Institute of Mathematics AS CR, v. v. i.
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The eigenvalues of symmetric Sturm-Liouville problem and inverse potential problem, based on special matrix and product formula
No full textsummary:The Sturm-Liouville eigenvalue problem is symmetric if the coefficients are even functions and the boundary conditions are symmetric. The eigenfunction is expressed in terms of orthonormal bases, which are constructed in a linear space of trial functions by using the Gram-Schmidt orthonormalization technique. Then an -dimensional matrix eigenvalue problem is derived with a special matrix , that is, if is odd.\looseness +1 \endgraf Based on the product formula, an integration method with a fictitious time, namely the fictitious time integration method (FTIM), is developed to obtain the higher-index eigenvalues. Also, we recover the symmetric potential function in the Sturm-Liouville operator by specifying a few lower-index eigenvalues, based on the product formula and the Newton iterative method
Degrees of compatible -subsets and compatible mappings
Get PDFsummary:Based on a completely distributive lattice , degrees of compatible -subsets and compatible mappings are introduced in an -approximation space and their characterizations are given by four kinds of cut sets of -subsets and -equivalences, respectively. Besides, some characterizations of compatible mappings and compatible degrees of mappings are given by compatible -subsets and compatible degrees of -subsets. Finally, the notion of complete -sublattices is introduced and it is shown that the product of complete -sublattices is still a complete -sublattice and the compatible degree of an -subset is a complete -sublattice
Lipschitz constants for a hyperbolic type metric under Möbius transformations
No full textsummary:Let be a nonempty open set in a metric space with . Define where is the distance from to the boundary of . For every , is a metric. We study the sharp Lipschitz constants for the metric under Möbius transformations of the unit ball, the upper half space, and the punctured unit ball
On monogenity of certain pure number fields of degrees
No full textsummary:Let be a pure number field generated by a complex root of a monic irreducible polynomial , where , , are three positive natural integers. The purpose of this paper is to study the monogenity of . Our results are illustrated by some examples
A probe into students’ (lack of) knowledge in the use of arithmetic and geometric means at university
No full textsummary:Článek se zabývá užítím aritmetického a geometrického průměru ve finanční matematice na vysoké škole. Z výsledků dotazníkového šetření vyplývá značná chybovost studentů při volbě aritmetického nebo geometrického průměru jako matematického nástroje při řešení úloh. Text připomíná matematickou definici, statistický význam a základní vlastnosti geometrického průměru. Jako vzor pro správné použití geometrického průměru obsahuje článek více typových úloh z finanční matematiky, jejichž řešení může významně přispět k většímu porozumění těchto středních hodnot, a tím i k vyšší úspěšnosti studentů v předmětu Finanční matematika na vysoké škole.summary:The article deals with using arithmetic and geometric mean in financial mathematics at university. The questionnaire results show a significant error rate of students when choosing the arithmetic or geometric mean as a mathematical tool when solving problems. The mathematical definition, statistical significance and basic properties of the geometric mean are given. To show how geometric mean can be used, the article contains several typical problems from financial mathematics, the solution of which can significantly contribute to a deeper understanding of mean values and, thus, to the higher success of students in the subject of Financial Mathematics at university
Invitation to EME2024 conference
No full textsummary:Pozvánka na tradiční konferenci EME (Elementary Mathematics Education). 28. ročník EME2024 s podtitulem "Výzvy primárního vzdělávání matematice jako součást učitelství pro 21. století" se bude konat v Osrblie na Slovensku. Pořadatelem tohoto ročníku je Katedra matematiky Fakulty prírodných vied Univerzity Mateja Bela v Banskej Bstrici ve spolupráci s Jednotou slovenských matematikov a fyzikov. Veškeré informace jsou dostupné na webové stránce konference: https://eme.upol.c
Asymptotic fuzzy contractive mappings in fuzzy metric spaces
Get PDFsummary:Fixed point theory in fuzzy metric spaces has grown to become an intensive field of research. However, due to the complexity involved in the nature of fuzzy metrics, the authors need to develop innovative machinery to establish new fixed point theorems in such kind of spaces. In this paper, we propose the concepts of asymptotic fuzzy -contractive and asymptotic fuzzy Meir-Keeler mappings, and describe some new machinery by which the corresponding fixed point theorems are proved. In this sense, the techniques used for the proofs in Section 5 are completely new
The minimal closed monoids for the Galois connection -
No full textsummary:The minimal nontrivial endomorphism monoids of congruence lattices of algebras defined on a finite set are described. They correspond (via the Galois connection -) to the maximal nontrivial congruence lattices investigated and characterized by the authors in previous papers. Analogous results are provided for endomorphism monoids of quasiorder lattices
Non-weight modules over the super Schrödinger algebra
No full textsummary:We construct a family of non-weight modules which are free -modules of rank 2 over the super Schrödinger algebra in -dimensional spacetime. We determine the isomorphism classes of these modules. In particular, free -modules of rank 2 over are also constructed and classified. Moreover, we obtain the sufficient and necessary conditions for such modules to be simple
Relaxation-time limits of global solutions in full quantum hydrodynamic model for semiconductors
No full textsummary:This paper is concerned with the global well-posedness and relaxation-time limits for the solutions in the full quantum hydrodynamic model, which can be used to analyze the thermal and quantum influences on the transport of carriers in semiconductor devices. For the Cauchy problem in , we prove the global existence, uniqueness and exponential decay estimate of smooth solutions, when the initial data are small perturbations of an equilibrium state. Moreover, we show that the solutions converge into that of the simplified quantum energy-transport model and the quantum drift-diffusion model for the moment relaxation limit, and the moment and energy relaxation limit, respectively