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41.
Logical theories for representing knowledge are often plagued by the so-called Logical Omniscience Problem. The problem stems from the clash between the desire to model rational agents, which should be capable of simple logical inferences, and the fact that any logical inference, however complex, almost inevitably consists of inference steps that are simple enough. This contradiction points to the fruitlessness of trying to solve the Logical Omniscience Problem qualitatively if the rationality of agents is to be maintained. We provide a quantitative solution to the problem compatible with the two important facets of the reasoning agent: rationality and resource boundedness. More precisely, we provide a test for the logical omniscience problem in a given formal theory of knowledge. The quantitative measures we use are inspired by the complexity theory. We illustrate our framework with a number of examples ranging from the traditional implicit representation of knowledge in modal logic to the language of justification logic, which is capable of spelling out the internal inference process. We use these examples to divide representations of knowledge into logically omniscient and not logically omniscient, thus trying to determine how much information about the reasoning process needs to be present in a theory to avoid logical omniscience. 相似文献
42.
Sergei B. Vakarchuk 《Journal of Mathematical Sciences》2013,188(2):146-166
A number of extremal problems of approximation theory of functions have been solved on the real line $ \mathbb{R} $ . Exact constants in the Jackson-type inequalities in the space L 2( $ \mathbb{R} $ ) are calculated. The exact values of average ν-widths are obtained for the classes of functions from L 2( $ \mathbb{R} $ ) defined by averaged moduli of continuity of the k-th order, as well as for the classes of functions defined by K-functionals. The quite complete analysis of the final results related to the solution of extremal problems of approximation theory in the periodic case and for the whole real axis is carried out in the chronological order. 相似文献
43.
In this paper, we discuss the classical ill-posed problem of numerical differentiation, assuming that the smoothness of the function to be differentiated is unknown. Using recent results on adaptive regularization of general ill-posed problems, we propose new rules for the choice of the stepsize in the finite-difference methods, and for the regularization parameter choice in numerical differentiation regularized by the iterated Tikhonov method. These methods are shown to be effective for the differentiation of noisy functions, and the order-optimal convergence results for them are proved.
44.
We prove the existence of a continuous family of positive and generally nonmonotone travelling fronts for delayed reaction-diffusion equations , when g∈C2(R+,R+) has exactly two fixed points: x1=0 and x2=K>0. Recently, nonmonotonic waves were observed in numerical simulations by various authors. Here, for a wide range of parameters, we explain why such waves appear naturally as the delay h increases. For the case of g with negative Schwarzian, our conditions are rather optimal; we observe that the well known Mackey-Glass-type equations with diffusion fall within this subclass of (∗). As an example, we consider the diffusive Nicholson's blowflies equation. 相似文献
45.
46.
Sergei Gukov Amer Iqbal Can Koz?az Cumrun Vafa 《Communications in Mathematical Physics》2010,298(3):757-785
We establish a direct map between refined topological vertex and sl(N) homological invariants of the of Hopf link, which include Khovanov-Rozansky homology as a special case. This relation provides
an exact answer for homological invariants of the Hopf link, whose components are colored by arbitrary representations of
sl(N). At present, the mathematical formulation of such homological invariants is available only for the fundamental representation
(the Khovanov-Rozansky theory) and the relation with the refined topological vertex should be useful for categorizing quantum
group invariants associated with other representations (R
1, R
2). Our result is a first direct verification of a series of conjectures which identifies link homologies with the Hilbert
space of BPS states in the presence of branes, where the physical interpretation of gradings is in terms of charges of the
branes ending on Lagrangian branes. 相似文献
47.
48.
We prove that the dynamical system defined by the hydrodynamical Euler equation on any closed Riemannian 3-manifold M is not mixing in the Ck topology (k>4 and non-integer) for any prescribed value of helicity and sufficiently large values of energy. This can be regarded as a 3D version of Nadirashvili's and Shnirelman's theorems showing the existence of wandering solutions for the 2D Euler equation. Moreover, we obtain an obstruction for the mixing under the Euler flow of Ck-neighborhoods of divergence-free vectorfields on M . On the way we construct a family of functionals on the space of divergence-free C1 vectorfields on the manifold, which are integrals of motion of the 3D Euler equation. Given a vectorfield these functionals measure the part of the manifold foliated by ergodic invariant tori of fixed isotopy types. We use the KAM theory to establish some continuity properties of these functionals in the Ck-topology. This allows one to get a lower bound for the Ck-distance between a divergence-free vectorfield (in particular, a steady solution) and a trajectory of the Euler flow. 相似文献
49.
Stishov SM Petrova AE Shikov AA Lograsso TA Isaev EI Johansson B Daemen LL 《Physical review letters》2010,105(23):236403
The heat capacity of MnSi at B = 0 and B = 4 T was measured in the temperature range 2.5-100 K. To analyze the data, calculations of the phonon spectrum and phonon density of states in MnSi were performed. The calculated phonon frequencies were confirmed by means of inelastic neutron scattering. The analysis of the data suggests the existence of negative contributions to the heat capacity and entropy of MnSi at T > T(c) that may imply a specific ordering in the spin subsystem in the paramagnetic phase of MnSi. 相似文献
50.
For the first time, a continuous ab initio potential energy surface (PES) taking into account all molecular degrees of freedom is built and used to model the reaction of a polyatomic molecule with a surface. DFT slab calculations are used to sample the configuration space of the system N2O/Cu(1 0 0), and the PES function is built with a method of Manzhos and Carrington [J. Chem. Phys. 127 (2007) 014103] using dimensionality reduction from only 4300 single-point energies. Molecular dynamics simulations are performed on the PES to calculate the probability of dissociative adsorption. 相似文献