f is a continuous map from the unit interval to itself, and ?f is a function which takes any element of the unit interval to the set of all subsequential limits of th...