Institute of Mathematics AS CR, v. v. i.
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44818 research outputs found
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WENO-Z scheme with new nonlinear weights for Hamilton-Jacobi equations and adaptive approximation
No full textsummary:A new fifth-order weighted essentially nonoscillatory (WENO) scheme is designed to approximate Hamilton-Jacobi equations. As employing a fifth-order linear approximation and three third-order ones on the same six-point stencil as before, a newly considered WENO-Z methodology is adapted to define nonlinear weights and the final WENO reconstruction results in a simple and clear convex combination. The scheme has formal fifth-order accuracy in smooth regions of the solution and nonoscillating behavior nearby singularities. A full account is given of the key role of parameters in WENO reconstruction and their selection. The latter half describes the adaptive stage on WENO approximation in convergence framework, which enables us to get the numerical solution to converge still achieving high-order accuracy for the nonconvex problems where the pure WENO scheme fails to converge. Detailed numerical experiments are performed to demonstrate the ability of the proposed numerical methods
Strongly Gorenstein-projective modules over Nakayama algebras
No full textsummary:We study finitely generated strongly Gorenstein-projective modules over artin algebras and show that each finitely generated strongly Gorenstein-projective module is a direct sum of some indecomposable periodic Gorenstein-projective modules and projective modules. Furthermore, we outline the structure of the category of the finitely generated strongly Gorenstein-projective -modules, where is a Nakayama algebra
Classification of irreducible representations of near-group fusion algebras
No full textsummary:We explicitly classify the irreducible representations of the near-group fusion algebra associated with a finite group over a field with arbitrary characteristic
Minimal completion of doubly substochastic matrices
No full textsummary:For a given doubly substochastic matrix , by adding a (cardinal) number of columns or rows, we want to obtain a doubly stochastic matrix that contains as a sub-matrix. Then it is shown that there are minimal (cardinal) numbers of such cardinal numbers, which we call row sub-defect and column sub-defect of . We also try to obtain these two values in some cases
Relative Rota-Baxter operators, modules and projections
No full textsummary:The present article is devoted to introduce, in a braided monoidal setting, the notion of module over a relative Rota-Baxter operator. It is proved that there exists an adjunction between the category of modules associated to an invertible relative Rota-Baxter operator and the category of modules associated to a Hopf brace, which induces an equivalence by assuming certain additional hypothesis. Moreover, the notion of projection between relative Rota-Baxter operators is defined, and it is proved that those which are called ``strong'' give rise to a module according to the previous definition in the cocommutative setting
On generalized bihyperbolic third-order Jacobsthal polynomials
Full text linksummary:A new generalization of third-order Jacobsthal bihyperbolic polynomials is introduced. Some of the properties of presented polynomials are given. A general Vajda formula for the generalized bihyperbolic third-order Jacobsthal polynomials is obtained. This result implies the Catalan, Cassini and d'Ocagne identities. Moreover, generating function and matrix generators for these polynomials are presented
A weighted hybrid conjugate gradient method for unconstrained multiobjective optimization problems
No full textsummary:We propose a weighted HS (Hestenes-Stiefel)-FR (Fletcher-Reeves) hybrid conjugate gradient method for unconstrained multiobjective optimization problem, in which a new positive coefficient of the multiobjective steepest descent direction is adaptively updated to keep its positiveness. The method takes advantage of a weighted hybrid of our modified HS and FR parameters and under the Armijo-type backtracking line search, it has global convergence to a Pareto critical point (point satisfying the first-order necessary condition for Pareto optimality) without convexity assumption on the objectives. Numerical experiments show that the practical performance of the method is competitive with the existing methods such as conjugate gradient method, steepest descent method, Newton method, and quasi-Newton method for unconstrained multiobjective optimization
Science vs. Conspiracy: What are proofs for?
No full textsummary:Zejména s rozmachem sociálních sítí se na Internetu stále častěji setkáváme s různými konspiračními teoriemi. V tomto seriálu si ukážeme, že i když diskuse s jejich zastánci je naprosto zbytečná, může kritický rozbor jejich „argumentů“ posloužit jako užitečné cvičení v kritickém myšlení a jako ukázka toho, jak funguje vědecká metoda. V prvním díle našeho seriálu se podíváme na teorii ploché Země
