4,292 research outputs found
Remarks on the stochastic transport equation with H\"{o}lder drift
We consider a stochastic linear transport equation with a globally H\"{o}lder
continuous and bounded vector field. Opposite to what happens in the
deterministic case where shocks may appear, we show that the unique solution
starting with a C^{1}-initial condition remains of class in space. We
also improve some results of Flandoli-Gubinelli-Priola (2009) about
well-posedness. Moreover, we prove a stability property for the solution with
respect to the initial datum.Comment: arXiv admin note: text overlap with arXiv:0809.131
Regularity of Stochastic Kinetic Equations
We consider regularity properties of stochastic kinetic equations with
multiplicative noise and drift term which belongs to a space of mixed
regularity (-regularity in the velocity-variable and Sobolev regularity in
the space-variable). We prove that, in contrast with the deterministic case,
the SPDE admits a unique weakly differentiable solution which preserves a
certain degree of Sobolev regularity of the initial condition without
developing discontinuities. To prove the result we also study the related
degenerate Kolmogorov equation in Bessel-Sobolev spaces and construct a
suitable stochastic flow
On triangular norms and uninorms definable in ŁΠ12
AbstractIn this paper, we investigate the definability of classes of t-norms and uninorms in the logic ŁΠ12. In particular we provide a complete characterization of definable continuous t-norms, weak nilpotent minimum t-norms, conjunctive uninorms continuous on [0,1), and idempotent conjunctive uninorms, and give both positive and negative results concerning definability of left-continuous t-norms (and uninorms). We show that the class of definable uninorms is closed under construction methods as annihilation, rotation and rotation–annihilation. Moreover, we prove that every logic based on a definable uninorm is in PSPACE, and that any finitely axiomatizable logic based on a class of definable uninorms is decidable. Finally we show that the Uninorm Mingle Logic (UML) and the Basic Uninorm Logic (BUL) are finitely strongly standard complete w.r.t. the related class of definable left-continuous conjunctive uninorms
Isotopic replacement in ionic systems: the 4He2+ + 3He -> 3He4He+ + 4He reaction
Full quantum dynamics calculations have been carried out for the ionic
reaction 4He2+ + 3He and state-to-state reactive probabilities have been
obtained using both a time-dependent (TD) and a time-independent (TI) approach.
An accurate ab-initio potential energy surface has been employed for the
present quantum dynamics and the two sets of results are shown to be in
agreement with each other. The results for zero total angular momentum suggest
a marked presence of atom exchange (isotopic replacement) reaction with
probabilities as high as 60%. The reaction probabilities are only weakly
dependent on the initial vibrational state of the reactants while they are
slightly more sensitive to the degree of rotational excitation. A brief
discussion of the results for selected higher total angular momentum values is
also presented, while the l-shifting approximation [1] has been used to provide
estimates of the total reaction rates for the title process. Such rates are
found to be large enough to possibly become experimentally accessible
decays at large recoil in the Standard Model: a theoretical reappraisal
We critically reassess the theoretical uncertainties in the Standard Model
calculation of the observables, focusing on the low
region. We point out that even optimized observables are affected by
sizable uncertainties, since hadronic contributions generated by
current-current operators with charm are difficult to estimate, especially for
GeV. We perform a detailed numerical analysis
and present both predictions and results from the fit obtained using most
recent data. We find that non-factorizable power corrections of the expected
order of magnitude are sufficient to give a good description of current
experimental data within the Standard Model. We discuss in detail the
dependence of the corrections and their possible interpretation as shifts of
the Standard Model Wilson coefficients.Comment: 33 pages, 7 figures, 11 tables. v2: fixed numerical error in S4 and
typos; added discussion of the impact of future measurements; conclusions
unchange
Quantifier elimination and other model-theoretic properties of BL-algebras
This work presents a model-theoretic approach to the study of firstorder theories of classes of BL-chains. Among other facts, we present several classes of BL-algebras, generating the whole variety of BL-algebras whose firstorder theory has quantifier elimination. Model-completeness and decision problems are also investigated. Then we investigate classes of BL-algebras having (or not having) the amalgamation property or the joint embedding property and we relate the above properties to the existence of ultrahomogeneous models. © 2011 by University of Notre Dame.Peer Reviewe
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