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Recognition of Finite Bitopological Spaces with Unique Isolated Point
Published 2025-01-01“…The {deck} of a bitopological space $(X, \tau_{1}, \tau_{2})$ is the set $\mathscr{D}(X)=\{[X_{x}]:x\in X\},$ where $[Z]$ denotes the pair-homeomorphism class of $Z$. …”
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Separation ratios of maps between Banach spaces
Published 2023-11-01“…Under the weak assumption on a Banach space $E$ that $E\oplus E$ embeds isomorphically into $E$, we provide a characterisation of when a Banach space $X$ coarsely embeds into $E$ via a single numerical invariant.…”
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Fuzzy Normed Linear Spaces Generated By Linear Functionals
Published 2024-07-01“…For a nonzero normed linear space X, we will define some different classes of fuzzy norms on X generated by linear and bounded linear functionals. …”
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Generalized Grand Lebesgue Spaces Associated to Banach Function spaces
Published 2024-07-01“…In this paper we introduce the class of grand Lebesgue spaces associated to a Banach function space $X$ by replacing the role of the $L^1$-norm by the norm $\|\cdot\|_X$ in the classical construction of the generalized grand Lebesgue spaces. …”
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Measurable Vizing’s theorem
Published 2025-01-01“…We prove a full measurable version of Vizing’s theorem for bounded degree Borel graphs, that is, we show that every Borel graph $\mathcal {G}$ of degree uniformly bounded by $\Delta \in \mathbb {N}$ defined on a standard probability space $(X,\mu )$ admits a $\mu $ -measurable proper edge coloring with $(\Delta +1)$ -many colors. …”
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On Bousfield’s conjectures for the unstable Adams spectral sequence for $SO$ and $U$
Published 2023-12-01“…The unstable Adams spectral sequence is a spectral sequence that starts from algebraic information about the mod $2 $ cohomology $H ^{ * } \left(X \right) $ of a space $X $ as an unstable algebra over the Steenrod algebra $\mathcal{A}$, and converges, in good cases, to the $2 $-localized homotopy groups of $X $. …”
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Bilinear control of evolution equations with unbounded lower order terms. Application to the Fokker–Planck equation
Published 2024-05-01“…We study the exact controllability of the evolution equation \begin{equation*} u^{\prime }(t)+Au(t)+p(t)Bu(t)=0 \end{equation*} where $A$ is a nonnegative self-adjoint operator on a Hilbert space $X$ and $B$ is an unbounded linear operator on $X$, which is dominated by the square root of $A$. …”
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Виклики і розвиток авіоніки: система переривання польоту
Published 2024-06-01“…Потім вимоги безпеки були змінені на основі теорії управління ризиками, що дозволило Space X розробити революційну нову систему FTS, яка є автономною, автоматичною, надійною та використовує два незалежні канали для прийняття рішення про припинення польоту. …”
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On the Scottish Book Problem 155 by Mazur and Sternbach
Published 2024-10-01“…Problem 155 of the Scottish Book asks whether every bijection $U\colon X\rightarrow Y$ between two Banach spaces $X, Y$ with the property that, each point of $X$ has a neighborhood on which $U$ is isometric, is globally isometric on $X$. …”
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