��ber Aus- und R��ckwanderung : Vortrag, geh. am Mittwoch, 17. Sept. 1902 in d. Henry Jones-Loge in Hamburg

von Paul Laskar

Monte Carlo modeling of polarized light propagation: Stokes vs Jones - Part I

This bipartite comparative study aims at inspecting the similarities and differences between the Jones and Stokes���Mueller formalisms when modeling polarized light propagation with numerical simulations of the Monte Carlo type. In this first part, we review the theoretical concepts that concern light propagation and detection with both pure and partially/totally unpolarized states. The latter case involving fluctuations, or ���depolarizing effects,��� is of special interest here: Jones and Stokes���Mueller are equally apt to model such effects and are expected to yield identical results. In a second, ensuing paper, empirical evidence is provided by means of numerical experiments, using both formalisms.

Monte Carlo modeling of polarized light propagation: Stokes vs Jones - Part II

In this second part of our comparative study inspecting the (dis)similarities between ���Stokes��� and ���Jones,��� we present simulation results yielded by two independent Monte Carlo programs: (i) one developed in Bern with the Jones formalism and (ii) the other implemented in Ulm with the Stokes notation. The simulated polarimetric experiments involve suspensions of polystyrene spheres with varying size. Reflection and refraction at the sample/air interfaces are also considered. Both programs yield identical results when propagating pure polarization states, yet, with unpolarized illumination, second order statistical differences appear, thereby highlighting the pre-averaged nature of the Stokes parameters. This study serves as a validation for both programs and clarifies the misleading belief according to which ���Jones cannot treat depolarizing effects.���

Jones, Kniest��ck

Signatur des Originals: S 36/F08915

Agnes Huntington als Paul Jones, Rollenbild, Brustbild

Signatur des Originals: S 36/F08873

Edwin J. Lonnen, Jones, Rollenbild, Doppelbildnis

Signatur des Originals: S 36/F09132

Annie Jones, Rollenbild, Brustbild

Signatur des Originals: S 36/F09560

A geometric characterization of the upper bound for the span of the jones polynomial

Let D be a link diagram with n crossings, sA and sB be its extreme states and |sAD| (respectively, |sBD|) be the number of simple closed curves that appear when smoothing D according to sA (respectively, sB). We give a general formula for the sum |sAD| + |sBD| for a k-almost alternating diagram D, for any k, characterizing this sum as the number of faces in an appropriate triangulation of an appropriate surface with boundary. When D is dealternator connected, the triangulation is especially simple, yielding |sAD| + |sBD| = n + 2 - 2k. This gives a simple geometric proof of the upper bound of the span of the Jones polynomial for dealternator connected diagrams, a result first obtained by Zhu [On Kauffman brackets, J. Knot Theory Ramifications6(1) (1997) 125���148.]. Another upper bound of the span of the Jones polynomial for dealternator connected and dealternator reduced diagrams, discovered historically first by Adams et al. [Almost alternating links, Topology Appl.46(2) (1992) 151���165.], is obtained as a corollary. As a new application, we prove that the Turaev genus is equal to the number k of dealternator crossings for any dealternator connected diagram

Flora of Illinois, containing keys for the identification of the flowering plants and ferns, by George Neville Jones ...

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