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].

And the relevant development is based on the mathematical calibration of various forms of partial differential equation with the first boundary condition called the

Dirichlet condition.

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.

Considering the limitations of the vector space model and the high dimensional unstructured nature of biomedical text documents, there are a number of representation schemes (such as the latent semantic analysis, the probabilistic latent semantic analysis, and the latent

Dirichlet allocation) employed to process biomedical text documents [7].

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.