Institute of Mathematics AS CR, v. v. i.
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A necessary condition for HK-integrability of the Fourier sine transform function
No full textsummary:The paper is concerned with integrability of the Fourier sine transform function when , where is the space of bounded variation functions vanishing at infinity. It is shown that for the Fourier sine transform function of to be integrable in the Henstock-Kurzweil sense, it is necessary that . We prove that this condition is optimal through the theoretical scope of the Henstock-Kurzweil integration theory
Convergence of ap-Henstock-Kurzweil integral on locally compact spaces
No full textsummary:We introduce an ap-Henstock-Kurzweil type integral with a non-atomic Radon measure and prove the Saks-Henstock type lemma. The monotone convergence theorem, -Henstock-Kurzweil equi-integrability, and uniformly strong Lusin condition are discussed
Discounted Markov decision processes with fuzzy costs
Full text linksummary:This article concerns a class of discounted Markov decision processes on Borel spaces where, in contrast with the classical framework, the cost function is a fuzzy function of a trapezoidal type, which is determined from a classical cost function by applying an affine transformation with fuzzy coefficients. Under certain conditions ensuring that the classical (or standard) model with a cost function has an optimal stationary policy with the optimal cost , it is shown that such a policy is also optimal for the fuzzy model with a cost function , and that the optimal fuzzy value is obtained from via the same transformation used to go from to . And these results are obtained with respect to two cases: the max-order of the fuzzy numbers and the average ranking order of the trapezoidal fuzzy numbers. Besides, a fuzzy version of the classical linear-quadratic model without restrictions is presented
A note on the uniformity of strong subregularity around the reference point
No full textsummary:This paper investigates strong metric subregularity around the reference point as introduced by H. Gfrerer and J. V. Outrata. In the setting of Banach spaces, we analyse its stability under Lipschitz continuous perturbations and establish its uniformity over compact sets. Our results ensure that the property is preserved under small Lipschitz perturbations, which is crucial for maintaining robustness in variational analysis. Furthermore, we apply the developed theory to parametric inclusion problems. The analysis demonstrates that the uniformity of strong metric subregularity provides a theoretical foundation for addressing stability issues in parametrized optimization and control applications
On parameter identification in the Stokes system with threshold leak boundary conditions
No full textsummary:This paper addresses the identification of the leak bound function in the Stokes system with threshold leak boundary conditions, where varies spatially. The state problem is solved using the dual formulation of the algebraic system, and the resulting optimization problem is formulated as a nonsmooth optimization problem. We establish the existence of solutions for both the continuous and discrete formulations of the problem. The theoretical developments are complemented by numerical experiments, which compare the performance of the nonsmooth optimization approach with traditional regularization-based methods and global optimization techniques
A note on nontrivial acting functions for homogeneous Besov and Triebel-Lizorkin spaces
No full textsummary:We prove the acting by composition of nontrivial functions (i.e., ) on homogeneous Besov and Triebel-Lizorkin spaces realized as subspaces of in case (Besov space) and (Triebel-Lizorkin space). These subspaces are dilation invariant and endowed with quasi-seminorms such that if and only if is constant
A boundedness criterion for the discrete Hardy operator on weighted Musielak-Orlicz sequence spaces
No full textsummary:We establish a necessary and sufficient condition on weight functions for the boundedness of the discrete Hardy operator on weighted Musielak-Orlicz sequence spaces. In particular, we get similar results for the dual operator of the discrete Hardy operator. We give sufficient pointwise conditions on generalized -functions that guarantee continuous embeddings between weighted Musielak-Orlicz sequence spaces. The results are illustrated by a number of corollaries
A note on the cooperative two-type SIR processes on Galton-Watson trees
No full textsummary:In the standard SIR model on a graph, infected vertices infect their neighbors at rate and recover at rate . We consider a two-type SIR process where each individual in the graph can be infected with two types of diseases, and . Moreover, the two diseases interact in a cooperative way so that an individual that has been infected with one type of disease can acquire the other at a higher rate. We prove that if the underlying graph is a Galton-Watson tree and initially the root is infected with both and , while all others are susceptible, then the two-type SIR model has the same critical value for the survival probability as the classic single-type model
Adaptive fractional distributed optimization algorithm with directed spanning trees
Full text linksummary:Distributed optimization has garnered significant attention in past decade, yet existing algorithms mainly rely on Laplacian matrix information for parameter settings, limiting their adaptability and applicability. To design the fully distributed algorithm, this paper uses an adaptive weight framework based on directed spanning trees (DST), which not only solves the consensus optimization problem but also can be extended to solve the resource allocation problem. The innovative integration of Nabla fractional calculus further improves performance, enabling efficient discrete-time distributed optimization. Moreover, The proposed algorithms optimality and convergence properties have been rigorously analyzed, which demonstrates that they can converge to the optimal solution of the problem under consideration. Finally, numerical simulations are conducted to validate the algorithm's feasibility and superiority