Institute of Mathematics AS CR, v. v. i.

Editorial

Author: Starý Novotný Vít
Publication venue: Československé sdružení uživatelů TeXu
Publication date: 01/01/2025
Field of study

summary:Úvodní slovo shrnuje obsah čísla.summary:The editorial presents an overview of the articles from this issue

OBITUARY

Author
Publication venue: Institute of Information Theory and Automation AS CR
Publication date: 01/01/2025
Field of study

Optimality conditions for interval-valued vector equilibrium problems

Author: Prasad Ashish Kumar
Khatri Julie
Ahmad Izhar
Publication venue: Institute of Information Theory and Automation AS CR
Publication date: 01/01/2025
Field of study

summary:In the article, one formulates Fritz John type and Karush-Kuhn-Tucker type necessary conditions for an interval-valued vector equilibrium problem having a locally LU-efficient solution, where convexificators demonstrate the solutions that are regular. Sufficient conditions for a locally weak LU-efficient solution have been entrenched by imposing appropriate assumptions along with generalized convexity. Some applications are presented for a constrained interval-valued vector variational inequality and a constrained interval-valued vector optimization problem

Instruction for authors

Author
Publication venue: Union of Czech Mathematicians and Physicists
Publication date: 01/01/2025
Field of study

Multilinear fractional maximal and integral operators with homogeneous kernels, Hardy-Littlewood-Sobolev and Olsen-type inequalities

Author: Chen Cong
Yang Kaikai
Wang Hua
Publication venue: Matematický ústav AV ČR
Publication date: 01/01/2025
Field of study

summary:Let

m\in \mathbb {N}

and

0<\alpha <mn

. Let

\mathcal {T}_{\Omega ,\alpha ;m}

be the multilinear fractional integral operator with homogeneous kernels, and let

\mathcal {M}_{\Omega ,\alpha ;m}

be the multilinear fractional maximal operator with homogeneous kernels. We will use the idea of Hedberg to reprove that the multilinear operators

\mathcal {T}_{\Omega ,\alpha ;m}

and

\mathcal {M}_{\Omega ,\alpha ;m}

are bounded from

L^{p_1}(\mathbb R^n)\times L^{p_2}(\mathbb R^n) \times \nobreak \cdots \times L^{p_m}(\mathbb R^n)

into

L^q(\mathbb R^n)

provided that

\vec {\Omega }=(\Omega _1,\Omega _2,\dots ,\Omega _m)\in [L^s({\bf S}^{n-1})]^{m}

s'<p_1,p_2,\dots ,p_m<\infty

s'/m<p<n/{\alpha }

\frac {1}{p}=\frac {1}{p_1}+\frac {1}{p_2}+\cdots +\frac {1}{p_m} \quad \text {and} \quad \frac {1}{q}=\frac {1}{p}-\frac {\alpha }{n}.

This result was first obtained by Chen and Xue. We also prove that under the assumptions that

\vec {\Omega }=(\Omega _1,\Omega _2,\dots ,\Omega _m) \in [L^s({\bf S}^{n-1})]^{m}

s'\leq p_1,p_2,\dots ,p_m<\infty

s'/m\leq p<n/{\alpha }

and

(*)

, the multilinear operators

\mathcal {T}_{\Omega ,\alpha ;m}

and

\mathcal {M}_{\Omega ,\alpha ;m}

are bounded from

L^{p_1}(\mathbb R^n)\times L^{p_2}(\mathbb R^n) \times \cdots \times L^{p_m}(\mathbb R^n)

into

L^{q,\infty }(\mathbb R^n)

, which are completely new. Moreover, we will use the idea of Adams to show that

\mathcal {T}_{\Omega ,\alpha ;m}

and

\mathcal {M}_{\Omega ,\alpha ;m}

are bounded from

L^{p_1,\kappa }(\mathbb R^n)\times L^{p_2,\kappa }(\mathbb R^n) \times \cdots \times L^{p_m,\kappa }(\mathbb R^n)

into

L^{q,\kappa }(\mathbb R^n)

whenever

s'<p_1,p_2,\dots ,p_m<\infty

0<\kappa <1

s'/m<p<{n(1-\kappa )}/{\alpha }

\frac {1}{p}=\frac {1}{p_1}+\frac {1}{p_2}+\cdots +\frac {1}{p_m} \quad \text {and} \quad \frac {1}{q}=\frac {1}{p}-\frac {\alpha }{n(1-\kappa )},

and also bounded from

L^{p_1,\kappa }(\mathbb R^n)\times L^{p_2,\kappa }(\mathbb R^n) \times \cdots \times L^{p_m,\kappa }(\mathbb R^n)

into

WL^{q,\kappa }(\mathbb R^n)

whenever

s'\leq p_1,p_2,\dots ,p_m<\infty

0<\kappa <1

s'/m\leq p<{n(1-\kappa )}/{\alpha }

and

(**)

. These results mentioned above are also completely new. In addition, some new estimates in the limiting cases are also established. Applications to the Hardy-Littlewood-Sobolev and Olsen-type inequalities are discussed as well

A stochastic version of Vidyasagar theorem on the stabilization of interconnected systems

Author: Florchinger Patrick
Publication venue: Institute of Information Theory and Automation AS CR
Publication date: 01/01/2025
Field of study

summary:The purpose of this paper is to provide sufficient conditions for the feedback asymptotic stabilization in probability for a class of affine in the control nonlinear stochastic differential systems. In fact, under the assumptions stated in this paper we prove the existence of a control Lyapunov function that according to the stochastic version of Artstein's theorem guarantees the asymptotic stability in probability by means of a state feedback law that is smooth except eventually at the equilibrium. This result generalizes the well-known theorem of Vidyasagar concerning the feedback stabilization problem for interconnected control systems

Honeycomb graphs for parametric identification of correlation classes in multidimensional datasets

Author: Dudáš Adam
Peregrín Tomáš
Publication venue: Institute of Information Theory and Automation AS CR
Publication date: 01/01/2025
Field of study

summary:In the process of gaining knowledge from large sets of data, one of the most significant methods from the area of descriptive statistics

-

correlation analysis

-

is applied to determine direct functional relationships between pairs of attributes. Even though the results of correlation analysis are measured through a crisp correlation coefficient, whose values belong to the

[-1,1]

interval, human interpretation of these values is conventionally vague and uses linguistic classes of correlation to describe the strength of relationships between attribute pairs. However, this interpretative vagueness

-

and the correlation classes themselves

-

are not commonly employed in the decision-making processes. Therefore, this work focuses on the design and implementation of so-called Honeycomb Graphs

-

a visualization method for parametric identification of correlation classes in multidimensional datasets based on graphical models. After implementing the proposed visualization technique, two case studies on benchmark datasets are conducted, and the model is evaluated from both qualitative and quantitative points of view. The results of these studies highlight interactive exploration of correlation analysis while adhering to qualitative and quantitative standards of scientific visualizations and high utilization potential of the method in feature selection tasks, making it a valuable tool for predictive analysis and data exploration

Číselná charakteristika podobných trojúhelníků

Author: Dlab Vlastimil
Publication venue: The Union of Czech Mathematicians and Physicists
Publication date: 01/01/2025
Field of study

Characteristic forms of complex Cartan geometries III: $G$ -structures

Author: McKay Benjamin
Publication venue: Department of Mathematics, Faculty of Science of Masaryk University, Brno
Publication date: 01/01/2025
Field of study

summary:Characteristic class relations in Dolbeault cohomology follow from the existence of a holomorphic geometric structure (for example, holomorphic conformal structures, holomorphic Engel distributions, holomorphic projective connections, and holomorphic foliations). These relations can be calculated directly from the representation theory of the structure group, without selecting any metric or connection or having any knowledge of the Dolbeault cohomology groups of the manifold. This paper improves on its predecessor [17] by allowing infinite type geometric structures

On the number of iterations in the Alternating Method for integer matrices in max-algebra

Author: Stojčetović Bojana
Publication venue: Institute of Information Theory and Automation AS CR
Publication date: 01/01/2025
Field of study

summary:The Alternating Method in max-algebra is an efficient approach for solving two-sided max-linear systems of the form

A \otimes x=B \otimes y

, where

A

B

are matrices and

x

y

are vectors of compatible sizes. This iterative procedure typically begins with a randomly chosen initial vector. In the case when matrices

A

and

B

are integer matrices and one is finite while the other has at least one finite element in each row and in each column, and provided that the initial vector is also an integer vector, an upper bound on the number of iterations can be determined. This paper proposes starting the Alternating Method with a vector selected based on the matrix elements of

\tilde{A}=(-A^\top) \otimes A

, where

A

is a finite matrix of the given system, instead of using a randomly selected vector. This choice of initial vector aims to minimize the number of iterations in the Alternating Method. We have proved that, with the proposed choice of initial vector, the number of iterations is bounded above by the expression containing the maximum element of matrix

\tilde{A}

. From this statement, we derive additional conclusions regarding this bound. Finally, we compare the number of iterations in the Alternating Method when it starts from a randomly chosen vector versus when it starts from the vector we propose in this study

24,815

full texts

44,818

metadata records

Updated in last 30 days.

Institute of Mathematics AS CR, v. v. i.

Access Repository Dashboard

Do you manage Open Research Online? Become a CORE Member to access insider analytics, issue reports and manage access to outputs from your repository in the CORE Repository Dashboard! 👇