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Unbounded functions in the unit disk
Published 1983-01-01“…A survey is made of results related to the value distribution of functions which are meromorphic or analytic in the unit disc and have unbounded growth according to some specific growth indicator.…”
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Composition of entire function and analytic functions in the unit ball with a vanished gradient
Published 2024-12-01Subjects: “…unit disc…”
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Functions developed by nurse in an intensive care unit
Published 2012-02-01“…This exploratory qualitative study aiming to identify the functions performed by the nurse in the Intensive Care Unit, following the Canadian frame about functions of nurse (care, educate, coordinate, collaborate and supervise). …”
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Functional tissue units in the Human Reference Atlas
Published 2025-02-01“…Abstract Functional tissue units form the basic building blocks of organs and are important for understanding and modeling the healthy physiological function of the organ and changes that occur during disease states. …”
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Remarks on applying unit function for calculation of convolutions
Published 1997-12-01“… The examples of calculations of convolutions using the unit function are given. …”
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Distances from Bloch functions to some Möbius invariant function spaces in the unit ball of ℂn
Published 2009-01-01“…Distance formulae from Bloch functions to some Möbius invariant function spaces in the unit ball of ℂn such as Qs spaces, little Bloch space ℬ0 and Besov spaces Bp are given.…”
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On the interpolation in some classes of holomorphic in the unit disk functions
Published 2024-09-01Subjects: Get full text
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Methodology for Functional and Technical Analysis of Power - Technological Unit
Published 2008-02-01Get full text
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MODELING OF THE PROCESS OF FUNCTION A CLEANING UNIT OF GRAIN
Published 2007-12-01“…A general approach of a mathematical model building of function a cleaning unit of grain with different structural schemes is given, a rational parameters and functional indexes are synthesis.…”
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Analyzing Functions Mapping the Unit Disk to Limaçon Domain
Published 2024-10-01“…This function maps the open unit disk $\mathbb{D}$ onto a Limaçon domain denoted by \[ \left[(u-1)^2+v^2-s^2\right]^2<(1-s)^2\left[\left(u-1-s\right)^2+v^2\right].\] The primary investigation concerns on analytic function families where $zh'/h$ maps the unit disk to a subset of this domain. …”
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Value Distribution for a Class of Small Functions in the Unit Disk
Published 2011-01-01“…If 𝑓 is a meromorphic function in the unit disk 𝐷={𝑧∶|𝑧|<1}, analogous results to the previous equation exist when limsup𝑟→1−(𝑇(𝑟,𝑓)/log(1/(1−𝑟)))=+∞. …”
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Analytic Gaussian functions in the unit disc: probability of zeros absence
Published 2023-03-01Get full text
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Some Results on Composition of Analytic Functions in a Unit Polydisc
Published 2024-09-01Subjects: “…analytic function…”
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Integral representations for harmonic and biharmonic functions in the unit ball (in Russian)
Published 2013-04-01Subjects: Get full text
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Analytic in the unit polydisc functions of bounded L-index in direction
Published 2023-09-01Subjects: “…analytic function; unit polydisc; bounded $l$-index in direction; directional derivative; maximum modulus; minimum modulus; logarithmic derivative; zero distribution; local behavior…”
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A criterion for p-valently starlike functions
Published 1994-01-01“…The object of the present paper is to prove a criterion for p-valently starlike functions in the open unit disk.…”
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Bernstein Approximations for Fuzzy-Valued Functions
Published 2025-07-01Subjects: Get full text
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Arbitrary random variables and Wiman's inequality for analytic functions in the unit disc
Published 2024-09-01“…We consider the class $\mathcal{A}(\varphi,\beta)$ of random analytic functions in the unit disk $\mathbb{C}=\{z\colon |z|<1\}$ of the form $f(z,\omega)=f(z,\omega_1,\omega_2)=\sum_{n=0}^{+\infty} R_n(\omega_1)\xi_n(\omega_2)a_nz^n,$ where $a_n\in\mathbb{C}\colon \lim\limits_{n\to+\infty}\sqrt[n]{|a_n|}=1,$ $\big(R_n(\omega)\big)$ is the Rademacher sequence, $\big(\xi_n(\omega)\big)$ is a sequence of complex-valued random variables (denote by $\Delta_{\varphi}$) such that there exists a constant $\beta>0$ and a function $\varphi(N,\beta)\colon\mathbb{N}\times\mathbb{R}_+\to[1;+\infty)$ non-decreasing by $N$ and $\beta$ for which $\displaystyle \Bigl(\mathbf{E}\Bigl(\max_{0\leq n\leq N}|\xi_n|^{\beta}\Bigl)\Bigl)^{1/\beta}\asymp\varphi(N,\beta),\ \ N\to+\infty,\ \ \alpha=\varlimsup_{N\to+\infty}\frac{\ln\varphi(N,\beta)}{\ln N}<+\infty,$ $\displaystyle (\exists \gamma>0)(\exists n_0\in\mathbb{N})\colon \sup\{ \mathbf{E}|\xi_n|^{-\gamma}\colon\ n\geq n_0\}<+\infty.$ By $\mathcal{A}_1(\varphi,\beta)$ we denote the class of random analytic functions in $\mathbb{D}$ of the form $f(z,\omega)=\sum_{n=0}^{+\infty} \xi_n(\omega)a_nz^n,$ where a sequence $\big(\xi_n(\omega)\big)\in\Delta_\varphi$ and, in particular, may be not sub-gaussian and not independent. …”
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Functional but not taxonomic diversity increases productivity of Populus in the southeastern United States
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