Pub Date : 2023-12-18DOI: 10.31926/but.mif.2023.3.65.2.11
∗. AndreeaNISTOR-S¸ERBAN, Dorina R ˘ aducanu
In this paper we consider a class of functions Mα(φ) defined by subordination, consisting of functions f ∈ A satisfying the condition (1 −α) zf′(z)/ f(z) + α (1 + zf′′(z)/ f′(z) )≺ φ(z), z ∈ U. In the study of univalent functions, estimates on the Taylor coefficients are usually given. Another significant problem deals with the estimates of logarithmic coefficients. For the class S of univalent functions no sharp bounds for the modulus of the individual logarithmic coefficients are known if n ≥ 3. For different subclasses of S the results are not better and in most cases only th e first three initial coefficients of log f(z)/z are considered. For the class Mα(φ) we obtain upper bounds for the logarithmic coefficients γn, n ∈ {1, 2, 3} and also for Γn, n ∈ {1, 2, 3}, the logarithmic coefficients of the inverse of Mα(φ). Connections with previous known results are pointed out.
在本文中，我们考虑一类由从属定义的函数 Mα(φ)，它由满足条件 (1 -α) zf′(z)/ f(z) + α (1 + zf′(z)/ f′(z) )≺ φ(z)、z∈ U 的函数 f∈ A 组成。在研究一元函数时，通常会给出泰勒系数的估计值。另一个重要问题涉及对数系数的估计。对于单值函数 S 类，如果 n ≥ 3，单个对数系数的模数没有明确的界限。对于 S 的不同子类，结果也不尽相同，大多数情况下只考虑 log f(z)/z 的前三个初始系数。对于 Mα(φ)类，我们得到了对数系数 γn, n∈ {1, 2, 3} 的上界，也得到了 Mα(φ)逆的对数系数 Γn, n∈ {1, 2, 3} 的上界。指出了与之前已知结果的联系。
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Pub Date : 2023-12-18DOI: 10.31926/but.mif.2023.3.65.2.14
∗. AlexandraB˘AICOIANU, Ioana Plajer
Each programming language needs a mechanism of translating source code into code understood by the computer, i.e., machine code or assembly. This is done by a compiler. A compiler is thus a fundamental tool for software development. Lexical analysis, as the first step of compilation, has an important role and should be performed in an optimal way. But not only compilers rely on lexical analysis. Its role lies nowadays also in pattern recognition or natural language processing. In this paper, we present some of the main aspects of lexical analysis and how to efficiently perform it. Our aim is to offer some guidelines in constructing a modern and efficient scanner (lexer), outlining the criteria, which should be considered, presenting some pitfalls, and comparing existent tools for compiler construction. The main contribution of the paper is to offer practical guidelines and recommendations, especially to graduate students and programmers, in constructing an efficient scanner (lexer), considering also the proper tools currently available.
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Pub Date : 2023-12-18DOI: 10.31926/but.mif.2023.3.65.2.1
U. Abel, O. Agratini
This note concerns the study of an approximation linear positive process introduced by R. Paltanea in 2008. Considering the impact of this class of operators that depends on two parameters, in a distinct section we present a brief radiograph of the main properties highlighted over time in various papers. Our contribution materializes in the definition and study of the approximation properties of the King variant of these operators.
本说明涉及对帕尔塔内亚（R. Paltanea）于 2008 年提出的近似线性正过程的研究。考虑到这一类取决于两个参数的算子的影响，我们在一个单独的章节中简要介绍了不同论文中强调的主要性质。我们的贡献体现在对这些算子的 King 变体的近似性质的定义和研究上。
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