Takens’ Embedding Theorem forms the basis of virtually all approaches to the analysis of time series generated by nonlinear deterministic dynamical systems. It typically allows us to reconstruct an unknown dynamical system which gave rise to a given observed scalar time series simply by constructing a new state space out of successive values of the time series. This provides the theoretical fou...

The Whitney embedding theorem gives an upper bound on the smallest embedding dimension of a manifold. If a data set lies on a manifold, a random projection into this reduced dimension will retain the manifold structure. Here we present an algorithm to find a projection that distorts the data as little as possible.

A shallow semantical embedding of a dyadic deontic logic by Carmo and Jones in classical higher-order logic is presented. This embedding is proven sound and complete, that is, faithful. The work presented here provides the theoretical foundation for the implementation and automation of dyadic deontic logic within off-the-shelf higherorder theorem provers and proof assistants.

We prove the following version of W lodarczyk’s Embedding Theorem: Every normal complex algebraic C∗-variety Y admits an equivariant closed embedding into a toric prevariety X on which C∗ acts as a one-parameter-subgroup of the big torus T ⊂ X. If Y is Q-factorial, then X may be chosen to be simplicial and of affine intersection.

We present a straightforward embedding of quantified multimodal logic in simple type theory and prove its soundness and completeness. Modal operators are replaced by quantification over a type of possible worlds. We present simple experiments, using existing higher-order theorem provers, to demonstrate that the embedding allows automated proofs of statements in these logics, as well as meta pro...

We present an elementary uniied and self-contained proof of sharp Sobolev embedding theorems. We introduce a new function space and use it to improve the limiting Sobolev embedding theorem due to Brrzis and Wainger. Let be an open subset of R n , where n 2, let 1 p < 1 and let W 1;p (() be the Sobolev space, that is, the set of all functions in L p ((), whose distributional derivatives of the r...

Abstract. We develop a theory of Lp spaces based on outer measures generated through coverings by distinguished sets. The theory includes as a special case the classical Lp theory on Euclidean spaces as well as some previously considered generalizations. The theory is a framework to describe aspects of singular integral theory, such as Carleson embedding theorems, paraproduct estimates, and T (...

The literature in the eld of interior point methods for linear programming has been almost exclusively algorithm oriented. Recently G uler, Roos, Terlaky and Vial presented a complete duality theory for linear programming based on the interior point approach. In this paper we present a more simple approach which is based on an embedding of the primal problem and its dual into a skew symmetric ...

Among the familiar basic facts concerning unrestricted permutational wreath products (sketched in the first few paragraphs of the last section of Cossey, Kegel, and Kov~cs [2]), the Embedding Theorem has the central role. It asserts the existence of an embedding; the proof is a construction which involves arbitrarily chosen coset representatives, with the effect that the embedding constructed m...