| 1. |
- Andersson, Fredrik K., et al.
(author)
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The mathematics of internet search engines
- 2008
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In: Acta Applicandae Mathematicae - An International Survey Journal on Applying Mathematics and Mathematical Applications. - : Springer. - 0167-8019 .- 1572-9036. ; 104:2, s. 211-242
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Journal article (peer-reviewed)abstract
- This article presents a survey of techniques for ranking results in search engines, with emphasis on link-based ranking methods and the PageRank algorithm. The problem of selecting, in relation to a user search query, the most relevant documents from an unstructured source such as the WWW is discussed in detail. The need for extending classical information retrieval techniques such as boolean searching and vector space models with link-based ranking methods is demonstrated. The PageRank algorithm is introduced, and its numerical and spectral properties are discussed. The article concludes with an alternative means of computing PageRank, along with some example applications of this new method.
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| 2. |
- Barza, Ilie, et al.
(author)
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Explicit formulas for Green's functions on the annulus and on the Möbius strip
- 1998
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In: Acta Applicandae Mathematicae - An International Survey Journal on Applying Mathematics and Mathematical Applications. - 0167-8019 .- 1572-9036. ; 54:3, s. 289-302
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Journal article (peer-reviewed)abstract
- Given a fixed point free antianalytic involution k of a domain G in thecomplex plane, bounded by a finite number of analytic curves, k-invariant Green sfunctions are defined on G. The Lindelöf s principle is extended to k-invariantGreen s functions. When G is the annulus, k-invariant Green s functions areobtained in the explicit form. Since the factorization of the annulus by the group k generated by k produces a Möbius strip, the respective result helped us to obtain explicitforms for Green s functions on the Möbius strip.symmetric Riemann surface - nonorientable Klein surface - Green s function - k-invariant Green s function
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| 3. |
- Basarab-Horwath, Peter, et al.
(author)
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Symmetry Classification of Third-Order Nonlinear Evolution Equations. Part I: Semi-simple Algebras
- 2013
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In: Acta Applicandae Mathematicae - An International Survey Journal on Applying Mathematics and Mathematical Applications. - : Springer Verlag (Germany). - 0167-8019 .- 1572-9036. ; 124:1, s. 123-170
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Journal article (peer-reviewed)abstract
- We give a complete point-symmetry classification of all third-order evolution equations of the form u (t) =F(t,x,u,u (x) ,u (xx) )u (xxx) +G(t,x,u,u (x) ,u (xx) ) which admit semi-simple symmetry algebras and extensions of these semi-simple Lie algebras by solvable Lie algebras. The methods we employ are extensions and refinements of previous techniques which have been used in such classifications.
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| 4. |
- Basarab-Horwath, Peter, et al.
(author)
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The structure of lie algebras and the classification problem for partial differential equations
- 2001
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In: Acta Applicandae Mathematicae - An International Survey Journal on Applying Mathematics and Mathematical Applications. - 0167-8019 .- 1572-9036. ; 69:1, s. 43-94
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Journal article (peer-reviewed)abstract
- The present paper solves completely the problem of the group classification of nonlinear heat-conductivity equations of the form u(t)=F(t,x,u,u(x))u(xx)+G(t,x,u,u(x)). We have proved, in particular, that the above class contains no nonlinear equations whose invariance algebra has dimension more than five. Furthermore, we have proved that there are two, thirty-four, thirty-five, and six inequivalent equations admitting one-, two-, three-, four- and five-dimensional Lie algebras, respectively. Since the procedure which we use relies heavily upon the theory of abstract Lie algebras of low dimension, we give a detailed account of the necessary facts. This material is dispersed in the literature and is not fully available in English. After this algebraic part we give a detailed description of the method and then we derive the forms of inequivalent invariant evolution equations, and compute the corresponding maximal symmetry algebras. The list of invariant equations obtained in this way contains (up to a local change of variables) all the previously-known invariant evolution equations belonging to the class of partial differential equations under study.
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| 5. |
- Bernhoff, Niclas, 1971-
(author)
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Linearized Boltzmann Collision Operator : I. Polyatomic Molecules Modeled by a Discrete Internal Energy Variable and Multicomponent Mixtures
- 2023
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In: Acta Applicandae Mathematicae - An International Survey Journal on Applying Mathematics and Mathematical Applications. - : Springer. - 0167-8019 .- 1572-9036. ; 183:1, s. 1-45
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Journal article (peer-reviewed)abstract
- The linearized Boltzmann collision operator appears in many important applications of the Boltzmann equation. Therefore, knowing its main properties is of great interest. This work extends some classical results for the linearized Boltzmann collision operator for monatomic single species to the case of polyatomic single species, while also reviewing corresponding results for multicomponent mixtures of monatomic species. The polyatomicity is modeled by a discrete internal energy variable, that can take a finite number of (given) different values. Results concerning the linearized Boltzmann collision operator being a nonnegative symmetric operator with a finite-dimensional kernel are reviewed. A compactness result, saying that the linearized operator can be decomposed into a sum of a positive multiplication operator, the collision frequency, and a compact operator, bringing e.g., self-adjointness, is extended from the classical result for monatomic single species, under reasonable assumptions on the collision kernel. With a probabilistic formulation of the collision operator as a starting point, the compactness property is shown by a splitting, such that the terms can be shown to be, or be the uniform limit of, Hilbert-Schmidt integral operators and as such being compact operators. Moreover, bounds on - including coercivity of - the collision frequency are obtained for a hard sphere like model, from which Fredholmness of the linearized collision operator follows, as well as its domain.
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| 6. |
- Bobylev, Alexander, 1947-, et al.
(author)
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DSMC Modeling of a Single Hot Spot Evolution Using the Landau-Fokker-Planck Equation
- 2014
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In: Acta Applicandae Mathematicae - An International Survey Journal on Applying Mathematics and Mathematical Applications. - : Springer Science and Business Media LLC. - 0167-8019 .- 1572-9036. ; 132:1, s. 107-116
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Journal article (peer-reviewed)abstract
- Numerical solution of a fully nonlinear one dimensional in space and three dimensional in velocity space electron kinetic equation is presented. Direct Simulation Monte Carlo (DSMC) method used for the nonlinear Landau-Fokker-Planck (LFP) collision operator is combined with Particle-in-Cell (PiC) simulations. An assumption of a self-consistent ambipolar electric field is used. The illustrative simulation results for the relaxation of the initial temperature perturbation are compared with the antecedent analytical and numerical results.
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| 7. |
- Bock, Wolfgang, et al.
(author)
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Stochastic quantization for the fractional Edwards measure
- 2017
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In: Acta Applicandae Mathematicae - An International Survey Journal on Applying Mathematics and Mathematical Applications. - : Springer. - 0167-8019 .- 1572-9036. ; 151, s. 81-88
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Journal article (peer-reviewed)abstract
- We prove that there exists a diffusion process whose invariant measure is the fractional polymer or Edwards measure for fractional Brownian motion, μg , H, H∈ (0 , 1) for dH< 1. The diffusion is constructed in the framework of Dirichlet forms in infinite dimensional (Gaussian) analysis. Moreover, the process is invariant under time translations.
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| 8. |
- Carlsen, Toke Meier, et al.
(author)
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On the Exel crossed product of topological covering maps
- 2009
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In: Acta Applicandae Mathematicae - An International Survey Journal on Applying Mathematics and Mathematical Applications. - : Springer. - 0167-8019 .- 1572-9036. ; 108:3, s. 573-583
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Journal article (peer-reviewed)abstract
- For dynamical systems defined by a covering map of a compact Hausdorff space and the corresponding transfer operator, the associated crossed product C *-algebras C(X)⋊ α,ℒℕintroduced by Exel and Vershik are considered. An important property for homeomorphism dynamical systems is topological freeness. It can be extended in a natural way to in general non-invertible dynamical systems generated by covering maps. In this article, it is shown that the following four properties are equivalent: the dynamical system generated by a covering map is topologically free; the canonical embedding of C(X) into C(X)⋊ α,ℒℕis a maximal abelian C *-subalgebra of C(X)⋊ α,ℒN; any nontrivial two sided ideal of C(X)⋊ α,ℒℕhas non-zero intersection with the embedded copy of C(X); a certain natural representation of C(X)⋊ α,ℒℕis faithful. This result is a generalization to non-invertible dynamics of the corresponding results for crossed product C *-algebras of homeomorphism dynamical systems.
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| 9. |
- Choquard, Philippe, et al.
(author)
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A one-dimensional inviscid and compressible fluid in a harmonic potential well
- 2007
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In: Acta Applicandae Mathematicae - An International Survey Journal on Applying Mathematics and Mathematical Applications. - : Springer Science and Business Media LLC. - 0167-8019 .- 1572-9036. ; 99:2, s. 161-183
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Journal article (peer-reviewed)abstract
- A Hamiltonian model is analyzed for a one-dimensional inviscid compressible fluid. The space-time evolution of the fluid is governed by the following system of the Hamilton-Jacobi and the continuity equations: S-t + 1/2(S-x(2) + omega(2)chi(2)) =0, S(x, 0) = S-0(x); rho(t) + (rho S-x)(x) =0, rho(x, 0) =rho(0)(x).Here S and rho designate the velocity potencial and the mass density, respectively. Unless S-0 is convex, shocks form and the velocity S (x) becomes discontinuous in {0 < omega t < pi/2}. It is demonstrated that there nevertheless exists a unique viscosity-measure solution (S,rho) when S-0 is globally Lipschitz continuous and locally semi-concave while rho(0) is a finite Borel measure. The structure of the velocity and the density is exhibited. For initial data correlated in a certain sense, a class of classical solutions (S,rho) is given. Negative time is also considered, and illustrating examples are given.
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| 10. |
- Douanla Yonta, Hermann, 1982
(author)
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Homogenization of Steklov spectral problems with indefinite density function in perforated domains
- 2013
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In: Acta Applicandae Mathematicae - An International Survey Journal on Applying Mathematics and Mathematical Applications. - : Springer Science and Business Media LLC. - 0167-8019 .- 1572-9036. ; 123:1
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Journal article (peer-reviewed)abstract
- The asymptotic behavior of second order self-adjoint elliptic Steklov eigenvalue problems with periodic rapidly oscillating coefficients and with indefinite (sign-changing) density function is investigated in periodically perforated domains. We prove that the spectrum of this problem is discrete and consists of two sequences, one tending to −∞ and another to +∞. The limiting behavior of positive and negative eigencouples depends crucially on whether the average of the weight over the surface of the reference hole is positive, negative or equal to zero. By means of the two-scale convergence method, we investigate all three cases.
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