Moreover, DAC_mmst model provides the more flexible method to select the number of visual-topics by introducing Hierarchical
Dirichlet Process (HDP) [28] to model each image as a
Dirichlet process for topics discovery.
It is defined as the
Dirichlet energy or [H.sup.1]-seminorm of the Laplacian under certain boundary conditions and thus closely related to certain physical quantities which also occur in engineering applications such as resistance values of integrated circuit networks; see, e.g., [22, 24].
The
Dirichlet problem for polyharmonic equations in bounded domains of [R.sup.n] has been studied, among the first, by Sobolev in [1].
Here we introduce the Cauchy integral method for the solution of the
Dirichlet problem in doubly connected domains.
where [B.sub.0](x) is given and [a.sub.0] = [[integral].sup.1.sub.0] [B.sub.0](x)dx; they used these generalized Bernoulli polynomials to derive formulas of certain
Dirichlet series.
This model is explored subject to both
Dirichlet and Neumann boundary conditions on the bounded domain [OMEGA] = [-1, 1] x [-1, 1] to satisfy the domain required by the Chebyshev polynomials with initial condition w(x, y, 0) = f(x, y).
Let s = [sigma] + it be a complex variable, [chi] be a
Dirichlet character and [alpha], 0 < [alpha] [less than or equal to] 1, be a fixed parameter.
We propose to forecast football games outcomes using a simple predictive elicitation approach (Garthwaite, Kadane, & O'Hagan, 2005; Kadane, 1980), where the hyperparameters of a Categorical
Dirichlet model are elicited using betting odds from different bookmakers.
Let [[gamma].sub.n]([chi]) denote the n-th Laurent-Stieltjes coefficients around s = 1 of the associated
Dirichlet L-series for a given primitive
Dirichlet character [chi] modulo q.