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Цілі функції мінімального зростання із заданими нулями
No full textLet be a positive continuous increasing to function on . For a positive non-decreasing on function , we found sufficient and necessary conditions under which, for an arbitrary complex sequence such that as and for all sufficiently large , there exists an entire function whose zeros are the (with multiplicities taken into account) satisfying \ln\ln M(r)=o\big(l^{-1}(\ln n(r))\ln n_{\zeta}(r)h(\lnn(r))\big),\quad r\notin E,\ r\to+\infty, where is a set of finite logarithmic measure. Here, is the counting function of the sequence , and is the maximum modulus of the function .Нехай додатна, неперервна, зростаюча до на функція. Знайдено достатні та необхідні умови на додатну, неспадну на функцію , за яких для довільної комплексної послідовності такої, що , якщо , і для всіх достатньо великих , існує ціла функція з нулями в точках і лише в них (з урахуванням кратності), для якої маємо де множина скінченої логарифмічної міри. Тут лічильна функція послідовності , а максимум модуля функції
Зростання цiлих функцiй в термiнах узагальнених порядкiв
Get PDFLet be a convex function on such that , , is a transcendental entire function, let be the maximum modulus of and let It is proved that for every transcendental entire function the generalized order is independent of the arguments of the coefficients (or defined by the sequence ) if and only if the inequality holds.Нехай така опукла на функція, що , , трансцендентна ціла функція, максимум модуля , Доведено, що умова є необхідною і достатньою для того, щоб узагальнений порядок кожної трансцендентної цілої функції не залежав від аргументів коефіцієнтів (чи визначався послідовністю )
Оцінки для сум рядів Діріхле
No full textIn the article, we prove approximation theorems that allow us to estimate, with sufficient accuracy, the supremum modulus of a Dirichlet series by the maximal term of another Dirichlet series associated with the given one. Using these theorems, we establish necessary and sufficient conditions on the sequence of coefficients of a Dirichlet series, under which the most general asymptotic and global estimates from above for its supremum modulus hold.У роботі доведено теореми апроксимаційного характеру, що дозволяють з достатньою точністю оцінити супремум модуля ряду Діріхле через максимальний член іншого ряду Діріхле, пов\u27язаного зі заданим. За допомогою цих теорем для ряду Діріхле отримано умови на послідовність модулів його коефіцієнтів, які є необхідними та достатніми для виконання найзагальніших асимптотичних та глобальних оцінок зверху для його супремуму модуля
Відносне зростання цілої функції та інтегральної лічильної функцiї її нулів
No full textLet be a sequence of complex numbers such that as , be the integrated counting function of this sequence, and let be a positive continuous and increasing to function on for which as . It is proved that for any set satisfying , there exists an entire function whose zeros are precisely the , with multiplicities taken into account, such that the relation holds, where is the maximum modulus of the function . It is also shown that this relation is best possible in a certain sense.Нехай комплексна послідовність така, що 0<|\zeta_1|\le|\zeta_2|\le\dots і , усереднена лічильна функція цієї послідовності, а додатна, неперервна, зростаюча до на функція, для якої , . Доведено, що для кожної множини , яка задовольняє оцінку , існує ціла функція з нулями в точках і лише в них (з урахуванням кратності), для якої правильне співвідношення де максимум модуля функції . Показано також, що наведене співвідношення є в певному сенсі остаточним
The growth of entire functions in the terms of generalized orders
No full textLet be a convex function on such that, , --- a transcendental entire function, let be the maximum modulus of and letIt is proved that for every transcendental entire function thegeneralized order is independent on the arguments of thecoefficients (or defined by the sequence ) if and only if theinequality holds
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Get PDFWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
Dispelling the Myths Behind First-author Citation Counts
Get PDFWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
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