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542. A note on the parabolic variation
- Creator:
- Dont, Miroslav
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- boundary value problem for the heat equation, integral equation, heat equation, boundary value problem, and parabolic variation
- Language:
- English
- Description:
- A condition for solvability of an integral equation which is connected with the first boundary value problem for the heat equation is investigated. It is shown that if this condition is fulfilled then the boundary considered is 1⁄2-Hölder. Further, some simple concrete examples are examined.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
543. A note on the powers of Cesàro bounded operators
- Creator:
- Léka, Zoltán
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- Volterra operator and stability of operators
- Language:
- English
- Description:
- In this note we give a negative answer to Zem�nek's question (1994) of whether it always holds that a Cesàro bounded operator $T$ on a Hilbert space with a single spectrum satisfies $\lim _{n \rightarrow \infty } \|T^{n+1} - T^n\| = 0.$.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
544. A note on the relation between strong and M-stationarity for a class of mathematical programs with equilibrium constraints
- Creator:
- Henrion, René, Outrata, Jiří, and Surowiec, Thomas
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- mathematical programs with equilibrium constraints, S-stationary points, M-stationary points, Fréchet normal cone, and limiting normal cone
- Language:
- English
- Description:
- In this paper, we deal with strong stationarity conditions for mathematical programs with equilibrium constraints (MPEC). The main task in deriving these conditions consists in calculating the Fréchet normal cone to the graph of the solution mapping associated with the underlying generalized equation of the MPEC. We derive an inner approximation to this cone, which is exact under an additional assumption. Even if the latter fails to hold, the inner approximation can be used to check strong stationarity via the weaker (but easier to calculate) concept of M-stationarity.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
545. A note on the three-segment problem
- Creator:
- Doležal, Martin
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- three-segment problem and cluster sets
- Language:
- English
- Description:
- We improve a theorem of C. L. Belna (1972) which concerns boundary behaviour of complex-valued functions in the open upper half-plane and gives a partial answer to the (still open) three-segment problem.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
546. A note on the transcendence of infinite products
- Creator:
- Hančl, Jaroslav, Kolouch, Ondřej, Pulcerová, Simona, and Štěpnička, Jan
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- transcendence and infinite product
- Language:
- English
- Description:
- The paper deals with several criteria for the transcendence of infinite products of the form $\prod _{n=1}^\infty {[b_n\alpha ^{a_n}]}/{b_n\alpha ^{a_n}}$ where $\alpha >1$ is a positive algebraic number having a conjugate $\alpha ^*$ such that $\alpha \not =|\alpha ^*|>1$, $\{a_n\}_{n=1}^\infty $ and $\{b_n\}_{n=1}^\infty $ are two sequences of positive integers with some specific conditions. \endgraf The proofs are based on the recent theorem of Corvaja and Zannier which relies on the Subspace Theorem ({P. Corvaja, U. Zannier}: On the rational approximation to the powers of an algebraic number: solution of two problems of Mahler and Mendès France, Acta Math. 193, (2004), 175–191).
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
547. A note on topological groups and their remainders
- Creator:
- Peng, Liang-Xue and He, Yu-Feng
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- topological group, remainder, compactification, metrizable space, and weak base
- Language:
- English
- Description:
- In this note we first give a summary that on property of a remainder of a non-locally compact topological group $G$ in a compactification $bG$ makes the remainder and the topological group $G$ all separable and metrizable. If a non-locally compact topological group $G$ has a compactification $bG$ such that the remainder $bG\setminus G$ of $G$ belongs to $\mathcal {P}$, then $G$ and $bG\setminus G$ are separable and metrizable, where $\mathcal {P}$ is a class of spaces which satisfies the following conditions: (1) if $X\in \mathcal {P}$, then every compact subset of the space $X$ is a $G_\delta $-set of $X$; (2) if $X\in \mathcal {P}$ and $X$ is not locally compact, then $X$ is not locally countably compact; (3) if $X\in \mathcal {P}$ and $X$ is a Lindelöf $p$-space, then $X$ is metrizable. Some known conclusions on topological groups and their remainders can be obtained from this conclusion. As a corollary, we have that if a non-locally compact topological group $G$ has a compactification $bG$ such that compact subsets of $bG\setminus G$ are $G_{\delta }$-sets in a uniform way (i.e., $bG\setminus G$ is CSS), then $G$ and $bG\setminus G$ are separable and metrizable spaces. In the last part of this note, we prove that if a non-locally compact topological group $G$ has a compactification $bG$ such that the remainder $bG\setminus G$ has a point-countable weak base and has a dense subset $D$ such that every point of the set $D$ has countable pseudo-character in the remainder $bG\setminus G$ (or the subspace $D$ has countable $\pi $-character), then $G$ and $bG\setminus G$ are both separable and metrizable.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
548. A note on transitively $D$-spaces
- Creator:
- Peng, Liang-Xue
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- transitively $D$, sequential, discretely Lindelöf, and $wcs^*$-network
- Language:
- English
- Description:
- In this note, we show that if for any transitive neighborhood assignment $\phi $ for $X$ there is a point-countable refinement ${\mathcal F}$ such that for any non-closed subset $A$ of $X$ there is some $V\in {\mathcal F}$ such that $|V\cap A|\geq \omega $, then $X$ is transitively $D$. As a corollary, if $X$ is a sequential space and has a point-countable $wcs^*$-network then $X$ is transitively $D$, and hence if $X$ is a Hausdorff $k$-space and has a point-countable $k$-network, then $X$ is transitively $D$. We prove that if $X$ is a countably compact sequential space and has a point-countable $wcs^*$-network, then $X$ is compact. We point out that every discretely Lindelöf space is transitively $D$. Let $(X, \tau )$ be a space and let $(X, {\mathcal T})$ be a butterfly space over $(X, \tau )$. If $(X, \tau )$ is Fréchet and has a point-countable $wcs^*$-network (or is a hereditarily meta-Lindelöf space), then $(X, {\mathcal T})$ is a transitively $D$-space.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
549. A note on triangular schemes for weak congruences
- Creator:
- Chajda, Ivan, Šešelja, Branimir, and Tepavčević, Andreja
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- triangular scheme, triangular principle, weak congruence, weak congruence modularity, and weak congruence distributivity
- Language:
- English
- Description:
- Some geometrical methods, the so called Triangular Schemes and Principles, are introduced and investigated for weak congruences of algebras. They are analogues of the corresponding notions for congruences. Particular versions of Triangular Schemes are equivalent to weak congruence modularity and to weak congruence distributivity. For algebras in congruence permutable varieties, stronger properties—Triangular Principles—are equivalent to weak congruence modularity and distributivity.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
550. A note on ultrametric matrices
- Creator:
- Zhang, Xiao-Dong
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- generalized ultrametric matrix, $ \mathcal U$ matrix, weighted graph, and inverse $M$-matrix
- Language:
- English
- Description:
- It is proved in this paper that special generalized ultrametric and special $\mathcal U$ matrices are, in a sense, extremal matrices in the boundary of the set of generalized ultrametric and $ \mathcal U$ matrices, respectively. Moreover, we present a new class of inverse $M$-matrices which generalizes the class of $\mathcal U$ matrices.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public