Models of linear logic

We engage a study of nonmodal linear logic which takes times ⊗ and the linear conditional ⊸ to be the basic connectives instead of times and linear negation ()^⊥ as in Girard's approach. This difference enables us to obtain a very large subsystem of linear logic (called positive linear logic) without an involutionary negation (if the law of double negation is removed from linear logic in Girard's formulation, the resulting subsystem is extremely limited). Our approach enables us to obtain several natural models for various subsystems of linear logic, including a generic model for the so-called minimal linear logic. In particular, it is seen that these models arise spontaneously in the transition from set theory to multiset theory. We also construct a model of full (nonmodal) linear logic that is generic relative to any model of positive linear logic. However, the problem of constructing a generic model for positive linear logic remains open. Bibliography: 2 titles. Published inZapiski Nauchnykh Seminarov POMI, Vol. 220, 1995, pp. 23–35. Original     

Quantitative Analysis of Long Chain Fatty Acids Present in a Type I Kerogen Using Electrospray Ionization Fourier Transform Ion Cyclotron Resonance Mass Spectrometry: Compared with BF3/MeOH Methylation/GC-FID

Long chain fatty acids (LCFAs) are present in various natural samples and are easily detectable using electrospray ionization Fourier transform ion cyclotron resonance mass spectrometry (ESI-FT-ICR-MS) in negative ion mode. The capability of the ESI-FT-ICR-MS for quantifying LCFAs was evaluated by performing a standard addition followed by an internal standard methodology to several kerogen extracts using n-C₂₀ fatty acid as standard. As the concentration of the standard increased, the magnitude of its peak (m/z 311.29525) increased linearly but with two separate slopes, leaving the entire mass spectra relatively unchanged, which shows evidence of reproducibility. Response factors of other LCFAs are obtained using a standard addition approach. We employed five LCFA standards (n-C₁₅, n-C₁₉, n-C₂₄, n-C₂₆, and n-C₃₀) with different carbon numbers. This allowed us to determine the response factor of all fatty acids (with carbon number between 15 and 30) by plotting the slope of each standard versus its carbon number. With the observed response factors and use of the internal standard, the concentrations of LCFAs in four kerogen extracts were measured by ESI-FT-ICR-MS and compared with those from GC-FID. The carbon number distribution obtained by ESI-FT-ICR-MS matched well the GC-FID distribution (5%–50%) with the exception of C₁₆ and C₁₈, considering that ESI-FT-ICR-MS does not differentiate between normal and branched LCFAs, whereas GC-FID does. This allows one to quantitatively compare samples with a relatively similar matrix for specific compounds such as LCFAs with no need of time-consuming derivatization procedures. Moreover, the calibration can be extended to higher carbon numbers with ESI-FT-ICR-MS, beyond the capabilities of GC/MS.

Active to sterile neutrino mixing limits from neutral-current interactions in MINOS

Results are reported from a search for active to sterile neutrino oscillations in the MINOS long-baseline experiment, based on the observation of neutral-current neutrino interactions, from an exposure to the NuMI neutrino beam of 7.07×10(20) protons on target. A total of 802 neutral-current event candidates is observed in the Far Detector, compared to an expected number of 754 ± 28(stat) ± 37(syst) for oscillations among three active flavors. The fraction f(s) of disappearing ν(μ) that may transition to ν(s) is found to be less than 22% at the 90% C.L.     

Measurement of the neutrino mass splitting and flavor mixing by MINOS

Measurements of neutrino oscillations using the disappearance of muon neutrinos from the Fermilab NuMI neutrino beam as observed by the two MINOS detectors are reported. New analysis methods have been applied to an enlarged data sample from an exposure of 7.25×10(20) protons on target. A fit to neutrino oscillations yields values of |Δm(2)|=(2.32(-0.08)(+0.12))×10(-3) eV(2) for the atmospheric mass splitting and sin(2)(2θ)>0.90 (90% C.L.) for the mixing angle. Pure neutrino decay and quantum decoherence hypotheses are excluded at 7 and 9 standard deviations, respectively.