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Journal articles on the topic '$(\infty'

Author: Grafiati

Published: 2 June 2025

Last updated: 31 July 2025

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1

Ginot, Grégory, and Gilles Halbout. "Lifts of $C_\infty $- and $L_\infty $-morphisms to $G_\infty $-morphisms." Proceedings of the American Mathematical Society 134, no. 3 (2005): 621–30. http://dx.doi.org/10.1090/s0002-9939-05-08126-8.

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2

Haugseng, Rune, and Joachim Kock. "$\infty$-operads as symmetric monoidal $\infty$-categories." Publicacions Matemàtiques 68 (January 1, 2024): 111–37. http://dx.doi.org/10.5565/publmat6812406.

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3

Hmidi, Taoufik, and Dong Li. "Small $\dot{B}^{-1}_{\infty , \infty}$ implies regularity." Dynamics of Partial Differential Equations 14, no. 1 (2017): 1–4. http://dx.doi.org/10.4310/dpde.2017.v14.n1.a1.

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4

Korkmaz, Recep. "On the closure of $$B_{( - \infty ,\infty )}^2 $$." Semigroup Forum 54, no. 1 (1997): 166–74. http://dx.doi.org/10.1007/bf02676599.

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5

Кузьмин, Леонид Викторович, та Leonid Viktorovich Kuz'min. "Арифметика некоторых $\ell $-расширений с тремя точками ветвления". Trudy Matematicheskogo Instituta imeni V.A. Steklova 307 (грудень 2019): 78–99. http://dx.doi.org/10.4213/tm4038.

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Пусть $\ell $ - простое регулярное нечетное число, $k$ - поле деления круга на $\ell $ частей, $k_\infty $ - круговое $\mathbb Z_\ell $-расширение поля $k$, $K$ - циклическое расширение $k$ степени $\ell $ и $K_\infty =K\cdot k_\infty $. В предположении, что в расширении $K_\infty /k_\infty $ разветвлены ровно три точки, не лежащие над $\ell $, и поле $K$ удовлетворяет некоторым дополнительным условиям, изучается структура модуля Ивасавы $T_\ell (K_\infty )$ поля $K_\infty $ как модуля Галуа. В частности, доказано, что $T_\ell (K_\infty )$ - циклический $G(K_\infty /k_\infty )$-модуль и группа

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6

Kofanov, V. A., and I. V. Popovich. "Sharp Nagy type inequalities for the classes of functions with given quotient of the uniform norms of positive and negative parts of a function." Researches in Mathematics 28, no. 1 (2020): 3. http://dx.doi.org/10.15421/242001.

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For any $p\in (0, \infty],$ $\omega > 0,$ $d \ge 2 \omega,$ we obtain the sharp inequality of Nagy type$$\|x_{\pm}\|_\infty \le\frac{\|(\varphi+c)_{\pm}\|_\infty}{\|\varphi+c\|_{L_p(I_{2\omega})}} \left\|x \right\|_{L_{p} \left(I_d \right)}$$on the set $S_{\varphi}(\omega)$ of $d$-periodic functions $x$ having zeros with given the sine-shaped $2\omega$-periodiccomparison function $\varphi$, where $c\in [-\|\varphi\|_\infty, \|\varphi\|_\infty]$ is such that$$ \|x_{+}\|_\infty \cdot\|x_{-}\|^{-1}_\infty = \|(\varphi+c)_{+}\|_\infty \cdot\|(\varphi+c)_{-}\|^{-1}_\infty .$$In particular, we ob

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7

Скасків, О. Б., та С. І. Дубей. "ПРО ОСНОВНЕ СПІВВІДНОШЕННЯ ТЕОРІЇ ВІМАНА-ВАЛІРОНА І АСИМПТОТИЧНА h-ЩІЛЬНІСТЬ ВИНЯТКОВИХ МНОЖИН". PRECARPATHIAN BULLETIN OF THE SHEVCHENKO SCIENTIFIC SOCIETY. Number, № 19(73) (10 грудня 2024): 18–23. https://doi.org/10.31471/2304-7399-2024-19(73)-18-23.

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Нехай $L$ --- клас додатних зростаючих на $[0;+\infty)$ функцій, а $L_{1}$ --- його підклас, який складається з функцій $h\in L$ таких, що $h\Big(x+\frac{1}{h(x)}\Big)=O(h(x)),(x\to +\infty).$ Для вимірної за Лебегом множини $E\subset [0;+\infty),$ що має скінченну міру Лебега $\mathop{\rm meas } E=\int_{E}dx < +\infty,$ визначимо її нижню асимптотичну $h$-щільність у нескінченності $\displaystyle {d}_{h}(E)= \varliminf_{R \rightarrow +\infty} h(R)\cdot \mathop{\rm meas }(E \cap [R;+\infty)).$ Нехай $S(a,b),$\ $-\infty\le a<b\le +\infty,$\ --- клас аналітичних в $\Pi(a,b)=\{z: a<{\rm

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8

Słowik, Roksana, and Driss Aiat Hadj Ahmed. "m-commuting maps on triangular and strictly triangular infinite matrices." Electronic Journal of Linear Algebra 37 (March 24, 2021): 247–55. http://dx.doi.org/10.13001/ela.2021.5083.

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Let $N_\infty(F)$ be the ring of infinite strictly upper triangular matrices with entries in an infinite field. The description of the commuting maps defined on $N_\infty(F)$, i.e. the maps $f\colon N_\infty(F)\rightarrow N_\infty(F)$ such that $[f(X),X]=0$ for every $X\in N_\infty(F)$, is presented. With the use of this result, the form of $m$-commuting maps defined on $T_\infty(F)$ -- the ring of infinite upper triangular matrices, i.e. the maps $f\colon T_\infty(F)\rightarrow T_\infty(F)$ such that $[f(X),X^m]=0$ for every $X\in T_\infty(F)$, is found.

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9

Лапин, Сергей Валерьевич, та Sergei Valerievich Lapin. "$D_\infty$-дифференциальные $A_\infty$-алгебры и спектральные последовательности". Математический сборник 193, № 1 (2002): 119–42. http://dx.doi.org/10.4213/sm623.

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10

Mihalik, Michael L. "Semistability at $\infty$, $\infty$-ended groups and group cohomology." Transactions of the American Mathematical Society 303, no. 2 (1987): 479. http://dx.doi.org/10.1090/s0002-9947-1987-0902779-7.

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11

Смирнов, Владимир Алексеевич, та Vladimir Alekseevich Smirnov. "$A_\infty$-симплициальные объекты и $A_\infty$-топологические группы". Matematicheskie Zametki 66, № 6 (1999): 913–19. http://dx.doi.org/10.4213/mzm1235.

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12

Lapin, S. V. "$ D_\infty$-differential $ A_\infty$-algebras and spectral sequences." Sbornik: Mathematics 193, no. 1 (2002): 119–42. http://dx.doi.org/10.1070/sm2002v193n01abeh000623.

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13

Sheremeta, Myroslav, and Oksana Mulyava. "Belonging of Laplace-Stieltjes integrals to convergence classes." Ukrainian Mathematical Bulletin 18, no. 2 (2021): 255–78. http://dx.doi.org/10.37069/1810-3200-2021-18-2-8.

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For positive continuous functions $\alpha$ and $\beta$ increasing to $+\infty$ on $[x_0,+\infty)$ and the Laplace--Stieltjes integral $I(\sigma)=\int\limits_{0}^{\infty}f(x)e^{x\sigma}dF(x),\,\sigma\in{\Bbb R}$, a generalized convergence $\alpha\beta$-class is defined by the condition $$\int\limits_{\sigma_0}^{\infty}\dfrac{\alpha(\ln\,I(\sigma))}{\beta(\sigma)}d\sigma<+\infty.$$ Under certain conditions on the functions $\alpha$, $\beta$, $f$, and $F$, it is proved that the integral $I$ belongs to the generalized convergence $\alpha\beta$-class if and only if $\int\limits_{x_0}^{\infty}\al

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14

Glyzin, Sergey Dmitrievich, та Andrei Yurevich Kolesov. "Критерий конусов на бесконечномерном торе". Известия Российской академии наук. Серия математическая 88, № 6 (2024): 82–117. http://dx.doi.org/10.4213/im9548.

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На бесконечномерном торе $\mathbb{T}^{\infty}=E/2\pi\mathbb{Z}^{\infty}$, где $E$ - бесконечномерное вещественное банахово пространство, $\mathbb{Z}^{\infty}$ - абстрактная целочисленная решетка, рассматривается специальный класс диффеоморфизмов $\mathrm{Diff}(\mathbb{T}^{\infty})$. Упомянутый класс состоит из отображений $G\colon \mathbb{T}^{\infty}\to\mathbb{T}^{\infty}$, для которых дифференциалы $DG$ и $D(G^{-1})$ равномерно ограничены и равномерно непрерывны на $\mathbb{T}^{\infty}$. Устанавливается справедливость для диффеоморфизмов из $\mathrm{Diff}(\mathbb{T}^{\infty})$ классического р

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15

Кузьмин, Леонид Викторович, та Leonid Viktorovich Kuz'min. "Арифметика некоторых $\ell$-расширений с тремя точками ветвления. II". Известия Российской академии наук. Серия математическая 85, № 5 (2021): 132–51. http://dx.doi.org/10.4213/im9070.

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Пусть $\ell$ - простое регулярное нечетное число, $k$ - поле деления круга на $\ell$ частей и $K=k(\sqrt[\ell]{a})$, где $a$ - натуральное число. В предположении, что в $K_\infty/k_\infty$ разветвлены ровно три точки, не лежащие над $\ell$, мы продолжаем изучать структуру модуля Тэйта (модуля Ивасавы) $T_\ell(K_\infty)$ как модуля Галуа. Доказано, что в случае $\ell=3$, если $T_\ell(K_\infty)$ конечен, то $|T_\ell(K_\infty)|=\ell^r$ для некоторого натурального нечетного $r$. При тех же предположениях, если $\overline T_\ell(K_\infty)$ - группа Галуа максимального абелева неразветвленного $\ell

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16

Глызин, Сергей Дмитриевич, Sergey Dmitrievich Glyzin, Андрей Юрьевич Колесов та Andrei Yurevich Kolesov. "Критерий гиперболичности одного класса диффеоморфизмов на бесконечномерном торе". Математический сборник 213, № 2 (2022): 50–95. http://dx.doi.org/10.4213/sm9535.

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На бесконечномерном торе $\mathbb{T}^{\infty} {=} E/2\pi\mathbb{Z}^{\infty}$, где $E$ - бесконечномерное вещественное банахово пространство, $\mathbb{Z}^{\infty}$ - абстрактная целочисленная решетка, рассматривается специальный класс диффеоморфизмов $\operatorname{Diff}(\mathbb{T}^{\infty})$. Упомянутый класс состоит из отображений $G\colon \mathbb{T}^{\infty}\to\mathbb{T}^{\infty}$, представляющих собой суммы линейных обратимых ограниченных операторов, сохраняющих решетку $\mathbb{Z}^{\infty}$, и $C^1$-гладких периодических добавок. Устанавливаются необходимые и достаточные условия, гарантиру

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17

Jiang, Renjin, Jie Xiao, and Dachun Yang. "Relative ∞-capacity and its affinization." Advances in Calculus of Variations 11, no. 1 (2018): 95–110. http://dx.doi.org/10.1515/acv-2016-0023.

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AbstractIn this paper, the so-called relative {\infty}-capacity is introduced and investigated in a close connection to the viscosity solution of the {\infty}-Laplace equation. We not only show that the relative {\infty}-capacity equals the limit of the p-th root of the relative p-capacity as {p\to\infty} and hence has a simple geometric characterization in terms of the Euclidean distance, but also establish several basic properties for the relative {\infty}-capacity. Consequently, we apply the relative {\infty}-capacity to the embedding theory of the {\infty}-Sobolev space. More geometrically

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18

Lapin, Sergey V. "Dihedral ∞-simplicial modules and dihedral homology of involutive homotopy unital A ∞-algebras." Georgian Mathematical Journal 26, no. 2 (2019): 257–86. http://dx.doi.org/10.1515/gmj-2019-2018.

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Abstract The notion of a dihedral {\infty} -simplicial module is introduced. The homotopy invariance of the structure of a dihedral {\infty} -simplicial module is proved. The concept of the dihedral homology of a dihedral {\infty} -simplicial module is developed. The notion of an involutive homotopy unital {A_{\infty}} -algebra is introduced. The dihedral {\infty} -simplicial module is constructed using an involutive homotopy unital {A_{\infty}} -algebra. The concept of the dihedral homology of an involutive homotopy unital {A_{\infty}} -algebra is developed. For the dihedral homology of invol

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19

GRANTCHAROV, DIMITAR, and IVAN PENKOV. "SIMPLE BOUNDED WEIGHT MODULES OF $$ \mathfrak{sl}\left(\infty \right),\kern0.5em \mathfrak{o}\left(\infty \right),\kern0.5em \mathfrak{sp}\left(\infty \right) $$." Transformation Groups 25, no. 4 (2020): 1125–60. http://dx.doi.org/10.1007/s00031-020-09571-7.

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Abstract We classify the simple bounded weight modules of the Lie algebras $$ \mathfrak{sl}\left(\infty \right),\kern0.5em \mathfrak{o}\left(\infty \right) $$ sl ∞ , o ∞ and $$ \mathfrak{sp}\left(\infty \right) $$ sp ∞ , and compute their annihilators in $$ U\left(\mathfrak{sl}\left(\infty \right)\right),\kern0.5em U\left(\mathfrak{o}\left(\infty \right)\right),\kern0.5em U\left(\mathfrak{sp}\left(\infty \right)\right) $$ U sl ∞ , U o ∞ , U sp ∞ , respectively.

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20

M. P. Chaudhary and Salahuddin. "On 3-Dissection Property." Malaya Journal of Matematik 2, no. 02 (2014): 129–32. http://dx.doi.org/10.26637/mjm202/004.

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The purpose of this paper is to derive 3- dissection for $\left(q^2 ; q^2\right)_{\infty}^{-1}\left(q^4 ; q^4\right)_{\infty}^{-1}, \quad\left(q^3 ; q^3\right)_{\infty}^{-1}\left(q^6 ; q^6\right)_{\infty}^{-1}$ and $\left(q^{\frac{1}{3}} ; q^{\frac{1}{3}}\right)_{\infty}^{-1}\left(q^{\frac{2}{3}} ; q^{\frac{2}{3}}\right)_{\infty}^{-1}$

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21

Xu, Mingzhou. "Complete convergence of moving average processes produced by negatively dependent random variables under sub-linear expectations." AIMS Mathematics 8, no. 7 (2023): 17067–80. http://dx.doi.org/10.3934/math.2023871.

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<abstract><p>Suppose that $ \{a_i, -\infty &lt; i &lt; \infty\} $ is an absolutely summable set of real numbers, $ \{Y_i, -\infty &lt; i &lt; \infty\} $ is a subset of identically distributed, negatively dependent random variables under sub-linear expectations. Here, we get complete convergence and Marcinkiewicz-Zygmund strong law of large numbers for the partial sums of moving average processes $ \{X_n = \sum_{i = -\infty}^{\infty}a_{i}Y_{i+n}, n\ge 1\} $ produced by $ \{Y_i, -\infty &lt; i &lt; \infty\} $ of identically distributed, negatively dependent ra

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22

Li, Qiang, and Mianlu Zou. "note on the regularity criterion for the micropolar fluid equations in homogeneous Besov spaces." New Zealand Journal of Mathematics 54 (December 20, 2023): 57–67. http://dx.doi.org/10.53733/315.

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This paper gives a further investigation on the regularity criteria for three-dimensional micropolar equations in Besov spaces. More precisely, it is proved that the weak solution $(u, \omega)$ is regular if the velocity $u$ satisfies $$\int_{0}^{T}\| \nabla_{h}u_{h}\|_{\dot{B}_{p,\frac{2p}{3}}^{0}}^{q} d t<\infty,\ with\ \ \frac{3}{p}+\frac{2}{q}=2,\ \frac{3}{2}<p\leq\infty,$$or $$\int_{0}^{T}\| \nabla_{h}u\|_{\dot{B}_{\infty ,\infty}^{-1}}^{\frac{8}{3}} d t<\infty,$$or $$\int_{0}^{T}\|\nabla_{h} u_{h}\|_{\dot{B}_{\infty,\infty}^{-\alpha}}^{\frac{2}{2-\alpha}} d t<\infty,\ with\ 0

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23

Gutik, O. V., and M. B. Khylynskyi. "On locally compact shift continuous topologies on the semigroup $\boldsymbol{B}_{[0,\infty)}$ with an adjoined compact ideal." Matematychni Studii 61, no. 1 (2024): 10–21. http://dx.doi.org/10.30970/ms.61.1.10-21.

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Let $[0,\infty)$ be the set of all non-negative real numbers. The set $\boldsymbol{B}_{[0,\infty)}=[0,\infty)\times [0,\infty)$ with the following binary operation $(a,b)(c,d)=(a+c-\min\{b,c\},b+d-\min\{b,c\})$ is a bisimple inverse semigroup.In the paper we study Hausdorff locally compact shift-continuous topologies on the semigroup $\boldsymbol{B}_{[0,\infty)}$ with an adjoined compact ideal of the following tree types.The semigroup $\boldsymbol{B}_{[0,\infty)}$ with the induced usual topology $\tau_u$ from $\mathbb{R}^2$, with the topology $\tau_L$ which is generated by the natural partial

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24

Mulyava, O. M., та M. M. Sheremeta. "Зауваження до достатнiх умов належностi аналiтичних функцiй до класiв збiжностi". Carpathian Mathematical Publications 5, № 2 (2013): 298–304. http://dx.doi.org/10.15330/cmp.5.2.298-304.

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Добре відомо, що якщо тейлорові коефіцієнти $f_k$ цілої функції $f$ задовольняють умови $|f_k|/|f_{k+1}|\nearrow+\infty$ при $k\to\infty$ і $\sum\limits_{n=1}^{\infty}|f_k|^{k/\varrho}<+\infty$, то $f$ належить до валіронового класу збіжності. Доведено, що у цьому твердженні умову $|f_k|/|f_{k+1}|\nearrow+\infty$ можна замінити умовою $(l_{k-1}l_{k+1}/l^2_k)|f_k|/|f_{k+1}\nearrow+\infty$, де додатна послідовність $(l_k)$ така, що $\root{k}\of{l_k/l_{k+1}}\asymp 1$ при $k\to\infty$. Подібні результати отримано для інших класів збіжності цілих та аналітичних в одиничному крузі функцій.

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Kim, Sung Guen. "Extreme points of ${\mathcal L}_s(^2l_{\infty})$ and ${\mathcal P}(^2l_{\infty})$." Carpathian Mathematical Publications 13, no. 2 (2021): 289–97. http://dx.doi.org/10.15330/cmp.13.2.289-297.

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For $n\geq 2,$ we show that every extreme point of the unit ball of ${\mathcal L}_s(^2l_{\infty}^n)$ is extreme in ${\mathcal L}_s(^2l_{\infty}^{n+1})$, which answers the question in [Period. Math. Hungar. 2018, 77 (2), 274-290]. As a corollary we show that every extreme point of the unit ball of ${\mathcal L}_s(^2l_{\infty}^n)$ is extreme in ${\mathcal L}_s(^2l_{\infty})$. We also show that every extreme point of the unit ball of ${\mathcal P}(^2l_{\infty}^2)$ is extreme in ${\mathcal P}(^2l_{\infty}^n).$ As a corollary we show that every extreme point of the unit ball of ${\mathcal P}(^2l_{\

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26

Glyzin, Sergey Dmitrievich, and Andrei Yurevich Kolesov. "Cone criterion on an infinite-dimensional torus." Izvestiya: Mathematics 88, no. 6 (2024): 1087–118. https://doi.org/10.4213/im9548e.

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On the infinite-dimensional torus $\mathbb{T}^{\infty} = E/2\pi\mathbb{Z}^{\infty}$, where $E$ is an infinite-dimensional real Banach space, $\mathbb{Z}^{\infty}$is an abstract integer lattice, a special class of diffeomorphisms $\mathrm{Diff}(\mathbb{T}^{\infty})$ is considered. This class consists of the mappings $G\colon \mathbb{T}^{\infty} \to \mathbb{T}^{\infty}$ such that the differentials $DG$ and $D(G^{-1})$ are uniformly bounded and uniformly continuous on $\mathbb{T}^{\infty}$. For diffeomorphisms from $\mathrm{Diff}(\mathbb{T}^{\infty})$, we establish the validity of the so-called c

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27

Sahakyan, B. A. "ON THE $ \langle \rho_j,W_j \rangle $ GENERALIZED COMPLETELY MONOTONE FUNCTIONS." Proceedings of the YSU A: Physical and Mathematical Sciences 54, no. 1 (251) (2020): 35–43. http://dx.doi.org/10.46991/pysu:a/2020.54.1.035.

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We consider sequences $ {\lbrace \rho_j \rbrace}_{0}^{\infty} $ $ (\rho_0 \mathclose{=} 1, \rho_j \mathclose{\geq} 1) $, $ {\lbrace \alpha_j \rbrace}_{0}^{\infty} $ $ (\alpha_0 \mathclose{=} 1, \alpha_j \mathclose{=} 1 \mathclose{-} (1/\rho_j )) $, $ {\lbrace W_j (x) \rbrace}_{0}^{\infty} \mathclose{\in} W $, where $$ W \mathclose{=} \lbrace {\lbrace W_j (x) \rbrace}_{0}^{\infty} / W_0 (x) \mathclose{\equiv} 1, W_j (x) \mathclose{>} 0, {W}_{j}^{\prime} (x) \mathclose{\leq} 0, W_j (x) \mathclose{\in} C^\infty [0,a] \rbrace, $$ $ C^\infty [0,a] $ is the class of functions of infin

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Vasylyshyn, T. V. "Topology on the spectrum of the algebra of entire symmetric functions of bounded type on the complex $L_\infty$." Carpathian Mathematical Publications 9, no. 1 (2017): 22–27. http://dx.doi.org/10.15330/cmp.9.1.22-27.

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It is known that the so-called elementary symmetric polynomials $R_n(x) = \int_{[0,1]}(x(t))^n\,dt$ form an algebraic basis in the algebra of all symmetric continuous polynomials on the complex Banach space $L_\infty,$ which is dense in the Fr\'{e}chet algebra $H_{bs}(L_\infty)$ of all entire symmetric functions of bounded type on $L_\infty.$ Consequently, every continuous homomorphism $\varphi: H_{bs}(L_\infty) \to \mathbb{C}$ is uniquely determined by the sequence $\{\varphi(R_n)\}_{n=1}^\infty.$ By the continuity of the homomorphism $\varphi,$ the sequence $\{\sqrt[n]{|\varphi(R_n)|}\}_{n=1

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29

Abellán García, Fernando. "Marked colimits and higher cofinality." Journal of Homotopy and Related Structures 17, no. 1 (2021): 1–22. http://dx.doi.org/10.1007/s40062-021-00296-2.

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AbstractGiven a marked $$\infty $$ ∞ -category $$\mathcal {D}^{\dagger }$$ D † (i.e. an $$\infty $$ ∞ -category equipped with a specified collection of morphisms) and a functor $$F: \mathcal {D}\rightarrow {\mathbb {B}}$$ F : D → B with values in an $$\infty $$ ∞ -bicategory, we define "Equation missing", the marked colimit of F. We provide a definition of weighted colimits in $$\infty $$ ∞ -bicategories when the indexing diagram is an $$\infty $$ ∞ -category and show that they can be computed in terms of marked colimits. In the maximally marked case $$\mathcal {D}^{\sharp }$$ D ♯ , our constr

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30

Koyama, Shin-Ya. "$L^{\infty}$ -manifolds." Duke Mathematical Journal 77, no. 3 (1995): 799–817. http://dx.doi.org/10.1215/s0012-7094-95-07724-2.

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31

Hinrichsen, D., and A. J. Pritchard. "Stochastic $H^\infty$." SIAM Journal on Control and Optimization 36, no. 5 (1998): 1504–38. http://dx.doi.org/10.1137/s0363012996301336.

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32

Katzourakis, Nikolaos I. "$\infty $-minimal submanifolds." Proceedings of the American Mathematical Society 142, no. 8 (2014): 2797–811. http://dx.doi.org/10.1090/s0002-9939-2014-12039-9.

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33

Serre, Denis. "Solutions globales $(-\infty." Annales de l’institut Fourier 48, no. 4 (1998): 1069–91. http://dx.doi.org/10.5802/aif.1649.

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Лапин, Сергей Валерьевич, та Sergei Valerievich Lapin. "$D_\infty$-дифференциальные $E_\infty$-алгебры и мультипликативные спектральные последовательности". Математический сборник 196, № 11 (2005): 75–108. http://dx.doi.org/10.4213/sm1393.

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Лапин, Сергей Валерьевич, та Sergei Valerievich Lapin. "$D_\infty$-дифференциальные $E_\infty$-алгебры и спектральные последовательности расслоений". Математический сборник 198, № 10 (2007): 3–30. http://dx.doi.org/10.4213/sm1582.

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Лапин, Сергей Валерьевич, та Sergei Valerievich Lapin. "$(DA)_\infty$-модули над $(DA)_\infty$-алгебрами и спектральные последовательности". Известия Российской академии наук. Серия математическая 66, № 3 (2002): 103–30. http://dx.doi.org/10.4213/im388.

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Zhu, Jian-Ping. "A note on subcontinua of $\beta[0,\infty)-[0,\infty)$." Proceedings of the American Mathematical Society 120, no. 2 (1994): 597. http://dx.doi.org/10.1090/s0002-9939-1994-1185283-2.

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Aizicovici, Sergiu, Nikolaos S. Papageorgiou, and Vasile Staicu. "Nonlinear periodic problems superlinear at $+\infty$ and sublinear at $-\infty$." LIBERTAS MATHEMATICA (new series) 33, no. 1 (2013): 27. http://dx.doi.org/10.14510/lm-ns.v33i1.48.

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Lubinsky, D. S. "Explicit orthogonal polynomials for reciprocal polynomial weights on $(-\infty ,\infty )$." Proceedings of the American Mathematical Society 137, no. 07 (2008): 2317–27. http://dx.doi.org/10.1090/s0002-9939-08-09754-2.

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Lapin, S. V. "$ (DA)_\infty$-modules over $ (DA)_\infty$-algebras and spectral sequences." Izvestiya: Mathematics 66, no. 3 (2002): 543–68. http://dx.doi.org/10.1070/im2002v066n03abeh000388.

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Lapin, S. V. "$ D_\infty$-differential $ E_\infty$-algebras and multiplicative spectral sequences." Sbornik: Mathematics 196, no. 11 (2005): 1627–58. http://dx.doi.org/10.1070/sm2005v196n11abeh003724.

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Younis, Rahman M. "$M$-ideals of $L^{\infty}/H^{\infty}$ and support sets." Illinois Journal of Mathematics 29, no. 1 (1985): 96–102. http://dx.doi.org/10.1215/ijm/1256045842.

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IZUCHI, KEIJI, and DANIEL SUREZ. "NORM CLOSED INVARIANT SUBSPACES IN $L^{\infty}$ AND $H^\infty$." Glasgow Mathematical Journal 46, no. 2 (2004): 399–404. http://dx.doi.org/10.1017/s0017089504001880.

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Yoo, WonSok. "The characterizations of matrix families (c_0(X), l^\infty(Y)) and (l^\infty(X), l^\infty(Y))." Applied Mathematical Sciences 10 (2016): 653–59. http://dx.doi.org/10.12988/ams.2016.512744.

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Kofanov, V. A., and K. D. Sydorovych. "Strengthening the Comparison Theorem and Kolmogorov Inequality in the Asymmetric Case." Researches in Mathematics 30, no. 1 (2022): 30. http://dx.doi.org/10.15421/242204.

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We obtain the strengthened Kolmogorov comparison theorem in asymmetric case.In particular, it gives us the opportunity to obtain the following strengthened Kolmogorov inequality in the asymmetric case:$$\|x^{(k)}_{\pm }\|_{\infty}\le \frac{\|\varphi _{r-k}( \cdot \;;\alpha ,\beta )_\pm \|_{\infty }}{E_0(\varphi _r( \cdot \;;\alpha ,\beta ))^{1-k/r}_{\infty }}|||x|||^{1-k/r}_{\infty}\|\alpha^{-1}x_+^{(r)}+\beta^{-1}x_-^{(r)}\|_\infty^{k/r}$$for functions $x \in L^r_{\infty }(\mathbb{R})$, where$$|||x|||_\infty:=\frac12 \sup_{\alpha ,\beta}\{ |x(\beta)-x(\alpha)|:x'(t)\neq 0 \;\;\forallt\in (\al

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Sheremeta, M. M. "On the growth of a composition of entire functions." Carpathian Mathematical Publications 9, no. 2 (2018): 181–87. http://dx.doi.org/10.15330/cmp.9.2.181-187.

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Let $\gamma$ be a positive continuous on $[0,\,+\infty)$ function increasing to $+\infty$ and $f$ and $g$ be arbitrary entire functions of positive lower order and finite order.In order that for $$\lim\limits_{r\to+\infty} \frac{\ln\ln\,M_{f(g)}(r)}{\ln\ln\,M_f(\exp\{\gamma(r)\})}=+\infty, \quad M_f(r)=\max\{|f(z)|:\,|z|=r\}, $$ it is necessary and sufficient that $(\ln\,\gamma(r))/(\ln\,r)\to 0$ as $r\to+\infty$. This statement is an answer to the question posed by A.P. Singh and M.S. Baloria in 1991.Also in order that $$ \lim\limits_{r\to+\infty}\frac{\ln\ln\,M_F(r)} {\ln\ln\,M_f(\exp\{\gamm

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LI, FANG, QI LI, and YUFEI LIU. "A REACTION–DIFFUSION–ADVECTION EQUATION WITH COMBUSTION NONLINEARITY ON THE HALF-LINE." Bulletin of the Australian Mathematical Society 98, no. 2 (2018): 277–85. http://dx.doi.org/10.1017/s0004972718000370.

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We study the dynamics of a reaction–diffusion–advection equation $u_{t}=u_{xx}-au_{x}+f(u)$ on the right half-line with Robin boundary condition $u_{x}=au$ at $x=0$, where $f(u)$ is a combustion nonlinearity. We show that, when $0<a<c$ (where $c$ is the travelling wave speed of $u_{t}=u_{xx}+f(u)$), $u$ converges in the $L_{loc}^{\infty }([0,\infty ))$ topology either to $0$ or to a positive steady state; when $a\geq c$, a solution $u$ starting from a small initial datum tends to $0$ in the $L^{\infty }([0,\infty ))$ topology, but this is not true for a solution starting from a large ini

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Filevych, P. V., and O. B. Hrybel. "The growth of the maximal term of Dirichlet series." Carpathian Mathematical Publications 10, no. 1 (2018): 79–81. http://dx.doi.org/10.15330/cmp.10.1.79-81.

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Let $\Lambda$ be the class of nonnegative sequences $(\lambda_n)$ increasing to $+\infty$, $A\in(-\infty,+\infty]$, $L_A$ be the class of continuous functions increasing to $+\infty$ on $[A_0,A)$, $(\lambda_n)\in\Lambda$, and $F(s)=\sum a_ne^{s\lambda_n}$ be a Dirichlet series such that its maximum term $\mu(\sigma,F)=\max_n|a_n|e^{\sigma\lambda_n}$ is defined for every $\sigma\in(-\infty,A)$. It is proved that for all functions $\alpha\in L_{+\infty}$ and $\beta\in L_A$ the equality$$\rho^*_{\alpha,\beta}(F)=\max_{(\eta_n)\in\Lambda}\overline{\lim_{n\to\infty}}\frac{\alpha(\eta_n)}{\beta\left

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Salo, T. M., and O. Yu Tarnovecka. "The convergence classes for analytic functions in the Reinhardt domains." Carpathian Mathematical Publications 10, no. 2 (2018): 408–11. http://dx.doi.org/10.15330/cmp.10.2.408-411.

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Let $L^0$ be the class of positive increasing on $[1,+\infty)$ functions $l$ such that $l((1+o(1))x)=(1+o(1))l(x)$ $(x\to +\infty)$. We assume that $\alpha$ is a concave function such that $\alpha(e^x)\in L^0$ and function $\beta\in L^0$ such that $\displaystyle\int_1^{+\infty}\frac{\alpha(x)}{\beta(x)}dx<+\infty$. In the article it is proved the following theorem: if $\displaystyle f(z)=\sum_{\|n\|=0}^{+\infty}a_nz_n$, $z\in \mathbb{C}^p$, is analytic function in the bounded Reinhard domain $G\subset \mathbb{C}^p$, then the condition $\displaystyle \int\limits_{R_0}^{1} \frac{\alpha(\ln^{+

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HONG, SHAOFANG, and K. S. ENOCH LEE. "ASYMPTOTIC BEHAVIOR OF EIGENVALUES OF RECIPROCAL POWER LCM MATRICES." Glasgow Mathematical Journal 50, no. 1 (2008): 163–74. http://dx.doi.org/10.1017/s0017089507003953.

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AbstractLet$\{x_i\}_{i=1}^{\infty}$be an arbitrary strictly increasing infinite sequence of positive integers. For an integern≥1, let$S_n=\{x_1, {\ldots}\, x_n\}$. Letr>0 be a real number andq≥ 1 a given integer. Let$\lambda _n^{(1)}\, {\le}\, {\ldots}\, {\le}\, \lambda _n^{(n)}$be the eigenvalues of the reciprocal power LCM matrix$(\frac{1}{[x_i, x_j]^r})$having the reciprocal power${1\over {[x_i, x_j]^r}}$of the least common multiple ofxiandxjas itsi,j-entry. We show that the sequence$\{\lambda _n^{(q)}\}_{n=q}^{\infty}$converges and${\rm lim}_{n\, {\rightarrow}\, \infty}\lambda _n^{(q)}=

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