Institute of Mathematics AS CR, v. v. i.
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Methodology of teaching word problems for elementary and lower secondary mathematics teachers
No full textsummary:Stručné oznámení o vydání metodiky výuky slovních úloh (https://slovni-ulohy-metodika.cz/)
A new diagonal quasi-Newton algorithm for unconstrained optimization problems
No full textsummary:We present a new diagonal quasi-Newton method for solving unconstrained optimization problems based on the weak secant equation. To control the diagonal elements, the new method uses new criteria to generate the Hessian approximation. We establish the global convergence of the proposed method with the Armijo line search. Numerical results on a collection of standard test problems demonstrate the superiority of the proposed method over several existing diagonal methods
Characterization of the order induced by uninorm with the underlying drastic product or drastic sum
Get PDFsummary:In this article, we investigate the algebraic structures of the partial orders induced by uninorms on a bounded lattice. For a class of uninorms with the underlying drastic product or drastic sum, we first present some conditions making a bounded lattice also a lattice with respect to the order induced by such uninorms. And then we completely characterize the distributivity of the lattices obtained
Inverse optimal dynamic boundary control for uncertain Korteweg-de Vries-Burgers equation
Get PDFsummary:We investigate Korteweg-de Vries-Burgers (KdVB) equation, where the dissipation and dispersion coefficients are unknown, but their lower bounds are known. First, we establish dynamic boundary controls with update laws to globally exponentially stabilize this uncertain system. Secondly, we demonstrate that the dynamic boundary control design is suboptimal to a meaningful functional after some minor modifications of the dynamic boundary controls. In addition, we also consider dynamic boundary controls for the case of unknown dissipation or dispersion coefficients, and obtain corresponding results. Finally, three examples are used to demonstrate the effectiveness of the proposed control design
News and Announcements
No full textsummary:Kamil John 82letý. Oborová matematická medaile JČMF 2024. Udělení ceny profesora Iva Babušky za rok 2024
On modeling flow between adjacent surfaces where the fluid is governed by implicit algebraic constitutive relations
No full textsummary:We consider pressure-driven flow between adjacent surfaces, where the fluid is assumed to have constant density. The main novelty lies in using implicit algebraic constitutive relations to describe the fluid's response to external stimuli, enabling the modeling of fluids whose responses cannot be accurately captured by conventional methods. When the implicit algebraic constitutive relations cannot be solved for the Cauchy stress in terms of the symmetric part of the velocity gradient, the traditional approach of inserting the expression for the Cauchy stress into the equation for the balance of linear momentum to derive the governing equation for the velocity becomes inapplicable. Instead, a non-standard system of first-order equations governs the flow. This system is highly complex, making it important to develop simplified models. Our primary contribution is the development of a framework for achieving this. Additionally, we apply our findings to a fluid that exhibits an S-shaped curve in the shear stress versus shear rate plot, as observed in some colloidal solutions
Unified-like product of monoids and its regularity property
No full textsummary:We first define a new monoid construction (called unified-like product ) under a unified product and the Schützenberger product . We investigate whether this algebraic construction defined with operations of the unified and Schützenberger product specifies a monoid or not. Then, we obtain a presentation of this new product for any two monoids. Finally, we define the necessary and sufficient conditions for to be regular
New bounds on the Laplacian spectral ratio of connected graphs
No full textsummary:Let be a simple connected undirected graph. The Laplacian spectral ratio of is defined as the quotient between the largest and second smallest Laplacian eigenvalues of , which is an important parameter in graph theory and networks. We obtain some bounds of the Laplacian spectral ratio in terms of the number of the spanning trees and the sum of powers of the Laplacian eigenvalues. In addition, we study the extremal Laplacian spectral ratio among trees with vertices, which improves some known results of Z. You and B. Liu (2012)
The relationship between and inner functions
No full textsummary:Let be an inner function and be the corresponding model space. For an inner function , the subspace is an invariant subspace of the unilateral shift operator on . In this article, using the structure of a Toeplitz kernel , we study the intersection by properties of inner functions and . If , then there exists a triple such that where the triple means that and are Blaschke products, is an invertible function in , denotes the outer factor of , and is some constant with Furthermore, for any nonconstant inner function , there exists a Blaschke product such that In particular, we discuss the finite-dimensional intersection . Moreover, we investigate connections between minimal Toeplitz kernels and