# Максимальная функция на дуальной гипергруппе Лагерра

Analysis Mathematica
Authors: Assal Miloud, Rahmouni Atef and Taieb Ahmed

## Abstract

In this paper, we are interested in the Laguerre hypergroup

\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathbb{K} = [0,\infty ) \times \mathbb{R}$$ \end{document}
which is the fundamental manifold of the radial function space for the Heisenberg group. So, we consider the generalized shift operator generated by the dual of the Laguerre hypergroup
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\bigcup\limits_{j \in \mathbb{N}} {\left\{ {(\lambda ,\mu ) \in \mathbb{R}^2 :\mu = \left| \lambda \right|(2j + \alpha + 1),\lambda \ne 0} \right\} \cup \left\{ {(0,\mu ) \in \mathbb{R}^2 :\mu \geqslant 0} \right\}} ,$$ \end{document}
by means of which the maximal function is investigated. For 1 < p, the L p()-boundedness and weak L 1()-boundedness result for the maximal function is obtained.

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# О расходимости кратных рядов Хаара

Analysis Mathematica
Author: G. Oniani

## Abstract

It is proved that for any dimension n ≥ 2, L(ln+ L)n−1 is the widest integral class in which the almost everywhere convergence of spherical partial sums of multiple Fourier-Haar series is provided. Moreover,it is shown that the divergence effects of rectangular and spherical general terms of multiple Fourier-Haar series can be achieved simultaneously on a set of full measure by an appropriate rearrangement of values of arbitrary summable function f not belonging to L(ln+ L)n−1.

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# О суммируемости методами Чезаро двойных рядов по блочно-ортонормированным системам

Analysis Mathematica

## Abstract

The extension of the coefficient test of Menshov and Kaczmarz ensuring the almost everywhere (C, 1, 1)-((C, 1, 0) or (C, 0, 1)) summability of double series with respect to block-orthonormal systems is studied.

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# The extension of the D(−k 2)-pair {k 2,k 2 + 1}

Periodica Mathematica Hungarica
Authors: Yasutsugu Fujita and Alain Togbé

## Abstract

Let n be a nonzero integer. A set of m distinct positive integers is called a D(n)-m-tuple if the product of any two of them increased by n is a perfect square. Let k be a positive integer. In this paper, we show that if {k 2, k 2+1, c, d} is a D(−k 2)-quadruple with c < d, then c = 1 and d = 4k 2+1. This extends the work of the first author [20] and that of Dujella [4].

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# On the sum of two divisors of (n 2 + 1)/2

Periodica Mathematica Hungarica
Authors: Andrej Dujella and Florian Luca

## Abstract

In this paper, given a pair of odd coprime integers δ and ɛ, we study the positive n such that (n 2 + 1)/2 has two divisors d 1 and d 2 summing up to δn + ɛ.

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# Weakly-Abel rings and weakly exchange rings

Acta Mathematica Hungarica
Author: Junchao Wei

## Abstract

Let R be an associative ring with identity. An element xR is said to be weakly exchange if there exists an idempotent eR such that exR and 1−e∊(1−x)R or 1−e∊(1+x)R. The ring R is said to be weakly exchange if all of its elements are weakly exchange. In this paper an element-wise characterization is given, and it is shown that weakly-Abel weakly exchange rings are weakly clean. Moreover, a relation between unit regular rings and weakly clean rings is also obtained.

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# A bibliometric portrait of the evolution, scientific roots and influence of the literature on university–industry links

Scientometrics
Authors: Aurora A. C. Teixeira and Luisa Mota

## Abstract

The study of university–industry (U–I) relations has been the focus of growing interest in the literature. However, to date, a quantitative overview of the existing literature in this field has yet to be accomplished. This study intends to fill this gap through the use of bibliometric techniques. By using three different yet interrelated databases—a database containing the articles published on U–I links, which encompass 534 articles published between 1986 and 2011; a ‘roots’ database, which encompasses over 20,000 references to the articles published on U–I relations; and a ‘influences’ database which includes more than 15,000 studies that cited the articles published on U–I relations—we obtained the following results: (1) ‘Academic spin offs’, ‘Scientific and technological policies’ and (to a greater extent) ‘Knowledge Transfer Channels’ are topics in decline; (2) ‘Characteristics of universities, firms and scientists’, along with ‘Regional spillovers’, show remarkable growth, and ‘Measures and indicators’ can be considered an emergent topic; (3) clear tendency towards ‘empirical’ works, although ‘appreciative and empirical’ papers constitute the bulk of this literature; (4) the multidisciplinary nature of the intellectual roots of the U–I literature—an interesting blending of neoclassical economics (focused on licensing, knowledge transfer and high-tech entrepreneurship) and heterodox approaches (mainly related to systems of innovation) is observed in terms of intellectual roots; (5) the influence of the U–I literature is largely concentrated on the industrialized world and on the research area of innovation and technology (i.e., some ‘scientific endogamy’ is observed).

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# Comments on the Discussion Paper

Scientometrics
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# Discussion Paper

Scientometrics
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# Ten challenges in modeling bibliographic data for bibliometric analysis

Scientometrics
Authors: Alfio Ferrara and Silvia Salini

## Abstract

The complexity and variety of bibliographic data is growing, and efforts to define new methodologies and techniques for bibliometric analysis are intensifying. In this complex scenario, one of the most crucial issues is the quality of data and the capability of bibliometric analysis to cope with multiple data dimensions. Although the problem of enforcing a multidimensional approach to the analysis and management of bibliographic data is not new, a reference design pattern and a specific conceptual model for multidimensional analysis of bibliographic data are still missing. In this paper, we discuss ten of the most relevant challenges for bibliometric analysis when dealing with multidimensional data, and we propose a reference data model that, according to different goals, can help analysis designers and bibliographic experts in working with large collections of bibliographic data.

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# On the relationship between citations of publication output and Hirsch index h of authors: conceptualization of tapered Hirsch index h T, circular citation area radius R and citation acceleration a

Scientometrics
Author: Keshra Sangwal

## Abstract

The nature of the empirical proportionality constant A in the relation L = Ah 2 between total number of citations L of the publication output of an author and his/her Hirsch index h is analyzed using data of the publication output and citations for six scientists elected to the membership of the Royal Society in 2006 and 199 professors working in different institutions in Poland. The main problem with the h index of different authors calculated by using the above relation is that it underestimates the ranking of scientists publishing papers receiving very high citations and results in high values of A. It was found that the value of the Hirsch constant A for different scientists is associated with the discreteness of h and is related to the tapered Hirsch index h T by A 1/2 ≈ 1.21h T. To overcome the drawback of a wide range of A associated with the discreteness of h for different authors, a simple index, the radius R of circular citation area, defined as R = (L/π)1/2h, is suggested. This circular citation area radius R is easy to calculate and improves the ranking of scientists publishing high-impact papers. Finally, after introducing the concept of citation acceleration a = L/t 2 = π(R/t)2 (t is publication duration of a scientist), some general features of citations of publication output of Polish professors are described in terms of their citability. Analysis of the data of Polish professors in terms of citation acceleration a shows that: (1) the citability of the papers of a majority of physics and chemistry professors is much higher than that of technical sciences professors, and (2) increasing fraction of conference papers as well as non-English papers and engagement in administrative functions of professors result in decreasing citability of their overall publication output.

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# Evaluation index system for academic papers of humanities and social sciences

Scientometrics
Authors: Quan'e Ren and Xuemei Gong

## Abstract

An index system for evaluating academic papers is constructed and verified based on the empirical analysis of papers that has gained the 6th Chinese Academy of Social Sciences Award for Outstanding Achievements. Some new index, such as paper discipline impact factor, discipline average cited rate per paper and discipline average downloaded rate per paper have been put forward in this paper. The empirical research results show that the ranking of papers calculated by this evaluation index system is in conformity with the awards determined by peer review in general, but still needs to be verified and improved in practice.

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# Approximation of functions of bounded variation by integrated Meyer-König and Zeller operators of finite type

Studia Scientiarum Mathematicarum Hungarica
Author: Tiberiu Trif

I. Gavrea and T. Trif [Rend. Circ. Mat. Palermo (2) Suppl. 76 (2005), 375–394] introduced a class of Meyer-König-Zeller-Durrmeyer operators “of finite type” and investigated the rate of convergence of these operators for continuous functions. In the present paper we study the approximation of functions of bounded variation by means of these operators.

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# Approximations in several variables with freud-type and A p-weights

Studia Scientiarum Mathematicarum Hungarica
Author: Nguyen Ky

We present direct (Jackson-type) and converse (Bernstein-Stechkin-type) theorems for polynomial approximations with Freud-type weights and trigonometric approximations with A p-weights, in the case of several variables.

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# Centrally symmetric convex bodies and sections having maximal quermassintegrals

Studia Scientiarum Mathematicarum Hungarica
Authors: E. Makai and H. Martini

Let d ≧ 2, and let K ⊂ ℝd be a convex body containing the origin 0 in its interior. In a previous paper we have proved the following. The body K is 0-symmetric if and only if the following holds. For each ωS d−1, we have that the (d − 1)-volume of the intersection of K and an arbitrary hyperplane, with normal ω, attains its maximum if the hyperplane contains 0. An analogous theorem, for 1-dimensional sections and 1-volumes, has been proved long ago by Hammer (see [2]). In this paper we deal with the ((d − 2)-dimensional) surface area, or with lower dimensional quermassintegrals of these intersections, and prove an analogous, but local theorem, for small C 2-perturbations, or C 3-perturbations of the Euclidean unit ball, respectively.

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# Limsup theorems and a uniform LIL for asymptotically negatively associated random sequences

Studia Scientiarum Mathematicarum Hungarica
Authors: Yong-Kab Choi and Kyo-Shin Hwang

In this paper we establish some limsup theorems and a generalized uniform law of the iterated logarithm (LIL) for the increments of the partial sums of a strictly stationary and asymptotically negatively associated (ANA) sequence of random variables.

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# Multidimensional matrix characterization of equivalent double sequences

Studia Scientiarum Mathematicarum Hungarica
Authors: Richard Patterson and Ekrem Savaş

In 1936 Hamilton presented a Silverman-Toeplitz type characterization of c0 (i.e. the space of bounded double Pringsheim null sequences). In this paper we begin with the presentation of a notion of asymptotically statistical regular. Using this definition and the concept of maximum remaining difference for double sequence, we present the following Silverman-Toeplitz type characterization of double statistical rate of convergence: let A be a nonnegative c0c0 summability matrix and let [x] and [y] be member of l″ such that with [x] ∈ P 0, and [y] ∈ P δ for some δ > 0 then µ(Ax) µ(Ay). In addition other implications and variations shall also be presented.

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# On B-injectors of symmetric groups S n

Studia Scientiarum Mathematicarum Hungarica
Authors: Mohammad Al-Shomrani and Mashhour. Al-Ali Bani-Ata

The aim of this paper is to describe the B-injectors of the symmetric group S n by proving the following main theorem, using a shorter proof than that followed in [1] and [3]. In this note the proof is mainly based on the minimal proof concept, and the parts we have used from these two papers are referred to.Main Theorem: Let Ω be a finite set of size n, and let BS Ω be a B-injector of S Ω. Then

1. a) If n ≢ 3 (mod 4) then B is a Sylow 2-subgroup of S Ω.
2. b) If n ≡ 3 (mod 4) then B = 〈d〉 × T where d is a 3-cycle and T is a Sylow 2-subgroup of \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $C_{S_\Omega } (d)$ \end{document}.

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# On the b-chromatic number of some graph products

Studia Scientiarum Mathematicarum Hungarica
Authors: Marko Jakovac and Iztok Peterin

A b-coloring is a proper vertex coloring of a graph such that each color class contains a vertex that has a neighbor in all other color classes and the b-chromatic number is the largest integer φ(G) for which a graph has a b-coloring with φ(G) colors. We determine some upper and lower bounds for the b-chromatic number of the strong product GH, the lexicographic product G[H] and the direct product G × H and give some exact values for products of paths, cycles, stars, and complete bipartite graphs. We also show that the b-chromatic number of P nH, C nH, P n[H], C n[H], and K m,n[H] can be determined for an arbitrary graph H, when integers m and n are large enough.

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# On the structure of graphs with path-width at most two

Studia Scientiarum Mathematicarum Hungarica
Authors: János Barát, Péter Hajnal, Yixun Lin and Aifeng Yang

Kinnersley and Langston used a computer search to characterize the class of graphs with path-width at most two. The excluded minor list consists of 110 graphs. This set is fairly large, and the list gives little insight to structural properties of the targeted graph class. We take a different route here. We concentrate on the building blocks of the graphs with path-width at most two and how they are glued together. In this way, we get a short and compact characterization of 2-connected and 2-edge-connected graphs with path-width at most two.

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# Pointwise convergence of Marcinkiewicz-Fejér means of two-dimensional Walsh-Fourier series

Studia Scientiarum Mathematicarum Hungarica
Authors: Ushangi Goginava and Ferenc Weisz

In this paper we characterize the set of convergence of the Marcinkiewicz-Fejér means of two-dimensional Walsh-Fourier series.

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# Strong approximation of two-dimensional Walsh-Fourier series

Studia Scientiarum Mathematicarum Hungarica
Authors: Ushangi Goginava and Larry Gogoladze

In this paper we study the exponential uniform strong approximation of two-dimensional Walsh-Fourier series. In particular, it is proved that the two-dimensional Walsh-Fourier series of the continuous function f is uniformly strong summable to the function f exponentially in the power 1/2. Moreover, it is proved that this result is best possible.

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# w-overrings of w-Noetherian rings

Studia Scientiarum Mathematicarum Hungarica
Authors: Huayu Yin and Youhua Chen

In this paper, we concern the w-analogue of Matijevic’s result. We show that if R is a w-Noetherian ring and T a w-overring of R such that TR wg. Then T has ACC on regular w-ideals.

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# Blockmodeling of co-authorship networks in library and information science in Argentina: a case study

Scientometrics
Authors: Zaida Chinchilla-Rodríguez, Anuska Ferligoj, Sandra Miguel, Luka Kronegger and Félix de Moya-Anegón

## Abstract

The paper introduces the use of blockmodeling in the micro-level study of the internal structure of co-authorship networks over time. Variations in scientific productivity and researcher or research group visibility were determined by observing authors’ role in the core-periphery structure and crossing this information with bibliometric data. Three techniques were applied to represent the structure of collaborative science: (1) the blockmodeling; (2) the Kamada-Kawai algorithm based on the similarities in co-authorships present in the documents analysed; (3) bibliometrics to determine output volume, impact and degree of collaboration from the bibliographic data drawn from publications. The goal was to determine the extent to which the use of these two complementary approaches, in conjunction with bibliometric data, provides greater insight into the structure and characteristics of a given field of scientific endeavour. The paper describes certain features of Pajek software and how it can be used to study research group composition, structure and dynamics. The approach combines bibliometric and social network analysis to explore scientific collaboration networks and monitor individual and group careers from new perspectives. Its application on a small-scale case study is intended as an example and can be used in other disciplines. It may be very useful for the appraisal of scientific developments.

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# Erratum to: Journal report card

Scientometrics
Author: Judit Bar-Ilan
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# On moduli of p-continuity

Acta Mathematica Hungarica
Authors: V. I. Kolyada and M. Lind

## Abstract

Moduli of p-continuity provide a measure of fractional smoothness of functions via p-variation. We prove a sharp estimate of the modulus of p-continuity in terms of the modulus of q-continuity (1<p<q<∞).

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# The ultrafilter number for singular cardinals

Acta Mathematica Hungarica
Authors: Shimon Garti and Saharon Shelah

## Abstract

We prove the consistency of a singular cardinal λ with small value of the ultrafilter number , and arbitrarily large value of 2λ.

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# Grim tales about the impact factor and the h-index in the Web of Science and the Journal Citation Reports databases: reflections on Vanclay's criticism

Scientometrics
Author: Peter Jacso

## Abstract

This paper reflects on the most current and some of the recent contributions of JK Vanclay, focusing on his methods, findings, and criticism about the journal citations reports and the web of science databases, the journal impact factor and the h-index. It is argued and demonstrated that some of the recent papers of the author about scientometric issues, measures and sources show so much demagoguery, ignorance and arrogance, have so much prejudice and bias, so profound errors in using the databases, calculating metrics, and interpreting search results that the papers are very unlikely to be meant as a genuine contribution from an academic who is a graduate of—among others—Oxford University, professor and dean in a respected university, a well-published and well-cited author and a recipient of the Queen's Award (all the above in forest science). The papers are much more likely to serve as props for a staged, mock-up scenario based on slipshod research in an experiment, to illustrate the deficiencies in the processes and in the assessment of scholarly publishing productivity and impact in order to present the idealized solution of Vanclay: using the h-index, portrayed as the Prince, mounted on the shoulder of the White Horse, Google Scholar.

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# Participation of women in software engineering publications

Scientometrics
Authors: Belén Vela, Paloma Cáceres and José María Cavero

## Abstract

To the best of our knowledge, no works analyzing the participation of women as authors and editors in software engineering research publications currently exist. We have therefore followed a well-defined procedure in order to conduct an empirical study of female participation in 12 leading software engineering journals. We have analyzed the gender of the authors, editorial board members, associate editors and editors-in-chief over a two-year period in order to analyze, on the one hand, the rate of participation of women as authors and as editors in software engineering publications, and on the other, whether women are underrepresented. We have also analyzed the female distribution of authors and editors according to the geographical location of their institutions. This was done by first selecting the journals to be used as the population for data collection which then allowed us to identify female authors of papers and female editors, including the country in which their institutions are located. This eventually led to an analysis of female participation in order to understand representation rates. We analyzed 3,546 authors of 1,266 papers in 61 different countries, and 363 members of editorial boards in 30 different countries. The results of this analysis provide quantitative data concerning the participation of women as authors and editors in major software engineering journals including their distribution per country, in which important differences have been found. The results obtained were first used to compare the participation of women as authors and editors and were then used to carry out a series of simulations in order to be able to statistically confirm whether women are underrepresented. The study shows, amongst other things, that women are not underrepresented as editorial boards members and as editors-in-chief of the journals studied, although their representation as editors-in-chief is low.

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# The d-index: Discovering dependences among scientific collaborators from their bibliographic data records

Scientometrics
Authors: Luigi Di Caro, Mario Cataldi and Claudio Schifanella

## Abstract

The evaluation of the work of a researcher and its impact on the research community has been deeply studied in literature through the definition of several measures, first among all the h-index and its variations. Although these measures represent valuable tools for analyzing researchers’ outputs, they usually assume the co-authorship to be a proportional collaboration between the parts, missing out their relationships and the relative scientific influences. In this work, we propose the d-index, a novel measure that estimates the dependence degree between authors on their research environment along their entire scientific publication history. We also present a web application that implements these ideas and provides a number of visualization tools for analyzing and comparing scientific dependences among all the scientists in the DBLP bibliographic database. Finally, relying on this web environment, we present case and user studies that highlight both the validity and the reliability of the proposed evaluation measure.

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# A general framework for describing diversity within systems and similarity between systems with applications in informetrics

Scientometrics
Authors: Qiuju Zhou, Ronald Rousseau, Liying Yang, Ting Yue and Guoliang Yang

## Abstract

Building on the ideas of Stirling (J R Soc Interface, 4(15), 707–719, ) and Rafols and Meyer (Scientometrics, 82(2), 263–287, ), we borrow models of genetic distance based on gene diversity and propose a general conceptual framework to investigate the diversity within and among systems and the similarity between systems. This framework can be used to reveal the relationship of systems weighted by the similarity of the corresponding categories. Application of the framework to scientometrics is explored to evaluate the balance of national disciplinary structures, and the homogeneity of disciplinary structures between countries.

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# An Inno-Qual performance system for higher education

Scientometrics
Authors: Jui-Kuei Chen and I-Shuo Chen

## Abstract

Due to the overall decrease in quality of Taiwanese universities in recent years and the resulting drastic loss of competitive advantage against foreign countries, improving the Taiwanese university system has become an urgent issue requiring immediate attention. Evidence suggests focusing on total quality management (TQM) and that innovation is the key way to effectively upgrade the operation performance and is thus highly advised. Although there are a number of measurement models for TQM and innovation, early models evaluate the performance of each element separately, making evaluation inefficient and inappropriate for practice. There is a new measurement system, the network hierarchical feedback system (NHFS), which integrates the concept and characteristics of both elements; however, the major concern is that the NHFS does not take external organization-oriented improvement into account, such as service quality in higher education, especially in innovation orientation. Additionally, due to the above dilemmas faced by Taiwanese universities, attracting more students has now been a major priority. Thus, we argue that in order to successfully attract potential students, improving TQM and innovation cannot just focus on internal organization-oriented improvement, and we further extend the effectiveness and suitability of the NHFS to a novel and more utilizable performance measurement system, the solid Inno-Qual performance system (IQPS). A hybrid model based on a decision-making trial and evaluation laboratory, a fuzzy analytic network process (FANP), an importance–performance analysis along with in-depth interviews; a fuzzy analytic hierarchical process, and a technique for order preference according to similarity to an ideal solution were adopted to complete the construction. The IQPS is the first measurement system with the most effective characteristics of TQM and innovation embedded for both new and traditional universities of different types. It is intended to enhance and evaluate performance on both external and internal organization-oriented levels, generating synergy and performance improvement.

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# Prescribed practices of authorship: review of codes of ethics from professional bodies and journal guidelines across disciplines

Scientometrics
Authors: Lana Bošnjak and Ana Marušić

## Abstract

Guidelines on authorship requirements are common in biomedical journals but it is not known how authorship is defined by journals and scholarly professional organizations across research disciplines. Prevalence of authorship statements, their specificity and tone, and contributions required for authorship were assessed in 185 journals from Science Citation Index (SCI) and Social Science Citation Index (SSCI), 260 journals from Arts & Humanities Citation Index (A&HCI) and 651 codes of ethics from professional organizations from the online database of the Center for the Study of Ethics in the Profession, USA. In SCI, 53 % of the top-ranked journals had an authorship statement, compared with 32 % in SSCI. In a random sample of A&HCI-indexed journals, only 6 % of the journals addressed authorship. Only 71 (11 %) codes of ethics carried a statement on authorship. Almost all journals had defined authorship criteria compared with 33 % of the ethics codes ( = 75.975; P < 0.001). The tone of the statements in the journals was aspirational, whereas ethics codes used a normative language for defining authorship ( = 51.709, P < 0.001). Journals mostly required both research and writing contributions for authorship, while two-thirds of the ethics codes defined only research as a mandatory contribution. In conclusion, the lack of and variety of authorship definitions in journals and professional organizations across scientific disciplines may be confusing for the researchers and lead to poor authorship practices. All stakeholders in research need to collaborate on building the environment where ethical behaviour in authorship is a norm.

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# S&T publications output of Nepal: a quantitative analysis, 2001–10

Scientometrics
Authors: B. M. Gupta and Adarsh Bala

## Abstract

This study analyses the research output of Nepal in S&T during 2001–10 on several parameters including its growth and country publications share in the world's research output, country publications share in various subjects in the national and global context, pattern of research communication in core domestic and international journals, geographical distribution of publications, share of international collaborative publications at the national level as well as across subjects and characteristics of high productivity institutions, authors and cited papers. The Scopus Citation Database has been used to retrieve the publication data for 10 years.

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# Erdős-Zaks all divisor sets

Periodica Mathematica Hungarica
Authors: Scott Chapman and William Smith

## Abstract

Let ℤn be the finite cyclic group of order n and S ⊆ ℤn. We examine the factorization properties of the Block Monoid B(ℤn, S) when S is constructed using a method inspired by a 1990 paper of Erdős and Zaks. For such a set S, we develop an algorithm in Section 2 to produce and order a set {M i}i=1 n−1 which contains all the non-primary irreducible Blocks (or atoms) of B(ℤn, S). This construction yields a weakly half-factorial Block Monoid (see [9]). After developing some basic properties of the set {M i}i=1 n−1, we examine in Section 3 the connection between these irreducible blocks and the Erdős-Zaks notion of “splittable sets.” In particular, the Erdős-Zaks notion of “irreducible” does not match the classic notion of “irreducible” for the commutative cancellative monoids B(ℤn, S). We close in Sections 4 and 5 with a detailed discussion of the special properties of the blocks M1 with an emphasis on the case where the exponents of M 1 take on extreme values. The work of Section 5 allows us to offer alternate arguments for two of the main results of the original paper by Erdős and Zaks.

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# Multiplicative character sums and products of sparse integers in residue classes

Periodica Mathematica Hungarica
Authors: Alina Ostafe and Igor Shparlinski

## Abstract

We estimate multiplicative character sums over the integers with a fixed sum of binary digits and apply these results to study the distribution of products of such integers in residues modulo a prime p. Such products have recently appeared in some cryptographic algorithms, thus our results give some quantitative assurances of their pseudorandomness which is crucial for the security of these algorithms.

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# Multiplicative character sums of Fermat quotients and pseudorandom sequences

Periodica Mathematica Hungarica
Authors: Domingo Gomez and Arne Winterhof

## Abstract

We prove a bound on sums of products of multiplicative characters of shifted Fermat quotients modulo p. From this bound we derive results on the pseudorandomness of sequences of modular discrete logarithms of Fermat quotients modulo p: bounds on the well-distribution measure, the correlation measure of order , and the linear complexity.

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# On the best approximation of periodic functions by trigonometric polynomials and the exact values of widths of function classes in L 2

Analysis Mathematica
Authors: М. Шлбоэов and С. Влклрчук

## Реэюме

Получены точные неравенства типа Джексона-Стечкина для ос-редненных с весом модулей непрерывности m-го (m ∈ ℕ) порядка. Для классов функций, определенных при помоши мажорант и укаэанных осредненных величин, вычислены точные эначения раэличных n-поперечников при выполнении определенных ограничений на мажоранты.

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# On the Davenport constant and on the structure of extremal zero-sum free sequences

Periodica Mathematica Hungarica
Authors: Alfred Geroldinger, Manfred Liebmann and Andreas Philipp

## Abstract

Let

\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$G = C_{n_1 } \oplus \cdots \oplus C_{n_r }$$ \end{document}
with 1 < n 1 | … | n r be a finite abelian group, d*(G) = n 1 +…+n rr, and let d(G) denote the maximal length of a zerosum free sequence over G. Then d(G) ≥ d*(G), and the standing conjecture is that equality holds for G = C n r. We show that equality does not hold for C 2C 2n r, where n ≥ 3 is odd and r ≥ 4. This gives new information on the structure of extremal zero-sum free sequences over C 2n r.

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# Optimal reparametrization and large sample likelihood inference for the location-scale skew-normal model

Periodica Mathematica Hungarica
Authors: Rolando Cavazos-Cadena and Graciela González-Farías

## Abstract

Motivated by results in Rotnitzky et al. (2000), a family of parametrizations of the location-scale skew-normal model is introduced, and it is shown that, under each member of this class, the hypothesis H 0: λ = 0 is invariant, where λ is the asymmetry parameter. Using the trace of the inverse variance matrix associated to a generalized gradient as a selection index, a subclass of optimal parametrizations is identified, and it is proved that a slight variant of Azzalini’s centred parametrization is optimal. Next, via an arbitrary optimal parametrization, a simple derivation of the limit behavior of maximum likelihood estimators is given under H 0, and the asymptotic distribution of the corresponding likelihood ratio statistic for this composite hypothesis is determined.

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# Sumsets of sparse sets

Periodica Mathematica Hungarica
Authors: Artūras Dubickas and Paulius Šarka

## Abstract

Let σ be a constant in the interval (0, 1), and let A be an infinite set of positive integers which contains at least c 1 x σ and at most c 2 x σ elements in the interval [1, x] for some constants c 2 > c 1 > 0 independent of x and each xx 0. We prove that then the sumset A + A has more elements than A (counted up to x) by a factor

\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $${{c\left( \sigma \right)\sqrt {\log x} } \mathord{\left/ {\vphantom {{c\left( \sigma \right)\sqrt {\log x} } {\log }}} \right. \kern-\nulldelimiterspace} {\log }}$$ \end{document}
log x for x large enough. An example showing that this function cannot be greater than ɛ log x is also given. Another example shows that there is a set of positive integers A which contains at least x σ and at most x σ+ɛ elements in [1, x] such that A + A is greater than A only by a constant factor. The proof of the main result is based on an effective version of Freiman’s theorem due to Mei-Chu Chang.

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# Абсолютная сходимость простых и двойных рядов Фурье по мультипликативным системам

Analysis Mathematica
Authors: B. Golubov and S. Volosivets

## Abstract

Several sufficient conditions for generalized absolute convergence of single and double Vilenkin-Fourier series of bounded type are obtained. These conditions give multiplicative analogues of results due to L. Gogoladze and R. Meskhia, F. Móricz and A. Veres, M. Izumi and S. Izumi. Some of them are sharp in a certain sense.

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# О сходимости синус-рядов в L 1

Analysis Mathematica
Author: László Leindler

## Abstract

Our aim is to find the source why the logarithm sequences play the crucial role in the L 1-convergence of sine series. We define three new classes of sequences; one of them has the character of the logarithm sequences, the other two are the extensions of the class defined by Zhou and named Logarithm Rest Bounded Variation Sequences. In terms of these classes, extended analogues of Zhou’s theorems are proved.

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# Об условии средней ограниченной вариации и его применении в двойных тригонометрических рядах

Analysis Mathematica
Authors: Dansheng Yu, Ping Zhou and Songping Zhou

## Abstract

We introduce a new kind of double sequences named MVBVDS and some new classes of weight functions to study the weighted integrability of the double trigonometric series. Several results of Chen, Marzuq, Móricz, Ram and Singh Bhatia (see [2]–[10]) are generalized and some new results are established.

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# Улучшенное обобщение одного неравенства типа Гёльдера

Analysis Mathematica
Authors: Josip Pečarić and Ksenija Smoljak

## Abstract

In this paper an extension of a Hölder-type inequality given in [C. E. M. Pearce and J. Pečarić, On an extension of Hölder’s inequality, Bull. Austral. Math. Soc., 51(1995), 453–458] is improved using log-convexity. Furthermore, new Cauchy-type means are defined and their monotonicity property is proven.

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# Comparison of trends in the quantity and variety of Science Citation Index (SCI) literature on human pathogens between China and the United States

Scientometrics
Authors: Deqiao Tian, Yunzhou Yu, Yumin Wang and Tao Zheng

## Abstract

The proportion of pathogenic microorganisms in the microbial world is relatively small, while their threat to human health, economic development and social stability is severe. The quantity and variation of Science Citation Index (SCI) literature related to pathogenic microorganisms may reflect the level of relevant research and the degree of attention. Here we compared trends in the quantity and variety of SCI literature relating to certain important pathogenic microorganisms published by scientists from United States and China from 1996 to 2010 by searching the Science Citation Index database. The pathogenic microorganisms in this study comprise two categories of pathogens: Bacillus anthracis, Yersinia pestis, Francisella tularensis, Ebola virus, Burkholderia pseudomallei, which belong to biodefense-associated pathogens (BDAPs) and the human immunodeficiency virus (HIV), SARS coronavirus, hepatitis B virus (HBV), Mycobacterium tuberculosis, influenza virus, which belong to the commonly encountered health-threatening pathogens. Our results showed that the United States (US) published much more SCI literature on these pathogens than China. Furthermore, literature on BDAPs published by scientists from the US has increased sharply since 2002. However, the numbers of literature relating to CEHTPs from China has demonstrated a gradual increase from 1996 to 2010. Research into pathogenic microorganisms requires three balance to be achieved: investment in BDAP and CEHTP studies; basic and applied research; a faster pace of research into pathogens and fulfilling biosafety and biosecurity requirements.

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# Discovery of factors influencing citation impact based on a soft fuzzy rough set model

Scientometrics
Authors: Mingyang Wang, Guang Yu, Shuang An and Daren Yu

## Abstract

In this paper, the machine learning tools were used to identify key features influencing citation impact. Both the papers’ external and quality information were considered in constructing papers’ feature space. Based on the feature space, the soft fuzzy rough set was used to generate a series of associated feature subsets. Then, the KNN classifier was used to find the feature subset with the best classification performance. The results show that citation impact could be predicted by objectively assessed factors. Both the papers’ quality and external features, mainly represented as the reputation of the first author, are contributed to future citation impact.

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# A new approach for automatizing the analysis of research topics dynamics: application to optoelectronics research

Scientometrics
Author: Jean-Charles Lamirel

## Abstract

The objective of this paper is to propose a new unsupervised incremental approach in order to follow the evolution of research themes for a given scientific discipline in terms of emergence or decline. Such behaviors are detectable by various methods of filtering. However, our choice is made on the exploitation of neural clustering methods in a multi-view context. This new approach makes it possible to take into account the incremental and chronological aspects of information by opening the way to the detection of convergences and divergences of research themes at a large scale.

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# On the convergence of Kergin and Hakopian interpolants at Leja sequences for the disk

Acta Mathematica Hungarica
Author: Van Manh Phung

## Abstract

We prove that Kergin interpolation polynomials and Hakopian interpolation polynomials at the points of a Leja sequence for the unit disk D of a sufficiently smooth function f in a neighbourhood of D converge uniformly to f on D. Moreover, when fC (D), all the derivatives of the interpolation polynomials converge uniformly to the corresponding derivatives of f.

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# Parallel subtraction of nonnegative forms

Acta Mathematica Hungarica
Authors: Zoltán Sebestyén and Tamás Titkos

## Abstract

The notions of parallel sum and parallel difference of two nonnegative forms were introduced and studied by Hassi, Sebestyén, and de Snoo in [13] and [14]. In this paper we consider the parallel subtraction with much circumstances. Criteria are established for the solvability of the equation with an unknown when and are given. We identify as the minimal solution, and characterize all the solutions under the assumption where λ>1. The Galois correspondence induced by the map is also studied. We show that if the equation is solvable, then there is a unique -closed solution, namely . Finally, we consider some extremal problems such as the extreme points of the interval , and the characterization of the minimal forms in terms of the parallel sum.

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# Planar zero divisor graphs of partially ordered sets

Acta Mathematica Hungarica
Authors: M. Afkhami, Z. Barati and K. Khashyarmanesh

## Abstract

We associate a graph G (P) to a partially ordered set (poset, briefly) with the least element 0, as an undirected graph with vertex set P =P∖{0} and, for two distinct vertices x and y, x is adjacent to y in G (P) if and only if {x,y}={0}, where, for a subset S of P, S is the set of all elements xP with xs for all sS. We study some basic properties of G (P). Also, we completely investigate the planarity of G (P).

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# Polynomial perturbations of transcendental entire functions in the Laguerre–Pólya class

Acta Mathematica Hungarica
Authors: George Csordas and Chung-Chun Yang

## Abstract

The principal goal of this paper is to investigate and report results concerning the following problem. Determine the family of all real entire functions of positive order, φ, in the Laguerre–Pólya class, such that if p is an arbitrary, non-constant real polynomial which has no zeros in common with φ, then the entire function f=φ+p possesses some non-real zeros. Ramifications of the results obtained are also considered in relation to the Hermite–Poulain Theorem and the theory of multiplier sequences.

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Acta Mathematica Hungarica
Authors: Daniel Ceretto, Esther García and Miguel Gómez Lozano

## Abstract

For an arbitrary group G and a G-graded Lie algebra L over a field of characteristic zero we show that the Kostrikin radical of L is graded and coincides with the graded Kostrikin radical of L. As an important tool for our proof we show that the graded Kostrikin radical is the intersection of all graded-strongly prime ideals of L. In particular, graded-nondegenerate Lie algebras are subdirect products of graded-strongly prime Lie algebras.

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# Separation properties at p for the topological category of Cauchy spaces

Acta Mathematica Hungarica
Author: Muammer Kula

## Abstract

An explicit characterization of each of the separation properties T i, i=0,1, , and T 2 at a point p is given in the topological category of Cauchy spaces. Moreover, specific relationships that arise among the various T i, i=0,1, , and T 2 structures at p are examined in this category. Finally, we investigate the relationships between generalized separation properties and separation properties at a point p in this category.

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# Editorial

Scientometrics
Author: Tibor Braun
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# A bibliometric analysis of solar power research from 1991 to 2010

Scientometrics
Authors: Bensi Dong, Guoqiang Xu, Xiang Luo, Yi Cai and Wei Gao

## Abstract

A bibliometric analysis was performed on solar power-related research between 1991 and 2010 in journals of all the subject categories of the Science Citation Index. “Solar cell”, “solar energy”, “solar power”, “solar radiation” and “solar thermal” were selected as keywords to search in a part of the title, abstract or keywords. The trends were analyzed with the retrieved results in the publication type and language, characters of scientific output, publication distribution by countries, subject categories and journals, and the frequency of title-words and keywords used. Articles on solar power showed a significant growth along with more participation of countries, while the percentage of international papers reduced. The USA was the country with the most related articles and the most-frequent partner among all the international collaborative articles. Articles of Mainland China and South Korea grew much faster than other countries in the latest 5 years. Chemistry and material fields gradually became the mainstream of the solar power research. Synthetically analyzing three kinds of keywords, it showed that thin film solar photovoltaic technology was a hot spot of the solar power research in the past 20 years. “Dye-sensitized solar cell” and “organic” had extremely high increasing rates, which indicated that more attention was paid to kinds of organic solar cells. It could be concluded that the materials of solar cells would be the emphasis of solar power research in the twenty-first century.

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# Effects of war on scientific production: mathematics in Croatia from 1968 to 2008

Scientometrics
Author: Jasna Dravec Braun

## Abstract

Since 1968 the Croatian Mathematical Society has issued annual reports on activities of its members in the scientific journal Glasnik Matematički. Based on these data was analysed production of mathematical scientific articles published in national and international journals in the period of forty years. A rough estimate of the intensity and dynamics of the publication shows that the publication of the reference period can be divided into two stages separated by the War in Croatia. After a period of uncertainty of the 2nd World war the period preceding was characterized by establishing new institutes, colleges and university departments. After the War in Croatia a gradual but large increase in the number of published articles was evident, especially in foreign journals. The War diminished technical writing almost to the zero while increase of scientific production was 9 times greater in 2008 than in 1968.

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# Deformation of and -modules of symbols

Acta Mathematica Hungarica
Authors: Imed Basdouri and Mabrouk Ben Ammar

## Abstract

We consider the -module structure on the spaces of symbols of differential operators acting on the spaces of weighted densities. We compute the necessary and sufficient integrability conditions of a given infinitesimal deformation of this structure and prove that any formal deformation is equivalent to its infinitesimal part. We study also the super analogue of this problem getting the same results.

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# Divisibility of class numbers of imaginary quadratic fields whose discriminant has only three prime factors

Acta Mathematica Hungarica

## Abstract

We prove the existence of infinitely many imaginary quadratic fields whose discriminant has exactly three distinct prime factors and whose class group has an element of a fixed large order. The main tool we use is solving an additive problem via the circle method.

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# Erratum to: Research evaluation. Part II: gender effects of evaluation: are men more productive and more cited than women?

Scientometrics
Authors: Hildrun Kretschmer, Alexander Pudovkin and Johannes Stegmann
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# A generalization of the unit and unitary Cayley graphs of a commutative ring

Acta Mathematica Hungarica
Authors: Kazem Khashyarmanesh and Mahdi Reza Khorsandi

## Abstract

Let R be a commutative ring with non-zero identity and G be a multiplicative subgroup of U(R), where U(R) is the multiplicative group of unit elements of R. Also, suppose that S is a non-empty subset of G such that S −1={s −1sS}⫅S. Then we define Γ(R,G,S) to be the graph with vertex set R and two distinct elements x,yR are adjacent if and only if there exists sS such that x+syG. This graph provides a generalization of the unit and unitary Cayley graphs. In fact, Γ(R,U(R),S) is the unit graph or the unitary Cayley graph, whenever S={1} or S={−1}, respectively. In this paper, we study the properties of the graph Γ(R,G,S) and extend some results in the unit and unitary Cayley graphs.

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# Multiplier sequences for simple sets of polynomials

Acta Mathematica Hungarica
Authors: T. Forgács, J. Tipton and B. Wright

## Abstract

We give a new characterization of simple sets of polynomials B with the property that the set of B-multiplier sequences contains all Q-multiplier sequences for every simple set Q. We characterize sequences of real numbers which are multiplier sequences for every simple set Q, and obtain some results toward the partitioning of the set of classical multiplier sequences.

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# On a question of V. I. Arnol'd

Acta Mathematica Hungarica
Author: Imre Bárány

## Abstract

We show by a construction that there are at least exp {cV (d−1)/(d+1)} convex lattice polytopes in ℝd of volume V that are different in the sense that none of them can be carried to an other one by a lattice preserving affine transformation.

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# Ultracompleteness of hyperspaces of compact sets

Acta Mathematica Hungarica
Author: Daniel Jardón