Condensed detachment is complete for relevance logic: A computer-aided proof

The condensed detachment ruleD is a combination of modus ponens with a minimal amount of substitution. EarlierD has been shown to be complete for intuitionistic and classical implicational logic but incomplete forBCK andBCI logic. We show thatD is complete for the relevance logic. One of the main steps is the proof of the formula ((a a) a) a found in interaction with our resolution theorem prover. Various strategies of generating consequences of the axioms and choosing best ones for the next iteration were tried until the proof was found.     

On relaxed nested factorization and combination preconditioning

The efficient solution of block tridiagonal linear systems arising from the discretization of convection–diffusion problem is considered in this paper. Starting with the classical nested factorization, we propose a relaxed nested factorization preconditioner. Then, several combination preconditioners are developed based on relaxed nested factorization and a tangential filtering preconditioner. Influence of the relaxation parameter is numerically studied, the results indicate that the optimal relaxation parameter should be close to but less than 1. The number of iteration counts exhibit an extremely sensitive behaviour. This phenomena resembles the behaviour of relaxed ILU preconditioner. For symmetric positive-definite coefficient matrix, we also show that the proposed combination preconditioner is convergent. Finally, numerous test cases are carried out with both additive and multiplicative combinations to verify the robustness of the proposed preconditioners.     

(E)-11,13-tetradecadienal: Major sex pheromone component of the eastern blackheaded budworm,Acleris variana (Fern.) (Lepidoptera: Tortricidae)

(E)-11,13-Tetradecadienal (E11,13–14:Ald) is the major sex pheromone component of the eastern blackheaded budworm (EBB),Acleris variana (Fern.). The compound was identified in female pheromone gland extracts by coupled gas chromatographic-electroantennographic detection (GC-EAD), coupled GC-mass spectrometry in selected ion monitoring mode, and retention index calculations of candidate pheromone components.E11,13–14:Ald alone as trap bait was very attractive to male EBB. Addition of the corresponding diene alcohol or acetate or both did not enhance attraction. (Z)-11,13-Tetradecadienal in binary combination with (E)-11,13–14:Ald neither enhanced nor reduced trap catches. Increasing the amounts of pheromone from 0.01 to 10 µg increased trap catches, but increase of pheromone quantity above 100 µg proportionately reduced attraction. Stabilization of slowly polymerizingE11,13–14:Ald and development of a sustained, adequate release rate is required for pheromone-based monitoring of EBB populations.     

Enantiomers of (Z,Z)-6,9-Heneicosadien-11-OL: Sex Pheromone Components of Orgyia detrita

(6Z,9Z,11S)-6,9-Heneicosadien-11-ol (Z6Z9-11S-ol-C21) and (6Z,9Z,11R)-6,9-heneicosadien-11-ol (Z6Z9-11R-ol-C21) were identified as major sex pheromone components of female tussock moths, Orgyia detritaGuérin-Méneville (Lepidoptera: Lymantriidae), on the basis of (1) analyses of pheromone gland extracts of female O. detrita by coupled gas chromatographic-electroantennographic detection (GC-EAD) and GC mass spectrometry, and (2) field trapping experiments with synthetic standards. Z6Z9-11S-ol-C21 and Z6Z9-11R-ol-C21 in combination, but not singly, attracted significant numbers of male moths. Racemic Z6Z9-11-ol-C21 was more attractive than the 1:3.5 (R:S) blend ratio found in pheromone gland extracts from female moths. Lower and higher homologues of Z6Z9-11-ol-C21 were also detected in GC-EAD recordings of pheromone extracts, and the racemic compounds enhanced attractiveness of Z6Z9-11-ol-C21 in field experiments. Because of trace amounts of these homologues in extracts, their enantiomeric composition could not be determined. This is the first report of secondary alcohols as pheromone components in the ditrysian (advanced) Lepidoptera.     

Towards an accurate performance modeling of parallel sparse factorization

We present a simulation-based performance model to analyze a parallel sparse LU factorization algorithm on modern cached-based, high-end parallel architectures. We consider supernodal right-looking parallel factorization on a bi-dimensional grid of processors, that uses static pivoting. Our model characterizes the algorithmic behavior by taking into account the underlying processor speed, memory system performance, as well as the interconnect speed. The model is validated using the implementation in the SuperLU_DIST linear system solver, the sparse matrices from real application, and an IBM POWER3 parallel machine. Our modeling methodology can be adapted to study performance of other types of sparse factorizations, such as Cholesky or QR, and on different parallel machines.     

Prediction of the relationship between the rate of deformation and the rate of stress relaxation in glassy polymers

Kim, et al. (Polymer, 54(15), 3949, 2013) recently reported on the unexpected relaxation behavior of an amorphous polymer in the T_g-region, where the rate of stress relaxation increased with deformation at a strain rate of 1.5 × 10⁻⁴ s⁻¹ but decreased at a strain rate of 1.2 × 10⁻⁵ s⁻¹. This inversion in the ordering with strain rate challenges the underlying structure of the existing nonlinear viscoelastic and viscoplastic constitutive models, where the key nonlinearity is a deformation dependent material clock. The nonlinear stress relaxation predictions of a recently developed stochastic constitutive model, SCM, (Medvedev, et al., J. Rheology, 57(3), 949, 2013) that acknowledge dynamic heterogeneity of the glass have been investigated. The SCM predicts the inversion in the ordering of the mobility with the loading strain rate as reported by the stress relaxation response. The change in perspective on the nonlinear viscoelastic behavior of glassy polymers engendered by the SCM is discussed.     

Mobility evolution during tri-axial deformation of a glassy polymer

In this study, the evolution of mobility with deformation in a glassy polymer is compared in cases of dilatationally dominated longitudinal and deviatorically dominated uniaxial deformation. The mobility is evaluated via stress relaxation experiments performed at various points along the stress–strain curve, including pre-yield, yield, and post-yield regions. At T_g−5 °C the mobility decreases with deformation in uniaxial extension, but increases with deformation in tri-axial extension. The τ_eff relaxation time calculated for longitudinal deformation exhibits a dramatically different dependence on the excess volume than the relaxation time obtained in structural relaxation experiments. Finally, the criterion for cavitational failure is proposed based on the thermodynamic stability considerations.     

On embedding default logic into Moore''s autoepistemic logic

Recently Gottlob proved [2] that there does not exist a faithful modular translation of default logic into autoepistemic logic, and presented a non-modular translation. Gottlob's translation, however, is indirect (it uses “nonmonotonic logic N” as an intermediate point), quite complex and exploits sophisticated encoding of proof theory in autoepistemic formulas. We provide a simpler and more intuitive (non-modular) direct translation. In addition, our argument is purely model-theoretic.