“…The numerical results generated as an illustration for the interior Dirichlet problem are accompanied by remarks regarding the efficiency and accuracy of the procedure.   …”
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“…Detailed proofs and an emphasis on basic ideas are provided for different boundary conditions for ordinary differential equations, including Neumann, Dirichlet, periodic, and antiperiodic conditions. Novel results of higher eigenvalues, systems of equations, partial differential equations as well as variational approaches are presented. …”
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“…With a focus on synchronization for a coupled system of wave equations, the text is divided into three parts corresponding to Dirichlet, Neumann, and coupled Robin boundary controls. …”
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“…Problems touch at key topics like the value-distribution of arithmetic functions, the distribution of prime numbers, the distribution of squares and nonsquares modulo a prime number, Dirichlet's theorem on primes in arithmetic progressions, and more. …”
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“…By extracting economic topics from news text data, we construct a news coincidence index with comprehensive information and strong timeliness and reveal the trend of topic contribution. The Latent Dirichlet Allocation (LDA) topic model is applied to extract economic topics from the news. …”
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“…A total of 713 original posts were processed from unstructured texts to tidy formats. Latent Dirichlet Allocation (LDA), a popular topic modeling method, was used to discover hidden themes within the corpus. …”
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“…This is achieved by marginalizing the mixing Dirichlet variables and then performing inference in the reduced variable space. …”
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“…Then, we show how complex curves of k-type can be constructed and how solutions to the Dirichlet problem for the Laplace equation on these complex domains can be derived using a semi-Fourier method. …”
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“…In this paper, a new three-time level implicit approach based on cubic trigonometric B-spline is presented for the approximate solution of this equation with Dirichlet boundary conditions. The usual finite difference approach is used to discretize the time derivative while cubic trigonometric B-spline is applied as an interpolating function in the space dimension. …”
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“…These boundary conditions arise naturally from PDEs defined on a disk with Dirichlet boundary conditions and the requirement of regularity in Cartesian coordinates. …”
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“…Throughout this paper, we mainly consider the parabolic p-Laplacian equation with a weighted absorption [Formula: see text] in a bounded domain [Formula: see text] ([Formula: see text] ) with Lipschitz continuous boundary subject to homogeneous Dirichlet boundary condition. Here [Formula: see text] and [Formula: see text] are parameters, and [Formula: see text] is a given constant. …”
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“…We apply the Latent Dirichlet Allocation (LDA) to generate multinomial distributions over words and topics to discover author-topic relations from text collections. …”
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“…Specifically, our manifold method automatically selects the cluster number with a Dirichlet Process (DP) prior. Then, a DP-based mixture model with constrained Mixture of Gaussians (MoG) is constructed to handle the manifold data. …”
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“…The kinematic approach allows the presentation of the problem as Dirichlet-type (i.e. driven by enforced motion of boundaries) and therefore weakly sensitive to unknown properties of the tissues and needle-tissue interaction. …”
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“…In this article we probe the proposed holographic duality between [Formula: see text] deformed two dimensional conformal field theory and the gravity theory of AdS(3) with a Dirichlet cutoff by computing correlators of energy-momentum tensor. …”
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“…Taking a Bayesian approach to inference, we choose a Dirichlet process prior for the distribution of a random effect to induce great flexibility in the specification. …”
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“…The process of data collection was conducted in five steps, including filtering initial post dataset using simulator tags, discovering NS-related tags, collecting the tagged posts, extracting the posts title and preprocessing for LDA (Latent Dirichlet Allocation), and finally applying the LDA topic modeling to obtain the NS posts clustered into eight different topic names. …”
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“…In the present study different topic modeling techniques are compared, as Latent Dirichlet Allocation (LDA) and topic modeling based on BERT transformer, to extract meaningful insights in the Italian narration of COVID-19 pandemic. …”
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“…Mathematically, the model under consideration is a boundary value problem for the system of strongly nonlinear partial differential equations of third order with the zero Dirichlet boundary condition. We propose the concept of a full weak solution (velocity–pressure pair) in the distributions sense. …”
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“…By combining the raw node features that minimize the Dirichlet energy with modern graph representation learning techniques, our learnable topological features can provide efficient structural information of phylogenetic trees that automatically adapts to different downstream tasks without requiring domain expertise. …”
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