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    ABSTRACT: The development of numerical methods for the solution of partial differential equations (PDEs) with nonlocal boundary conditions is important, since such type of problems arise as mathematical models of various real-world processes. We use radial basis function (RBF) collocation technique for the solution of a multidimensional linear elliptic equation with classical Dirichlet boundary condition and nonlocal integral conditions. RBF-based meshless methods are easily implemented and efficient, especially for multidimensional problems formulated on complexly shaped domains. In this paper, properties of the method are investigated by studying two- and three-dimensional test examples with manufactured solutions. We analyze the influence of the RBF shape parameter and the distribution of the nodes on the accuracy of the method as well as the influence of nonlocal conditions on the conditioning of the collocation matrix.
    Computers & Mathematics with Applications 04/2014; 67(7):1407-1420.
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    ABSTRACT: Objectives: To promote the further development of HTA, this study aims to design a model for HTA priority setting, which would address national needs for a country with little experience in the field of HTA, and assess its feasibility for the health system. Methods: Literature search and review, as well as qualitative research have been used in the design and testing of the model for HTA priority setting. To test the model and the methodology, a three-round Delphi study was conducted in 2011 in the form of an electronic questionnaire, which was distributed to the panel of eleven national experts. The panel was composed of experts representing various fields of the health care sector: policy-makers, health care service professionals and academics, with diverse professional roles. Results: The designed model consists of four stages: (i) selection of experts for the panel, (ii) indication and selection of health policy topics, (iii) identification of health technologies, and (iv) priority setting. Three rounds of the Delphi study were performed to test the model and reach expert consensus on a list of health technologies for assessment, including pharmaceuticals, vaccines, medical devices, diagnostic methods, public health interventions, organizational systems, etc. Conclusions: Based on the Delphi technique as a method for consensus building, the model for HTA priority setting was developed for Lithuania; however, it could also be used for other countries with little experience in the field of HTA.
    International Journal of Technology Assessment in Health Care 10/2013; 29(4):450-5.
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    ABSTRACT: We provide necessary and sufficient conditions for a tempered distribution F∈S′(R)F∈S′(R) to be positive definite. A generalized Cauchy transform F˜ of FF is used as a numerical continuation of FF to the open upper and lower half-planes in CC. In fact, our necessary and sufficient conditions for FF are determined completely by the properties of the restriction of F˜ to the imaginary axis in CC. The main result is given in terms of completely monotonic and absolutely monotonic functions.
    Indagationes Mathematicae 06/2013; 24(3):505–517.


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