Ordering arc-reversal operations when eliminating variables in lazy AR propagation

This paper considers the problem of ordering arc-reversal operations and breaking ties in cost measures when eliminating variables in Lazy AR Propagation (LPAR). In particular, the paper presents the BreakTies algorithm for breaking ties in cost measures when selecting the next arc to reverse in a variable elimination operation. BreakTies is based upon using a sequence of cost measures instead of randomly selecting an arc to reverse when multiple arcs share the same cost. The paper reports on an experimental evaluation of LPAR for belief update in Bayesian networks considering six sequences of five cost measures for breaking ties using BreakTies. The experimental results show that using BreakTies to select the next arc to reverse in a variable elimination operation can improve performance of LPAR.     

Cubical Version of Combinatorial Differential Forms

The theory of combinatorial differential forms is usually presented in simplicial terms. We present here a cubical version; it depends on the possibility of forming affine combinations of mutual neighbour points in a manifold, in the context of synthetic differential geometry.     

Synthesis of Diverse α-Fluoroalkoxyaryl Derivatives and Their Use for the Generation of Fluorinated Macrocycles

Introduction of difluorinated functionality has emerged as a powerful means for conformational design with minimal steric footprint. Synthetic approaches for the preparation of aryl difluoromethylene ether containing novel building blocks were established, enabling the inclusion of the aryl difluoromethylene ether system into macrocyclic scaffolds for the first time.     

Synthesis of both enantiomers of the docosahexaenoic acid ester of 13-hydroxyoctadecadienoic acid (13-DHAHLA)

Recently, several different classes of endogenous lipids have been reported that display antidiabetic and anti-inflammatory effects. Due to their minute presence in human samples, access to synthetic material of each enantiomer becomes necessary for exact structural elucidation and extensive biological evaluation. Herein we report the multi-milligram synthesis of both enantiomers of the docosahexaenoic acid ester of 13-hydroxyoctadecadienoic acid (13-DHAHLA) from commercially available starting materials.     

Planar elongation of soft polymeric networks

A new test fixture for the filament stretch rheometer (FSR) has been developed to measure planar elongation of soft polymeric networks with application towards pressure-sensitive adhesives (PSAs). The concept of this new geometry is to elongate a tube-like sample by keeping the perimeter constant. To validate this new technique, soft polymeric networks of poly(propylene oxide) (PPO) were investigated during deformation. Particle tracking and video recording were used to detect to what extent the imposed strain rate and the sample perimeter remained constant. It was observed that, by using an appropriate choice of initial sample height, perimeter, and thickness, the planar stretch ratio will follow l(t) = h(t)/h₀ = exp([(e)\dot] t)\lambda(t) = h(t)/h_0= \exp({\dot{\varepsilon}} t), with h(t) being the height at time t and [(e)\dot]{\dot{\varepsilon}} the imposed constant strain rate. The perimeter would decrease by a few percent only, which is found to be negligible. The ideal planar extension in this new fixture was confirmed by finite element simulations. Analysis of the stress difference, σ _zz  − σ _xx , showed a network response similar to that of the classical neo-Hookean model. As the Deborah number was increased, the stress difference deviated more from the classical prediction due to the dynamic structures in the material. A modified Lodge model using characteristic parameters from linear viscoelastic measurements gave very good stress predictions at all Deborah numbers used in the quasi-linear regime.     

Deformation of Dupuit''s parabola in a dam with sheet piling

If the flow in an earth dam is plane and steady, the shape of the phreatic surface can be approximated by Dupuit's parabola. Thin sheet piling in the dam, deforms the phreatic surface in the vicinity of the sheet piling and at its tip the hydraulic gradient is singular. If the length of the sheet pile is much smaller than the thickness of the dam, the flux through the dam per sheet pile length is equal to the undisturbed flux, whereas if the length of the sheet pile is much larger than the thickness of the dam the corresponding flux is negligible.Nomenclature a length of sheet pile - A auxiliary parameter - b thickness of dam - G Greens function - h height of phreatic surface - K hydraulic conductivity - Q flux per sheet pile length - Q ₀ reference flux - r, auxiliary variables - r ₀ auxiliary parameter - R half-strip in thex-y-plane with a cut - R ₁ strip in thex-y-plane - R₁ half-strip in thex-y-plane - R ₂ half space in the--plane - R radius of curvature of the tip of the sheet pile - z=x+iy complex variable inR,R ₁ andR₁ - w=+i complex in variable inR ₂ - h ² potential - ÷ unknown at a part of the boundary ofR ₂     

On the absolute configuration of 1-cyclopropylethan-1-amine

We observed a discrepancy between the reported specific rotation for the enantiomers of 1-cyclopropylethan-1-amine and the values for commercial material. Analyses by VCD of the free amine, by NMR analysis of the derived (S)-O-methylmandelamides and an X-ray crystal structure of one of the mandelamides defined the specific rotation for each enantiomer.