Institute of Mathematics AS CR, v. v. i.
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-submodules of modules over commutative rings
No full textsummary:We explore the existence of -submodules in the context of module theory. Then we generalize our results by considering an additive, left-exact functor defined on the category of modules, which is either covariant or contravariant, and preserves multiplications. Within this broader framework, we identify and characterize an -submodule of , derived from the structure of and the action of the functor
On general Dedekind sums
No full textsummary:As a far generalization of the Dedekind sum with the product of periodic Bernoulli polynomials, Mikolás introduced the Dedekind type sum with the product of the Hurwitz zeta-functions , . We adopt the motivation suggested by Mikolás that the Dedekind sum is a generalized inner product in the second variable. The Hurwitz zeta-function has a simple pole at and cannot assume the value while its counterpart, the Lerch zeta-function , is more tractable and we study the Dedekind type sum with the product of the Lerch zeta-functions. We establish a striking identity between these Dedekind type sums to the effect that with a correction term is a constant multiple of -- the base change formula. This implies a new expression for the ordinary Dedekind sum in terms of the one with Apostol's generalized Bernoulli polynomial. In another direction, by letting the second variables vary independently with first variables fixed as , we may elucidate the Hecke correspondence in the previous derivations of the general eta transformation formula. We can also establish many interesting properties of which supplement those of . Moreover, we show that also appears in the pseudo-transformation formula for non-modular functions
A simple proof of Fefferman-Stein type characterization of space
No full textsummary:We give a simple proof of Fefferman-Stein type characterization of the space , that is, if and only if where and , , are the Riesz transforms. Notice that this result was established by G. Bourdaud (2002), but his proof depends on the Fefferman-Stein type decomposition of the space obtained by D. Sarason (1975). We will provide a direct method to prove this conclusion
Boundedness and Hölder continuity of weak solutions of the nonlinear boundary-value problem for elliptic equations with general nonstandard growth conditions
No full textsummary:We study a nonlinear boundary-value problem for elliptic equations with critical growth conditions involving Lebesgue measurable functions. We prove global boundedness and Hölder continuity of weak solutions for this problem. Our results generalize the ones obtained by P. Winkert and his colleagues (2012) not only in the variable exponent case but also in the constant exponent case
Local accuracy in finite element analysis using curved isoparametric elements
No full textsummary:The finite element method (FEM) is popularly used for numerically approximating PDE(s) over complicated domains due to its rich mathematical background, versatility, and ease of implementation. In this article, we investigate one of its important features, i.e., the approximation of PDE(s) over nonpolygonal Lipschitz domains by higher-order simplicial elements in 2D and 3D. This important issue is not well understood and often ignored by engineers due to its mathematical complexity, i.e., the FEM approximation of curved domains results in inexact boundary conditions, which is a variational crime. This article explores the role of approximation at curved boundaries. Further, the effect of incompleteness of the approximation space also contributes to the error induced in the curved elements. A simple benchmark test for errors is proposed. Tests are conducted for subparametric and isoparametric approximations. Comparison with isogeometric analysis (IGA) is also presented to highlight the basic differences and advantages of isoparametric elements
Hybrid algorithms for fixed charge transportation problem
No full textsummary:In this paper, we consider the fixed-cost transportation problem. This problem is known to be NP-hard. Therefore, various heuristic and metaheuristic approaches have been proposed to find an approximate optimal solution. In this paper, we propose three hybrid algorithms that combine the ideas of metaheuristic and heuristic approaches in different ways. Two of the proposed algorithms consist of the sequential implementation of metaheuristic and heuristic algorithms, while the third one is a full hybrid algorithm designed by completely intertwining these two approaches. Experimental results on medium-size problems show that our proposed full hybrid algorithm provides approximately a
The Korean Suneung Exam
No full textsummary:Článek uvádí ukázky úloh z matematiky, které byly součástí přijímací zkoušky na vysoké školy v Jižní Koreji v roce 2023. Řešení uvedených úloh jsou od autora tohoto článku, což nevylučuje že existují lepší řešení těchto úloh
Certain subclass of alpha-convex bi-univalent functions defined using -derivative operator
No full textsummary:The present investigation deals with a new subclass of alpha-convex bi-univalent functions in the unit disc defined with -derivative operator. Bounds for the first two coefficients and Fekete-Szegö inequality are established for this class. Many known results follow as consequences of the results derived here
Some lower bounds for the quotients of normalized error function and their partial sums
No full textsummary:The purpose of the present paper is to determine lower bounds for , and , where is the generalized normalized error function of the form and its partial sum. Furthermore, we give lower bounds for and , where is the Alexander transform of . Several examples of the main results are also considered
Periodic analogs of Wigner transforms and Weyl transforms
No full textsummary:The periodic Wigner transform is introduced. We show that most of the properties of the Euclidean Wigner transform are satisfied in this new setting. Using the periodic Wigner transform, we define the periodic Weyl transform. -boundedness of periodic Weyl transforms are investigated. We give a necessary and sufficient condition on the symbol to ensure that the corresponding periodic Weyl transform is a Hilbert-Schmidt operator. We show that the product of two periodic Weyl transforms and the adjoint of a periodic Weyl transform are again periodic Weyl transforms. The connection between pseudo-differential operators on and periodic Weyl transforms is given