Proposition A.2. (Discrete Green’s Identities:) Let φ, ψ ∈ Cm×n .
Convergence Analysis of a Second Order Convex Splitting Scheme for the Modified Phase Field Crystal Equation
By Proposition 7.2, for every n ∈ Z+ , (Z ζn )(x, y ) is a discrete analytic polynomial.
On discrete analytic functions: Products, Rational Functions, and some Associated Reproducing Kernel Hilbert Spaces
Proposition 2.5, ˆg0 has ﬁnite support and g is a discrete analytic polynomial.
On discrete analytic functions: Products, Rational Functions, and some Associated Reproducing Kernel Hilbert Spaces
In the discrete time setting, the renewal shift is fairly well understood (see Proposition 6.1 and [Sa3]).
Parabolic suspension flows
The integral representation (36) follows from the discrete FeynmanKac formula (31) and the invariance principle by virtually the same argument as in the proof of Proposition 9.
On the Maximal Displacement of a Critical Branching Random Walk
We note that the uniqueness requirement in the statement of the proposition holds if and only if G is nearly discrete, that is if and only if the intersection of all the open subgroups of G is equal to the singleton {e}.
Topological Galois Theory
For a quasitriangular discrete multiplier Hopf algebra A we can express the inner automorphism S 4 by using the modular multiplier in A and in the reduced dual ˆA, see Proposition 2.9.
Quasitriangular (G-cograded) multiplier Hopf algebras
We are ready to calculate the grouplike multiplier g = uS (u)−1 for a discrete multiplier Hopf algebra which is quasitriangular. 2.9 Proposition.
Quasitriangular (G-cograded) multiplier Hopf algebras
Combining the embedded discrete time coin-tossing game with Proposition 2.1, we can test whether a continuous price process chosen by Market is a measure-theoretic martingale.
New procedures for testing whether stock price processes are martingales
From the above proposition, it follows that applying the BH procedure on midP -values will result in an FDR level at most 2 m0 m q − origF DR. A tighter upper bound on the midF DR, that is calculable from the known discrete null distributions, is derived in the following proposition.
False discovery rate controlling procedures for discrete tests
The proposition implies that for independent test statistics, the DBL procedure should always be preferred over the BL procedure with discrete data since it will be uniformly more powerful than the BL procedure and has guaranteed FDR control.
False discovery rate controlling procedures for discrete tests
It follows from the main result of [ST10], cf. [STZ12, Proposition 2.2(3)] that if we can show that the F -jumping numbers of τ (ωW , η∗ (KX + ∆), (a · OW )t ) are discrete and rational, then so are the F -jumping numbers of τ (ωX , KX + ∆, at ) = τ (X, ∆, at ).
Test ideals of non-principal ideals: Computations, Jumping Numbers, Alterations and Division Theorems
Proposition 3.4 ([18, §3]). (1) Gs (p) is an r-discrete, second countable, local ly compact, Hausdorff groupoid with counting measure as Haar system. (2) S (X , f ) is strongly Morita equivalent to C ∗ (Gs (p)).
K-theory of C^*-algebras from one-dimensional generalized solenoids
Proposition 3.3 An inﬁnite discrete group Γ is amenable if and only if the universal cover of any compact manifold with fundamental group Γ is amenable.
A Surgery Theory for Manifolds of Bounded Geometry
Proposition 4.2 Let G1 and G2 discrete groups which possess a ﬁnite dimensional model for the classifying space for proper bundles.
Nullification functors and the homotopy type of the classifying space for proper bundles
***