It is well-known that one cannot inside the pure untyped lambda calculus determine equivalence. I.e., one cannot determine if two terms are beta-equivalent, even if they both have normal forms. This implies that it is impossible in the pure untyped lambda calculus to do Godelisation, i.e. to write a function that can convert a term to a representation of (the normal form of) that term, as equi...

The present paper summarizes the activities at LTT-Erlangen on the field of thermophysical properties research for pure refrigerants and refrigerant mixtures. For the characterization of their thermophysical properties dynamic light scattering (DLS) has been intensively applied as a key tool during the past two decades. Beside a representation of the essential features of DLS for the determinat...

We discuss a rigorous foundation of the pure scale relativity theory for a one-dimensional space variable. We define several notions as ‘‘representation’’ of a continuous function, scale law and minimal resolution. We define precisely the meaning of a scale reference system and space reference system for non-differentiable one-dimensional manifolds. 2002 Elsevier Science Ltd. All rights reserved.

Multivariate curve resolution techniques in chemometrics allow to uncover the pure component information of mixed spectroscopic data. However, the so-called rotational ambiguity is a difficult hurdle in solving this factorization problem. The aim of this paper is to combine two powerful methodological approaches in order to solve the factorization problem successfully. The first approach is the...

Recently, the complete characterization of a general Gaussian dissipative system having a unique pure steady state was obtained. This result provides a clear guideline for engineering an environment such that the dissipative system has a desired pure steady state such as a cluster state. In this paper, we describe the system in terms of a quantum stochastic differential equation (QSDE) so that ...

The reduced Gassner representation is a multi-parameter representation of Pn, the pure braid group on n strings. Specializing the parameters t1, t2,...,tn to nonzero complex numbers x1,x2,...,xn gives a representation Gn(x1,...,xn): Pn GL( n 1 ) which is irreducible if and only if x1...xn 1.We find a sufficient condition that guarantees that the tensor product of an irreducible Gn(x1,...,xn)wit...

This video demonstrates the program MU, the Mathematics Understander, which learns University level Pure Mathematics. The video is both concerned with MU's performance in learning and performing mathematics, and its underlying cognitive architecture, the Contextual Memory System, (CMS). The changes in knowledge representation during proof checking and problem solving are demonstrated graphically.

Studies have showed significant convenience in remembering pictorial representation of passwords over the textual passwords. The motivation behind exploring a graphical password scheme is based on the remarkable ability of humans to recall pictures easily. In this paper we are presenting the novel approaches for security of pure recall based techniques with the help of biometric authentication ...

The generalized Weierstrass representation for surfaces in R is used to study quantum effects for strings governed by Polyakov-Nambu-Goto action. Correlators of primary fields are calculated exactly in one-loop approximation for the pure extrinsic Polyakov action. Geometrical meaning of infrared singularity is discussed. The Nambu-Goto and spontaneous curvature actions are treated perturbatively.