By a theorem of Mclean, the deformation space of an associative sub-manifolds of an integrable G2 manifold (M, ϕ) at Y ⊂ M can be identified with the kernel of the Dirac operator D / : Ω 0 (ν) → Ω 0 (ν) on the normal bundle ν of Y. We generalize this to non-integrable case, and also show that the deformation space becomes smooth after perturbing it by natural parameters, which corresponds to mo...

In this paper, the problem of stochastic synchronization analysis is investigated for complex networks perturbed by the Poisson noise. By using the key tool such as the infinites-imal operator for stochastic differential equations driven by the Poisson process, this paper proposes a globally exponentially synchronization criterion in mean square for complex networks perturbed by the Poisson noi...

The purpose is to formulate a Fourier transformation for the space of functionals, as an infinitesimal meaning. We extend R to ( ∗R) under the base of nonstandard methods for the construction. The domain of a functional is the set of all internal functions from a ∗-finite lattice to a ∗-finite lattice with a double meaning. Considering a ∗-finite lattice with a double meaning, we find how to tr...

ly considered from such construction; and which doth accompany it though otherwise constructed than is supposed.7 Wallis thus saw geometrical knowledge as more concerned with construction-invariant features of geometrical figures than with features deriving from their construction. In addition, he saw algebraic 5. Idem, p. 230 6. Knowing via minimal or simplest cause would have been better stil...