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;Miškinis, Paulius ;Krylovas, AleksandrasMathematical modelling and analysis : the Baltic journal on mathematical applications, numerical analysis and differential equations. Vilnius : Taylor&Francis, VGTU, 2017, vol. 22, iss. 3., p. 337-351Show more In the paper, an asymptotic analysis of G.F. Carrier's mathematical model of string oscillation is presented. The model consists of a system of two nonlinear second order partial differential equations and periodic initial conditions. The longitudinal and transversal string oscillations are analyzed together when at the initial moment of time the system's solutions have amplitudes proportional to a small parameter. The problem is reduced to a system of two weakly nonlinear wave equations. The resonant interaction of periodic waves is analyzed. An uniformly valid asymptotic approximation in the long time interval, which is inversely proportional to the small parameter, is constructed. This asymptotic approximation is a solution of averaged along characteristics integro-differential system. Conditions of appearance of combinatoric resonances in the system have been established. The results of numerical experiments are presented.Show more WOS© IF 0.716WOS© AIF 0.855Scopus© SNIP 0.601 - research article
; Kosareva, NataljaMathematical modelling and analysis : the Baltic journal on mathematical applications, numerical analysis and differential equations. Vilnius : Technika, 2015, Vol. 20, no. 3., p. 409-421Show more The problem of ranking (sorting) of m alternatives is considered when experts evaluate each alternative according to k criteria. Functions of arithmetic and geometric averages are constructed for decision making. We present a generalization of this scheme when there are evaluation matrices of several experts and this information is aggregated in the form of triangular intuitionistic fuzzy numbers. Fuzzy triangles were constructed with di erent uncertainty levels, experts decision matrices and the number of experts varied from 2 to 5. Moreover, method for construction of experts decision probability matrices is proposed in the paper. Ranking results obtained by performing Monte Carlo simulations. Probabilities of errors are compared for arithmetic, geometric, fuzzy arithmetic and fuzzy geometric averages.Show more WOS© IF 0.468WOS© AIF 0.735Scopus© SNIP 0.667 - research articleNonlinear analysis : modelling and control. Vilnius : Institute of Mathematics and Informatics, 2015, vol. 20, no 2., p. 210-225
Show more We propose necessary and sufficient conditions for a distribution (generalized function) f of several variables to be positive definite. For this purpose, certain analytic extensions of f to tubular domains in complex space Cn are studied. The main result is given in terms of the Cauchy transform and completely monotonic functions.Show more 1WOS© IF 1.075WOS© AIF 1.524Scopus© SNIP 0.814 Characteristic functions as distributional boundary values of analytic functions in tube domainsPublicationresearch articleLithuanian mathematical journal. New York : Springer, 2014, vol. 54, no. 2., p. 192-202Show more We propose necessary and sufficient conditions for a complex-valued function f on Rn to be a characteristic function of a probability measure. Certain analytic extensions of f to tubular domains in Cn are studied. In order to extend the class of functions under study, we also consider the case where f is a generalized function (distribution). The main result is given in terms of completely monotonic functions on convex cones in Rn.Show more WOS© IF 0.667WOS© AIF 0.741Scopus© SNIP 0.851 Distortions introduced by normalisation of values of criteria in multiple criteria methods of evaluationPublication[Normalizavimo algoritmų, naudojamų daugiakriterijuose vertinimo metoduose, įnešami iškraipymai]research articleLietuvos matematikos rinkinys : Lietuvos matematikų draugijos darbai. Vilnius : VU, 2014, t. 55, ser. A., p. 51-56Show more Quantitative multiple criteria decision aid (MCDA) methods of evaluation gain increasing popularity among researchers. The idea of the methods is to comprise values of criteria characterising each object into a single non-dimensional cumulative criterion, which reflects attractiveness or position of the object in view of an objective chosen. Normalisation of weights is a compulsory procedure whenever criteria of different dimensions are present. There several methods of normalisation available. Nevertheless, each method may introduce distortions into transformed data. The paper is devoted to exploration of problems related to such distortions and reveals particular cases.Show more - research articleComputers and mathematics with applications. Kidlington : Pergamon, 2014, vol, 67, no 7., p. 1407-1420
Show more 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.Show more WOS© IF 1.697WOS© AIF 1.097Scopus© SNIP 1.863 - research article
;Gorin, E.A.Norvidas, SauliusFunctional analysis and its applications. New York : Springer New York LLC, 2013, Vol. 47, No. 1., p. 1-13Show more From the viewpoint of elementary functional analysis, Bernstein inequalities are mainly sharp estimates for the norms of certain operators of convolution of entire functions bounded on the real line and having finite exponential type not exceeding a given one with (complex) Borel measures of finite total variation. If we assume that the functions are defined on a locally compact Abelian group and use the uniform norms, then the generalized Bernstein spaces are parametrized by compact sets in the dual group X and the symbols of the operators are the restrictions to compact sets in X of functions locally coinciding with the Fourier transforms of measures. There exists symbols such that, in the case of uniform norms (and then, as it turns out, also in more general cases), the norm of the corresponding operator coincides with its spectral radius. The main result of the paper is a description of these (universal) symbols in terms of positive definite functions. Connected groups play a special role here.Show more WOS© IF 0.457WOS© AIF 0.919Scopus© SNIP 1.148 A note on positive definite distributionsPublicationresearch articleIndagationes mathematicae. Amsterdam : Elsevier BV, 2013, vol. 24, no. 3., p. 505-517Show more We provide necessary and sufficient conditions for a tempered distribution F∈S′(R)F∈S′(R) to be positive definite. A generalized Cauchy transform View the MathML sourceF˜ 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 View the MathML sourceF˜ to the imaginary axis in CC. The main result is given in terms of completely monotonic and absolutely monotonic functions.Show more 1WOS© IF 0.186WOS© AIF 0.729Scopus© SNIP 0.737 - research articleEngineering analysis with boundary elements. Oxford : Pergamon-Elsevier, 2013, Vol. 37, iss. 4., p. 788-804
Show more Various real-world processes usually can be described by mathematical models consisted of partial differential equations (PDEs) with nonlocal boundary conditions. Therefore, interest in developing computational methods for the solution of such nonclassical differential problems has been growing fast. We use a meshless method based on radial basis functions (RBF) collocation technique for the solution of two-dimensional Poisson equation with nonlocal boundary conditions. The main attention is paid to the influence of nonlocal conditions on the optimal choice of the RBF shape parameters as well as their influence on the conditioning and accuracy of the method. The results of numerical study are presented and discussed.Show more WOS© IF 1.437WOS© AIF 1.403Scopus© SNIP 1.633 The construction of test reliability statistical criteria by a computer simulationPublication[Testų patikimumo statistinių kriterijų konstravimas kompiuterine simuliacija]research article; ; Kosareva, NataljaLietuvos matematikos rinkinys : Lietuvos matematikų draugijos darbai. Serija A. Vilnius : VU Matematikos ir informatikos institutas, 2013, T. 54., p. 37-42Show more The paper describes a computer simulation experiment of knowledge assessment test when item’s characteristic functions are power functions and knowledge level of the population has uniform or normal distribution. The inversions of the conditional means were calculated and probability distributions of the numbers of inversions were simulated. In practice of construction of knowledge tests for checking their suitability (validity) observed values of inversions are compared with reference values obtained byMonte Carlo experiments.Show more