Institute of Mathematics AS CR, v. v. i.
Not a member yet
44818 research outputs found
Sort by
Piers Bohl Still Inspiring
No full textsummary:Článek je věnován památce Pierse Bohla (1865-1921), lotyšského matematika a šachisty, jehož mnohé výsledky předběhly svoji dobu a zůstaly tehdejší matematickou komunitou často nedoceněny. Kromě uvedení základních životopisných údajů komentuje tento text jeho dnes již všeobecně uznávaný přínos do několika oblastí matematické analýzy, zejména pak vět o pevném bodě a teorie kvaziperiodických funkcí. Hlavní inspirací pro sepsání tohoto článku byl však jiný Bohlův výsledek, tentokrát z oblasti teorie polynomů. Ten, ač publikován v roce 1908, zůstal matematické veřejnosti donedávna prakticky neznámý. Přínos tohoto polynomiálního výsledku je přitom zásadní nejen pro teorii polynomů samotnou, ale nachází své významné uplatnění také při kvalitativní analýze diferenčních rovnic a v dalších souvisejících oblastech. Snahou autorů (a současně hlavním cílem příspěvku) je uvedení osobnosti Pierse Bohla a tohoto jeho výsledku do širšího matematického povědomí
A new method based on least-squares support vector regression for solving optimal control problems
Get PDFsummary:In this paper, a new application of the Least Squares Support Vector Regression (LS-SVR) with Legendre basis functions as mapping functions to a higher dimensional future space is considered for solving optimal control problems. At the final stage of LS-SVR, an optimization problem is formulated and solved using Maple optimization packages. The accuracy of the method are illustrated through numerical examples, including nonlinear optimal control problems. The results demonstrate that the proposed method is capable of solving optimal control problems with high accuracy
Thermo-viscous fluid flow in porous slab bounded between two impermeable parallel plates in relative motion: Four stage algorithm approach
No full textsummary:The problem of an approximate solution of thermo-viscous fluid flow in a porous slab bounded between two impermeable parallel plates in relative motion is examined in this paper. The two plates are kept at two different temperatures and the flow is generated by a constant pressure gradient together with the motion of one of the plates relative to the other. The velocity and temperature distributions have been obtained by a four-stage algorithm approach. It is worth mentioning that reverse effects are noticed on velocity and temperature distributions. These effects can be attributed to Darcy's friction offered by the medium. The approximation results obtained in the present paper are in good agreement with the earlier numerical results of thermo-viscous fluid flows in plane geometry
A self-scaling memoryless BFGS based conjugate gradient method using multi-step secant condition for unconstrained minimization
No full textsummary:Conjugate gradient methods are widely used for solving large-scale unconstrained optimization problems, because they do not need the storage of matrices. Based on the self-scaling memoryless Broyden-Fletcher-Goldfarb-Shanno (SSML-BFGS) method, new conjugate gradient algorithms CG-DESCENT and CGOPT have been proposed by W. Hager, H. Zhang (2005) and Y. Dai, C. Kou (2013), respectively. It is noted that the two conjugate gradient methods perform more efficiently than the SSML-BFGS method. Therefore, C. Kou, Y. Dai (2015) proposed some suitable modifications of the SSML-BFGS method such that the sufficient descent condition holds. For the sake of improvement of modified SSML-BFGS method, in this paper, we present an efficient SSML-BFGS-type three-term conjugate gradient method for solving unconstrained minimization using Ford-Moghrabi secant equation instead of the usual secant equations. The method is shown to be globally convergent under certain assumptions. Numerical results compared with methods using the usual secant equations are reported
Reducing the lengths of slim planar semimodular lattices without changing their congruence lattices
Get PDFsummary:Following G. Grätzer and E. Knapp (2007), a slim planar semimodular lattice, SPS lattice for short, is a finite planar semimodular lattice having no as a sublattice. An SPS lattice is a slim rectangular lattice if it has exactly two doubly irreducible elements and these two elements are complements of each other. A finite poset is said to be JConSPS-representable if there is an SPS lattice such that is isomorphic to the poset of join-irreducible congruences of . We prove that if and is an -element JConSPS-representable poset, then there exists a slim rectangular lattice such that , the length of is at most , and . This offers an algorithm to decide whether a finite poset is JConSPS-representable (or a finite distributive lattice is ``ConSPS-representable''). This algorithm is slow as G. Czédli, T. Dékány, G. Gyenizse, and J. Kulin proved in 2016 that there are asymptotically slim rectangular lattices of a given length , where is the famous constant . The known properties and constructions of JConSPS-representable posets can accelerate the algorithm; we present a new construction
Sufficient conditions on the existence of factors in graphs involving minimum degree
No full textsummary:For a set of graphs, an -factor of a graph is a spanning subgraph of , where each component of is contained in . It is very interesting to investigate the existence of factors in a graph with given minimum degree from the prospective of eigenvalues. We first propose a tight sufficient condition in terms of the -spectral radius for a graph involving minimum degree to contain a star factor. Moreover, we also present tight sufficient conditions based on the -spectral radius and the distance spectral radius for a graph involving minimum degree to guarantee the existence of a -factor, respectively
